to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, ... I. A Steady-State. Computer. Design Model for Air-to-Air. Heat Pumps. S. K. Fischer. C. K. Rice ..... consulting engineers, research ...
Printed
in the United States of America. Available from National Technical Information Service U.S. Department of Commerce 5285 Port Royal Road, Springfield, Virginia 22161 NTIS price codes-Printed Copy: ,410 Microfiche ,401
This report was prepared as an account of work sponsored by an agency of the UnitedStatesGovernment. NeithertheUnitedStatesGovernment noranyagency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its usewould not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United StatesGovernment or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United StatesGovernment or any agency thereof.
ORNL/CON-80/Rl
Contract
No. W-7405-eng-26
Energy
Division
The Oak Ridge Heat Pump Models: I. Design Model for Air-to-Air
'/ i
A Steady-State Heat Pumps
S. K. Fischer C. K. Rice
:
DEPARTMENTOF ENERGY Division
,
of Building
Date Published:
Equipment
Auqust
1983
OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830 operated by UNION CARBIDE CORPORATION for the DEPARTMENTOF ENERGY
Computer
.
-
TABLE OF CONTENTS
r
Page LIST OF FIGURES ................................................
vii
LIST OF TABLES .................................................
ix
ABSTRACT .......................................................
1
1.
INTRODUCTION AND BACKGROUND...............................
2.
UTILIZATION
3.
CALCULATIONAL PROCEDUREAND ORGANIZATION .................. 3.1 Modeling Procedure for the Vapor Compression Cycle 3.2 Organization of the Computer Program ................. 3.3 Input and Output Description .........................
4.
5.
6.
3
...............................................
COMPRESSORMODELS ......................................... 4.1 Introduction ......................................... 4.2 General Calculational Scheme ......................... 4.3 Map-Based Compressor Model ........................... 4.4 Loss and Efficiency-Based Compressor Model
7 *I 9 ... 1: 16
...........
FLOW CONTROL DEVICES ...................................... 5.1 Introduction ......................................... 5.2 Capillary Tube Model ................................. 5.3 Thermostatic Expansion Valve Model ................... 5.4 Short Tube Orifice Model .............................
37 37
CONDENSERAND EVAPORATORMODELS ........................... 6.1 Introduction ......................................... 6.2 Single-Phase Heat Transfer Coefficients in Heat Exchanger Tubes ...................................... 6.3 Two-Phase Heat Transfer Coefficients in Heat Exchanger Tubes ................................................ .................. 6.4 Air-Side Heat Transfer Coefficients 6.5 Heat Exchanger Performance ........................... 6.6 Fan Motor and Compressor Shell Heat Losses ...........
47 47
PRESSURE DROPS AND FAN POWERS ....................
65
7.
AIR-SIDE
8.
PRESSURE AND ENTHALPY CHANGES IN REFRIGERANT LINES ........
iii
z; 44
50 51 55 2:
Page .
9.
10.
MODEL VALIDATION .......................................... 9.1 Introduction ........................................ ................................. 9.2 Compressor Modeling .......................... 9.3 Heat Exchanger Calibration 9.4 Heat Pump Validation at 5.4"C (41.7OF) Ambient 9.5 Heat Pump Validation at 10.6"C (51.0°F) Ambient'::::: ................................ 9.6 Cooling Mode Results
73 73 73 74
RECOMMENDATIONS . . . . . . . . . . . . . ..*..........................
83
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
:: 81
85
APPENDIX A.
DEFINITIONS
OF INPUT DATA . . . . . . . . . . . . . . . . . . . . . . . .
89
APPENDIX B.
SAMPLE INPUT AND OUTPUT DATA . . . . . . . . . . . . . . . . . . . . .
95
APPENDIX C.
DEFINITIONS OF CONSTANTS ASSIGNED IN BLOCK DATA SUBROUTINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
APPENDIX D.
DEFINITIONS
OF VARIABLES IN COMMONBLOCKS . . . . . . . .
105
APPENDIX E.
CROSS-REFERENCE OF COMMONBLOCKS . . . . . . . . . . . . . . . . .
131
APPENDIX F.
SUBROUTINE DESCRIPTIONS AND CROSS-REFERENCE OF SUBROUTINE CALLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
133
ALGEBRAIC NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
139
APPENDIX H. DERIVATION OF DEHUMIDIFICATION SOLUTION . . . . . . . . . . H.l Introduction ........................................ H.2 Heat Transfer Equations - Air to Wall . . . . . . . . . . . . . . . H.3 Heat Transfer Equations - Air to Mean Surface Conditions .......................................... - Mean Surface to Refrigerant H.4 Heat Transfer Equations Conditions .......................................... H.5 Derivation of Coil Characteristic and Total Heat Flow Equation ............................................ H.6 Derivation of the Solution for the Exit Effective Surface Temperature, Tf, ,(x0) ...................... H.7 Derivation of the Soluti6n for the Exit Air Dry Bulb Temperature T (x ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References for App%aixOH ...............................
147 147 147
APPENDIX I. DESCRIPTION OF THE DEHUMIDIFICATION ALGORITHM . . . . References for Appendix I ...............................
163 170
APPENDIX G.
APPENDIX J.
RATIOS OF GEOMETRIC PARAMETERSUSED IN HEAT EXCHANGERCALCULATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv
149 150 151 153 156 161
171
. .
Page .
APPENDIX K. .
AVAILABILITY AND DISTRIBUTION OF THE HEAT PUMP MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OF COMPUTERMODEL ........................
179 185
APPENDIX L.
LISTING
APPENDIX M.
SAMPLE INPUT DATA ................................
185
APPENDIX N.
LISTING
PROGRAM. . . . . . . . . . . . . . .
185
APPENDIX 0.
SAMPLE COMPRESSORMAP DATA . . . . . . . . . . . . . . . . . . . . . . .
185
APPENDIX P.
LISTING
OF THE INTERACTIVE SUBROUTINES . . . . . . . . . . .
185
APPENDIX Q.
LISTING
OF THE INTERACTIVE PREPROCESSOR. . . . . . . . . .
185
OF THE MAP FITTING
. .
V
.
LIST OF FIGURES Page c
Fig. Fig.
3.1 3.2
Pressure vs. Enthalpy Diagram for the Heat Pump Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
Block Diagram of Iterative Loops in the Main ....................................... Program
15
Models
21
........
27
for the Model . . . . .
31
Fig.
4.1
Computational
Sequence
in the
Fig.
4.2
Components
Fig.
4.3
Iteration on Internal Energy Balance Loss and Efficiency-Based Compressor
of Compressor
Energy
Compressor Balance
Fig.
6.1
General
Structure
of the
Condenser
Fig.
6.2
General
Structure
of the
Evaporator
Fig.
6.3
Computational
..
57
Fig.
6.4
Computational Sequence in the Evaporator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
Sequence
Fig.
I.1
Block
Fig.
J-1
Sample Tube-and-Fin
Diagram
of the
in the
Model
Condenser
Dehumidification Heat Exchanger
vii
Model
.......
48
......
49
Model
Algorithm
164
.............
172
.
*
. .
.
LIST OF
TABLES
P c
Page .
c
Table Table Table
9.1 9.2 9.3
Comparison Predictions
of Experimental of Compressor
Data with Map Model
............
75
Heat Pump Model Validation at 5.4'C (41.7"F) ........................................ Ambient
77
Heat Pump Model Ambient Without
79
Validation Corrections
at 5.4"C (41.7OF) to Compressor Map . .
Table
9.4
Heat Pump Validation
Table
E-1
Cross-Reference
of Common Blocks
Table
F-1
Cross-Reference
of Subroutine
Table
K-1
Sample Pages of Input Data for Interactive Version of Heat Pump Model . . . . . . . . . . . . . . . . . . ...183-184
at 10.6OC (51°F)
Calls
Ambient
..
80
...............
132
............
137
I. A Steady-State The Oak Ridge Heat Pump Models: Design Model for Air-to-Air Heat Pumps* S. K. Fischer C. K. Rice Energy Division Oak Ridge National Laboratory Oak Ridge, Tennessee 37830
Computer
ABSTRACT The ORNL Heat Pump Design Model+ is a FORTRAN-IV computer program to predict the steady-state performance of conventional, vapor compression, air-to-air heat pumps in both heating and cooling electrically-driven, This model is intended to serve as an analytical design tool for modes. use by heat pump manufacturers, consulting engineers, research instituand universities in studies directed toward the improvement of tions, The Heat Pump Design Model allows-the user to heat pump performance. specify: 0
system
l
compressor
0
refrigerant
0
fin-and-tube
l
fan
l
any of ten
The model will
operating
conditions,
characteristics, flow
control
heat
and indoor
exchanger
duct
parameters,
characteristics,
and
refrigerants.
compute:
system
capacity
compressor
and COP (or
and fan motor
coil
outlet
air
dry-
air-
and refrigerant-side
a summary of the the cycle, and overall compressor effectiveness.
.
devices,
EER),
power consumptions,
and wet-bulb pressure
refrigerant-side efficiencies
This report provides thorough documentation This is a revision of an earlier the model. corrections and information on availability including an interactive version. *Research sponsored by the Office U.S. Department of Energy under Carbide Corporation. 'The ORNL Heat Pump Design Laboratory.
temperatures, drops, states and heat
throughout exchanger
of how to use and/or modify report containing miscellaneous and distribution of the model -
of Buildings and Community contract W-7405-eng-26 with
Model was developed 1
at Oak Ridge
Systems, the Union National
.
3
INTRODUCTION AND
1.
The ORNL Heat Pump Design developed
to predict
compression,
an analytical
consulting
design
engineers
directed
toward
the
The current
[6].
routines
in Ref.
in
tool
for
of heat
has evolved
served
1978,
improved
version
informal
documentation.
model.
indicated
Many of these
This
report
rections
is
identified
the
greatest
extent
correlations
derived
and algorithms critically appropriate
correlations
The model earlier
has thus
versions
been reorganized be able
by vertical
bars
principles
to readily
[7,8]
and documented
as well
An limited, to a
as the
capabilities with
and generalized the
experiences in the
1979 and 1981. miscellaneous
cor-
or additions
have
limitations
and efficient
standpoint.
into
format specific
The correlations
to include
from an engineering
to
of empirical
of the model
improved
pro-
correlations
literature.
or replaced
to their
pump modeling
has been to base the
been significantly
it
and Kusuda
in the left margin.
and more accurate
adapt
heat
corrections
releases
a more modular
[5],
between
so as to avoid
and improved
Flower
makes use
in 1979 with
version
from manufacturers'
reviewed
and also
for
additional
where
used in the previous
[3]
have been distributed
programs
The places
possible,
to
institutions.
of an earlier
physical
is
at ORNL [l,Z]
ORNL Heat Pump Model.
of the model development
gram on underlying
model
in studies
was modified
needs were incorporated
a revision
The philosophy
point
of the
the need for
and additions.
been made are
[4],
program
,and research
heating
pump manufacturers,
written
code was made available
Our own use of the previous users
programs
starting
version
vapor
pump efficiency.
These two versions
number of manufacturing
of this
and universities
and Erth
as the
program
pumps in both
of Technology
the original
of this
heat development
from
Institute
computer
of conventional,
use by heat
improvement
1 as a preliminary
of other
the
by Kartsounes
The MIT model
at ORNL, where
for
institutions,
and at the Massachusettes of selected
performance
, research
model
Fortran-IV
a
air-to-air
The purpose
modes.
is
steady-state
electrically-driven,
and cooling provide
the
Model
BACKGROUND
have been
more recent algorithms.
and expanded Furthermore,
so that needs.
or
reseachers
from
the
it will
has
4
The ORNL Heat Pump Design e
.
System Operating 1. 2. .
0
0
0
0
l
Model
allows
the
user
to specify: II
Conditions
the desired indoor relative humidities,
and outdoor
air
temperatures
*
the arrangement of the compressor and fans up or downstream of the flow stream, i.e.,
Compressor
in the air heat exchangers;
Characteristics
1.
either a map-based equipment,
2.
or an efficiency compressors;
Refrigerant
model
for
and loss
Flow Control
designs
model
a capillary a short-tube
2.
a specified value of refrigerant at the condenser exit (in this the equivalent capillary tube, parameters);
Fin-and-Tube
with
for
tube, thermostatic orifice, or
Heat Exchanger
advanced
expansion
reciprocating
valve
(TXV),
or
subcooling (or quality) case the program calculates TXV, and short-tube orifice
Parameters
1.
tube size, spacing, parallel circuits,
and number of rows,
2.
fin pitch, thickness, fins (smooth, wavy,
and thermal or louvered),
3.
air
flow
available
Devices
1.
Fan and
and
and number of
conductivity;
type
of
rates;
Indoor
Duct Characteristics
1.
overall fan fans, or
efficiency
2.
a specified
fan
3.
the
diameter
values
efficiency
of one of six
for
curve
indoor for
the
equivalent
and outdoor outdoor
fan,
ducts;
Refrigerants 1.
either
2.
one of six additional refrigerants (Rll, R113, and C318) by adding the appropriate constants given by Downing [9];
R12, R22, R114, or R502 as a standard
option,
R13, R21, R23, thermodynamic
5 Refrigerant
0
1.
lengths
2.
pipe
specifications
3.
heat
losses
The user is
Lines
cannot
implicity
specify
satisfactory
the
specified
model
for
heat
a low level
charge
over
unless
the
known.
a range level
of ambient
and liquid
with
the
having
instead,
proper This
a suction
excess
is
line
the
performance
superheat
however,
model
and output
has evolved
system
from
a accumulator
refrigerant with
cannot
and
a given
be accurately
at each ambient
single
of measurement
of the
computer and it
design
would
The specific
parameter
in Appendices
the
user
output
are given to control
includes
the
refrigerant modeled
temperature studies
can still
English
units.
(The
Sensible Outlet Air-
dry-
effort
to convert
each input
Four
output
output.
British
and output
options
The basic
allow program
heat
power consumption transfer
and wet-bulb
isentropic
of program
ratio
temperatures pressure
and volumetric effectiveness
capillary
Summary of the
A.
used for
A and B.
and refrigerant-side
Equivalent parameters
Appendix
units
and fan motor
Heat exchanger
levels
based on the
have been a major
amount of printed
to total
Overall
Other
were
and COP
Compressor
l
are-in
tube,
output
drops compressor
efficiencies
and UA values TXV, and short-tube
refrigerant-side are discussed
states
is
point
(as appropriate):
Capacity
0
program codes that
them to SI units).
it
amount
be made. The input
mode,
lines.
charge;
conditions.
temperatures
of evaporator
or cooling
superheat.
systems,
For such systems,
charged
can store
of evaporator
For charge-sensitive
is
operating
which
of heating
refrigerant
pump systems
systems)
pipes,
discharge,
system
system
for
(charge-insensitive
suction,
the the
of interconnecting independent
from
assumed that
of refrigerant
maintain
and diameters
orifice
throughout
in Section
3.2
the and
cycle
6
This from
its
second
generation
predecessors
heat
pump model contains
and many additional
significant
capabilities.
This
changes report
is
intended: e
to serve as a rigorous documentation (where correlations, and algorithms the assumptions, the program, to provide equations
e
A basic
a complete list of references were obtained, and
to serve as a user's manual for intact and to aid those who will understanding
been presumed
for
of vapor-compression this
report.
appropriate) of that are used by
from which
data
and
those who will use the code need to add new capabilities. air-to-air
heat
pumps has
7 2. UTILIZATION The physical outdoor
operating
described
in
less
complete
listing
Although program,
software. numerical optimization
than
are read
A; tape
The program
executes
of the
conditions
in Appendix
required.
alone
specification
drives
requires
5
of the
and other
seconds
on the
program
is
provided
is generally
and graphical
display [7,8].
file,
and as
are not
computer
in Appendix
of the model studies
data
peripherals
IBM 3033
Model
indoor
of memory and typically
version
and parametric
pump and the a single
has been used in conjunction
An earlier analysis
from
56 K words
the Heat Pump Design it
heat
with
at ORNL.
A
K. run as a stand-
other
computer
has been used at ORNL with
programs
in
heat
pump design
P CALCULATIONAL PROCEDUREAND
3. 3.1
Modeling
The heat sections. flow
pump model device
routines
into
low-side
unit,
Calculations
the proceed
overall
independent
the
the
into
compressor,
an interrelated contains between
is obtained.
of whether
Compression
functionally
combines
iteratively
balance
the Vapor
is organized
section
section,
desired
for
The first
control
second
Procedure
ORGANIZATION
two major condenser,
high-side
the these
is
operating
the
basic
and
unit.
evaporator
model.
two sections
until
The calculational
unit
Cycle
in
the
The the
scheme is heating
or cooling
mode. Figure
3.1
an exaggerated The user
is
pressure-enthalpy required
vapor
compression that
diagram,
cycle,
is modeled
shown on
by the
program.
to specify:
l
the
l
design parameters for a flow-control device condenser exit subcooling (or quality),
l
condenser
l
dimensions
l
heat
The user
level
of evaporator
exit
and evaporator of components
losses
must also
from
provide
superheat
inlet
air
(or
quality), or the
estimates
of
temperatures,
and interconnecting
interconnecting
level
pipes,
and
pipes.
for:
e
the
refrigerant
saturation
temperature
at the
evaporator
exit,
l
the refrigerant and
saturation
temperature
at the
condenser
inlet,
e
the
mass flow
These
three
final
results
values
represents
refrigerant
estimates
used
are
of the model
are chosen;
as starting
do not
however,
rate.
better
points
for
iterations.
depend on how well guesses
will
The
or how poorly
yield-shorter
these
running
times.
High-Side
Computations
The computations refrigerant which
state
is defined
for
at the by the
the exit
high-side of the
specified
system evaporator
superheat
balance
begin
(point
a in
and the
estimate
with Fig.
the 3.1),
of the
10
I(
.
ORNL- DWG 81-4749
ENTHALPY a
EVAPORATOR EXIT b COMPRESSOR SHELL INLET C COMPRESSOR SHELL OUTLET d CONDENSER INLET e CONDENSER OUTLET
f g
INLET TO EXPANSION DEVICE EVAPORATOR INLET Fig.
3.1
Pressure vs. Enthalpy Heat Pump Cycle
Diagram
for
the
11
saturation the
This
temperature.
compressor,
condenser,
The compressor
model
point
remains
expansion
uses
state
fixed
device,
one iteration
and evaporator
a along
point
for
the estimates of the refrigerant mass fl ow rate temperature at the condenser inlet, and
l
the specification of the dimensions suction and discharge lines the
condenser
Fixed
state
at the
d, as well
inlet,
shell
calculations.
with:
l
to calculate
and heat
and saturation
losses
b, she1 1 outlet,
inlet,
of
as a new estimate
for c,
the
and the
of the mass flow
rate.
Condenser Subcooling The remainder
flow
control
exit
subcooling
described
of the
device (or
quality)
since
l
the
physical
l
the
calculated
0
the
condenser
l
the
refrigerant
the
of condenser compared a fixed
states
inlet
compressor
b, c,
condenser
device,
f,
is
value.
computed
submodel
and relative inlet,
of state
the
two values
do not
the
saturation
calculations
are
achieved,
is
e, and agree
within at point
pressure),
changed,
mass flow updates the
The level
repeated.
temperature model
e.
entrance
and
d,
temperature
a new condenser
condenser
uses:
point
knowledge
C),
is
humidity,
from
a new refrigerant is
case
rate,
condenser
saturation
subcooling
The latter
outlet,
specifying
calculates
of condenser
condenser
If
a
value
at the
is computed
and d and the
desired
at the
on whether
exchanger,
temperature
state
condenser
heat
mass flow
air
and condenser
the
model
of the
state
effect
a desired
The condenser
refrigerant
(see Appendix
(in
Each time
simpler.
description
specified
tolerance
compressor
is
subcooling
d, is changed and the
it
or if
depend
has been specified.
refrigerant
to the
calculations
has been chosen
first
to evaluate
high-side
state
the
rate
and new
e.
Once the
state
at the
flow
control
using:
l
the
state
at the
l
the
dimensions
l
the most recent
condenser
and heat calculation
loss
exit, for
e, the
of the
liquid
refrigerant
line,
and mass flow
rate.
Refrigerant
state
the
equivalent
that
would
f and the mass flow
capillary produce
Specified
When condenser has a flow the the
the
exit
heat
pressure
is
expansion
rate
This
balance
characteristic
refrigerant turn,
is
flow
rate
found
obtained
flow is
control fixed.
inlet the
at the
at the
condenser
liquid
0
the
line
dimensions
computed
mass flow entrance
required,
the
rate
outlet
expansion
at the
evaporator
pressure
at point
in mass
exit,
subcooling
for
the
Since
estimate the
proceed
of
condenser
to the
using:
e,
the
loss,
and
rate.
flow
calculated
control
device
using
state
valve
or short-tube
entrance,
point
g is
a specified
and condenser
inlet.
mass flow
is
which,
with
f is evaluated
state
which
conditions
case of a thermostatic pressure
shell
and heat
compressor
on the
condenser
the calculations
state
0
low-side is
been specified,
the
the mass flow
refrigerant
balance
condenser
where
the
the
with
high-side
device
case where
compressor
entrance
of the
model.
to the
device
e
using
a high-side
at the
high-side
dependent
e, d, and e, are computed
states temperature
control
control
model
compressor
The states
The refrigerant the
the
is
by
of the
the
since
device
to flow
to achieve
has not
based on its
entrance
are similar
subcooling flow
flow-control
balance
capability
proper
iteratively
is,
(constrained
model must be coupled the
it
that
by the
characteristics
to achieve
as if
opening,
specified,
drop
control
device
saturation
is
acts
condenser
pumping
device
condenser
from
and outlet,
of the
must be found
the
The calculations
determined
routines
at the
from
is completely
pressure
flow
of the
state
parameters
system
variable
refrigerant
by the
so the
the
an infinitely
control
and condenser
balance.
specified,
capability
and the
controlled
device,
compressor
with
rejection
When a flow
compressor.
is
pressure
subcooling),
orifice
Device
device
system
used to calculate
subcooling.
subcooling
control
high-side
between
specified
Flow Control
are then
TXV, and short-tube
tube,
the
rate
initially
g.
will
f and, orifice,
If
pass
the
in the
latter
assumed to be equal
13
to that then the
at point
later
calculations If
estimate.
and flow
in the
the
control
device
a new estimate
balance
do not
of the
computing
Low-Side
agree
two mass flow
rates
of the
calculations
temperature are
compressor tolerance
are repeated
at the
condenser
in agreement,
analysis
the
a high-side
can now be completed
by
performance.
or low-side,
computations
l
the
refrigerant
condition
l
the
refrigerant
enthalpy
l
the
refrigerant
mass flow
These values
have all
temperature
and specified
the
inlet
the
assumed exit is
air
temperature
executed
one execution evaporator
exit
would
quality)
pressure
drop
at the
at
evaporator yield
a,
inlet,
point
g,
the
the
and
inlet
saturation evaporator point
specified
inlet
air heat
since
the
temperature
from
at the
exchanger exit
at
The evaporator
of superheat
the
g, and
superheat
unknown.
a value
across
the
inlet,
are still
to calculate
and a pressure
hence a saturation
(or
varying
next,
state
based on the estimated
temperature
iteratively,
evaporator
exit,
rate.
at the
which
saturation
to the
at the
superheat
pressure
are based on:
at the evaporator
been computed
The saturation
model
are used to improve
device rates
and
Computations
The evaporator,
exit.
model
evaporator),
a specified
One cycle
the evaporator
the
within
saturation
has been obtained.
in
mass flow
and expansion
Once the
entrance.
drop
evaporator
refrigerant
condenser,
compressor, with
no pressure
a (i.e.,
(and
conditions
are
fixed). A system air
temperature,
calculated given
tolerance. flow
has been completed
though
exit
thermostatic the
solution
not
superheat
agrees
(The highexpansion
control
device
pressure
is used during
solution
is found
changing
the
for
saturation
necessarily
valve
the
with
the
or a short-tube that
high-side
desired
temperature
some evaporator
the desired
and low-side
to ensure the
for
one, value
loops
repeated
orifice
an accurate
is
at the
inlet evaporator
within
a
once if
specified
evaporator
calculations.)
evaporator
when the
specified are
inlet
a
as
inlet
The system air
temperature exit,
point
by a,
14 and repeating state
point
agrees
with
sequence inlet
entire
calculational until
the
the
value
within
is
summarized
desired
air
temperature
is
temperature
outermost
loop
as the
distinct into
distinct
for
example,
the
of these
other.
This
subroutines,
is
shown in
components
one for
the
the
accomplished
flow
in the
the
compressor
l
modeling
the
condenser
l
modeling
the
flow
*
iterating
iterations
properties,
pressure
(Appendix
F contains
control
on condenser
each of these
inner
The evaporator of the
exit
refrigerant over
Program
3.2
are divided
these
computations
of the
system
performance control
into are divided
high-side
of the
compressor,
device
and then
interconnecting
pipes
heat
pump model
balance,
using
balancing with
each
individual
each task:
modeling
perform
Fig.
and the
l
In addition
The
one or two iterations
to perform
computing
and (optionally)
temperature
3.2.
Computer
The calculation
condenser,
on
tolerance.
function
of the
subroutines
requires
air
in Fig. only
iteration
are required.
Organization
modules.
output
3.2
inlet
a specified
usually
calculations
sections,
computed
a linear
so that
in Fig.
3.2 Just
nearly
This
process.
a continues
of calculations
saturation the
the
device saturation
subroutines and calculate
drops , and heat a cross-reference
temperature
calls
other
thermodynamic transfer of all
service
routines
to
and thermophysical
coefficients, subroutines
etc. called
from
each subroutine.) The advantages
to this
program
and identifiable
structure tasks
are that:
0
separate
are performed
by each subroutine,
0
modules can be easily modified to make improvements, replaced to use models for a different component type, or added to increase system analysis capability
l
familiarization with the code can be done at different levels, depending upon the needs of a specific user.
‘
ORNL-DWG
81-4741
READ INDOOR AND OUTDOOR AMBIENT TEMPERATURES AND ESTIMATES OF THE CONDENSING AND EVAPORATING TEMPERATURES
TXV, CAP-TUBE ,OR ORFICE
SPECIFIED
FIND THE CONDENSING TEMPERATURE T sti,o, WHICH BALANCES THE COMPRESSOR AND EXPANSION DEVICE MASS FLOW RATES
SUBCOOLING
FIND THE CONDENSING TEMPERATURE T so+,e, WHICH GIVES THE SPECIFIED SUBCOOLING
IENT TEMPERATURE
Fig.
3.2
Block
Diagram
of
Iterative
Loops in the
Main Program
r
x
I
16
One consequence large
of this
program
variables E are
passed
between
them through to identify
which
common blocks
As part data
with
that
a single
a large
common blocks. variables
number of
Appendices
D and
used in common blocks
are used to pass data
input
and output of the There
output. not
read
output
than
data,
between
amount
of data
the
output
results
The program
Appendix
A.
The first
computed
results energy
summary.
in cases out
where
the
proper
been made.
Intermediate
with
of
either
Appendix
A, is
standard
iteration
sequence
to another
other
operation
B is a system in
are for
3.2,
of computations.
variable,
to print
the
heat
Further,
in
pump and
diagnostic
pur-
or for
use in
changes
have
are printed
out
as defined abbreviated
B, a summary after
or continuous
has
one page of
of the
after
3.2
as defined
to converge
An input
summary as in Appendix
Fig.
to only
in the computations whether
summary and
options,
two options
two options.
in Fig.
loop
output
fails
the
them as necessary.
of the program
results
to reduce
can change
COP and capacity loop
are assigned These parameters
the output
The other
to be
each run.
for
outermost
limits
used to specify
output
of each major entire
these
has three
an iterative
and
parameters,
are unlikely
program
the user
the
the
input
of printed
tolerance
which
must specify
C so that
gives
sample
levels
(BLOCK DATA) in order
option
which
(e.g.,
pressure)
after
A contains
used by the model which
shown in Appendix
computed
of the
B.
constants
user
all
Appendix
are other
one use of the
in Appendix
The printed
almost
B contains
constants
and there
subroutine
that
are described
checking
other
atmospheric from
in a single
converged.
and Appendix
and physical
number,
Description
of the program,
shown in Appendix
frequently
a brief
data
as input
values
poses
input
however,
that
refrigerant
contains
and Output
are done by two subroutines.
are,
Parameters changed
Input
of the modularization
definitions
the
is
subroutines. 3.3
the
however,
subprograms
as aides
and to identify
are
approach,
becomes many short
included
which
modular
in output,
completion
output
throughout
the output
statements
17 in most of the from print
a particular control
subroutines
are arranged
subroutine statements
so that
can be obtained
in that
routine.
detailed,
by removing
diagnostic one or two
output
19 4.
