modification of atrium design to improve thermal and ... - QUT ePrints

QUEENSLAND UNIVERSITY OF TECHNOLOGY CENTRE FOR MEDICAL, HEALTH AND ENVIRONMENTAL PHYSICS

SCHOOL OF PHYSICAL AND CHEMICAL SCIENCES

MODIFICATION OF ATRIUM DESIGN TO IMPROVE THERMAL AND DAYLIGHTING PERFORMANCE

Submitted by John Ashley MABB, Centre for Medical, Health and Environmental Physics, School of Physical and Chemical Sciences, Queensland University of Technology in partial fulfilment of the requirements of the degree of Masters of Applied Science (Research).

December 2001

Modification of Atrium Design to Improve Thermal and Daylighting Performance

Keywords:

Abstract

Atrium, Daylight Penetration, Thermal Stratification, Laser Cut Panel, Computer Simulation. ABSTRACT

The inclusion of a central court or atrium within a building is a popular design due to its aesthetic, open appearance. The greater penetration of natural light aids in the reduction in use of artificial lighting during the day. Care must be taken to balance the solar heat gain against the daylight penetration. This balance is critical for the reduction of the electrical energy load of the building, whilst maintaining a high level of comfort for the occupants. In the tropics modifications to atrium building designs are necessary to diminish high elevation direct solar heat gain. Traditionally, shading the window apertures or lowering the transmission through the glazing was used. These solutions limit the view and reduce the light level. The use of angular selective glazing upon atria allows the rejection of high elevation direct sunlight whilst redirecting and therefore improving low elevation skylight penetration. Tilted angular selective glazing used upon adjoining spaces to atria help vertical light in the atrium well to be redirected horizontally deep into the space. These effects reduce overheating which would normally restrict the use of atria in warmer environments as well as improve illumination penetration into adjoining spaces. The research showed that under clear sky conditions the modified glazing gave a lower temperature in the middle of the day within the atrium well. A more even distribution of illuminance across the course of the day was found and a higher level of illuminance was achieved within the well and its adjoining spaces under clear skies. These effects were simulated using computer algorithms. The algorithms were verified by field data collected from the QUT Daylighting Research Test Building located at the Brisbane Airport Bureau of Meteorology site where two simultaneously monitored model (1:10 scale) atriums were studied for several months.

ii


Contents

TABLE OF CONTENTS Title

.../i

Keywords Abstract Contents

…/iii

List of Figures

…/vi

List of Symbols and Abbreviations

…/xii

Statement of Original Authorship Acknowledgements Chapter 1: Aims & Objectives

.../1

1.1 Aim 1.2 Objective 1.3 Research Hypothesis 1.4 Proposed Research 1.5 New Aspects of Research Chapter 2: Introduction

.../4

2.1 Introduction 2.2 Building 2.3 Environment 2.4 Energy Consumption 2.5 Human Comfort 2.6 Daylight Penetration 2.7 Thermal Penetration 2.8 Atria 2.9 Problem with Tropical Atria 2.10 Proposed Solution to Tropical Atria Chapter 3: Literature Review

.../19

3.1 Introduction 3.2 Daylighting in Atria 3.3 Daylighting in Adjoining Spaces to Atria 3.4 Thermal Performance in Atria iii


Contents

3.5 Advanced Fenestration Systems 3.6 Computer Prediction Simulations 3.7 Conclusion 3.8 Background Chapter 4: Theory

.../37

4.1 Light 4.2 The Sky 4.3 Solar Geometry 4.4 Laser Cut Panels 4.5 Thermal Theory Chapter 5: Daylight Simulation

.../55

5.1 Introduction 5.2 Computer Simulation Theory 5.3 Procedure 5.4 Daylight Simulation Results 5.5 Simulation Validation Chapter 6: Theoretical Thermal Simulation

.../93

6.1 Introduction 6.2 Theory 6.3 Procedure 6.4 Thermal Simulation Validation 6.5 Thermal Simulation Comparison Chapter 7: Field Experiments

.../115

7.1 Introduction 7.2 Equipment 7.3 Building Description 7.4 Model Atria Description 7.5 Daylight Measurements 7.6 Irradiance Measurements 7.7 Temperature Measurements iv


Contents

7.8 Ventilation Measurements Chapter 8: Data Analysis

.../164

8.1 Daylight Modification Analysis 8.2 Thermal Modification Analysis Chapter 9: Conclusions

.../189

9.1 Conclusion 9.2 Future Work Appendices

.../193

A.1 2D Daylighting Code A.2 3D Daylighting Code A.3 Thermal Code A.4 Daylight Theory A.5 Daylight Experiment Results A.6 TRY Data A.7 Glossary References

.../265

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Tables

LIST OF FIGURES Figure 1.01:

LCPs in atrium and adjoining room configuration

Figure 2.01:

Ancient building and modern office building

Figure 2.02:

Map of Australia divided into climate zones

Figure 2.03:

Sun position at equinox

Figure 2.04:

Uncomfortable and comfortable person in building

Figure 2.05:

Daylight entering building

Figure 2.06:

Illuminance with and without lights

Figure 2.07:

Diagram of daylight penetration into building

Figure 2.08:

Commercial atria in Australia

Figure 2.09:

Solar penetration and heat gain into atrium

Figure 2.10:

LCPs redirect light through pyramid skylight

Figure 2.11:

LCPs in tilted vertical window

Figure 2.12:

LCP angular selective skylight

Figure 3.01:

Diagram of daylight penetration into atrium well

Figure 3.02

Room index ratio of atrium well

Figure 3.03:

Graph of relationships between daylight factor and well index

Figure 3.04:

Atrium with varying glazing size with respect to depth of well

Figure 3.05:

Nomograph of illuminance in adjoining room to atrium well

Figure 3.06:

Building ratio effect upon thermal stratification

Figure 3.07:

LCP application

Figure 3.08:

Luxfer Prism design at turn of 20th century

Figure 3.09:

Radiance generated picture of atrium

Figure 4.01:

Electromagnetic wave spectrum

Figure 4.02:

The sun

Figure 4.03:

Fish eye view of intermediate sky

Figure 4.04:

Solar position with respect to season

Figure 4.05:

Earth revolution causing seasons

Figure 4.06:

Diagram of LCP with labelled rays

Figure 4.07:

Angular selective LCP skylight

Figure 4.08:

Representation of stratification boundary conditions

Figure 5.01:

2D daylight simulation screen output of room with rays

Figure 5.02:

Axis and angles in 3D geometry

Figure 5.03:

Simulated room boundary labels and geometry vi


Tables

Figure 5.04:

Diagram of hemisphere showing greater solid angle near surface

Figure 5.05:

Pseudo code of 2D program

Figure 5.06:

2D picture of sky distribution

Figure 5.07:

2D daylight simulation screen output of room and skylight with rays

Figure 5.08:

2D daylight simulation screen output of atrium with illuminance bars

Figure 5.09:

2D daylight simulation screen output of room with illuminance line

Figure 5.10:

Pseudo code of 3D program

Figure 5.11:

Graph of 3D daylight simulation results

Figure 5.12:

Graph of relationship between DF% and surface reflectivity in well

Figure 5.13:

Graph of DF% and WI with normal and LCP glazing in 2D well

Figure 5.14:

Graph of light level in 2D well for both glazings at various solar altitudes

Figure 5.15:

Graph of light level in adjoining room with varying surface reflectivity

Figure 5.16:

Graph of relationship between light level and well index in adjoining room

Figure 5.17:

Graph of glazing comparison within 2D adjoining room under overcast sky

Figure 5.18:

Graph of sky distribution comparison

Figure 5.19:

Diagram of simulated test site building

Figure 5.20:

Graph of light level programs comparison under overcast skies

Figure 5.21:

Graph of light level programs comparison under clear skies

Figure 5.22:

Graph of well index daylight penetration comparison

Figure 5.23:

Graph of simulated and scale model results in adjoining room

Figure 6.01:

Thermal simulation of test site scale model atrium wells

Figure 6.02:

Geometrical representation of fraction of light accepted through skylight

Figure 6.03:

Graph of transmission through LCP pyramid shaped skylight

Figure 6.04:

Diagram of atrium well with basic heat flow directions

Figure 6.05

Pseudo code diagram of thermal program

Figure 6.06:

Graph of field and sim temperatures in plain atrium on July 22nd

Figure 6.07:

Graph of field and sim temperatures in LCP atrium on July 22nd

Figure 6.08:

Graph of field and sim temperatures in plain atrium on September 15th

Figure 6.09:

Graph of field and sim temperatures in plain atrium on September 25th

Figure 6.10:

LCP atrium comparison between field and simulated average temperatures

Figure 6.11:

LCP atrium comparison between field and simulated average temperatures

Figure 6.12:

Capsol simulated plain glazed atrium temperatures under clear skies

Figure 6.13:

Capsol simulated plain glazed atrium temperatures under overcast skies

Figure 6.14:

Capsol simulated LCP glazed atrium temperatures under overcast skies vii


Tables

Figure 6.15:

Capsol simulated LCP glazed atrium temperatures under clear skies

Figure 7.01:

Computer logging equipment

Figure 7.02:

AD590 temperature sensor electrical circuit

Figure 7.03:

Test site building side

Figure 7.04:

Test site building end

Figure 7.05:

Test site building inside room

Figure 7.06:

Northern LCP glazed skylight

Figure 7.07:

Southern normal glazed skylight

Figure 7.08:

Southern foam atrium well inside test site building

Figure 7.09:

Outside storm damaged test site building

Figure 7.10:

Inside storm damaged test site building

Figure 7.11:

Graph of logged illuminance level data

Figure 7.12:

Graph of light level in small model atrium wrt surface reflectivity & WI

Figure 7.13:

Graph of light level in adjoining room of model with various glazings

Figure 7.14:

Picture inside test site room

Figure 7.15:

Graph of illuminance level under overcast sky on work height

Figure 7.16:

Graph of illuminance level under overcast sky on floor

Figure 7.17:

Graph of illuminance level under clear sky on work height

Figure 7.18:

Graph of illuminance level under clear sky on floor

Figure 7.19:

Diagram of meter and tube describing solid angle

Figure 7.20:

Picture of diffuse and global pyranometers

Figure 7.21:

Graph of measured irradiance on 22/8

Figure 7.22:


Figure 7.23:

Graph of hourly averaged corrected irradiance on 22/7

Figure 7.24:


Figure 7.25:


Figure 7.26:


Figure 7.27:


Figure 7.28:


Figure 7.29:


Figure 7.30:


Figure 7.31:


Figure 7.32:

Graph of measured and reference diffuse irradiance validation

Figure 7.33:

Graph of theoretical measured and TRY direct normal irradiance validation viii


Tables

Figure 7.34:

Temperature sensor AD590 in ping-pong ball

Figure 7.35:

Diagram of test site with instrument sensor location after 24th August 1999

Figure 7.36:

Graph of measured temperatures on 22/8

Figure 7.37:


Figure 7.38:


Figure 7.39:


Figure 7.40:


Figure 7.41:


Figure 7.42:

Graph of hourly averaged temperatures on 22/7

Figure 7.43:


Figure 7.44:


Figure 7.45:


Figure 7.46:

Graph of reference and measured temperature validation on 14/8

Figure 8.01:

Diagram of atrium well sizes and glazing types

Figure 8.02:

Graph comparing 2 glazing in summer in a 3D well WI=3.75

Figure 8.03:

Graph comparing 2 glazing in winter in a 3D well WI=3.75

Figure 8.04:

Graph comparing 2 glazing in summer in a 3D well WI=2.0

Figure 8.05:

Graph comparing 2 glazing in winter in a 3D well WI=2.0

Figure 8.06:

Graph of relationship between horizontal DF% and WI for both glazings

Figure 8.07:

Diagram of atrium geometry and glazing types

Figure 8.08:

Graph of light level in adjoining room to well for 2 glazings in 2 seasons

Figure 8.09:

Graph of glazing comparison in room adjoining well in summer

Figure 8.10:

Graph of glazing comparison in room adjoining well in winter

Figure 8.11:

Diagram of test site with sensor locations before 24th August 1999

Figure 8.12:

Graph of hourly temperature sensor comparison and stratification on 22/7

Figure 8.13:

Diagram of test site with sensor locations after 24th August 1999

Figure 8.14:


Figure 8.15:


Figure 8.16:

Graph of temperature gradient in normal glazed well on 22/7

Figure 8.17:

Graph of temperature gradient in LCP glazed well on 22/7

Figure 8.18:

Graph of stratification equation comparison to hourly averaged field data

Figure 8.19:

Matlab screen graph of predicted temperatures in both atria in summer

Figure 8.20:

Matlab screen graph of predicted temperatures in both atria in winter

Figure 8.21:

Graph of simulated atrium temperature comparison across year at midday ix


Figure 9.01:

Tables

LCP glazed atrium well in office building in Herschel Street, Brisbane LIST OF TABLES

Table 4.01:

Sky cloud description

Table 5.01:

Surface reflectivity percentages

Table 5.02:

Light levels within room

Table 5.03:

Table of wall labels and description within 3D simulation

Table 5.04:

Light level within room

Table 5.05:

Relationship between horizontal DF% & surface reflectivity in well

Table 5.06:

Comparison between DF% and WI with 2 glazings in 2D well

Table 5.07:

Comparison between glazings and WIs for many solar altitudes in 2D well

Table 5.08:

Relationship between light level and surface reflectivity in adjoining room

Table 5.09:

Relationship between light level and well index in adjoining room to well

Table 5.10:

Glazing comparison within 2D room adjoining well under overcast sky

Table 5.11:

Sky luminance data comparison at 10° increments with ratio to zenith

Table 5.12:

Surface reflectivity comparison

Table 5.13:

Well index simulation comparison to algorithm

Table 6.01:

Simplified convection coefficient (hc) equations for air

Table 6.02:

Comparison between sim and field temperature across 1 day for 2 glazings

Table 6.03:

Comparison between sim and field temperature for 2 days for clear glazing

Table 6.04:

Comparison between sim and field temperature for 2 days for LCP glazing

Table 6.05:

Simulated temperatures comparing 2 glazings under 2 sky conditions

Table 7.01:

Surface reflectivity

Table 7.02:

Clear sky days monitored

Table 7.03:

Illuminance in atrium well for different orientations and glazings

Table 7.04:

Illuminance in small model atrium well with changing reflectivity and WI

Table 7.05:

Illuminance in adjoining room with white surfaces and 4 glazing options

Table 7.06:

Illuminance levels under overcast sky on work height

Table 7.07:

Illuminance levels under overcast sky on floor

Table 7.08:

Illuminance levels under clear sky on work height

Table 7.09:

Illuminance levels under clear sky on floor

Table 7.10:

Sky luminance data across sky at 10° increments with ratio to zenith

Table 7.11:

Sky luminance values

x


Tables

Table 7.12:

Temperature sensor calibration correction

Table 8.01:

Illuminance comparison in a 3D well between 2 seasons with LCP glazing

Table 8.02:

Illuminance comparison in a 3D well between 2 seasons with norm glazing

Table 8.03:

Relationship between horizontal daylight factor and well index in 3D

Table 8.04:

Comparison in a room adjoining well between LCP and plain glazing

Table 8.05:

Illuminance within adjoining room in summer with various glazing options

Table 8.06:

Illuminance within adjoining room in winter with various glazing options

Table 8.07:

Temperature difference equations produced from field data

Table 8.08:

Simulated temperature comparing 2 glazings options in 2 seasons

Table 8.09:

Atrium temperature comparison across year at 12pm

xi


Symbols

NOMENCLATURE LCPs laser cut angular selective panels DF% daylight factor percentage WI

well index

RI

room index

f

fraction of tilted panel incident upon cross sectional aperture

fd

fraction deflected

fud

fraction undeflected

fad

fraction accepted deflected

faud

fraction accepted undeflected

T

Temperature

FET

Fresnel energy transmitted

α

absorption

r

reflection

τ

transmission

i

angle of incident ray upon LCP

io

angle of total deflection

r

angle of refraction

W

width of the panel

D

distance between laser cuts

A

Area

E

Solar Elevation

Jd

Julian date = day number

m

relative optical air mass

dec

declination

ET

equation of time

srh

sunrise hour-angle

srt

sunrise time

sst

sunset time

lat

latitude

rlong reference longitude meridian slong site longitude meridian

xii


Symbols

GMT Greenwich Mean Time hra

hour angle

t

time

I

luminous intensity

E

Illuminance

Eext

extraterrestrial solar illuminance

Esc

solar illuminance constant

Edn

direct normal illuminance

L

Luminance

P

Power

h

heat transfer coefficient

Φ

luminous flux

ω

solid angle

salt

solar altitude

sazi

solar azimuth

Lz

zenith luminance

Ig

solar irradiance

Iext

extraterrestrial direct solar irradiance

Idn

direct normal irradiance

Idif

diffuse irradiance

Ap

Area of input aperture

As

Area of surface of atrium that re-radiates energy

τ

transmission through glazing

To

temperature outside

e

emissivity of material

σ

Stefan -Boltzmann constant

SC

sky component

ERC

external reflected component

IRC

internal reflected component

ARC atrium reflected component SAR

section aspect ratio

PAR

plane aspect ratio

QUT Queensland University of Technology

xiii


em

electromagnetic

uv

ultraviolet

sr

steradian

Q

luminous energy

L

length

W

width

H

height

R

radius

HGI

horizontal global illuminance

Z

zenith angle

n

refractive index

U

thermal conductivity

R

thermal resistivity

ξ

angle between measuring sky point to zenith in radians

γ

angle between sun and measuring sky point

ρ

density

ε

clearness index

cf

correction factor

lux

unit of illuminance

cd

candela

AIP

average intensity product

ref

reflectivity

tit

tilt angle of receiving plane from vertical

has

horizontal shadow angle

n'

effective refractive index

2D

two dimensional

3D

three dimensional

TRY

test reference year

hc

heat transfer coefficient for convection

hr

heat transfer coefficient for radiation

Nu

Nusselt number

Ray

Rayleigh number

Symbols

xiv


Gr

Groshof number

Pr

Prandtl number

g

gravity

µ

viscosity of the fluid

Cp

specific heat

β

coefficient of cubical expansion

RT

relative transmission

W/D

width to depth ratio of the cuts in the LCP

Symbols

RAPS remote area power supply ADC analogue to digital convertor A1

clear glazed atrium well at test site

A2

LCP glazed atrium well at test site

PTAT proportional to absolute temperature Ω

ohm

CIE

International Commission of Illumination

LCPyramid ac/hr

pyramid shaped skylight with LCP as 2nd glazing layer

air changes per hour

RND random number distribution

xv


Authorship

STATEMENT OF ORIGINAL AUTHORSHIP

The work contained in this thesis has not been previously submitted for a degree or diploma at any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made.

Signed: .....................................

Date: ........................................

xvi


Acknowledgements

ACKNOWLEDGEMENTS I wish to acknowledge the School of Physical and Chemical Sciences, the Centre for Medical, Health and Environmental Physics, and the Daylight Research Group. All of which form part of Queensland University of Technology. The work described in this paper has been supported by the Australian Cooperative Research Centre for Renewable Energy (ACRE). ACRE’s activities are funded by the Commonwealth’s Cooperative Research Centres Program. In particular, I wish to acknowledge the help and support of Dr. Ian Edmonds, Steve Coyne, Phillip Greenup, my girlfriend Michelle Neil and my parents. Contributions from the following people helped: Jeremy Mathews, Kane Usher, Dr. Ian Moore, Bill Lim, Kelvin Tang, Lawrence Leong, Yvonne Wolring, David Pitt, Bob Organ, Bureau of Meteorology, Dr. Brian J. Thomas and Darren Pearce.

QUOTATION

“We shape our buildings and afterwards our buildings shape us” - Sir Winston Churchill (28/10/1943 to House of Commons) - (In The Mind of the Architect, ABC, 2000)

xvii


Aims

Chapter 1: AIMS AND OBJECTIVES 1.1 Aim The research aimed to determine the effectiveness of reducing the building energy load by regulating the passive solar thermal circulation and improving daylight penetration in atrium buildings and their adjoining spaces in the tropics. In so doing, maintaining a level of comfort for the occupants and reducing the contribution a building has to pollution levels such as greenhouse gases. This study was concerned with designs for the improvement and redevelopment of existing and future building structures within sub-tropical climates. 1.2 Objective The objective of this research was to improve the thermal and daylighting performance of atrium buildings. This was investigated by comparing the temperature and thermal stratification in clear glazed roof atriums versus that of atriums that incorporate the use of the angle selective laser cut panels (LCPs). This research project also investigated the daylight penetration into the atrium and adjoining spaces comparing clear to LCP glazing. Both the thermal and daylighting performance was modelled theoretically so as to assess and demonstrate that the modified design using the LCPs was beneficial. Computer simulated results were compared with measurements undertaken in scale models and related to previous results. The author in 1997 conducted preliminary research in this area. This involved a scale model study of the improvement that laser cut panels made in the depth of the daylight penetration into an atrium and it’s adjoining spaces. The atrium and adjoining space modelled was at a scale of 1:75 and tested under an artificial sky. This research project was a continuation of that work. [Figure 1.01: LCP in atrium and adjoining room configuration] summer light winter light

1


Aims

1.3 Research Hypothesis The hypothesis of this project was that with the inclusion of the laser cut angular selective glazing upon the roof of the atrium well, there would be less thermal stratification at times of the day and year when a large proportion of the light was being deflected. These times occur when there was a maximum angular difference between the cuts in the glazing and the incident direct beam radiation. For example, early morning, late afternoon and midday mid summer. A more even distribution of illuminance level across the course of a clear sky summer day in the tropics would also occur due to the redirecting effect. The LCP modification is expected to have three overall effects. (1) Human comfort is improved by redirecting the radiation input and stabilising the natural stratification and lighting. (2) The need for artificial environmental controls such as lighting and cooling during the day is eliminated. (3) The electricity usage and therefore the running costs are reduced. 1.4 Proposed Research Program This research outline includes areas of introduction, theory, experiment, data analysis and conclusion. 1) The criteria establishing the desired performance objectives will be explained in Chapter 2. The methods used to investigate these objectives are through simulation and scale models. 2) Literature reviews on thermal stratification and daylighting in buildings particularly those containing atriums is discussed in Chapter 3. 3) Construction of a theoretical computer simulation of light and thermal performance in atrium spaces with and without LCPs will be explained in Chapter 5 and 6. 4) The design and construction of a model on a 1:10 scale of an atrium building are provided in Chapter 7. 5) Simultaneous monitoring of atrium wells (one normal glazed and the other with LCP glazing) with several temperature sensors at various heights within them to measure the stratification under various climatic conditions. The model is to be varied with different ventilation modes throughout the seasonal climatic changes. 6) Comparison with professional theoretical simulation programs and improvement to the theoretical simulations formulated during this research. 7) Comparison between theoretically simulated results and collected field data. 2


Aims

1.5 New Aspects of Research •

The thermal stratification in model sub tropical atria was a new area of investigation.

•

The balance between the solar gain and the daylight penetration.

•

The experimental daylight penetration investigation was conducted under real subtropical skies so validation to the theoretical simulation was possible.

•

The application of LCP technology on a larger scale to enclose an entire atrium roof glazing in a similar design to a pyramid shaped skylight (Edmonds 1996).

•

The scale of the experimental model is also a significant improvement upon previous research into this area (Mabb 1997; Edmonds 1998; Sharples 1999).

•

The length of time of data collection, while not as long as initially expected, still significantly improved upon previous data collection research periods.

•

The computer simulation of LCPs to investigate both thermal and daylight penetration into atria using heat transfer and backward ray tracing techniques respectively.

3


Introduction

Chapter 2: INTRODUCTION 2.1 Introduction This initial chapter introduces the concepts of modern office buildings and the inclusion of an atrium built into the design. A building, which contains an atrium space, is a unique structure, which has many benefits and disadvantages compared to normal high rise buildings. The inclusion of an atrium well encourages the penetration of more of the natural environment in the form of light and heat into the well and its adjoining spaces. This chapter also includes the topics of comfort, the tropical environment and energy consumption and the impact of atria upon these areas. Finally, the thermal and daylighting penetration is looked at along with proposed design solutions for atria in the tropics. The proposed modification to the atrium glazing is discussed and the justification for this modification is detailed. This chapter defines the broad research area and introduces the specific research topic, which will be discussed in detail in the following chapters.

Daylighting in architecture is an area in which we know so much and yet practice so little. (Moore 1991)

4


Introduction

2.2 Building [Figure 2.01: Ancient building and modern office building]

The basic requirement for a building is to provide shelter from the environment and harsh weather. A building structure has a basic form containing a roof, walls and apertures including doorways to allow access by the occupants and windows to allow access by environmental elements such as light and air. High-rise buildings were first constructed in the late 19th century in the US. They first were built in urban areas where the population density created a demand for buildings that rose vertically rather than horizontally. These buildings occupy less expensive land area. High-rise buildings have become the predominant feature of any big city and mostly contain commercial businesses. (www.brittanica.com, 2000) Buildings are not just structures. They house occupants who have to be comfortable and healthy in the environment provided. The average urban office worker in modern day society spends less than one hour per day outside (Cooke 2000). This design of modern building relies upon electrical lighting and artificial ventilation to achieve adequate occupant comfort. Windows are an important element in any building that has occupants. A window may be described simply as a glazed opening in a wall of a building. The complete window 5


Introduction

assembly includes the glazing, frames, sash and any moving parts. They provide a barrier from the extremes of the external weather, while still providing light penetration, fresh air, and views of the outside world. Windows are a significant origin of heat transfer through the building envelope and require regular cleaning maintenance. The problem with high-rise commercial buildings is that they generally have large depth to height ratios to maximise the number of floors and therefore the rental area. This produces gloomy, stuffy, cramped areas for occupants, which have to rely heavily upon artificial controls to achieve comfortable and safe working environments. Artificial lighting and mechanical air conditioning can be expensive (rising fuel costs), unreliable (black outs, brown outs), unhealthy, and polluting (greenhouse gas emissions, heavy metals). Maximum reduction in artificial lighting and air conditioning in building requires major redesign of the style of most large buildings. Buildings with large internal open spaces and horizontal apertures are required if adequate supply of light and air circulation is to be achieved via natural methods. 2.3 Environment In Australia, the sun is predominantly in the northern part of the sky. This means that the orientation of our buildings has to be changed from the traditional Northern Hemisphere design. The north facing glazing on our buildings is shaded to eliminate direct summer sun while still allowing the penetration of winter sunlight. The buildings are also elongated east to west, reducing the cross sectional area seen from the low elevation rising and setting sun. Natural cross ventilation needs to be encouraged in the direction of the prevailing breezes in the occupied area as well as in the roof cavity. Australia is a land of harshness and extremes with an area of 7.682 million square kilometres and a population of 18.918 million people but only 10% of the land is arable (National Geographic website, 1999). Australia spreads over a large latitude range from Cape York at 10° south to Hobart at 43° south. The tropic of Capricorn runs across the upper part of the continent through Rockhampton at 23° 27’ S. This marks the boundary of the tropical zone and also the point at which the sun reaches the zenith at mid summer.

6


Introduction

At the opposite extreme in mid winter in Hobart, the sun reaches a maximum of only 23° altitude. [Figure 2.02: Map of Australia divided into climate zones, (BOM, 2000)]

The sub tropical and mild climate of the lower half of the continent results in a building energy load that requires heating in winter and cooling in summer. The South East of the country experiences some snowfall each winter therefore negative temperatures can occur. However, Melbourne can also have summer temperatures above 40° C. The hot humid tropical climate of the upper half of the continent means that the main building energy load is the cooling load in summer rather than the heating load in winter. The latitude of Brisbane where the experiment was conducted was 27° 28’ South, which is only 4° below the tropic zone and generally regarded as a sub-tropical city. This all means that the building design has to vary across the continent to allow for the different climates, sun paths and occupancy requirements. Seasonal climatic variations also mean that the design has to be adequate or adjustable to provide comfortable conditions all year round.

7


Introduction

[Figure 2.03: Sun position at equinox]

W

S

N

E

2.4 Energy Consumption The main objective of the design, development and operation of a sustainable building is energy efficiency. To this end the reduction of artificial heating, cooling and lighting has to be achieved as the energy consumption in these three areas is a substantial fraction of the total energy used and a significant source of running costs and environmental pollution. The Australian commercial sector consumed 151 PJ of energy in 1990. This produced 32 MT of CO2 emissions, which included 21% for lighting, and 41% for heating and cooling (AGO 1999). Therefore, if commercial buildings can be redesigned to increase the amount of natural lighting while controlling the heat gain and loss then a large amount of money, energy and emissions can be reduced. With passive solar architecture, it is possible to reduce to a minimum the need for any additional electrical energy to heat, cool or illuminate the interior of a building in any climate. Relying more on passive design systems means that reliability is improved, maintenance is minimised and the design is more sustainable. Reducing running energy costs are also an advantage. Daylight produces less heat per lumen than artificial lighting. This means that as long as the daylight penetration is controlled and maintained at the required level then overheating can be reduced.

8


Introduction

Rather than renewable energy used as the solution to greenhouse gas emission reduction and rising electricity costs, zero energy use solutions should be sort, which will reduce the energy usage and supply to a minimum. (http://renewable.greenhouse.gov.au/home/passive_solar.html, 2000) 2.5 Human Comfort [Figure 2.04: Uncomfortable and comfortable person in building]

The comfort of the occupants of a building is why the structure was originally designed. If comfort were not an issue then buildings would be small cubes with low ceilings, no windows and electricity for the equipment only. Human comfort takes into account thermal comfort, visual comfort, acoustic comfort, physical comfort and occupants’ behaviour. Although human comfort is subjective, and is affected by personal factors, it is mainly affected by environmental factors. The personal factors include activity, clothing, age, gender, metabolism, health, or sensory perception. The environmental variables include temperature, airflow, humidity, light level, noise level, or building properties (AWC 2000). Daylight, while essentially needed only to aid in the visual comfort of the occupants of a building, may also have other positive benefits including both psychologically and physiologically. Contact with the outside world regulates the bodies clock, benefits the metabolism and balances the hormone levels. The creation of healthier, brighter and more enjoyable working conditions can improve productivity by reducing fatigue (Ruck 1989).

9


Introduction

The reason for heating or cooling a building occupied by people is to provide thermal comfort. The comfort level achieved by the occupants depends upon their location to the windows, air-conditioning vents and radiative or other airflow sources. As the windows are the main source of heat transfer through a building’s envelope the comfort achieved by the occupants depends upon their location with respect to the window. If the window is openable or if infiltration around the windowsill occurs then cool drafts or high velocity airflow can occur. If the window is closed then the main cause of discomfort is direct radiation. Airflow and direct radiation can be discomforting or comforting depending upon the season and the nominal weather conditions outside. Visual comfort is the main reason we require good lighting conditions. Visual comfort includes: suitable intensity and direction of illuminance upon the work area, appropriate colour rendering, absence of contrast and glare discomfort and a variety of lighting quality and intensity over time and place. Comfort in buildings that include atria vary depending upon the occupants location. In the atrium well itself, which is generally used as a relaxing, transitional space, the requirement of comfort is less stringent. Lighting levels can vary from 50 lux to 5000 lux and temperature can vary from 21°C up to 27°C without the occupants feeling uncomfortable. This is because the space is usually not occupied for long periods of time. The requirement of strict comfort levels is more necessary in the adjoining spaces to atrium wells. These spaces are usually used as shops or offices and as working spaces can be occupied for long periods of time. The temperature and lighting levels in these spaces are affected by the conditions within the atrium well and the outside climate. The minimum maintenance illuminance level in office spaces is 320 lux and in shops is 160 lux (Australian Standards 1680.2.0 1990). Air-conditioned office spaces are usually kept within the temperature range of between 21°C and 24°C. The subjective nature of adequate lighting conditions not only requires a minimum lighting level but also a minimum quality of light. Contrast is the difference between the visual appearance of an object and the background. Contrast may occur when (1) one wall is brightened by the sun while the rest of the room is in shadow, or, (2) when the room is illuminated and one corner is shadowed and dark.

10


Introduction

Too much direct light can cause uncomfortable glare. Reducing the transmission of the window through the use of advanced glazing or controlling elements can reduce glare conditions. Glare is the discomfort caused when the eye has extremely different light levels in the field of view at the same time. Glare can be caused directly, indirectly or by reflection. Direct glare can be caused from the view of a light bulb or the sun. The positive physical effects from daylight upon occupants were clearly shown in two recent case studies involving school children. A study in Canada used 4 different artificial lighting strategies to show that full spectrum artificial light gave the best results. Full spectrum light is produced naturally by the sun. It showed the students were healthier (higher attendance), happier (less moody) and more productive (academic achievement) when exposed daily to full spectrum light. This result highlights the non-visual effect of light upon occupants (Hathaway 1994). Based upon the previous study, another investigation was conducted in North Carolina comparing daylit schools to non-daylit schools. The daylit schools showed a scholastic performance 5% higher than at artificially lit schools. New and old artificially lit schools were investigated and both showed a negative impact upon student’s performance (Nickolas et. al. 1996). 2.6 Daylight Penetration [Figure 2.05: Daylight entering building]

[Figure 2.06: Illuminance with and without lights]

11


Introduction

We need light to see! Daylight penetration into buildings has been a design consideration for as long as buildings have been built. Egyptians reflected light into tombs and calculated the position of shafts of light so they could draw and decorate their tombs without the use of candles that would have deposited soot upon the surfaces. [Figure 2.07: Diagram of daylight penetration into building] Sky light

Sun light SC

Obstruction light ERC

IRC

Ground light

The natural light level in rooms is a summation of the sky component (direct and diffuse), the externally reflected component (ERC) and the internally reflected component (IRC). This light penetrates into our buildings and eventually onto the work surface where we focus our attention. Before the light gets to our eyes it has to pass through the atmosphere, be transmitted through the glazing and reflect off surfaces both externally and internally. Upon each reflection the intensity of the light is reduced by absorption. The further from the window the light rays penetrate the greater the surface area they reflect off and the more the light is absorbed. This reduction in intensity and therefore light level has a characteristic exponential decay with respect to the depth of the room. It is this decay in natural light level that results in the need for artificial lights. There are several benefits of daylight penetration into buildings. As mentioned above human health can be affected. Daylighting can also reduce the buildings electrical energy usage, saving money, as well as conserving the Earth’s non-renewable energy resources (Steemers 1994). The disadvantages of daylight penetration include the potential for undesirable heat gain, excessive contrast and glare, and inconsistent variable light levels over the course of the day. To reduce the impact of these disadvantages modifications to the generic architecture design such as advanced fenestration systems are required.