COMPRESSORMODELS 4.1
Since primary
the
user
compressor
of electrical
to good system be tempered
of the
models
design
parameters.
models
depending The first
Model
manufacturers' type;
for
Accurate
available
to
the
has built-in
superheat
those
for
for
use with
rotary,
simulation
between
two simpler
of existing
compressor
corrections
to adjust compressors
generated. it
or for
which
Although
should
or centrifugal
compressors
the
use of compressor
compressors,
screw,
heat
which
hardware
a specific
the maps were
reciprocating
reasons
detailed
in reciprocating
which
of
a subroutine
based on the
maps) for
types
For these
using
needs.
the model
different
incorporate
specific
model was written modify
information
upon their
of refrigerant from
of
can choose
(compressor
important must
users
data
is
however,
may be used.
is
modeling
criterion,
performance
model
and the
This
Instead,
compressor
pump system
compressor
and of
does not
compressor
a heat
type
program
the program
ORNL Heat Pump Design
of
accurate
of the
in which
different
power,
by consideration
pump studies
levels
heart
prediction.
users
compressor
the
performance
most potential
rigorously
is
Introduction
are this
be easy
to
compressors.
is
possible
with
this
model. The second is
intended
changes It ant.
for
model,
a loss
use in heat
in compressor
can also This
more general
efficiency
values.
This
over
the
based model without
performance
routine
values.
improvements about
using
same range
is well
suited,
and interactions
a particular
the predict
design
energy
heat
conditions
for
and their point.
loss
compressor
of some of the however,
system with
internal
model,
to predict
affect
performance
of operating
adjustment
e.g.,
terms
user-supplied
model cannot
local It
models
compressor
studies,
and efficiency
compressor
as accurately
compressor
pump design
be used to model compressor
a reciprocating
and loss
loss
and efficiency-based
how
performance.
a new refrigerbalances
in
and internal performance as the map-
input
efficiency
studying
internal
effect
on system
20
4.2 Both
compressor
models
with
rest
and interact general
the
calculational
tions
of those
temperature refrigerant
the
sequence
frigerant
degree
at the at
pressure
volume
refrigerant
procedures
inlet
exit
Figure
the evaporator
exit
is
the
estimated
shows simulation.
outlet
the
condenser
entrance.
using
and the
refrigerant
re-
corresponding
identified
or quality
the refrigerant
4.1
and evaporator and the
superheat
and on
of compressor
are used to calculate
in the
suction
8 using
the
the
calculated
saturation
temperature,
enthalpy,
suction
point,
gain
and discharge current
refrigerant
at the‘compressor
of heat
From this
exit.
exit
and average
calculated
value
evaporator
saturation
entropy,
are computed.
drops
state
refrigerant
evaporator
(from
in Section rate
condenser
by descrip-
are different.
on the
method
The
same way.
followed
and the
either
in common
in the
which
evaporator
for
from which
as described
the
at the
temperatures
The pressure mass flow
entrance
of evaporator
exit
and specific
two routines dependent
of the
state
temperature),
estimates
temperatures shell
line
inlet
pressure
in the
each of the
lines
is
drop
suction
for in
are computed the
the
refrigerant
lines.
then
identified
and the
specified
The
line.
compressor
models
use different
to calculate:
0
the
refrigerant
0
the
compressor
motor
input
0
the
compressor
shell
heat
0
the
refrigerant
the
previously
(input)
of the
pressures
evaporator
the
first,
estimates
The refrigerant
(input)
scheme is discussed
condenser
saturation
specified
of the
of calculations
refrigerant
using
model
superheat
The current
Scheme
have a number of calculations
are functionally
at the
the
Calculational
system
sections
Both models
Finally
General
value
refrigerant calculated of discharge
mass flow
state state
power, loss
at the
(optional), compressor
at condenser
discharge line
rate,
heat
line loss.
entrance pressure
and shell is drop
exit. computed
using
and the
specified
21 ORNL-DWG
(
COMP OR CMPMAP
Sb4745R
J
CALCULATE THE PRESSURES AT THE CONDENSER INLET AND THE EVAPORATOR OUTLET /
c 1
r
3
CALCULATE REFRIGERANT PROPERTIES AT THE EVAPORATOR EXIT _I
\
r .
1 , CALCULATE b P IN THE DISCHARGE LINE AND TqcmpAND Pcut,cmp J t 7 CALCULATE AP IN THE SUCTION LINE AND Tin,cmp AND Pin,cmp + CALCULATE REFRIGERANT CONDITIONS AT THE SHELL INLET
LOSS AND
I
EFFICIENCY-BASED
6 SUCTION GAS ENTHALPY ITERATION FROM FIG. 4.3
,
MAP -BASED t CALCULATE POWER AND RATE FROM AND SHELL
ti CALCULATE THE REFRIGERANT STATE AT THE SHELL OUTLET
.
AND CORRECT MASS-FLOW CURVE FITS HEAT LOSS I
CALCULATE THE REFRIGERANT STATE AT THE SHELL OUTLET .
i 1
f
I
I
CALCULATE THE REFRIGERANT STATE AT THE CONDENSER INLET
r CALCULATE NEW AVERAG TEMPERATURES AND t- SPECIFIC VOLUMES IN THE COMPRESSOR LINES
CALCULATE OVERALL VOLUMETRIC, ISENTROPIC,AND SUCTION GAS HEATING EFFICIENCIES \ i END
Fig.
4.1
Computational
Sequence
in the
Compressor
Models
22 Upon completion and specific
of these
volumes
in the
These are used with flow
rate
suction
latest
to recalculate The entire
drops. the
the
drops
agree
After
completion
new average
and discharge
calculation
the
process
pressure
calculations,
suction
is within
lines
of the
are computed.
refrigerant
and discharge
repeated,
temperatures
line
pressure
as shown in Fig.
tolerances
from
mass
4.1,
until
one iteration
to the
next. ficiency
indices
of the
pressure
are computed.
In both
efficiency
indices
are calculated
efficiency
and the
overall
is
used to refer
appropriate)
The overall the
outlet
compressor
compressor
models,
two basic
isentropic
compression
The term
efficiency.
based on compressor
shell
ef-
"overall"
inlet
and (when
conditions.
isentropic
compression
efficiency,
nCm is
given
by
equation
n cm "k
flow
Qcm,ideal
rate
represents (ideal)
the
outlet
isentropic
compressor specific
specific inlet
and the
a given
mass per unit
outlet, completely
ratio
be emphasized houtlets
is
insulated
The overall
not
)
inlet
(4.1)
of
that
refrigerant
would
time)
used
in Eq. 4.1; would
pressure
i r,actual %ol = fir,ideal
refrigerant
nvol,
_
is
tilr,actual
given
'inlet DS
case, of
outlet.
(to
required
the
an
entropy
at shell
enthalpy
were this
irom
refrigerant
have an ncm value
efficiency,
isen
be obtained
to the actual
actual
mass
houtlet
the minimum power required
the
volumetric
The term
based on the
that
compressor
power and refrigerant
enthalpy.
process
the
refrigerant
motor
enthalpy
compression
shell
-h
R cm,actual
Thus T-Icm represents should
(houtlet,isen
cm,actual
and h represents
at compressor
lilr,actual
=
i cm and mr represent
where
It
iteration,
- the overall
volumetric
to a value
shell
drop
compress power.
at shell any 1.0.
by
(4.2)
23 where
v
inlet, rated
inlet D is
is
the
the
total
compressor
with
actual
motor
and efficiency conditions
compressor as discussed
The next compressor methods,
for
measurements provide and/or
performed
saturation condenser maps,
"evaporator"
1 in Appendix
loss port
the
two
calculational
is
of
for
the
superheat
to six
shell
outlet).
fixed
with
Given
in
gas temperature the
or fixed
of
For some
changes
suction
"condenser"
values
superheat.
to vary
constant.
saturation
four
for
curves
rate
"evaporator"
inlet
while
curves
calorimeter
mass flow
compressor
allowed
held
performance
compressor
inlet)
at the
inlet
rate
condenser
suction
exit
gas temperature,
values for
can be derived from refrigerating ,, performing these calculations is given
N. routine
(kW) and the
of compressor
shell
the
published
performance
Cl'
c,,
**a,
the
Model
map is generated
is
A routine
The map-based input
shell
temperature inlet
mass flow data.
for
between
refrigerant
and compressor
and compressor
refrigerant
power
(i.e.,
saturation
subcooling
be confused
These performance
as functions
superheat
shell
from
input,
at compressor
the
at compressor
capacity
power
subcooling
however,
model.
and discharge
uses empirical
obtained
each performance exit
not
requirements,
by the manufacturers.
temperatures
Usually
should
efficiencies
Compressor
model
capacity
(i.e.,
and efficiency
differences
input
Map-Based
motor
refrigerating
temperature
3450 or
output.
compressors
compressor
the
in
compressor
reciprocating
(e.g.,
the
4.4.
describe
4.3 The map-based
loss
based on suction
- differences
and resulting
the
ncm and nVol
in Section
two sections
models
model
compressor
model
shell
the map-based
speed for
internal
at compressor and S is either
indices,
defined
volume
displacement,
speed for
two efficiency
similarly
specific
compressor
motor
3500 rpm) or the These
refrigerant
for
uses curve refrigerant
inlet
bi-quadratic
to the
mass flow
and outlet data.
fits
saturation
The user functions
compressor
rate
(lbm/h)
temperatures
must provide
of the
form
sets
given
motor as functions to model of coefficients;
by Eq. 4.3
24 for
the
outlet
power
input
saturation
and mass flow
rate
as functions
of the
inlet
and
temperatures, .
f(T outlet'
T inlet)
=
'1 Tiutlet '4
I
A short
computer
compute
these
below,
these
rated
must also
or temperature
at the
based)
compressor
for
the
displacement
is
also
map-based
model
represent
a compressor
as the
original
fits model the
specify
the
total
actual
and the
fixed
speed,
an input
to scale
with
Dabiri compressor rate,
the but
and Rice motor
which
factors
at actual power
presented
input,
they
displacement,
refrigerant
superheat the map is
The desired
value
is
compressor
used by the
curves
performance
for
the
linearly
to
characteristics
biquadiatic superheat
were generated. empirical
level
or
The map-based
curve
fits
to model
conditions. a technique
i
for
and the cm,map' of superheat or suction
than give
their
factors
compressor.
capacity.
m for values r,map those for which the maps were generated. correction
as noted
compressor
maps and the only
to
Except
performance
to the
operating
[lo]
this
of a different
applicable for
N.
(upon which
same general
(4.3)
'6
algorithm
modeled.
compressor
'
+
one particular
inlet
being
the compressor
correction
compressor
is
only
parameter;
the
gas temperature applies
shell
which
to them are strictly
suction
in Appendix for
compressor
earlier,
squares
apply
compressor
As noted
listed
Tinlet
will motor
+ '3 TLet
+ '5 Toutlet
uses a least
is
coefficients
compressor
TinIet
which
coefficients
The user the
program
+ '2 Toutlet
to account
for
correcting
refrigerant
the mass flow
gas temperature Equations
non-standard
4.4
other and 4.5
superheat
values,
rilr,actual
= [l
t F (Vmap v v actual
- 1)-J lil
r ,maP
(4.4)
25 and
(4.5) where of
and Ah represent
v
the
"actual",
conditions,
port
suction
1 respectively, a value
"map",
map superheat
estimated
and "isen"
conditCons
in the
the suction
shell
inlet
conditions
using
gain
to the
gas between
Ah
from
of a constant inlet
(assigned
C).
conditions
shell
pressure, factor
see Appendix
assumption compressor
outlet
from
the
enthalpy and suction
, of 21 kJ/kg (9 Btu/lbm), due to motor and port by the suction gas [lo]. This assumption has been
inlet,suction compressor cooling improved
the
superheat
correction
port
The
process
shell
efficiency
respectively,
conditions. actual
to compressor
Data subroutine,
estimated
port,
represent
Block
and Rice
port
change,
and an isentropic
a volumetric
Dabiri
suction
and enthalpy
suction
conditions,
and Fv is
of 0.75
volume
based on estimated
refrigerant
subscripts
specific
upon in our map-based
model
by assuming
instead
that
.
Ah
where
Fs,
is
inlet,suction
an appropriate
a value
of 0.33
in the
Eq. 4.6
assumes
that
inlet
to suction
temperatures compressor
input
has been observed Once the to the shell
Block will
and higher work
values
suction
gas heating
condensing per unit
corrections
at lower saturation
mass flow reciprocating
for
actual
houtlei, h
outlet
is = (A
compuied
cm,actual
Fsh is
assigned
(see Appendix
C).
Use of
change (from evaporating
rate
from
- 'can"'r
as the
increases.
compressors level
enthalpy
shell
saturation
temperatures
superheat
of icm map and mr map, the
outlet,
factor.
gas temperature
increase
in typical
r4w
Data subroutine
the suction
port)
= Fs, +
port
Such a trend [ll].
have been applied
at the
compressor
Eq. 4.7
, actual
+ hinlet
(4.7)
26 where
is
i,,
the
specified
by the
fraction
of actual
are
not
usually
in
at the
the
loss
user
at the
power,
by the
calculations
then
proceed
as described
in Section
outer
balances
supplied
design , internal of the 4-2.
of (j
can
manufacturers.) at this
thermodynamic
are computed pressure
Loss and Efficiency-Based
energy
Fig.
is
or as a specified (Values
relevant
entrance
to the
value
i,,
properties
next.
drop
The
convergence
loop
4.2.
internal
shown in
input
shell.
has been identified
the
and efficiency-based
representation
compressor
icrn actual.
exit
and all
and condenser
The loss
the
compress&
compressor
exit
4.4
from a fixed
compressor
calculations
shell
rate
as either
provided
The state point
heat
Compressor
compressor
in a reciprocating efficiency,
loss
routine
models
the
compressor
from
user-
and heat-loss
and efficiency-based
The user
is
Model
required
values.
A conceptual
compressor
to specify
the
model
is
following
values: D
-
total
c
-
actual
S input
-
synchronous appropriate),
i
s,fl
-
4.8
motor
maximum compressor
n.lsen
isentropic discharge
low-side
compressor
are also
full
mechanical
loss
gas,
specified
from
compressor
motor
speed
load
power
(optional),
shaft
efficiency compressor
and the user
(as
efficiency,
efficiency,
the
i hilo, by the
ratio,
motor
compression port.
heat
refrigerant
volume
or actual
nmot,maxnmech -
displacement,
clearance
compressor
The interna 6 can,
compressor
and from
discharge
compressor
according
suction
shell
to the
to
tube
to the
heat
loss,
choices
in Eqs.
and 4.9. specified . 4 hilo
=
Qhilo 0.03
directly,
'cm,actual' i
cm,actual
or
(see Appendix
A)
(4.8)
27
ORNL-DWG
1
IIII I
77-19443R
-DISCHARGE TUBE
hr
SUCTION TUBE
houtlet
. my
hsuction
mr
port
Fig.
4.2
Components
of Compressor
hdischorge
Energ.y Balance
port
28
specified
I
=
' can
'can
'cm,actual'
Oeg (lso
The explicit the
program
directly,
losses,
- rlmotor i,
as described
The unknowns
which
ih
suction
h h
port
discharge
port
outlet
(see Appendix .
Or 'mech)
(4.9)
'cm , actual ~1, are part
or fractions, in Appendix
A.
of the
input
data
to
'
need to be calculated
are:
refrigerant
rate
mass flow
enthalpy
at the
suction
port
enthalpy
at the
discharge
enthalpy
at the
shell
port
outlet
cl r
work done on the
refrigerant
ii
work
done on the
shaft
work
input
ii
A)
S
cm
they
compressor
rate of heat loss due to cooling compressor and motor
4 cooling and if
to the
are not
specified
explicitly,
the:
6 can
rate
of compressor
'hilo
rate of heat transfer from gas to the suction gas
These ten unknowns are calculated in Eqs.
from
of
the
shell
three
heat
loss,
and
the discharge
energy bahace
equations
4.10 - 4.12,
(. (hsuction
port
ir (hdischarge
-h
inlet)
port
-h
'= 'hilo
suction
+ 'cooling
port )=c$
-'can
3
'
(4'10)
(4.11)
29
and
'r
(h outlet
- hdischarge
and the seven through
port)
equations
defining
= -'hilo
(4.12)
'
given
in Eqs.
suction
port
4.8
and 4.9
and Eqs.
4.13
4.17.
fir = I& (h isen,discharge
port
-h
s = irhmech
Bcm=
nisenl
(4.13)
3
(4.14)
,
's'Tlmotor
=(1---l
il cooling
)/(3413
(4.15)
'
mech'motor"cm
(4.16)
'
and Ii
r
The combination compressor
i
cm
which
port
S oper
D'u suction
- 4.16
yields
Eq. 4.18
vol,suction
of Eqs.
4.10
(4.17)
port for
the
overall
balance,
(4.18)
= ~~r(houtlet - hinlet) + EIcan1/34’3 is
map-based c
energy
=n
refrigerant dependent
identical model.
to Eq. 4.7, Equations
properties), on hsuction
the
corresponding
4.8 - 4.15 coupled
port-
set
form
a non-linear
of equations
The enthalpy
expression
at the
where suction
for
the
(through ir
the
and mr are port
is
I
30
of W r’ calculational
The iterative is
equations
shown in Fig. is
h
suction port is calculated
h
from
suction
values
4.3.
the
= h
port
conditions
using
Eq. 4.20
(which
form
and the
discharge
where
port
al 1 of
to the
shell
the
outlet
4.20
compression
refrigerant
gas.
actual
modeled the
the
process
result
This
is,
process
compressor
body to the
Davis
and Scott
heat [12],
efficiency
term
frictional
sources.
Once h conditions at
port
by Eq. 4.19. (4.19)
are computed
pressure discharge
using
at the port
shell
is
computed
and 4.13),
isen,discharge
loss
discharge Dart at the discharge the discharge
is
through
in Eq. 4.16
assumption
that
in additional is
of polytropic
extra
hsuction
- 'can)"r
refrigerant
of course,
as sequence This
calculations,
given
port
at the
of
-h
port n.men
suction
port(4.20)
pressure).
contains
compression
shell.
pressure
port
+
system
is the enthalpy after an isentropic compression port conditions to discharge port pressure (assumed
isen,discharge the suction port Equation
from
suction
h
equal
the
=
h
suction
Eq. 4.11
this
Thereafter
+ 'cooling
enthalpy
h
in
and tcan.
the
of Eq. 4.10,
at the
combines
to begin
to hinlet.
+ (0 hilo
inlet
suction port the refrigerant
Next,
In order
rearranged
of h
inlet.
from
, thilo,
scheme used to solve
assumed to be equal
The refrigerant
h
tcooling
can be dependent
which
the
1 osses,
on mr and on theeheat
dependent
not
(and
processes).
There
in a manner might
has been calculated,
the
port
are computed is equal
to that
for
the since
is more properly is
heat the
similar
increase
which
port
that
gain correct
gas inside
an artifical
inefficiencies
enthalpy
nonadiabatic
handled
the
theoretically
refrigerant
above
all
in
transfer
compressor to that
the mechanical
be expected remaining
assuming at the
of
the shell
due to refrigerant
refrigerant outlet.
. b.
31 ORNL- DWG
v
a
CALCULATE THE REFRIGERANT CONDITIONS AT THE SUCTION PORT
.
81- 4743
4 ,
I c
COMPUTE THE ENTHALPY AT THE DISCHARGE PORT AFTER ISENTROPIC COMPRESSION
J
1
+ COMPUTE
I
CALCULATED
SPECIFIED
c
+ CALCULATE THE COMPRESSOR MOTOR SPEED c
4
COMPUTE REFRIGERANT MASS Fu)W RATE AND WORK DONE ON THE < REFRIGERANT r
\
4
COMPUTE MASS FLOW RATE OF THE REFRIGERANT 4
j
/
L
,
4
\
0
\
4.3
/
I
1,
I
&r Fig.
,
CALCULATE THE FULL- LOAD MOTOR SHAFT POWER
DETERMINE THE FRACTION OF FULLLOAD MOTOR POWER
CALCULATE THE COMPRESSOR MOTOR EFFICIENCY
\
DETERMINE WORK DONE ON THE REFRIGERANT
. CONVERGENCE
Iteration on Internal Energy Balance Efficiency-Based Compressor Model
for
the
Loss and
32
The volumetric from
efficiency
Eq. 4.21
given
nvol,suction
based on suction
by Davis
and Scott
=
port,actual
port
conditions
is computed
[12].
'vol,suction
port,theoretical
-b
(4.21)
where
11 vol,suction
=
port,theoretical
1-c
-
refrigerant
pressure
at discharge
-
refrigerant
pressure
at suction
Y
-
specific evaluated
heat ratio at suction
C
-
actual
P discharge P suction
and "a"
port
and "b"
compressors Data).
valid
for
clearance
Davis
clearance
empirical
capacities
port
derived
refrigerant
ratio, from
test
data
but of the same series
[12]
similar
port
for the specific port conditions
volume
constants
and Scott
"basically
note
units
that
which
their
differ
(defined
in
should
be
equation
only
for
in stroke
or
volume."
Once the is
power,
are
of different
Block
point
port
is
reached fl,
of compreisor
operating the
refrigerant,
are
then
on the efficiency.
motor
4.3.
If
for
compressor
the
, and the from is motkr
Eqs. fl
is
a decision
compressor-motor as input
speed and efficiency
S oper The refrigerant i
has been evaluated,
been specified
i.e.,
computed value
efficiency
in Fig.
has not
values,
respectively.
computed
volumetric
data,
full the
are taken
input
load
shaft
values
to be the actua2
= S and n input motpr = 'motor max' mass flow rate, m , the work input required
4.17, the
full
4.13, rated
to achieve
load
iotor
and 4.14, (full)
load
power,
is
to fl
respectively.' that
The
must be imposed
the assumed maximum rated
motor
33 Alternatively,
if
is
speed, Soper'
and efficie;cy,
of fractional
rated
fl
of ffl,
motor
specified
as input
nmot , are
(full)
load,
f
The operating
is
fl
speed,
f,,,
computed
functions
in Eq. 4.23.
(4.23)
's,fl)
is assumed to be a linear
function
i.e.,
Soper = (l-0
+ afl ffl)
is the synchronous motor speed (e.g. S sync specified in the input data, i.e., S sync = S. The value of afl is determined by solvi?::. conditions
full-load
(f,,
motor
= 1.0)
speeds
using
known values
afl =
(i.e.,
'fl
(4.24)
Ssync
where
load
the motor
as built-in
as defined
= 'r'(?nech Soper,
data,
3600 or 1800 rpm) as . 4.24
under
of synchronous
fulland
- 'sync). s
Since 4.13), not
and s%~
directly
used with results
S
is
a function
G
is dependent
solva;rble Eqs.
4.13
for
of i
S
in Eq. 4.25, S oper
onrS oper .
and 4.1?':0'
(tE%Ggh
Eqs.
(from
However, Eqs. solve for S oper
4.24,
4.23,
Eq. 4.17), 4.23
Eq. 4.24
and 4.24
algebraically.
=
and is
can be This
(4.25) G&-
afl
($)(g5J
where
60~1 vol,suction
discharge
port
port
D(l728v
-h
suction
suction
port
port >
3
(4.27)
34
and
H f
fl
=
T/(3413
(4.28)
rlmech ws,fJ
iJ r
and the
constants
Once 'oper are calculated After
has been evaluated from ffl
calculated
1728 and 3413 are used to maintain Eqs.
from
the,fit
=
The coefficients a fit
slot
size
Eq. 4.25,
4.27,
the compressor efficiency
nmotor,max
5 i=O
published
i
1;r'
C).
efficiency
motor
'Imotor,i
and ffl
r'
efficiency
given
(4.29)
(ffl.'i
are assigned
[13]
can be
by Eq. 4.29.
values
These coefficients
by Johnson
and maximum motor
for
to f,,,
i in Eq. 4.29
(see Aipendix
to data
values
units.
and 4.28.
of motor
nmotor
Data subroutine
from
4.26,
has been computed,
rlmotor
Block
from
consistent
for
the
were obtained
a motor
of 86% at a load
in
with
"medium"
of 6.8
N-m (80
oz-ft). The next
step
and efficiency
in the
calculations,
have been computed
value
has been calculated
input
from
for
i r,
value
of i
(optionally)
ihilo
and can
A new refrigerant
next
using the is
compressor two methods
is
the
to calculate
motor
speed
and a
compressor
power
Eq. 4.30.
The computed
until
the
by one of these
GJ cm = fir/h
culated
after
Eq. 4.19
change
smaller
in the than
is
then
mech'motor
used to evaluate
using
Eqs.
enthalpy
at the
and the
sequence
value
a specified
of h
4.16,
4.8,
compressor
suction tolerance.
(4.30)
>
4
suction
shown in Fig. port
and
cooling and 4.9. 4.3
port is
is
repeated
from one iteration The refrigerant
calto the
enthalpy
at
-
35
compressor
shell
rearranged
form
exit,
outlet
outlet
= hdischarge
the
associated
and the
refrigerant
been computed, vergence
the
state
Once all
of these
iterative
efficiency-based
model
to the
values
in Section
defined
Eq. 4.31
(a
by Shaffer
in Section loops
of overall
isentropic
The suction
and Lee [14]
Ah
=
Ah
compressor
at condenser outer
shell
inlet
pressure
have
drop
con-
4.2.
have converged,
a suction
n sh
(4.31)
at the
to the
calculates
4.2.
d hilo hr
--
properties
proceed
earlier
is
using
and properties
calculations
described
described
computed
port
refrigerant
loop
addition
then
of Eq. 4.12), h
After
is
houtlet,
the
gas heating
loss
efficiency
and volumetric
gas heating
and in
efficiency
efficiency,
nsh,
as
isen,inlet
(4.32)
isen,suction
port
where
Ah
specific enthalpy change for an isentropic compression from she22 inZet conditions to shell outlet pressure
F
isen,inlet
and
Ah
isen,suction
The overall
isentropic
rl sh by Eq. 4.33
=
port
specific enthalpy change for an isentropic compression from suction port conditions to shell outlet pressure
compression
efficiency,
no,
is
related
to
[7,14-j. 11
cm
=
rl
sh 'isen
'mech
'motor
(4.33)
36
The terms five
on each side
efficiency
terms
magnitude input
values
in the
lossthan
note, for
n,,,h,
of the heating
with
be checked suction
four
between
for
by the
gas enthalpy
Eq. 4.16
this
dividing
through
model.
the
caution
the
loss
check
relative
This
the compressor
+ 'cooling
in suction
gas cooling
inlet
and suction
in termination
and the
requirement
port.
of the
Such a situation
or zero,
- 'can
(oracan) certain
Data Set."
be positive
selecting
is because
shell
and results
in and iC,
can result
use of Eq. 4.10 change
for
as an independent
(orahilo),
"Inconsistent
a message
i hilo
or,
must exercise
situation
output
All
inefficiencies.
parameters
dhilo Using
to identify
nmOtoTP ihilo
is an unrealistic
program
and also
user
independently.
in the
serve
compressor the
computed
are printed
and efficiency-based
combinations rather
various
thus
These values
calculations
of the
As a final
This
model.
compressor
are
in Eq. 4.33
and efficiency-based on the
of Eq. 4.33
that
can the
i.e.,
(4.34)
2 '
gives
+ ('
- n,,,hn,oto,)
w,
by i cm, an alternative
- km
(4.35)
2 '
expression
is
(4.36)
37
5.
FLOW CONTROL DEVICES 5.1
Introduction
The ORNL Heat Pump Design fixed
level
expansion high
of condenser device
which
employ
valves devices held
of the
each of these
to compute
the
design
TXV, and orifice
that
involves
using
to obtain
rate
from
the
described
three
would
the
between
compressor
One of the
at the empirical for
requires
inlet
pressure through
an equivalent
or more, the
subcooling
(this
from
BLOCK
and condenser
models
Capillary
corresponding in an iterative
refrigerant expansion
mass flow device
as
Tube Model
capillary
refrigerant tube
given
capillary
and subcooling the capillary
tube,
the
the
is
capillary
is specified, the calculated
three
in such a way as
characteristics
through
expansion
subcooling
called
in the Heat Pump Model
to curves
a standardized
is
the
subroutines
any of these
condenser
a particular
between
thermostatic
the specified
and that
of the capillary fits
flow
a
3.1.
options
of one,
model
produce
compressor
5.2
tube
for
device
a balance
in Section
operation
that
submodels
parameters
control
is used with
loop
event
for
contains
so that
some assumed operating
When a flow
DATA). model
In the
to specify
refrigerant tubes,
orifices
user
parameters
The program
capillary
and short-tube
can be modeled.
fixed,
the
system. for
the
or design
to control
correlations
(TXV),
allows
subcooling
in order
and low sides
Model
for tube
tubes
is
to simulate
in parallel.
pressure
and degree
or tubes.
The model
in the ASHRAE Equipment tube
flow
rate
R-12 and R-22. is given
as a function The actual
the
The capillary of subcooling consists
of
Handbook
[15]
of inlet mass flow
rate
by
in = +N r cap "k
(5.1)
38 where Ii;
-
standardized
N cap
-
number of capillary
@
-
flow
The capillary Equipment inside
flow
factor,
Handbook
[15]
for
tubes
each particular
mass flow
rate
from
the ASHRAE
combination is
of N
also
mi isciyven
P, and two functions
pressure,
in parallel,
4, must be obtained
The value
diameter.
The standardized
rate,
factor.
tube
tube
inlet
mass flow
of length
required
by Eq. 5.2
of the degree
and
as input. in terms
of
of subcooling,
m
0
and k.