12


Introduction

Good daylight penetration means lighting of the right quality, delivered to the greatest plan-depth possible. Quality rather than quantity counts, low glare and low contrast lighting are most desirable (Saxon 1983). Even task lighting can be supplemented with natural lighting reducing the dependence upon artificial lighting. This can save money and conserve the Earth’s non-renewable resources (Steemers 1994). 2.7 Thermal Penetration The penetration of heat into and out of the building envelope determines the temperature within the building. The heat flow depends upon the building properties and the environment. The building properties include the mass of the building, the amount of glazing, the ventilation and the number of occupants and other internal heat loads. The ambient environment properties that influence the thermal penetration include the temperature, humidity, air velocity and the amount of radiation that falls upon the building surface. Within atrium style buildings the increased solar penetration through the roof glazing and the temperature difference between the top and bottom of the well have a great impact upon the temperature within the building and its thermal performance. 2.8 Atria [Figure 2.08: Commercial atria in Australia: Brisbane and Melbourne]

13


Introduction

Atria are central courts within or between buildings with adjoining working areas. They allow natural light into the interior of the structure from the entire sky above through a horizontal aperture. The atrium has been a very popular style of building, especially, in countries located at high latitudes. This is due to the fact that atria provide a semi-outdoor area that the occupants can gather in or walk through without having to worry about the extremes of the climatic conditions outside. Originally atriums were open central courts that allowed light into the interior of the ancient Roman and Greek houses. The buildings were of a defensive style with thick, closed off outside walls, so the interior courtyard provided a private, open area suitable for reading, relaxing and socialising. In medieval ages, a second storey was added with a view down to the court floor. Protection from some of the weather was then added to the second storey with the use of overhangs. The 19th century brought the industrial revolution with great advances in iron and glass manufacturing techniques. Courtyards could then have horizontal glazing overhead, eliminating some of the weather elements from the space and giving birth to the modern atrium. The atrium style lost popularity for two thirds of the 20th century due to the development of artificial lighting and the cheapness of energy to power this lighting. In the 1970’s, there was an energy crisis and fuel prices skyrocketed resulting in a resurgence in energy efficient architecture and the popularity of atrium style buildings was recaptured. Today, central atria are used in relatively modern buildings including office buildings, shopping malls and hotels. These atria are built in the form of large glassed in spaces that allow occupants access to the positive aspects of the environment including the natural light, space and vegetation without the extremes of the external climatic conditions. Atria are often designed to give a natural appearance to an otherwise sterile environment. They can be used to maximise the reduction of artificial lighting, but careful planning is needed in the atrium design of modern buildings to achieve this.

14


Introduction

While atria are designed primarily for aesthetic reasons, this style of building can be beneficial for energy efficiency and psychological reasons. Living and transition spaces within buildings could be covered by transparent or translucent material which provides decreased and less contrasting light levels to the spaces connected to the atrium. In the tropics, atria are not a popular building design due to the increased penetration of the direct sunlight, which causes discomfort to the occupants within the building. The glazing material and the cross ventilation strategy can be modified and improved to compensate for this fundamental problem. 2.9 Problem with Tropical Atria [Figure 2.09: Solar penetration and heat gain into atrium]

The disadvantage of atriums and skylights is the accompanying heat gain associated with the direct beam radiation and the creation of thermal differentials in large volumes of air. Sunlight penetration into atria is different from normal buildings due to the vertical view through the glazing. As the sun’s elevation rises, the light penetrates further into the well of the atrium but less into the adjoining spaces. As the solar elevation decreases the light penetrates further into the adjoining spaces on the upper levels but penetrates less in the well and the adjoining spaces on the lower levels. With clear single glazing in atria in the tropics and the sun at a high solar altitude, there is greater heat penetration. The large amount of glazing in atria results in an overheating greenhouse effect. This is the process that is used advantageously in glassed covered gardens in cold climates to provide a warmer temperature to grow plants. Short-wave

15


Introduction

solar energy is transmitted through the glazing and absorbed by the solid elements of the building or in the building. These elements then re-emit long wave radiation, which is prevented from re-transmitting back through the glazing (Goulding 1992). The human comfort zone for a sub tropical zone such as Brisbane is between 21° and 27° Celsius (Willrath 1998) so the temperature within buildings should be kept within this temperature range. The large amount of glazing which results in excess heat gain via direct radiation input also overrides the natural convection process. This produces a thermal stratification stack effect within the atrium well. The result is a much higher temperature towards the top of the atrium. The hot air also flows into the upper level adjoining spaces, making them hot as well. If the thermal stratification can be reduced then the comfort in the adjoining spaces is improved. Thermal stratification within atria is a relatively new area of research (Luther 1991, Togari 1993, Kolsaker 1995). It is an important concept in terms of the energy running costs of the building and increasing the human comfort level. If there is no access to the upper areas of the atrium well then a thermally stratified atrium will in fact keep the hot air away from the occupants at the bottom of the well. In an air-conditioned atrium, the placement of the temperature sensor with respect to the thermally stratified medium will influence the amount of energy the mechanical ventilation system expends to produce a comfortable indoor climate. More expended energy means a higher running cost for the building’s tenants. Rather than avoiding these lighting solutions due to the accompanying heat load, designers should seek a way to reduce the heat without reducing the light. Some solutions have involved adjustable screens to block light or monitor skylights but these are still inefficient at transmitting low elevation light.

16


Introduction

2.10 Proposed Solution to Tropical Atria Advanced glazing systems can improve the effectiveness and usefulness of atrium style buildings in the tropics. This is achieved by reducing the solar heat gain during times when it is not needed and enhancing the light level and penetration into the building at times when it is needed. Atriums in tropical architecture have become more popular due to their aesthetic appearance and many strategies have been used to reduce the overheating problem. Some of these solutions include using translucent instead of transparent glazing, double glazing or shading. [Figure 2.10: LCPs redirect light through pyramid skylight]

Reject high elevation direct sunlight

Redirect low elevation skylight

Less solar energy gain through out the middle of the day will result in lower temperature and less thermal stratification The solution discussed here to improve the daylight penetration into buildings, while not increasing the solar thermal penetration, is to use light redirecting devices to control light from the bright part of the sky. This particular solution involves using angular selective glazing (Edmonds 1996) used initially for vertical fenestration and then applied to skylights.

17


Introduction

It is produced in clear acrylic sheets containing parallel laser cuts. The glazing deflects or rejects the incident light that hits the laser cuts depending upon the angle of incidence of the direct light rays. As in the case of a pyramidal shaped skylight the vertical light rays are rejected while the low angle light rays are redirected through the glazing. This should have a stabilising effect upon the lighting and heating level within the atrium over the course of the day and the year. [Figure 2.11: LCPs in tilted vertical window]

[Figure 2.12: LCP angular selective skylights]

18


Review

Chapter 3: LITERATURE REVIEW 3.1 Introduction The quantitative improvement of comfort within buildings was a relatively new area of research considering the history of building structures and the time, effort and expense placed upon construction. The areas of comfort investigated in this research include visual and thermal. The specific building structure that is looked at in this research is the atrium style due to its recent popularity and the potential for adequate comfort supplied within the structure via natural, passive methods. Daylight penetration research has traditionally been investigated with the use of scale models under artificial skies to establish daylight factor data tables or generic analytical equations. Models of buildings usually include simplified geometry and are placed under artificial skies. With this type of model, only a rough estimate of the final illuminance can be obtained. The prediction of thermal flow within building structures is a difficult area of research due to the interaction between conduction, convection, radiation and stratification of heat transfer. Generally, only energy consumption simulations have been conducted, though computational fluid dynamics models have been used to some success (Jones 1991). Recent developments in light and thermal computer simulations have allowed a greater depth of research into the performance of buildings. The development, improvement and usefulness of these programs are briefly commented upon towards the end of this chapter. Research into advanced glazing and fenestration design to increase the penetration and usefulness of natural daylight to improve upon the level of comfort within modern commercial buildings is an area under current review and investigation, particularly by the International Energy Agency Task 21 and 31 (IEA 2000, Ruck 1989). 19


Review

3.2 Daylighting in Atria [Figure 3.01: Diagram of daylight penetration into atrium well]

Sun light

Sky light

SC

ARC

ARC

Research into daylight penetration into atriums takes the form of predicting the light levels in the wells and adjoining spaces by using either scale model studies, analytical equations or computer simulations. Some investigations used a combination of these methods. In the research, comparisons were made between designs after changing one particular atrium parameter. These parameters include atrium geometry, surface reflectivity, glazing and sky distribution. The most commonly used sky distribution and the easiest to simulate is the overcast sky because there is no direct sun and the ratio of zenith luminance to horizon is simply 3:1. Most of the previous modelling uses this distribution and all results are given in terms of daylight factors (Aizlewood 1997; Littlefair 1994; Boubekri 1995; Aschehoug 1992; Iyer-Raniga 1994). The daylight factor is the ratio of the internal to external horizontal global illuminance. Artificial skies were chosen to test ideas because stable reproducible light conditions were needed. The worst sky conditions (eg., overcast sky distribution) were chosen as the artificial sky model to find the lowest internal illuminance levels (Iyer-Raniga 1994). Due to atriums’ view of the sky zenith, which is the brightest part of the overcast sky, the overcast sky distribution may not be the worst case scenario for this building structure (Wright 1998).

20


Review

The prediction of the light levels was equated in a lot of papers by using zonal methods or by creating analytical equations (Boubekri 1996, Liu 1991, Aizlewood 1996). These methods are a simplification of the real situation. Atrium glazing allows the occupants to view the sky and therefore have a connection to the external environment. The type, shape and position of the glazing can vary the daylight penetration in the atrium dramatically. Frames, shading and external obstructions also affect the amount and the direction of the daylight (Sharples 1999). Admitting as much of the diffuse skylight while also minimising the direct solar gain was the design requirement for most atrium glazing. Generally, the structure reduces the transmission by 10%, while single glazing reduces it by a further 10%. The acceptance of some direct sunlight can be desirable to give an edge and sharpness to the atrium design. Overheating, however, has to be avoided to maintain occupants’ comfort (Aizlewood 1995). Atrium geometry was found to be one of the most important factors that affected the penetration of light. The depth and the cross sectional area of the well affected the solid angle of the sky component and, thus, determined the amount of direct daylight reaching the floor of the atrium. Some papers discuss the variation in lighting due to the changing geometry of the atrium well, shape of the well and the number of glass covered walls (Liu 1991; Boubekri 1996; Kristl 1999, Zumbo 1998). One particular review of illuminance in atria (Wright 1998), includes analytical equations that predict: sky components, dimensional aspect ratios, internally reflected components and daylight factors. Wright comments on the limited amount of literature with corresponding results.

21


Review

[Figure 3.02: Room Index Ratio of atrium well]

W 80

L

H

Sky component at centre of atrium floor %

70 60 50 40 30 20 10

0

0.2

0.4

0.6

0.8

1.0

1.2

Kr (Room Index of Atrium) L x W / (L x W) x H

The most important empirical relationships in daylight penetration involve the dimensional aspect ratios. Liu (1991) related three geometric proportions in atrium spaces to the distribution of daylight. These geometric distributions include plane aspect ratio (PAR=W/L), section aspect ratio (SAR=H/W) and well index (WI). All the results were based on computer simulations and real atrium monitoring was only over a few days. With a well index of 2.0 a comparison of various PAR and SAR ratios gave daylight factors between 10% and 14%. The relationship between the daylight factor and the well index (WI) was the most useful and therefore the most investigated in the area. Analytical equations gathered from papers by Wright and Letherman (1998), Aizlewood (1995) and Tregenza (1997) show that the relationship between daylight factor and well index was in fact an exponential decay, similar to the exponential decay from side lighting rooms. Kim and Boyer:

DF = 117 exp(-0.996*WI)

Neal and Sharples: DF = 84 exp (-0.73*WI) Tregenza: E hh total = Eh0[(2a-R1)exp(-akWI)+R1]/[2a(1-R1R2)] Hopkinson:

SC = 100 ALAB/π(0.25AL2+D2) ; SC = 50(1-cosθr) IRC= KWA R/A (1-R)

22


Review

where DF = SC + IRC Phillips and Littlefair: DF=2KWA/A (1-R2) Littlefair: DF=Waθt/A(1-R2) Liu: DF=103.56 - 121.09x + 64.203x2 - 17.61x3 + 2.3934x4 - 0.12676x5 where x=WI [Each variable explained individually in the particular source paper]

The validity of these equations will be discussed and compared to the simulated and experimental results found in this research in later data analysis sections. The leading constants in some of the above equations could be interpreted as incorrect since when the well index variable approaches zero then the daylight factor should approach 100 per cent. For example the Kim and Boyer equation would be 117%; the Neal and Sharples equation would be 84% and the Liu equation would be 103.56. [Figure 3.03: Graph of relationships between Daylight Factor and Well Index (Wright 1998)]

The other important variable that affects daylight penetration was found to be the atrium surface reflectivity. This area of research was covered in the review paper by Aizlewood (1995) and investigated in the scale model experiments by Iyer-Raniga (1994). Light coloured walls aided in daylight penetration deeper into the atrium well.

23


Review

The proportion of glazing between the atrium and its adjoining spaces effects the light penetration further into the well and the spaces. Windows act as areas of low reflectance so several authors suggest that the proportion of glazing upon each level within the well should vary with less at the top of the well and more at the bottom (See figure 3.04). Atrium wells are typically social gathering areas so the light levels are not as critical as in the adjoining rooms where people often work and need task level lighting. The idea of modifying the atrium well to improve the light level in the adjoining spaces was discussed in a general manner by Steemers (1994), Matusiak (1998), and Saxon (1983). Modifying the size of the glazing to the adjoining space so that it became larger as the depth into the atrium increased was discussed, as well as splaying the walls of the atrium. These modifications resulted in improved light levels on the lower levels of the adjoining spaces to the atriums. [Figure 3.04: Atrium with varying glazing size wrt depth of well]

3.3 Daylighting in Adjoining Spaces to Atria The areas adjoining atriums can be used for shops, offices or classrooms. In these areas specific tasks are often performed which require stable, high quality, light conditions. There are many factors that affect light levels in these areas including atrium geometry, reflectivity, and glazing, and the geometry and the reflectivity and glazing of the adjoining space.

24


Review

The daylight factor in the adjoining spaces has been measured in two different ways. One way was directly measuring the light level at several positions within the space by using scale models. The other way was by relating the vertical daylight factor on an atrium wall to the average daylight factor in the room using analytical equations. Aizlewood (1996) used the second method of relating the vertical daylight factor on the adjoining window to the average daylight factor in the adjoining space. This was described as a very general analysis that could result in high values. Aizlewood (1995) summarises the methods other authors had used including Lynes (1989) who used the same method. Degelman (1988) used a combination of both methods. Cartwright (1985), Cole (1990), Baker (1993) and Szerman (1992) used the direct method. Kristl (1999) varied the acceptance of the light from the atrium well into the adjoining space by using semi-individual light wells. Matusiak (et al.) (1998) discussed the daylight penetration to adjoining spaces due to variations in the glazing area and glazing type in scale model atriums under artificial overcast skies. Equations were established to estimate the daylight factor in the adjoining rooms. The measurements were taken on the vertical window wall and in the adjoining rooms on several levels. The investigation was concerned with rooms with plane depths of only 6 metres whereas other investigations were concerned with adjoining rooms of up to twice that depth (Aizlewood (12m) 1997; Iyer-Raniga (9m) 1994; Szerman (5m) 1992). Therefore these results were difficult to compare with other results. Szerman (1992) created a nomograph for deriving mean daylight factor in adjoining rooms from atrium width, height to depth ratio, reflectance of wall and floor and glazing types. This was based on artificial sky scale model experiments.

25


Review

[Figure 3.05: Nomograph of illuminance in adjoining room to atrium well (Szerman 1992)]

Baker (1993) suggested splaying the walls within the atrium, as did Tregenza (1997). The use of prismatic control elements was also mentioned (Baker 1993). Both of these modifications have been found to improve the light level in the adjoining spaces. Aizlewood (1995) also mentioned the possible advantage of innovative daylighting systems to direct daylight away from video display units. The idea of improving light levels in adjoining spaces by modifying the glazing has been discussed by Edmonds (1998). In model research experiments, Matusiak (1998b), upon infinitely long atria the mean, minimum and vertical daylight factor (DF%) in adjoining rooms could be found using these rules: DFmin = 0.25 x DFvert x (Agl / Afl) x T/Tclear DFmean = 0.5 x DFvert x (Agl / Afl) x T/Tclear DFsidewall = 0.05 DFvert x Agl x T/Tclear Aizlewood (et al.) (1997) found average DF in adjoining room as: DFmean = 2(Aw x Tw x DFvert) / Asurf (1-R2) He also found DF in atrium well as DF = SC + ARC where 26


(

Review

)

SC = 100 1 − 3 7 sin 2 θ − 4 7 sin 3 θ and WR  7  W ARC = (100-SC)  + R   A − W A(1 − R)  3 + 4 sin θ Generally the variables are: A = area T = transmission R = reflectivity DF = daylight factor SC = sky component ARC = atrium reflected component W = width 3.4 Thermal Performance in Atria Thermal stratification within atria is a new area of research. The importance related to reducing the energy running costs of the building and to increase the human comfort level. In an air conditioned atrium if thermal stratification exists then the mechanical ventilation system has to do more work to produce a comfortable climate. More work means more energy and therefore more money. In a naturally ventilated atrium where the convection process means that the hot air rises and the cold air sinks, the hot air also flows into the upper level adjoining spaces making them hot. If the thermal stratification can be reduced then the comfort in the adjoining spaces will be increased. The main problem with thermal environment within atrium wells is the vertical height over which the air is distributed. The temperature variation with respect to height in a fluid is known as thermal stratification. This also gives rise to a non-uniform density variation in the fluid (Juluria 1980). Thermal stratification is a significant problem in tall atria style buildings due to the large glazing area, large internal air volume, the convection process and the direct solar radiation. The temperature differences between the lowest and highest points could be as much as 7 degrees (Jones 1991).

27


Review

Thermal stratification in atriums has mostly been investigated in cold climates where direct solar radiation is beneficial because the temperature outside is often lower than the inside temperature. In tropical climates direct solar gain is often avoided due to the accompanying heat gain. This means that the atria design is not as popular in hot countries. Atriums are still liked the world over for their aesthetic appearance and for the ability to gather people together in a casual environment. In tropical areas, diffusing glazing or shading under skylights and atrium roofs are often used to deflect or reject the direct solar radiation. This makes these glazing systems more comfortable but also has the effect of reducing the daylight penetration and therefore the light level. The theory of thermal stratification concentrates on heat transfer, natural convection or zonal models (Juluria 1980, Allard 1998). Allard (1995) reviews thermal stratification and heat transfer by zonal models including single zone models, multizone models and pressure zonal models. Research has been performed with computer simulations using zonal models (Wolring 1999; Kolsaker 1995) and computational fluid dynamics (Schild 1995, Noble 1998), as well as some full scale monitoring (Jones 1991, Luther 1996). Computational fluid dynamics is useful to predict the change in stratification due to changes in ventilation but is generally time consuming. While ventilation does have a big impact on the internal temperature, most commercial atriums are mechanically ventilated and therefore the more ventilation needed the more energy used. Two dimensional simulation programs such as “Flow in an enclosed cavity” by Hijikata and Kotake (1993) are useful to understand how geometry and heated surfaces affect natural convection in a tall narrow cavity Both Moser (1996) and Luther (1996) use computational fluid dynamics for thermal comfort analysis and commercial thermal building programs to estimate the energy consumption. Such programs include DOE-2 and TRNSYS. A paper by Gordon (1991) compared building measurements to computer simulations for atriums at latitudes from Norway to Southern U.S. (only cold climate results were presented). Cold climate investigations generally cover situations where the outside 28


Review

temperature is less than the inside temperature and heating is required. This is not applicable to the tropics where cooling energy loads are more significant than heating energy loads. Kolsaker and Frydenlund (1995) found a linear thermal stratification with respect to height. This is unlike other literature, which found exponential thermal stratification with respect to height. They used a case study of a building in Norway and the computer simulation comparison used a single zone energy simulation program. Full-scale thermal investigation data has been obtained for an actual atrium (Jones 1991, Luther 1996 and Nobel 1998). The presented data is seasonally specific and shows thermal stratification and the destratification. Other data shows the prediction of internal and external temperatures associated with the glazed skylight. Luther in his paper discussed the positioning of his temperature sensors within the atrium well along with the time interval between measuring points. This information is useful in reproducing experimental results. [Figure 3.06: Building ratio effect upon thermal stratification]

Analysis of how changing the geometry of the atrium affects the thermal stratification within a building has been studied (Jones and Luther 1991 and 1993). They conclude that tall, narrow atriums have a more localised direct solar impact area, less air mixing and less emitted radiation and therefore more stratification compared to shorter, wider atriums (Jones 1991). A strategy to reduce the stratification within atriums is discussed by Luther and Smith (1995) but the conclusion is an expensive double glazed system with low emissivity surfaces and inert gas between the double-glazing.

29


Review

Other solutions include monitor skylights and retractable shading (Saxon 1983). These solutions do not improve the use of low elevation light. Edmonds (1996) discusses using angular selective glazing in skylights to improve daylighting and suggests that they might reduce overheating when the sun is at high elevation. Modifications to atria glazing to affect the thermal stratification gradient within the system in the sub-tropical climates is the area of research in this investigation and an area largely not researched to date. 3.5 Advanced Fenestration System Advanced passive daylighting systems such as light shelves (Beltran 1994), light pipes (Travers 1998, Ruck 1989), light guiding shades and skylights (Edmonds et al. 1998b) have been researched and improved but are still not commonly used in building design. These systems could be advanced and improved even further by the inclusion of bidirectional glazing. Systems such as the Fresnel lens panel (Ruck 1982) and the laser cut panel (Edmonds 1993, Travers 1996) use properties governed by the Fresnel equations, refraction and total internal reflection theory to divide the incident daylight beam up into a transmitted component and a deflected component. [Figure 3.07: Laser cut panel applications]

The idea behind these types of light redirecting systems has been around since the turn of the 20th century (Wadsworth 1903, Nobel 1898). Only since the late 20th century, however, has the mechanical technology and material been around to enable

30


Review

the economical manufacturing of these systems with the accuracy to obtain the desired effect. In the late 19th century, many attempts were made to redirect and diffuse light through vertical fenestration. Luxfer Prisms were designed to improve the natural lighting in buildings by redirecting diffuse light from the zenith towards the back of the room. They were applied to spaces facing narrow streets and basements (Neumann 1995). [Figure 3.08: Luxfer Prism design at turn of 20th century (Neumann 1995)]

Sunlight directing prisms were that could be fixed or tilted in vertical fenestration above the eye height investigated by Ruck in the 1970’s. Sunlight excluding prisms that aim to reject direct sunlight but deflect zenithal skylight were investigated by Bartenbach in the 1980’s (Baker et al. 1993). Light deflecting panels can now be produced using a programmed laser beam to place cuts in plain acrylic sheets. The improved accuracy allows more cuts, this results in a

31


Review

greater surface for total internal reflection so more of the light is deflected. The acrylic material also provides greater strength because it is less brittle than glass (Edmonds 1991). The objective of most advanced daylighting systems were to deflect the light up onto the ceiling, deeper into the room and therefore to illuminate the room to a greater depth. This reduces the electric light usage. The source of illumination upon the work plane still appeared to be from the ceiling as in artificial lighting but it actually originates from the side window. The use of light deflecting panels to distribute daylight into adjoining rooms of an atrium is a promising application of such panels. The panels are located at the glazing between the atrium well and the adjoining space and are tilted at an angle of approximately 40 degree to the vertical (Edmonds 1998). A variation on this application is to locate the tilted LCP in the middle of the atrium space in a V shape above the floor to achieve a similar deflection of light to the adjoining room and to shade the atrium floor (Matusiak 1998). In this orientation the LCP is referred to as a light spreader instead of a concentrator (QUT Daylight Research Group 1996). Another useful application of the panels is in pyramid shaped skylights. Here, the high elevation direct sun is deflected twice and is actually rejected back out of the skylight, while the low elevation sky luminance is directed deep into the atrium all day (Edmonds 1993). The skylight design could be incorporated into a larger idea and used as the glazing of an atrium, this could provide a more even distribution of illuminance levels throughout the day in the atrium well. Previous works (Edmonds 1993, 1996, 1997, 1998) on the benefits of laser cut panel (LCP) have mainly been performed with small LCPs and on scale model buildings. Greenup (1998) has only recently theoretically modelled LCPs in a computer simulation.

32


Review

3.6 Computer Prediction Simulations Computer modelling offers the opportunity to compare and vary design parameters to meet requirements of different site orientations with climatic conditions. A lengthy computation time may still be faster than the alternative of building physical models (Close 1996). Simulations can also prove to be better because of the inability to monitor scale models under real varying conditions for extended periods of time to account for all the possible changes in climatic conditions. Computer simulations rarely give absolute values, they are generally used as a comparison tool to find the relative best design solution. Simulation programs can simultaneously look at the best, worst and long term climatic conditions to establish the relative best design. Whereas, monitoring under real conditions can take at least 6 months to account for these conditions, if not longer. [Figure 3.09: Radiance generated picture of atrium]

Computer modelling of building performance has advanced considerably over the last few decades. Robert Clear wrote the original daylighting program, called Quicklite 1, on a programmable calculator at Lawrence Berkeley Laboratory in the 1970’s.

33


Review

Through the 1980’s programs such as Microlite, CADLight, and Superlite were the standards. In the late 1990’s Radiance and Lightscape were the visually elite (Navvab 1989). Computer ray tracing is one method to simulate the interaction between the daylight sources and the building. Ray tracing began as very primitive algorithms written in FORTRAN language in the 1970-80’s, with little knowledge of the physical principles just merely as a computer programming exercise (Reid 1989; Zeitler 1987). They have now developed into highly advanced programs (eg., Radiance, and Lightscape) which take almost everything into account. These programs provide highly realistic visualisations but they take several months to learn how to use. It was also difficult to obtain useful quantitative data from such programs. Radiance had problems handling advanced daylighting systems such as complex bi-directional light devices (eg., LCPs) and parabolic reflectors (eg., Light Guiding Shades). Both devices of which are under development within the Daylighting Research Group at QUT. It has been stated (Apian-Bennewitz 1998 and Greenup 1998) that the simulation of some of these advanced daylighting systems and materials using Radiance has been achieved but detailed analysis was not yet widely known. The use of a geometrical framework to determine the intersection point of internal surface reflections to find light levels within buildings was well set out by Tregenza (1994). This method outlines the basis of the method used in this research. See the theory in Chapter 5. Tegenza produced a forward radiosity computer program. This process traces patches of light rays from the source to the working plane and the accuracy is based upon the size of the patches. A different method for determining light levels is a backward ray tracing method where rays are traced from the measuring point on the work surface back to the source. This method was chosen in this research. Wright (1998) stated “Ray tracing allows the designer to simulate building features with a good degree of accuracy under a range of sky luminance distributions. Ray tracing techniques only have a limited appeal. Programs are typically complex, not user-friendly, and require comparatively powerful computers to run them. For

34


Review

complex buildings, the time required for data input and the program running can be prohibitive, particularly if the designer wishes to explore a series of possibilities.” The most widely accepted and used lighting simulation program to date is Radiance (Ward 1999). Radiance uses both ray-trace and radiosity methods. Ray tracing is used for the indirect component and zonal/radiosity is used for the direct component. A review of the daylight penetration prediction computer programs show that they use either zonal models or ray-tracing models. Zonal models calculate the contribution of one patch of wall to all the other patches on all the other walls (Moore 1999). Tracing rays can be performed either forwards (light source to surface) (Pearce 1998) or backwards (work plane surface to light source) (Navvab 1989). Thermal simulation programs such as Trnsys, GSL, Capsol, DOE2, Therm, Heat, FRES and PHOENICS, fall into one of 2 types of programs. Either they use zonal models similar to the daylight simulations mentioned previously or they use computational fluid dynamics (CFD). The zonal models either calculates the equivalent electrical energy used to maintain a comfortable temperature within the system (GSL) or they equate the temperature within the system using electrical circuit analogues (Trnsys, Capsol). The most accurate but also the most computationally expensive method is CFD, which uses the physical principles of fluid flow and the associated non-linear conditions. This method can be used to predict the spread of contaminates like fire and poisons or the temperature. Validation of field data and simulated data is compared to some professional simulation programs in Chapter 5 and 6. 3.7 Conclusion Literature in this area is mostly based upon northern hemisphere buildings in cold climates where solar gain is an important beneficial element in building design. To obtain the full benefits from atriums in hot climates, modifications to the traditional design are needed. Reduction of excessive solar gain and thermal stratification while still reducing non-renewable energy usage (eg.. artificial lights, mechanical ventilation) is needed. 35


Review

The simulation of buildings both thermally and visually can best be performed today on expensive computers software programs. The recent nature of this research topic can be seen by the recent publication dates of the literature reviewed. This literature reviewed here contains some of the background within the general research area investigated herein. More so I have taken ideas from all of these different papers to build my own research area looking at modifying glazing in tropical atria and looking at the lighting and thermal effects. The construction of a large scale model atrium to investigate the daylight and thermal penetration and the comparison of clear glazed to advanced glazed atrium is the basis of this investigation and a logical extension of the work in the literature reviewed. 3.8 Background The Daylighting Research Group was established as a part of the Centre for Medical and Health Physics under the supervision of Dr Ian Edmonds. The Centre’s research areas include: -Design of optical systems to improve natural lighting of inside buildings -Prediction of interior illumination at design stage based on computer simulation and modelling studies -Monitoring of illuminance levels within buildings Previous research and publications by the author in similar area: - Australian Window Council Inc.; (2000); Window Energy Rating Scheme 2; unpublished. -Mabb J.; (1999); “Modification of atrium design to improve thermal performance”; Solar ‘99 Proceedings Case Studies; WA. -Edmonds I., Close J., Lim W., Mabb J.; (1998); “Daylighting Street Level Offices in City Buildings with Light Deflecting Panels”; Architectural Science Review Vol. 41, p173-184. -Edmonds I., Greenup P., Mabb J.; (1998); “Performance of Advanced Daylighting Systems”; Solar ‘98 Proceedings. -Mabb J.; (1997); “Modification of atrium design to improve daylight penetration”. 3rd year undergraduate project; unpublished. 36


Theory

Chapter 4: THEORY The theory section covers relevant areas relating to the input of light and heat energy into buildings and the form and structure of atrium buildings. It also covers general optics, solar geometry and the transmission of light through laser cut panels. A detailed discussion of the equations used in the simulations and experiments are included in the following chapters. 4.1 Light [Figure 4.01: EM wave spectrum: gamma rays, x-rays, ultraviolet, visible, infra-red, micro, radio]

Humans need visible light to see. Visible light is a natural phenomenon that stimulates the sense of sight in the form of radiation from the sun, fire or artificial source. Seeing is a humans most dominant sense. There is more, however, to the electromagnetic (em) spectrum than just visible light. In fact the visible part of the spectrum is only 1 of 7 sections. Three of these sections make up what is known as the solar spectrum and are called Ultraviolet (100nm400nm), Visible (400nm-700nm) and Infra-red (700nm-1mm). Radiation from each section has different advantages and disadvantages including their effects upon humans.

37


Theory

The ultraviolet (UV) spectrum can be divided up into 3 areas known as UV-A (400300nm), UV-B (320-280nm) and UV-C (280-100nm). Most of the UV-C radiation is absorbed by the ozone layer of the atmosphere. UV-B radiation is harmful and causes skin cancer. UV-A radiation causes sun reddening. Clear glass reduces the amount of transmission of UV-B radiation. The visible spectrum can be divided into 6 main colour regions: violet (400-450nm), blue (450-520), green (520-560), yellow (560-600), orange (600-625), red (625700nm). The sensitivity of our sight peaks at 555nm, which is in the middle of the visible spectrum. The infra-red spectrum also has a number of divisions including the near, medium and far infra-red. This radiation spreads out over a large range of wavelengths from 700nm to 1mm. All objects reradiate heat energy in the infra-red range of the spectrum. However, this part of the spectrum does not transmit through glass. Therefore, once the radiation has entered an enclosed space through the glazing and been absorbed and reradiated by the internal mass, it can not retransmit out through the glazing again. This effect is known as the Greenhouse Effect due to its beneficial effect upon growing plants in cold climates in buildings covered totally in glass. (Purdue University 2000, www.purdue.edu/REM/RAD/uv.htm) People need an adequate amount of light to perform any prescribed task. The more precise the task, the more light is needed. The measurement of light level is based upon the idea of a standard candle with known output. Luminous energy (Q) is visually radiant energy travelling as electromagnetic waves. The quantity of luminous energy flowing from a source is measured in lumen seconds (lm-s). A solid angle (ω) is the ratio of the sphere surface area (A) enclosed to the square of the radius (R). The unit is steradian (sr). ω= dω =

A R2

Eq. 4.01

dA R2

38


Theory

Luminous flux (Φ) is the time rate of flow of luminous energy. The lumen is the amount of luminous flux per unit solid angle from a uniform source of 1 candle. Φ=

dQ dt

Eq. 4.02

Luminous intensity (I) is the luminous flux per unit solid angle in a given direction. I =

dΦ dω

Eq. 4.03

A candela is the unit of luminous intensity in a given direction of a source which emits monochromatic radiation of frequency 540 x 1012 hertz and has a radiant intensity in that direction of 1/683 watt per unit solid angle (Merriam-Webster 2001). The brightness of any object in a particular direction in the field of view is known as the luminance (L) of that object. Luminance can be defined as the luminous intensity of a surface in a given direction (θ) per unit projected area (A) as viewed from that direction. (Helms and Belcher, 1991)

L= d

2

Φ

dωdA

=

dI dA

Eq. 4.04

The luminance efficacy of a source is a measure of how efficient that source is in producing visible light. It is the ratio of the light output to the total power input. Sunlight is a very efficient source of light with an efficacy of 94.2 lm/W (IES 1995). Light from the sun produces less heat for the same light output (lumens) than most artificial sources. This compares to an incandescent lamp (17.5 lm/W) and a fluorescent lamp (78.8 lm/W) (Helms 1991). When light falls upon a surface it produces illumination. The measure of illuminance (E) is the luminous flux (Φ) incident per unit surface area. E=

dΦ dA

Eq. 4.05

The unit is the lumen/m2 or lux. The minimum recommendations of illuminance level for specific tasks and interiors are stated in the Australian Standards (AS 1680.2.0 - 1990).

39


Theory

4.2 The Sky [Figure 4.02: The Sun]

Direct radiation comes from the sun which emits 63 MW of power per square metre of its surface area (this is equivalent to approximately 6 thousand million lumens). It takes the light from the sun just over 8 minutes to reach the Earth. Travelling in a vacuum at 3 x 108 m/s this equates to a distance of 150 million kilometres. This light either reflects off, is absorbed by or refracts through our atmosphere (Steemers 1994). The fraction that refracts through our atmosphere reaches the ground directly as sunlight or is diffused by the atmosphere as skylight. The diffuse skylight is produced by light that is scattered by particulates in the atmosphere. Due to the Rayleigh scattering by air molecules, the red end of the visible spectrum with longer wavelengths is scattered more and blue is scattered less so the sky appears blue. The reduction in transparency of the atmosphere due to scattering of the solar radiation by particulate matter is known as turbidity. To calculate the amount of sunlight reaching the ground both the elliptical orbit of the earth and the earth’s atmosphere have to be taken into account. The extraterrestrial solar illuminance (Eext), corrected for the elliptical orbit by using the day number of the year, known as the Julian date (Jd), is (IES 1995):

2π ( Jd − 2)   Eext = E sc  1 + 0.034 * cos    365

Eq. 4.06

40


Theory

The solar illumination constant, (Esc), is equal to 128 Klux. The direct normal illuminance, (Edn), corrected for the attenuating effects of the atmosphere is given by: Edn = Eext . e-cm

Eq. 4.07

Where c is the atmospheric extinction coefficient (clear=0.21, partly cloudy=0.8) and m is the relative optical air mass. The direct normal irradiance (Idn) can be found either theoretically or calculated from the global and diffuse irradiance measured at the test site (see section 7.6.3). The theoretical value is based upon the relative optical air mass (m) and the extraterrestrial direct solar irradiance (Iext) which is the solar constant stated as 1350 W/m2 (IES, 1995).