(>
P k = m. 1500
ii;
mo, and exponent,
The coefficient, subcooling, within
AT, as given
1.5% of the
(5.2)
k, have been fit
by Eq. 5.3 and 5.4,
curves
across
the
range
as functions
such that of Fig.
of
mC agrees
40 in Ref.
to
15
3.56 m
0
= 356 + 0.641
k = 0.4035
In the level
situation
of condenser the
capillary
compute
the
flow
pressure fit
tube
factor,
tube
additional
curves
be added by the
user
critical
conditions.
in
Design lieu
Model
is used with
of a specific
would
give
pressure. capillary
control
the desired
subcooling.
assumes that However,
in the ASHRAE Equipment to predict
flow
a specified
are used in such a way as to
used in the program critical
(5.4)
e-0*04AT
correlations 0, which
model
is at or below
+ 0.4175
the
subcooling
device,
The capillary
where
(5.3)
tube
Handbook
the downstream
Smith
[16]
[15]
which
performance
under
has could non-
39
The current capillary the
tube
final the
to zero will
not
incomplete the
For all
flow
cases
zero
is
0 is
5.3
state
set
Expansion
l
specific empirical nozzle and tubes,
l
additional empirical equations tube liquid line temperatures, loadings.
used by Smith
ii
where
lil
r,TXV
in
r,TXV
=c TXIJtAToper
on the
keeping
with
the
rate
AT
- actual
operating
AP TXV
entrance. value
Model
one size
expansion of distributor
to correct for nonstandard lengths, and nozzle and tube TXV is a form
- available
ATstatic)
of the
equation
that flow
liquid
line
density,
of the
TXV will area
p,,
standard
in Eq. 5.5 are defined
has orifice
as follows:
pass, coefficient,
superheat,
superheat (superheat open), and pressure
(5.5)
(p??AplXV)1’2
genera 1 form
parameters
- mass flow
static barely
-
refrigerant
orifice
static-
for
of a cross-charged
- general
AT
required
thermostatic
correlations and
C TXV oper
the
Valve
model of a cross-charged
The remaining
equation.
tube
[16]:
a dependence
been added,
the
,'
a general valve,
model
that
capillary
contains:
0
The general
liquid
to zero.
Thermostatic
The TXV subroutine
in the
as input,
that
subcooling.
to make sure
at the
specified
assuming
of condenser
"flashing
at the
condensation,
continue
degrees
be checked
in a two-phase
factor
condensation
of incomplete
concerning
should
condensation
incomplete
and calculations
have
results
is
handle
are printed
final
refrigerant for
set
messages
line," If
is
conditions
error
cannot
entrance.
subcooling
1 the If
model
drop
at which
from TXVinlet
the
valve
to TXVexit.
is just
40
The assumption
AT
oper' that is the
p, and AP,,,,
independent
of evaporator
efficiency
such valves
tend
heat
the
effective
actual
*Tmax eff,
= ATstatic
be used to compute
AT AT
defined
static'
b fat,
the
The given factor
valve
in the
mass flow
greater
(ATrated
mass flow the
rating
bleed
over
a
the maximum
(5.6)
- ATstatic)
input
before
rate. data
pressure
drop
Eq. 5.5 can
The value
of CT,,
[17]: (tons),
of the
valve
(at
75% of
and
factor.
rating
TXV rating Block
than
of the TXV valve
earlier,
capacity
and standard
(specified
used in above since
superheat
have to be calculated
from
capacity
is
the rated operating superheat the maximum valve opening),
rated'
described
of AT in Eq. 5.5. oper C,,, and the available
a refrigerant
variables
the
6 rated'
type
opening
where
+ 1*33
AP,,,,
the TXV valve, on four
valve
Most TXV valves constant
superheat
is used in place ATmax eff The flow area coefficient,
depends
a given
a certain
pressure.
a relatively
operating
superheat,
across
provide
that
conditions.
ATmax , eff
then
will
implies
pumps are of the
to maintain
of operating
If
TXV valve
at a given
higher
range
of a cross-charged
is used in conjunction conditions
Data routine)
for
with
a specific
to calculate
the
the
bleed
refrigerant rated
refrigerant
rate:
f2,OOO 0 r-i r,rated
=
h
rated
evap out,rated
bfac -h
liquid
(5.7)
line,rated
where the
constant
Btu/hr.
12,000
is
used to convert
from
tons
of capacity
to
41 h
is the evaporator outlet refrigerant enthalpy rated evaporator pressure and superheat,
evap out,rated
at
and h
liquid
is
line,rated
CTXV is calculated
'TX,
the refrigerant line temperature.
from
= --)(hT
Eq. 5.8
enthalpy
using
at rated
liquid
mr rated: ,
Iir,rated rated
,p
static
----TPr,rated
rated
at rated
liquid
(5.8)
)V
where =
Pr,rated
refrigerant
density
line
temperature
and =
AP rated
rated
The available remaining
pressure
unknown
the TXV inlet
pressure drop
nozzle
The pressures pump model tube for
pressure
drops
one set
additiona
empirical
data
A,11 the
equations
pressure
are computed
da~~'~~~pthe
the drops
the
ptfessures
at
in the
to correct
and distributor
non-standard
fits
heat
and
R-22 fZow and
for
loading from
the
empirica7Y fits
sizes for
in
The nozzle
specific
and tube
were obtained
(5.9)
elsewhere
TXV routine. using
nozzle
equations lengths,
using
is
for
liquid
R-22,
to published
line
22, and performance
[18]. Distributor
the
tube
AP,,,,
- APnoz - APtube
in,evap
are calculated
of distributor
temperature,
502.
input
computed
and the
Pin TXV and P. and ari
device.
i.e.,
-P
aP P TXV = in,TXV
expansion
the TXV valve,
is
inlet
and tubes,
across
across
This
in Eq. 5.5.
and evaporator
distributor
drop
refrigerant
nozzles flow
and tubes
are
in each evaporator
often circuit
used with
TXV's
and to assure
to equalize proper
42 TXV operation.
At standard
have a pressure
drop
(15 psi)
for
R-121
69 kPa (10 psi) the
user
nozzle
culation
of the
in the
actual
capacity
tube do not
=
i no2
r;lr(h
",
is
-h
evap out,rated
0tube
~,,,,
for
components. is
the
cal-
and of each tube
the mass flow
liquid
across
the
cj,,
rated
,
nozzles
calculated
and tubes,
acor
(5.10)
(5.11)
= qnoz'Ncircuits
rate
= (3)12000
>
line,actual
by the
compressor
is the number of circuits in the evaporator. N circuits Next, the capacities are computed which yield the drops
allows
computations
have these
nozzle,
kPa
which
of nPnoz and nPtube
of the
will
each have
has been provided
which
nozzle
i.e.,
tube'
where
will
and distributor evaluation
distributor
R-22 and R502 [103
tubes
option
to systems
step
the
for
distributor
An input
applications
The first tj
and the
the
conditions
172 kPa (25 psi)
drop.
to omit
specific
of
rating
model
rated
and
pressure
i.e.,
10
(T
- 40)/201.0
(5.12)
sat,evap
and
4tube,rated
= (1.1)12000
aCOr .sor
10
(T
sat*evaP
- 40)/177.64
(5.13)
where the
constants
specifications acor
=
3 and 1.1 are tonnage
ratings
from
the
equipment
[18], correction factor than lOO"F, i.e.,
for
liquid
line
temperature
other
43
= lo(‘OO a
car I
- Tin
T
,)/155.18
T
(100 -Tin:,,,),140.19 10
in,TXV in,TXV
'.'O"
(5 ,4J
,100
.
and =
Bcar
correction i.e.,
factor
tube lengths
for
other
than
30 inches,
I3car = (30/&be)1’3 Equations
5.12
and 5.13,
a Sporlan
[ll]
nozzle
respectively,
No. 2.5
represent
and l/4
other nozzZe or tube, or refrigerant, replaced (the correction terms acor do not
the
5.11
and the
tube
loadings
drops,
inch
the
OD copper
R-22 capacity tubes.
of
FOP any
Eqs. 5.22 and 5.13 must be and BcOr, Eq. 5.14
and 5.15,
need to be replaced).
Given
0 tube"
(5.15)
actual
rated
nozzle
capacities
Lnoz and Ltube,
and tube from
capacities
Eqs.
defined
5.12
from
Eqs.
and 5.13,
the
as ~,,,/~,,,
respectively, and the tube,rated APnoz and aPtube, can be found.
nozzle
rated and'tube
5.10 nozzle
and and
and pressure
For R-22 or R-502
I
25.0 (L
AP = no2
29.4
)1.838
AP tube
.
Il.2 no2 > 1.2 L no2
(5.16)
5 1.1 noz > 1.1 L noz
(5.18)
L
noZ 0.9547 (Lnoz)
= 10.0(Ltube)'.8'22
For R-22
AP = noz
I
15.0(Lno2)'*8'7 )I.265 15.8l(L noz
L
44
A!'
=
tube
I
Equation
5.9
Eq. 5.5
lo.o(Ltube)'.772
L tube
'
12.265(Ltube)1'3377
L tube
>lS6
is
then
to evaluated
subroutine
from
the
which,
(5.19)
in turn,
is
used in
mr TXV.
In a case where the
AP,
used to obtain
l-6
a +ixed
calculates
level
the
of condenser
required
rated
subcooling
capacity
is
of the
specified, TXV valve
equations ii C TXV
rir,rated
=
6
AT
oper Or by ATrated tube pressure cooling
is
is
(AT oper
sta:ic)(","PTXV'1'2
CTXV(ATrated
replaced
- ATstatic)(Pr,ratedAPrated'1'2
(5*21)
out,rated - hliquid 12000 bfac
(5 . 22)
by ATmax eff
if AToper 5 aT,t,ti~* drop computations is model
is
not
In such cases,
calculations
continue
as described
incomplete
condensation
values
is
The short-tube Heat Pump Design
ratios
also
AToper > ATmax,eff
if
to omit
available
the
nozzle
when condenser
and sub-
data
incomplete
the
subcooling
in the
capillary
the
program
specified,
five
from 7.5
Short
orifice Model
for
diameters from
to handle
is
set
tube will
condensation to zero
If
case.
set
the
and
TXV
to zero. 5.4
with
Eq. 5.6
The option
intended
at the TXV entrance.
obtained
from
line,rated)
specified.
The current
rating
(5.20)
- AT
il r,rated(hevap
=
rated
where
=
subroutine
which
uses correlations 0.127
1.067
to 11.9)
Tube Orifice
m (0.5
to 1.694 using
R-22.
Model is
included
developed in.)
long
mm (0.0420
in
by Mei [19].
Carrier
ORNL He
Accurators
to 0.0667
He observed
the
pressure
inches) drops
(L/D
45 between
620 and 1515 kPa (90 and 220 psi)
levels
of subcooling
observed
from
refrigerant
470 lbm/h).
The standard
was solved with
both
level
for
r
orifice
orifice
of subcooling
rates
ranged
at the
across
0.63683 - 0.019337
x
=
C which short
tube
Equation
(P
-P
2Prgc(Pin
- 0.00325AT
4 i
to correlate
difference
occuring
the at
data
orifice,
AP, and the
+ 0.006aT I
,
AT < 40
1 l/2
2Prgc(Pin
- 'in,sat)
to within
low subcooling
7.5% (with
levels), inlet
the maximum
where
P in' to the orifice,
pressure
(5.24)
AT > 40 ,
at the
P in,evap' the inlet
inlet
to the
respectively.
If
the
rather
than
solved
for
As in
correlated
5.24,
q/2
- 'in
(5.23)
orifice,
in,evap
I[
are the pressures at the and P in,sat to the evaporator, and the saturation
(150 to
,
for
was found
The
to 213 kg/h
for
l-ID2
inlet.
was then
AT.
in
and
in Eq. 5.23,
C
the
inlet,
68.0
c(2g PAP)"~
=
coefficient
drop
restrictor
at the
from
relation
$/Aorifice
the pressure
IID2 4
r;l
the
=
the
0 to 28 Co (0 to 50 F")
mass flow
G r
across
user
has specified
selecting the
orifice
the case of the
specified,
the
a fixed
a particular diameter other
corresponding
flow that
control
would
two models, orifice
of condenser
level
device
provide
Eq. 5.24
that
if
incomplete
diameter
is
set
subcooling is
subcooling. condensation
to zero.
is
46
The user at the the
flow
three
results extended
should
always
control flow
should beyond
device
control not their
check
that
entrance
device
models.
be used because intended
is the
range.
the
computed
refrigerant
equal
to zero when using
If
is
flow
it
not,
control
quality any of
the calculated models
have been
47
CONDENSERAND EVAPORATORMODELS
6.
6.1
Introduction
The ORNL Heat Pump Design air-to-refrigerant
and evaporators
performance
a modified version of the effective surface approach when there is dehumidification,
0
the Thorn correlation the Moody friction phase refrigerant
0
friction partially
vs.
principal
NtU correlations
for
the
differences
there
heat
exchangers
with
unmixed
and the
flow
superheated
differences
on both
the
, and subcooled
6.1
is
a general
organization
and iterative
6.2
is
diagram
a similar
The air-side density
air
calculated the
Universal
the
air
temperature.
inlet
several being
equivalent specified
estimated
divided
by the
flow
for
the
refrigerant
Since
the
for the
data),
mass flow
number of circuits
the
The for
the
the
condenser.
chart,
outlining
model.
Figure
calculations. in air
heat
exchanger
is calculated
the
input
data and the
using
atmospheric
(given
in BLOCK DATA),
exchangers
are modeled
circuits the rate
[3].
condenser
gas equation
refrigerant input
the
or flow
specified ideal
they circuits
and for
for
each heat
gas constant
parallel with
rate
are
computations
evaporator
diagram,
for
from the
pressure,
the
into
the evaporator rate
out where
sides
dry,
algorithm.
refrigerant
regions
loops
for
mass flow
volumetric
block
for
identical,
and evaporator
parallel
for
drop
are not
and refrigerant
regions
the
the
air
drops and the single-
have been used assume that
are separated
and two-phase
Figure
which
a
temperature
pressure
are pointed
of equivalent,
two-phase
for
the dehumidification
the condenser
calculations
superheated,
transfer
and evaporator
around
methods
consist
refrigerant-side
from
condenser
center
The calculational
occur.
heat
for the air-side wetted coils.
are many similarities, together
for
for two-phase refrigerant pressure factor chart plus momentum terms for pressure drop, and
factor equations wetted, or fully
the models
of
by using:
0
discussed
the
the
effectiveness dry coil,
Since
air
calculates
0
Although the
condensers
Model
(the
air-side from
to obtain
the
values
actual
mass flow compressor
for
and
as
number rate model
each circuit.
and are
48 ORNL-DWQ
Sb4750R
.
CALCULATE AIR-AND REFRIGERANTSIOE MASS FLOW k4TE PER CIRCUIT AND QEOMttRlC PARAMETERS DETERMINE SUBCOOLED AND SUPERHEAlEO REFRlGERANt PROPERTIES AND REFRIQERANTSIDE HEAT TRANSFER COEFFICIENTS
*
4 DETEf3MI~E REFRIGERANT PROPERTIES At@ HEAT TRANSFER ,3%F&IENT FOR TWO-PHASE 4 ’
k AOJUST THE TWO-PHASE HEAT TRANSER COEFFlCkNT FOR THE REQION WHERE THE BULK TEMPERATURE EXCEEDS THE SATURATION TEMPERATURE
COMPUTE AIR-SIDE PROPERTIES AND PRESSURE DROPS, OPTIONALLY ADD FAN AND/OR COMPRESSOR HEAT LOSS TO INCOMING AIR .AND COMPUTE AIRSIDE HEAT TRANSFER COEFFICIENT
RETURN CODE
t 1'
v
1
COMPUTE REFRIGERANT- SIDE PRESSURE DROP FOR SUPERHEATED ,TWO-PHASE, AND SUGCOOLEO REGION I
QPTIONALLY ADD FAN AND/OR COMPRESSOR HEAT LOSS TO OUTLET AIR AN0 COMPUTE UA VALUES
.
Fig.
6.1
General
Structure
of the Condenser
Model
ORNL-
DWG
864751
. f INITIALIZE ITERATION I PARAMETERS 1 c CALCULATE AIR- AND REFRIGERANTSIDE MASS FLOW RATE PER CIRCUIT AND GEOMETRIC PARAMETERS
.
I
f
DETERMINE SUPERHEATED REFRIGERANT PROPERTIES AND SUPERHEATED VAPOR HEAT TRANSFER COEFFICIENT
*
t DETERMINE ENTERING QUALITY AND AVAILABLE HEAT TRANSFER IN THE TWO-PHASE REGION * DETERMINE REFRIGERANT PROPERTIES AND HEAT TRANSFER COEFFICIENT FOR THE TWO-PHASE REGION L CALCULATE AIR-SIDE PROPERTIES AND PRESSURE DROPS, OPTIONALLY ADD FAN AND/OR COMPRESSOR HEAT LOSS TO INCOMING AIR,AND COMPUTE AIR-SIDE HEAT TRANSFER COEFFICIENT
COMPUTE REFRIGERANT-SIDE PRESSURE DROP FOR SINGLE AND TWO-PHASE REGION A I
+
COMPUTE NEW AVERAGE EVAPORATING TEMPERATURE
OPTIONALLY ADD FAN AND/OR COMPRESSOR HEAT LOSS TO OUTLET AIR AND COMPUTE U A VALUES
Fig.
6.2
General
Structure
of
the
Evaporator
Model
50
The average
densities
two-phase
region
calculated
from
peratures
in the
the
of each coil the
current
heat
single-phase
for
conductivity,
the
6.2
computes
the
Single-Phase
region
in the
condenser
by Eq. 6.1.for throughout
gas flow
this
report
average
i.e.,
of ah at
p
an abrupt
heat
=
for
the
condenser
thermal according
for
the
by Kartsounes
to a
vapor
region,
and Erth
[4]
cp,vm in Heat Exchanger
coefficient
is calculated for
viscosity,
heat
tem-
properties for
the are
saturation
are calculated
Coefficients
transfer
from
the
in
of vaporization
and superheated
developed
Heat Transfer heat
of the
The specific
by a routine
The refrigerant
heat
heat,
[5]. value
and vapor
latent
(subcooled specific
local
liquid
The thermophysical
evaporator),
by Flower
Cp V, is determined which
estimates
exchangers.
and liquid
written
refrigerant
and the
refrigerant
and superheated routine
of the
for
the
Tubes
superheated
(as reported
in the
MIT Model
contraction
entrance
[ZO]
transfer
coefficients
and h for
[3])
(h is used enthalpy
variables). h
where
N,
=
GrD/p
=
c,
=
=
-2/3 *I+
N '2 Re
(6.1)
and,
I
for
NRe < 3500
0.01080
for for
3500 5 NRe < 6000 NRe 2 6000
-0.78992
for
NRe < 3500
1.03804
for
3500 5 NRe < 6000
-0.13750
for
NRe 2 6000
1.10647
c,
C G c 1 r p,v
3.5194
x 10 -7
(6.2)
(6.3)
51 The constants Eqs.
6.2
Appendix
used to define
and 6.3
the
are assigned
step
in the
functions
C1 and C2 defined
BLOCK DATA subroutine
in
(see
C).
The heat
transfer
condenser
and the
using
Dittus-Boelter
the
coefficients
superheated
for
region
correlation
the
subcooled
in the
evaporator
for
fully
region
of the
are computed
developed
flow
[Zl]:
(6.4)
where
"C" is 0.3
when being
when the
Two-Phase
The two-phase the
evaporator
local
values
where
tube
wall.
to assuming coefficient,
being
cooling
Refrigerant Heat Transfer in Heat Exchanger Tubes
heat
transfer
are average over
the
the
of tube
change
Assuming
over
the
and 0.4
range
related
heat
flux)
is given
Z
ave
= J Z
the
practically
[3,22],
the
s
=
' dz
and
integrating The actual quality
in quality
[3] of dx by
refrigerant
and the
constant
(as opposed
average
X
0
condenser
refrigerant
by
lz i
of
between
h(x)dz h
the
region.
to a change
AT remains
Coefficients
by effectively
two-phase
in temperature that
for
obtained
of the
dz is
a constant have,
coefficients
values
length
is performed
a length
and AT is
is
heated. 6.3
integration
refrigerant
x Odx i ,
heat
transfer
which
reduced
The local calculated Travis
to
heat
transfer
as a function
coefficient,
of the
quality
h(x),
for
according
the
condenser
is
to a correlation
by
[22].
I
0 9 F(Xtt) kl
h(x)
*Pr *Re ’
F(Xtt)
DF2
< 1.0
= 4
(6.5) kL *Pr
o g *Re ’
F(Xtt)1*15
1.0 < F(Xtt)
DF2
< 15
where (6.6)
Gr D (1 -xJ N = Re
F(xtt)
= 0.15
Yl
(6.7)
,
+ 2.85Xtt-o'476
(6.8)
, and
>
N
0.707 Npr NReoe5 5.0 Npr + 5.0 F2
lntl.0
Re
+ Npr(0.09636
=
NReo'585
l.O)l --l.O)]
50 < N
Re
LnCl.0 5.0 Npr + 5.0 Ln[l.O
+'5.0
c: 50
NPr] + 2.5 1nC0.00313
< 1125
NRe0s8121 NRe0S812]
NRe > 1125 i
(6.9)
53
The integration
is
carried
Ax and has been changed
MIT Model [3]. to liquid adjusted where bulk
slightly
heat
from
condensation
given
temperature
in
steps
the
to the
heat
and Glicksman
manner
at
the
transfer
of extrapolating
end points
coefficient
is occurring
exceeds
of a constant
Hiller
by Rohsenow [23]
(desuperheating)
refrigerant
over
coefficients
two-phase
a correlation
that
pertain
transfer
The average using
equation
by a summation
The modifications
and vapor
integration.
out
for
is
the
region
at the wall
the saturation
of the
but
the
temperature.
The
>
(6.10)
is
T h
The bulk begins
=
tP
refrigerant at the
v,ds
h
wall
h
P9v
is calculated
v’T T v,ds
tp,in r-l
=
sat,in
fg
TV ds, where
temperature,
tube
l/4
-T
refrigerant
from Eqs. -T
6.11
condensation
and 6.12
where
a,in
(6.11)
and
(6.12)
T
tp,in phase
and Ta in are the region
And the
The average the
evaporator
is for
derived
[24]
and from
the general
region.
Equation of the
inlet
air
local
heat
for
from a correlation
expresses transfer
12 in
of Sthapak the
heat
coefficients
the
the
two-phase
developed
of refrigerant
observations
entering
two-
respectively.
coefficient
evaporation 6.13
temperature
temperature,
heat-transfer
Noerager
terms
refrigerant
[25]
transfer
region
of
by Chaddock
and
horizontal for
the
coefficient
as functions
tubes dry-out in of refrigerant
54 quality
from
and from
the
dry-out
inlet
to the
to exit
quality, 'do - s xi
1 h
dry-out h2(x)
the
for
Xtt
liquid
is
between
from
xi
to xdo, .
xdo and x . 0
..
o dx s + Xdo h2(x)
(6.13)
tP
two integrals
xxodx i
separately,
h&x) where
$(x)
X
dx hlTx) s
Examining
point,
as defined
= 3*OhQ(Xtt
in Eq. 6.6
refrigerant
obtained
hi(X)
hi(x)
given
Eq. 6.4.
'R l/3
by Eq. 6.14
1 )2/3
(6.14)
and hL is the
from
= 3.0$(;;-)
is
'v $1
heat
transfer
coefficient
Thus
0.0667(;
x x)O.6
V
and
J X
'do k i
Xdo (1 - x)06 xO.6
J X
dx
(6.15)
i
where
0 0 Pt
C
Equation yield
6.15
=
3*0ht
can be expanded,
l/3
-7
truncated,
lJ
V
0.0667
5
and integrated
term
by term
to
55
The second nonlinear phase pure
integral
in
interpolation
value
at the h
vapor,
of the dry-out
from
V'
the
numerator heat
point,
Eq. 6.4,
of Eq. 6.13
transfer
hl(xdo),
from
of the
The second Eq. 6.17,
evaporator
integral
from
Eq. 6.14
the
to value
twoof
i.e.,
x do and x0 are refrigerant
outlet
based on a
coefficient
h’ltxdo) where
is
qualities
or the
in Eq. 6.13
at the
two-phase
region
can be evaluated
- “VI dry-out
(6.17) point
(whichever in closed
and the
comes first). form
using
i.e.,
(h, (Xdo)Ch(Xdo)- hvlF
X
0
+j-=
/
X
2(xo
- 'do)
'do
A value
of 0.65
is
assumed for
6.4
Air-Side
The air-side McQuiston the
heat
[26,27],
correlation
h
given
Ch,fXdo)
- h,])
{ h&xdo)
b'l(xdo)
- hvl}
xdo in the model Heat Transfer
transfer
Yoshii
{ hl(Xdo)
[28],
coefficients and Senshu
[25].
Coefficients are based on the work of [29]
and are calculated
a
by
by Eq. 6.19.
1 - 1280 N, NRe-lm2 =
(6.18)
C G c N _ -2'3 0 a pa Pr
j 1 - 5120 NRe-ls2
1
(6.19)
where j = 0.0014 N Re=
+ 0.2618
(,
1 FJ-o*15
(y
)
-OB4 ,
GawT I lJ
and C
0
= 1.0, 1.45, or 1.75 depending on whether the fins are smooth, wavy, or louvered (see Appendix G for parameter definitions).
/
Equation
6.19
over
Reynolds
the
transfer
was obtained for
approximately
extensive of 3,000
constant
C .
a number of fin-and-tube
surfaces
are assumed to be referenced
increases smooth
for
fin
heat
values.
Equation
number of geometric spacing,
and the
calculated which
using
is
Heating,
a modified
version
based on correlations
evaporator dry
heat
which
is wetted
coefficient,
The fin and for
on the work a tube
the
of Schmidt
surrounded fin
arrangement).
This
tube
changes
spacings
[32]
shape
calculate
the
surface
a the
fin
properties
are
[5]
Society
of
[30]. portion
of the
is calculated
from
[31]. (6.20)
effectiveness
evaporator
as reported fin
segment
surrounding
that
occur
as the
fin
longitudinal
[33]
for
(the
in a staggered to properly
conbased
and Tree
of a sheet
each tube
has been generalized
for.the
are calculated
by McQuiston
work
tube
handle
and transverse
are varied. 6.5
Figures
the
for
($)“.lolha
of the
by a hexagonal
representative orientation
region
for
rows,
Engineers
from Myers
= 0.626
a,w
thus
from
by Flower
due to dehumidification
and overall
dry
to adjust
by the American for
area;
area
The air-side
coefficient
fin
to account
of a subroutine
h a, by Eq. 6.20
efficiency
surface
intended
Conditioning
transfer
available.
wavy and louvered
number of tube
published
increased
assumption
are not
terms
spacing.
and Air
h
denser
such as the tube
equation
and surface
includes
transverse
Refrigeration,
are
The heat
this
for
coefficient 6.19
effects
The air-side the
transfer
fin
to smooth-fin fins
fins
are assumed to be
however,
so calculated
wavy and louvered
in both
on smooth
Data to verify
transfer
Co values
fins smooth
geoietries,
coefficients
data
2 NRe 5 15,000.
wavy and louvered
The heat the
test
by the use of the
by the multiplicative for
from
number range
coefficients
predicted
56
6.3
and 6.4
performance
Heat Exchanger are block of the
Performance
diagrams condenser
for
the
subroutines
and evaporator,
which
respectively.
57 ORNL-DWG
El-4742R
CALCULATE THE REFRIGERANT TEMPERATURE AT THE STARTOF THE DESUPERHEATING REGION
f
1
COMPUTE THE EFFECTIVE DRIVING ENTHALPY DIFFERENCE FOR TWO-PHASE REGION
ITERATE TO FIND FRACTION OF COIL IN VAPOR REGION f” \\
f SET
ftp= 1 - f,
AND
CALCULATE
THE
EXIT QUALITY
I
>
COMPUTER FRACTION OF COIL IN TWO-PHASE REGION f
tp
NO
1
SETf
=f-(f
AND
C&PUTE?,q
u&
tf,, AND
FOR SUBCOOLED
REGION
1
1 ‘COMPUTE C, FROM ESTIMATED cp FOR THE SUBCOOLED REGION t
I
,
CALCULATE EFFECTIVENESS AND NTU FOR SUBCOOLED REGION AND A NEW EXIT STATE , r
\ CALCULATE ESTIMATE
A NEW OF cP
FOR THE REGION
SUECOOLED
CONVERGENCE
ON
/ , 2. \
Fig.
6.3
Computational
CALCULATE HEAT TRANSFER RATES AND EXIT AIR TEMPERATURE FOR EACH FLOW REGION
Sequence
in the
Condenser
Model
ORNL-DWG
CALCULATE
81-4744R
PROPERTIES
OF MOIST AIR AND SUkFACE EFFECTIVENESS AND THERMAL RESISTANCE OF DRY COIL
COMPUTE AIR TEMPERATURE WHEN DEHUMIDIFICATION BEGINS,
Toid
I
\ CALCULATE
NTU
AND
EFFECTIVENESS TWO-PHASE ASSUMING REMOVAL
FOR REGION
NO
MOISTURE
OCCURS
COMPUTE EXIT AIR TEMPERATURE FROM PHASE REGION NO MOISTURE
TWO-
ASSUMING REMOVED,
/ CALCULATE HEAT TRANSFER RATE AND THE FRACTION OF THE COIL IN TWO-PHASE \
YES
.
FLOW,f+P
MOISTURE REMOVAL OCCURS SEE FIG.5.1
I
AND
FOR THE
ESTIMATE
COMPUTE
VAPOR
REGION
OF
YES \ CALCULATE CONDITIONS c
6.4
Computational
. ORIFD Diameter of the orifice GERANT LINES
Card 5
1
1.0
3 0.0544
BeTB
FORMAT(5F10.5) Inside diameter of liquid line from indoor coil to outdoor coil (in). XLEQLL Equivalent length of liquid line from indoor coil to outdoor coil (ft).
DLL
5.44;
0.1900 30.4
91 QDISLN Heat loss rate in the compressor discharge line (Btu/h) QSUCLN Rate of heat gain in the compressor suction line (Btu/h) from the indoor coil QLIQLN Heat loss rate in the liquid-line to the outdoor coil (Btu/h). c
Card 6
Card 7
FORMAT(4F10.5) DLRVOC Inside diameter of refrigerant line from the reversing valve to the outdoor coil (in). length of the refrigerant line from the XLRVOC Equivalent reversing valve to the outdoor coil (ft). DLRVIC Inside diameter of refrigerant line from the reversing valve to the indoor coil (in). XLRVIC Equivalent length of the refrigerant line from the reversing valve to the indoor coil (ft). FORMAT(4F10.5) Inside diameter of the refrigerant line from the compressor shell inlet to the reversing valve (in). length of the refrigerant line from the XLEQLP Equivalent compressor suction port to the reversing valve (ft). DDLRV Inside diameter of the refrigerant line from the compressor shell outlet to the reversing valve (in). XLEQHP Equivalent length of the refrigerant line from the compressor discharge port to the reversing valve (ft).
DSLRV
2000.0 300.0
200.0 0.68 6.00 .5556 30.40
0.680 2.00 0.556 2.00
S INITIAL, ESTIMATES m BEGIN SITERATION Card 8
FORMAT(3F10.2) TSATEO Estimate of the of the evaporator TSATCI Estimate of the of the condenser XMR Estimate of the
saturation (F). saturation (F). refrigerant
temperature
at the outlet
temperature
at the inlet
mass flow rate
(lbm/h).
30.0 115.0 400.0
COMPRESSOR Q&E,A Card 9 ICOMP
DISPL SYNC
QCAN
FORMAT(I10,7F10.0) switch to specify which compressor submodel is to be used, =I, for the efficiency and loss model, ~2, for the map-based compressor model. Total compressor piston displacement (cu in). when ICOMP = 1, synchronous compressor motor speed when FLMOT (on card 11) is specified (rpm); actual compressor motor speed when FLMOT (on card 11) is to be calculated (rpm). when ICOMP = 2, rated compressor motor speed (rpm); Heat rejection rate from the compressor can, used if CANFAC= 0.0 (Btu/h).
2
4.520 3600.0 3450.0 3450.0
0.0
92 CANFAC Switch to control the method of specifying QCAN ~0.0, to specify QCANexplicitly, C1.0, to set QCAN= CANFAC* compressor power, ~1.0, to set QCAN= 0.9*(1.0 - actual motor efficiency mechanical efficiency)*compressor power (not used with the map-based model). The variables is chosen. Efficiency Card 10
Card 11
0.350 *
on the next two cards depend on which compressor model
and Loss Model: FORMAT(8FlO.O) VR Compressor actual clearance volume ratio. EFFMMX Maximum compressor motor efficiency. ETAISN Isentropic compressor efficiency. ETAMEC compressor mechanical efficiency. FORMAT(I10,7F10.0) MTRCLC Switch to determine whether compressor full load motor power is specified as input data or if it is calculated, =0, compressor full load motor power is specified as input, =I, compressor full load motor power is calculated. FLMOT Compressor motor output at full load, i.e. (0.7457 kW/hp)x(brake hp at rated load), used only if MTRCLC=O(kW). rate from the compressor discharge line QHILQ Heat transfer to the inlet gas, used if HILOFC=O.O (Btu/h). HILOFC Switch to control method of specifying QHILO ~0.0, to specify QHILO explicitly, .Thickness of the fins in the indoor coil (in). Fin pitch for the indoor coil (fins/in). Thermal conductivity of the fins in the indoor coil (Btu/h-ft-F). Frontal area of the indoor coil (sq ft).
FORMAT(2FlO.O) Number of row of tubes in the indoor coil in the direction of the air flow. refrigerant circuits in the NSECT Number of parallel indoor coil.
NT
2.0
0.400 0.336 0.00636 14.00 128.00 3.1667
3.0 3.0
94 Card 14
FORMAT(3F10.5) HCONT Contact conductance between fins and tubes for the indoor coil (Btu/h-sq ft-F). ST The vertical spacing of tube passes (in). WT The spacing of tube rows in the direction of air flow (in).
Card 15 QA TAI RH RTB FANEF
Card 16 FINTY
DEA DER DELTA FP XKF AAF Card 17 NT NSECT Card 18
30000.0
1.00 0.875
FORMAT(5F10.4) Air flow rate for the indoor coil (cfm). Inlet air temperature for the indoor coil (F). Relative humidity of the inlet air for the indoor coil. The number of return bends in the indoor coil. Combined fan and fan motor efficiency for the indoor coil.
FORMAT(7F10.6) Switch to specify the type of fins, ~1.0, for smooth fins, ~2.0, for wavy fins, ~3.0, for louvered fins. Outside diameter of tubes in the outdoor coil (in). Inside diameter of the tubes in the outdoor coil (in). The thickness of the fins in the outdoor coil (in). The fin pitch for the outdoor coil (fins/in). The thermal conductivity of the fins in the outdoor coil (Btu/h-ft-F). The frontal area of the outdoor coil (sq ft). FORMAT(2FlO.O) The number of rows of tubes in the outdoor direction of air flow. The number of parallel refrigerant circuits outdoor coil.
coil
in the
in the
FORMAT(3F10.5) HCONT The contact conductance between the fins and tubes for the outdoor coil (Btu/h-sq ft-F). The vertical spacing of tube passes for the outdoor ST coil (in). The spacing of tube rows in the direction of air flow WT for the outdoor coil (in).
Card 19 QA TAI RH RTB FANEF
FORMAT(5F10.5) The air flow rate for the outdoor coil (cfm). The inlet air temperature for the outdoor coil (F). The relative humidity of the air entering the outdoor coil. The number of return bends in the outdoor coil. The combined fan and fan motor efficiency for the outdoor coil, not used if MFANFT=l on Card 3.
1200.0 70.0 0.50 72.00 0.200
2.0
0.400 0.336 0.00636 14.00 128.00 5.040
3.0 4.0
30000.0 1 .oo 0.875
2300.0 47.0 0.70 64.00 0.160
95 Appendix B: Sample Input and Output Data SAMPLEDATA SET FOR ORNLHEAT PUMPDESIGNMODEL-- @ 47.OF AMBIENT 15000.0
8.00 2
* o.,,o: 0.6800 0.6800 30.00
f .5
2
10.00 1
30.40 45.0 6.00 2.00 130.00 4.520
1 2000.00 0.5550 0.5550 400.0 3450.00
2 300.00 30.40 2.00
1
0
200.00
0.350
-1.5093-04 4.0893-02-1.3383-04 5.86OE% 3.6383-04 9.7593-05 -2.6753-02 4.6333+00 4.703E-02 9.6403+00-1.8683-02 1.207E-04 3.z
l
4.523+00
0.4000 3.000
0.3360
0.00636
14.0
128.0
3.1667
30000.00 1200.0 3.;;:
1.00 70.0 0.4000 4.000
0.875 0.500 0.3360
72.00 0.00636
0.200 14.0
128.0
5.0400
30000.00 2300.0
1.0 47.00
0.875 0.700
64.00
0.160
****
2O.OE+OO
INPUT DATA l **** SAMPLEDATA SET FOR ORNLHEAT PUMPDESIGNMODEL-- @ 47.OF AMBIENT HEATINGMODEOF OPERATION(NCORHz2) THE HOUSELOADIS 15000. BTU/H DIAMETEROF 6 EQUIVALENTDUCTS- 8.000 IN COMPRESSOR CAN HEAT LOSS ADDEDTO AIR BEFORECROSSINGTHE OUTDOOR COIL. POWER TO THE INDOORFAN ADDEDTO AIR AFTERCROSSINGTHE COIL. POWER TO THE OUTDOOR FAN ADDEDTO AIR BEFORECROSSINGTHE COIL. CONDENSER SUBCOOLING IS HELDFIXED AT 45.00 F EVAPORATOR SUPERHEAT IS HELDFIXED AT 10.00 F
L
DESCRIPTIONOF CONNECTING TUBING: LIQUID LINE FROMINDOORTO OUTDOOR HEAT EXCHANGER ID 0.19000 IN EQUIVALENTLENGTH 30.40 FT FROMINDOORCOIL TO REVERSINGVALVE FROMOUTDOOR COIL TO REVERSINGVALVE ID ID 0.55500 IN 0.68000 IN EQUIVALENTLENGTH 30.40 FT EQUIVALENTLENGTH 6.00 FT FROMREVERSINGVALVE TO COMPRESSOR INLET FROMREVERSINGVALVE TO COMPRESSOR OUTLET ID ID 0.68000 IN 0.55500 IN EQUIVALENTLENGTH 2.00 FT EQUIVALENTLENGTH 2.00 FT HEAT LOSS IN DISCHARGELINE HEAT GAIN IN SUCTIONLINE HEAT LOSS IN LIQUID LINE
2000.0 BTU/H 300.0 BTU/H 200.0 BTU/H
ESTIMATEOF: 400.000 LBM/H REFRIGERANT MASSFLOWRATE 130.000 F SATURATIONTEMPERATURE INTO CONDENSER SATURATIONTEMPERATURE OUT OF EVAPORATOR 30.000 F COMPRESSOR CHARACTERISTICS: 4.520 CUBIC INCHES TOTALDISPLACEMENT SYNCHRONOUS MOTORSPEED3450.000 RPMS MAP-BASEDCOMPRESSOR INPUT: POWER CONSUMPTION. -1.509%04*CONDENSING TEMPERATURE**2+ 4.089E-02'CONDENSING TEMPERATURE + -1.338E-04'EVAPORATINGTEMPERATURE**2+ 5.860E-04*EVAPORATINGTEMPERATURE + 3.638E-04'CONDENSING TEMPERATURE*EVAPORATING TEMPERATURE,+9;i59E:05 MASSFLOWRATE-
-2.675E-02*CONDENSING TEMPERATURE**2+ 4.633E+OO*CONDENSINGTEMPERATURE + 4.703E-02*EVAPORATINGTEMPERATURE**2+ 9.640E+OO*EVAPORATING TEMPERATURE + -1.868E-02*CONDENSING TEMPERATURE*EVAPORATING TEMPERATURE + 1.2073-04
CORRECTION FACTORFOR SUCTIONGAS CORRECTION FACTORFOR VOLUMETRIC EFFICIENCY BASE SUPERHEAT FORCOMPRESSOR MAP BASE DISPLACEMENT FOR COMPRESSOR MAP
0.330 0.750 20.000 4.520
F CU IN
HEAT REJECTEDFROMCOMPRESSOR SHELL IS 0.35 TIMES THE COMPRESSOR POWER
INDOOR UNIT: CONDENSER 0.40000 OD OF TUBES IN HX ID OF TUBES IN HX 0.33600 FRONTAL AREA OF HX 3.167 3.00 NUMBEROF PARALLEL CIRCUITS 3.00 NUMBEROF TUBES IN DIRECTION OF AIR FLOU 72.00 NUMBEROF RETURN BKNDS AIR PLOWRATE 1200.00 70.000 INLET AIR TEMPERATURE WAVY FINS OUTDOORUNIT: EVAPORATOR 0.40000 OD OF TUBES IN HX 0.33600 ID OF TUBES IN HX FRONTAL AREA OF HX 5.040 4.00 NUMBEROF PARALLEL CIRCUITS NUMBEROF TUBES IN DIRECTION OF AIR FLOW 3.00 64.00 NUMBEROF RETURN BENDS 2300.00 AIR FLOWRATE 47.000 ISLET AIR TKMPERATURE WAVY FINS
IN IN SQ FT
CFM F
IN IN SQ
FT
CFM F
FIN THICKNESS FIN PITCH THERMAL CONDUCTIVITY OF FINS CONTACT CONDUCTANCE HORIZONTAL TUBE SPACING VERTICAL TUBE SPACING FAN BFFICIENCY RELATIVE HUMIDITY
FIN THICKNESS FIN PITCH THERMAL CONDUCTIVITY OF FINS CONTACT CONDUCTANCE HORIZONTAL TUBE SPACING VERTICAL TUBE SPACING FAN EFFICIENCY RELATIVE HUMIDITY
0.00636 14.00
IN
1.000 0.20000 0.50000
IN
0.00636
IN
FINS/IN 128.000 BTU/H-FT-F 30000.0 BTU/H-SQ FT-F 0.875 IK
14.00 FINS/IN 128.000 BTU/H-FT-F 30000.0 BTU/H-SQ FT-F 0.875 IN 1.000 IN 0.16000 0.70000
i
’ I
;
l
****
CALCULATED HEAT PUMP PERFORMANCE*****
COMPRESSOR OPERATING CONDITIONS: COMPRESSORPGWER MOTORSPEED
4.011 3450.000
REFRIGERANT MASS FLOW RATE COMPRESSOR SHELL HEAT LOSS SYSTEM SUMMARY COMPRESSOR SUCTION LINE INLET SHELL INLET SHELL OUTLET CONDENSERINLET OUTLET
EFFICIENCY VOLUMETRIC OVERALL
Km
RPH
LBWH BTU/H
413.828
4791.414
REFRIGERANT TEMPERATURE 39.470 F 43.687 206.498
0.6311 0.5053
POWERPER UNIT MASS FLOW POWERCORRECTIONFACTOR MASS FLOW RATE CORRECTIONFACTOR
183.889 F 81.217
F
126.558
126.196
EXPANSION DEVICE
79.607
F
120.765
F
EVAPORATORINLET OUTLET
34.916 F 39.470
34.916
F
TOTAL SEAT EXCHANGEREFFECTIVENESS
NTU HEAT EXCHANGEREFFECTIVENESS CR/CA FRACTION OF HEAT EXCHANGER HEAT TRANSFER RATE OUTLET AIR TEHPERATURE AIR SIDE: MASS FLOW RATE PRESSUREDROP HBAT TRAESFER COEFFICIENT UA VALUES: VAPOR REGION (BTU/H-F) REFRIGERANT SIDE AIR SIDE conB1NED
0.0 0.0 0.0
29.577
BTlJ/LBM
1:0089
SATURATION REFRIGERANT REFRIGERANT TEMPERATURE ENTHALPY QUALITY 108.958 BTU/LBM 1 .oooo 29.577 F 29.263 109.683 1.0000 126.899
PERFORMANCEOF EACH CIRCUIT IN THE CONDENSER INLET AIR TEMPERATURE 70.000 OUTLET AIR TEMPERATURE 100.147 HEAT LOSS FROM FAN 1257.1 AIR TEMPERATURECROSSINGCOIL 99.193
33;3;9";;
REFRIGERANT PRESSURE 69.054 PSlA
131.185
1.0000
68.660 299.682
126.352 BTU/LB!4
1 .oooo 0.0
298.411 297.060
PSIA
33.477
32.994 BTU/LBM
0.0
277.316
PSIA
32.994 BTU/LBM
0.1483 1.0000
'V$E~ .
PSlA
108.958
70.000 100.147
F
47.000 38.908
F
F F BTU/H F
W U
0.6949
SUPERHBATER REGION 0.0 1.0000 0.0 0.0 0.0 BTU/H 70.000
AIR TEMPERATURE
9
1798.1 0.5224
LBH/H IN H20
13.136
BTU/H-SQ FT-F
TWO-PHASE REGION 1.1351 0.6786 0.6453 10838.4 108.270
BTU/H F
suBcooLED RRGION 1.9987 0.8005 0.2816 0.3547 1973.0 82.676
BTU/H F
REFRIGERANT SIDE: MASS FLOW RATE 137.9 PRESSURE,DROP 1.351 HEAT TRANSFER CORFFICIENT VAPOR REGION 102.905 453.291 TWO PHASE REGION SUSCOOLBD REGION 110.787
TV0 PBASE REGION (BTU/B-P) REFRIGERANT SIDE 2933.419 AIR SIDE 1436.706 COKBINED 964.380
LBWH
PSI BTU/H-SQ FT-F BTU/B-Sp
FT-F
BTU/H-SQ PT-F
SUB~OGLEDREGION (BTU/H-F) REFRIGERANT SIDE 394.035 AIR SIDE 789.615 COMBINED 262.862
n .ow
CONTROLDRVICE - CONDENSERSUBCOOLINGIS SPECIFIED AS 45.000 F CORRESPONDINGTXV RATING PARAMRTERS: CORRESPONDINGCAPILLARY TUBE PARAMETERS: RATRD OPERATING SUPERHEAT 11.000 F NUMBEROF CAPILLARY TUBES 1 STATIC SUPERHEATRATING 6.000 F CAPILLARY TUBE FLOW FACTOR 2.626 PERMANENTBLEED FACTOR 1.150 1.880 TONS TXV CAPACITY RATING INCLUDING NOZZLE AND TUBES
PERFORMANCEOF EACH CIRCUIT IN THE EVAPORATOR INLET AIR TEMPERATURE 47.000 HEAT LOSS FROM COMPRESSOR 4791.4 HEAT LOSS FROM FAN 2274.5 AIR TEMPERATURECROSSING COIL 49.696 OUTLET AIR TEMPERATURE 38.908
CORRESPONDINGORIFICE PARAMRTER: ORIFICE DIAHETER 0.0544 IN
F BTU/H BTU/H F F
MOISTURE REMOVAL OCCURS SUNMARYOF DEHUMYDIFICATION PERFORMANCE(TWO-PHASE REGION) LEADING EDGE OF COIL AIR DRY BULB TEMPERATURE 49.696 F 0.00475 HUMIDITY RATIO 17.090 BTU/LBH ENTHALPY
POINT WHEREMOISTURE REMOVAL BEGINS AIR WALL 37.740 F 44.912 F 0.00475 0.00475 14.191 BTU/LB!+! 15.930 BTU/LBM
RATE OF MOISTURE REMOVAL FRACTION OF NAPORATOR THAT IS WET LATENT HEAT TRANSFER RATE IN TWO-PHASEREGION SENSIBLE HEAT TRANSFER RATE IN TWO-PHASEREGION SENSIBLE TO TOTAL HEAT TRANSFER RATIO FOR TWO-PHASE REGION
0.7345 LBM/H 0.6941 789. BTU/H 6896. BTU/H 0.8974
OVERALL SENSIBLE TO TOTAL HEAT TRANSFER RATIO
0.8996
OVERALL CONDITIONS ACROSS COIL ENTERING AIR DRY BULB TEMPERATURE 49.696 F 43.924 F WET BULB TMPERATURE 0.633 RELATIVE HUMIDITY 0.00475 HUMIDITY RATIO
AIR SIDE MASS FLOW RATE PRESSUREDROP HEAT TRANSFER COEFFICIENT DRY COIL WET COIL DRY FIN EFFICIENCY WET FIN EFFICIENCY
0.6476
SUPERHEATED REGION 0.7608 0.4834 0.4025 0.0682 172.2 ,-.- BTU/H ~~_~~ 184.36 LBM/H 45.845 F 2702.1 LBM/H 0.395 IN HZ0 14.462 BTU/H-SQ FT-F 16.803 BTU/H-SQ FT-F 0.791 0.763
COIL WALL 35.434 F 0.00433 13.183 BTU/LBM
EXITING AIR 38.908 F 37.659 F 0.901 0.00448
TOTAL HEAT EXCHANGEREFFECTIVENESS (SENSIBLE)
NTU HEAT EXCHANGEREFFECTIVENESS CR/CA FRACTION OF HEAT EXCHANGER HEAT TRANSFER RATE AIR MASS FLOW RATE OUTLET AIR TEMPERATURE
LEAVING EDGE OF AIR 38.400 F 0.00446 14.036 BTU/LBM
TWO-PHASE REGION 1.0590 0.6532 0.9318 7684.9 BTU/H 2517.70 LBM/H 38.400 F REFRIGERANT SIDE MASS FLOW RATE 103.5 PRESSUREDROP 7.005 HEAT TRANSFER COEFFICIENT VAPOR REGION 63.625 TN0 PHASE REGION 631.979
LBM/H PSI ,- BTU/H&Q Fr-r BTU/H-S9 FT-F
UA VALUES: REFRIGERANT SIDE AIR SIDE DRY COIL WET COIL COMBINED DRY COIL WET COIL
VAPOR REGION 69.286 261.250 54.763
TWO PHASE REGION 9398.352 BTU/H-F 1091.526 2772.596
BTU/H-F BTU/H-F
791.186 BTU/H-F 1945.610 BTU/H-F
SUMMARYOF ENERGYINPUT AND OUTPUT: SAMPLE DATA SET FOR ORNL HEAT PUMP DESIGN MODEL -- @ 47.0F AMBIENT AIR TBMPERATUREINTO EVAPORATOR 47.00 F HEAT FROM CONDENSERTO AIR 38434. BTU/H HEAT TO EVAPORATORFROM AIR 71428. BTU/H POWERTO INDOOR FAN -1257. BTU/H POWERTO OUTDOORFAN BTU/H 2275. POWERTO COMPRESSORMOTOR 13690. BTU/H COMPRESSOR SHELL HEAT LOSS 4791. BTU/H TOTAL HEAT TO/FROM INDOOR AIR 39691. BTU/H SYSTEM EFFICIENCY: cop (HEATING) COP (WITH RESISTANCE HEAT)
2.305 2.305
HEAT OUTPUT: HEAT FROM HEAT PUMP RESISTANCE HEAT HOUSELOAD
39691.29 BTU/H 0.0 BTU/H 15000.00 BTU/H
101
C - Definitions
Appendix
of Constants
A number of variables Design
Model
that
quently
they
are
simply
of input
data.
each set
DATA subroutine routines into
several
they
order.
Physical
Air-Side
values
values
which
are used via
common blocks.
determined
by-use;
and consespecified in the
passed
are defined
with
BLOCK
to the
These data
they
sub-
are divided in that
Parameters of filter
AHEATR
cross-sectional 1.28 ft*
area
of resistance
PA
atmospheric
RACKS
number of resistance
RAU
universial
pressure,
14.7 heater
gas constant,
Tubing
on indoor heaters
unit,
2.78
in
indoor
ft* unit,
lbf/in* racks,
53.34
3.0
ft-lbf/lbm-OR
Parameter
roughness Motor
Heat Pump
being
together
are in turn
area
Compressor
often,
than
They have been brought
cross-sectional
E
very
rather
AFILTR
Refrigerant
in BLOCK DATA Subroutine
are used by the
to be changed
assigned
categories
"natural"
and constants
are unlikely
and given
where
Assigned
of interior
tube
walls,
5
x
low6 ft
Efficiency
CETAM
coefficients for the 0th through 5th order terms of the fit of the compressor motor efficiency as a function of the fractional motor load (Eq. 4.29), 0.4088, 2.5138, -4.6289, 4.5884, -2.3666, and 0.48324
RPMSLR
slope of linear fit speed as a function (see Eq. 4.24)
for fraction of fraction
of no-load compressor motor of full load power, -0.042
102 --Data for COFAN
Outdoor
Fan Efficiency
constant term for the fit of outdoor fan specific speed, -3.993
fan
static
efficiency
to
. .
ClFAN
coefficient for static efficiency
the linear term of the fit of outdoor to the fan specific speed, 4.266
C2FAN
coefficient for static efficiency
the quadratic term of the fit of outdoor to fan specific speed, -1.024
EFFMOT
constant
motor
efficiency
RPMFAN
constant
motor
speed for
Tolerance
Parameters
AMBCON
convergence 0.20 F".
parameter
CMPCON
convergence calculations,
parameter for the Ah iteration 0.05 Btu/lbm
CNDCON
convergence parameter for iterations and refrigerant temperature at the 0.20 F"
CONMST
tolerance parameter temperatures, 0.003
for F"
the
EVPCON
tolerance 0.5O"F.
for
iterations
FLOCON
convergence rate through
TOLH
tolerance parameter used in calculating properties heated vapor when enthalpy is known, 10e3
of super-
TOLS
tolerance parameter used in calculating properties heated vapor when entropy is known, 10 4
of super-
Refrigerant NR
the outdoor
the outdoor
for
fan,
the outdoor
iterations
fan,
fan
0.55
825 rpm
ambient
air
interation,
in the
compressor
on condenser subcooling flow control device, 0.20 on evaporator on evaporator
criteria for iterations the expansion device,
fan
tube
wall
superheat,
on refrigerant 0.2 lbm/h
mass flow
Specification refrigerant
Refrigerant-Side ClR,
parameter
for
.
number,
Heat Transfer
C3R, and C5R (Eq. 6.2),
coefficients 1.10647,
22 Correlation for 3.5194
for
Single-Phase
Regions
single-phase heat transfer x 10m7, and 0.01080
coefficient
.^
103
I
exponents -0.78992,
CZR, C4R, and C6R (Eq. 6.3),
for single-phase heat 1.03804, and -0.13750
transfer
coefficient
-.
. I
ULR
lower limit refrigerant,
for the 6,000
XLLR
upper limit ant, 3,500
on the
Reynolds
Valve
Constants
Thermostatic BLEEDF
Expansion
Reynolds
bypass or bleed meters
factor when condenser
number for number for
coefficient subcooling
is
turbulent laminar
flow flow
of
of refriger-
used to compute TXV paraheld fixed, 1.15
DPRAT
rated pressure drop across the TXV at the design 100 psi for R-22 and R-502, 50 psi for R-12
conditions,
NZTBOP
switch to bypass nozzle and distributor tube calculations when calculating TXV parameters subcooling is held fixed, 0
pressure drop if the condenser
STATIC
static superheat setting used to compute the when the condenser subcooling is held fixed,
TXV parameters
SUPRAT
rated operating superheat used to compute the TXV parameters when the condenser subcooling is held fixed, 1l.O.F"
TERAT
rated
TLQRAT
rated liquid lOO.O"F
Capillary
Tube Parameter
NCAP
number of capillary tubes factor, $, when condenser
6.0 F”
f
Compressor
evaporating
Efficiency
temperature
refrigerant
for
the TXV, 4O.O"F
temperature
at the
inlet
to the
used to compute capillary subcooling is held fixed,
tube 1
TXV,
flow
Parameters
ETAVLA
intercept volumetric parameter
of the fit of theoretical minus actual compressor efficiencies as a linear function of the correlating of Davis and Scott, -0.0933
ETAVLB
slope of the fit of theoretical minus actual volumetric efficiencies as a linear function parameter of Davis and Scott, 0.733
SUCFAC
suction
VOLFAC
volumetric Eq. 4.4,
gas heating efficiency 0.75
factor
Fsh used
correction
compressor of the correlating
in Eq. 4.6,
factor
0.33
Fv used in
105 Appendix
D:
Definitions
of Variables
in Common Blocks
Variable A
Definition constant used in a first order approximation of the saturation temperature in the logarithm of the refrigerant pressure. assigned a value in TABLES and used in TSAT.
Common SUPER
AAFC
the frontal area of the condenser, by CALC and COND (sq ft).
CONDEN
AAFE
the frontal area of the evaporator, by CALC and EVAPR (sq ft).
read by DATAIN, used read by DATAIN, used
EVAPOR
ACV,BCV,..., FCV constants used in calculating refrigerant heat capacity with temperature and specific volume, assigned values in TABLES and used in SATPRP.
OTHER
AFILTR
AIR
frontal area of filter for the indoor unit, in BLOCK DATA and used in PDAIR (sq ft).
assigned
AHEATR cross-sectional area of the resistance heaters, value in BLOCK DATA and used in PDAIR (sq ft).
a value
assigned
a
AIR
AL.BL,...,GL coefficients for expressing density of the liquid refrigerant as a function of absolute temperature (R), assigned values in TABLES and used in SATPRP (lbm/cu ft).
DENSIT
ALFAAC ration of the air-side heat transfer area for the condenser to the total volume of the condenser, calculated in CALC, used by COND, EFFCT, and EXCH (/ft).
CONDEN
ratio of the air-side heat transfer area for the evaporator to the total volume of the evaporator, calculated in CALC, used by EVAP and EVAPR (/ft).
EVAPOR
ALFARC ratio of the total refrigerant-side heat transfer area for the condenser to the volume of the condenser, calculated in CALC, used by COND, EFFCT, and EXCH (/ft).
CONDEN
ALFARE ratio of the total refrigerant side heat transfer area for the evaporator to the volume of the evaporator, calculated in CALC, used by EVAP and EVAPR (/ft).
EVAPOR
ALPHA
STATEQ
AALFE
constant used in refrigerant equation of state correlating pressure with temperature and specific volume, assigned a value in TABLES, used by SATPRP, SPVOL, and VAPOR.
AMBCON tolerance parameter for the ambient air temperature iteration in the main program, assigned a value in BLOCK DATA and used in the main program (F).
MPASS
ARFTC
CONDEN
inside cross-sectional area of the tubes in the condenser calculated in CALC and used in COND (ft).
,
106
ARFTE
inside cross-sectional area of the tubes in the evaporator calculated in CALC and used by EVAPR (sq ft).
EVAPOR
ARHTC
total refrigerant-side heat transfer area for each circuit in the condenser, calculated and used in CALC, used by COND, EFFCT, and EXCH (sq ft).