Idn =

I

ext

2

-0.65m

[e

+ e-0.095m ]

Eq. 4.08

The relative optical air mass varies with respect to the amount of particulate matter in the sky. The particles can include gases, dust and aerosols. The representation of the relative optical air mass (m) derived by Pirsel (1991), is m=

(626.08 cos( Z )) 2 + 1253.16 − 626.08 cos( Z )

Eq. 4.09

Where Z is the zenith angle of sun. This can be found in radians from equation 4.21 by subtracting π/2.

41


Theory

4.2.1 Sky Distributions [Figure 4.03: Fish eye view of intermediate sky]

The sky is broadly divided into several different categories depending upon the number of cloud covered oktas present. [Table 4.01: Sky cloud description]

Sky Description

Oktas

Clear

1-3

Intermediate

4-5

Overcast

6-8

The variations in sky luminance caused by the weather, seasons and time of day are vast and difficult to quantify. However, the theoretical sky distribution included in the programming in this research includes the isotropic sky, the standard overcast sky and the clear sky (IES 1995; CIE 1994). The isotropic sky has a constant luminance from all directions. The standard overcast sky has a varying luminance from horizon to zenith, being one third as bright at the horizon compared to the zenith. The clear blue sky, which is applicable to a lot of the sub-tropics, has a variable luminance with respect to the horizon, zenith and position of the sun. Overcast sky The luminance distribution of the overcast sky was originally stated by Moon and Spencer as:

42


Lp =

L (1 + 2 cosθ ) z

Theory

Eq. 4.10

3

Lp is the luminance at a point in a particular direction. θ is the zenith angle of the point and Lz is the luminance in the zenith direction. This equation is equivalent to the CIE standard overcast sky distribution. The horizontal global illuminance (HGI) under overcast skies is usually about 20Klux and from this the zenith luminance (Lz) can be found by using the equation: Lz =

9(HGI ) 7π

Eq. 4.11

This equation can be found from first principles by first finding the illuminance on a horizontal surface produced by a differential element of sky (Helms 1991): dEh = L cos θ dω where L = Lz/3 (1+2 cosθ)

for overcast sky

and dω = sin θ dθ dφ dEh = [ Lz/3 (1+2 cosθ)] cos θ sin θ dθ dφ This equation is then integrated over the whole sky.

dEh =

2π π /2

∫∫ 0

=

0

2π π /2

∫∫ 0

=

2π π /2

∫∫ 0

0

0

 L z 2 L z cos(θ )   cos(θ ) sin (θ ) d θ d φ  3 + 3

 L z cos(θ ) sin(θ ) 2 L z cos(θ ) cos(θ ) sin(θ )  +  dθdφ   3 3

L = z 3

2π =

 Lz   3 (1 + 2 cos(θ ) ) cos(θ ) sin (θ ) d θ d φ  

2π π /2

∫ ∫ cos(θ ) sin(θ ) + 2 sin(θ ) cos 0

2

(θ )d θ d φ

0

2π

∫ 1dφ 0

=

2πLz 3

π /2

∫ (sin(θ ) cos(θ ) + 2 cos 0

2

)

(θ ) sin(θ ) dθ

The illuminance Eh can then be stated as:

43


2πLz Eh = 3

Theory

π /2

2  1 2 2  2 sin (θ ) − 3 cos (θ )  0

The integral when evaluated from zenith to horizon simplifies to 7 / 6. HGI = Eh = 2π Lz / 3 x 7/6 = 7/9 π Lz The standard CIE overcast sky luminance distribution can also be stated as: −0.52 / cos ζ −0.52 / cos ζ  1− e e  Lp = LZ 0.864 + 0.136 − 0.52 − 0.52  1− e e 

   

Eq. 4.12

Where ζ is the angle of the measuring point to the zenith in radians. The constants in equation 4.12 for the overcast sky have been chosen to correspond with the original empirical Moon-Spencer equation 4.10. The first term in equation 4.12 provides the luminance contribution of the cloud layer and the second term provides the luminance contribution of the atmosphere between the clouds and the ground (IES 1995). A lot of daylight penetration research has been conducted in the northern hemisphere, especially, in Europe, where the overcast sky is used as the standard for artificial skies. The tropics, however, have on average more hours of sunshine (Aynsley and Edmonds, 1997) and a higher solar elevation. The equations that simulate the sky distribution are different at different locations due to latitude, altitude and turbidity factors. Clear Sky The standard CIE clear sky luminance distribution (IES 1995) was developed by Kittler and can be stated as:

Lp = Lz

(0.91 + 10e −3γ + 0.45 cos 2 γ )(1 − e −0.32 / cos ζ ) (0.91 + 10e −3 Z + 0.45 cos 2 Z )(1 − e 0.32 )

Eq. 4.13

Where Z is zenithal sun angle and γ is the angle between the sun and sky point both in radians. The intensity of the sun patch can be modified within equation 4.13 to correspond closer to the local sky conditions. The equation also includes the effect upon the luminance as a result of polarisation at 90° from the sun.

44


Theory

Clear blue skies are the most common sky distribution in the winter and spring months in the tropics, therefore this sky distribution was included in this research. (Aynsley and Edmonds 1997, BOM 2000) Isotropic sky An isotropic sky is a sky with the same luminance from every point on the sky. A direct sun patch can also be included with appropriate luminance and positioned with respect to the solar altitude and azimuth. The horizontal illuminance produced by a sky of constant luminance is equal to π times the luminance (Lim et al. 1979). This can be found by considering a hemisphere of uniform sky luminance. At an angle θ, an elemental ring of width dθ around the hemisphere will have an area of: A = 2πR2 cos θ dθ If the luminance is L then the intensity can be found: I = L.A The illuminance according to the inverse square law is: dE = I sin θ / R2 Therefore, by substituting in for I and then A: dE = L. 2πR2 cos θ dθ / R2 dθ = 2π.L sin θ. cos θ dθ Integrating to get the illuminance from the whole sphere gives: π /2

E = πL ∫02 sin θ .cosθdθ The illuminance Eh can then be stated as: cos 2θ  Eh = π L −  

2

π /2

0

Eh = π L

Eq. 4.14

This value can be obtained experimentally by measuring the HGI with the sun shaded. These theoretical sky distributions were investigated and used within the computer simulation programs described in Chapter 5.

45


Theory

4.3 Solar Geometry

The position of the sun in the sky is expressed in terms of angles called altitude and azimuth. These angles depend upon factors such as latitude, declination, and hour angle. These factors in turn have equations that involve the day of the year and the time of the day. [Figure 4.04: Solar position with respect to season]

W

N Winter

S

E

Equinox

Summer

The day of the year known as the Julian date (Jd) is needed and can be found by using one of 3 different equations depending upon the month of the year. (Pearce 1999) For January and February the Julian date is simply equal to: daynumber (Jd) = 31 x (month - 1) + day

Eq. 4.15

For the months, March to August, the equation is more complicated: daynumber (Jd)= 59 + 31 x (month - 3) - INT(((month - 3) / 2) + 0.1) + day Eq.4.16 For the months September to December the equation is: daynumber (Jd)= 243 + 31 x (month - 9) - INT(((month - 8) / 2) + 0.1) + day

Eq.4.17

The time of the day is usually expressed as a 24-hour time and is known as the solar time. It is found from the summation of standard clock time and the equation of time. The equation of time gives the difference between solar time and clock time due to the elliptical orbit of the earth and the solar declination of the axis.

46


 4π ( Jd − 80)   2π ( Jd − 8)  Equation of Time (ET) = 017 . * sin  −     373 355 

Theory

Eq. 4.18

The declination is then found with respect to the Julian date (Szokolay 1996; IES 1995).  2π ( Jd − 81)  Declination (DEC) = 0.4093 * sin    368

Eq. 4.19

[Figure 4.05: Earth revolution causing seasons] N Summer Solstice December 22 - Longer days 23.3 N Tropic of Capricorn

23.3 S

Sun - Noon sun vertical at tropic of Capricorn

N

23.3 N

Tropic of Cancer

Winter Solstice June 22 - Shorter days

23.3 S

Sun - Noon sun vertical at tropic of Cancer

N Equator

Vernal Equinox

23.3 N

Equal hours of day and night

23.3 S

Sun - Noon sun vertical at the equator

The latitude (lat) of the site affects the position of the sun in the sky and the time of sun rise and set while the longitude affects the solar time. The experimental scale model was located near the Brisbane airport, the longitude (slong) at the site is 153° 05’ E. However, the nearest reference longitude (rlong) meridian is 150° E which corresponds to 10 hours ahead of Greenwich Mean Time (GMT). Therefore, a longitude correction has to be made to find the solar time.

47


Theory

The correction in time from clock time to solar time is therefore: Solar Time = Clock Time + ET + (slong - rlong)/15

Eq. 4.20

The hour angle (hra) is the angle of the sun away from maximum. The sun moves at 15° per hour so the hra = 15 x (Time - 12) in radians From this the time of sunrise and sunset can be found: Sunrise hour-angle (srh) = arcos [-tan (dec) * tan (lat)] Sunrise time (srt) = 12 - (srh/15) Sunset time (sst) = 12 + (srh/15) These times are solar time. Then the solar altitude (salt) and azimuth (sazi) can then be found in radians (Szokolay 1996): salt = arcsin [ sin(lat) x sin(dec) + cos(lat) x cos(dec) x cos(hra) ]

Eq. 4.21

sazi = arccos[ cos(lat) x sin(dec) - cos(dec) x sin(lat) x cos(hra) / cos(salt) ] Eq. 4.22 The solar altitude is the angle of the sun above the ground. The solar zenith angle is then found by subtracting π/2 from the solar altitude and is therefore the angle with respect to the zenith. The solar azimuth is stated with respect to the North direction where a negative azimuth would mean West of North and a positive azimuth is East of North.

48


Theory

4.4 Laser Cut Panels

The angular selective glazing is made from a thin column of transparent rectangular parallelepipeds produced from cutting a clear acrylic sheet with a laser. This produces what is called a Laser Cut Panel (LCP). The panel appears transparent when viewed perpendicularly, however, each laser cut which is normally perpendicular to the surface of the panel acts like a little mirror to off axis light rays. The deflection of light in these panels occurs by refraction and total internal reflection. As the light ray passes from air to acrylic it enters the medium of higher refractive index and refracts towards the normal following Snell’s Law, figure 4.09. The ray is then transmitted until it either hits the exit face or the cut. If the ray hits the cut then total internal reflection occurs. Total internal reflection can only occur when light attempts to move from a medium of higher refractive index to a medium of lower refractive index. The critical angle of incidence with respect to the normal that determines whether or not total internal reflection occurs is found from the inverse sine of the ratio of the refractive indices.   θc = Sin -1  n2     n1 

(for n1>n2)

Eq. 4.23

The ray reflects off the cut and then progresses onto the exit face. At the exit face all the rays again refract as they go from a medium of higher refractive index to a medium of lower refractive index, therefore, they refract away from the normal to the surface. The angle of incidence upon the exit aperture is i2 = r1. A fraction fd of the incident beam that totally internally reflects is deflected through twice its angle of incidence from its original path (i1+r2). The angle at which deflected rays leave the element is: r2 = arcsin(n sin(r1)).

Eq. 4.24

The remaining fraction that does not hit the cuts (fud = 1-fd) continues undiverted.

49


Theory

[Figure 4.06: Diagram of LCP with labelled rays]

i1

r1 i2

fd

r2

1-fd

The fraction deflected follows simply from rules of geometrical optics: fd = (W/D) tan r

(iio)

Eq. 4.25

Where W/D is the ratio of panel width (W) to cut spacing (D), r is the projected angle of refraction in the panel and io is the angle of total deflection (Edmonds 1993). The incidence angle i at which the fraction deflected is 100% is known as the angle of total deflection io. It is found for each ratio of W/D. Example: When W/D=2 and fd=1 then r = arctan [fd / (W/D)] = 26.56 degrees using Snell’s law the incidence angle can be found from the refracted angle using io = arcsin(n2 sin(r)) = 42.13 degrees when n2=1.5 Tilting the angle of the cuts with respect to the normal to the surface can modify the panels. This complicates the theory more and is discussed further in Edmonds (1993). The orientation of these LCPs on each of the four tilted sides of a pyramid shaped glazing aperture results in a device called an angular selective skylight. High elevation sunlight at midday in summer is reflected back out of the atrium. The light hits the angled panel in the vertical direction and is deflected across the top of the pyramid, figure 4.10. It undergoes a similar deflection through the other side of the pyramid and so is deflected out of the pyramid. This reduces the heat and harmful effects of the midday sun. When the sun is at a low angle at morning and afternoon, the design redirects the daylight deep into the building space, in a similar manner as described above. This illuminates and warms the interior of the building.

50


Theory

The overall effect is a more even distribution of light over the day while still eliminating the harmful midday sun rays. [Figure 4.07: Angular selective LCP skylight]

Reject high elevation direct sunlight

Redirect low elevation skylight

Less solar energy gain through out the middle of the day will result in lower temperature and less thermal stratification A major development within this research project was the inclusion of the LCPs within a computer generated backward ray tracing program. The LCPs were included in the glazing aperture of a normal side lit room and on top of an atrium well. The incidence angle, refracted angle and the exit angle through the LCPs were determined as well as the fraction deflected, fraction undeflected and the total percentage transmitted. The light rays exit out of the LCPs in both the deflected and undeflected directions simultaneously. The intensity of the two rays sum to the total percentage transmitted. In the room simulation, the laser cut glazing was tilted out to a maximum angle of 45° from the vertical. The various tilts of the LCP effects the sky angle at which the backward ray traced light ray is deflected towards. In the atrium well simulation, the LCP is in a fixed tilted position. The deflected rays mostly go towards the horizon resulting in lower luminance levels under overcast sky conditions. There is not much difference in the algorithms between the LCP in the 2D and 3D daylight simulation.

51


Theory

4.5 Thermal Theory

Heat is a form of energy, which can be transmitted between bodies via conduction, convection and radiation until the temperature of each body reaches equilibrium. Heat gain or heat loss by a building refers to the transfer of heat from the outside to the inside or visa versa through all surfaces of the building. Conduction is the heat flow through a solid material. It transfers energy through a buildings' walls and window frames. Convection is the heat transfer by the movement of fluids. It results from hot air expanding and rising and cool air contracting and falling. Radiation transfers energy through space from an object that is hotter than its surroundings. Radiation from the sun falls upon all external surfaces of a building. The interaction of these heat transfer processes is complicated and so they are not generally measured independently. Instead energy performance characteristics of the building materials is calculated including the thermal transmission, thermal conductivity (U-value), and thermal resistivity (R-value). R = 1/ U

Eq. 4.26

In this research, the separate thermal processes are investigated individually. Thermal Stratification Thermal stratification was initially investigated in environmental areas such as lakes and the atmosphere, where the fluid appears to be vertically segmented into layers depending upon its temperature gradient. It is now increasingly being investigated in areas such as the internal air volume of buildings with high ceiling. Stratification of a medium occurs when the fluid density in the ambient medium is non-uniform and varies with height. It arises when a heated body transfers energy into an enclosed region causing hot fluid to rise, and stratification of medium results with the hotter, lighter fluid overlaying the colder, heavier fluid. The fluid flow that results from the heat loss from the heated body rises above it as a buoyant flow and a recirculating flow is set up. If the heat is stopped, the flow stops with a temperature variation in the medium, with lighter fluid above heavier fluid.

52


Theory

[Figure 4.08: Representation of stratification boundary conditions (Juluria 1980)]

Adiabatic Stratification Height Stable Stratification Unstable Stratification

Temperature

There are three types of stratification including adiabatic, unstable and stable. If the temperature increases with height or decreases at a rate less than the adiabatic rate, then stable stratification results. The condition of adiabatic stratification represents neutral equilibrium and a temperature decrease faster than that results in unstable stratification. Adiabatic stratification occurs when the medium is in neutral equilibrium and there is no change in temperature with respect to height in an ideal fluid. The increase in density due to temperature decrease is balanced by the decrease due to pressure decrease with respect to height. If there is no stratification then the volume of air circulates until an equilibrium temperature is reached. Unstable stratification occurs when hotter, lighter fluid lies below colder, heavier fluid. The lighter fluid element displaces vertically giving rise to a convective fluid motion. Stable stratification occurs when the hotter, lighter fluid lies above the colder, heavier fluid. The density (ρ) of the fluid must decrease vertically (x), decrease as the temperature (T) increases,

∂ρ ∂T

∂ρ < 0 , as well as ∂x

< 0 , which is true for most fluids.

This results in the relationship of the temperature (T) increasing vertically (x),

∂T > 0. (Juluria 1980) ∂x

53


Theory

In the case of an atrium building where the heat radiates into the space from the direct solar beam, the heat is absorbed by the internal walls and reradiates into the enclosed space. Due to the relatively large height of the enclosure the direct radiation usually does not penetrate very deeply into the space. The upper section of the walls, frames and sometimes glazing act as the heated bodies which lose energy in to the enclosed space. However, this region is already at the top and so the hotter fluid can not rise any further. No convective flow is set up even when more heat is added to the system.

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Simulation 1

Chapter 5: DAYLIGHT SIMULATION 5.1. Introduction

The daylight computer simulation programs have been created as part of this research to predict the daylighting performance concerned with the various modifications of three different building structures. These building structures include a room, a well and an atrium with adjoining spaces. The modifications to these building structures include the glazing, the dimensional ratios and the surface reflectivities. The daylight simulations were initially produced as two dimensional geometrical spaces. These were designed and developed as learning tools. Later the simulations were updated to simulate three dimensional geometrical spaces. Computer simulation programs are potentially much quicker than measurements made on scale models due to the ease at which the programs can be modified to be simulated with different climatic conditions, dimensions and fenestrations. The simulations are potentially more accurate than empirical equations based upon one off experiments because the simulations were mostly based upon first principle physics. They were written from first principles because at the time of initialisation complex bi-directional glazing such as the laser cut panels could not be simulated in commercial lighting programs. The speed of computer processes now allow raytracing techniques to be used and results achieved within a reasonable amount of time. Due to the simplicity of the scale models in the experimental monitoring in this work, simple simulations could be written to predicted light levels within these spaces. Commercial lighting simulation programs were not found to be suitable for this research because they were quite expensive and time consuming to learn, had excessively large material libraries which were not needed while still not being able to handle bi-directional glazing materials that did need to be simulated. Two computer-programming languages were used in this research. BASIC was initially used and within this environment the two dimensional daylight simulation programs were constructed. The other program used was MATLAB, in which the three dimensional daylight simulation programs and the thermal simulation programs were completed.

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Simulation 1

The daylight simulation programs included 16 different algorithm variations, which covered two and three dimensional geometry, three different building structures and two different glazing types. See the appendices in Chapter 10 to view the program codes. The three dimensional daylight simulation program includes a room or an atrium well simulation with clear or LCP glazing. It also includes an atrium well with adjoining room at the bottom of the well with four glazing combination options. These include clear glazed well and adjoining room, LCP glazed well and adjoining room, clear glazed well and LCP glazed adjoining room and finally LCP glazed well and clear glazed adjoining room. The two dimensional daylight simulation programs includes all the same building and glazing simulation variations. Simulation programs using a Monte Carlo, backward ray-tracing technique were created. These programs were used to predict the light levels within buildings with the inclusion of laser cut panels in the fenestration system. The program consists of a series of algorithms that simulate the natural processes involved in the propagation of daylight within buildings. The program simulates the sky, ground, fenestration, and internal building surfaces. It was designed to give an array of illuminance levels across the working surface in the area of interest. The simulation was not designed to predict precise illuminance measurements corresponding to measured data. Instead, it was designed as a comparison tool to show the effect on the lighting level upon varying the system. The geometry of the buildings was basic rectangular with no internal or external obstructions. The two dimensional and three dimensional versions of the daylight simulation programs are similar in methodology and outline except in the ray-tracing algorithms and the differences in programming languages. The simulations should show that with the inclusion of the modified angular selective glazing upon the atrium well that the light level would be more consistent across the day and higher in the morning and afternoon compared to normal clear glazing. The LCPs upon the adjoining spaces to the atrium wells should redirect the light from the well onto the ceiling of the room and increase the level towards the back of the room. The analysis of the simulations will be discussed in Chapter 8. 56


Simulation 1

[Figure 5.01: 2D daylight simulation screen output of room with rays]

5.2 Computer Simulation Theory

The daylight penetration simulation program consists of a series of algorithms that simulate the sky, building geometry, ground, window, surfaces within the building and the progression of light through this environment. The equations are mostly based upon previously published material and are explained in detail in Chapter 4 and below. They can also be viewed in context in the program code appendices. In these programs, the only light source simulated is the sky so the distribution of light across it must be thoroughly described. The luminance of the sky for each ray was evaluated using the equations set out in section 4.2.1 for overcast and isotropic/direct sky distributions. The illuminance of each ray was evaluated using the method described in section 5.2.1. The equations and methods were chosen because of their simplicity to represent applicable sky distributions and summed illuminances upon surfaces. In the theoretical simulations of the overcast sky, the value of the horizontal global illuminance (HGI) was obtained from field data. The zenith luminance (Lz) and the luminance at any other point (Lp) was found from the HGI using the equations 4.10 and 4.11 respectfully.

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Simulation 1

The HGI was generally measured in the range between 20-50 Klux for overcast skies depending upon cloud type and density. The Lz was also measured in the field in the range between 8-20 Kcd/m2 for overcast skies. The clear sky distribution was measured and found to have a horizontal global illuminance between 60-110 Klux, an indirect sky luminance between 1000-5000 cd/m2 (25-120 lux) and the direct sun luminance between 70-110 Klux (3-7 x106 cd/m2). See Chapter 7 for an explanation of how the sky distribution measurements were recorded. The constants that were used in the theoretical simulations for the isotropic/direct sky distribution were Lsun = 4x106 cd/m2 and Lsky = 3000 cd/m2. 5.2.1 Illuminance Algorithms in simulation

The luminance (L) of each light ray is found in the simulation programs using the following method. L = Lp * Average Intensity Product * Cosine Correction * Solid Angle Element

Eq. 5.01

The luminance of point (Lp) in the sky as described above is found using the particular sky distribution equation appropriate (4.10 or 4.13). This value is in candela per square meter and may be high if it corresponds to the point where the sun is. It might be low if it corresponds to the isotropic blue sky or it might depend upon altitude as with the overcast sky. The luminance (Lg) value given to a ray that has a negative exit altitude (to ground) was determined by the incidence angle, the reflectivity (ref) of the ground and the horizontal global illuminance. Lg = HGI * ref * sin (i)

Eq. 5.02

The Average Intensity Product (AIP) in equation 5.01 takes into account the reduction in intensity of each individual ray (IP) due to multiple reflections (ref) and transmission (τ) through glazing from the measuring point to the sky. AIP = IP * ref * τ

Eq. 5.03

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Simulation 1

The Cosine Correction in equation 5.01 accounts for the angle at which the light ray hits the measuring point. The greater the angle from the normal the more reduced is the intensity following a cosine function. The Solid Angle Element (dω) in equation 5.01 is a fraction of the hemispherical sky divided up into as many segments (k) as stated.

Where

dω = 2π sin (θ) dθ

Eq. 5.04

dθ = π / k

Eq. 5.05

The illuminance (E) was then found by: dEi = Li (θ).dωi (θ)

i = 1…k

Eq. 5.06

Where i is the sky segment counter k

∑

k

∑

dEi =

1

Li dωi

Eq. 5.07

1

k

n=

∑ jp

Eq. 5.08

1

Where n is the total number of rays in all sky segments. J is the number of rays in each sky segment and p is the ray counter. k

dEi (θ) =

∑

dE / jp

Eq. 5.09

1

All the individual segmented illuminances are summed together to find the horizontal illuminance (E) at the measuring point for between 1000 to 10000 rays. The luminance of each ray that goes to a sky sector is summed. Then after all the rays are traced, each sectors summed luminance is averaged and the sum of all the sectors gives an illuminance level from the whole hemisphere. k

E=

∑ dE (θ ) i

Eq. 5.10

1

The two dimensional daylight simulation program used a similar method to that outlined in the above equations. The sky luminance distributions for isotropic/direct (4.14), clear (4.13) and overcast (4.10)* were all modified for the two dimensional sky view and included in the program.

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Simulation 1

The main difference between the two and three dimensional daylight simulation programs was the number of angular segments the sky was divided up into. In the three dimensional simulation, the hemispherical sky covered a solid angle of 2π steradians. In the two dimensional simulation, however, the semicircular sky only covered an angle of π radians. The greater view of the sky in the three dimensional simulation meant a greater number of sky segments. However, the number was limited by the array limit in the programming language. 5.2.2 Optics and Geometrical Ray Tracing

When a ray intersects with the boundary of another transparent medium part of the ray is reflected and part is transmitted. The transmitted fraction is bent at the boundary. If the ray enters a medium of greater density, then the ray is bent towards the normal to the surface. If the ray enters a medium of lesser density, then the ray is bent away from the normal. This is known as Snell’s law and can be stated as:

n1 sin θ1 = n2 sin θ2

Eq. 5.11

Where the n1 and n2 are the refractive indices of the two media. For example a light ray travelling from air to glass would have n1=1 and n2=1.5. Rearrangement of the equation can give the angle of refraction:

θ2 = arcsin (n1/n2 sin θ1)

Eq. 5.12

For off axis incident rays a generalised form of Snell’s law for projection onto the transverse plane can be found (Szokolay 1996; Whitehead 1992).

θ1 = arccos (sin (alt). sin (tit) + cos (alt). cos (tit). cos (hsa))

Eq. 5.13

Where θ1 is the angle of incidence of off axis incident ray alt = the altitude of incidence ray tit = the tilt angle of receiving plane from vertical hsa = the horizontal shadow angle = azimuth difference between ray and plane

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Simulation 1

Once the angle of incidence is found then the effective refractive index can be found. Whitehead (1992) provided a useful alternative way of finding the effective refractive index of off axis rays transmitting through an optical system. This equation was used within the three dimensional daylight penetration program upon the light rays as they exited the room through the glazing.

n` = sqrt( n22 - n12.sin2(θ1))

Eq. 5.14

Where n’ is the effective refractive index. The refractive index of a medium is the ratio of the wavelength of light in that medium with respect to that in a vacuum. Crown glass has a refractive index of 1.523 where as acrylic has a refractive index of 1.5. A vacuum has a refractive index of 1 and air has a refractive index of 1.0003. 5.2.3 Ray Trace Algorithm in 2D Simulation

The method used to find the interception points within the two dimensional daylight penetration simulation program was based upon a simple random number generation. This gave the angle of the ray with respect to the wall, and basic trigonometry was used to find the point along the wall at which the ray intercepts. An angle is selected using a standard Monte Carlo random number generator: angle = INT((max angle – min angle + 1) * RND + min angle)

Eq. 5.15

The angles are chosen between 1 and 179 degrees. The random number (RND) is automatically selected within the range from 0 to 1 and scaled up to the boundaries of the acceptable angles. The ray is directed away from the current wall. The slope of this ray is determined by using the standard formula: slope =

y 2 − y1 = TAN (angle) x 2 − x1

Eq. 5.16

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Simulation 1

The distance to the opposite wall is selected and substituted in for either y2 or x2 and the point on the boundary wall for a ray with that slope is determined by rearranging the slope formula. If the point exceeds the horizontal or vertical boundaries then the distance to that boundary is selected and, again using the rearranged slope formula, the point on this wall is found. 5.2.4 Ray Trace Algorithm in 3D Simulation [Figure 5.02: Axis and angles in 3D geometry]

(x2,y2,z2)

u3

φ

r

u2 θ (x1,y1,z1)

Z

u1

Y X

The three dimensional geometrical framework in the daylight penetration computer simulation in this thesis was based upon work by Tregenza (1983, 1994). Who describes how to find the angle of incidence of a ray onto a plane, the length of that ray and the co-ordinates of the intercept point. Using the standard Cartesian to spherical co-ordinate relationship: x = r cos φ sin θ

Eq. 5.17

y = r sin φ sin θ

Eq. 5.18

z = r cos θ

Eq. 5.19

Where r is the distance between point and origin and φ was the azimuth angle and θ was the altitude angle.

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Simulation 1

The direction of a straight line in space can be described by its direction cosines: c1 = cos φ sin θ

Eq. 5.20

c2 = sin φ sin θ

Eq. 5.21

c3 = cos θ

Eq. 5.22

A plane can also be described by its direction cosines (normal to the surface) and the perpendicular distance (P) from the plane to the origin. The direction cosines of the normal are denoted by n1, n2, n3 then the angle can be

cos (alt) = - (c1n1 + c2n2 + c3n3)

found from:

Eq. 5.23

The length of the ray between a point and a plane is

r=

n1 x1 + n2 y1 + n3 z1 − P c1n1 + c2 n2 + c3 n3

Eq. 5.24

Provided c1n1 + c2n2 + c3n3 < 0. The length of the ray from that point to every plane at that angle can then be found and the smallest positive distance corresponds to the intercept plane where the intercept point can be found from: x2 = x1 + rc1

Eq. 5.25

y2 = y1 + rc2

Eq. 5.26

z2 = z1 + rc3

Eq. 5.27

[Figure 5.03: Simulated room boundary labels and geometry] 5 7

Window x = 0

Ceiling z = H

2

Side Wall y = W

y>H/2

3 Back Wall x = L

1 Front Wall x = 0

6

Floor z = 0

4

Side Wall y = 0

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Simulation 1

5.2.5 Surface Reflections

In the three dimensional ray trace algorithm each ray is allocated a randomly generated azimuth and altitude (elevation) angle with which it is sent out from the last intersect point in a random direction. The altitude values are stated between 0 and π/2 (0 to 90°) or between -π/2 and π/2 (-90° to 90°). This depends upon whether or not the azimuth is stated between 0 and 2π (0 to 360°) or between 0 and π (0 to 180°). Either way a full hemisphere of possible angles is covered. As seen from any plane surface. The altitude angle is then skewed towards the current surface with a sine function to simulate the larger solid angle near the horizon of a sphere and therefore the increased chance of a ray proceeding in that direction. Alt = asin (rand)/rad

(0 to 90°)

Eq. 5.28

Azi = 360 * rand

(0 to 360°)

Eq. 5.29

Alt = asin ((2 * rand)-1)/rad

(-90° to 90°)

Eq. 5.30

Azi = 180 * rand

(0 to 180°)

Eq. 5.31

[Figure 5.04: Diagram of hemisphere to show greater solid angle near surface]

d θ1

d θ2

The solid angle subtended in the lower band is greater than that subtended in the upper band even though dθ1 and dθ2 are the same angle.

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Simulation 1

Whenever standard reflectivity of diffuse surfaces within buildings is mentioned then the values stated in table 5.01 are the approximate values. [Table 5.01: Surface reflectivity percentages]

Area

Low

Standard

Reflectivity % Reflectivity %

High Reflectivity %

Ceiling

50

75

90

Wall

25

50

75

Floor

5

25

50

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Simulation 1

5.3 Procedure

The objective of these simulation programs was to find the illuminance levels within a prescribed building structure at any time and compare them to the illuminance levels obtained with modified glazing. The two dimensional program was created as a learning tool before the more accurate three dimensional program was constructed. The program codes are included in the appendices. 5.3.1 Two Dimensional Simulation

The base case program simulated a room with four boundary lines, a clear glazed window space and a working plane in two dimensions. At the start of the program the user is given a brief description of what the program does followed by a prompt to either use the default settings or enter variable values for the room dimensions, window size, surface reflectivity, sky conditions and the number of rays simulated. The measuring positions along the working plane were determined, the room was drawn and the two dimensional backward ray-tracing algorithm within a rectangular space was initiated. The ray tracing process involved sending thousands of rays from the measuring point back through the room until they hit the window aperture. Each surface, with a given reflectivity, acts as a perfect diffuser, which means the reflection angle is independent of the incidence angle. A Monte Carlo technique is applied to the reflected rays giving them random angles ranging between 1 and 179 degrees. The slope of a ray at this randomly set angle is found. Each ray travels off until it hits a vertical boundary upon which it is calculated to see if it exceeds the horizontal boundary value. Trigonometric equations were used to determine the distance from the initial point to the other boundary at the prescribed angle of incidence. [Extract from 2D daylight simulation program code, refer to equation 5.16 and see appendix 10.1] slope = TAN(angle * RAD) y = y1 x = (ABS(y - py) + (px * slope)) / slope nwall = 1 IF x > x2 THEN x = x2 y = ABS((slope * (px - x)) + py)

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Simulation 1

[Figure 5.05: Pseudo code of 2D program]

Initial Position Loop

Boundary Conditions

Light ray loop

Flow chart of 2D Daylight Penetration Program

Ray trace algorithm within a rectangle

Random altitude and azimuth angles

Geometrical Framework

No

Overcast Sky

Is intersection point within the window aperture area ?

Find the transmission through the window glazing

Yes

Sky Luminance Distribution

Clear Sky

Find the illuminance level for that ray Yes

Next ray

No

Yes

Find solar altitude and azimuth

Sum all the illuminances to find the light level at that point Next position

No

Plot results and end

A true/false loop was set up where if the interception point was within the horizontal boundaries then at that point on the vertical wall a new ray was sent off at a random angle. If the point was beyond the horizontal boundary, then a new ray was sent off from the point at which the ray intercepted the horizontal boundary.