CONDEN
ARHTC
total refrigerant side heat transfer area for each circuit in the evaporator, calculated and used in CALC, used by EVAP and EVAPR (sq ft).
EVAPOR
used in correlating refrigerant AVP,BVP,..., FVP constants pressure with absolute temperature (R), assigned in TABLES, used in SATPRP and TSAT. A2,B2,C2
vapor values
constants used in refrigerant equations of state correlating pressure with temperature and specific volume, assigned values in TABLES, used by SATPRP, SPVOL, and VAPOR.
A3,B3,C3
SAT
STATEQ
constants used in refrigerant equations of state correlating pressure with temperature and specific volume, assigned values in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
constants used in refrigerant equations of state correlating pressure with temperature and specific volume, assigned values in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
A5,B5,C5
constants used in refrigerant equations of state correlating pressure with temperature and specific volume, assigned values in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
A6,B6,C6
constants used in refrigerant equations of state correlating pressure with temperature and specific volume, assigned values in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
B
constant used in a first order approximation to the refrigerant saturation temperature as a function of the logarithm of the saturation pressure, assigned value in TABLES and used in TSAT.
SUPER
A4,B4,C4
BLEEDF by-pass or bleed factor coefficient expansion valve, assigned a value DATAIN, used by TXV. Bl
for the thermostatic by BLOCK DATA or read by
constant used in refrigerant equation of state correlating pressure with temperature and specific volume, assigned a value in TABLES, used by SATPRP, SPVOL, and VAPOR.
* c
1
TXVDAT
STATEQ
_
107 CA c
.
air-side heat capacity rate of the condenser, calculated
for the superheated portion of the in EFFCT, used by EXCH (Btu/h-F).
capacity of the evaporator at the operating conditions with an assumed 10 F of superheat at the evaporator exit, calculated in and used in TXV, printed by OUTPUT (Btu/hr),
FLOWBA
CAPNOZ heating capacity valve, calculated
of the nozzle of the thermostatic expansion and used in TXV, printed by OUTPUT (Btu/hr).
TXVDAT
CAPTUB heating capacity of each tube from the thermostatic expansion valve to the evaporator, calculated and used in TXV, printed in OUTPUT (Btu/hr).
TXVDAT
CARC
ratio of the fin heat transfer area to the contact area between the fins and the tubes in the condenser, calculated in CALC and used in COND.
CONDEN
CARE
ratio of the fin heat transfer. between the fins and the tubes in CALC and used by EVAP.
area to the contact area in the evaporator, calculated
EVAPOR
CETAM
coefficients for a fit to the motor efficiency as a function of the fraction of full load power output, assigned values in BLOCK DATA and used by COMP.
CMPMOT
CLCXMR refrigerant calculated (lbm/hr).
mass flow rate through each capillary in CAPTUB, used by FLOBAL, and printed
CMPCON tolerance parameter for entering the compressor in BLOCK DATA (Btu/h-F).
the iteration suction port
tube, in OUTPUT
on the enthalpy in COMP, assigned
COIL
evaporator coil resistance to heat transfer, used in EVAP, used by TWISOL.
calculated
PRNT2
MPASS a value
parameter for the condenser subcooling iterations CNDCON tolerance in the main program and in COND, and the refrigerant temperature at the flow control device in FLOBAL, assigned value in BLOCK DATA, used in the main program, COND, and FLOBAL (F). II
TXVDAT
CAPFLO capillary tube flow factor, default value assigned in BLOCK DATA, read by DATAIN if capillary tube submodel is used, calculated or used by CAPTUB, printed by OUTPUT.
2.
‘
COMPR
as CANFAC factor used to express compressor shell heat rejection a fraction of compressor power consumption, read by DATAIN end used by COMP. CAP
EFFARG
and
MPASS a
TWI
108 parameter for the iterations CONMST tolerance temperature in EVAP, assigned a value in EVAP (F).
on the tube wall in BLOCK DATA and used the heat pump with in the main program
MPASS
COP
operating coefficient of performance for any necessary resistance heat, calculated and printed by OUTPUT.
COPHP
operating coefficient of performance for the heat pump, does PRNT8 not include any resistance heat, calculated by the main program and printed in-OUTPUT.
CPA
specific heat of dry air, calculated COND and EVAPR, used by COND, EVAPR, XMOIST, and WBF (Btu/lbm-F).
AIR
CPM
specific heat of moist air, calculated by CONDand EVAPR and used by COND, EFFCT, EVAP, and EXCH (Btu/lbm-F).
AIR
CPOW
coefficients for compressor power consumption as a function MAPFIT of the condensing and evaporating temperatures, read by DATAIN if the map-based model is used and used by CMPMAP.
CPR
constant used in refrigerant equation of state correlating pressure with temperature and specific volume, assigned a value in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
CPSCC
specific heat for the subcooled refrigerant in the condenser, calculated by MUKCPand EXCH, used by COND, EFFCT, EXCH, and SPHTC (Btu/lbm-F).
CONDS
CPSP
specific heat for the superheated refrigerant in the condenser calculated in COND, modified in EXCH, and used by COND, EFFCT, and EXCH (Btu/lbm-F).
CONDS
CPSPC
specific heat for the condensing superheated refrigerant in the condenser, calculated in COND and used by COND and EXCH (Btu/lbm-F).
CONDS
CPSPE
specific heat for the superheated refrigerant ator calculated and used by EVAPR (Btu/lbm-F).
EVAPS
CR
refrigerant-side heat capacity rate for the superheated region of the condenser, calculated in EFFCT and used in EXCH (Btu/hr-F).
in the evapor-
PRNT8
EFFARG
CSCOOL ratio of refrigerant to air-side heat capacity rates for the subcooled region of the condenser, calculated in EXCH and printed in OUTPUT.
PRNT4
CSUPER ratio of the refrigerant to air-side heat capacity rates for the superheated region of the evaporator, calculated in EVAP and printed in OUTPUT.
PRNT5
e *
109 CUASC
.
overall thermal conductance times the heat transfer area (UA) for the subcooled region of the condenser, calculated in COND and printed in OUTPUT (Btu/hr-F).
thermal conductance times the heat transfer CUASCA air-side for the subcooled region of the condenser, calculated and printed in OUTPUT (Btu/hr-F).
area (UA) in COND
thermal conductance times the heat transfer CUASCR refrigerant-side area (UA) for the subcooled region of the condenser, calculated in COND and printed in OUTPUT (Btu/hr-F). CUATP
overall thermal conductance times heat transfer area (UA) for the two-phase region of the condenser, calculated in COND and printed in OUTPUT (Btu/hr-F).
thermal conductance times the heat transfer CUATPA air-side for the two-phase region of the condenser, calculated and printed in OUTPUT (Btu/hr-F).
area (UA) in COND
UAS
UAS
UAS
UAS
UAS
CUATPR refrigerant-side thermal conductance times the heat transfer area (UA) for the two-phase region of the condenser, calcuated in COND and printed in OUTPUT (Btu/hr-F).
UAS
CUAV
overall thermal conductance times the heat transfer area for the vapor region of the condenser, calculated in COND and printed in OUTPUT (Btu/hr-F).
UAS
CUAVA
air-side thermal conductance times the heat transfer area (UA) for the vapor region of the condenser, calculated in COND and printed in OUTPUT (Btu/hr-F).
UAS
CUAVR
refrigerant-side thermal conductance times heat transfer for the superheated region of the condenser, calculated COND and printed in OUTPUT (Btu/hr-F).
UAS
CXMR
coefficients for the refrigerant mass flow rate as a function of the condensing and evaporating temperatures, read by DATAIN, if the map-based compressor model is chosen, and used by CMPMAP.
area in
MAPFIT
COFAN,ClFAN,C2FAN coefficients for the fan static efficiency for the outdoor heat exchanger as a function of the static speed of the fan, assigned values in BLOCK DATA and used by FANFIT.
FANMOT
coefficients and exponents for ClR,C2R ,...,C6R heat transfer coefficient as a function Reynolds and Prandtl numbers, assigned and used in SPHTC.
VAPHTC
fit to single-phase of refrigerant values in BLOCK DATA
/
110
DDL
inside diameter of the compressor reversing valve to the condenser, and used by COMP (ft).
discharge line from the assigned a value by DATAIN
LINES .
DDLRV
inside diameter of the line from the compressor discharge port to the reversing valve, read by DATAIN and used by COMP (ft).
LINES
DDUCT
diameter of each of 6 identical air ducts with equivalent lengths of 100 ft, read by DATAIN and used by COND and EVAPR (ft).
BLANK
DEAC
outside diameter of the tubes in the condenser, DATAIN, used by CALC and COND (ft).
CONDEN
DEAE
outside diameter of the tubes in the evaporator, DATAIN, used by CALC, EVAP and EVAPR (ft).
of the fins DELTAC thickness by CALC and COND (ft).
in the condenser,
read by read by
read by DATAIN, used
of the fins in the evaporator, DELTAE thickness by CALC and EVAPR (ft).
read by DATAIN, used
-
EVAPOR CONDEN EVAPOR
DERC
inside diameter of the refrigerant tubes in the condenser, read by DATAIN, used by CALC and COND (ft).
CONDEN .
DERE
inside diameter of the refrigerant tubes in the evaporator, read by DATAIN, used by CALC and EVAPR (ft).
EVAPOR *
DISPL
total compressor by COMP (cu in).
COMPR
DLL
inside diameter of the liquid line connecting the indoor and outdoor heat exchangers, read by DATAIN and used by FLOBAL (ft).
LINES
DP
air-side pressure drop across the outdoor coil, calculated in FANFIT and printed by OUTPUT (inches of water).
PRNTS
DPDL
pressure drop in the compressor discharge line from the discharge port to the condenser, calculated and used by COMP (psi).
LINES
DPLL
pressure drop in the liquid line connecting the heat exchangers, calculated and used in FLOBAL (psi).
LINES
DPNOZ
pressure drop in the nozzle for the thermostatic expansion valve, calculated and used in TXV, print in OUTPUT (psi).
TXVDAT -
DPRAT
rated pressure drop across the thermostatic at the design conditions, assigned a value used by TXV (psi).
TXVDAT *
piston
displacement,
read by DATAIN and used
expansion valve in BLOCK DATA and
111 DPSL
LINES
pressure drop in the suction line connecting the evaporator and compressor, calculated and used in COMP (psi).
expanDPTUBE pressure drop across the tubes from the thermostatic sion valve to the evaporator, calculated and used in TXV, printed in OUTPUT (psi).
h s
TXVDAT
DPTXV
pressure drop across the valve of the thermostatic valve (does not include nozzle and tube losses), and used in TXV, printed in OUTPUT (psi).
expansion calculated
DSL
inside diameter to the reversing
DSLRV
inside diameter of the line from the compressor suction port to the reversing valve, read by DATAIN and used by COMP (ft).
LINES
DTROC
specified condenser subcooling, read by DATAIN used by CNDNSR, FLOBAL, and FLODEV, and printed by OUTPUT (F).
FLOWBA
DZC
equivalent calculated
length of the refrigerant tubing in CALC and used by COND.
in the condenser,
CCNDEN
DZE
equivalent calculated
length of the refrigerant tubing in CALC and used by EVAPR.
in the evaporator,
EVAPOR
E
roughness factor for all of the refrigerant lines, assigned a value in BLOCK DATA, used by COMP, COND, EVAPR, and FLOBAL (ft).
TXVDAT
of the suction line from the evaporator valve, read by DATAIN and used by COMP (ft).
LINES
LINES
and the mechanical EFFMMX product of the maximum motor efficiency efficiency for the compressor, read by DATAIN and used by COMP. for the outdoor EFFMOT fan motor efficiency BLOCK DATA and used in FANFIT.
fan,
assigned
COMPR
a value
fan, calculated printed by
in
EINDF
rate of power consumption for the indoor COND or EVAPR, used by the main program, OUTPUT (Btu/hr).
in
EOUTF
rate of power consumption for the outdoor fan, calculated COND or EVAPR, used by the main program, printed by OUTPUT (Btu/hr).
ETAISN
isentropic efficiency from the suction port to the discharge port of the compressor, read by DATAIN and used by COMP, printed and used by OUTPUT.
in
FANMOT PRNT8
PRNT8
COMPR
112
ETAMEC mechanical efficiency used by COMP.
of the compressor,
read by DATAIN and
ETAMOT operating motor efficiency for used in COMP, used and printed
the PRNTlessor, by OUTPUT.
ETASUP compressor and printed
efficiency,
suction gas heating by OUTPUT.
calculated
calculated
and
by COMP
COMPR
COMPR * PRNTI
isentropic efficiency from the shell inlet ETATOT compressor overall to the shell outlet, calculated by COMP, used and printed by OUTPUT.
PRNTl
of the fit of theoretical minus actual compressor ETAVLA intercept volumetric efficiency as a linear function of the correlating parameter of Davis and Scott, assigned in BLOCK DATA and used in COMP.
COMPR
minus actual compressor ETAVLB slope of the fit of theoretical volumetric efficiency as a linear function of the correlating parameter of Davis and Scott, assigned in BLOCK DATA and used in COMP.
COMPR
efficiency of the compressor based on the shell ETAVOL volumetric inlet conditions, calculated and used in COMP, printed by OUTPUT.
PRNTl
ETP
heat exchanger effectiveness for the two-phase region of the calculated and used in EXCH, used and printed in condenser, OUTPUT.
PRNT4
ETPE
heat exchanger effectiveness for the two-phase region of the evaporator, calculated and used in EVAP, printed by OUTPUT.
PRNT5
EUATP
overall thermal conductance times heat transfer area (UA) for the two-phase region of the evaporator, calculated in EVAPR, printed in OUTPUT (Btu/hr-F).
UAS
thermal conductance times the heat transfer area (UA) EUATPA air-side for the two-phase region of the evaporator, calculated in EVAPR and printed in OUTPUT (Btu/hr-F).
UAS
thermal conductance times the heat transfer EUATPR refrigerant-side area (UA) for the two-phase region of the evaporator, calculated in EVAPR and printed in OUTPUT (Btu/hr-F).
UAS
EUAV
EUAVA
i
overall thermal conductance times the heat transfer area (UA) for the superheated region of the evaporator, calculated in EVAPR and printed in OUTPUT (Btu/hr-F).
UAS
air-side thermal conductance times the heat transfer area (UA) for the superheated region of the evaporator, calculated in EVAPR and printed in OUTPUT (Btu/hr-F).
UAS
L 1 -
.
113 UAS
tolerance parameter for the iteration on evaporator in the main program and in EVAPR, assigned a value DATA and used in the main program and EVAPR (F).
MPASS
superheat in BLOCK
heat exchanger effectiveness for the subcooled region condenser based on effectiveness-NTU correlations for flow heat exchangers, calculated and used in EXCH.
of the cross-
EFFARG
EXFRC
heat exchanger effectiveness condenser, assigned a value OUTPUT.
of the in
PRNT4
EXFRE
heat exchanger effectiveness for the superheated evaporator, calculated and used in EVAP, printed
region of the by OUTPUT.
PRNT5
EXFS
heat exchanger effectiveness for the superheated condenser based on heat capacity rates and delta ulated in EFFCT and used by EXCH.
region of the T's, calc-
EFFARG
EXFSC
heat exchanger the condenser, in OUTPUT.
' EXFR
3.
refrigerant-side thermal conductance times the heat transfer area (UA) for the superheated region of the evaporator, CalCulated in EVAPR and printed in OUTPUT (Btu/hr-F).
for the subcooled region in EXCH, used and printed
effectiveness for the superheated region of assigned a value in EXCH, used and printed
PRNT4
for the condenser, the FANEFC the combined fan-fan motor efficiency value is either read by DATAIN or calculated by FANFIT;used by COND.
CONDEN
for the evaporator, FANEFE the combined fan-fan motor efficiency the value is either read by DATAIN or calculated by FANFIT, used by COND.
EVAPOR
efficiency FANOUT combined operating calculated in FANFIT, printed
PRNT8
of the outdoor by OUTPUT.
fan-fan
motor,
FARC
ratio of the fin heat transfer area for the condenser to the total heat transfer area on the air side, calculated in CALC and used in COND.
CONDEN
FARE
ratio of the fin heat transfer area for the evaporator to the total heat transfer area, calculated in CALC, used by EVAP and EVAPR.
EVAPOR
FINTYC
switch to specify the type of fins in the condenser (smooth, wavy, or louvered), read by DATAIN, used by HAIR and PDAIR.
CONDEN
114 FINTYE
switch to specify the type of fins in the evaporator read by DATAIN, used by HAIR (smooth, wavy, or louvered), and PDAIR.
EVAPOR
FIXCAP
specified heating load for the heat pump, read by DATAIN and used by the main program (Btu/hr).
BLANK
FLMOT
full load motor power for the compressor, either read by DATAIN or calculated in COMP, used by COMPand printed by OUTPUT (kW).
COMPR
FLOCON relative tolerance parameter used in the refrigerant mass flow rate iteration in the main program, assigned a value in BLOCK DATA and used in the main program.
MPASS
FMOIST fraction of the evaporator where moisture removal from the air and used in EVAP, used in EVAPR and printed occurs, calculated in OUTPUT.
EVAPRS
CONDEN
FPC
the fin pitch for the condenser, by CALC and COND (fins/ft).
read by DATAIN and used
FPE
the fin pitch for the evaporator, by CALC and EVAPR (fins/ft).
FSCC
fraction of each circuit in the condenser which is subcooled calculated in EXCH, used by COND and EXCH, printed in OUTPUT.
CONDS
FSPC
fraction of each circuit in the condenser that is superheated, calculated and used in EXCH, used in COND, and printed in OUTPUT.
CONDS
FSPE
fraction heated, printed
EVAPS
FTPC
fraction of each circuit in the condenser which is in twophase flow, calculated and used in EXCH, used in COND, and printed in OUTPUT.
CONDS
FTPE
fraction of each circuit in the evaporator which is in twophase flow, calculated and used in EVAP, used in EVAPR, and printed by OUTPUT.
EVAPS
HAC
air-side heat transfer coeffiqient for the condenser, calculated by HAIR, used by COND, EFFCT, EXCH, and SEFF, printed by OUTPUT (Btu/hr-sq ft-F).
CONDS
air-side heat transfer coefficient for the evaporator, calculated and used by EBAPR, used by EVAP, and printed OUTPUT (Btu/hr-sq ft-F).
EVAPS
read by DATAIN and used
EVAPOR ' ,
HAE
of each circuit in the evaporator that is supercalculated and used in EVAP, used in EVAPR, and in OUTPUT.
by
L *
115 HAIR1
enthalpy of the moist air entering the evaporator, calculated and used in EVAP, used by TWISOL, and printed by OUTPUT (Btu/lbm).
TWI
HAIR0
enthalpy of the air leaving the evaporator, used in EVAP, printed by OUTPUT (Btu/lbm).
PRNT5
HAIR1
enthalpy of the air in the evaporator at the point where and used in EVAP, printed moisture removal begins, calculated by OUTPUT (Btu/lbm).
PRNT5
HAW
air-side heat transfer coefficient for the. wetted surface of the evaporator, calculated in EVAPR, used by EVAP and EVAPR, printed by OUTPUT (Btu/h-sq ft-F).
EVAPRS
.
calculated
and
A
. .
HCONTC contact conductance between the fins and tubes in the ft-F). condenser, read by DATAIN and used by COND (Btu/hr-sq
CONDEN
HCONTE contact conductance between the fins and the tubes evaporator, read by DATAIN, used by EVAij.~~iu/hr-sq'
EVAPOR
in the ft-F).
HIC
enthalpy of the refrigerant entering the condenser, calculated in COMP, modified by DESUPR, used by COMPand FLOBAL, printed by OUTPUT (Btu/lbm-F).
CONDSR
HIE
enthalpy of the refrigerant entering the evaporator, calculated in the main program, used by EVAPR, then calculated and used by FLOBAL, used by TXV, and printed by OUTPUT (Btu/lbm-F).
EVAPTR
HILOFC factor used to express the internal compressor heat transfer from the high side discharge line to the low side suction line as a fraction of compressor power, read by DATAIN and used by COMP.
COMPR
HINCMP enthalpy of the refrigerant at the compressor calculated and used in COMPor CMPMAP;'printed (Btu/lbm).
CMPRSR
shell inlet in OUTPUT
HOC
enthalpy of the refrigerant leaving the condenser, calculated CONDSR in COND and FLOBAL, used by the main program, COND, and FLOBAL, printed by OUTPUT (Btu/lbm-F).
HOE
enthalpy of the refrigerant leaving the evaporator, calculated and used by COMP, used by FLOBAL, and printed by OUTPUT (Btu/lbm-F).
at the compressor shell outlet HOUCMP enthalpy of the refrigerant calculated and used in COMPor 'CMP~P,"pn;ntea~in"OUTPUT (Btu/lbm).
EVAPTR
CMPRSR
116 refrigerant-side heat transfer coefficient for the subcooled region of the condenser, calculated in SPHTC, used by CHTC, COND, and EXCH, printed by OUTPUT (Btu/hr-sq ft-F).
CONDS
HSPC
refrigerant-side heat transfer coefficient for the superheated region of the condenser, calculated by SPHTC, used by COND, EFFCT, and EXCH, printed by OUTPUT (Btu/hr-sq ft-F).
CONDS .
HSPE
refrigerant-side heat transfer coefficient for the superheated region of the evaporator, calculated and used by EVAPR, also used by EVAP, printed by OUTPUT (Btu/hr-sq ft-F).
EVAPS
HTPC
refrigerant-side heat transfer coefficient for the two-phase CONDS region of the condenser, calculated in CHTC, adjusted by COND, used by COND and EXCH, printed by OUTPUT (Btu/hr-sq ft-F).
HTPE
refrigerant-side heat transfer coefficient for the two-phase calculated and used by EVAPR, also region in the evaporator, used by EVAP, printed by OUTPUT (Btu/hr-sq ft-F).
HSCC
HWALLI enthalpy of the air at the tube walls on the leading edge of the evaporator where moisture removal begins, calculated in EVAP, calculated and used in TWISOL, printed in OUTPUT (Btu/lbm-F). HWALLO enthalpy of the air at the tube walls on the leaving the evaporator, calculated and used in EVAP, printed (Btu/lbm-F).
.
EVAPS
TWI
PRNT5 edge of in OUTPUT
ICOMP
switch to specify which compressor DATAIN and used by FLOBAL.
read by
FLOWBA
IREFC
switch to specify type of flow control device, read by DATAIN, used by the main program, CAPTUB, FLOBAL, OUTPUT, and TXV.
FLOWBA
ITITLE
descriptive and printed
BLANK
title for labelling by OUTPUT.
model is used,
output,
read by DATAIN
constant used in correlating refrigerant heat capacity at a constant volume with temperature and specific volume, assigned a value in TABLES and used in SATPRP.
.
OTHER
* .
117 constant used in refrigeration equations of state correlating pressure with temperature and specific volume, assigned a value in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
LElO
multiplication constant used to convert to natural logarithms, assigned a value SATPRP and TSAT.
SUPER
LPRINT
switch to control levels of printed output, read by DATAIN, used by the main program, COMP, COND, EVAP, EVAPR, and FLOBAL.
MPASS
LlOE
multiplicative to logarithms SATPRP.
used to convert natural logarithms assigned a value in TABLES, used in
SUPER
for adding heat from the compressor read by DATAIN, used by COND,
MPASS
MFANFT switch to specify whether or not to use efficiency curve for the outdoor fan, read by DATAIN, used by the main program, COND, EVAPR, and OUTPUT.
MPASS
MFANIN switch to specify option for adding heat loss from the indoor fan to the air-stream, read by DATAIN, used by COND, EVAPR, and OUTPUT.
MPASS
MFANOU switch to specify option for adding heat loss from the outdoor fan to the air-stream, read by DATAIN, used by COND, EVAPR, and OUTPUT.
MPASS
MTRCLC switch ressor
COMPR
. .
*.
. c
constant base ten,
MCMPOP switch to specify option shell to the air-stream, EVAPR, and OUTPUT.
logarithms base ten in TABLES, used by
used to specify whether or not to calculate the compmotor speed, read by DATAIN, used by COMP.
MUNITC switch to specify whether the condenser is the indoor or the outdoor heat exchanger, assigned a value by DATAIN -nd used by COND.
CONDEN
MUNITE switch to specify whether the evaporator outdoor heat exchanger, assigned a value by EVAPR.
EVAPOR
is the indoor or the by DATAIN and used
118
NCAP
number of capillary tubes used, default value assigned in BLOCK DATA, optionally read by DATAIN if capillary tube submodel is used, used by CAPTUB and printed by OUTPUT.
FLOWBA
NCORH
switch to specify heating or cooling by DATAIN, used by the main program,
MPASS
NR
refrigerant number, assigned a value in BLOCK DATA, used by the main program, MUKCP, SATPRP, TSAT, TXV, and VAPOR.
mode of operation, read COND, EVAPR, and OUTPUT.
REFRIG
parallel refrigerant circuits in the NSECTC the number of equivalent condenser, read by DATAIN, used by OUTPUT, CALC, and COND.
CONDEN
parallel refrigerant circuits in the NSECTE the number of equivalent evaporator, read by DATAIN, used by EVAPR and OUTPUT.
EVAPOR
NTC
the number of tubes in the direction of' the air flow condenser, read by DATAIN, used by CALC and COND.
in the
CONDEN
NTE
the number of tubes in the direction of the air flow in the evaporator, read by DATAIN, used by CALC and EVAPR.
EVAPOR
tube pressure NZTBOP switch to bypass the nozzle and distributor drop calculations for the thermostatic expansion valve, assigned a value in BLOCK DATA or read by DATAIN, used by TXV.
ORIFD
diameter of the orifice or short tube, read by DATAIN or calculated by ORIFIC, used by ORIFIC and printed by OUTPUT (ft)
-
TXVDAT
FLOWBA
l
PA
the atmospheric pressure, assigned a value in BLOCK DATA, used by COND, EVAP, EVAPR, and XMOIST (psia).
AIR
PC
inside perimeter of each tube in the condenser, and used in CALC, used in COND (ft).
CONDEN
PCTFL
fraction of the full-lOad,compressor motor power, and used in COMP, printed in OUTPUT.
calculated calculated
pressure drop for the condenser, calculated PDAIRC air-side and used by COND and FANFIT, printed by OUTPUT (psi).
by PDAIR
PRNTl CONDS
h d
119
PDAIRE air-side pressure drop for the evaporator, initialized to 0 in the main program, calculated by PDAIR, used by EVAPR, and printed by OUTPUT (psi). PDC
CONDS refrigerant-side pressure drop for the condenser, calculated by PDROP in calls from FLOBAL. and COND, used by FLOBAL and COND, printed by OUTPUT (psi).
PDE
refrigerant-side pressure drop for each circuit in the evaporator, calculated and.used by EVAPR, printed by OUTPUT (psi).
EVAPS
PE
inside perimeter of each tube in the evaporator, and used by CALC, used by EVAPR (ft).
EVAPOR
-5
calculated
PFLODV pressure of the refrigerant entering the flow control device, calculated and used in FLOBAL, printed in OUTPUT (psia).
pressure of the refrigerant entering the condenser, calculated CONDSR in COMP, modified by DESUPR and FLOBAL, used by COMPand COND, printed by OUTPUT (psia).
PIE
pressure of the refrigerant entering the evaporator, calculated and used by EVAPR, also calculated and used by TXV, printed by OUTPUT (psia). shell inlet in OUTPUT
EVAPTR
CMPRSR
POC
pressure of the refrigerant leaving the condenser, calculated in COND and FLOBAL, used by COND and FLOBAL, printed by OUTPUT (psia).
POE
pressure of the refrigerant leaving the evaporator, calculated EVAPTR and used by COMP, used by EVAPR and TXV, printed by OUTPUT (psia).
POUCMP pressure of the refrigerant at the compressor calculated and used in COMPor CMPMAP, printed (psia).
l
PRNT2
PIG
PINCMP pressure of the refrigerant at the compressor calculated and used in COMPor CMPMAP, printed (psia).
.
EVAPS
shell outlet in OUTPUT
POW
compressor power consumption, in the main program, printed
POW2
rate of power consumption used by the main program,
PRA
Prandtl
PRINT
logical variable to control the output of intermediate calculations, set to TRUE or FALSE in the main program depending on the value of LPRINT.
number of air,
computed and used in COMP, used by OUTPUT (kW).
by the compressor, calculated printed by OUTPUT (Btu/hr).
calculated
and
and used by COND and EVAPR.
CONDSR
CMPRSR
COMPR PRNT8 AIR Al
120 QAC
air flow rate through by COND (cfm).
the condenser,
QAE
air flow rate through by EVAPR (cfm).
the evaporator,
QAIR
rate of heat transfer to or from,the air, includes heat transfered from the coil and the indoor fan, calculated and used by the main program, printed by OUTPUT (Btu/hr).
QC
rate of heat transfer from the condenser to the air, ulated in COND and used by the main program, printed (Btu/hr).
QCAN
rate of heat rejection from the compressor shell, read by DATAIN, optionally computed and used in COMP, used in COND and EVAPR, printed in OUTPUT (Btu/hr).
QDISLN heat loss rate in the compressor DATAIN, used by COMP (Btu/hr).
read by DATAIN, used read by DATAIN, used
discharge
-line,
read by
total rate of heat transfer for the evaporator, in EVAPR, used by the main program, and printed (Btu/hr).
QFANC
heat loss from the condenser printed by OUTPUT (Btu/hr).
QFANE
rate of heat loss from the evaporator and printed in OUTPUT (Btu/hr).
QHILO
internal heat tra,nsfer rate from the discharge line of the compressor to the suction line, read by DATAIN, optionally calculated and used by COMP, and printed by OUTPUT (Btu/hr).
QLIQLN rate of heat loss in the liquid line, the main program and FLOBAL (Btu/hr).
calculated by OUTPUT
calculated fan,
calculated
EVAPOR A PRNT8
_
calcCONDS by OUTPUT
QE
fan motor,
CONDEN
by COND,
COMPR
LINES EVAPS
PRNT3
-I
in EVAPR PRNT7
I
read by DATAIN, used by
COMPR
LINES
QMTPL
latent heat transfer rate for the two-phase region of the evaporator, calculated and used by EVAP, printed by OUTPUT (Btu/hr).
PRNTfj
QSCC
rate of heat transfer for the subcooled region of each circuit in the condenser, calculated in EXCH, used by COND and EXCH, and printed and used by OUTPUT (Btu/hr).
CONDS
QSPC
rate of heat transfer for the superheated region of each circuit in the condenser, calculated in EXCH, used by COND and EXCH, andp printed by OUTPUT (Btu/hr).
CONDS
QSPE
rate of heat transfer for the superheated region of each circuit of the evaporator, calculated and used by EVAP, also used by EVAPR, printed and used by OUTPUT (Btu/hr).
EVAPS
.
'
121 QSTPT
sensible heat transfer evaporator, calculated (Btu/hr).
rate for the two-phase region of the and used in EVAP, printed by OUTPUT ._... ...____-..".._. _ . I
PRNT5
.
4
QSUCLN rate of heat gain in the suctin line‘. ". between .,.., .,. the evaporator and the compressor, read by DATAIN and used by either'CMPMAPor COMP (Btu/hr).
LINES
QTPC
rate of heat transfer for the -. ‘.,. two-phase region (.*xIW-I ..__"~1 .^ "_- of each circuit in the condenser;“"' calculated and used in-‘%XCH*, used by COND, printed by OUTPUT (Btu/hr).
CONDS
QTPE
rate of heat transfer for the two-phase region of each circuit of the evaporator, calculated and used by EVAP, also assigned a value and used by EVAPR, printed by OUTPUT (Btu/hr).
EVAPS
R
constant used in refrigerant equations of state correlating pressure with temperature and specific volume, assigned a value in TABLES, used by SATPRP, SPVOL, and VAPOR.
STATEQ
RACKS
number of racks of resistance heaters, BLOCK DATA and used in PDAIR.
AIR
RAU
universal gas constant for air, assigned a value BLOCK DATA, used by COND and EVAPR (ft-lbf/lbm-R).
RESIST
amount of resistance heat-required to meet the house load, calculated and used in the main program, printed by.OUTPUT (Btu/hr).
PRNT8
RHI
the relative humidity of the air entering the evaporator calculated and used in EVAP, printed in OUTPUT.
PRNT5
RHIC
the relative humidity of the air entering the condenser read by DATAIN and used in COND and EXCH.
RHIE
the relative humidity of the air entering read by DATAIN, used by EVAP and EVAPR.
RHO
relative humidity of the air at the leaving edge of the evaporator, calculated and used by EVAP, printed by OUTPUT.
RHTERM constant in dehumidificati-on and used in TWOSOL. RPM
solution,
actual compressor motor speed, assigned COMP, printed by OUTPUT (rpm's).
assigned
a value
in
in
the evaporator
AIR
coil, unit, unit,
CONDEN EVAPOR PRNT5
calculated
in EVAP
TWO
a value
and used in
,PRNTl
122
RPMFAN motor speed for the outdoor fan, DATA, used by FANFIT (rpm's).
assigned
a value
in BLOCK
FANMOT .
RPMSLP slope of the linear fit to the fraction of no-load motor speed as a function of fraction of full-load assigned a value in BLOCK DATA and used in COMP. RTBCND the number of return bends in the condenser, scaled and used by CALC. RTBEVP the number of return bends in the evaporator, scaled and used by CALC.
compressor power,
CMPMOT
read by DATAIN,
CONDEN
read by DATAIN,
EVAPOR
for the superheated region in EFFCT and used by
EFFARG
RTOT
overall resistance to heat transfer of the condenser (l/UA), calculated EXCH (hr-F/Btu).
SEFFD
overall surface efficiency for hexagonal fins (staggered tubes) EVAPRS in the evaporator, calculated and used in EVAP, used by EVAPR, and printed by OUTPUT.
SEFFWA average surface efficiency for the portion of the evaporator where moisture removal occurs, calculated and used in EVAP, used in EVAPR, and printed in OUTPUT.
EVAPRS
SEFFXC overall surface efficiency for the condenser, SEFF, and used by COND, EFFCT, and EXCH.
CONDS
calculated
in
SIGAC
ratio total
of the free flow frontal frontal area, calculated
area of the condenser to the in CALC and used in COND.
CONDEN
SIGAE
ratio total
of the free flow frontal frontal area, calculated
area of the evaporator to the in CALC and used in EVAPR.
EVAPOR
ss
specific printed
STATIC
static superheat setting valve, assigned a value used by TXV and printed
STC
vertical spacing between tube passes in the condenser, by DATAIN, used by CALC and COND (ft).
STE
vertical spacing between tube passes in the evaporator, by DATAIN, used by CALC, EVAP, and EVAPR (ft).
speed of the outdoor by OUTPUT.
STRTOT ratio of the sensible evaporator, calculated
fan , calculated
in FANFIT and
PRNT8
for, the thermostatic expansion TXVDAT in BLOCK DATA or read by DATAIN, by OUTPUT (F).
to total heat transfer rates for in EVAP, printed by OUTPUT.
read read the
CONDEN EVAPOR PRNT5
123
STRTP
of the
sensible
to .total
heat
two-phase region of the evaporator, printed in OUTPUT.
.
e
ratio
!?zS?z.,rate?.
calculated
.,.,for.. the. ._
factor for suction gas heating in the compressor, SUCFAC correction assigned a value in BLOCK DATA and used in CMPMAP. SUPER
specified superheat of the refrigerant leaving the evaporator read by DATAIN, used by COMP, EVPTR, OUTPUT, and TXV (F).
SUPERB base superheat value for and used by CMPMAP(F).
the compressor
PRNT5
in EVAP and
map, read by DATAIN
MAPFIT FLOWBA MAPFIT
superheat for the thermostatic expansion SUPRAT rated operating valve, assigned a value in BLOCK DATA or read by DATAIN, used by TXV, and printed by OUTPUT (F).
TXVDAT
SYNC
synchronous or actual compressor motor speed depending whether or not the full load motor power is calculated, read in DATAIN and used in COMP (rpm's).
COMPR
TACI
temperature of the air at the point where moisture removal begins, calculated and used in EVAP, printed in OUTPUT (F).
TAIC
temperature heat losses and printed
TAIE
air temperature crossing the evaporator coil, inlet air temperature with any additions due to fan motor and compressor heat losses, calcul.ated in EVAPR and printed in OUTPUT (F).
PRNT7
TAIIC
air temperature entering the condenser, read by DATAIN, used by COND and EFFCT, printed by OUTPUT (F).
CONDSR
TAIIE
air temperature entering the evaporator which corresponds to EVAPTR the current values of TSATEI and TSATEO, the desired value for the ambient air temperature is read by DATAIN, current value is calculated and used by the main program, also used by EVAPR, EVPTR, and OUTPUT, printed by OUTPUT (F).
TAOC
air temperature after it passes over the condenser coil, ulated in EXCH, used by COND, and printed in OUTPUT (F).
calc-
CONDSR
TAOE
air temperature leaving the evaporator with any additions for compressor and fan motor heat losses, calculated and used by EVAP, used by EVAPR, and printed by OUTPUT (F).
EVAPTR
on
.
. L
of the air crossing the condenser, includes from the fan motor or compressor, calculated in OUTPUT (F).
PRNT5
any PRNT3 in COND
124
TAOOC
air temperature leaving the condenser, includes from the compressor and fan motors, calculated printed in OUTPUT (F).
any heat losses in COND and
TAOOE
air temperature leaving the evaporator, includes any additions due to heat losses from the fan and compressor motors, calculated in EVAPR and printed in OUTPUT (F).
PRNT7
TAOSC
outlet air condenser,
temperature calculated
from the subcooled region of the in EXCH, printed in OUTPUT (F).
PRNT4
TAOSPC outlet air condenser,
temperature calculated
from the superheated region of the in EXCH, printed in OUTPUT (F).
PRNT4
TAOSPE outlet air evaporator,
temperature calculated
from the superheated region of the and used in EVAP, printed in OUTPUT (F).
PRNT3
PRNT5
TAOTPC outlet air temperature from the two-phase region of the condendser, calculated in EXCH, printed in OUTPUT (F).
PRNT4
TAOTPE outlet orator,
PRNT5
air temperature from the two-phase region of the evapcalculated and used in EVAP, printed in OUTPUT (F).
TC
critical temperature for the refrigerant, assigned TABLES, used in SATPRP, SPVOL, and VAPOR (R).
TERAT
evaporating temperature used for rating the thermostatic expansion valve, assigned a value in BLOCK DATA, used in TXV (F).
TFLODV refrigerant temperature entering the flow control ulated and used in FLOBAL, printed in OUTPUT (F).
a value
device,
in
SUPER TXVDAT
talc-
PRNT2
TFR
constant used to convert from Farenheit to absolute temperature when using correlations for refrigerant properties (i.e. the value assumed by researcher deriving the correlation), assigned a value in TABLES, used by SATPRP, SPVOL, TSAT, and VAPOR (F).
SUPER
TIC
temperature of the refrigerant entering the condenser, initialized by COMP, calculated in DESUPR and COMP, used by COND, DESUPR, EFFCT, and EXCH, printed by OUTPUT (F).
CONDSR
TIE
temperature calculated
EVAPTR
of the refrigerant by EVAPR and printed
entering the evaporator, by OUTPUT (F).
TLQCOR correction factor to adjust tube and nozzle pressure drops in the thermostatic expansion valve for liquid temperatures entering the valve other than the rating temperature, calculated and used in TXV, printed in OUTPUT.
TXVDAT
125
of the.liquid refrigerant TLQRAT rating temperature the thermostatic expansion valve, assigned DATA and used in TXV (F). I
TOLH
TOLS
tolerance properties enthalpy,
t
MPASS
of the refrigerant at the compressor shell inlet and used in COMPor CMPMAP, printed in OUTPUT (F).
of the refrigerant at the compressor shell in COMPor CMPMAP, printed in OUTPUT (F).
TXVDAT
and
temperature of the refrigerant at the condenser exit, estimated in FLOBAL, calculated in EXCH, used by CNDNSR, COND, FLOBAL, and FLODEV, printed in OUTPUT (F).
TROCMP temperature calculated
.
parameter used to calculate superheated vapor when the two known properties are the pressure assigned a value in BLOCK DATA _....~_--..-..._ .,.,f used by COMP.
tolerance parameter used to calculate. .)_, superheated vapor properties when the two known properties are pressure and entropy, assigned a value in BLOCK DATA and used by COMP.
TRICMP temperature calculated TROC
at the inlet to a value in BLOCK
outlet
MPASS
CMPRSR CONDSR
CMPRSR
TROE
temperature of the refrigerant leaving the evaporator, calculated and used in EVAP, used by EVAPR and EVPTR, printed by OUTPUT (F).
EVAPTR
TRVDS
refrigerant temperature at the end of the desuperheating region in the condenser, initialized in COND, calculated by EXCH, and used by COND, EFFCT, and EXCH (F).
CONDS
TSATCI
saturation temperature of the refrigerant entering the condenguess read by DATAIN, calculated in the main ser, initial program, used by COMP, FLOBAL, COND, EXCH, and DESUPR, printed by OUTPUT (F).
CONDSR
TSATCO saturation temperature of the refrigerant leaving the condenser calculated in COND and FLOBAL, used by CNDNSR, COND, EXCH, FLOBAL, and FLODEV, printed in OUTPUT (F).
CONDSR
TSATEI
the evapand used
EVAPTR
TSATEO saturation temperature of the refrigerant leaving the evaporator, initial guess read by DATAIN, calculated and used by the main program, used by COMP, EVAPR, EVPTR, FLOBAL, and TXV, printed by OUTPUT (F).
EVAPTR
TSATFL saturation temperature of the refrigerant entering the flow control device, calculated and used in FLOBAL, printed in OUTPUT (F).
PRNT2
saturation temperature of the refrigerant orator, initialized in the main program, by EVAPR and TXV, printed by OUTPUT (F).
entering calculated
126
TSATRl
average saturation temperature in the evaporator, value in EVAP, used in TWISOL (F).
assigned
a
TWI
TSATR2 average saturation temperature in the evaporator, value in EVAP, used by TWOSOL(F).
assigned
a
Two
* 7
TSICMP saturation temperature shell inlet calculated in OUTPUT (F).
of the refrigerant at the compressor and used in COMPor CMPMAP, printed
TSOCMP saturatin temperature of the refrigerant at the compressor shell outlet calculated in COMPor CMPMAP, printed in OUTPUT (F). TWALLI
CMPRSR
tube wall temperature at the leading edge of the evaporator where moisture removal begins, calculated and used in EVAP, used by TWOSOL, printed in OUTPUT (F).
TWALLO air temperature at the tube walls on the leaving evaporator, calculated and used in EVAP, printed
edge of the in OUTPUT (F).
TWBI
wet bulb temperature of the air entering ulated in EVAP, printed in OUTPUT (F).
TWBO
wet bulb temperature of the air at the leaving edge of the evaporator, calculated in EVAP, printed in OUTPUT (F).
the evaporator,
expansion TXVRAT rated capacity of the thermostatic a value in BLOCK DATA and used in TXV (tons).
valve,
CMPRSR
calc-
assigned
TWO
PRNT5 PRNT5 PRNT5 TXVDAT
UATPAW air-side thermal conductance times the heat transfer area (UA) for the portion of the two-phase region of the evaporator which is wetted due to dehumidification, calculated in EVAPR, and printed in OUTPUT (Btu/hr-F).
UAS
UATPW
refrigerant-side thermal conductance times the heat transfer area (UA) for that portion of the two-phase region of the evaporator whose outside surface is wetted due to dehumidificalculated in EVAPR and printed in OUTPUT (Btu/hr-F). cation,
UAS
ULA
upper limit refrigerant,
V
constant in dehumidification solution, and used in TAOSOL and TWOSOL.
on the Reynold's number for laminar flow of the VAPHTC assigned a value in BLOCK DATA and used in SPHTC.
calculated
in EVAP
TWO
127
I
factor for the compressor volumetric efficiency, VOLFAC correction assigned value in BLOCK DATA and used in CMPMAP.
-
VR
compressor clearance used by COMP.
W
constant in dehumidification solution, and used in TAOSOL and TWOSOL.
WAIRI
humidity ratio ator calculated
WAIRO
humidity ratio of the air and used in EVAP, printed
calculated
PRNTS
WOUT
humidity ratio of the 'air at the leaving edge of the evaporator, calculated and used by EVAP, printed by OUTPUT.
PRNT5
WTC
spacing of the tubes in the condenser in the direction flow, read by DATAIN, used by CALC and COND (ft).
CONDEN
WTE
spacing of the tubes in the evaporator in the direction air flow, read by DATAIN, used by EVAP and EVAPR (ft).
. L ..
volume ratio,
read by DATAIN and
calculated
MAPFIT COMPR
in EVAP
of the air at the leading edge of the evaporand used in EVAP, printed in OUTPUT. leaving the evaporator, in OUTPUT.
of air of the
TWO PRNT5
EVAPOR
WWALLI humidity ratio at the tube walls on the leading edge of the evaporator where moisture removal begins, calculated and used in EVAP, calculated in TWISOL, printed in OUTPUT.
TWI
WWALLO humidity ratio of the air at the tube walls on the leaving edge of the evaporator, calculated and used in EVAP, printed in OUTPUT.
PRNT!j
X
constant used in correlating enthalpy of refrigerant vapor with OTHER temperature and specific volume, assigned a value in TABLES and used in SATPRP.
of the refrigerant entering XFLODV vapor quality in FLOBAL and printed device, calculated
the flow control in OUTPUT.
PRNT2
XIC
refrigerant vapor quality entering the condenser, set to 1.0 in FLOBAL, modified in DESUPR, used by COND and EXCH, printed in OUTPUT.
CONDSR
XIE
refrigerant vapor quality entering the evaporator, and used in EVAPR and printed in OUTPUT.
EVAPTR
calculated
128
XINCMP refrigerant calculated
CMPRSR -
shell inlet vapor quality at the compressor and used in COMPor CMPMAP, printed in OUTPUT.
XKFC
thermal conductivity of the fins in the condenser, DATAIN, used by CALC and COND (Btu/hrFt-F).
XKFE
thermal conductivity of the fins in the evaporator, DATAIN, used by CALC and EVAP (Btu/hr-ft-F).
read by
CONDEN r
read by
EVAPOR
factor for the pressure drop in distributor tubes XLCORR correction of the thermostatic expansion valve for tubes of lengths other than the rated length, calculated and used in TXV, printed in OUTPUT.
TXVDAT
XLLR
lower limit refrigerant,
XLEQDL equivalent reversing COMP (ft).
on the Reynold's number for laminar flow of the assigned a value in BLOCK DATAand used in SPHTC. length of the compressor discharge line from the valve to the condenser, read by DATAIN -nd used by
length of the high pressure XLEQHP equivalent discharge port to the reversing valve, by COMP (ft).
VAPHTC LINES
line from the compressor read by DATAIN and used
LINES
length of the liquid line connecting the indoor and XLEQLL equivalent outdoor heat exchangers, read by DATAIN -nd used by FLOBAL (ft).
LINES
length of the low pressure line from the compressor XLEQLP equivalent suction port to the reversing valve, read by DATAIN and used by COMP (ft).
LINES
length of the suction line from the evaporator XLEQSL equivalent the reversing valve, read by DATAIN -nd used by COMP (ft).
LINES
to
XMAC
mass flow rate of air condenser, calculated in OUTPUT (lbm/hr).
across each parallel circuit in the in COND, used by EFFCT and EXCH, printed
XMAE
mass flow rate of airy across each parallel circuit in the calculated in EVAPR and used in EVAP, printed evaporator, in OUTPUT (lbm/hr).
EVAPS
XMASP
mass flow rate of the air across the superheated region of calculated and used in EVAP, each circuit in the evaporator, printed in OUTPUT (lbm/hr).
PRNT5
XMATP
mass flow rate of the air across the two-phase region of each circuit in the evaporator, calculated and used in EVAP, printed in OUTPUT (lbm/hr).
PRNT5
XMM
rate of moisture removal from the air, printed in OUTPUT (lbm/hr).
calculated
in EVAP and
CONDS
PRNT5
129
XMR
guess or estimate read by refrigerant mass flow rate, initial DATAIN, calculated in COMP, used by the main program, COND, EFFCT, EVAPR, FLOBAL, and the flow control device subroutines, printed and used by OUTPUT (lbm/hr).
FLOBAL
XMUA
viscosity (lbm/hr-ft).
AIR
of air,
calculated
and used by COND and EVAPR
XNTUSC number of transfer units for the subcooled region of the condenser, calculated in EXCH, printed in OUTPUT.
PRNT4
XNTUSP number of heat transfer units for the superheated region of PRNT4 the condenser, calculated and used in EXCH, printed in OUTPUT. XNTUSU number of heat transfer units for the superheated region of PRNT5 the evaporator, calculated and used in EVAP, printed in OUTPUT. XNTUTP number of heat transfer units for the two-phase region of PRNT4 the condenser, calculated and used in EXCH, printed in OUTPUT. XNTUTP number of heat transfer units for the two-phase region of PRNT5 the evaporator, calculated and used in EVAP, printed in OUTPUT. . c c
xoc
refrigerant vapor quality leaving the condenser, initialized CONDSR in COND, calculated in EXCH, used by CNDNSR, COND, EXCH, FLOBAL, and FLODEV, printed in OUTPUT.
XOE
vapor quality of the refrigerant leaving the evaporator, calculated and used in EVAPR, used in EVPTR and COMP, and printed in OUTPUT.
XOUCMP refrigerant calculated
Y
vapor quality at the compressor shell outlet in COMPor CMPMAPand printed in OUTPUT;
constant used in correlating with temperature and specific TABLES and used in SATPRP.
entropy of refrigerant vapor volume, assigned a value in
EVAPTR
CMPRSR
OTHER
/
,
131
Appendix
E - Cross-Reference
The common blocks data marks.
to or from
the
listed
subroutines
of Common Blocks in
the
rows of Table
identified
by the
1 are columns
used to transmit with
the
"X1'
132
SUBROUTINES
AIR Al BLANK CMPMOT CMPRSR COMPR CONDEN CONDS CONDSR DENSIT EFFARG EVAPOR EVAPRS EVAPS EVAPTR FANMOT FLOWBA LINES MAPFIT MPASS OTHER PRNTl PRNTZ PRNT3 PRNT4 PRNT5 PRNT7 PRNT8 REFRIG
I 1x1 I lxlxl
SAT
I
lxlxl
STATE4
I
I
SUPER TWI TWO TXVDAT UAS VAPHTC
I iii/iii/
I I
X r.
I
XII
IIII
I
I
I
I
I IXIXI I I lxlxl
lxlxl I I I I4 II II 1x1 I I Ixlxlxl Ixlxlxl I I 1x1 1 I
I
I
4
I
I
X
x
1,x,,,
I
1
,,,,,
X ,,,.
I
I
133
Appendix
Subroutine
F - Subroutine Calls
Descriptions
and Cross-Reference
of Subroutine
Descriptions
serves as driving program for high- and low-side computaMain Program tions and contains iterative loop converging on evaporator inlet air temperature assigns BLOCK DATA parameters
geometric
to constants
CAPTUB
submodel
CHTC
calculates two-phase
CMPMAP
computes refrigerant mass flow from compressor map data
CNDNSR
serves as ,driving routine for COMP, COND and FLOBAL and returns the difference between the calculated and specified condenser subcooling or between the compressor and expansion device refrigerant mass flow rates
COMP
computes sumption
COND
calculates total condenser heat transfer rate, air ant properties and refrigerant and air-side pressure fixed inlet refrigerant conditions
capillary
tube
refrigerant-side region of the
for flow
both
heat
changed
calculates for
constants
and infrequently
CALC
exchangers
rate
heat transfer condenser
coefficient
and compressor
for
the
power consumption
refrigerant mass flow rate and compressor from efficiency and loss parameters
drops
for
DPFSOL
calculates the difference between the known saturation pressure of water vapor at the tube wall and the saturation pressure corresponding to an estimated, or given tube wall temperature
DPLINE
determines lines
EFFCT
computes the difference in condenser effectiveness values between the general effectiveness equation and the specific cross-flow effectiveness equation as a function of the fraction of the coil, fV, containing superheated refrigerant vapor
EHTC
calculates two-phase
refrigerant-side region of the
pressure
drop
heat transfer evaporator
in
for
and refriger-
determines an approximate dew-point vapor pressure of moist air
the single-phase
temperature
power con-
DPF
h 5
values
the
coefficient
a given
refrigerant
for
the
134
EVAP
determines the heat transfer, moisture removal, and outlet air temperatures and humidities from one circuit of the evaporator for given heat transfer coefficients and saturation temperatures at the beginning and end of the two-phase region
EVAPR
calculates properties, fixed exit
EVPTR
serves as a driving between the specified value
EXCH
determines the heat transfer and outlet temperatures for one circuit of the condenser for given heat transfer coefficients and saturation temperatures at the beginning and end of the two-phase region
EXF
determines using the
FANFIT
calculates pressure
FLOBAL
determines refrigerant conditions at the inlet control device and drives the expansion device
to the models
flow
FRICT
computes the general flow in tubes
s ingle
phase
GUESS2
brackets a solution prior to using end points by factors of 10
a root
finder
by shifting
GUESS3
brackets a solution prior to using end points by constant step
a root
finder
by shifting
INTER
interpolate
HAIR
computes air-side tube geometry
MUKCP
calculates viscosity, of 13 refrigerants
thermal
conductivity,
and specific
heat
MUKCPA
calculates of air
thermal
conductivity,
and specific
heat
OR1FIC
computes orifice
OUTPUT
prints
evaporator heat transfer rate, and refrigerant and air-side refrigerant conditions routine for evaporator
air and refrigerant pressure drops for
EVAPR and returns the difference superheat and the calculated
the effectiveness of a cross-flow effectiveness - NTU method combined fan-fan drop and volumetric
Moody friction
in a single
viscosity, refrigerant a detailed
motor efficiency air-flow rate
factor
dimension
heat
transfer
mass flow
using
summary of output
through data
exchanger
given
air-side
for
Lagrangian
coefficient
rate
heat
for
polynomial smooth
a short-tube
fin
and
135
a
PDAIR
calculates air-side fin and tube heat
PDRQP
determines singleand two-phase heat exchanger tubes
PVSF
calculates
SATPRP
evaluates refrigerant
SEFF
determines surface
SLAG
computes single dimensions from
SPFHT
calculates refrigerant volume and specific
SPHTC
computes transition, entrance
single-phase heat transfer coefficient for laminar, or turbulent gas flow from an abrupt contraction
SPHTCZ
computes developed
single-phase heat transfer liquid or gas flow
SPVOL
evaluates
SUPCOR
calculates power and mass flow correction factors for based compressor model to correct for superheat level
TABLES
assigns routines
TAOSOL
computes the exit air temperature evaporator where moisture removal
TRIAL
determines thermodynamic properties vapor given two known properties
TSAT
pressure exchangers
partial the
pressure
saturation
surface
drop
for
volume
for
'calculates saturation tion pressure
temperature
shaped
coefficient
thermodynamic from the occurs
of superheated of refrigerant
TXV
computes expansion
at the rate
and
fully
refrigerant given
exit
sub-
of the
moisture
through
map-
property
region
used to compute evaporator
mass flow
two
refrigerant
TWOSOL
the refrigerant valve
fin
pressure
for
used to compute the wall temperature at which begins on the leading edge of the evaporator temperature
in air
in
at constant
TWISOL
the wall
flow
of a specified
interpolation
of superheated
refrigerant
for
properties
heats
or louvered
in saturated
a hexagonal
Lagrangian data
specific heat ratio
wavy,
drops
vapor
thermodynamic
precision tabulated
constants
smooth,
pressure
of water
efficiency
specific
for
from
saturaremoval the
a thermostatic
1 3-6
VAPOR
determines thermodynamic vapor given temperature
WBF
determines
WTSFIT
computes coefficients to enthalpy of moist
for air
XMOIST
calculates wet-bulb
temperature, or relative
ZERO's
each of these routines solves for the function from two points which bracket section and Newton's method
wet-bulb
the
subprograms
"X'S".
temperature
dew point temperature
The subroutines listed
listed
properties and pressure
of moist
a quadratic
in the columns
in the
of superheated
rows of Table
refrigerant
air
fit
humidity humidity root, the
of Table F.1 which
of wall
temperature
ratio enthalpy, of moist air
and
or zero, of a solution using bi-
F.1 are called are
indicated
from by
137
. . +,
139
Appendix
G - Algebraic
A
frontal
a
intercept context
A A
a contact
area
of heat
fin contact
area
fin
frontal
area
A ft
air-side
fin
A heater
cross-sectional
A min
ratio of total free-flow area
A orifice
cross-sectional
A
total
A
filter
r
A side
heat
A
total
A
0
b b
fat
heat
transfer
of filter
transfer exposed
bypass
heat
and tubes
short
area
of each side
transfer
fit
to data
area
section
to the minimum
orifice area
for
each parellel
circuit
of each fin
of tubes
heat
for
heater
tube
transfer
transfer
factor
area
transfer
heat
area
unit
resistance
of the
surface
by
area
transfer
heat
heat
or bleed
fins
of the
area
of a linear
transfer
is determined
area
air-side
area
which
on indoor
and tube
refrigerant-side slope
heat
refrigerant-side
refrigerant-side
to data
between
area
A rh
tubes
fit
and tube
air-side
Af
exchanger
of a linear
air-side total
Notation
area which
in heat
exchanger
per unit
air
flow
is determined
a thermostatic
rate
by context
expansion
valve
C
compressor flow area
C
heat
C
ratio
C
max
maximum of the refrigerant
heat
capacity
rates
for
the
air
and the
C min
minimum of the refrigerant
heat
capacity
rates
for
the
air
and the
a fat
piston clearance volume ratio coefficient or Dittus-Boetter
capacity
rate
of humidity
of air ratio
or expansion exponent
device
(macPa) gradient
to the
temperature
gradient
140 C r
heat
C
constant
in Eq. 6.15
C P C pa C pm
specific
heat
of the
specific
heat
of air
specific
heat
of moist
C r
heat
C
correction factor to the air-side for wavy and louvered fins
D
total compressor piston displacement diameter depending on context
d
depth
D a
air-side
or outer
D ducts,
diameter
of air
D r
refrigerant-side
f
fraction of rated value, determined by context
F a
fin heat area
F moist
fraction of that part of the evaporator which flow that is wetted due to dehumidification
F P F sh
fin
f
combined
0
tot
capacity
rate
capacity
of refrigerant
rate
of heat
(mrcp)
refrigerant
air
of the
refrigerant heat
transfer
coefficient
or refrigerant
tube
exchanger diameter
of heat
exchanger
tubes
ducts or inner
transfer
area
diameter
of heat
fraction per unit
of coil, total
exchanger
tubes
or friction
air-side
heat is
in
factor transfer two-phase
pitch
compressor
suction
gas heating
wet and dry
F
W
fraction of the dehumidification
f
wet
friction wetted
friction
evaporator
factor that
factor for the region due to dehumidification
F
compressor
Fktt)
correlating transfer
volumetric function coefficient
factor
efficiency for
the
for
is wetted of the
the
evaporator
due to
evaporator
correction refrigerant-side
which
is
factor two-phase
heat
141
correlating
r F* .