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Simulation 1

Once it had hit the boundary a reflectance value and a new randomly generated angle was given to the ray. This loop process continued until the ray hit a boundary within a set window aperture region. The luminous intensity of a ray reduces upon every deflection off a surface and it also reduces intensity upon transmission through the glass window exit aperture, which obeys the Fresnel laws. The ray also has a cosine dependence upon the initial intersect angle of the measuring point. Upon hitting the window, the product of the reflectances is made. Depending upon whether the ray is above horizontal or below horizontal, the ray continues on to the sky or to the ground where it is given a luminance value. The ground has a luminance value that depends only upon the angle of incidence. [Figure 5.06: Sky distribution in 2D daylighting simulation]

A choice of clear, overcast or isotropic/direct sky distribution models can be made in the two dimensional daylight simulation program. The entire hemispherical sky distribution was located within a two dimensional cross section of the sky. The clear sky distribution was based upon equation 4.13 where the luminance at a point on the diffuse sky is dependent upon the position with respect to the solar position and the zenith. The solar position was determined based upon the equations 4.22 and 4.23 and an appropriate direct luminance value was used. The increased intensity of the luminance from the sun was represented via an increased luminance ratio with respect to the zenith at the solar position. 68


Simulation 1

The overcast sky luminance distribution depends only upon the elevation of a point of the sky with respect to the zenith. The only meaningful relationship that can be made between the horizontal global illuminance (HGI) and the internal illuminance within a building is known as the daylight factor and can only be obtained under overcast sky conditions were there is no direct solar component of the sky. In the isotropic sky distribution the indirect sky luminance was constant across the sky and day but was varied depending upon what time of the year was being simulated. The sky was divided up into sections and the average luminance from each section was summed together to find the overall illuminance level. See the explanation in section 5.2.1. [Figure 5.07: 2D daylight simulation screen output of room and skylight with rays]

Both a well and a room were simulated in the two dimensional program. These building structures are similar but have different height to width ratios and the position of the glazing is different. A room with a centrally located skylight was also simulated (figure 5.07). The screen output shows the initial position on the floor in the middle of the room and the splay of light out of the skylight. Diffusing and/or clear glazing was included in this simulation.

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Simulation 1

A well is equivalent to a tall narrow room with the window exit aperture being located in the ceiling. A well can be quite deep and the angular view of the sky from the bottom of the well decreases as the well gets deeper. This building structure has no external obstructions unlike a room, which has a view of the ground. The view is of the sky only from within a well. [Figure 5.08: 2D daylight simulation of adjoining rooms to an atrium well with light level bars]

The duplication of a room structure several times on top of each other and the inclusion of a vertical obstruction opposite the rooms’ window was used to simulated a two dimensional atrium well with adjoining spaces (figure 5.08). This structure was simulated under each of the 3 (above mentioned) sky conditions, employing a range of window and LCP glazing options on the adjoining room and on top of the atrium well. The simulation also included various glazing options including no glazing, plain glazing, LCP glazing, tilted LCP glazing, eaves, skylights and various window sizes. Not all the incident light that falls upon the LCP is redirected. The amount of light that hits the cuts and is therefore redirected depends upon the depth of the acrylic (D) and the distance between each cut (W). This is known as the W/D ratio (See section 4.5). To allow for this, once the angle of redirection has been determined the fraction deflected is also found. Within the sky distribution equations a luminance value is assigned to both the direction deflected and the direction undeflected. With weighting applied to each luminance equation, they are then summed together. Within the room simulation the LCP glazing could be tilted out from the vertical and thereby redirect the zenith luminance onto the ceiling within the room.

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Simulation 1

Within the atrium simulation, the well glazing was tilted at 45° to form a triangular shaped aperture. The inclusion of the LCPs in this configuration meant that the low elevation light was directed deep into the atrium well while the high elevation light was rejected. Sample of a 2D simulation program result [Figure 5.09: 2D daylight simulation screen output of room with light level line]

This simulation is of a room in two dimensions with a window half the size of the front wall under an overcast sky. The room had dimensions of 3m high and 8m long. The units are arbitrary due to the two dimensional space. [Table 5.02: Light level within room]

Position in room 0 1 2 3 4 5 6 7 8 9

Light Level 0 376 478 492 410 462 375 153 177 111

The result shows the normal peak in light level near the window and the drop off as the distance from the window increases. The peak is not as extreme as in reality and the drop off is not as severe. This is due to the window having no width and the room having less surface area with respect to depth compared to the real three dimensional case.

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Simulation 1

5.3.2 Three Dimensional Simulation [Figure 5.10: Pseudo code of 3D program]

Measurement Position upon work plane Loop

Set building dimensions and light ray limits

Light ray loop

Flow chart of 3D Daylight Penetration Program

Backward Ray trace algorithm within building

Calculate path of light ray

Select Random altitude and azimuth angles for reflection off diffuse surfaces

Determine which surface is intercepted

Find intersection point upon this surface

No

Does light ray intersect with window ?

Yes

Find transmission through window glazing

Select Sky Luminance Distribution

Overcast Sky

Clear Sky

Find the illuminance level for that ray

Yes

Next ray

Yes

No

Next position

Find solar altitude and azimuth

Sum all the illuminances to find the light level at that point

No

Plot Predicted illuminance results and end

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Simulation 1

The program begins with setting the boundary wall dimensions, counters and ray number limits. The initial measuring co-ordinate point is selected at a prescribed position anywhere upon the working plane. [Table 5.03: Table of wall labels and description within 3D simulation]

Wall Number 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17

Wall Description Work plane in room Vertical wall in room Vertical wall in room Vertical wall in room Vertical wall in room Ceiling of room Floor of room Exit room loop condition Work plane in atrium well Vertical wall in well Vertical wall in well Vertical wall in well Vertical wall in well Ceiling of atrium well Floor of atrium well Exit well loop condition

The three dimensional geometrical ray tracing algorithm within a rectangular room was then initiated following the equations in section 5.2.4. The rays were traced backwards from the measuring point to the exit aperture and off to the sky or ground. The walls, which act as surface boundaries, are labelled in numeric order as Table 5.03 shows. Within the ray tracing algorithm the appropriate skewed reflection angle and reflectivity is applied to each ray upon intersection with a wall. A Monte Carlo random number generator was used to simulate the diffuse reflections off the surfaces by determining a random azimuth angle and a skewed altitude angle. With the azimuth and altitude selected, the distance to all six boundaries was found. The closest positive distance was selected as the intersect wall and the co-ordinate point of intersection was also found upon that wall. This process was continued until the ray intersects a boundary plane at a point within the window aperture area. A transmittance through the aperture was found based upon incidence angle (equation 4.27) and the refractive index of the medium (equation 5.14).

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Simulation 1

Once a ray refracts through the window it proceeds off to the sky or ground, depending upon whether the altitude is positive or negative, and a luminance value is obtained. The product of the reflectivities and transmissions are applied to the luminance along with the cosine corrections for the intersections with the surfaces and finally the direction division for that ray. The sky is divided into a number of set regions across the sky and the average luminance from each region is summed together to find a total illuminance level. See the three dimensional simulation equations in section 5.2.1. Two sky distributions have been simulated in the three dimensional program, these are the overcast sky and the isotropic/direct sky. The overcast sky distribution is based upon the classic Moon-Spencer equation (4.10) with the standard relationship between the zenith luminance and the horizontal global illuminance. If the sky type is overcast then a corresponding daylight factor (DF) as well as the illuminance level was found (equation 4.24). If the sky distribution is isotropic with direct sun then the position of the sun has to be found with respect to the global co-ordinates (latitude, longitude) and the time of the year. The declination, solar time, solar azimuth and solar altitude are all found to determine the position of the sun (see section 4.3). When a clear sky was used enough rays had to go to the sun to be a correct representation so 10 000 rays were sent out for clear sky while only 1000 rays were used for an overcast sky. The amount of direct radiation falling upon the measuring point is determined by allowing only one ray with zero reflections inside the room to trace back to the sun patch. To create a building structure of a light well, the entire ceiling is made into the exit aperture and the height is increased to the appropriate well index ratio. The glazing over the well is a clear glazed pyramid shaped dome with a tilt of 45°. The room and well building structures are positioned next to each other where upon the light rays that exit the room’s window aperture orientated north enter the well on the southern wall and eventually exit the well through the roof aperture. This combination allows the light level in a room adjoining to an atrium well to be simulated.

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Simulation 1

Fresnel equations for the transmission through the glazing with respect to the incident angle were applied to both the clear glass and the laser cut panels (LCP). The glazing is positioned within the exit aperture. When a ray intersects with an area prescribed as within the exit aperture then the looping ray tracing algorithm stops. The progression of the light through two different glazings is simulated, these being plain 6mm clear glass (n=1.53) and laser cut 6mm clear acrylic (n=1.50). The three dimensional incident angle is calculated and then the Fresnel equation is applied to find the intensity of the transmitted ray. Refraction at each air-glass interface is simulated and the total internal reflection off the cuts within the LCPs is also simulated. The LCP can be inserted into the glazing aperture and positioned on any room or well surface where upon it is tilted to the appropriate angle to redirect and therefore modify the penetration of direct radiation. With the LCP included in the roof aperture the glazing becomes a double glazed unit, whereas, when the LCP is placed in the room aperture it replaces the existing clear glazing. Not all the incident light falling upon the LCP is redirected. The amount of light that is redirected depends upon the depth of the acrylic and the distance between each cut. This is known as the W/D ratio. To allow for this, once the angle of redirection has been determined the fraction deflected is also found and then within the sky distribution equations the luminance has to be found for both the direction deflected and the direction undeflected. With weighting applied to each luminance equation, they are then summed together. The program was set up with a large number of rays from each measuring point so that consistent, reproducible results were obtained. The averaging process of between 1000 and 10000 rays resulted in a very small variation in repeatable run results and therefore a small uncertainty.

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Simulation 1

Sample of a 3D simulation program result [Figure 5.11: Graph of 3D daylight simulation result]

Illuminance (lux)

Illuminance measured under overcast sky in room

mid/floor

1600 1400 1200 1000 800 600 400 200 0 0

2

4

6

8

Position in room (m)

This simulation is of a room in three dimensions with a window half the size of the front wall under overcast skies. The room had dimensions of 3m high, 3m wide and 8m long with diffuse surface reflectivities of 75% for the ceiling, 50% for the walls and 25% for the floors. The horizontal global illuminance was set at 22 Klux. [Table 5.04: Light level within room]

Position in room (m) 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5

Illuminance level (Lux) 774 1351 737 419 320 239 153 138

Daylight Factor (%) 3.5 6.1 3.4 1.9 1.5 1.1 0.7 0.6

The simulation shows a realistic peak in illuminance near the window upon the work plane and a reasonable drop off in light level with respect to depth from the window. The daylight factors relate the horizontal global illuminance to the illuminance inside the room upon the working plane. They indicate that a daylight factor below 1% results in inadequate light levels. This is the case beyond the six metre mark inside this room.

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Simulation 1

5.3.3 Assumptions in the Daylight Simulation Programs

The simulation of any physical process will include some approximations or assumptions. The key is to make sure that they do not make a large difference in the overall result and that they are clearly stated. Simulations can not give absolute values, the best they can do is consistently provide realistic values within an acceptable range. The daylight penetration programs created in this research can not compare to the accuracy of three dimensional rendering daylight simulation programs such as Radiance. It should be pointed out, however, that these programs created within this research can be modified, are very simple to use and can easily handle LCPs. The two dimensional simulation is an assumption in itself because it assumes that the side walls of a room do not contribute significantly to the penetration of the light in a building. The simulation only looks at a cross section along the depth of the room so only the reflections off the ceiling, floor and end walls are included. The two dimensional simulation includes sky luminance values that were taken from field data of the real sky. In this simulation these values combined with two dimensional geometry result in erroneous values for the daylight factor (DF) percentage and so a correction factor is made to the calculation. Other assumptions such as the LCP and sun simplifications are mentioned below in the three dimensional simulation assumption explanation. The three dimensional simulation is a vast improvement upon the two dimensional simulation because it takes into account all the internal boundary surfaces and traces the rays with regard to all possible angle directions. The imperfections in the glazing especially the LCPs are not taken into account. The laser cuts in the panels are not perfect, there is in reality as much as an 8° spreading of light either side of the intended direction when transmitted (Edmonds 1993). The fraction of the incident ray deflected and undeflected by the LCPs is simulated simultaneously. The reflection off the glazing surfaces does not contribute to the light level within the building.

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Simulation 1

The solid angle of the sun is set much larger than in reality. The sun has an angular diameter of 0.5° but in these program it had a 10° diameter, which is the size of the solar aureole. The increase in the apparent diameter allowed a greater number of rays to be traced back to the sun. This resulted in a reasonable sky distribution representation without having to simulate millions of light rays. Skylight comes from every point of the hemispherical sky, but to simulate this using backward ray tracing would be very time consuming and require hundreds of thousands of rays. The assumption is made that the light level can be achieved with fewer rays each set to a higher luminance than in reality. The daylight penetration simulation programs use theoretical sky distribution equations for overcast and direct/isotropic sky conditions for any time of day or year. Perfect sky conditions that correspond to isotropic or overcast sky never actually occur and are only simplified representations. These theoretical distributions are, however, recognised as an acceptable simplification of the real sky. All the building surfaces are presumed to be perfectly diffusing such that the reflection angle from a surface is independent from the incident angle. Each surface has a constant reflectance and all surfaces are smooth but non-specular. This is not how internal building surfaces reflect light. There are also no internal or external obstructions. Obstructions are the most detrimental element upon daylight penetration and can severely reduce the success of any advanced daylight penetration system. The ground outside the room has a constant unobstructed reflectivity of 0.3. This is a significant assumption because there are always obstructions outside buildings and the texture of the ground, in reality, can dramatically change between dirt, concrete, grass, etc. With approximately 50% of the exit rays out of a normal window having a negative elevation angle and therefore hitting the ground, the description of the ground is very important but impossible to simulate accurately.

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Simulation 1

5.4 Daylight Simulation Results

This section looks at the light level in the atrium well and in the adjoining spaces to atrium wells. The results included in this section are mainly from the 3 dimensional simulation program with only some 2 dimensional simulations of daylight levels in adjoining spaces to the atrium well towards the end. The simulations results of side lit rooms with and without laser cut panel tilted glazing can be seen in appendix A4. Following this section is a validation section where simulation results are compared to daylight levels collected in buildings and scale models. These comparisons show a good correlation between the simulations and field data. 5.4.1 Daylight Well Simulations

The horizontal daylight factor at the bottom of a well under overcast sky conditions was also effected by the average reflectivity of the wall surfaces. A simulation was set up with the well index equal to 2.0 and the horizontal global illuminance equal to 24.4 Klux. The wall surface reflectivity was varied from very low (5%) up to very high (90%). [Table 5.05: Relationship between horizontal daylight factor and surface reflectivity in well]

Wall Reflectivity (%) 5 25 50 75 85 90

Light Level (Lux) 2497 2975 4179 6505 8307 9342

Daylight Factor (%) 10 12 17 27 34 38

[Figure 5.12: Graph of relationship between horizontal daylight factor and surface reflectivity in well]

Daylight Factor %

Wall Reflectivity Comparison for a DF% plain atrium WI=2

Poly. (DF%)

50 40 30 20 10 0

2

y = 43.957x - 10.451x + 11.15 2 R = 0.9943

0

0.5 Wall Reflectivity

1

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Simulation 1

A high surface reflectivity such as 75% produce illuminance levels more than twice as high at the bottom of the well compared to low surface reflectivities such as 25%. Light coloured surfaces reflect more light, which aids in penetration and increases the illuminance within the well area. The lower reflectivities such as 25% and 5% produce inadequate light levels and additional lighting would be required. Two dimensional simulation data for a well was also produced. A comparison was made between clear and LCP glazing at a tilt of 45° under simulated CIE overcast sky conditions. The horizontal global illuminance was set at 35 Klux. The illuminance was measured at the bottom of the well. [Table 5.06: Comparison between DF and well index with normal and LCP glazing in 2D well]

Width

Height

80 80 80 80 80 80 80 80 80

300 280 240 200 160 120 80 40 8

WI Plain glaze (light level) 3.8 135 3.5 150 3.0 180 2.5 220 2.0 267 1.5 350 1.0 463 0.5 772 0.1 1042

Plain glaze DF% 3.9 4.3 5.1 6.3 7.6 10.0 13.2 22.1 30.0

LCP glaze (light level) 220 250 300 350 430 550 720 1060 1632

LCP glaze DF% 6.3 7.2 8.5 10.0 12.3 15.7 20.6 30.3 46.6

[Figure 5.13: Graph of comparison between DF and WI with normal and LCP glazing in 2D well]

Comparision between Well Index and Daylight Factor Daylight Factor %

50 40 30

LCP glaze Plain glaze

20 10 0 0

1

2

3

4

Well Index

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Simulation 1

The light level at the bottom of a very shallow well should be approaching a level similar to the horizontal global illuminance. This is not the case in the two dimensional simulation. It also shows that the light level in a LCP glazed well is higher which it is not because the brighter vertical light from a CIE overcast sky is rejected out of the system. Another two dimensional simulation of a well was produced for a comparison between glazings and geometrical ratios for various solar altitudes. The simulated clear sky had a HGI set at 70 Klux and an indirect luminance of 50 lux. [Table 5.07: Comparison for both glazing and two well indices for various solar altitudes in 2D well]

Solar Altitude (degrees) 10 20 30 40 50 60 70 80

LCP glazing WI=3.75 4923 2513 993 850 1163 1378 2076 2105

LCP glazing WI=2.0 6750 5933 2258 2230 3200 3052 4400 2755

Plain glazing WI=3.75 19 23 50 150 200 215 550 2260

Plain glazing WI=2.0 95 105 112 400 577 1850 2544 5664

[Figure 5.14: Graph of light level in 2D well for both glazing at various solar altitudes] LCP glazing WI=3.75

Light level in atrium well with varying solar altitude

LCP glazing WI=2.0 Plain glazing WI=3.75 Plain glazing WI=2.0

Light level

8000 6000 4000 2000 0 0

20

40

60

80

Solar Altitude

The only clear result out of this simulation was that the LCPs improve the light level within the well from low elevation sun light and that the light level increased in the clear glazed well as the solar elevation increased. While this result seems correct the levels are way off realistic values.

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Simulation 1

5.4.2 Daylight Simulation of Room Adjoining Atrium Well

The light levels in an adjoining room at the bottom of an atrium were obtained from three dimensional simulations with different surface reflectivities under overcast skies. The simulation set up was similar to the previously described three dimensional simulations. The adjoining room window was half the size of the wall and the well index was set at 3.75. Standard reflectivities shown in table 4.02. [Table 5.08: Relationship between Light level and surface reflectivity in an adjoining room]

Position

High Reflect. (Lux) 484 379 284 215 190 161 144

10 20 30 40 50 60 70

Standard Reflect. (Lux) 92 83 67 48 34 19 18

Low Reflect (Lux) 44 16 24 2 3 6 5

[Figure 5.15: Graph of light level in an adjoining room to well with varying surface reflectivity]

standard high low

Illuminance (lux)

Light level in adjoining room with differing reflectivity 500 450 400 350 300 250 200 150 100 50 0 0

20

40

60

Position in room (m)

80

The use of high surface reflectivities produces dramatically higher illuminances compared to low surface reflectivities. Light coloured surfaces reflect more light, which helps penetration and increases the illuminance within the area.

82


Simulation 1

The standard and low reflectivity options had diffuse floor reflectivities of 25% and 5% respectively which is comparable to values corresponding to carpeted floors. These options produced inadequate light levels and additional lighting would be required to meet minimum light standards. The light levels in an adjoining room at the bottom of an atrium were also obtained from three dimensional simulations with different geometrical ratios under overcast skies. [Table 5.09: Relationship between light level and well index within 3D sim of room adjoining well]

Position

WI=1

WI=1.5

WI=2

WI=3

WI=3.75

lux

lux

lux

lux

lux

10

1518

922

829

256

92

20

1375

681

320

160

83

30

900

328

195

110

67

40

375

245

121

95

48

50

280

151

105

57

34

60

204

141

77

29

19

70

150

126

66

23

18

[Figure 5.16: Graph of relationship between light level and well index in room adjoining well]

Light level in adjoining room with differing Well Index Illuminance (lux)

1500

WI=3 WI=2 WI=1 WI=3.75 WI=1.5

1000

500

0 0

20

40 60 Position in room (m)

80

83


Simulation 1

The results show that as the well index decreases the light level increases in the adjoining room. This is because at the bottom of a shallow well there is a greater angular view of the sky than at the bottom of a deep well. The amount of surface area is also smaller for shallow wells. The drop off in light level from the front to the back of the room for WI=1 appears to be the most dramatic. However, the ratio of illuminance from the front to the back of the adjoining room for each well index is approximately 10 times. For wells with indexes greater than 2.0 under overcast skies with clear glazing the light level in the bottom level adjoining room was found to be below acceptable levels. Therefore, artificial lighting or advanced natural lighting design would be required in these areas to meet the minimum standard lighting levels. The light levels in an adjoining room at the bottom of an atrium were obtained from two dimensional simulations with different glazing options under overcast skies. The horizontal global illuminance was set at 35 Klux for this simulation. [Table 5.10: Glazing comparison within 2D room adjoining well under overcast sky]

Position 1 2 3 4 5 6 7 8 9

LCP+LCP glaze 69 62 66 67 55 43 39 28 24

LCP+Plain glaze 115 47 35 30 19 26 19 17 17

Plain+LCP glaze 86 83 103 105 101 86 70 70 62

Plain Glaze 95 55 38 30 25 14 17 15 13

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Simulation 1

[Figure 5.17: Graph of glazing comparison within 2D room adjoining well under overcast sky]

Illuminance level

Level 1 adjoining room glazing comparision with 2D simulation 140 120 100 80 60 40 20 0

LCP+LCP LCP+plain Plain+LCP Plain

0

2

4 6 8 Position in room

10

The best glazing option was achieved when the plain atrium glazing was combined with the tilted adjoining room LCP glazing. The two glazing combinations, which had the tilted adjoining room LCP glazing, both produced illuminance levels that did not decay smoothly with respect position in the room. The main differences in the results obtained between the 2D and 3D simulations are explained in sections 5.3.1 and 5.3.2 in the sample simulation results. 5.5 Simulation Validation with collected data

The computer simulation results are compared to data collected from field experiments to show the validity of the programs and their results. 5.5.1 Sky Distribution Comparison

A clear blue sky theoretical distribution was included in the two dimensional daylight simulation program this was compared to the field data collected above M block at QUT. The data is presented as a relative ratio with respect to the zenith luminance instead of absolute luminance values.

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Simulation 1

[Table 5.11: Sky luminance data comparison across the sky at 10° increments with ratio to zenith]

Angle (deg) 10 20 30 40 50 60 70 80 90

Computer Zenith (%) 1.76 1.08 0.75 0.60 0.56 0.58 0.64 0.77 1.00

Field Zenith (%) 0.74 0.59 0.57 0.42 0.44 0.46 0.51 0.55 1.00

Angle (deg) 100 110 120 130 140 150 160 170

Computer Zenith (%) 1.40 2.11 3.40 5.88 4.30 3.45 3.06 3.07

Field Zenith (%) 1.38 2.97 3.40 10.60 8.51 3.19 3.19 0.85

[Figure 5.18: Graph of sky distribution comparison]

Sky Ratio (% )

Comparison between field data and computer simulation sky ratio distribution

Field Zenith Ratio Computer Zenith Ratio

10 9 8 7 6 5 4 3 2 1 0 0

20

40

60

80

100

120

140

160

180

Angle (deg)

Simulated luminance levels across a clear sky compare reasonably well to the collected field data except around the sun position. The theoretical distribution algorithm does not include a direct sun and therefore it severely underestimates the luminance values compared to the direct solar measurements. The simulated results also show a greater rise in luminance at the horizon then the measured data. This is known as the gradation of the sky.

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Simulation 1

5.5.2 Room Illuminance Comparison

Illuminance data was collected within model rooms of various sizes and compared to the computer simulated results, which are detailed in Appendix A4. A limited amount of data was collected due to inclement weather conditions over the monitoring period of this research. The main validation of the computer simulation of a room was the comparison to the measured illuminances within the test site room. Two sets of measured field data from the test site room were collected and compared to simulated results. The simulation programs included the two and three dimensional daylight programs produced within this research along with two professional programs Lighting (Moore & Bell, 1999) and Radiance. The Radiance simulations were preformed within the ADELINE version 2.0 environment. ADELINE is an acronym which stands for Advanced Daylighting and Electric Lighting Integrated New Environment. Radiance is a program for the analysis and visualisation of lighting in and around architectural spaces. It uses a combined approach of backward ray tracing and radiosity and from the entered parameters about the scene geometry, materials, luminaries, and sky conditions it can calculate spectral radiance or irradiance and display these results as colour images, numerical values or contour plots. Greenup (1999) performed Radiance simulations of the daylighting performance within buildings. The Lighting program was developed at QUT by Ian Moore to evaluate the daylighting level within buildings from the selection of window glazing (Moore & Bell 1999). The program uses a radiosity calculation method to find the contribution of illumination upon each patch within the room. It also uses a ray tracing method to find the direct illuminance through the window. [Figure 5.19: Diagram of simulated test site building]

3m

3m 8m

87


Simulation 1

The building had dimensions of 8m x 3m x 3m and a small window in the North facing window of 1.2 metres square. The test site room was simulated under two different sky conditions, which corresponded to the measured field data. These included the room under overcast sky conditions, with a horizontal global illuminance (HGI) of 20 Klux and the room under clear sky conditions with a HGI of 74 Klux. The illuminance was measured upon a working plane with a height of 0.8m. [Figure 5.20: Graph of light level programs comparison under overcast skies]

Comparison between different computer programs and measurements in test site under overcast skies on work plane

Illuminance (lux)

2500 2000

Measured Radiance Radiosity 2D raytrace 3D raytrace

1500 1000 500 0 0

2

4

6

8

Distance from window (m) [Figure 5.21: Graph of light level programs comparison under clear skies]

Illuminance (lux)

Comparison between different computer programs and measurements in test site under clear skies on work plane 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0

2

4

6

Measured Radiance Radiosity 2D raytrace 3D raytrace

8

Distance from window (m)

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Simulation 1

All the simulated results compare reasonably well with the measured data. The least accurate simulated results were produced by the 2D ray trace program. This program produced almost a level illuminance level along the depth of the room for the overcast sky conditions. Under clear sky conditions, it overestimated the illuminance level. The 3D ray trace program simulated the illuminance levels fairly accurately but under estimated the illuminance close to the window under both sky conditions. The Radiance calculations were not a lot more accurate than the 3D ray trace simulation. However, under overcast sky conditions it underestimated the illuminance while under clear sky conditions it overestimated the illuminance levels. The most accurate simulation was made using the radiosity based Lighting program, which compared almost perfectly with the measured data.

5.5.3 Well Illuminance Comparison

Computer simulations allow for quick comparisons between systems where one variable is changed to see how it affects illuminance levels. Presented below are the comparisons when the surface reflectivity and well index were changed. The reflectivity of the internal surfaces was varied to see how they effect the illuminance level. The undergraduate scale model results were compared to those obtained from the three dimensional simulation. The simulation was of a well with index of 2.0 under an artificial overcast sky. The reflectivities varied all the way across the possible range from low to standard and high values. [Table 5.12: Surface reflectivity comparison]

Wall Reflectivity %

Model DF%

Simulation DF%

5

12

10

50

19

17

75

32

27

The daylight factors at the bottom of the well can be compared to the simulation with reasonable accuracy. Although the simulation does tend to underestimate the DF% for each reflectivity.

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Simulation 1

The well index is also a very significant design factor for any atrium so its effect upon illuminance is well documented. A comparison is shown here between the three dimensional computer simulated results and those presented by Aizlewood using a analytical geometry based algorithm (Aizlewood et.al. 1996). [Table 5.13: Well index simulation versus algorithm comparison]

Well Index

0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 3.75

3D Ray trace Simulation DF% 99 74 42 26 17 11 9 7 6

Aizlewood Algorithm DF% 99.6 74.3 41.1 25.6 17.9 13.6 10.9 9.0 8.3

[Figure 5.22: Graph of well index daylight penetration comparison]

The results correspond very well which gives considerable weight to the validity of the ray tracing algorithm that these results are based upon.

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Simulation 1

Neither algorithm exceeds the 100% daylight factor boundary as the well index approaches zero. The DF% also continues towards zero as the WI increases instead of levelling off to infinity. This is an improvement upon other mentioned algorithms discussed in the literature review. 5.5.4 Room adjoining Well Illuminance Comparison [Figure 5.23: Graph of comparison between simulation and scale model results in adjoining room] Model Clear glazed

Comparison between field and simulation results of light level within adjoining room of atrium

Model LCP(x2) glazed Sim Clear glazed Sim LCP(x2) glazed

Illuminance (lux)

140 120 100 80 60 40 20 0 0

2

4

6

8

10

12

14

Position in room (cm)

The three dimensional atrium simulation was compared to the undergraduate scale model data under overcast sky with different glazing options. The small scale model under an artificial overcast sky showed that the clear glazed roof and adjoining room option produced higher illuminance levels then the LCP glazed roof and adjoining room option. The light level in the adjoining rooms still produced the expected decay with respect to the distance from the window and all options produce light levels below recommended minimum standards. The three dimensional simulation was set up to replicate the scale model and artificial sky with a well index of 2.0 and a horizontal global illuminance of 3 Klux. The clear glazed roof and adjoining room option produced higher illuminance levels then the LCP glazed roof and adjoining room option.

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Simulation 1

The light level in the adjoining rooms still produced the expected decay with respect to the distance from the window and all options produce light levels below recommended minimum standards. The three dimensional simulation was found to have a very good correlation between the simulation and the scale model though the simulation generally overestimated the light levels. Overall, the three dimensional daylight penetration simulation has proven to be reasonably accurate with respect to the collected experimental data. The program was compared to full scale field data, scale model experimental data and previously established theoretical models. It has shown to be adequate in producing realistic illuminance levels under a range of building and environmental conditions.

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Simulation 2

Chapter 6: THERMAL SIMULATION 6.1 Introduction

The thermal computer simulation program was created as part of this research to predict the thermal performance within the model atrium wells. The modifications to the building parameters that can be varied within the program include the glazing, the geometrical ratios and the surface reflectivities of the well. The thermal simulation was initially produced to investigate the radiative heat gain and loss. This was designed and developed as a learning tool. Later the simulation was improved to include the convection and conduction losses, which made the program more realistic. The thermal simulation program includes two different algorithms for the different glazing types and two different sources of input data. The program Therm4 and Therm5 simulated two atrium wells to find the average zonal temperature in each. Each well had different glazing. The external environmental temperatures could be entered in from collected field and test reference year (TRY) data. The program used geometrical fraction transmitted to find the heat transfer input and only investigated the radiation heat transfer output. The program Therm59.m simulated two atrium wells to find the average zonal temperature in each. Each well had different glazing. The external environmental temperatures could be entered in from collected field and TRY data. The program used experimental relative transmittance equation to find the heat transfer input and investigated the convection, conduction and radiation heat transfer process to find the thermal output. The simulations should show that with the inclusion of the modified angular selective glazing upon the atrium well that the temperature would be more consistent across the day and lower in the middle of the day when the solar altitude was high compared to normal clear glazing. It should be able to predict the temperature within the atrium well at any hour of the day during the year. The analysis of the simulation results will be discussed in Chapter 8.

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Simulation 2

The thermal simulation program consists of a series of algorithms that simulate the natural processes involved in the heat transfer into buildings. The program was designed to find the thermal transfer through the glazing into a small, insulated space, which is subject to large amounts of direct radiation. It predicts the internal temperature within an atrium space across the course of a clear sky day for any day of the year. This program specifically simulates an isotropic sky with sun and an atrium well with horizontal apertures with LCP or clear pyramid shaped glazing. [Figure 6.01: Thermal Simulation of test site scale model atrium wells] Irradiance Meter

Clear Glazed Skylight

LCP Skylight

Solar Panel

Foam Atrium Wells

TEST SITE

Due to the simplicity of the experimental scale models, simple programs were written to simulate the thermal performance of these models. Commercial thermal simulation programs include excessively large material libraries but still struggle to handle angular selective glazing. These programs however, written in Matlab are quick, easy and give a general guide to the thermal performance with respect to the two included glazing options. These programs differ mainly from the daylighting program methodology described in Chapter 5 by the fact that they do not trace the path of each ray. Instead, they define a source and radiative zones. These programs show how the internal temperature is modified due to the installation of angular selective glazing and can compare these results to collected field data.

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Simulation 2

6.2 Theory

The thermal simulation programs consist of a series of algorithms that simulate the sun, building geometry, horizontal skylight aperture, surfaces within the building and the progression of radiant power through this environment. The equations are mostly based upon previously published material and explained in detail below. They can be viewed in context in the program code appendices. The thermal computer simulation equates the internal temperature of the atrium space when the heat transfer gain and losses are in equilibrium. The heat gain entering the model atrium wells in this investigation under clear sky conditions was assumed to be mainly by radiation from the direct beam component of the sun. The program finds one temperature for the whole volume of the well. This is known as a single temperature per zone model. 6.2.1 Old thermal simulation theory

If all the energy that entered the enclosure was absorbed and reradiated via adiabatic surfaces then all the energy would contribute to the increase in temperature. The power loss (PL1) from the system via radiation would be dependent upon the temperature difference between the internal (T) and external temperatures (To) (Eastop & Croft 1995). PL1 = e. As.σ. (T4-To4)

Eq. 6.01

The power gain (Pin) through the aperture from the incident radiation is (Serway 1993): Pin = I. Ap. sin (alt)

Eq. 6.02

If the power input is in equilibrium with the power loss via radiation through the skylight aperture. Then these two equations can be equated PL1 = Pin e. As.σ. (T4-To4) = I. Ap. sin (alt) Then rearranged to find the internal temperature: T=

4

P + eσ A T in

4 o

Eq. 6.03

s

Equation 6.03 was adjusted to determine the fraction of incident radiant power input through a normal pyramid skylight and a LCP pyramid skylight.

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Simulation 2

For a plain glazed skylight if the solar altitude is greater than the tilt of the glazing then all the incident direct beam sun light will be enter through the aperture. However, if the solar altitude is lower than the tilt then some of the incident light upon the glazing will miss the aperture and hit the roof surface (figure 6.02). For this situation a fraction of the total incident light that is accepted through the aperture (fa) is found by simple geometry and included in the power input formula. The transmission through a material is dependent upon the angle of incidence and the type of material. See transmission equation in appendix A.4. The projection of the top point of the pyramid forms a triangle in plan view. The total area of this triangle (At) is found and the area that lies within the square aperture (Aq) is found.

fa = Aq / At

Eq. 6.04

The power input through 2 sides of the pyramid for solar altitudes below the angle of the tilted glazing is found. P=2.I. Aq. sin (alt). fa . τ

Eq. 6.05

The same situation with the inclusion of laser cut panels means that upon the intersection with the glazing the deflected angle (length L*) and the undeflected angle (length L) is used to find the fraction of the total incident light that enters the aperture (Edmonds et al. 1996). P=2.I.A.sin (alt).[fd.fad + (1-fd).faud].τm

Eq. 6.06

[Figure 6.02: Geometrical representation of fraction of light accepted through LCP skylight] E

55

55

E

L* L

B

C L* P P*

A

D

L

96


Simulation 2

When the solar altitude is greater than the tilt of the glazing then the fraction accepted (fa) is equal to one. The total radiant power through four sides of clear pyramid is approximated in the thermal simulation as: P=(2.I. At. sin (alt). fa . τ1) + (2.I. At. sin (90+alt). fa . τ2) + Idif . Ap. τm

Eq. 6.07

Radiant power through 4 sides of LCP skylight: P=[2.I.At.sin (alt).[fd.fad+(1-fd).faud].τ1] + [2.I.At.sin(alt).[fd.fad+(1-fd).faud].τ2] + Idif.Ap.τm Eq. 6.08

Where: τ1 = transmission through material on closest sides of pyramid τ2 = transmission through other 2 far sides of pyramid τr = transmission through LCP τm = combination of transmission through LCP + clear pyramid In practice, some of the radiant energy intersects with the laser cut panel at an oblique angle. The theory then gets a lot more complicated. The relative transmission difference due to the diagonal intersection is only slightly different at incident angles between 20 and 50 degrees (Edmonds et al. 1996). See figure 6.03. As mentioned, not all the incident light that hits the tilted clear glazing enters the horizontal aperture. This situation is complicated further with the inclusion of LCPs because some of the incident light that falls upon the LCPs is redirected. The LCPs are positioned under the existing clear acrylic glazed pyramid in its own pyramid shape. This results in the glazing acting like a double glazed unit. Equation 6.08 evaluates the transmission through four sides of an angular selective pyramid and a clear glazed pyramid to find the power input into the atrium well. The amount of light that is redirected depends upon the angle of incidence, depth of the acrylic and the distance between each cut. This is known as the W/D ratio. To allow for this, once the angle of redirection has been determined, the fraction deflected and undeflected is determined. This has to be combined with the fact that not all the incident radiation that hits the skylight enters the aperture, so the fraction accepted deflected (fad), unaccepted deflected (1-fad), accepted undeflected (faud) and unaccepted undeflected (1-faud) all have to be found.

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Simulation 2

6.2.2 New thermal simulation theory

The new thermal simulation included the heat transfer losses due to convection, conduction and radiation. It also evaluates the thermal performance of both glazed wells and used a different method to equate the angular dependent transmission through the LCPs. This method used to evaluate the radiant power through an angular selective skylight was based on the relative transmission data through a 45° tilted angular selective skylight compared to clear glazed horizontal aperture presented in (Edmonds et al. 1996). A polynomial equation to the sixth order was fitted to the data in figure 6.03 and used to find the relative transmission (RT). RT = 3.2832*10-10 alt6 – 1.0413*10-7 alt5 + 1.3118*10-5 alt4 – 8*10-4 alt3 + 0.0281 alt2 -0.4804 alt + 4.0214 Eq. 6.09

The transmission through the LCP glazed skylight is relative to the clear glazed skylight. [Figure 6.03: Graph of transmission through LCP pyramid shaped skylight (normal and diagonal)]

Transmission through LCP model skylight

Transmission in plane of normal incidence Transmission in plane of diagonal incidence

2.5

Transm ission %

2 1.5 1 0.5 0 0

10

20

30

40

50

60

70

80

90

Angle of Incidence (deg)

The transmission is similar at both normal and diagonal incidence to the baseline so the normal incidence is assumed for all orientations.

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Simulation 2

The new simulation constructed finds the heat loss via conduction, convection and radiation and equates it to the heat gain via radiation. Pin = PL1 + PL2 + PL3

Eq. 6.10

An incremented test internal temperature is substituted into the equation and increased until the heat loss and gain reaches equilibrium. At this equilibrium point, the tested temperature is the predicted internal temperature. 0 = Pin – (PL1 + PL2 + PL3)

Eq. 6.11

[Figure 6.04 Diagram of atrium well with basic heat flow directions] R a d ia tio n L o ss R a d ia n t H e a t G a in C o n v e c tio n L o ss

H o tte r A ir

C o n d u c tio n / C o n v e c tio n L o ss

C o ld e r A ir

The heat transfer loss via radiation is equated for the glazed aperture and is equal to Power Loss1 = Qrad = e. As. σ. (Tg4-To4)

Eq. 6.12

Where σ is the Stefan-Boltzmann thermal conductivity constant 5.67 x 10-8 W/m2.K4 The emissivity of glass, e, is equal to 0.85. The surface area of the atrium dome aperture As is found by finding the hypotenuse of

0 .5 + 0 .5 2

one side of the pyramid dome, which is

The area of one triangular side is found At = number of sides. As = 1.4 m =

2

2

.

height × base which is multiplied by the 2

0 .5 + 0 .5 2

2

2

×1

×4

Eq. 6.13

99


Simulation 2

The heat transfer via conduction is equated for all the surface area of the atrium well and is equal to: Power Loss2 = Qcond = k. Aa. (T- To) / L

Eq. 6.14

Where the thermal conductivity of the foam atrium walls (k) = 0.033 W/m.K The surface area of the foam walls Aa = 0.8x3x4 = 9.6 m2 The depth of the foam walls L = 0.05 m The heat transfer loss via convection is equated for the glazed aperture and is equal to: Power Loss3 = Qconv = hc. As. (Tg - To)

Eq. 6.15

The loss due to the convection is complicated because it depends upon the properties of the fluid and the interaction with the boundary surface. The surface area of the atrium dome aperture As is the same as equation 6.13. The basic heat transfer model that this simulation is based upon is diagrammed in figure 6.04. It includes heat gain via radiation only and heat loss via conduction, radiation and convection. The convection loss through the glazing is considered to be a loss of heat through an inclined plane via laminar flowing fluid. The temperature difference in the convection and radiation equations is found from the difference between the glazing temperature (Tg) and the external temperature (To). The glazing temperature in the clear glazed normal atrium is taken as being the same as the internal temperature (Tin).

Tg = Tin

However, the glazing temperature in the LCP glazed atrium is taken as Tg =

Tin + To 2

Therefore, Tg is half way between the internal and external temperatures because the LCP glazing actually consisted of a clear glazed shell and laser cut panels. The heat transfer coefficient due to convection, hc, is expressed non-dimensionally as the Nusselt number, Nu = hc.x/k, where x is the length dimension and k is the thermal conductivity of the fluid. Rearranged,

h

c

=

Nu × k x

Eq. 6.16

The Nusselt number is dependent upon the orientation of the surface and the type of flow. The Nusselt number can be found for one of the following situations. 100


Simulation 2

Horizontal surface turbulent flow = Nu = 0.14*(Ray)1/3

Eq. 6.17

Horizontal surface laminar flow = Nu = 0.54*(Ray)1/4

Eq. 6.18

Inclined surface laminar flow = Nu = 0.56*(Ray*cosθ)1/4

Eq. 6.19

The Rayleigh number (Ray), is the product of the Grashof (Gr) number and the Prandtl (Pr) number. Grashof number = Gr = β.g.ρ2.∆T.x3 / µ2

Eq. 6.20

Where β is the coefficient of cubical expansion of the fluid and is equal to the inverse of the temperature (1/T). The other factors include g, which is the acceleration due to gravity, ∆T is the temperature difference, ρ is the density of the fluid and µ is the viscosity of the fluid and finally x is the depth of the fluid. Prandtl number = Pr = cp. µ / k

Eq. 6.21

Where cp is the specific heat of the fluid and µ is the viscosity of the fluid. [Table 6.01: Simplified convection coefficient (hc) equations for air (Holman 1997)]

Surface Vertical plane Inclined plane Horizontal plane

Laminar Flow 1.42*(∆T)1/4 1.37*(∆T)1/4 1.32*(∆T)1/4

Turbulent Flow 1.31*(∆T)1/3

1.52*(∆T)1/3

In the simulation, the heat loss coefficient (hc) for an inclined plane with laminar flow was used.

101


Simulation 2

6.3 Procedure [Figure 6.05: Pseudo code diagram of thermal program]

Input measured outdoor temperatures

Time across day array

Enter date, location and building parameter details

Flow chart of Thermal Simulation Program

Determine Direct Normal Irradiance

Find solar position

Find Transmission Through LCP Glazing

Find Transmission Through Clear Glazing

Determine Heat gain into clear glazed building

Determine Heat gain into LCP glazed building Select Test Predicted building Temperature (initial temperature = external temperature)

Find the glass temperature and temperature differences Find the heat transfer loses due to these temperature differences

Conduction Heat Loss

Convection Heat Loss

Radiation Heat Loss

Calculate the net heat transfer Gains - Losses

Is Yes

Thermal Gain > Thermal Loss ?

No

Yes

Final building temperature at which system is in equilibrium

Next hour

No

Plot Predicted Temperature Results and end

The program initially lists several hourly averaged field and reference data arrays of temperature stated for specific days at the location of the experiment. The external temperature (To) is required either from the field data recorded or from the TRY 1986 database (see Appendix A6). 102


Simulation 2

The atrium well measured field data temperatures are included as a comparison to see if the predicted temperature lies between the upper and lower temperature boundaries. An hour array across the day from 700 hours to 1700 hours is initiated for which all other variables will be calculated. The simulation finds the position of the sun (azimuth and altitude) with respect to the declination, latitude, Julian date and time of day (See section 4.3). The zenith angle of the sun, which is the complement of the altitude, is also found. The optical air mass equation 4.07 is used to determine the direct normal irradiance (4.06) incident upon the glazing aperture. The theoretical irradiance values are used instead of the field data to eliminate inaccurate values recorded at solar altitudes below 10°. The simulation is only valid for clear sky days, which are simulated using an isotropic/direct sky distribution. Two different methods were used to determine the transmission through the glazing. The old simulation equated the fraction transmitted through the glazing based upon the Fresnel transmission equation 4.28 and the fraction of power transmitted equations (6.04 - 6.08) through either the clear glazed or both the LCP and clear glazed pyramid. The other method used to determine the transmission through the atrium well glazing was to use a polynomial fit to the experimental relative transmittance through a scale model pyramid data instead of using the trigonometric geometry of the pyramid shaped glazing (shown above). Two data sets of relative transmittance were investigated for incident radiation normal to the pyramid baseline and diagonal to the pyramid baseline. The polynomial fits to this data are shown in equation 6.09 Edmonds (1996). The power of the incident radiation through the aperture is based upon the standard formula in equation 6.02. This equation takes into account the incident irradiance, the surface area, angle of incidence from the radiation source and the transmission through.

103


Simulation 2

The original temperature prediction program established an equilibrium between the reradiated energy and the input energy. The temperature within the atrium space was found by rearranging the equation 6.03. The input data, equations and power equilibrium enables a theoretical internal temperature to be equated hourly across the course of a clear sky day and compared to the field temperatures recorded in the model. The new temperature prediction program uses a different method. Once the power input into the atrium wells had been determined then the heat transfer losses were calculated. These were based upon the amount of surface area and the temperature differences between one side of the surface and the other side of the surface. The heat losses include radiation (6.12), conduction (6.14) and convection (6.15) but the only heat gain into the system is by direct radiation. The losses are calculated for both atrium wells. The heat losses are summed (6.10) and compared to the heat gains using an iteration style method. The initial temperature is set at the external temperature, which is assumed to be lower. The iteration is completed and the internal temperature is found for the situation when the heat losses and gains are equal (6.11). The input data, equations and power equilibrium enables a theoretical internal temperature to be equated hourly across the course of a clear sky day and compared to the field temperatures recorded in the model.

104


Simulation 2

Assumptions in the Thermal Simulation Program

The thermal simulation program is a very basic set of algorithms that is reasonably accurate even with the following assumptions. The program only equates one temperature per zone and can not take into account the obvious thermal stratification in the model atrium wells. The analysis does look at the heat transfer losses due to conduction, convection and radiation. However, it only includes heat transfer gains via direct solar radiation. The input radiation is assumed to be in the plane of normal incidence to base line of the pyramid shaped skylight aperture and that all the radiation goes to increasing the internal temperature of the well. Theoretical direct normal incident irradiance was calculated instead of using the measured field data to determine the power input into the enclosure because the irradiance field data was not collected over a whole year and the data was inaccurate for solar elevations below 10° (Middleton 1994). A comparison between the theoretical and measured values will be shown in Chapter 7. All the surfaces within the atrium wells are assumed to be adiabatic and the re-emitted radiation is assumed to only radiate out of the input aperture. The transmittance through the LCPs is based upon equation 6.09, which is a polynomial fit to theoretically generated relative transmission plots (Edmonds 1996). The plots are based upon equations 6.06 to 6.08 and figure 6.02, which are also explained within Edmonds (1996). The temperature of the double glazed LCP skylight material is assumed to be equal to half way between the internal atrium well temperature and external ambient temperature. The temperature of the clear glazed skylight material, however, is assumed to be equal to the internal atrium well temperature. Other assumptions and simplifications in the thermal simulation program such as the sky distribution are mentioned in Chapter 5 in the daylight simulation assumption section. 105


Simulation 2

6.4 Thermal Simulation Validation

On clear sky days, the simulation shows the hourly predicted temperature in both clear and LCP glazed test site atria. This would represent an average temperature within the atrium spaces. A comparison to the measured field data can be found below. [Table 6.02: Comparison between simulated and field temperatures for clear and LCP glazed atrium]

Time (hr) 7 8 9 10 11 12 1 2 3 4 5

Simulated Clear Atrium 22/7 (°C) 12.0 30.0 37.5 43.5 47.5 48.5 47.0 42.5 36.0 28.5 12.0

Field Clear Atrium 22/7 (°C) 11.8 29.3 40.6 46.1 49.2 51.1 50.2 46.8 38.5 24.3 16.0

Simulated LCP Atrium 22/7 (°C) 26.5 33.5 40.5 47.0 49.0 49.5 49.0 46.0 39.0 32.5 12.0

Field LCP Atrium 22/7 (°C) 13.7 25.4 39.0 47.8 49.7 50.8 50.2 47.2 34.6 28.3 20.0

[Figure 6.06: Graph of field and simulated temperatures in plain glazed atrium on July 22nd]

Temperature comparison between simulation and field data for 22nd July 1999

norm sim T4

Temperature (degC)

55 50 45 40 35 30 25 20 15 10 7

9

11Time (hr)13

15

17

106


Simulation 2

[Figure 6.07: Graph of field and simulated temperatures in LCP glazed atrium on July 22nd]

Temperature comparison between simulation and field data for 22nd July 1999

LCP sim T7

55 50 Tem perature (degC)

45 40 35 30 25 20 15 10 7

9

11

Tim e (hr)

13

15

17

The simulation under estimates the temperature in the middle of the day in the winter month of July in the clear glazed well. A maximum difference of 4.3 °C occurred at 2pm. The simulation overestimated the temperature in the morning and afternoon in the winter month of July in the LCP glazed well. A maximum difference of 12.8 °C occurred at 7am. The comparison throughout the middle of the day, however, had an average deviation of 1.0 °C. [Table 6.03: Comparison between simulated and field temperatures for clear glazing on two clear days]

Time (hr) 7 8 9 10 11 12 1 2 3 4 5





107


Simulation 2

[Table 6.04: Comparison between simulated and field temperatures for LCP glazing on two clear days]

Time (hr) 7 8 9 10 11 12 1 2 3 4 5





The simulation program produces a predicted temperature to a half of a degree Celsius accuracy. The field data supplies the averaged atrium temperature to a tenth of a degree Celsius accuracy. [Figure 6.08: Graph of field and simulated temperatures in plain glazed atrium on September 15th]

Thermal Simulation Comparison to field data on 15/9/99

Norm Sim Meas T4

Tem perature (degC)

70 60 50 40 30 20 7

9

11

13

15

17

Tim e (hr)

The maximum difference occurred at 3pm with the simulation overestimating by 9°C. A minimum difference of 0.7°C occurred at 10am.

108


Simulation 2

[Figure 6.09: Graph of field and simulated temperatures in plain glazed atrium on September 25th]

Temperature (degC)

Thermal Simulation Comparison to field data on 25/9/99 70

Norm Sim Meas T4

60 50 40 30 20 7

9

11 13 Time (hr)

15

17

The maximum difference occurred at 3pm with the simulation overestimating by 9°C. A minimum difference of 0.4°C occurred at 10am. [Figure 6.10: Graph of LCP atrium comparison between field and simulated average temperature]


LCP Sim Meas T7

Tem perature (degC)

60 50 40 30 20 7

9

11

13

15

17

Tim e (hr)

The maximum difference occurred at 5pm with the simulation overestimating by 8°C. A minimum difference of 0.7°C occurred at 10am.

109


Simulation 2

[Figure 6.11: Graph of LCP atrium comparison between field and simulated average temperature]


LCP Sim Meas T7

Tem perature (degC)

60 50 40 30 20 7

9

11

13

15

17

Tim e (hr)

The maximum difference occurred at 5pm with the simulation overestimating by 9.5°C. A minimum difference of 0.1°C occurred at 9am. In spring, the simulation in both these wells generally overestimates the internal temperature compared to the field data. The measured data in the LCP model atrium shows a dip in the middle of the day on these two September days due to the some of the incident irradiance being deflected out of the atrium well and therefore lowering the internal temperature. The simulated data does show a corresponding flattening in the temperature distribution across the middle of the day. This is clearly a lot flatter then in the clear glazed atrium well. The correlation between the data sets is quite good across the day except for the early morning and afternoon. Overall, the comparison between the field and simulated data shows a good correlation. This enables the prediction of temperatures in both wells to be made for times outside the monitoring period. This data is presented in Chapter 8.

110


Simulation 2

6.5 Thermal Simulation Comparison

Yvonne Wolring was a visiting researcher who worked closely with the project during the period from July 1999 to September 1999. She simulated the thermal performance of the test site atria & room using the program CAPSOL Version 3.0 (Wolring 1999, Physibel 1999). The results and accuracy of this program could be compared to that obtained by the thermal simulation written within this research. CAPSOL is a computer program that calculates the multi-zone transient heat transfer, and was developed by Physibel Company in Belgium. The program is based upon the physical laws of heat and mass transfer in relation to the behaviour of buildings. It is used to calculate the temperature within each building zone due to the input climate data. CAPSOL uses the Crank Nicolson finite difference method and equivalent electrical circuit modelling with a network of thermal resistors and capacitors (RC network). Boundary conditions define each zone and heat flows in and between each zone in each time step. Walls separate each zone and each wall is represented by a series of resistors and capacitors. Climate data entered into the program includes the location of the site, the outside air temperature, ground temperature and the irradiance (direct and diffuse). The simulation of the test site was divided into four zones. One external zone, one zone for each of the two atria wells and one zone for the internal room area. The only heat gain into the building simulated is that by direct and diffuse solar irradiation through the skylights and the northern window. The heat transfer model used to simulate the infra-red radiation and convection in the internal zone is simplified by assuming that both are coupled and therefore only one resistance between each zone is needed. The output file gives a measure of the average temperature within the room and the normal and LCP glazed atriums. Each program outputs one average temperature per zone per hour across the course of the day.

111


Simulation 2

[Table 6.05: Simulated temperatures comparing between 2 glazings under clear and overcast skies]

Time (hr) 7 8 9 10 11 12 13 14 15 16 17

Normal Atrium 14/8 clear sky 14.6 26.1 36.9 42.6 46.4 50.4 51.7 49.4 45.5 40.4 33.3

LCP Atrium 14/8 clear sky 13.9 23.1 33.1 38.8 41.6 43.7 44.6 44.1 41.9 38.1 31.9

Normal Atrium 22/8 overcast sky 17.4 25.9 32.3 29.2 28.2 27.6 29.8 30.8 27.4 24.9 22.1

LCP Atrium 22/8 overcast 16.8 23.4 29.2 27.2 26.3 25.7 27.2 28.2 25.8 23.8 21.5

The graphs show a comparison between the field temperature data within both glazed atrium and the Capsol simulated temperatures on the 14th and 22nd of August. The simulated values show a general overestimation of the average temperatures within the atria compared to the averaged measured data collected at the top and bottom of the model atrium wells. [Figure 6.12: Graph of Capsol simulated plain glazed atrium temperature under clear sky] Tem perature Com parison betw een field data and Capsol sim on clear sky day in Norm al Atrium - 14/8/99 55.0

Temperature (degC)

50.0 45.0 40.0 normal bot

35.0

normal top

30.0

normal sim

25.0 20.0 15.0 10.0 0:00 2:00

4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 Tim e (hr)

The simulation of the normal glazed atrium under a clear sky on the 14th of August shows that during the middle of the day the simulated temperature is between the top and bottom measured temperature. The simulated results are just below the top temperature sensor from 11am and 3pm. Before and after this time the simulation overestimates the temperature.

112


Simulation 2

[Figure 6.13: Graph of Capsol simulated plain glazed atrium temperatures under overcast sky] Tem perature Com parison betw een field data and Capsol sim on overcast sky day in Norm al Atrium - 22/8/99 55.0

Tem perature (degC)

50.0 45.0 40.0

normal bot

35.0

normal top

30.0

normal sim

25.0 20.0 15.0 10.0 0:00

3:00

6:00

9:00

12:00

15:00

18:00

21:00

Tim e (hr)

The heavily overcast sky day on the 22nd of August had a temperature difference between night and day within the atriums of about 10° C. Whereas the simulation shows approximately 15° C change. It also shows that the measured maximum temperatures in both atria where approximately 25°C whereas the simulation shows a maximum temperature around 30°C.

[Figure 6.14: Graph of Capsol simulated LCP glazed atrium temperatures under overcast sky] Tem perature Com parison betw een field data and Capsol sim on overcast sky day in LCP Atrium - 22/8/99 55.0

Tem perature (degC)

50.0 45.0 40.0

LCP bot

35.0

LCP top

30.0

LCP sim

25.0 20.0 15.0 10.0 1 2

3 4 5 6 7

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Tim e

113


Simulation 2

[Figure 6.15: Graph of Capsol simulated LCP glazed atrium temperatures under clear sky] Tem perature Com parison betw een Field data and Capsol sim on clear sky day in LCP Atrium - 14/8/99 55.0

Tem perature (degC)

50.0 45.0 40.0

LCP bot

35.0

LCP top

30.0

LCP sim

25.0 20.0 15.0 10.0 1

3

5

7

9

11

13

15

17

19

21

23

Tim e (hr)

During the month of August the temperature sensors in the LCP atrium had accidentally relocated. The top positioned sensor was in fact located at the mid point of the atrium well while the bottom positioned sensor was on the floor. The simulated average temperatures should be able to be directly compared to the top temperature sensor within the LCP glazed atrium. It can be seen that the simulation overestimates the temperature in the middle of the clear sky day by about 6°C and under overcast sky by about 2°C. The Capsol thermal simulation program generally overestimated the temperature within the building and both atrium wells under clear and overcast sky conditions. The thermal simulation program developed in this research also generally overestimated the temperature. However, it was also shown (figure 6.09, 6.10) that as the solar altitude increased and a flattening of the temperature in the middle of the day occurred that the simulation was able to reproduce this effect. No simulation using the Capsol program was run for these later dates in the year so further testing of this program is necessary.

114


Experiment

Chapter 7: FIELD EXPERIMENTS 7.1 Introduction

In order to monitor, analyse and simulate the thermal performance of the model wells, it was necessary to measure various environmental parameters including temperature outside and inside the model, global and diffuse irradiance, and ventilation. This was collected over a period of four months in the winter and spring of 1999. To analyse and simulate the lighting performance of the model, illuminance levels were collected within the model as well as within smaller model rooms and atriums (2D & 3D). Luminance measurements of the sky were also recorded at various locations during the research period. This data will be discussed further at the end of this chapter. These experiments were conducted to investigate the penetration of radiation into a modified model atrium well. This was compared to the penetration of radiation into a reference model atrium well. The modification within one well was in the form of a second glazing layer made of laser cut panels (LCPs). Due to the redirecting effect of the LCPs the hypothesis was that the thermal stratification and temperature would be reduced and that the light level would be more constant over the course of a clear sky day. Measurements were recorded of temperature, irradiance, light level and airflow within a three month period of the winter and spring of 1999 in the temperate climate of Brisbane. It was the intention of the research to monitor the temperature and lighting within the model over a period of 12 months but due to the denial of permission to locate the model on campus, the relocation and set up of the experiment was not completed until June 1999. The experiment was to be conducted within a 4.5 metre tall by 1.5 metre square atrium with a steel frame and colorbond steel covered polystyrene sheet walls on the top of the S block building at QUT. Due to safety regulations the experiment was relocated to our test facility at the Brisbane airport. It was then the intention to monitor the model for 6 months and extrapolate over the 12 month period. Due to severe weather conditions, the monitoring was unexpectedly stopped after only 3 months.

115


Experiment

Two simultaneously monitored atria were set up within a modular building at the airport. Temperature sensors were positioned within the models to record the thermal performance. The temperature experiment was conducted for comparative purposes only because the scale of the model affects the thermal transfer processes of conduction, convection and radiation. A scale model can not simulate a full size buildings’ thermal performance but is capable of modelling the lighting performance. The relative performance of the two models was determined to find which atrium was more comfortable via lower air temperatures and less thermal stratification. Ventilation and daylight penetration experiments were also conducted in the model atria within this period. Daylight experiments were also performed upon smaller scale models. These experiments are also discussed within this chapter. 7.2 Equipment for Experiments Modular Building - Retracom Insulated Panel Systems 8m x 3m x 3m with 75mm

thick walls of polystyrene covered with 0.6mm colorbond galvanised steel sheeting. Sky Solutions Skydome Skylight (x2) - These consisted of a clear acrylic pyramid

shaped dome with a tilt of 45°. An aluminium base with an outside dimension of 1m x 1m and an internal aperture of 0.8m x 0.8m. Laser Cut Panel (x4) - Laser cut light deflecting acrylic triangular shaped panels.

Width=6mm and W/D ratio of 0.5 with perpendicular cuts. Located under the skydome on all four sides of the pyramid at a tilt angle of 42° to the vertical. Polystyrene Sheets - 3m x 1m x 50mm (x8) from RMax Rigid Cellular Plastics. Right Angle Aluminium - 24m x 50mm x 50mm from Aluminium Services and

Supplies. Light Meters - LX-102 Emtek for logging light measurements

Topcon IM-5 for high quality light measurements Gossen Panlux for hand held scale model measurements Blackened tube for zenith luminance measurements Temperature Sensors - (x8) AD590 Two terminal integrated circuit temperature

transducer which produces an output current proportional to the absolute temperature for temperature measurements.

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Experiment

Pyranometer - (x2) first class EP08 pyranometers, which produce an output voltage

proportional to the irradiance; mount and shadow band. Remote Area Power Supply- solar panel - (x2) NESTE Advanced Power Systems

Batteries - (x4) Regulator - Solarex SC18 - 12 volts Inverter - Latronics DC-AC Sinewave Power Inverter Laptop Computer - Toshiba T1200XE PicoLog - Data logging software (Version 1.18 February 1997) and hardware (ADC) Ladder - to access the roof of the test building Scale Model Rooms: Cardboard box - for conduct daylight penetration experiments.

Semi-infinite box - Mirror walled box for daylight experiments. Mini-Atrium - undergraduate model for daylight experiments. Miscellaneous - Masking tape, plastic tape, ping-pong balls, wire, nuts, bolts, screws,

jig saw, knife, soldering iron, circuit board, heat shrink, fan, garbage bags, stopwatch. Data Logging Equipment

The temperature and irradiance were continuously monitored and the data logged onto a computer over the period from the 21st of July 1999 to the 12th October 1999. The PicoLog data logger collected sets of measurements simultaneously from eight different channels. The data was processed through an analogue to digital convertor (ADC) and stored on a laptop computer. Each channel was used to measure a voltage from an instrument, which was a representation of a real world parameter like temperature or illuminance. The program took a number of readings from each channel and averaged them to form a recorded sample. The program was set up to have a logging period of a week before it was stopped. Each of these sequences of samples is referred to as a run. [Figure 7.01: Computer logging equipment]

117


Experiment

Each recorded voltage was scaled to represent a real world parameter by using an equation. A report can be produced within the PicoLog software to allow visualisation of the data as it is received. The report can be graphical or text based. With a maximum of 8 channels to record upon, 6 temperatures and 2 pyranometers were recorded all with a sampling interval of 30 seconds. Each week the sampling was stopped and the run copied off the laptop (due to insufficient hard drive space) and a new run was started. This data was taken back to QUT and analysed. The solar panels on the roof of the test site produced energy that was stored by the 4 batteries within the room. The batteries supplied a DC voltage to the connected circuit. An invertor was also connected to the batteries so additional AC electrical equipment could be used while on site, such as drills, jigsaws, radios and fans. A laptop computer was connected to the batteries via a regulator and a transformer. This kept the supplied voltage within the acceptable range and converted it to AC. The laptop supplied through the ADC a voltage to the temperature and irradiance instruments that were connected in series with resistors. A channel from the ADC was connected in parallel across the resistor to record the analogue voltage, which was then converted to a digital voltage within the acceptable range. The ADC supplied to the circuit 5 volts in parallel so each sensor had a maximum supply of 5 volts. Each AD590 two terminal integrated circuit (IC) temperature transducers have a sensitivity of 1µA / °K. The temperature range in Kelvin recorded (0 °C = 273.2 °K) was 250 - 350 Kelvin. Therefore, current draw was between 250 and 350 µA so to keep the output voltage under 5 volts a maximum resistance of 14 kΩ was used. These sensors provided an output voltage proportional to absolute temperature (PTAT) (Analog Devices, 1978). A 4.67 kΩ resister was finally chosen for the temperature circuit. Using I.R = V

1µA / °K x 4.67 kΩ = 4.67 mV/ °K

Eq. 7.01

For the current range 250 - 350 µA this meant that 1.2 to 1.6 volts was required which was easily under the 5 volt supply limit.

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Experiment

The AD590’s were soldered onto lengths of wire and encased within heat shrink tubing. They were then placed within blackened plastic integrating spheres. Similar circuits were constructed for the pyranometer and illuminance monitoring. [Figure 7.02: AD590 temperature sensor electrical circuit]

Laptop Computer

AD 590 4.67 KΩ

Regulator

Invertor

Batteries

ADC

Solar Panel

7.3 Building Description [Figure 7.03: Test site building side]

The atriums were placed inside the QUT Daylighting Research Modular Building, which was located at the Bureau of Meteorology airport site on Lomandra Drive, Eagle Farm, in Brisbane. The geographical co-ordinates of this location was 27° 25’ S, 153° 07’ E and elevation four metres (www.bom.gov.au/cgi-bin/climate, 2001).

119


Experiment

The building was a demountable panel style built by Retracom Insulated Panel Systems, which had dimensions of 8 metres long, 3 metres wide and 3 metres high. It was positioned so that the long axis was orientated North-South. A small window, 1.2 metres square, made of clear 3mm thick glass was located in centre of the North wall with a normal transmission of 92% and a maintenance factor of 90%. A door was located at the South Western corner of size 2m x 0.8m. The buildings’ walls and roof were made of two layers of colorbond steel with polystyrene insulation with a total thickness of 75mm. The internal surfaces were a creamy, brown colour, which was slightly specular. The approximate reflectivities of the surfaces are listed in the table 7.01. [Table 7.01: Surface reflectivities]

Area

Surface Reflectivity %

Ceiling

75

Walls

75

Floor

65

The building was run as a remotely powered weather monitoring station with global and diffuse pyranometers on the roof along with tilted solar panels. The 4 batteries that stored the power received by the solar panels were located within the building. The building was naturally ventilated with a rotational turbine ventilator (whirly bird) located at the Southern end next to the solar panels. During the experiment, the window and the vent were blocked off to prevent uncontrolled air circulation or solar penetration.

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Experiment

[Figure 7.04: Test site building end]

7.4 Model Atria Description

The model atria were constructed at a scale of 1:10 to simulate a 30 metre tall building. The atria wells were 0.8 metres square and 3 metres tall. They were positioned symmetrically within each half of the room, where upon two square holes were cut in the roof of the building to act as the apertures of the atria. To do this the pyranometers were relocated to the northern end of the buildings’ roof and the solar panels were moved slightly further to the southern end of the buildings’ roof. The artificial light fixtures within the room were also removed. The square apertures were cut out using a jig saw with a 50mm long blade so they were cut approximately half way through from both sides of the roof panel. [Figure 7.05: Test site building inside room]

121


Experiment

Four lengths of L section aluminium were welded into a square. This was used as a mounting bracket around the square aperture. The external bracket was used to mount the pyramid dome. Lids were also made to cover the apertures if the skylights had to be removed. The brackets were bolted into place above and below the square aperture. The internal square bracket was also used as a lip to position the polystyrene atrium wall panels. See figure 7.03. The apertures were covered by small (0.64m2) clear pyramid shaped glazed skylights from Skydome Industries. The southern atrium (A1) was the reference model and had a single layer of clear acrylic glazing. The northern atrium (A2) also had clear acrylic glazing but was modified with the inclusion of tilted laser cut panels to alter the penetration of daylight and thermal radiation. They were placed on the top of both of the square aluminium mounts and screwed into place. [Figure 7.06: Northern LCP glazed skylight]

[Figure 7.07: Southern normal glazed skylight]

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Experiment

The atrium well walls were placed within the test site building from floor to ceiling around the glazed apertures. They were made from 50mm thick, 1m wide and 3m long polystyrene sheets. Eight sheets were purchased of which half of them were cut with a jig saw into appropriate 0.8m wide pieces so that the internal cross section of the atrium well was 0.8 metres square. Once the atrium wells and glazing where installed, the temperature sensors were placed within each atrium well and connected to a computer. The position of the sensors will be discussed later in this chapter. The model then had to be sealed to minimise the penetration of air and water and so the heat transfer into the atrium well could be reduced to only the glazed aperture that protruded out of the top of the building. Firstly, Selleys All Clear sealant was used on all external joints to provide waterproof seals. Then the ventilation holes around the edge of each pyramid aperture and the turbine ventilator were covered to provide an air tight internal atrium volume. The North orientated window of the room was also covered and finally all the internal joins of each well wall were sealed over with plastic packing tape. [Figure 7.08: Southern foam atrium well inside test site building]

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Experiment

Significant thermal stratification only occurred within the model atria when the weather was fine and the sky was relatively cloud free for the entire day. In winter and spring when this experiment was conducted, fine weather is normally the most dominant weather condition. For July, August September on average the total number of clear sky days is 46. (www.bom.gov.au/climate/averages/tables/cw_040223.shtml, 2000) In 1999, however, the eastern seaboard of Australia was under the influence of a La Nina weather pattern which resulted in above average rainfall and a greater percentage of cloudy sky conditions. In the three months of recording data only 14 total clear sky days occurred. A list of the clear sky days recorded within the monitoring period is listed in table 7.02. The sun rise, sun set and sky clearness information is also included. The sky clearness is categorized into divisions where below 1.5 is overcast, 1.5 to 3 is intermediate sky clearness, above 3 is a clear sky and above 6 is a perfectly clear sky. The sky clearness was hourly averaged from 9am to 3pm on the day in question for this research. [Table 7.02: Clear sky days monitored]

Month Total Clear Sky Day Sky Clearness 22nd 9.6 July 10th 7.9 August th 13 5.8 August th 14 8.7 August 15th 8.1 August th 16 6.0 August th 19 5.5 August 20th 5.9 August th 13 8.6 September 15th 5.4 September th 16 5.2 September th 24 6.5 September 25th 6.3 September th 9 6.6 October

Sun Rise 6:45 6:34 6:32 6:31 6:30 6:29 6:28 6:26 6:07 6:06 6:05 5:58 5:58 5:46

Sun Set 17:15 17:26 17:28 17:29 17:30 17:31 17:32 17:34 17:53 17:54 17:55 18:01 18:02 18:14

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Experiment

The installation process was also hampered due to the unseasonable rain, which resulted in the drill holes and atrium apertures leaking water and delaying the installation of electric equipment inside the test site. On the 20th of October 1999, after only 3 months monitoring, a micro storm cell passed over the airport resulting in the test building being structurally reoriented (it blew over). This caused extensive damage to the building and equipment, which resulted in the end of monitoring for this research. [Figure 7.09: Outside storm damaged test site building]

[Figure 7.10: Inside storm damaged test site building]

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7.5 Daylight Measurements

Light levels were to be logged within the atrium wells on a continuous basis in the summer of 1999. The solar altitude during summer would be great enough to enable a noticeable difference in light level between the two model atria. However, the experiment was stopped before summer. The equipment had been set up and preliminary monitoring had already been conducted in the spring. Therefore, this data will be presented instead. Another laptop with a different ADC had to be used to record the light levels because the initial ADC had only 8 channels and all of them were being used. In addition, the light meters were powered by their own 9 volt alkaline battery, which only lasted for a few days before needing to be replaced. If the batteries were not replaced and the light meters were connected in the same circuit with the other sensors then they would have disrupted the measurements from the other sensors. A practice logging period of one hour was recorded on the 2/9/99 using a LX-102 light meter. This light meters’ analogue output had a sensitivity of 0.1 mV/Lux. The logging parameter equation to convert the input voltage to the real world parameter of lux was: Light = 10000 x A

where A is the input voltage

Hand held data was also obtained on several occasions within the test site atria using the Topcon IM-5 light meter. It is important to measure the reflectivities of all the surfaces, the sky luminance and the illuminances when conducting any daylighting measurements under real skies. Under overcast sky conditions the light level within the buildings may be stated as a daylight factor (DF) which is the ratio of the exterior HGI to the interior HGI. Under real skies it is important to record the light levels at all prescribed points within the building quickly so the sky condition does not change considerably. The positions that the light levels were recorded had to be reproducible so after every modification the same positions could be used to enable direct comparisons between models.