. *
parameter
mass flux
G
gravitational
SC
acceleration
constant
enthalpy
of refrigerant
enthalpy
of saturated
air
ha, a, h fg h' fg h
enthalpy
of moist
at freestream
h
average
h h
a,s
ave
heat
driving
tP
enthalpy
difference
air or refrigerant heat subscript or context)
sensible
h* W
effective
condensation
h2
transfer
heat
transfer
heat
transfer
heat
coefficient
transfer heat
for
coefficient transfer
of tubes
in heat
exchangers
length
of tubes
in
exchanges
l
I
surface
using
Chaddock-
local evaporation heat transfer coefficient for the dry-out region using nonlinear interpolation between the Chaddockvapor Noerager value at xdo and the value for saturated
length
m
by
a wet surface
coefficient
e
ril
a wetted
for
equivalent
tubes
(determined
coefficient
L
c
condenser
coefficient
thermal
exposed
temperature
conditions
in the
k
L
surface
coefficient
local evaporation Noerager correlation
%
exchanger
average condensing or evaporating heat transfer coefficient (condensation value includes an adjustment due to Rohsenow)
h
W
air
at wall
of heat
of vaporization
mass transfer
‘d h
latent
or height
conductivity length
equivalent valve
length
mass flow
rate
mass flow
rate
of refrigerant
heat
of distributor
at "standardized"
pipes
exposed tubes
test
in
to the
air
thermostatic
or rating
expansion
conditions
,
.
.-.
142 N cap N circuits
number of parallel
tubes
number of equivalent heat exchanger
parallel
total
number of fins
in the
N Le
Lewis
number
N Pr N Re
Prandtl
Nf
refrigerant heat
circuits
in the
exchanger
number
Reynolds
number
NT
number of tube the air flow
f
N tot
total
/
NtU
rows in the
number of tubes
number of heat
heat
in the
transfer
exchanger
heat
in the
direction
of
exchanger
units
N
number of tubes
P
pressure
6
heat
transfer
6 can
rate
of. heat
6 cooling
rate of heat transfer to the suction gas
from
the
compressor
and compressor
motor
'hilo
rate of heat transfer the suction gas
from
the
compressor
discharge
to
V
volumetric
I
capillary
stacked
vertically
in the
air
rejection
flow
from
the
compressor
r
ratio
of UA values
used in Eq. 6.11
ratio
of UA values
used in Eq. 6.23
S
motor
speed
S
heat
exchanger
S oper
actual
S
specific
S sync
synchoronous
resistance
coil
or operating
shell
line
rate
thermal
S
exchanger
rate
R
rl
heat
per unit
of refrigerant
side-area
characteristic motor
speed of the
fan
speed for
the
speed of compressor
outdoor motor
heat
exchanger
143
3
vertical
T
air
T
aid
T T
aie v,ds
T
sat
temperature
bulk refrigerant heating region refrigerant
air
W
humidity
ratio
i
work
wa, m
humidity
i
fan motor
dehumidification
the evaporator at the
start
of the desuper-
temperature
performed ratio
occupied
of air
full
of heat
input
at freestream
load
exchanger
vapor
X tt
correlating
parameter
c1
total air-side volume
cx can
fraction from the
a
correction factor for inlet to a thermostatic fraction discharge
exchanger
conditions
power consumption
compressor-motor spacing
by heat
or energy
refrigerant
ahilo
by context)
conductance
X
corr
entering
saturation
of space
a
exchanger
(determined
vapor temperature of the condenser
volume
wT
in heat
temperature
of the
V hx
s,fl
tubes
evaporator inlet air temperature for which would occur at the finned tube surface
thermal
fan
between
or refrigerant
U
I;
.
spacing
shaft tubes
power in
the
direction
for
two-phase
transfer
area
heat per
transfer
unit
heat
of the compressor power consumption shell to the ambient air liquid refrigerant expansion valve
of compressor power consumption line to the suction line
r
total refrigerant-side exchanger volume
a
racks
correction factor number of resistant
flow
quality
heat
01
of air
heat
transfer
to adjust air-side heater racks
area
coefficient exchanger
which
is
rejected
temperatures at the other than 100°F transferred per unit
pressure
drop
from heat for
the
the
144
Bcorr
correction 30 inches
Y
ratio of specific heat at constant volume
6
fin
Ah
enthalpy
change
Af’
pressure
drop
pressure
drop
APJ3 0 2
factor
for
TXV distributor at constant
measured
in inches
level temperature difference, superheat depending on context
E
heat
E cf
effectiveness
n
compressor effectiveness
1-I
viscosity
V
specific
P
density
0
capillary
tube
free-flow exchanger
frontal -
a
pressure
lengths
other
to specific
than heat
thickness
AT
u
tube
exchanger
of water
of subcooling,
or level
of
effectiveness of a counter-flow
efficiency
or heat
heat
exchanger
exchanger
overall
surface
volume
flow
factor area
per unit
total
frontal
where
there
area
of heat
Subscripts a
air
actual
at modeled
ave
average
cm
compressor
d
dry
do
dry-out liquid
dp
dew point
operating
conditions
point in the evaporator film on the tube wall
is
no longer
a
145
eff
effective
evap
evaporator
f
fin
fl
compressor
frict
friction
ft
fin
i
heat
in
entering
inlet
compressor
isen
isentropic
R
liquid
lot
local
m
mean
map
from
max
maximum
mech
mechanical
mom
momentum
noz
TXV nozzle
0
heat
oper
at modeled
out
exiting
outlet
compressor
r
refrigerant
rated
at rating
rb
return
S
compressor
motor
full
load
and tube exchanger
inlet
shell
compressor
exchanger
inlet
map
outlet
operating
shell
conditions bends shaft
outlet
conditions
,
.
-
-,
,.~
._.
-^,“l
._..-
“__l^_._-“...
146 sat
saturation
sh
suction
static
static static
t
tube
tP
two-phase
tubes
heat
TXV
thermostatic
V
vapor
vol
volumetric
w
region
co
freestream
gas heating
L
fan efficiency or static expansion valve
exchanger
or TXV distributor expansion
wetted
valve
due to dehumidification
condition
superheat
tubes
value
of a thermo-
147 H - Derivation
Appendix H.l
of Dehumidification
Introduction A method
is
described
of an air-to-refrigerant The method
represents
Goodman [H.l], Threlkeld
[H.4],
H.2
Heat Transfer
be described,
evaporator
under
and Wiley from
as noted
The local
section
and McQuiston
derived
[H.7]
in this
an assimilation
McElgin
coefficients Myers
Solution
[H.2],
heat
in Section Equations
driving using
force
computing
the
dehumidification
and/or
[H.5,
dry
for
conditions.
expansion
Hiller H.61,
performance
of the work
and Glicksman
[H.3],
and uses wet heat
transfer
values
via
the
of
transfer
equation
of
6.
-Air
to Wall
for
simultaneous
simplifying
heat
assumptions,
and mass transfer
by Eq. H.l
can
[H.6]
db = h, (h a, to -ha , ,JdAs where a differential
quantity
of
local
dQ
-
‘d
-
ha, m
-
the
-
the enthalpy perature
of saturated
air
-
a differential
element
of wetted
h
a,s
dA Equation
S
H.l
the mass transfer
contains
enthalpy
heat
and mass transfer
coefficient
of humid
air
the assumption
at the
that
the
freestream
at the wall surface Colburn
condition surface
tem-
area. analogy,
given
by
Eq. H.2 CH.61,
h
W
’ pm ‘d
=
213
N
Le
(H-2)
148
where
hW
-
sensible
c
-
moist
heat air
transfer
specific
coefficient
heat,
c
pm
woo a, N Le holds is
humidity
-
Lewis
-
and that
neglected
(except wetted
and Elmahdy
assumptions; the
effect
transfer
rates
parallel
flat
equation
presented
the
+ .444 wa,co
pa
energy
content
film
thickness
the water sensible
heat
are analyses
in the
[~.8]
which
require
these heat
is
for
surface
and
There
simplified H.l
of
on the
however,
Equation
Also,
c: 1.
effect
surface).
[H.4] with
(MLe)2'3
the
of air,
= c
a wetted
number,
and the
for
ratio
pm
for
do not analyses
exchanger
strictly
plates.
such as humid air
by McQuiston
[H.5,
H.61
for
a
for
use
by Threlkeld of these
heat
pump model.
describing
heat
ignored
too complicated
in the for
condensate
coefficient
some or all
routines
For a fin-and-tube
is
literature
were judged
applicable
situations
transfer
of the
heat
flowing
and mass
between
exchanger,
two
an appropriate
is
di = hd nw,ft(ha,m- h,)dA,, where
the
subscripts
surface,
"t"
respectively.
is
subscript
a wet fin
similar meter
"m", m
fin
wet surface
= 1 --AAf ft
"f".refers
efficiency
to usual
to tube
and total
fin-and-tube
effectiveness,
nw ft, ,
as
nw,ft
the
refer
The overall
in Eq. H.3 is defined
where
and "ft"
(H-3)
which efficiency
where ,
to fin is
(1 - 'Iw,f)
surface.
defined equations
The term
by McQuiston except
that
nw f in Eq. H.4
[H.5]'in the
usual
a manner para-
149
is
replaced
by M, i.e.,
M = +)(l
+
C h fat fg)-jl/2 c pm
(H.5)
where h
h
W
h*
W
kf
heat
transfer
coefficient
for
a dry
sensible
heat
transfer
coefficient
for
a wet surface
effective
heat
thermal
conductivity
fin
6 h
sensible
coefficient of the
for
a wet surface
fin,
thickness
enthalpy
fg
transfer
surface
of vaporization
of the water
vapor,
and ratio of humidity ratio gradient to temperature (specifically defined in Appendix I).
C fat
C,__ in Eq. H.5 is
Since heat
gradients,
the
dehumidification H.3
Equation portion
tube
is
wall
-A ir
Equations
ht --
ratio
of
efficiency
latent
will
external
heat
when both
temperature).
to Mean Surface the
Since
temperature.
the mean temperature
surface
of wet fin
value
H.3 contains
of the
in determining
on the
to sensible
be dependent
on-the
rate.
Heat Transfer
at the
dependent
gradient,
transfer
the fin
enthalpy
of saturated
the
surface
tube
surface,
and tube
a better
start
of the fin-and-tube From Threlkeld
Conditions
[H.4],
is
air only
it
is
a small
variable
to condense
combination
evaluated
(the
shown that
for
water
use
vapor
effective for
a dry
surface
'd,f
T , = T:,,
- Tf,m - Tt
b-4.6)
150
where
the
subscript
wet surface, T
a,
03, it
"f,m"
since
follows
refers
McQuiston's
to a mean fin solution
for
Similarly,
value.
nm f is ,
in terms
for
a
of Tt and
that
T
rlw,f
a,03 - Tf,m
= T
(H-7)
a,03 - Tt
and T
a,a =T /Tt a,
nw,ft
Next,
using
a relationship
implied
-T
ft,m '
in the derivation
of nw f, ,
i.e.,
(H.9)
ha, co- hft ,m = (’ + Cfac)(Ta,az- Tft,m) the
overall
wet surface
rlw,ft
il
Substitution
of Eq.H.10
into
db
H.4
Heat Transfer Next,
and tube
=
hd(ha
Equations
a relationship temperature,
nw ft ,
effectiveness
is Tft
,
=
can also
-h ft,m a,m h co -ht a,
be written
as
h
(H.10)
'
Eq. H.3 yields
,
co
-
hft
,
(H.11)
l
m)dAft
-Mean
Surface
to Refrigerant
needed
between
conditions
m, and the
refrigerant
Conditions at the mean fin
temperature,
T,.
151
Using
McQuiston's
written
definition
in two ways,
of nw , ft,
,
do = h*w(Ta,m
of
Eqs.
total
heat
flow
can be
i.e.,
do = h*w 11, ft(Ta,m
Combination
the
- Tt)dAft
(H.12)
(H.13)
- Tft , m)dAft
H.12 and H.13 to eliminate
- VdAf
dQ = h*w "y,ft(Tft,m
T,,;
yields
(H.14)
t
- nw,ft The total
heat
flow
from
the
tube
dQ =
to the
refrigerant
is
given
by (H.15)
hr(Tt - Tr)dAr
t
Using
Eqs.
H.14 and H.15. to eliminate
Tt yields
(H.16)
M.5
Derivation Equations
ship
between
known as the
of the
Coil
Characteristic
H.16 and H.11 are next [ha,m coil
- hft
,]
characteristic,
and [Tft
and Total combined
m - T,].
s,'and
is
Heat Flow Equation
to arrive at a relationThis relationship is
given
here
by
(H.17) .
where
hd in Eq. H.11 has been replaced
by
hw/cpm.
152 Assuming
that
dAft dA=K-r
Aft r .
and using
the
relationship
C
h*
W
= h,(l + c fat
hfg)
,
pm
Eq. H.17 can be written
s
= Tft,m h a, m
At this
point,
we have a local
one cross-sectional gives
the
change
element
relation
in energy
content
i,
is
the
in Tft
air
local
of the
air
= -h,(h,,,
the mass flow
Equations equation
a,03
relationship
in the
between
r;ladh
where
as
flow
stream,
,
can then
from T,,,
Eq. H.17 and H.18 to solve for Tft 3m (x0) follows, Ta,03 ('0) is given.
after
flow
and the
is,
(H.19)
to give
be integrated
to Tft for
heat
H.19
,)dAft
th& exit of the heat exchanger ft,m at '0' evaluated, Eq. H.17 can be used to evaluate equation
Equation
of air.
T
transfer
that
H.18 and H.19 can be combined m which
ha,m and Tr at
direction.
cross-sectional
- hft
rate
between
T,,: which
coil. h
m can alsoaLe (x0). the
a differential
to solve
for
With co (x ).
Tft m (x0) A sinsible
wrytten
The derivation derivation
of the
the
value
of
heat
and used with of the
solution
solution
for
153
H.6
Derivation T ft,m ('0) First,
of the
Eq. H.18
dT
For a direct
Solution
is written
saturation
ventional
line
=
r
=
of T ft
since
is
and Wiley
calculations second
conditions if
instead,
are broken section hft
,
first
m is
Surface
form,
Temperature,
i.e.,
(H-20)
- dhft,m)
(H.21)
to - dhft,,)
m and T,,
m (between
chart)'is
into
related
ft,m
a* + b*Tft
is only
,
h and T on
required.
The con-
m
valid
has typically two sections of This
to Tf,
,
[H.3]) air
and "b"
sectionalization
,
small
where flow
derived
m by a quadratic
= a t bTft
a very
been recommended in the
"a"
(H.22)
within
and Glicksman
section.
m + CT& m ,
range
(see the
coil
direction from
and
the
exit
can be avoided expression,
i.e.,
(H.23)
of Eq. H.23 yields
dh ?
=
and Hiller
h
Differentiation
ft,m
uses new values
of the
Effective
that
solution
[H.2]
a,
hft
relationship
m, a sequential
McElgih the
this
s (dh
psychromet;ic
h
However,
S(dha,co
between
of the
assumption
Exit
dT, = 0, and Eq. H.20 becomes
ft,m
a relationship
the
in differential
coil,
dT
the
-dT
ft,m
expansion
Next,
for
ft,m
= dT
ft , mtb + 2CTft,m)
(H.24)
154 Using
Eq. H.24,
Eq. H.21 becomes . dT
Solving
=
ft,m
Eq. H.25 for
dh
a,
s [dh
H.19 is
replaced
by [Tft
,
now solved
for
m - TJ/s,
i.e.,
dh
Equating
Eqs.
where
9
m , )I
(H.25)
* 1 *
=-
,
+ b + 2cTft
,+-
dh a,oo and the
m) 9
term
[ha,m
(~26)
- hft , m1 is
-hd Oft m - Tr) dAft fi
(H.27)
S
a
H.26 and H.27 yields
(-+-I S Collecting
a,O"
o. - dTf m(b + 2cTft
o. yields,
dha,m = dTft
Equation
a,
like
b + 2cT ft,m)dTft,m
terms
on each side
= .$s a of
(Tft2;
the equation
-Tr)dAft
(~.28)
yields
u = 1 + bs and v = 2cs.
Integration are
the
of Eq. H.29 from
beginning
Tft
m (xi)
and end of the:wet
coil
to Tft
m (x ), where x. and x 1 0 0 regi& in the air flow direction,
yields
I
(u + vTr) Rn[Tf, , m(~) - T,l +
v(Tft
,
,(x)
- Tr)
I
T T
ft,mcxo)
= -hclAft
Fmoist ma
ft,mO(i) (H.30)
*
155
where
Fmoist
is
the
value
of Tft
m (xi)
fraction is
of the
calculated
coil
from
depth
that
is wetted.
Eq. H.18 and Fmoist
The
is
known from
v
the
of the
calculat!on
point
at which
dehumidification
first
occurs
L
I
(described T ft
in Appendix
m (x0).
of the
Rearrangement
equation
(u + vi,)
for
Ln[Tft,m(xo)
Eq. H.31 Tft the
is
the
transfer
term
knowns on one side
TJ
hdAft
-
(H.31)
Fmoist
6 a
it
must be solved
Eq. H.18 is
to calculate
flow
from
the
iteratively
h
air
used in conjunction
o3 (x ).
toaihe
With
h
rzfrigerant
a3 (x0) zin
be
the
the
ratio
with,
the dry
air
air
coil
heat
bulb
of
The solution bulb
transfer for
exit
either the
on,
do not rates
in
the
used in
the
and is preceding
air
total term
for
are not temperature
to obtain
Heat Pump Model derived
in
equations
the
region
ratio bulb
required
is
heat
a separation
the wet coil dry
(H.32)
region.
provide
and humidity is
the
second
in the wet coil
coil
temperature
and dependent
point
represents
and the
temperature
solution
dry
of Eq. H.31
section
to this
dry
at the
side
and latent)
equations
information. exit
right
(sensible
An additional
or humidity
on the
and latent exit
1 + inaCha,m(xi) - ha,,‘Xo’ 1
- T,,,(xI)
in
transfer
sensible
and thus
sistent
heat
(sensible)
the
of the
-
equation
has been evaluated,
~,[T,,,(n)
However,
extra
- T,l + v[Tft , m(xi)
routines
total
first
heat
known.
all
from
a=
of
in Eq. H.30 is
Trl + vDf t m(Xo) - Trl = ,
a transcendental
m (x0)
the
computed
total
unknown
of Eq. H.30 to collect
-
psy&rometric
evaluated,
where
only
m (x0)-
Onte Tft with
the
gives
(U + vTr) ln[Tft,m(xi)
Since
Therefore,
I).
is
a manner
this in terms con-
as follows.
'
156
H.7
Derivation T a,* ('0)
of the Solution
The sensible
heat
at a cross-section
for
transfer
in the
the
from
air
flow
Exit
the
Air
air
Dry Bulb
to the
direction
Temperature,
fin-and-tube
can be written
surface
as
dQ, = hwnw , ftcTa,m - Tt)dAft or,
alternatively,
using
Eq. H.7,
(H.33)
as
do, = $,$Ta,m - Tft ,,)dAft Equations
H.33 and H.34 contain
efficiency
for
transfer.
It
sensible
efficiency
for
for
total
transfer.
heat
slightly
to the
total
numerical
heat analysis
the
is
the
transfer
sensible
is heat
as well
local
sensible
heat
[H.9]
slightly
for
transfer to avoid
heat
the wet than
that
H.33 and H.34 rate
effect
total
that
lower Eqs.
this
and here
the wet fin
same as that
results,
However,
rate.
that
and Turner
[H.5]
in proportion
is the
ignored necessity
in of a
solution. change
the
in sensible
energy
macpdT
the
heat
assumption
Based on their
transfer
By equating to the
sensible
overestimate
McQuiston's
transfer
has been shown by O'Brien
fin will
heat
the
(H.34)
basic
governing
a,
equation
content
o3 = -h,(T,
for
the
,
gain
at the
of the
o. - T
air
a,
a,
=
-h,(T
a,
cQ- Tft
m ,)
stream,
sensible
surface
i.e.,
(H.35)
ft,mjdAft
transfer
When transforming Eq. H.35 into a integrable form, . . eliminate the term "dAftI' from Eq. H.35, i.e.,
macpdT
fin-and-tube
rate
is
obtained.
Eq. H.29 is used to
(~.36)
157
Cancellation
of terms
dTa,coz
Since
Tr is
yields
(Ta,m - Tft,m) - T (T ft,m r)
('
+ VTft,m)
Eq. H.37 can be rewritten
a constant,
dTft,m
(H.37)
in terms
of
(T - Tr)'s
to give
d(T, , a3- Tr) d(T
ft,m
-T
r
(Tap2 - Tr) Cu + v(Tft ,m - Tr) + vTrl )
T
-
ft,m
-T
r
-[u + v(Tft ,m - Tr) + vTrl Equation
H.38
is of the
=
(H.38)
form
+j$ + YPW = Q(z)
(H.39)
where '
-
Tft , meTr
p(z) -
‘(U + VTr + vz)/z
Q(z) -
‘(U + VTr + vz)
The solution
to Eq. H.39 can be written
yefdz
=pefdzdz
as:
t constant
(H.40)
158 Evaluating
the
innermost
1
Pdz
=
-
integral,
(u + vTr + vz)dz 1
1 Pdz =
- [(u
-
, and
2 + vTr)ln(z)+vt]
(H.41)
Then
z- (u + vT,),vz
Next,
the
outer
integral
(H.42)
becomes
(H.43) ./
1J Qe
PdZdz = -
J
(w + vz)z-'
eBVZ dz
(H.44)
159
Substitution the
of Eq. H.45
into
Eq. H.44 yields
an integrable
form,
with
result
f Qe
f
Pdz
(
"z(3'w) 3-w
wz(w
v
2-w
V2
2!
(
V3
3-r
Equation
i
H.46 can be written
+
wz(3'w) 3-w
wz(4-w) 4-w
+
1
+
vz(4-w) 4-w
+
vz(w 5 -w
>
-
+
(~.46)
--a
)
in summation
form
as
(H.47) i=l where the
'In"
series
is
the
number of terms which
expansion
solution.
gives
Substituting
acceptable
convergence
of
Eq. H.47 and H.42 into
Eq.
H.40 gives
y(z-’ eevz) =
t
,,C(i+U - WI (i
+ 1) -w)
+ C
(H.48)
i=l Equation
H.48 can be written
YF#)
in shorthand
= F&z) + C
form
as
(H.49)
160 The known conditions used to evaluate
at the the
beginning
constant
F1(zi)
in Eq. H.49 yields
z and y back to their
Ta,co(Xo)- Tr = fd
1
ft,m
0
the
exTiaairoW
Wa,,(xo)
=
The sensible the
coil,
values
is
a,m pa,&,,
heat
calculated
m , are obtained
(H.50)
for
exit
'.
conditions,
(H.51)
- F2(zi)l
yields
-Trl
+ *
- ‘r) - ‘2(‘Ft , m(x i ) from from
Eq. H.52,
the
-T,)>
(H.52)
humidity
ratio
' L?
of
the equation
+ 0.444*Ta,,.Jx
rate
4, and the rate
from
Eqs. H.54 and H.55,
and Wa,-
the
F2 CTft,m('o)
- cpTa ,(xo)]/[1061.2 , transfer
of TW a,m (x0)
Fl(Zi)
. i
representations
) - Tr'
(x ) has been evaluated
Once T
Yi
are
i.e.,
the solution
original
CT,, (Xi) - ‘,I ‘1(‘ft,m(~i’
region
- F2(zi)
(‘0) ’ y.=,&--r [FP Expanding
dehumidification
C in Eq. H.49,
c = yi
Use of Eq. H.50
of the
of water using
0
,]
(H.53)
condensation the
on
computed
(x0):
4
(H.54)
and
y
-5 ri
W
=1;1 a [wa,co'xi)
- wa,co(xo3
(H.55)
2
161
The calculations
.
heat
pump model
in a two-phase refrigerant of the
only
transfer References
for the
H.2
air
rates
and exit
air
for
Appendix
H
Engineering,
in
this
region
of
a fraction
in a two-phase
W. Goodman,
H.l
the
If
state.
vapor, coil
described
flow
the
coil
of the
rate
ia
for
state,
appendix
where
coil
the
use in in
the
the
of Air with p. 225-274.
and L. R. Glicksman,
No. 24525-96, of Technology
heat
Ref'igemrting Surface
Areas
Piping,
Improving Heat Pwnp Performance
- AnuZysis and Test, Laboratory, Massachusetts
Control
Heat Transfer (1976).
fraction
region.
"Calculation of Coil McElgin and D. C. Wiley, Air Cooling and Dehumidification," Heating, March, 1940, pp. 195-201. and Air Conditioning, C. C. Hiller
is
of the
Coils,"
J.
via Compressor Capacity
, the
calculati%
two-phase
the
superheated
by f
for
H.3
in
refrigerant
contains
is multiplied
conditions
"Dehumidification October, 1936,
are performed
Report
Institute
. l
L F
H.4
J.
H.5
F. C. McQuiston, "Fin Efficiency Transfer," ASHRAETransactions,
H.6
F. C. McQuiston
L. Threlkeld, Thermal Environmental Engineering, Hall, Inc., Englewood Cliffs, New Jersey, 1970.
and
and Air Conditioning
J.
Prentice-
with Combined Heat and Mass Vol. 81, Pt. 1, 1975.
Heating, Ventilating, and Design, Wiley, New York,
D. Parker,
Analysis
1977. H
f
l
7
of Dehumidification on the Air Side R. J. Myers, "The Effect Heat Transfer Coefficient for a Finned Tube Coil," Master's Thesis, University of Minnesota, 1967.
H.8
A. H. Elmahdy and R. C. Biggs, "Performance Simulation of Multi-Row Dry (and/or Wet) Heat Exchangers", Sixth IntemationaZ Heat Tpansfep Conference, Toronto, Aug 7-11, 1978, pp. 327332.
H.9
N. G. O'Brien and R. L. Turner, "Fin Simultaneous Heat and Mass Transfer," 1965, pp. 546-548.
Thermal
Efficiency
AICHE Joumal.,
During May
163
Appendix
I - Description
of the
The calculational the in
evaporator this
Appendix
(as shown in
The solutions
appendix. surface
respectively,
at H form
Algorithm
scheme used in the moisture
routine
fin-and-tube
Dehumidification
for
temperature
the the
trailing basis
Fig.
6.4
and air'dry edge of the
for
of the
m (x0)
Tft
the
removal text)
is
of
described
and Ta,,(xo)
bulb
(the
mean
temperature,
evaporator)
calculational
section
derived
procedure
in
discussed
here. A flow
1.1.
diagram
The algorithm
dehumidification exit
of the dehumidification is
would
air
temperature
calculated
assuming
occurs,
is
Taid
used only occur
T
compared
the
at the
a,m,senS only sensible
then
if
algorithm
(x0)
air
is
temperature,
fin-tube
surface
from
two-phase
Taid, is this
evaporator
inlet
air
is greater than Taid, moisture If Taie aie' the leading edge of the coil and the fraction
removal
than
region
If
T
at which
greater
transfer.
heat
to the
the
shown in Fig.
that
coil
is
condition temperature,
does not
of the
the
depth
occur
on
which
1
has only
*-
sensible
heat
transfer,
FSenS,
is
computed
-
TrJ] 'NtU,tp
from
the
equation
c w
F
sens
= en [ (Taie - T,)(T,,,
(1.1)
I
Equation Cmin'C max
I.1
is obtained
from
the
standard
effectiveness
equation
for
= 0, i.e.,
%
= 1 - e -N tu,tP
(1.2)
by using
T E=
T
ai,e aie
-T -T
aid r
0.3)
164 ORNL-DWG
81-4746~
Qa
t1
COMPUTE
Cfac (01,
7/w,ft
5 K%~/,
f+(O),
s(q)
CALCULATE
s(O)
ESTIMATE
Tft ,(x0),
COMPUTE
pyo AND
I
SET
L IEIRkJCH = 0
, 4
,
I
FMOIST
ha,a, (x0),
k;
= Sd
>
COMPUTE COEFFICIENTS FOR i, FIT -a +b Tft m+c T2 hf+,m , ft,m I , \ SOLVE FOR 7 c
Tft,m “J ITERATIVELY
I
NO
COMPUTE
hft ,Cx,‘,
I
ho ,(x,J
T~,oD(xb)~Wa,oD(:o),ct~~(~ol,
I
Fig.
I.1
Block
Diagram
of the
Dehumidification
Algorithm
4
165 The value
and rep1aci w NtU tp by Fsens N,,, tp. 1
at the
temperature,
Tf,
equal
dew'point
to the
i,
transition
point
temperature
of the
from
of the dry
entering
effective
surface
to wet coil,
air,
xi,
is
i.e.,
I
T ft,m('i)
-3.3
Values is
for
Cfa,(xi),
defined
r~,~~(x~),
by the
equation
(1.4)
= Tdp 9a , in
S(Xi)
and
are computed
next.