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Experiment

Daylight measurements were taken in the test site building on the floor and work height under clear (14/7/99) and overcast (9/7/99) skies across the whole floor area. The floor was divided up into a grid of 15 squares with 1 measurement taken within each square. The squares were 1.6m x 1m and the meter was placed at the centre of each square. The work height measurement was recorded with the meter attached to a tripod set to 0.8 metres off the floor. The floor height measurement was recorded with the meter on the floor. Lawrence Leong assisted with the recording of the measurements on both days. The position of the table in the back south-east corner of the room, which covered the batteries and supported the computer and electrical logging equipment meant that the corner floor points could not be recorded. Many daylighting measurements were taken within smaller basic box models to validate the daylight simulation programs. The results of these experiments are included in Appendix 6. A square cardboard box was used on the roof of M Block at QUT. All the internal surfaces had the reflectivity (0.3) due to being made of the same brown cardboard material. The box represented a room with an aperture of half the wall. The cardboard box had dimensions of 0.26m long, 0.22m high, 0.3m wide. A long thin model room was used in the park near L Block at QUT. The side vertical walls of the model have removable sliding mirrors on them. This allows a representation of a semi-infinite 2 dimensional room that can be compared to the 2 dimensional theoretical computer simulation. Upon the removal of these mirrors the room represents a normal 3 dimensional model. The model had an aperture of half the end wall. The model room has dimensions of 1m long, 0.3m high, 0.3m wide and the reflectivities of the surfaces were floor (0.1), ceiling (0.7), end walls (0.4), side walls (0.4 or mirrored). This room was also stood on its end to simulate an atrium well. Measurements were taken down the middle of the room at 0.1m intervals at the floor height.

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Experiment

7.5.1 Model Atrium Well under real skies

Light levels within the test site model atria were not thoroughly logged and investigated due to the sudden damage and premature ending of the experiment. However several trial data measurements were recorded and will be presented here. The reflectivities of the surfaces were 0.85 for the foam atrium walls and 0.6 for the floor. The well index of this model was 3.75. On the 12th of October at 3 p.m. under a clear sky the horizontal illuminance levels at the bottom of both atrium wells were measured with the Topcon IM-5 digital illuminance meter as: LCP glazed atrium well (A1) = 10.35, 9.51 Klux Normal clear glazed well (A2) = 10.68, 10.00 Klux On the 2nd of September at 12 p.m. under overcast sky horizontal illuminance levels at bottom of the atriums were data logged onto a laptop computer from an Emtek LX102 illuminance meter for 45 minutes at 30 second intervals. Over a period of 20 minutes, the average illuminance in the normally glazed atrium (A2) was found to be 6.1 Klux. Over a period of 15 minutes, the average illuminance in the LCP glazed atrium (A1) was found to be 4.8 Klux. [Figure 7.11: Graph of logged illuminance level data]

Light level in atria on 2/9/99 Illuminance Level (lux)

light level 8000 7000 6000 5000 4000 3000 2000 1000 0 12:00

12:14

12:28 Time (hrs)

12:43

12:57

The light level in the LCP glazed model atrium well was found to be less than in the clear glazed model atrium well. 128


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The measurements were not taken simultaneously though, so it can not be ruled out that the light level was lower due to a change in sky conditions. However, the LCP glazed model atrium well did appear noticeably darker due to some of the light being deflected out of the glazing from high elevation angles. Smaller model The illuminance levels measured within a smaller model atrium well were obtained using the model as described above (p153), however, it was stood on it’s end with the open aperture facing upwards. Data was collected within this model well under clear skies on 11/6/98 at 10 am. The sky luminance data for this experiment included a horizontal global illuminance, HGI, of 62.5 Klux, a zenith luminance, Lz, of 190 lux which with a solid angle, ω, of 0.023 steradians was equal to 8 Kcd/m2. [Table 7.03: Horizontal illuminance in atrium well for different orientations and glazing options]

Open Clear Pyramid Flat LCP

Sun on brown (Klux) 1.3 1.4 1.4

Sun on white (Klux) 7.5 2.3 2.2

Shaded (Klux) 2.0 0.5 0.6

The walls of this model were not all the same colour. One wall was painted brown while the other 3 walls were white. The model was rotated so that the sun was shining on different coloured walls. The model was also shaded so that no direct sun was shining upon the model. The data from these experiments do not show a significant difference between the two glazings examined. The LCP glazing will only modify the light level when the cuts deflect a large fraction of the incident light. Under the clear sky conditions during this experiment the solar altitude was near to the normal of the pyramid glazing and in this situation a lot of the direct light was undeflected.

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Experiment

7.5.2 Model Atrium under artificial sky

Data collected and presented by Mabb (1997) can be used in this research to compare to the theoretical simulation results. The scale model atrium in that research was at scale of 1:75 and was positioned under an artificial sky mirror box. The sky represented a CIE overcast sky with a horizontal global illuminance (HGI) of 3000 lux and a ratio of the zenith luminance to horizon luminance of one third. The atrium sat on the desktop so the dimensions were very small: (30cm(high), 15cm(wide), and 15cm (length)). The room dimensions were even smaller (3cm(high), 15cm(wide), 15cm(length)) with a window space equal to 50% of the wall. The reflectivities of the internal wall surfaces were as follows: 70%(white), 25%(wood), 6%(black). [Table 7.04: Illuminance level in small model atrium well with changing reflectivity and Well Index]

Height (cm) 4 13 22 31

Well Index (WI) 0.27 0.87 1.47 2.07

White (lux) 2970 2100 1200 960

Wood (lux) 2910 1800 930 570

Black (lux) 2700 1350 540 360

[Figure 7.12: Graph of illuminance level in small model atrium well wrt surface reflectivity and WI] Relationship between Daylight Factor % and Well Index in small model well

White Wood Black

Daylight Factor %

120 100 80 60 40 20 0 0

0.5

1

1.5

2

Well Index

These results show that the higher illuminance levels were achieved when wells with surfaces of higher reflectivity were used.

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Experiment

The illuminance was also measured in the bottom level adjoining room to the model atrium well that was positioned under the artificial overcast sky. Four glazing options were investigated including clear glazing upon the atrium well and adjoining room window, LCP glazed atrium well and clear glazed adjoining room window, clear glazed atrium well and LCP glazed adjoining room and finally LCP glazing upon the atrium well and the adjoining room. [Table 7.05: Illuminance in adjoining room (level 1) with all white surfaces and 4 glazing variations]

Distance from window (cm) 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 12.5

Clear Glaze (lux) 123 90 60 45 39 30 27 23 18

LCPyramid (lux) 72 57 42 30 24 22 20 18 15

LCP (lux) 112 91 67 52 45 37 30 24 21

LCP & LCPyramid (lux) 69 52 42 30 24 22 19 17 12

[Figure 7.13: Graph of light level in adjoining room of scale model with various glazing options]

Light level in adjoining room of model atrium with various glazing options 140

Clear glaze LCPyramid LCP tilted LCP (x2)

Light level (lux)

120 100 80 60 40 20 0 0

5 10 Distance from window (cm)

15

The graph clearly shows an increased illuminance level with two of the glazing options over the other two options. The clear glazed atrium well with the LCP glazed adjoining room and the other glazing option of clear glazing upon the atrium well and adjoining room provided the highest illuminances.

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Experiment

7.5.3 Test site room [Figure 7.14: Pictures inside test site room]

Illuminance data was collected inside the test site room on two separate days. The first day was an overcast sky day on the 9th of July 1999 at 12pm and the other was a clear sky day on 14th of July 1999 at 12pm. The dimensions of the room were 8m long, 3m wide, 3m high with a small window of 1.2 metres square in the northern wall. The reflectivities of the surfaces were 75% for the vertical walls and ceiling and 65% for the floor. The sky luminance data for this experiment on the cloudy day was the horizontal global illuminance, which was equal to 20.8 Klux. The sky luminance data on the clear sky day included the zenith luminance (Lz) equal to 45 lux recorded over a solid angle (ω) of 0.023 sr. This equates to a Lz of 1957 cd/m2. Then using equation 4.12 from Chapter 4. π.Lz = Eh = 6147 lux This result corresponds fairly well with field data recorded at 7000 lux under clear sky with the direct solar beam shaded. The HGI was 74.8 Klux. Illuminance values measured in lux were recorded within the room in set grid positions across the floor and on the work height using a tripod to mount the light meter.

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[Table 7.06: Illuminance level under overcast sky on work height]

Distance (m) 0.8 2.4 4.0 5.6 7.2

Column 1 922 345 154 100 104

Column 2 2380 357 132 116 114

Column 3 928 293 120 77 65

[Figure 7.15: Graph of illuminance level under overcast sky on work height]

Test site under overcast skies on work height on 9/7/99 Illuminance (lux)

2500 2000 1500 A

1000

B

500 C

0 1

2

3 Depth of room (m)

C

A

4

5

[Table 7.07: Illuminance level under overcast sky on floor]

Distance (m) 0.8 2.4 4.0 5.6 7.2

Column 1

Column 2

Column 3

616 510 310 83 77

1185 494 330 92 70

980 537 280 xxx xxx

[Figure 7.16: Graph of illuminance level under overcast sky on floor]

Illuminance (lux)

Test site under overcast skies on floor on 9/7/99 1500 1000 500 C

0 1

2

3

4

A

A B C

5

Depth of room (m)

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Experiment

[Table 7.08: Illuminance level under clear sky on work height]

Distance (m) 0.8 2.4 4.0 5.6 7.2

Column 1

Column 2

Column 3

1430 1200 820 560 380

3080 1260 880 625 450

1450 1260 830 615 520

[Figure 7.17: Graph of illuminance level under clear sky on work height]

Test site under Clear skies on workplane on 14/7/99

Illuminance (lux)

4000 3000 2000

A B C

1000 0 1

2

3

4

A 5

Depth of room (m)

[Table 7.09: Illuminance level under clear sky on floor]

Distance (m) 0.8 2.4 4.0 5.6 7.2

Column 1

Column 2

Column 3

1150 1245 795 525 340

1380 1750 850 550 360

1085 1140 750 XXX XXX

[Figure 7.18: Graph of illuminance level under clear sky on floor]

Test site under clear skies on floor on 14/7/99

Illuminance (lux)

2000 1500 1000 500 C

0 1

2

3

4

A B C

A 5

Depth of room (m)

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The following explanation will discuss the proceeding four graphs (figures 7.17 – 7.20) of the illuminance within the test site room. The illuminances recorded at the work height under overcast skies (figure 7.17) showed a peak near the window in the middle column of 2.3 Klux, which dropped off quickly down to 357 lux at the next measuring position. The illuminances measured in the outside columns (1 & 3) were similar except upon the table in the back corner. The illuminances measured on the floor under overcast skies (figure 7.18) showed that the peak near the window in the middle column was half as big (1.19 Klux) as that measured at the work height. There was also no data obtained at the back corner of the room due to the equipment table position. The illuminances measured on the work height under clear skies (figure 7.19) showed that the light level was higher than that under overcast skies. The peak in illuminance near the window in the middle column was 3.1 Klux. The rest of the points were similar in each column with illuminances dropping from 1.4 Klux at the front down to 0.4 Klux at the back. The illuminances recorded on the floor under clear skies (figure 7.20) showed that the peak in illuminance near the window in the middle column was further back in the room compared to the other data sets. A peak of 1.8 Klux occurred at the 2nd measured position while only 1.4 Klux at the 1st position. There was also no data obtained at the back corner of the room due to the equipment table position. The illuminances in the outside columns (1 & 3) were at similar levels.

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7.5.4 Sky Distribution Measurements

Sky luminance field data was recorded from the roof of M block, QUT, across a totally clear sky. The suns’ position at 2pm on the 15/3/99 was at 50° altitude and 290° azimuth. This data is shown as a comparison to simulated data in section 5.5.1. The overall horizontal global illuminance was recorded as 75 Klux. While the zenith luminance using a tube with a solid angle (ω) of 0.023 sr was measured at a level of 47 lux which corresponds to 2050 cd/m2. [Table 7.10: Sky luminance data across the sky at 10° increments with ratio to zenith]

Angle 10 20 30 40 50 60 70 80 90

Light Level (lux) 35 28 27 20 21 22 24 26 47

Zenith Ratio (%) 0.74 0.59 0.57 0.42 0.44 0.46 0.51 0.55 1.0

Angle 100 110 120 130 140 150 160 170

Light Level (lux) 65 140 160 500 400 150 150 40

Zenith Ratio (%) 1.38 2.97 3.40 10.64 8.51 3.19 3.19 0.85

Solid Angle A solid angle can be expressed as the projection of an angle on to a sphere, which can be expressed in steradians (sr) between 0 and 4π. The angular space that an object occupies in the field of view can be calculated as the area of the object (A) divided by the square of the distance (R) between the object and the observer: Solid angle (ω) =

A R2

Volume of a sphere = 4/3 π r3 Surface area of a sphere = 4 π r2 Therefore, the area of sphere is substituted into the solid angle equation to give ω = 4 π r2 / r2 = 4 π steradians For example: experimentally, the solid angle was determined to find the angular view of a tube attachment to the light meters used to obtain light levels from one direction, this method approximately measured luminance. Solid angle (ω) = π r2 / l2

Eq. 7.05

ω = 3.14 x (0.01)2 / (0.25)2 = 0.005 sr or = 3.14 x (0.02)2 / (0.23)2 = 0.023 sr 136


Experiment

[Figure 7.19: Diagram of meter and tube describing solid angle (ω)]

ω

Other sky distribution measurements were recorded with the Topcon IM-5 light meter for the illuminance measurements. A PVC black painted tube was attached to enable the measurement of luminance levels. The solid angle of this tube was ω = 0.005 sr. A clear sky distribution was measured upon the 5th of July. It had a HGI of 60 Klux, a Lz of 15 lux = 2.5 Kcd/m2 and a Lsun of 80 Klux = 16 Mcd/m2. A cloudy sky distribution was measured upon the 4th of July. It had a HGI of 15 Klux and a Lz of 50 lux = 10 Kcd/m2. The following values were found on the 1st and 2nd of September 1998, with solid angle of ω = 0.023 sr. [Table 7.11: Sky luminance values]

Sky Position Light Level Overcast Zenith Luminance 230 lux = 10 Kcd/m2 Overcast Global Illuminance 22000 lux Clear Indirect Luminance 50 lux = 2.1 Kcd/m2 Clear Direct Luminance 85 Klux = 3.7 Mcd/m2 Clear Global Illuminance 70000 lux The measurements in table 7.11 differ from the above paragraphs mainly due to the

different solid angle over which these measurements were taken.

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Experiment

7.6 Irradiance Measurements [Figure 7.20: Picture of diffuse and global pyranometers]

The thermal performance of the models is dependent upon the incident irradiance. The irradiance was monitored by two Middleton EP08-E pyranometers. Solar radiation absorbed by the internal blackened sensor within the pyranometer, results in a temperature increase. This causes a temperature difference between the hot and cold junctions of the thermopile, resulting in a linear electromagnetic field (emf) output that is proportional to the irradiance (Middleton 1994). Diffuse irradiance was measured by one pyranometer that was located under a shadow band and global irradiance was measured with the other unshaded pyranometer. These sensors were also logged onto the PicoLog software. The global pyranometer was placed at the North end of the building on the roof away from any possible shadowing. The other was placed 2 meters to the South of the first. This was positioned under a shadow band that blocked the direct component. The band was adjusted on a weekly basis to keep the sensor continuously shadowed. When the well apertures were cut out, the pyranometers were moved so that the shadow band pyranometer was at the NW corner and the global pyranometer was at the NE corner of the roof.

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Experiment

The equation within the PicoLog software to convert the input voltages from the sensors into the real world parameter of irradiance in Watts per metre squared were: Global = 1000 x A / 0.91

Eq. 7.06

Diffuse = 1000 x A / 1.07

Eq. 7.07

Where A is the input voltage. The irradiance data logging began several months before the temperature logging and concluded at the same time when the building was damaged. Diffuse and global irradiance data was collected over a period of 10 months at the daylighting research test site. Within the 4 month period of July to October 1999, 6 separate days are presented below that represent the 3 different sky cloud cover conditions of clear, intermediate and overcast. A series of corrections were applied to the raw irradiance data that was collected from the instruments monitored at the test site. These corrections included the initial calibration between the meters to allow for slightly different sensitivities between the sensors. The initial correction was: Diffuse (correction 1) = 1.0217 x diffuse - 2.0235

Eq. 7.08

The diffuse irradiance must also be corrected for the effect of the shadow band which blocks out more than just the view of the sun. The correction factor (cf) is added to the diffuse measurement, where: cf = 1/(1-X)

Eq. 7.09

and X is found from Drummond and Roche (1965): X = (2w/π.r). cos3 (dec).[t. sin(lat).sin(dec) + cos(lat).cos(dec).sin(hra)]

Eq. 7.10

where: hra = hour angle of sun w = width of shadow band (80 mm) r = radius of shadow band (310 mm) lat = latitude of site dec = declination of site

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Experiment

Diffuse (correction 2) = Diffuse (correction 1) + cf The next correction to the diffuse irradiance depends upon the sky condition (cloudy, intermediate or sunny). The sky condition is determined using the Perez sky clearness equation: (Perez et.al. 1990)

  + I dn I dif   ε= 3  + 1.041 * (Z )    I dif

3  1 + 1.041 * ( Z )  

Eq. 7.11

where: Z = zenith angle Idif = diffuse horizontal irradiance Idn = direct normal irradiance The sky clearness index ε is grouped such that:

0 to 1.4 → cloudy sky 1.4 to 3 → intermediate sky 3.0 to __ → sunny sky

The diffuse irradiance correction for sky conditions was: Overcast sky -

Diffuse (correction 3) = Diffuse (correction 2) x 1.03

Intermediate sky -


Clear sky -


Once the correct diffuse irradiance value has been determined the direct normal irradiance can be determined from:

Idn = Ig - Idif / sin(alt)

Eq. 7.12

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Experiment

Diffuse and global irradiance data was collected from the test site and by applying the formula in section 4.7, corrected diffuse and direct irradiance was obtained. Raw measured irradiance data for 6 separate days including 1 intermediate sky on the 9/10/99; 1 overcast sky on the 22/8/99; and 4 clear skies on the 25/9, 22/7, 16/9, 14/8 are presented on the following pages. The hourly averaged irradiance data for the 4 clear skies days are also presented. [Figure 7.21: Graph of measured diffuse and global irradiance on overcast sky day on 22/8/99]

Irradiance (W/m2)

Measured Irradiance on 22/8/99 400 350 300 250 200 150 100 50 0 0:00

4:48

9:36

14:24

19:12

Diffuse Global

0:00

Time (hr)

This graph shows very little difference between the diffuse irradiance level and the global irradiance level, which suggests a lack of a direct solar component all day due to cloud cover. The irradiance level spikes as low as 50 W/m2 and up to 400 W/m2 during the day. The next four pages show the raw data along with the hourly averaged direct, diffuse and direct normal irradiance analysed for four clear sky days. The hourly averaged interval irradiance graphs show a very smooth distribution across the day compared to the raw 30 second interval data presented. 141


Experiment

[Figure 7.22: Graph of diffuse and global irradiance on a clear sky day on 22/7/99]

Irradiance (W/m2)

Measured Irradiance on 22/7/99

Diffuse Global

700 600 500 400 300 200 100 0 0

5

10 Time (hr)15

20

[Figure 7.23: Graph of hourly average corrected irradiance data for 22/7/99]

Direct

Hourly Averaged Corrected Irradiance on 22/7/99

Diffuse

1000 900 800 700 600 500 400 300 200 100 0

Irradiance (W/m2)

Dir Norm

6

8

10

12 Time (hr)

14

16

18

The clear sky days of the 22nd of July and the 14th of August show (Figure 7.25, 7.26) that the direct normal irradiance rises too steeply in the morning due to inaccuracies in the measuring equipment. The equipment specifications also state that measurements are not accurate for solar elevations below 10°.

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Experiment

[Figure 7.24: Graph of diffuse and global irradiance on a clear sky day on 14/8/99]

Diffuse Global

Irradiance (W/m2)

Measured Irradiance on 14/8/99 800 600 400 200 0 0

4

8

12

16

20

24

Time (hr) The diffuse and global irradiance measured upon the 22nd of July and the 14th of August show two perfectly clear sky days. The diffuse irradiance does not rise above 50 W/m2 and the global irradiance reaches a maximum of 630 W/m2 on the 22nd and 720 W/m2 on the 14th. The maximum global irradiance rises as summer approaches when the solar elevation will reach 85°. The irradiance distribution shows that it is fairly symmetrical about the maximum peak and that it reaches this peak just before noon. [Figure 7.25: Graph of hourly averaged corrected irradiance on 14/8/99]

Hourly Averaged Corrected Irradiance measured on 14/8/99

Diffuse Direct

Irradiance (W/m2)

DirNorm 800 600 400 200 0 6

8

10

12 Time (hr)

14

16

18

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Experiment

[Figure 7.26: Graph of diffuse and global measured irradiance on a clear sky day on 25/9/99]


Diffuse Global

Irradiance (W/m2)

800 600 400 200 0 0.00

5.00

10.00 15.00 Time (hr)

20.00

[Figure 7.27: Graph of hourly averaged corrected irradiance for 25/9/99]

Field Diffuse

Hourly Averaged corrected Irradiance measured on 25/9/99

Field DirNorm Field Direct

Irradiance(w/m2)

800 600 400 200 0 6

8

10

12

14

16

18

Time (hr)

The graph of the corrected irradiance on the 25/9/99 shows that the direct normal irradiance is lower than that shown on the 22/7 and 14/8 graphs. The diffuse irradiance is also much higher at a level above 100 W/m2 compared to the other graphs, which show diffuse levels below 100 W/m2. This suggests that the day was not quite as clear as the other two days.

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Experiment

[Figure 7.28: Graph of diffuse and direct irradiance on a clear sky day on 16/9/99] Diffuse


Direct

800

Irradiance (W/m2)

700 600 500 400 300 200 100 0

0

4

8

12 Time (hr)

16

20

24

The diffuse and direct irradiance measured upon the 16th and 25th of September show totally clear sky days but the sky probably had a light cover of high level wispy cloud which made the irradiance distributions slightly rough and produce diffuse irradiance levels above 100 W/m2. It also kept the direct normal irradiance at about 800 W/m2, on the 25/9, which is below the theoretical maximum for that time of the year. [Figure 7.29: Graph of hourly averaged corrected on a clear sky day on the 16/9/99]

Diffuse Direct

Hourly Averaged Corrected Irradiance on 16 Sept 1999

Dir Norm

Irradiance (W/m2)

1000 800 600 400 200 0 6

8

10

12 14 Time (hr)

16

18

145


Experiment

[Figure 7.30: Graph of diffuse and direct irradiance on a mostly clear sky day on 9/10/99]


Diffuse Direct

900

Irradiance (W/m2)

800 700 600 500 400 300 200 100 0 0

4

8

12

16

20

24

Time (hr)

The irradiance graphs from the 9th of October shows the dramatic difference between clear and overcast sky conditions. As the cloud cover envelops the sky at approximately 8:30 am the diffuse component increases. By 9 am the clouds cover the sun and the direct irradiance component drops down to 50 W/m2 which is now below the diffuse irradiance level. Then at approximately 10 am the clouds dissipate and the sky is perfectly clear for the rest of the day. [Figure 7.31: Graph of hourly averaged corrected irradiance a mostly clear sky day on 9/10/99]

Diffuse Direct DirNorm

Hourly Average Corrected Irradiance on 9/10/99

Irradiance (W/m2)

1000 800 600 400 200 0 6

8

10

12

14

16

18

Time (hr)

146


Experiment

The corrected irradiance graph for the 9/10/99 shows the effect of a small period of cloud cover in the morning as a clear rise in the diffuse irradiance and a fall in the direct normal irradiance. The rest of the day, however, is fine with a diffuse irradiance level of around 100 W/m2. Validation of irradiance field data [Figure 7.32: Graph of measured (14/8/99) and reference (TRY 19/8/86) diffuse irradiance validation]

TRY diffuse

Measured and Reference Diffuse Irradiance for validation

Diffuse

80 Irradiance (W/m2)

70 60 50 40 30 20 10 0 6

8

10

12 Time (hr)

14

16

18

This graph shows a comparison between measured and reference diffuse irradiance. The corrected hourly averaged measured irradiance over a clear sky day on the 14th August 1999 was compared to a clear sky day in the test reference year (TRY) on the 19th August 1986. The reference diffuse irradiance peaked in the middle of the day at 80 W/m2 while the field diffuse data had a steady distribution across the day with a maximum in the middle of the day at 60 W/m2. This means that the diffuse sky on the 19/8/86 was a slightly lighter colour, which was possibly due to high level wispy clouds. The difference is only 20 W/m2, which is not even noticeable to the naked eye. The graph illustrates the difficulty in comparing weather data on separate days, as no two days are exactly alike. These are both very clear sky days measured at the same location at the same time of the year, with similar equipment, but 13 years apart. 147


Experiment

[Figure 7.33: Graph of theoretical, measured (14/8/99) and TRY (19/8/86) direct normal irradiance]

DirNorm Theory DirNorm TRY DirNorm

Theoretical, Measured and Reference Direct Normal Irradiance for validation

Irradiance (W/m2)

1000 800 600 400 200 0 6

8

10

12

Time (hr)

14

16

18

The direct normal irradiance on the 14/8/99 and 19/8/86 was also compared along with the theoretical direct normal irradiance distribution based upon equation 4.08 which was used in the computer simulation programs. The graph shows a good correlation except in the morning when the measured data is much higher than the reference or theoretical values. This is due to the inaccuracy of the measuring equipment when the solar elevation is below 10° as stated in the equipment specifications.

148


Experiment

7.7 Temperature Measurements

To measure a temperature that relates to human comfort each sensor was insulated and then placed in black spheres of 40 mm diameter (ping-pong balls) to integrate the radiant heat (Humphreys 1977). The optimum diameter for a globe thermometer for use indoors is the size of a ping pong ball. This is because at low air speeds this size of approximately 40 mm diameter has a similar radiant response to a human body due to the fact that the body is clothed and not entirely convex. [Figure 7.34: Temperature sensor AD590 in ping-pong ball]

The globe temperature (TL) represents the warmth of the room for human comfort and is the weighted mean of the air temperature (Ta) and the mean radiant temperature (Ts).

TL =

hc hr Ta + Ts hc + hr hc + hr

Eq. 7.02

The surface heat transfer coefficient for convection (hc) and radiation (hr), have a ratio of the value of 0.5 in equation 7.02 to indicate a equal response to changes in air temperature and mean radiant temperature. Experimentally, thermal stratification within an enclosed space is defined as the difference between the maximum temperature (at the highest level) and the minimum temperature (at the lowest level) (Jones 1991). Thermal Stratification = ∆T = Ttop – Tbot

Eq. 7.03

149


Experiment

The temperature gradient with respect to height is another important factor (Said, 1996) that can be investigated. Temperature Gradient = ∆T / ∆h

Eq. 7.04

The temperature at six different positions enabled the thermal performance of the model to be monitored. The sensors were calibrated within an oil bath and later in a 100 mm diameter copper globe sphere for two weeks (7/7 to 21/7). The sensors were labelled T3 to T8 and the corresponding corrections are listed in the following table. Finally, they were placed within blackened ping-pong balls to integrate the incident radiation. [Table 7.12: Temperature sensor calibration correction]

Temperature Sensor

Correction

T3

-1.5

T4

-2.5

T5

0.0

T6

4.4

T7

0.7

T8

0.2

These corrections were applied to each temperature parameter equation, which was in the form:

Temp = 1000 x A / 4.67 - 273.2 + correction

Where A is the input voltage. This converted the input voltage from the sensor into the real world parameter of temperature in degrees Celsius. The temperature sensors were placed in corresponding positions in each of the two atrium wells on the 21st of July. They were placed in a vertical column down the centre of each well, initially three sensors each, at heights of 1m, 2m and 3m from the bottom. The middle position sensors in each well were removed on the 28th of July so measurements of the outside temperature and the inside room temperature could be obtained. This left two sensors within each well, one at the top and the other one metre from the bottom of the well. Figure 7.12 shows the sensor positions.

150


Experiment

[Figure 7.35: Diagram of test site with instrument sensor locations after 24th August 1999] Solar Panel R1

R2

Skylights T7

T3 T4

Foam Atrium Wells

3m

T8

T6

T5

R1 = global irrad. R2 = diffuse irrad. T3 = outside T4 = normal top T5 = normal bot T6 = inside T7 = LCP top T8 = LCP bot

Sensor T3 was initially in the clear glazed atrium at the 2m height. It was relocated to the outside of the building on the 3rd of August to measure outside temperature on the roof in the shade. This temperature could relate to the Bureau of Meteorology (BOM) recorded outside shaded data such as the hourly averaged Test Reference Year (TRY) data. Sensor T4 was the top sensor in the clear glazed atrium. It was in direct sunlight for a majority of the day. It can be related to the top sensor in the LCP glazed atrium and related to T5 to find the thermal stratification. The sensor reached a maximum of 50 to 60 degrees C and was rising towards summer. The minimum temperature was in the area of 0 to 10°C and rising towards summer. This sensor was found to be out from calibration value by 2 degree several weeks into recording. The calibration correction was wrong so it was adjusted from -2.5 to -0.5. Sensor T5 was the bottom sensor in the clear glazed atrium and was in direct sunlight only in middle of the day. This can be seen by the sharp but steady rise and fall of temperature around midday. It can be related to the bottom sensor in the LCP atrium and related to T4 to find the thermal stratification. The sensor reached a maximum of 20 to 30 °C and rising towards summer, while the minimum temperature was in the area of 0 to 10 °C and rising towards summer.

151


Experiment

Sensor T6 was initially positioned in the LCP glazed atrium at the 2m height until the 28th of July when it was placed inside the test room to measure inside temperature. It was placed at the work height in shade in the room. It was used to find the convection through the foam atrium well walls found in the thermal simulation program. The maximum had a distinct thermal mass time lag due to the mass of the building. Sensor T7 was initially positioned at the bottom of LCP glazed atrium until the 4th of August when the sensors in the LCP atrium fell down. The sensor was repositioned to the top of the LCP atrium on the 24th of August and stayed there for the duration of the measuring period. It can be related to the sensors in the normal glazed atrium and related to sensor T8 to find the thermal stratification. Sensor T8 was initially positioned at the top of LCP glazed atrium until the 4th of August when the sensors in that well fell down. During that period, 4th to 24th of August, this sensor was in a position to approximate the average temperature in the well. The sensor was then repositioned to the bottom of the LCP atrium for the duration of the measuring period. It can be related to the sensors in the normal glazed atrium and related to sensor T7 to find the thermal stratification. Experimentally, thermal stratification within a tall, narrow, enclosed space is defined as the difference between the maximum (highest point) and the minimum (lowest point) temperature. The goal of monitoring vertically orientated temperature sensors is to build up a database of field data that enables you to predict the stratification based upon other variables, see the analysis in Chapter 8.

152


Experiment

Data

Temperature data inside and outside the atrium wells were collected over a period of three months from 21/7/99 to 12/10/99. Over this period only 14 total clear sky days were recorded including 13 days when the atrium wells were not ventilated and one day in which the wells were ventilated. The ground temperature in Brisbane, one metre below the surface, is approximately 17° C and only varies by 2° C annually (BOM obtained). During July, no external temperatures were recorded because all the sensors were positioned within the building. During August, no LCP atrium temperatures were recorded due to equipment malfunction. Corrected (non-averaged) temperature data from within the atrium wells for 6 separate days including one intermediate sky on the 9/10; one overcast sky on the 22/8/99; and four clear skies on the 25/9, 22/7, 16/9, 14/8 are presented on the following pages. [Figure 7.36: Graph of atrium temperatures for an overcast sky on August 22nd]

T4 T5

Temperatures in atrium on 22/8/99

Temperature (degC)

35 30 25 20 15 10 0

5

10

15

20

Time (hr)

Due to the severely overcast sky conditions on the 22nd of August there was not a great difference in temperature readings between any of the top and bottom sensors, though a temperature difference can be seen overnight. The temperature sensors within the LCP atrium had been accidentally relocated on this date. 153


Experiment

[Figure 7.37: Graph of atrium temperatures under clear sky on July 22nd]


T3

T4

T5

T6

T7

T8

Temperature (degC)

60 50 40 30 20 10 0 0:00

2:24

4:48

7:12

9:36

12:00 14:24 16:48 19:12 21:36 0:00

Time (hr)

The 22nd of July was at the beginning of the monitoring period and was the first full clear sky day recorded. All six temperature sensors where positioned within the 2 model atrium wells. The temperatures within both wells were almost identical at corresponding positions except at mid morning and mid afternoon at the top positioned temperature sensors. This illustrates that when the maximum solar altitude (52°) is approximately perpendicular to the tilt of the pyramid shaped glazing (45°) and therefore the laser cuts are parallel with the incident radiation, that very little deflection of light occurs and therefore both model wells reach similar temperatures.

154


Experiment

[Figure 7.38: Graph of atrium temperature under clear sky on August 14th]

Temperatures in atrium on 14/8/99 Temperature (degC)

60

T3

T4

T5 aver

T6

50 40 30 20 10 0 0:00

4:48

9:36

14:24

19:12

0:00

Time (hr) The 14th August was also a very clear sky day but the sensors in the LCP well had accidentally relocated and only an average temperature in that well could be obtained. The top sensor in the plain glazed well shows a plateau effect across the middle of the day. The bottom sensor shows a peak in temperature in the middle of the day. The average temperature in the LCP well was only slightly higher than the minimum temperature in the plain glazed well.

155


Experiment

Temperature (degC)

[Figure 7.39: Graph of atrium temperatures on September 16th under clear sky]


T3

T4

60

T5

T6

T7

T8

50 40 30 20 10 0:00

4:48

9:36 14:24 Time (hr)

19:12

0:00

[Figure 7.40: Graph of atrium temperatures on September 25th under clear sky]

Temperatures in atriums on 25/9/99

T4

T5

T7

T8

Temperature (degC)

60 50 40 30 20 10 0:00

3:36

7:12

10:48

14:24

18:00

21:36

Time (hr)

The temperatures recorded on the 16th and the 25th of September clearly show the difference between the two systems. The spikes and the troughs in T7 show the LCP effect on both of these days. It also shows that the temperature at the top of the wells is higher in the middle of the day in the plain glazed well and higher in the morning and afternoon in the LCP glazed well.

156


Experiment

The bottom temperature sensors also show a marked difference between the two systems with the plain glazed well temperature peaking sharper and higher than in the other well. [Figure 7.41: Graph of atrium temperatures on October 9th under clear sky]

Temperature (degC)

Temperatures in atrium on 9/10/99 60

T3 T5 T7

T4 T6 T8

50 40 30 20 10 0:00

4:48

9:36 14:24 Time (hr)

19:12

0:00

The graph of the atrium temperatures on the 9th of October shows a much more jagged temperature response which indicates that it was not as clear on this day compared to the other shown days. Between 9 am and 10 am it was completely overcast which can be seen by all the temperatures coinciding and also seen in the irradiance graphs.

157


Experiment

7.7.1 Average Field Temperature Analysis

The raw field data recorded at the test site presented above was sampled at 30 second intervals. This data was then averaged over hour intervals to allow validation of the thermal simulation program and to create input data for the external temperature in the thermal program. The hourly averaged data gives a much smoother temperature distribution across the course of a clear sky day than the raw data. [Figure 7.42: Graph of hourly averaged field data for clear sky day on 22/7/99]

Hourly Averaged Temperatures on 22/7/99 Temperature (degC)

60

t3

t4

t5

t6

t7

t8

50 40 30 20 10 0 0

4

8

12

16

20

Time (hr) [Figure 7.43: Graph of hourly averaged field data for clear sky day on 25/9/99]

Hourly Averaged Temperatures on 25/9/99

T3 T5 T7

T4 T6 T8

Temperature (degC)

60 50 40 30 20 10

0

4

8 Time12(hr) 16

20

158


Experiment

[Figure 7.44: Graph of hourly averaged field data for clear sky day on 16/9/99]

T4 T6 T8

Temperature (degC)

Hourly Averaged Temperatures T3 T5 on 16/9/99 T7 60 50 40 30 20 10 0 4 8 12 16 20 Time (hr)

[Figure 7.45: Graph of hourly averaged field data for clear sky day on 9/10/99]

Temperature (degC)

60

t3 t5 t7

Hourly Averaged Temperature on 9/10/99

t4 t6 t8

50 40 30 20 10 0

2

4

6

8

10

12

14

16

18

20

22

Time (hr)

159


Experiment

The hourly averaged data does not show as clearly as the raw data the various changes (spikes) across the day with respect to the amount of light that is redirected through the glazing. Generally, the temperature data from the sensors positioned within the atrium wells shows a steady increase in the morning; a plateau during the middle of the day and a rapid drop off in the afternoon. The bottom temperature sensor in the plain glazed atrium (T5) shows a lot more peaked temperature response at midday then the bottom sensor in the LCP glazed atrium (T8). The top temperature sensor in the LCP glazed atrium (T7) is generally lower in the middle of the day. The external temperature sensor, T3, was unfortunately placed in a position where it was exposed to direct sunshine for a period of time each day and therefore gave a peak in temperature in the morning around 9 am. This peak due to direct radiation gain was less significant when averaged over the whole hour. The temperature sensor, T6, was repositioned at the start of August to a place within the test site room, which surrounded the atrium model wells. The room was considerably insulated and therefore a time lag occurred before the maximum temperature was reached which was around two hours after the other sensors reached their peaks. The temperature sensors at the start of the monitoring period were all located within the atrium wells and so the temperature graph from the 22nd of July does not have room or external temperature data. Due to the winter solar elevation, there is not a lot of difference between the two model wells on this date. The measured temperatures on the 16th and 25th of September show the clearest differences in the thermal response of both atrium wells. Each graph shows a dip in the temperature around midday at the top of the LCP atrium well. This is due to the redirecting effect of the glazing. These well defined thermal responses indicate clear sky distributions, which are confirmed from figures 7.30 and 7.28. The cloud cover on the morning of the 9/10 can still be seen to effect the internal temperature at the top of both atrium wells but to a less extent then seen in the raw data.

160


Experiment

The difference in thermal performance between the two atrium model wells from the temperature graphs across the day is not obvious. Instead, thermal stratification and sensor position comparisons can be made that display the differences between the systems more clearly. This data will be presented in Chapter 8. 7.7.2 Validation of Temperature data [Figure 7.46: Graph of TRY temperature compared to measured temperatures for 14/8/99]

Measured and Reference Outside Temperature Validation 21

TRY temp Field temp

Temperature (deg C)

19 17 15 13 11 9 7 0

2

4

6

8 10 12 14 16 18 20 22 Time (hr)

Test reference year data was used to compare with field data collected. A comparison was made earlier for the direct normal irradiance between the 14th of August 1999 and the 19th of August 1986 because of the similar dates and cloud cover on those days. A similar comparison is made here for the outside ambient temperature. It shows a very good correlation between the two sets of data across the day. Over night, however, something causes a rise in measured temperatures at 9pm and 4am. The reference outside temperatures and direct normal irradiance for certain clear sky days across the year are presented in the appendix.

161


Experiment

7.8 Ventilation Measurements

The thermal performance of the model is greatly affected by the air circulation and ventilation to outside areas. All ventilation was blocked off from inside the test room and the atrium wells for the most of the monitoring period. In the last two weeks, the ventilation grid around the edge of each aperture was uncovered and a small inlet hole cut in the bottom of each atrium on the 29/9/99. This resulted in only obtaining 2 weeks (29/9 - 12/10) of ventilated data of which only one clear sky day occurred on the 10/10 and an almost clear day occurred on the 9/10. The air flow rate was measured using a plastic bag and a stop watch on the 7th and 12th of October. Both of these days were considered to have intermediate sky clearness conditions with patches of clear weather and patches of cloudy weather. The rate at which the air was sucked out of the bag when placed over the inlet hole in the bottom of the atrium well was recorded and related to the volume of the bag and the volume of the well. Two situations were measured, (1) when the door to the building was open which it only was when the room was occupied, and (2) when the door was closed which it was most of the time. The number of air changes per hour (ac/hr) was calculated for both these scenarios. Volume of air in bag = 0.3 m x 0.4 m x 0.5 m = 0.06 m2 Volume of air in atrium well = 0.8 m x 0.8 m x 3.0 m = 1.92 m2 Density of air = 1.2 kg/m3 Weight of air in bag = 0.06 m2 x 1.2 kg/m3 = 0.072 kg Weight of air in atria = 1.92 m2 x 1.2 kg/m3 = 2.304 kg Unit of flow rate = kg/second or air changes/hour

162


Experiment

Door open so unimpeded air flow rate Rate of air sucked out of bag into atria = 30 sec (sunny), 60 sec (cloudy) Flow rate of bag Sunny flow rate = 0.072 / 30 = 2.4 x10-3 kg/sec Cloudy flow rate = 0.072 / 60 = 1.2 x10-3 kg/sec A complete air change of the atrium well means that 2.3 kg of air is vented out. Sunny conditions: 2.3/2.4x10-3 = 960 sec = 16 minutes ≈ 4 ac/hr Cloudy conditions: 2.3/1.2x10-3 = 1917 sec = 32 minutes ≈ 2 ac/hr Door closed so impeded air flow rate - normal condition Rate of air sucked out of bag into atria = 120 seconds Flow rate of bag = 0.072 / 120 = 6 x 10-4 kg/sec A complete air change of the atrium well means that 2.3 kg of air is vented out. 2.3/ 6 x 10-4 = 3833 sec = 64 minutes ≈ 1 ac/hr When the door was open an unimpeded air flow rate was calculated. This rate of air sucked out of bag into atria was equal to 30 seconds in sunny sky conditions and 1 minute in cloudy sky conditions. When the door was closed an impeded air flow rate was calculated. This was the normal condition of the test site and such the rate of air sucked out of bag into atria was equal to 2 minutes. One air change per hour is a fairly low ventilation rate but it is a lot greater than no air changes per hour, which was the condition within the model wells during the majority of the monitoring period. This change in ventilation did have a noticeable effect upon the temperatures within the atrium wells. Upon the 9th and 10th of October which were the only clear sky days during the ventilated set up the bottom temperature sensors were found to be 1-2°C cooler during the middle of the day compared to those recorded on the 25th of September. The top temperature sensors were also found to be 3-5°C cooler. This must be due to ventilation because the temperatures should increase towards the end of the year (summer).

163


Analysis

Chapter 8: DATA ANALYSIS

This chapter illustrates through computer simulation and field results how the laser cut panel glazing modifies the thermal and daylighting performance of an atrium and its adjoining spaces in a sub tropical climate. The field data included in this chapter was collected at the daylighting research test site at Brisbane Airport and is detailed and described in Chapter 7. The computer simulation data included in this chapter was obtained from programs created by the author in Matlab and are detailed and described in Chapter 5 (daylighting), Chapter 6 (Thermal) and the appendix (program code). Included in this chapter is the simulated comparison between the LCP and the clear glazing across a clear sky day upon an atrium well. The relationship between daylight factor and well index under overcast sky conditions is also investigated for both types of glazing. The light level in an adjoining room to an atrium well at the bottom of the well is also investigated for all possible glazing combinations using both clear and LCP glazing. Also in this chapter is an analysis of the collected field temperature data to find a comparison in the temperature difference and thermal gradient. Rounding out this chapter is the predicted temperature measurements using the simulation program shows the comparison between the two glazed systems in summer and winter.

164


Analysis

8.1 Daylight Modification Analysis 8.1.1 Daylight Well Simulation Analysis

Clear Sky Analysis The effect of placing LCPs on top of an atrium well under tropical clear skies is to reduce the penetration of high altitude direct solar gain and to improve the low altitude gain. The first computer simulation of the atrium wells shows the effect upon light levels for two seasons with two different geometrical ratios across the course of a clear sky day with LCP or clear glazing. Figure 8.01 shows the simulation geometry.

LCP glazed atrium well WI=2.0

LCP glazed atrium well WI=3.75

[Figure 8.01: Diagram of atrium well size and glazing types]

Plain glazed atrium well WI=2.0

Plain glazed atrium well WI=3.75

165


Analysis

This data is from a three dimensional simulated well across a clear sky summer and winter day with LCP glazing and two different geometrical ratios. [Table 8.01: Illuminance comparison in a 3D well between 2 season with LCP glazing]

Time (hr) 7 8 9 10 11 12 1 2 3 4 5

Summer WI=2 Summer WI=3.75 Winter WI=2 Winter WI=3.75 (Lux) (Lux) (Lux) (Lux) 19234 4036 8561 4263 13735 4712 20997 12303 6960 2457 21159 5954 12687 3073 15990 1837 5598 2779 16610 1342 1918 1708 4856 1055 7867 2550 10850 1297 13648 4650 20444 3666 18322 2308 30040 7011 21955 1366 12513 9850 20240 5912 7772 5823

[Figure 8.02: Graph comparing between 2 glazing types in summer in a 3D well (WI=3.75)]

Plain summer LCP summer

Comparison between plain and LCP glazing in well (3.75) over a clear sky day in summer

Illuminance (lux)

20000 15000 10000 5000 0 7

9

11

13

15

17

Time (hr)

The four graphs in figure 8.02 to 8.05 shows the same seasonal and glazing comparison for different well indices. The deeper well (WI=3.75) in figures 8.02 and 8.03 shows a lower light level for all glazing and seasonal variations compared to the shallower well (WI=2.0) in figures 8.04 and 8.05.

166


Analysis

[Figure 8.03: Graph comparing 2 glazing types in winter in a 3D well (WI=3.75)] Comparison between plain and LCP glazing in well (3.75) over a clear sky day in winter

Plain winter LCP winter

Illuminance (lux)

20000 15000 10000 5000 0 7

9

11

13

15

17

Time (hr)

This data is from a three dimensional simulated well across a clear sky summer and winter day with normal glazing and two different geometrical ratios. [Table 8.02: Illuminance comparison in a 3D well between 2 season with normal glazing]

Time (hr) 7 8 9 10 11 12 1 2 3 4 5

Summer WI=2 Summer WI=3.75 Winter WI=2 Winter WI=3.75 (Lux) (Lux) (Lux) (Lux) 6041 636 975 330 9006 411 1554 467 20381 2309 2608 689 24610 3915 6899 1433 77172 8621 10791 1665 77739 20088 7315 4102 54222 9122 6167 4395 38376 2776 6767 2126 113120 3912 4962 1085 3883 2062 4358 674 1854 621 1694 315

167


Analysis

[Figure 8.04: Graph comparing 2 glazing types in summer in a 3D well (WI=2.0)]

Illum inance (lux)

Comparison between plain and LCP glazing in well (2.0) over a clear sky day in summer

Plain summer LCP summer

80000 70000 60000 50000 40000 30000 20000 10000 0 7

9

11

13

15

17

Time (hr)

[Figure 8.05: Graph comparing 2 glazing types in winter in a 3D well (WI=2.0)]

Plain winter

Illum inance (lux)

Comparison between plain and LCP glazing in well (2.0) over a clear sky day in winter

LCP winter

80000 70000 60000 50000 40000 30000 20000 10000 0 7

9

11

13

15

17

Time (hr)

The effect of the LCPs is clearly seen in these simulated results. The graphs show a major peak in the middle of the day in mid summer under clear glazing (figure 8.02, 8.04). The LCP glazing does not allow a peak in illuminance in the middle of the day because the high altitude direct solar gain is rejected. The illuminance under the LCP glazing is at a fairly constant level across the course of the whole day compared to the illuminance under the plain glazing.

168


Analysis

In the morning and afternoon when the solar altitude is low there is an increase in illuminance at the bottom of the LCP well due to the redirecting effect. This effect is more noticeable in winter but also occurs in summer (figure 8.03, 8.04). In winter, the inclusion of LCPs does not change the light level in the middle of the day compared to the light level in the clear glazed well (figure 8.03, 8.05). This is due to the fact that the tilt of the panels is perpendicular to the solar altitude and so little deflection of incident light occurs. The light level in the bottom of the well of index 3.75 in mid winter with clear glazing shows that it is at the lowest level of the four situations presented (figure 8.03). The light level does increase slightly around the middle of the day. Overcast Sky Analysis The next analysis of the modification of the light level due to the glazing was made with the three dimensional simulation of wells under overcast skies with varying well index. [Table 8.03: Relationship between Horizontal daylight factor and well index in 3D]

Length/Width (cm) 80 80 80 80 80 80 80 80 80 80

Height (cm) 8 40 80 120 160 200 240 280 300 320

WI 0.1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 3.75 4.0

Clear Glaze Lux 24241 17978 10309 6281 4179 2720 2254 1714 1456 1513

Clear Glaze DF% 99 74 42 26 17 11 9 7 6 6

LCP Glaze Lux 23323 15430 7590 4139 2633 1624 1243 834 737 634

LCP Glaze DF% 95 63 31 17 11 7 5 3 3 3

The simulation showing the relationship between the daylight factor (DF%) and the well index (WI) was validated with the comparison in section 5.5.3. This analysis investigates this relationship between the clear glazing and the LCP glazing.

169


Analysis

[Figure 8.06: Graph of relationship between Horizontal daylight factor and well index for both

LCP DF% clear DF%

Relationship between Daylight Factor and Well Index for both glazings Daylight Factor %

100

80 60 40 20 0 0

1

2 Well Index

3

4

glazings]

The horizontal global illuminance was set at 24400 lux in the simulation program. The light level and the daylight factors listed in the table show that when the well is very shallow the light level is almost equal to the horizontal global illuminance and therefore the daylight factor is almost 100%. Both glazings produce decaying daylight factors with respect to increasing well index. This is due to the decrease in the angular view of the sky from the bottom of the well and an increase in internal reflections. The drop off in light level from WI=0.1 to WI=1 is the most dramatic. When the daylight factor is less than 10% in the bottom of the wells, it is considered to be inadequate. A polynomial regression function can be fitted to the relationship between daylight factor and well index as was listed in the literature review (Chapter 3 p.28). The best polynomial found was that produced by Liu et.al. (1991) DF% = 103.56 - 121.09x + 64.203x2 - 17.61x3 + 2.3934x4 - 0.12676x5 (Liu no glaze) This can be compared to the polynomials produced from data from figure 8.06 for both clear and LCP glazing. DF% = 106.35 - 66.972x - 11.676x2 + 22.324x3 - 6.851x4 + 0.6639x5 (3D sim clear glaze) DF% = 105.74 - 101.88x + 26.168x2 + 5.818x3 - 3.542x4 + 0.4106x5 (3D sim LCP glaze)

170


Analysis

The clear glazing allows unrestricted penetration of light from the whole overcast hemisphere. The LCP glazing however, rejects the light rays from high elevation angles, thereby eliminating light penetration from the brightest part of the overcast sky. The LCP glazing system also reduces the intensity of the light rays due to the added layer of glazing. The investigation leads to the theory that a LCP glazed atrium roof would be inappropriate for buildings with deep wells under skies, which were predominantly overcast. 8.1.2 Daylight Adjoining Room to Well Simulation Analysis

The light level in an adjoining room to a well is greatly affected by the amount of direct light falling upon the adjoining rooms glazing, known as the sky component, which is subsequently affected by the angular view of the sky. In the 3D simulations the only adjoining room investigated was that at the bottom of the well because this is the area, which normally receives the least amount of natural illuminance. The simulation was based upon an experimental model set up where a tilted LCP was placed outside the window aperture of the adjoining room as well as the pyramid shaped LCP glazing upon the atrium well. Four different glazing system combinations were investigated. These are all described in figure 8.07 on the next page. 1. The plain glazed atrium well was combined with the plain glazed adjoining room. 2. The LCP glazed atrium well was combined with the plain glazed adjoining room. 3. The plain glazed atrium well was combined with the LCP glazed adjoining room. 4. The LCP glazed atrium well was combined with the LCP glazed adjoining room.

171


Analysis

Plain glazed atrium well and plain glazed adjoining room

[Figure 8.07: Diagram of atrium geometry and glazing type]

LCP glazed atrium well and plain glazed adjoining room

Plain glazed atrium well and LCP glazed adjoining room

LCP glazed atrium well and LCP glazed adjoining room

172


Analysis

The simulations showed a natural exponential decay in light level as the distance from the adjoining rooms window increased. In the three dimensional simulation of the atrium well the backward traced rays underwent a collimation effect as they were traced from the bottom of the well to the sky. Resulting in more rays exiting the top of the well at near zenith elevation angles. This resulted in higher light level within these atrium spaces then conventional spaces with side light windows whose light mainly comes from the horizon. The tilted adjoining rooms’ LCP glazing effected the path of the backward traced light rays by reducing the number of reflections that the rays underwent in the atrium well before reaching the sky. Therefore, the reduction in luminance intensity was reduced which gave higher light levels. A similar observation was deduced with the light levels in the adjoining room under overcast skies as was established in section 8.1.1 with light levels in the atrium well. The majority of light rays exit the atrium well at near zenith angles and are therefore redirected through the LCP towards the horizon. As the horizon is only one third as bright as the zenith under overcast skies, the illuminance obtained via this glazing selection provides lower light levels then if clear glazing was used under overcast sky conditions. A simulation of the adjoining space at the bottom of an atrium well was conducted with a clear sky distribution. The surfaces were of standard reflectivity and a window to the adjoining room was half the size of the rooms' wall. The well index was set at 2.0 and the illuminance was measured from a point directly in the middle of the room using 5000 rays for each illuminance measurement. The sky had a 10° diameter sun with a direct luminance of 3.4 Mcd/m2, while the sky had a diffuse luminance of 2.1 Kcd/m2. The illuminance was equated across a clear sky summer and winter day. Only two glazing system combinations were investigated in this simulation. The plain glazed atrium well combined with the plain glazed adjoining room was investigated. In addition, the LCP glazed atrium well combined with the LCP glazed adjoining room was also investigated. Both of these glazing combinations were simulated across a clear sky day in summer and winter so a comparison could be made.

173


Analysis

[Table 8.04: Comparison in a room adjoining well between LCP and plain glazing]

Time (hr)

Plain+Plain winter (lux)

LCP+LCP winter (lux)

Plain+Plain summer (lux)

7 8 9 10 11 12 1 2 3 4 5

33 35 37 44 34 33 33 37 34 36 34

418 512 518 400 414 442 522 598 420 458 444

33 36 38 44 34 34 33 37 34 36 34

LCP+LCP summer (lux) 394 429 562 420 430 413 375 442 408 402 485

The results from this simulation show that the light level in the adjoining room with the use of the LCPs is approximately ten times greater in summer and winter across the whole day than with the use of the plain clear glazing. The laser cut panels have the effect upon low elevation sky light where upon it redirects the light vertically down the well than the tilted laser cut panel on the adjoining room redirects this light on to the ceiling of the adjoining room. This results in the dramatic increase light level, which can be seen in the figure 8.08 below. [Figure 8.08: Graph of light level in adjoining room to well for 2 glazing in summer and winter] summer plain+plain

Light level in middle of adjoining room to atrium across clear sky day

winter plain+plain summer LCP+LCP

600

winter LCP+LCP

Illuminance (lux)

500 400 300 200 100 0 7

9

11

13

Time (hr)

15

17

174


Analysis

The light level in figure 8.08 achieved in the adjoining room with the use of plain glazing was found to be inadequate and additional artificial lighting would be required to achieve minimum standards. The light levels in the middle of the room was found to be fairly constant across the day because no direct light could reach this point and therefore the light level was less dependent upon the position of the sun. The next simulation was of an atrium well with adjoining room under clear sky conditions with all four glazing system combinations. The simulation was conducted at midday in summer and winter conditions at positions along the length of the adjoining room. The adjoining room had dimensions of 8x8x3 metres and the well was 16 metres tall. This produced a WI = 2.0. The surfaces were all of standard average reflectance. The atrium glazing was in the form of a pyramid with a 45° tilt and the adjoining room glazing was either clear glazed or 40° tilted LCP. Each illuminance measurement was the average of 5000 rays. The sky had a 10° diameter sun with a direct luminance of 3.4 Mcd/m2, while the sky had an indirect luminance of 3.4 Kcd/m2. [Table 8.05: Illuminances within adjoining room in summer with various glazing options]

Position (m) 1 2 3 4 5 6 7

Plain + Plain summer (lux) 356 170 87 54 40 35 28

LCP + LCP summer (lux) 800 892 760 594 589 474 460

LCP + Plain Summer (lux) 213 84 51 37 43 22 17

Plain + LCP Summer (lux) 539 548 507 445 391 310 277

175


Analysis

[Figure 8.09: Graph of glazing comparison in room adjoining atrium well in summer]

Glazing Comparison for light level in room adjoining atrium well (summer)

Illuminance (lux)

1000

Plain+Plain LCP+LCP LCP+Plain Plain+LCP

800 600 400 200 0 0

20 40 60 Position in room (m)

80

[Table 8.06: Illuminances within adjoining room in winter with various glazing options]

Position (m) 1 2 3 4 5 6 7

Plain + Plain LCP + LCP Winter (lux) Winter (lux) 313 861 128 1204 75 722 53 766 43 571 41 451 27 472

LCP + Plain Winter (lux) 320 145 99 68 41 35 26

Plain + LCP Winter (lux) 882 863 762 713 597 548 430

[Figure 8.10: Graph of glazing comparison in room adjoining atrium well in winter]

Glazing Comparison for light level in room adjoining atrium well (winter) 1400

Plain+Plain LCP+LCP LCP+Plain Plain+LCP

Illuminance (lux)

1200 1000 800 600 400 200 0 0

20 40 60 Position from window (m)

80

176


Analysis

The results show a distinctive difference in light level between the two glazing combinations that used the tilted LCP upon the adjoining room and the other two glazing combinations that only had clear glazing upon the adjoining room. The most important component in trying to improve the light level in adjoining rooms is to redirect the light that is coming vertically down the well up onto the ceiling of the adjoining room. These results produced by the ray tracing program clearly show that when the redirecting LCPs are installed upon the adjoining room that the light level is dramatically improved. In the summer simulation (figure 8.09) the glazing option that provided the highest light levels in the adjoining room at the bottom of the well was the double LCP system, followed by the tilted LCP outside the room with the clear well glazing. Next was the plain glazed option and the lowest light levels resulted from the use of the LCP well glazing combined with the clear room glazing. The light level at the front of the room was between two and four times higher compared to the clear glazed adjoining room and at least ten times higher at the back of the room. In the winter simulation (figure 8.10) the two glazing options with the tilted LCPs upon the adjoining room clearly produced greater illuminance levels than the plain glazed adjoining room systems. The light levels at the front of the room were 2.5 times higher compared to the clear glazed adjoining room and 15 times higher at the back of the room.

177


Analysis

8.2 Thermal Modification Analysis 8.2.1 Stratification Analysis

The stratification analysis discussed in this section is based upon field data taken over a three month period at the test site facility. Solar Panel R1

R2

Skylights T8

T6

T7

Sensors

T4 Foam Atrium Wells

T3

T5

3m

R1 = global irrad. R2 = diffuse irrad. T3 = normal mid T4 = normal top T5 = normal bot T6 = LCP mid T7 = LCP bot T8 = LCP top

[Figure 8.11: Diagram of test site with sensor locations before 24th August 1999]

The temperature difference between the top and bottom of the atrium wells is known as the thermal stratification. The stratification in both atrium wells is shown along with the comparison between corresponding positioned sensors in both atrium wells. Thermal stratification usually has an exponential increase in temperature with respect to height in the enclosed fluid. A greater temperature difference may mean that the heat is not reaching the bottom of the atrium well and instead is trapped at the top of the well. The thermal stratification plots in the following graph (figure 8.12) shows that a positive temperature difference means that the top sensor is at a higher temperature then the bottom sensor, (T8-T7) in the LCP atrium and (T4-T5) in the normal glazed atrium. The atrium temperature sensor comparison plots on the following graph shows that a positive temperature difference means that the normal clear glazed well is at a higher temperature then the LCP glazed well (T4-T8) at the top of the wells and (T5-T7) at the bottom of the wells.

178


Analysis

[Figure 8.12: Graph of hourly temperature comparison between atria and stratification on the

Temperature (degC)

22/7/99]

Hourly Atrium Temperature Comparison on 22/7/99

T4-T8

20

T8-T7

T5-T7 T4-T5

15 10 5 0 -5

0

4

8

12

16

20

Time (hr)

The first clear sky day analysed was on the 22nd of July (figure 8.12). The stratification comparison between the two atria shows that the temperature difference was less in the LCP glazed atrium in the morning and afternoon compared to the normal glazed atrium and at a similar level in both atria in the middle of the day. In winter, the vertical temperature difference in both model atrium wells over a distance of two meters is approximately 15 degrees Celsius under clear skies in the middle of the day with an open aperture of 0.64 square metres. The difference in thermal stratification between systems is as much as 5 degrees in the morning at 8 am and 7 degrees in the afternoon at 3 p.m. The atrium temperature sensor comparison for the top positioned sensors (T4-T8) shows that in the morning (7:30-9:30 am) and the afternoon (2:00-3:30 p.m.) the normal glazed atrium is hotter than the LCP glazed atrium. This corresponds to when the cuts are deflecting the direct sun light deep down into the atrium. The atrium temperature sensor comparison for the bottom positioned sensors (T5-T7) show that the bottom of the LCP atrium is hotter in the morning and afternoon, this also corresponds to the previously mentioned redirection of the direct light.

179


Analysis

Similar stratification levels and temperature comparisons were found in the middle of the day because the tilt angle of the panels was perpendicular to the incident direct sun rays. The slight difference in the middle of the day could be due to the LCP, which is positioned under an existing normal glazing cover and so results in a double glazed unit. [Figure 8.13: Test site with sensor locations after 24th August 1999] Solar Panel R1

R2

Skylights T7

T3 T4

Foam Atrium Wells

3m

T8

T6

T5

R1 = global irrad. R2 = diffuse irrad. T3 = outside T4 = normal top T5 = normal bot T6 = inside T7 = LCP top T8 = LCP bot

The thermal stratification plots in figure 8.14 and 8.15 show that a positive temperature difference means that the top sensor is at a higher temperature then the bottom sensor, (T7-T8) in the LCP atrium and (T4-T5) in the normal glazed atrium. The atrium temperature sensor comparison plots on the following graph shows that a positive temperature difference means that the normal clear glazed well is at a higher temperature then the LCP glazed well (T4-T7) at the top of the wells and (T5-T8) at the bottom of the wells.

180


Analysis

[Figure 8.14: Graph of temperature comparison between atria and stratification on the 16/9/99]

Hourly Atrium Temperature Comparison on 16/9/99 Temperature (degC)

16 12

T7-T8 T4-T5 T4-T7 T5-T8

8 4 0 -4 -8

0

4

8

12

16

20

Time (hr)

In figure 8.14, the atrium temperature analysis of the 16th of September clearly shows the temperature difference between the top and bottom sensors was greater in the LCP glazed atrium (T7-T8) than the normal glazed atrium (T4-T5) especially in the morning and afternoon. The atrium temperature sensor comparisons also show a negative temperature difference in the morning and afternoon which indicates that it is hotter in the LCP atrium at the top (T4-T7) and bottom (T5-T8) than the other atrium well. In the middle of the day, however, when the ambient temperature is at its peak and the solar elevation is the greatest, the stratification in both wells is similar. (T7-T8) and (T4-T5) are at a very similar level at 12pm and 1pm around the level of 12°C difference. The temperature difference between corresponding sensors in the middle of the day shows a positive rise, which means the temperatures in the normal glazed well was higher by 9°C at the bottom (T5-T8) and by a maximum of 6 °C at the top (T4-T7).

181


Analysis

[Figure 8.15: Graph of temperature comparison between atria and stratification on the 9/10/99]

T7-T8

Hourly Atrium Temperature Comparison on 9/10/99

T4-T5 T4-T7

Temperature (degC)

21

T5-T8

14 7 0 0

4

8

12

16

20

-7 Time (hr)

The atrium temperature comparison on the 9th of October corresponds with mid spring. The maximum solar altitude by this date had reached 68°. There was not a lot of difference in the stratification between the two model wells (T7-T8) and (T4-T5). Both wells reaching a peak in the morning at 8 am and in the afternoon at 2 p.m. The corresponding sensor comparison, (T4-T7) and (T5-T8), still shows that in the middle of the day it was cooler in the LCP glazed well by up to 8 °C. However, in the morning (2 °C) and afternoon (6 °C) it was slightly cooler in the normal glazed well. 8.2.2 Thermal Gradient

The thermal gradient is another factor that could be analysed from the field data to determine if the modified glazing was improving the thermal performance of the atrium well. The thermal gradient within the atrium wells was investigated for the initial month of monitoring because at this time there were three temperature sensors in each well (figure 8.11). After this period, one sensor from each well was moved to obtain the room and external temperatures (figure 8.13). The thermal gradient was analysed for the 22nd of July.

182


Analysis

[Figure 8.16: Graph of temperature gradient at 3 heights in normal glazed atrium on 22/7] Temperature gradient in normal atrium on 22/7/99 Temperature (degC)

60 50 40

8 am

30

12 pm

20

3 pm

10 0 0

0.5

1 1.5 2 2.5 Height in atrium (m)

3

3.5

[Figure 8.17: Graph of temperature gradient at 3 heights in LCP glazed atrium on 22/7] Temperature gradient in LCP atrium on 22/7/99

Temperature (degC)

60 50 40

8 am

30

12 pm

20

3 pm

10 0 0

0.5

1 1.5 2 2.5 Height in atrium (m)

3

3.5

The graph shows that the temperature gradient (slope of the line) in the top (2m-3m) of the normal glazed atrium (figure 8.16), is greater than in the bottom (1m-2m) of the atrium well. The slope of the lines are very similar at each of the three times across the day. This indicates a stable stratified environment across the day, which is due to the sun’s elevation not changing greatly across this period. In the LCP glazed atrium (figure 8.17), the temperature gradient is similar in the middle of the day (12 p.m.) for winter to the normal glazed atrium. This is due to the near normal incidence of direct light upon the LCP, which results in little deflection of the incident rays. In the morning and afternoon, there is no increase in gradient at the top of the well. This indicates that the temperature increase is linear with height within the well instead of being greater at the top of the well. This shows an improved thermal performance with the inclusion of the LCP glazing modification.

183


Analysis

8.2.3 Stratification Data Regression

Multiple linear regression method was applied to field temperature difference (Tdiff) data to enable a prediction of the stratification with respect to other environmental parameters (Jones et.al. 1991). The temperature difference within the normal glazed model under clear sky days was used. Given this set of field data, this approach fits a least squares line through the data. The independent parameters considered in this analysis are outside temperature, global solar radiation, and solar zenith angle. Equations for five of these clear sky days between August and October 1999 are presented below for the normal atrium. [Table 8.07: Temperature difference equation produced from field data]

Where :

Date

Temperature Difference Equations

10/08/99

-2.9377 + 0.0182X1 + 0.0294X2 + 0.0150X3

14/08/99

-1.5552 - 0.0457X1 + 0.0288X2 + 0.0103X3

20/08/99

-5.7000 + 0.0610X1 + 0.0270X2 + 0.0170X3

16/09/99

-3.6904 + 0.1727X1 + 0.0141X2 + 0.0044X3

10/10/99

-7.5206 + 0.5115X1 + 0.0069X2 + 0.0006X3

X1

=

outdoor air temperature (° C)

X2

=

global solar irradiance (W/m2)

X3

=

solar zenith angle (degrees from zenith)

Observations made about these equations show that for the clear sky days in August the coefficients for the variables X2 and X3 appear reasonable constant, whereas the coefficient for X1 and the constant seems to vary considerable. The coefficient for X1 on the 14/8 was the only day that it was found to be negative. The constants on all days were found to be negative. Finally, the coefficients corresponding to X2 and X3 in September and October seem very small compared to those in August. This shows that one equation alone can not be used to predict the temperature difference within a structure for the whole year. Instead, a number of equations must be used and applied to different times of the year. A comparison was shown between the linear regression equation and the data for the 10/8 and is shown in figure 8.18 below.