Cfac(X)
[I.11
wa,b) - Wft,b4 'faccx)
It
follows
Wa.,(xi)
from
Eq. I.4
= Wftam(xi)
appropriate
that
and,
to-use
is just
replace
h at xi,
the
because
of an increase
occur
in the where
predicted place
from
characteristic
from
Eq. H.5 that
transfer
coefficient.
was predicted Thus,
s(xi). W
Note that
It
is is
hw at xi Were
not since
into
temperature
the
Cfac(xi)
coil
due to the
A situation the
dry,
hw used to
further
effectiveness since
coil
when h was used,
h is used at
of fin
the
= 0.0.
shift
heat
calculation h*
would
surface
removal
of
point.
effective
when Fz~ was used.
coil
at this point
l
coefficient
in the
air-side
of kw in the
part
Cfac(xi)
transfer
beginning
(1.5)
' ft,JXJ
first
Eq. 1.5,
transition
moisture
- T
(x)
when the
the wet heat
dehumidification
increase
= T ' a,-
could
but
not
transition
point
nw ft(xi)
and the
='0,
it
in
follows
Therefore,
= h
W’
T.q,ftcXi)
= ~d,ft(Xi)
(1.6)
and
s (Xi)
at the
transition
point.
=
Sd
(1.7)
166 One feature
of this
procedure
needs to be explained
before
proI
ceeding
to discuss In the
edge e
in Appendix
the
case where
derivation
H, the
of the
integrations
dehumidification
solutions over
for
the
occurs Tft
coil
at the
m (x0)
depth,
leading d
and Ta,,(xo)
represented
by the .v-
variable (and is
"x",
were carried
from
Eq. H.16,
handled
by using
region
of
and exit f(xO)
h*w,
average
integration.
entrance
Returning
conditions
to Fig.
occurs
values
the 1.1,
on the
leading
values
entering
air.
iteratively
using
evaluated
at leading
(at
the
by f(O),
the entrance
f(xi),
and to calculate
is greater
the
and local
Tale,
In this
dehumidifi-
case,
the
m(O) is below the dew point The vilue of Tft m(O) must be found equation'from
edge conditions,
Appendix
l-l * *
i.e.,
1
a, m(O) - hft ,m(O) = nw, ,+$
than
T ft
characteristic
- Tr
simplified
parimeters
edge of the coil.
of the
which
assumption
and s over
as denoted
values
when Taid
temperature
h
That
s
more exactly.
surface
ft,nl(O)
of these
average
fin-tube
T
characteristic
was constant.
region)
at the
coil
the coil
&f hw, Jz*~, nw ft,
temperature
the
that
and nw ft)
removal
used to obtain and exit
assuming
Local
of the moisture
are
cation
h,,
out
hw(0)
w f&O)
i~~-~';c,~~tO), ,
Aft
+h c A r pm r
(1.8)
,'
is
s(O) = sw(o>
(I.9
For the
first evaluation of Tft m(OL s(O) , a-. and h (0) in Eq. I.8 are not known where f I3 and hfg(0) is given by
hf,(0)
= 1061.2 + 0.444 Tf,
is not known because C fat(O) C is given by Eq. I.5 facto)
, I?)O)
+ h&N
(1.10)
and T ft,m-32 hQ(0)
=
I0
, if Tft,m 1
32
,
if
T
ft,m
< 32
(1.11)
*
167
The initial
evaluation
of Tft
,
m(O) is made assuming
s(o)
Equation
I.9
then
used with
(0)] 7-l. ft m(O) to Tft m
to solve
ini&ial are is
is
value
calculated until
iteration
The value is heat
If
transfer
caused
the
entering the
dry
Cfac(o) an error
smaller is
humidity
air.
the
enthalpy
of the
found
fraction air
dehum idification
ft,mtx) conditions
coil
transition
occurs
at the
for
the
start
of the
The coefficients
are determined
CTft
and an equation
,
m(xi)
h ft,m(~)
- 51,
= 0.24Tft,,(x)
point
point, leading
from
using
T
ft,m('i" relating hft
+ Wf,,,(x)
region
LlC61.2
,
If
of calculations, stopped. coil
or
to wet conand the
= 1 and xi
= 0.
as a function
once the
of
initial
have been obtained.
an estimate m to Tft
by
are evaluated.
,(x)
H) can be estimat;d dehumidification
replaced
FmoiSt,
,(x,),
of hft
has
of the
dry
edge~'fmoist fit
coil
edge of the
is wetted, h
a dry
repeated. is
leading
that
to surface
s(O)]
series
execution
that
quadratic
(as assumed in Appendix at the
depth
one
is
m(O) is
seco;d
at the
from
from
dew point
program
process
freestream
switch
of Tft
This
positive,
above the
transition
at the
The coefficients T
and the
of the
is
[in
end of the
at the
it
the wet coefficient
m(O) has been evaluated
) has'been
the
,(O)
coefficient
calculation
message is printed
and s(O)
tilerance.
from
to zero,
hf,(0),
of Tft
relate
Once an
computed.
difference
to rise
at the
j:
to see if
to a wet coil
positive
is
[to
m(O)a
checked
is equal
and the
Tft
a prescribed
such has occurred,
coefficient is not
ft,m"' in the value
then
temperature
If
for
T
than
ratio
Cfa,(0)
surface
ditions, If
is
coefficient
Once Tft
Tft,m (xi
next
the
positive.
for
routines
found, Cfac(
m(O) has been
of Cfac(0)
to see if
psychrometric
iteratively
the difference
to the
(IJ2)
Sd
the
and a Aew value
repeated
is,
T ft
f&
=
of T
ft rn"o' m and Wft ,,'i.e., , J
+ O*444Tft,m(x)]
(1.13)
168 The saturation Wft
curve
on the
m as a function
by i quadratic derived
of Tft
equation;
from T ft
,
standard m.
This
hiwever,
m(xi)
and Tft
,
Wft,m(x)
-' ASHRAE psychrometric
curve
is most closely
we will
assume that
m(xO) will
be adequate,
=
chart
represents
approximated
a linear
equation
. @. a' + b'Tft,,(x)
(1.14)
-
(1.15)
b" Tft,m(Xj,)
and
b'=
Substitution
[Wft,mo(i)
- Wft,m(Xo)l'CTft
of Eq. I.14
hft,mb)
into
,
Eq. I.13
m('i)
- Tft,m(Xo)l
(1.16)
yields
= a + b Tft,mb)
+ c T:t,mb)
(1.17)
where
Note that
the
a
= 1061.2
b
= 0.24
C
= 0.444
assumption h
ft,mtx)
d
i.e.,
where
a' =W ft,m(xi)
.
a'
+ 1061.2
(1.18) b'
+ 0.444
b'
a'
(1.19) (1.20)
of = a* + b*T
ft,mcx)
(1.21)
169
made in simpler
analyses
implies
1
that
wft,m(x)
(1.22)
= a*
t 4 Once estimates culated, H is
the
of the
coefficients
transcendental
evaluated
solution a.., .,.."~," ^ .
iteratively
until
on T
Tf,
is
to obtain
h ft
a value
The exit the
values
humidity
air
dry
of the
‘a ,m(‘c)) = Values using
averages calculate until
from
new value
and c
b, until
more
convergence
Tr' After
of s(xo)
routines
[s(O)
or sd]
of Eq. H.17,
exit
Ta,,(xo)
s(xO),
b
Ta mu
air,
are
is
used
i.e.,
(X.23)
and
c
is computed and the
and h,,,(xd)
ia,_
next
series
using
solution
are evaluated,
can be calculated
- cpa -&,ho)l/Wj~.2
the
surface
computed
are then
from
the
a rearrange-
exit
computed
for
conditions is
obtained
of Cfac(xo) ,(x0).
on T is
If
hft(x,),
and air
T-I, ft(xo),
condition:.
hW and ?z; from which from
nW ft
ave and aie
This
iteration
a positive
value
used to continues
co(xO).
checakid
Cfac(xO)
coil.
and
Arithmetic
of s ave and s(xdi the
(L24)
+ 0.444 Ta,Jxo)l
Cfac(~o)9
The new estimates
new exit
a,
psychrometric
temperature,
for
on T
a,
are repeated
a form
can be calculated
convergence
iteration
co(xo)
bulb
ba,,(xo)
The value '1 -_
This
i.e.,
Save are obtained. t
in Appendix
ig obtained.
coefficients
and an estimate
a,
of T
ratio
derived
= Uft,m(xO) - T,l/s(xo) + hft,m(xo)
ment of Eq. 1.13,
s(xO)
m(xO)
ft lnW~ in Appendix H.
derived
m(~o)
has been evaluated,/the +or h
ha/&)
-*i
and c have been cal-
achieved.
m(~o)
used to obtai;
Tft
m(xo)
T
ft ,I& xo) Once T ft
b,
for *_",
is used to evaluate thk ft ,JXo) accurately, upon which the calculations for
a,
is
for
equal
to zero,
the
following value
of
the
I
170 J?.Jxd)
is
solution
set of T ft
bega"ns near from
equal
m(~O)m
the
and latent
two-phase
Appendix
edge of the
could
Upon completion region
iterations
Such a situation
the'trailing
h to k,(x,)
sensible
to h and the
-
cause of the
heat
might coil
where
the wet region calculation
transfer
of the
repeated
rates
evaporator
starting
occur the
if
of the exit and the water are computed
dehumidification
discrete
to revert
at the jump
to a dry air
surface.
conditions, removal
as described
the
rate
in in
Ma
References “for Appendix I 6.1
F. C. McQuiston, "'Fin Efficiency Transfer," ASHRAETransactions,
with Combined Heat and Mass Vol. 81, Pt. 1, 1975.
171 J - Ratios of Geometric Calculations
Appendix
*
The correlations
. -4
for
make use of ratios The need for repeated are
of air-
calculated;
This
manipulations
section
and they
A
-
NT
-
transfer
coefficients
geometric
parameters.
discussed
is-devoted
elsewhere
to deriving
the
equations
were obtained
and is
how these degrees
The input
data
not
parameters
used are not
by various
of terms,
area,
number of tubes
In the
*= number of equivalent, distance
between
horizontal
D
outer,
or air-side,
D r
inner,
or refrigerant-side,
FP
fin
pitch,
6
fin
thickness,
suff icient
distance
altogether
of algebraic required
for
between
diameter
the
h
height
of the
heat
exchanger
e
length
of the
heat
exchanger
d
depth
geometric
calculated:
of the
heat
number of tubes basic ratios
of tubes,
and condenser
nor explicitly
geometry-related
some basic
evaporator
as input
These remaining
(center-to-center),
of tubes,
there
V
c'ircujts,
(center-to-center),
tubes
diameter
(horizontally),
refrigerant
tubes
However9
N
of ajr-flow
and
to describe are
direction parallel
wT a
c
is
cross-sectional
vertical
are
and heat
the Heat Exchanger
exchanger:
N eLircl.lit
I* c
terms
and cancellation
each heat
drops
Used in
and refrigerant-side
in many instances
straightforward,
*
pressure
and use of these
here.
Parameters
parameters
parameters (see
Fig.
completely,
that
are not
required
J.1)
exchanger in
a row (vertically) are not
can be computed
computed by careful
because
all
use of the
of the given
172
h
--_ I w I J-1 I
I I I
Fig.
J.l
Sample Tube-and-Fin
Heat Exchanger
173
input
The following
parameters.
geometric
ratios
N,
number of fins
=
used in the
equations Design
N,=R
N tot
total
=
are
used to compute
Model.
(J+U
Fp
number of refrigerant N tot
the
tubes =
NvNT
d
=
h
= NV s,
(J-2)
NT!!,
(J-3)
CJ.4)
(J-5)
V
hx
volume
=
V
hx
A
side =
A,
of heat
exchanger
=
=
lhd
~(NVST)(NTWT)
the area of each side
Aside
=
=
fin
of each fin
Ntot~Da2 = N
hd-
NtotRSTW,
(5.6)
is
TID '
totSTWT - NtotT-
4 heat
=
transfer
area, (J-7)
Af
=
2NfAside
=
21FFpNtot
.
174 A
=
contact
contact
area
A
A a
=
total
heat
A a
area
A
,where l
exposed be written using
is
=
contact
air-side
Atubes =
between
transfer
of exposed
=N
the
=
XFpNtOtnDa6
(5.8)
area
tubes
tube
surfaces
totnDa
length
and tubes
NN f totnDaS
=A,+A
tu'bes
fins
' exposed
of each tube
not
' covered
by fins,
which
can
Eq. J.l:
&
= 1 - Nfcs = L(1
exposed
- Fp6)
(J 09)
rrD ' A a
A r
=
= 2Ntot~Fp~S,W,
refrigerant-side
- -+I
heat
A r
A free-flow
=
free-flow
A
free-flow
frontal
+
NtotD~aR(l
transfer
=
NtotRIID
P
(J.10)
area
r
area
= A - A*tUbes
- F 6)
-A*,
(J.11)
175 where
A”
and using
total
=
tubes
obstructing
air
flow
NvDa 'exposed
free-flow
The ratios
that
=
NvD, le(l
Eqs.
=
area
Nfh6
l(NVST)
=
RNV[S, - D,(l
=
lNV(S,
fin
J.l,
-
=
=
are needed
c,
Substituting
=
cross-sectional
A*f A
=
tubes
of tubes
Eq. J-9
A"
PIQ,
' area
= "projected
AXtubes
of the
fins
obstructing
NVD,R(l
- Fps) - R(NVS,)Fp6
- Fp6) - STFpS]
-- Da)(l
(3.72)
- FpS)
by the heat
pump model
=
A
contact
and 5.8
2RF Ntot(STWT -4 =
are: Af
area
lIDa Cf
air-flow
RFp"(NVST)
heat transfer contact area
5.7,
- FpS)
rrD 6 RF N p tot a
)
=
m,w,
l-IDa2 - -q-1 __riDas
(5.13)
176
a
Substituting
a
= total air-side volume of heat
Eq. J.6
a
a
and J.10: llDaL (S,W, ---q-)
2NtotLF
=
A a = V hx
area exchanger
+
NtotKDal(l
- F 6)
=
Ntot%WT
2F (S,W, -+
)
+
r~D,(l
-F
6) (5.14)
%Jm
a
= refrigerant-side volume
r
of
heat transfer heat exchanger
area
c b
Substituting
Eq. J.6
and J.11: f
a
N toPD N,,pTw;
=
nDr s,w,
= fin heat transfer area total air-side heat transfer
F a Substituting
r
=
5.7
(5.15)
area
and J.10:
lIDa 2&F Ntot(S,W, F a
= 2LN totFp(S,W,
-4
)
Trn 2 - "T ) + N&D
(J.16) a
J
(1 - F a) P
6
177
u
Substituting
I free-flow frontal frontal area
a
u
=
a
+,(S,
7r
Eqs.
( NVNT) ((q) 0
=
rrDr
GaAaa
(5.18)
area
A +zGA a 5.2, flDr
5.5,
(3.19)
N#nDr =
refrigerant-side heat transfer mass flow rate of air
Substituting
transfer ci,rcuits
llDrL N tot Ncircuits
N circuits
0
- F 6)
ST
=
A (NAN,) G
=
A
(ST - Da)(l
=
and then Eqs. 5.2 and 5.5:
A r =N circuits
A
Q
- F 6)
(5.17)
= refrigerant-side heat number of parallel
Eq. J.11
Arh
=
a
R(NvsT)
Substituting
0
Afree-flow A
=
- Da)(l
A rh
A
and 5.12:
Eq. 5.4
u
area
(5.20)
'TNcircuits
area
A r a free-flow J.11,
and 5.17
(5.21)
into
5.21:
178
A min
=
total total
air-side heat transfer area free-flow frontal area A A
min
=
A
a
(5.22)
free-flow
Note that
Aa = ($)A, r
and then
A
min
=
=
'2"ArhNcircuits' r
substituting
'aArhNcircuits LXrAo
a
Eq. J.. 17 into
5.22:
179
AVAILABILITYAND DISTRIBUTIONOF
APPENDIX K:
THE HEAT PUMP MODEL
4
\ The ORNL Heat Pump Model heat
pump research
form
of six
(1)
is
available
It
development.
files
on a nine
FORTRAN source
track
to organizations
is customarily
magnetic
of the model
set
tape
performing
distributed which
up for
in
consist
batch
the
of:
processing
on a
computer,
(2)
sample
input
(3)
FORTRAN source evaporating
data
for
the
of a program
temperatures
I
4 I
I
compressor
(4)
sample
input
(5)
FORTRAN source batch
the
a fuction
in Section
the map fitting
version
program
that
of the
(some of these
addition
in file
1 and others
FORTRAN source set
up a file
for of
1 that
have the
an interactive input
data
for
program
to use the 4.3),
in file
Heat Pump Model
program
in file
and
3,
can be used to convert
to an interactive to those
(this
required
described
subroutines
of condensing
map data
coefficients
model
for
for
processing
subroutines
(6)
data
to fit
to compressor
can be used to generate map-based
Heat Pump Model,
subroutines
1 are
in
are used to replace
same name),
program the
in file
the
batch
that version
and can be used to of the
Heat
Pump Model. These files the
FORTRAN source The tapes
e
are
listed
in Append ices
L-Q (with
files).
are written
on an IBM computer
and:
cross-references
of
180
o
can be at
800, 1600,
e
can be in
ASCI,I or EBCDIC,and
e
can have either
After
a tape
Model
(file
on the
tape
The printed from
these they
logical
It
compressor
are executed
using
of the
who wish contain
is
not
recipient
of the
programs
The interactive into
seven
compressor to fit
on the
shown in Table
input
user
is
screen
for
value.
Data
giving
the
e save the
data
for
save the
data
so that
to override
computer
can vary related
for
indoor
the
returned.
features.
in files
The
one computer will is
be different. left
5 and 6 is
related
changed
to each
exchanger)
by first the
version
can be read
by the
default and get
data
designed
an item which Once the
he can: of the model, interactive
values,
output
:
pages are
specifying
results
batch
(e.g.,
and is
of these
I( B
organized
information
number and new value.
the
the
output
need to be aware
and it
heat
with
Heat Pump Model
terminal.
is
subroutines
Examples
item
use with
or replace
tape
are
2 and 4).
on a page is assigned
satisfied
it
3) that
himself.
programs
is
Heat Pump
and the
from
differences
entry
and is
o execute
I/O
the
tape
programs
Each page contains
Each data
on and then
the
(ffle (files
dependent
of a CRT terminal.
K-1.
data
when the
interactive
the
has made changes
l
generated
these
for
parameters
number and a default page it
that
to do this
pages of data. data,
appropriate
and output
to identify
of the
program
the
and installation input
fiies. copies
map fitting
and some of the
difficult
and the
are enclosed
to use the
used for
to another
job
runs
system
or non-labeled
is rewound
1) and the
units
system
it
two computer
People that
labeled
is written
listing
6250 BPI,
or
listed
model
and/or on the
i
I !
181 The user 0 C
needs to be aware that
(e.g.,
map-based
control
device)
when he selects
or loss-and-efficiency the
The programs
last
that
provided
as a convenience
formally
documented
to be understandable.
compressor
one chosen
is what will
are distributed to the
although
there
from
with
users
model,
type
of flow
be used.
the Heat Pump Model
of the model.
should
two or more alternatives
be sufficient
are
They are not comments
in them
4
P .
t
183 Table K.l
I
Sample Pages of Input Data for Interactive of Heat Pwnp Model
Version
c I
. I
PAGEO-1: COMPRESSOR DATA (EFFICIENCY & GEOMETRY: 1. DISPLACEMENT (CU IN) 4.520 2. CLEARANCE-VOLUME RATIO .060 14OTOR: 3. SPEED(RPM) -. 3450. 4. OUTPUTAT FULL LOAD (KW) 2.149 EFFICIENCIES: 5. MAXIMUMMOTOR .820 6. ISENTROPIC .700 7. MECHANICAL .800
LOSSMODEL) LOSSES: 8. HEATREJECTIONRATE FROM COMPRESSOR SHELL (BTU/HR) 0.0 OR POWER 9. FRACTIONOF COMPRESSOR REJECTEDFROMTHE SHELL -350 HEATTRANSFERRATE FROMHIGH SIDE TO LOWSIDE (BTU/HR) 300.0 OR 11. FRACTIONOF COMPRESSOR POWER TRANSFERED FROMHIGH SIDE TO LOWSIDE .ooo 10.
NOTES: 1. ITEM 8 OR 9 IS SPECIFIED, NOTBOTH 2. ITEM 10 OR 11 IS SPECIFIED, NOTBOTH 3. IF ITEM 4 IS SET TO 0, THE NECESSARY OUTPUTAT FULL LOADWILL BE CALCULATED AND ITEM 3 IS THE ACTUALMOTORSPEED 4. IF ITEM 4 IS NOT 0, ITEM 3 IS THE SYNCHRONOUS MOTORSPEEDAND THE ACTUALSPEEDIS CALCULATED TYPE "RETURN"TO CONTINUE
PAGE#2: COMPRESSOR DATA (MAP-BASEDMODEL) GEOMETRY: LOSSES: 1. DISPLACEMENT (CU IN) 4.520 6. HEAT REJECTIONRATE FROM 0.0 2. BASEDISPLACEMENT FOR COMPRESSOR SHELL (BTU/HR) 4.520 THEMAP (CU IN) 7. FRACTION':F COMPRESSOR POWER MOTOR: 3. RATEDSPEED(RPM). REJECTED FROM SHELL .350 3450. SUPERHEAT AT SHELL INLET: 4. BASESUPERHEAT FOR MAP (F) 20.00 CURVEFITS FROMCOMPRESSOR MAP (AS FUNCTIONSOF CONDENSING & EVAPORATING TEMPERATURES): 8. .REFRIGERANT&SSFLOWRATE 5. POWERCONSUMPTION -1.509E-04 -2.6753-02 CONDENSING **2 CONDENSING l *2 4.089E-02 4.633E+OO CONDENSING CONDENSING -1.3383-04 4.7033-02 EVAPORATING l *2 EVAPORATING l "2 5.8603-04 9.64OE+OO EVAPORATING EVAPORATING CONDENSING*EVAPORATING 3.6383-04 CONDENSING*EVAPORATING -1.8683-02 1.207E-04 CONSTANT 9.7593-05 CONSTANT 'NOTE: 1. ITEM 6 OR 7 IS SPECIFIED, NOT BOTH TYPE,"RETURN"TO CONTINUE
x.
I.,
(2
. .
.\..,a.
/.
._
.L^
..“”
,
.”
..-.,
. .
”
.._.
PAGE#3: INDOORHEATEXCHANGER GEOMETRY: 3.167 1.. FRONTALAREA (SQ FT) 2. NUMBEROF PARALLELCIRCUITS 3.0 3. NUMBER OF TUBE ROWS 3.0 4. NUMBER OF RETURNBENDS 72.0 FAN - FAN MOTOR: 5. COMBINEDEFFICIENCY .200 INLET AIR: 6. FLOWRATE (CFM) 1200.0 7. TEMPERATURE (F) 70.0 8. RELATIVE HUMIDITY .500
FINS:
TYPE (1 SMOOTH,2 WAVY, OR 3 LOUVERED) PITCH (FINS/INCH) THICKNESS(IN) THERMALCONDUCTIVITY (BTU/HR-FT-F) CONTACTCONDUCTANCE (BTU/HR-FT2-F) TUBES: 14. O.D. (IN) 15. I.D. (IN) 16. VERTICAL SPACING(IN) 17. HORIZONTALSPACING(IN)
2. 14.0 .00636 128.0 30000. .400 -336
1.ooo 0.875
TYPE "RETURN"TO CONTINUE
OUTDOOR HEAT EXCHANGER PAGEf4: GEOMETRY; 1. FRONTALAREA (SQ FT) 5.040 2. NUMBEROF PARALLEL-CIRCUITS 4.0 3. NUMBEROF TUBEROWS 4. NUMBER OF RETURNBENDS 62:: FAN - FAN MOTOR: 5. COMBINED EFFICIENCY .160 INLET AIR: / 6. FLOWRATE (CFM) 2300.0 7. TEMPERATURE (F) 47.0 8. RELATIVE HUMIDITY .700
FINS: 9. TYPE (1 SMOOTH,2 WAVY, OR 3 LOUVERED) lo. PITCH‘ (FINS/INCH) 11. THICKNESS(IN) 12. THERMALCONDUCTIVITY (BTu/HR-FT-F) 13. CONTACTCONDUCTANCE (BTU/HR-FT2-F) TUBES: 14. O.D. (IN) 15. I.D. (IN) 16. VERTICAL SPACING(IN) 17. HORIZONTALSPACING(IN)
2. 14.0 .00636 128.0 30000.
NOTES: 1. IF ITEM 85 IS SET TO 0, THE FAN VS STATIC EFFICIENCY CURVEIS USED WITH A 55% EFFICIENT MOTOR TYPE "RETURN"TO CONTINUE
.400 -336 1.000 0.875
Table K.1
(continued)
DEVICE PAGEP5: FLOWCONTROL FIXED CONDENSOR SUBCOOLING IS BEING USED THERMOSTATIC EXPANSIONVALVE: SPECIFIED CONDENSER SUBcooLING:. '5. VALVE CAPACITY RATING (TONS) .ooo 45.00 1. DESIREDSUBCOOLING(F) 0.0 STATIC SUPERHEAT (F) 6. OR 7. RATEDOPERATING CAPILLARYTUBES: o*o SUPERHEAT(F) 0 2. NUMBEROF CAPILLARYTUBES .ooo BLEEDFACTOR 3. CAPILLARYTUBE FLOW . NOZZLE& TUBE PRESSURE ;: 0.000 FACTOR 0 DROP(1 INCLUDE, 0 EXCLUDE) OR SHORT-TUBEORIFICE: .ooooo 4. DIAMETEROF ORIFICE (IN) OR NOTES: 1. CATEGORIESARE MUTUALLYEXCLUSIVE, I.E. SPECIFY 1, OR 2 & 3, OR 4, OR5-9 2. IF CONDENSER SUBCOOLING IS SPECIFIED, THE VALUESOF ITEMS 2-9 THAT WOULDPRODUCE THAT LEVEL OF SUBCOOLING ARE COMPUTED TYPE "RETURN"TO CONTINUE
I
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184
PAGEP6:
CONNECTING REFRIGERANT LINES
GEOMETRY: LIQUID LINE SUCTIONLINE DISCHARGELINE VAPORLINE VAPORLINE
FROM: INDOORHX REVERSINGVALVE COMPRESSOR OUTLET REVERSINGVALVE REVERSINGVALVE
TO: OUTDOOR HX COMPRESSOR INLET REVERSINGVALVE OUTDOOR HX INDOORHX
ID (IN) 1. 0.190 3. 5. 7. 9.
0.000 0.000 0.680 0.556
EQUIVALENT LENGTH(FT) 2. 30.4 4. .6. 8.
10.
RATESOF LOWSIDE HEATGAINS: RATESOF HIGH SIDE HEAT LOSSES: 13. IN SUCTIONLINE (BTU/HR) 11. FROMDISCHARGE LINE (BTU/HR)2000. 200. 12. FROMLIQUID LINE (BTU/HR)
0.0 0.0 6.0 30.4
> +
300.
NOTE: 1. GAIN & LOSSESIN ITEMS 11-13 C!N BE FORVALIDATION RUNSOR TO SIMULATEHIGH TO LOWSIDE HEATEXCHANGERS ANDREVERSINGVALVES TYPE "RETURN"TO CONTINUE
PAGE#7: MISC. DATA 1. TITLE: EFFECTSOF HEAT LOSSESON INLET AIR: 2. HOUSELOADAT OUTDOOR 7. INDOORFAN (SEE NOTEBELOW) 15000. 2 AMBIENT(BTU/HR) 8. OUTDOOR FAN (SEE NOTEBELOW) 10.0 i SUPERHEAT(F) 3. EVAPORATOR 9. COMPRESSOR (SEE NOTEBELOW) 8.0 1 4. DUCTSIZE (IN) ESTIMATESTO BEGIN ITERATIONS: 5. MODEOF OPERATION TEMPERATURE (F) 2 10. EVAPORATING (1 COOLING,2 HEATING) 30.0 11. CONDENSING TEMPERATURE (F) 115.0 6. LEVEL OF OUTPUT(0 SUMMARY, 12. REFRIGERANT MASSFLOW 1 COMPRESSOR, 2 COILS, RATE (LBM/HR) 1 400.0 3 STANDARD) NOTE: 1. HEATLOSSESFROMTHE FANS AND COMPRESSOR CANBE ADDEDTO THE AIRSTREAM EITHER BEFOREOR AFTER‘IT CROSSES THE COIL (SIMULATEBLOW-THROUGH & DRAW-THROUGH FANS) SPECIFY 0 TO NEGLECTTHE HEATLOSS THE COIL 1 TO ADD THE HEAT To THE AIR BEFOREIT CROSSES HEAT To THE AIR AFTER IT CROSSES THE COIL 2 TO ADD'THE TYPE "RETURN"TO CONTINUE
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185 Appendices
L, M, N, 0, P, and Q are
J
8 ;
1 -li
i :
zr
to the
back cover.
.
on microfiche
in an envelope
attached