184


Analysis

[Figure 8.18: Graph of stratification equation comparison to hourly averaged field data]

Temperature Difference (degC)

Comparison between formulated and experimental stratification in normal glazed atrium well for 10/8/99 20

Tdiff T4-T5

15 10 5 0 -5

0

5

10

15

20

Time (hr) 8.2.4 Simulated atrium model Temperature Predictions

The thermal simulation program (Chapter 6) included test reference year external temperature data for one clear sky day each month for the whole year. This data was used so that a direct comparison could be made between the two glazed atrium systems (clear versus LCP) for any month across the whole year. The simulations were set up to represent the model atriums at the test site (see section 7.4 for description) and to predict the thermal comparison between the two systems at any time of the year. [Table 8.08: Simulated temperatures across the whole day comparing 2 glazing options in 2 seasons]

Time (hr) 7 8 9 10 11 12 1 2 3 4 5

Plain Atrium Summer (°C) 44.0 53.0 60.5 66.0 69.0 69.5 68.0 63.5 57.0 48.5 39.0

Plain Atrium Winter (°C) 16.5 29.5 36.5 42.0 45.5 46.5 44.5 40.5 34.0 27.0 16.0

LCP Atrium Summer (°C) 45.0 53.0 55.0 56.0 49.0 44.0 54.5 56.0 54.5 50.0 40.0

LCP Atrium Winter (°C) 26.0 33.0 39.5 45.5 48.5 49.0 47.5 43.5 37.0 31.5 16.0

185


Analysis

[Figure 8.19: Matlab screen graph of predicted atrium comparison in summer]

[Figure 8.20: Matlab screen graph of predicted atrium comparison in winter]

186


Analysis

The first simulation looked at the thermal comparison between both glazed systems across a clear sky summer and winter day. The domed shape of the predicted temperature distribution curve for the normal glazed atrium is clearly apparent in both the summer and winter simulations though the maximum temperature reached is approximately 20 °C different between summer and winter. The predicted temperature profile for the LCP glazed atrium is vastly different between summer and winter due to its angular selective nature. In winter when the solar elevation is parallel with the angle of the cuts then there is little difference in the temperature comparison between the two systems. In summer, however, a large dip in temperature can be seen in the middle of the day when the solar elevation reaches a maximum of 85°. As the solar elevation increases to an angle near that of the zenith, an increasing amount of direct radiation is redirected out of the system. With less radiation gain, the temperature in fact decreases (see figure 1.01). In spring and autumn, a plateau effect in observed in the predicted temperature in the LCP glazed atrium in the middle of the day. This midday temperature dips in summer [Table 8.09: Atrium temperature comparison across year at 12pm]

Month 1 2 3 4 5 6 7 8 9 10 11 12

Normal Atrium Temperature LCP Atrium Temperature At midday (deg C) At midday (deg C) 70.0 44.5 68.5 50.5 65.0 55.0 59.5 54.0 53.0 52.0 46.5 49.0 48.0 49.5 53.0 51.0 60.0 53.0 66.0 52.5 65.5 45.5 69.5 44.0

The thermal simulation program was also run for every month of the year at mid day in both atriums. It shows that at the middle of the year when the maximum solar altitude is approximately 42° which is similar to the tilt angle of the cuts in the LCP so only a small amount of incident light is deflected. This results in only a small temperature difference.

187


Analysis

From September to April however, a major difference between the two differently glazed atriums can be noticed. A maximum difference occurs in December and January of 25.5°C, which corresponds to the maximum solar altitude and therefore the maximum amount of incident irradiance deflected. [Figure 8.21: Graph of simulated atrium temperature comparison across the year at midday]

Simulated Atrium Comparison at 12pm across year

Norm 12pm LCP 12pm

Temperature (degC)

70 60 50 40 1

3

5

7

Month

9

11

These results tend to overestimate the temperature in the model by about five degrees Celsius but the trends are accurate. The stratification does not show a consistent significant difference between the two atrium systems. This is most likely due to the size of the model. Some differences however, are noticeable and can be contributed towards the LCP modified glazing. The atrium temperature sensor comparison (figures 8.12,14,15) does show a significant difference between the two systems. This comparison between the temperature in the LCP and normal glazed well shows an increasing difference between the two atria towards the end of the year when the greatest solar elevation occurs (figure 8.19, 20). The LCP glazed well produces illuminance and thermal conditions, which in fact dip during the middle of the day when the external environmental light and temperature conditions are reaching a maximum. This reduces these environmental factors at times when they are in excess and thereby produces a more comfortable internal climate.

188


Conclusion

Chapter 9: CONCLUSION 9.1 Conclusion

The research aimed to show that by modifying the glazing with the inclusion of laser cut panels (LCPs), that there could be an improvement in the overall thermal and daylighting performance of atrium wells and their respective adjoining spaces. Achieving this would reduce the energy load of the building whilst maintaining occupancy comfort. The simulation analysis and collected field data were able to determine that the laser cut panels are a superior glazing option compared to clear glazing. The LCPs did improve the temperature and light level in atrium wells and their adjoining spaces in a sub tropical climate at certain times of the year under certain sky conditions. The light level was improved under clear sky conditions in both the LCP well and adjoining spaces by being at a higher level and at a steadier level across the day. The temperature in the LCP glazed well compared to the clear glazed well was found to be lower in the middle of the day but higher in the afternoon and morning. It was also found to be at a similar level in winter and dramatically lower in summer. This research accomplished its objectives in several areas both experimentally and theoretically. The computer simulation algorithms were produced and successfully validated with respect to the experimental field data. Simulations The daylight simulation program, described in Chapter 5, achieved a level of accuracy when validated with field data that was above expectation. The program still produces noisy results with a significant uncertainty if a low number of rays are included in the simulation. The program accurately simulated the effect that LCPs have upon the resultant daylight penetration into spaces such as atrium wells, side lit rooms and adjoining spaces to atrium wells. It was able to find the illuminance level at any point upon the working surface of the building type investigated. The program showed that the illuminance level within the buildings was increased but that the light level still dropped off exponentially with respect to distance from the aperture. 189


Conclusion

The light level within the well and adjoining room across the day and year was investigated. An analysis under overcast sky conditions of the relationship between daylight factor and well index showed that a shallow well has greater illuminance level at the bottom as expected. It also showed that the clear glazed well resulted in illuminance at a greater level compared to the LCP glazed well. Under clear skies, the LCP glazing eliminated the excessive peak in illuminance in the middle of the day in summer. The thermal simulation program, described in Chapter 6, was a simple thermal heat transfer algorithm to find the resultant temperature within the model atrium well located at the test site. This program was written to find the temperature within the well in mid summer because the damage to the test site prevented physical monitoring. The program was validated (Section 6.4) with the collected field data from both the clear and LCP glazed model wells and compared better to the field data than did the commercial Capsol simulation program. The temperature within the well across the day and year was also investigated to show the effect of the LCP glazing under clear sky conditions. In summer, the effect was quite dramatic with a significantly lower temperature in the middle of the day in the LCP glazed well. In winter the temperature was shown to be slightly greater in the LCP glazed well which is also an advantage. Experiment The experiment was successful considering the length of the collection period. The data shows that the light levels in the building with the modified glazing were not always greater. In overcast sky conditions, the modification actually results in lower light levels in the atrium well and the adjoining space. Even under clear sky conditions little difference in light level could be detected due to near normal incident direct solar irradiance, which occur in the morning and afternoon and in winter at midday. The temperature within the LCP glazed well was found to be lower than the clear glazed model atrium well but at times in the morning and afternoon the temperatures within the LCP glazed well were higher. Thermal stratification was shown to be in existence in tropical model atriums but the results did not show a clear reduction in stratification with the inclusion of laser cut light redirecting panels. 190


Conclusion

In winter, the stratification was greater in the clear glazed well but in spring, the LCP glazed well had greater stratification. The difference in stratification between the systems was not significant and could be due to either the LCP glazing acting as a double glazed unit or the light redirecting effect. The small size of the models could have also contributed to the variation in stratification with respect to the time of the day and year. The temperature difference over a vertical distance of 2 meters was on average in the middle of the day approximately 15 degrees Celsius under clear skies with a LCP glazed aperture of 0.64 square metres. The effect that the ventilation made upon the temperature and thermal stratification was also impossible to conclude upon due to the severely limited amount of experimental data. The effect of ventilation on stratification and seasonable changes is yet to be fully investigated. Analysis Atrium buildings in sub tropical climates suffer from overheating and with the use of LCP glazing the internal temperature and overheating of the atrium well space can be reduced at times when the sun is at its greatest altitude which is when the reduction is needed most. Thermal stratification within atrium wells is difficult to reduce by mechanical air conditioning and so a reduction by passive means in the temperature difference with respect to height within an atrium well would reduce the electrical load upon the air conditioning system and therefore lower the cost of the electricity. The use of simulation programs in this project has been highly beneficial due to the inconsistent nature of the environment and weather making actual measurements difficult. Simulation programs can not generally give you absolute data applicable to the real world. However, they are very useful when comparing similar systems and can give meaningful data as to which is the better system. Atrium spaces are transient and relaxed meeting spaces which can be regarded as visually comfortable over a wide range of illuminance levels. Improved illuminance in the morning and afternoon can result in less reliance upon artificial lighting at the start and end of the day.

191


Conclusion

The redirecting of light upon the ceiling of the adjoining spaces to atrium wells is vital for the increased penetration of natural illuminance and the reduction in artificial light usage. 9.2 Future Work

1/ Improvement and generalisation of the theoretical computer simulations to enable them to be easily modified and applicable to a wider range of building and sky types. This must be conducted and run on computers with fast processors to enable the programs to give results in reasonable amounts of time. 2/ The use of professional computer simulation programs such as Adeline (Radiance) to simulate the daylight penetration with LCP modification. This will allow realistic images of how the LCPs improve the light level to be produced. Thermal simulation programs such as TRANSYS or computational fluid dynamic programs need to be used to enable the prediction of the complex thermal stratification that occurs within atrium wells and how the LCPs modify this effect. 3/ Monitoring of a full scale atrium building of the natural light levels and temperature that has been modified by LCPs must be conducted. An office building in Herschel Street, Brisbane had a retrofit in 1999, which included the installation of laser cut panels in the glazing of a central atrium well. No monitoring has been conducted within this building to date. [Figure 9.01: LCP glazed atrium well in office building in Herschel Street, Brisbane]

192


Appendix

APPENDICES

The appendices in this research include the computer simulation source codes; Daylight penetration theory; Daylight model experimental data; Test Reference Year (TRY) data and finally a glossary. A.1 Two Dimensional Daylight Simulation Program Code The 2 dimensional daylight simulation programs include: Roomt6.bas – rectangular room with LCP glazing Room100.bas – rectangular room with clear glazing Well26.bas – atrium well with tilted LCP glazing Well30.bas – atrium well with tilted clear glazing Atrium67.bas – combination of Well30 and Room100 Atrium61.bas – combination of Well26 and Roomt6 Atrium63.bas - combination of Well26 and Room100 Atrium64.bas - combination of Well30 and Roomt6 Only Atrium 64 will be presented below. Atrium64.bas – LCP glazed atrium well combined with LCP glazed adjoining room CLS SCREEN 0 OPEN "atrium64.txt" FOR OUTPUT AS #1 CONST PI = 3.141592654# CONST RAD = PI / 180 CONST nf = 1.52 'refractive index CONST CA = 26.5 'critical angle of tot intern refl due to D/W ratio y=0 COLOR 10 PRINT "" PRINT "" PRINT "Daylight Simulation in an Atrium" PRINT "2D DSA by John Mabb October 1998" COLOR 15 PRINT "" PRINT "" PRINT "This program simulates diffuse reflections in an atrium onto a working" PRINT "plane in adjoining room from a CIE overcast sky. All rays are displayed and DF values stated" PRINT "LCP skydome on roof with transmitted and deflected rays simultaneously" PRINT "tilted LCP on adjoining room; north to left of screen" PRINT "Press any key to continue" 'DO 'LOOP UNTIL INKEY$ "" CLS sun = 20 ray = 500 sky = 2 IF sky = 2 THEN hgi = 35000 'horizontal global illuminance in lux lz = 450 ELSEIF sky = 3 THEN hgi = 70000 'with direct sun clear sky lz = 50 ELSE sky = 1 hgi = 5400 'HGI without sun clear sky

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lz = 75 END IF FOR j = 1 TO 9 CLS SCREEN 12 FOR shift = 1 TO 15 'moves the position the results are printed out on the screen PRINT " " NEXT PRINT "j="; j x1 = 360 x2 = 480 x3 = 240 y10 = 175 y20 = 420 y40 = y10 - (x1 - x3) / 2 'y5 = 10 x5 = x3 + (x1 - x3) / 2 LINE (x1, y10)-(x5, y40), 14 '45 degree LCP in yellow LINE (x3, y10)-(x5, y40), 14 ' " " LINE (x5, y10)-(x5, y40), 14 'vertical roof divide LINE (x1, y20)-(x3, y20), 4 'ground/bottom of atrium too = 385 bo = 420 'top 175 = y10 m=0 s=1 kk% = 8 FOR lv = 1 TO 7 kk% = kk% + 1 COLOR kk% top(lv) = too - m bot(lv) = bo - m m = 35 * lv 'rooms on the right iy = bot(lv) - ((bot(lv) - top(lv)) / 4) win = bot(lv) - ((bot(lv) - top(lv)) / 2) LINE (x1, top(lv))-(x2, top(lv)), 10 LINE (x2, top(lv))-(x2, bot(lv)), 10 LINE (x2, bot(lv))-(x1, bot(lv)), 10 LINE (x1, bot(lv))-(x1, win), 10 LINE (x3, bot(lv))-(x3, top(lv)), 10 x4 = x1 - (bot(lv) - top(lv)) / 2 LINE (x4, win)-(x1, top(lv)), 12 '45 degree tilted LCP window REDIM sum(20) REDIM n(20) REDIM aver(20) FOR zz = 1 TO ray COLOR kk% nwall = 0 angle = 0 lo = 0 reff = 1 ref = 1 y1 = top(lv) y2 = bot(lv) y3 = win

'number of rays

ix = x1 + ((j / 10) * (x2 - x1)) px = ix

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py = iy DO RANDOMIZE TIMER IF nwall = 0 THEN 'ray from starting pt ref = 1 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 k = angle slope = TAN(angle * RAD) y = y1 x = (ABS(y - py) + (px * slope)) / slope nwall = 1 IF x > x2 THEN x = x2 y = ABS((slope * (px - x)) + py) nwall = 2 ELSEIF x < x1 THEN x = x1 y = ABS((slope * (px - x)) + py) IF y > y3 THEN nwall = 4 ELSE nwall = 5 END IF ELSE END IF LINE (px, py)-(x, y) ELSEIF nwall = 1 THEN 'ray from ceiling ref = .75 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 angle = 180 + angle slope = TAN(angle * RAD) y = y2 x = (-(y - py) + (px * slope)) / slope nwall = 3 IF x > x2 THEN x = x2 'change y1 to y2 y = ((-slope * (x - px)) + py) nwall = 2 ELSEIF x < x1 THEN x = x1 y = ((slope * (px - x)) + py) IF y > y3 THEN nwall = 4 ELSE nwall = 5 END IF END IF LINE (px, py)-(x, y) ELSEIF nwall = 2 THEN 'ray from back of room ref = .5 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 angle = angle + 90

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slope = TAN(angle * RAD) x = x1 y = (slope * (-x + px)) + py IF y > y1 AND y < y3 THEN nwall = 5 ELSEIF y > y3 AND y < y2 THEN nwall = 4 ELSEIF y < y1 THEN y = y1 x = (-(ABS((y - py) / slope))) + px nwall = 1 ELSEIF y > y2 THEN y = y2 x = (-((y - py) / slope)) + px nwall = 3 ELSE END IF LINE (px, py)-(x, y) ELSEIF nwall = 3 THEN 'ray bounce from floor ref = .25 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 slope = TAN(angle * RAD) y = y1 x = ((py - y) + (px * slope)) / slope nwall = 1 IF x > x2 THEN x = x2 y = (-(slope * (x - px)) + py) nwall = 2 ELSEIF x < x1 THEN x = x1 y = (-(-slope * (px - x)) + py) IF y > y3 THEN nwall = 4 ELSE nwall = 5 END IF END IF LINE (px, py)-(x, y) ELSEIF nwall = 4 THEN 'ray from front wall ref = .5 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 angle = 270 + angle 'ray come off wall 4 slope = TAN(angle * RAD) x = x2 y = -(slope * (x - px)) + py nwall = 2 IF y < y1 THEN y = y1 x = ((ABS((y - py) / slope))) + px nwall = 1 ELSEIF y > y2 THEN y = y2 x = (ABS((y - py) / slope)) + px nwall = 3

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ELSE END IF LINE (px, py)-(x, y) ELSEIF nwall = 5 THEN 'window ray will hit window IF lang < 225 THEN ref = .95 lange = 180 - lang slope = TAN(lange * RAD) x = (py - y1) / (1 + slope) 'sim equ to find pt on angled window y=x 'cause 45 degrees x = x1 - x y = y1 + y ia = ABS(135 - lang) 'cause at 45 deg then incidence angle changes r2 = ia 'r1 = asin(SIN(r2) / n) 'no arcsin in basic so u = SIN((r2 * RAD)) / nf 'find r1 from r2 v = ATN(u / (SQR(1 - u ^ 2))) 'atan swop cause no asin in basic programming v = v * 180 / PI r1 = v IF r1 < CA THEN fd = 2 * TAN(r1 * RAD) ELSEIF r1 > CA THEN fd = 2 - 2 * TAN(r1 * RAD) ELSE r1 = CA fd = 1 END IF fdr = RND IF fd > fdr THEN 'if fract deflect > random no. then deflects 'COLOR 9 IF lang > 135 AND lang < 224 THEN angle = -(2 * ia) + lang ELSEIF lang < 135 THEN angle = (2 * ia) + lang ELSE angle = lang END IF ELSEIF fd < fdr THEN 'COLOR 15 angle = lang ELSE END IF IF y < win THEN LINE (px, py)-(x, y) px = x py = y ELSE x = px y = py angle = lang END IF ELSEIF lang > 224 THEN 'nwall = 6 'it can hit at 210 and not hit tilted window? x = px y = py angle = lang ELSE 'nwall = 7

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END IF slope = TAN(angle * RAD) IF angle < 180 THEN y = y10 x = (ABS(y - py) + (px * slope)) / slope nwall = 9 'roof IF x > x5 THEN nwall = 9 'right LCP ELSE nwall = 10 'left LCP END IF IF x > x1 THEN x = x1 y = ABS((slope * (px - x)) + py) nwall = 6 'window wall ELSEIF x < x3 THEN x = x3 y = ABS((slope * (px - x)) + py) nwall = 8 'opposite wall ELSE END IF ELSEIF angle > 180 THEN y = y20 x = (-(y - py) + (px * slope)) / slope nwall = 7 'floor IF x > x1 THEN x = x1 y = ((-slope * (x - px)) + py) nwall = 6 'window wall ELSEIF x < x3 THEN x = x3 y = ABS((slope * (px - x)) + py) nwall = 8 'opposite wall ELSE END IF ELSE END IF 'PRINT lang; angle; px; py; nwall; x; y LINE (px, py)-(x, y) ELSEIF nwall = 6 THEN 'ray off front/window wall of atrium ref = .5 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 angle = angle + 90 slope = TAN(angle * RAD) x = x3 y = (slope * (-x + px)) + py nwall = 8 IF y < y10 THEN y = y10 x = (-(ABS((y - py) / slope))) + px IF x > x5 THEN nwall = 9 'right LCP ELSE

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nwall = 10 'left LCP END IF ELSEIF y > bo THEN y = bo x = (-((y - py) / slope)) + px nwall = 7 ELSE END IF LINE (px, py)-(x, y) ELSEIF nwall = 7 THEN 'ray bounce from floor of atrium ref = .25 DO angle = INT((179 - 1 + 1) * RND + 1) '150 LOOP UNTIL angle 90 slope = TAN(angle * RAD) y = y10 x = (ABS(y - py) + (px * slope)) / slope IF x > x5 THEN nwall = 9 'right LCP ELSE nwall = 10 'left LCP END IF IF x > x1 THEN x = x1 'change y1 to y2 y = (-(slope * (x - px)) + py) nwall = 6 ELSEIF x < x3 THEN x = x3 y = (-(-slope * (px - x)) + py) nwall = 8 END IF LINE (px, py)-(x, y) 'PRINT "w= "; nwall; "a="; angle; "s= "; slope; " y= "; y; " x= "; x ELSEIF nwall = 8 THEN 'ray from opposite wall of atrium ref = .5 DO angle = INT((179 - 1 + 1) * RND + 1) LOOP UNTIL angle 90 angle = 270 + angle 'ray come off wall 4 slope = TAN(angle * PI / 180) x = x1 y = -(slope * (x - px)) + py nwall = 6 IF y < y10 THEN y = y10 x = ((ABS((y - py) / slope))) + px IF x < x5 THEN nwall = 10 'left LCP ELSE nwall = 9 'right LCP END IF ELSEIF y > bo THEN y = bo x = (ABS((y - py) / slope)) + px nwall = 7 ELSE END IF LINE (px, py)-(x, y)

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ELSEIF nwall = 9 THEN 'rightside of skydome window IF lang > 360 THEN lang = lang - 360 ELSEIF lang = 135 THEN 'to eliminate div by zero lang = lang + 1 END IF COLOR 15 ref = .95 'put in fresnel nwall = 11 h = lang wslope = TAN(135 * RAD) 'tilt at 45 degrees slope = TAN(lang * RAD) y = ((x1 - px) * TAN(lang * RAD)) / (wslope - slope) x=y x = x1 - (-x) '? y = y10 - (-y) IF lang > 135 THEN 'if lines diverge x = x5 - 1 END IF IF x < x5 THEN x = x5 y = ((slope * (px - x))) + py LINE (px, py)-(x, y), 14 px = x py = y lange = 180 - h slope = TAN(lange * RAD) x = (py - y40) / (-wslope + slope) 'sim equ to find pt on angled window y=x 'cause 45 degrees x = x5 - x y = y40 + y LINE (px, py)-(x, y), 14 ia = ABS(135 - h) ELSE LINE (px, py)-(x, y), 15 ia = ABS(45 - h) END IF r2 = ia 'r1 = asin(SIN(r2) / n) 'no arcsin in basic so w = SIN(r2 * RAD) / nf 'find r1 from r2 v = ATN(w / (SQR(1 - w ^ 2))) 'atan swop cause no asin v = v / RAD r1 = v IF r1 < CA THEN fd = 2 * TAN(r1 * RAD) ELSEIF r1 > CA THEN fd = 2 - 2 * TAN(r1 * RAD) ELSE r1 = CA fd = 1 END IF fud = 1 - fd COLOR 9 IF x > x5 THEN IF h > 45 THEN angle = -(2 * ia) + h ELSE

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angle = (2 * ia) + h END IF END IF IF x < x5 THEN IF h > 135 THEN angle = -(2 * ia) + h ELSE angle = (2 * ia) + h END IF END IF ELSEIF nwall = 10 THEN 'leftside of LCP skydome IF lang > 360 THEN lang = lang - 360 END IF IF lang = 45 THEN 'to eliminate div by zero lang = lang + 1 END IF COLOR 15 ref = .95 'put in fresnel nwall = 11 h = lang wslope = TAN(45 * RAD) 'tilt at 45 degrees lange = 180 - h slope = TAN(lang * RAD) y = ((px - x3) * TAN(lange * RAD)) / (wslope + (-slope)) 'still have div by zero but why at 45' x=y x = x3 + x y = y10 - y IF lang < 45 THEN x = x5 + 1 END IF IF x > x5 THEN x = x5 y = ((slope * (px - x))) + py LINE (px, py)-(x, y), 14 px = x py = y slope = TAN(lang * RAD) x = (py - y40) / (wslope + slope) 'sim equ to find pt on angled window y=x 'cause 45 degrees x = x5 + x y = y40 + y LINE (px, py)-(x, y), 14 ia = ABS(45 - h) ELSE LINE (px, py)-(x, y), 15 ia = ABS(135 - h) END IF r2 = ia 'r1 = asin(SIN(r2) / n) 'no arcsin in basic so w = SIN(r2 * RAD) / nf 'find r1 from r2 v = ATN(w / (SQR(1 - w ^ 2))) 'atan swop cause no asin v = v / RAD r1 = v IF r1 < CA THEN fd = 2 * TAN(r1 * RAD) ELSEIF r1 > CA THEN fd = 2 - 2 * TAN(r1 * RAD)

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ELSE r1 = CA fd = 1 END IF fud = 1 - fd COLOR 9 IF h > 135 AND x < x5 THEN angle = -(2 * ia) + h ELSE angle = (2 * ia) + h END IF IF h > 45 AND x > x5 THEN angle = -(2 * ia) + h ELSE angle = (2 * ia) + h END IF ELSEIF nwall = 11 THEN 'sky ref = 1 'transmitted ray slope = TAN(h * RAD) ptx = COS(h * RAD) pty = SIN(h * RAD) pt = SIN(h * RAD) x = px + (ptx * px) y = py - (pty * py) LINE (px, py)-(x, y), 15 nwall = 13 'deflected ray ref = 1 wall = nwall IF lang > 180 OR lang < 0 THEN lange = lang slope = TAN(lange * RAD) ptx = COS(lange * RAD) pty = SIN(lange * RAD) pt = SIN(lang * RAD) x = px + (ptx * px) y = py - (pty * py) LINE (px, py)-(x, y), 14 nwall = 12 ELSEIF angle < 180 THEN ref = 1 wall = nwall lange = lang slope = TAN(lange * RAD) ptx = COS(lange * RAD) pty = SIN(lange * RAD) pt = SIN(lang * RAD) x = px + (ptx * px) y = py - (pty * py) LINE (px, py)-(x, y), 9 nwall = 13 ELSE END IF

'to ground

ELSEIF nwall = 12 THEN 'ground ref = .2 pt = ABS(SIN(lange * RAD))

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l = ((hgi / 2) * ref * pt) 'cosine correction loo = l * fd * tpp * PI * PI / 20 * tp * reff 'meter and solid angle nwall = 14 'to end IF sky = 1 THEN t = h * RAD '10 to 90 degrees in 10' increments measure pt z = sun * RAD 'angle of sun to zenith eg42 a = -1 b = -.32 c = 10 d = -3 e = .45 f = .91 IF h > 90 AND h < 180 THEN g = ABS((t - (PI / 2)) + z) og = 1 + a * EXP(b / COS(t - (PI / 2))) ELSEIF h < 90 THEN g = ABS(((PI / 2) - t) - z) og = 1 + a * EXP(b / COS((PI / 2) - t)) ELSE PRINT stuffed END IF fas = f + (c * EXP(d * g)) + (e * COS(g) * COS(g)) IF h < (sun + 5) AND h > (sun - 5) THEN fas = fas * 20 'sun position width END IF op = 1 + a * EXP(b) fpg = f + (c * EXP(d * z)) + (e * COS(z) * COS(z)) ol = lz * ((fas * og) / (fpg * op)) 'pt = SIN(lang * RAD) lao = ol * fud * tpp * PI * PI / 20 * tp * reff 'meter and solid angle loo = lao + lo ELSEIF sky = 2 THEN pt = SIN(h * RAD) ol = (lz / 3) * (1 + (2 * pt)) loo = ol * reff * fud * tp * PI * PI / 20 * tpp loo = loo + lo ELSE 'direct sky END IF ELSEIF nwall = 13 THEN 'choose sky type nwall = 14 'to end ref = 1 IF sky = 1 THEN 'clear sky w = lang t = w * RAD '10 to 90 degrees in 10' increments measure pt z = sun * RAD 'angle of sun to zenith eg42 a = -1 b = -.32 c = 10 d = -3 e = .45 f = .91 IF w > 90 AND w < 180 THEN g = ABS((t - (PI / 2)) + z) og = 1 + a * EXP(b / COS(t - (PI / 2))) ELSEIF w < 90 THEN g = ABS(((PI / 2) - t) - z)

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og = 1 + a * EXP(b / COS((PI / 2) - t)) ELSE PRINT stuffed END IF fas = f + (c * EXP(d * g)) + (e * COS(g) * COS(g)) IF w < (sun + 5) AND w > (sun - 5) THEN fas = fas * 20 'sun position width END IF op = 1 + a * EXP(b) fpg = f + (c * EXP(d * z)) + (e * COS(z) * COS(z)) ol = lz * ((fas * og) / (fpg * op)) pt = SIN(lang * RAD) lao = ol * reff * fd * tp * PI * PI / 20 * tpp t = h * RAD IF h > 90 AND h < 180 THEN g = ABS((t - (PI / 2)) + z) og = 1 + a * EXP(b / COS(t - (PI / 2))) ELSEIF h < 90 THEN g = ABS(((PI / 2) - t) - z) og = 1 + a * EXP(b / COS((PI / 2) - t)) ELSE END IF fas = f + (c * EXP(d * g)) + (e * COS(g) * COS(g)) IF h < (sun + 5) AND h > (sun - 5) THEN fas = fas * 20 'sun position width END IF op = 1 + a * EXP(b) fpg = f + (c * EXP(d * z)) + (e * COS(z) * COS(z)) ool = lz * ((fas * og) / (fpg * op)) pt = SIN(lang * RAD) lo = ool * reff * fud * tp * PI * PI / 20 * tpp loo = lo + lao ELSEIF sky = 2 THEN 'overcast sky pt = SIN(lang * RAD) lo = (lz / 3) * (1 + (2 * pt)) loo = lo * reff * fd * tp * PI * PI / 20 * tpp 'put in pt cause angle of incidence on meter is at angle pt = SIN(h * RAD) ol = (lz / 3) * (1 + (2 * pt)) lo = ol * reff * fud * tp * PI * PI / 20 * tpp loo = loo + lo ELSE sky = 3 'direct/clear sky w = lang sunn = 180 - (90 - sun) IF w > (sunn - 5) AND w < (sunn + 5) THEN l = 85000 ELSE l = 50 END IF pt = ABS(SIN(lang * RAD)) lo = l * reff * fd * tp * PI * PI / 20 * tpp w=h sunn = 180 - (90 - sun) IF w > (sunn - 5) AND w < (sunn + 5) THEN l = 85000 ELSE l = 50

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END IF pt = ABS(SIN(lang * RAD)) loo = l * fud * reff * tp * PI * PI / 20 * tpp loo = loo + lo 'pi*tpp*PI/20 is for solid angle 'put in tp cause angle of incidence on meter is at angle END IF END IF reff = reff * ref px = x py = y tp = SIN(k * RAD) 'solid angle tpp = ABS(COS(k * RAD)) 'cosine correction lslope = slope lang = angle LOOP UNTIL nwall = 14 p = INT(k / 9) + 1 '20 divisions of 9' each n(p) = n(p) + 1 sum(p) = sum(p) + loo aver(p) = sum(p) / n(p) NEXT 'next ray choose a increment angle and find aver E in each then sum up maver = 0 FOR p = 1 TO 20 maver = maver + aver(p) NEXT lux = maver df = (lux / hgi) * 1000 PRINT lux; df PRINT #1, lux; df NEXT 'next room above last NEXT 'initial position CLOSE #1 END

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A.2 Three Dimensional Daylight Simulation Program Code The three dimensional daylight simulation programs include: Room12.m - rectangular room with clear glazing Room10.m - rectangular room LCP glazing Well04.m - atrium well clear pyramid glazing Well05.m - atrium well LCP pyramid glazing Atrium3 - room adjoining atrium well with normal room and well Atrium5 - room adjoining atrium well with LCP on room and normal well Atrium4 - room adjoining atrium well with LCP on room and well Atrium6 - room adjoining atrium well with normal room and LCP well Room12.m – Rectangular room with clear glazing % Daylight Simulation in a Room (DSR) % 3D DSR by John Mabb June 2000 % This ray tracing program simulates the daylight penetration into a 3D room onto a working plane. % A graph is displayed showing the light level along the work plane in lux. % This program includes a clear glazed north oriented window, diffuse interior surfaces, exterior ground % and 2 sky distribution models. rad=pi/180; % degree to radian conversion % boundary distances b6=0; b5=300; b4=0; b3=0; b2=300; b1=800; % perpendicular distance from origin to plane p6=-b6; p5=-b5; p4=-b4; p3=-b3; p2=-b2; p1=-b1; s=1; for ixp=80:160:720 % for h=7:1:17 q=0; % no. of indirect rays to sun j=0; % no. of rays to ground av=0; avref=0; nu=0; solang=20; % solid angle divisions over pi sol=1:20; ray=1000; % number of rays per point sky=2; % type of sky distribution 1=overcast, 2=direct %ixp=400; % initial position iyp=150; izp=80; % height of work plane (0 or 80) m=zeros(size(sol)); su=zeros(size(sol)); avlux=zeros(size(sol)); for light=1:ray % no of rays per pt reff=1; iw=0; % initial wall num=0; x2=ixp; % initial coordinate position y2=iyp; z2=izp; % on work plane

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% Ray tracing algorithm within rectangular prism while iw~=7 % loop until hit exit aperture x1=x2; y1=y2; z1=z2; ref=1; % reflectivities of the surfaces t=1; % transmission of the glass % Random altitude and azimuth angles % Simulation diffuse reflections off surfaces if iw==6 az=360*rand; alt=asin(rand)/rad; ref=0.65; % reflectivity of the surface elseif iw==5 az=360*rand; alt=asin(-rand)/rad; ref=0.75; elseif iw==0 % work plane az=360*rand; alt=asin(rand)/rad; ref=1; elseif iw==4 az=180*rand; alt=asin((2*rand)-1)/rad; ref=0.75; elseif iw==3 az=180*rand-90; alt=asin((2*rand)-1)/rad; ref=0.75; elseif iw==2 az=180*rand+180; alt=asin((2*rand)-1)/rad; ref=0.75; elseif iw==1 az=180*rand+90; alt=asin((2*rand)-1)/rad; ref=0.75; else end zen=(90-alt)*rad; azi=az*rad; % Geometrical Framework - (Tregenza 1994) % Direction Cosines c1=cos(azi)*sin(zen); c2=sin(azi)*sin(zen); c3=cos(zen); % Distance to Planes r6=-(-z1+p6)/(-c3); r5=-(z1+p5)/(c3); r4=-(-y1+p4)/(-c2); r3=-(-x1+p3)/(-c1); r2=-(y1+p2)/(c2); r1=-(x1+p1)/(c1); r=[r1,r2,r3,r4,r5,r6];

% Distance array

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% Select the smallest positive element in distance array for n=1:6 if sign(r(n))==-1 r(n)=r(n)*(-inf); elseif r(n)==0 r(n)=r(n)+inf; else r(n)=r(n)*1; end end i=min(r); for n=1:6 if r(n)==min(r) iw=n; % Intercept Wall end end % Find initial angle for cosine correction if num==0 k=alt; tp=sin(k*rad); tpp=cos(k*rad); end % Find Interest Coordinates x2=x1+min(r).*c1; y2=y1+min(r).*c2; z2=z1+min(r).*c3; if iw==1 & z2>120 & y2>120 & z2