Kravvaritis et al., Int J Mech Syst Eng 2015, 1: 102 http://dx.doi.org/10.15344/2455-7412/2015/102
International Journal of Mechanical Systems Engineering
Open Access
Research Article
Solar Energy Management Using Phase Change Materials Passive Systems in the Athens Area Buildings E. D. Kravvaritis, K. A. Antonopoulos, C. Tzivanidis* and E. Bellos
National Technical University of Athens, School of Mechanical Engineering, Thermal Department, Heroon Polytehniou 9, 15773 Zografou, Athens, Greece
Abstract
Publication History:
A numerical procedure is developed for the management of solar energy in buildings using passive systems, which are based on Phase Change Materials (PCM). For the simulation of the phase change process, the concept of effective thermal capacity function is used, which is determined experimentally and then generalized using triangular functions. The developed procedure is applied along the typical year in the Athens area buildings for studying the effect of main PCM parameters, including the phase change temperature range, the phase change heat and the thickness, location and way of embodiment of PCM within buildings elements. It is found that energy savings up to 33% may be obtained along the Athens typical year by placing at the proper building location PCM layers with the right thermal properties. The conclusions of the study may be used, apart from the Athens area, to regions of similar climate and moreover, because of their generality, most of them may be useful to any climatic conditions.
Received: February 18, 2015 Accepted: April 23, 2015 Published: April 25, 2015
Keywords: Phase Change Materials, PCM Passive Systems, Solar Energy Management, Athens Buildings
Nomenclature A B b Cp or C Cp,eff d Ff, Fw GT g H h k L M m N Q q R S T To Tl , Ts Tm, Tr t U v x
Area (m2) Initial temperature field (K or 0C) Temperature width of PCM phase change Thermal capacity (J/kg K) Effective thermal capacity (J/kg K) Part of solar radiation absorbed by indoor air and any other obstable Areas of fenestration and opposite wall, respectively (m2) Incident total solar radiation (W/m2) Radiation heat-transfer factor (W/m2K) Phase change heat (KJ/kg) Convection heat transfer coefficient (W/m2K) Thermal conductivity (W/mK) Normalized Radiation Losses (K or 0C) Quantity defined by Eq.(9) Mass (kg) Quantity defined by Eq. (10) Indoor load (W) Heat flow (W/m2) Absorbed solar radiation by a wall (W/m2) Exterior tube surface (m2) Temperature (K or oC) Equivalent outdoor temperature (K or 0C) Temperatures at the ends of two-phase region (K or 0C) PCM and reference fluid temperatures, respectively (K or 0C) Time (s) Overall heat transfer coefficient of a wall or rood (W/m2K) Volume (m3) Cartesian coordinate (m)
Introduction The intensity of solar radiation may be not “in-phase” with the energy demands in a considerable number of solar energy applications. The resulting shortage-surplus problem, which may be encountered in a seasonal, daily or even hourly level, can be remedied by the various energy storage techniques, applied in the active or passive mode. With reference to building applications, among the numerous storage techniques , a promising one is the use of Phase Change Materials (PCM). These may store considerably greater amounts of Int J Mech Syst Eng ISSN: 2455-7412
Greek symbols α Absorption coefficient for incident solar radiation ρ Density (kg//m3) τ Fenestration transmission coefficient for solar radiation
Subscripts a Refers to air amb Refers to the ambient b Refers to initial condition (t=0) c Refers to the middle of PCM phase change temperature width e Element of buildings envelope f Refers to furniture i Indoor J Number of wall layers j Wall layer k , k+1 Refer to the time step (tk+1 – tk) l Refers to liquid state m Refers to a PCM max Refers to a maximum value o Outdoor p Refers to indoor walls (partitions) r Refers to a reference fluid s Refers to solid state t Refers to tube u Refers to an indoor surface
* Corresponding Author: Dr. Christos Tzivanidis, National Technical University of Athens, School of Mechanical Engineering, Thermal Department, Heroon Polytehniou 9, 15773 Zografou, Athens, Greece; E-mail:
[email protected]
Citation: Kravvaritis ED, Antonopoulos KA, Tzivanidis C, Bellos E (2015) Solar Energy Management Using Phase Change Materials Passive Systems in the Athens Area Buildings. Int J Mech Syst Eng 1: 102. doi: http://dx.doi. org/10.15344/2455-7412/2015/102 Copyright: © 2015 Kravvaritis et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
IJMSE, an open access journal Volume 1. 2015. 102
Citation: Kravvaritis ED, Antonopoulos KA, Tzivanidis C, Bellos E (2015) Solar Energy Management Using Phase Change Materials Passive Systems in the Athens Area Buildings. Int J Mech Syst Eng 1: 102. doi: http://dx.doi.org/10.15344/2455-7412/2015/102 Page 2 of 3
heat than those stored in liquid or solid materials owing to the extra heat absorbed or released during phase change (latent or phase change heat) [1]. For building applications, the properly designed use of PCM, under favourable conditions and right temperature levels may increase up to five times (in case of organic PCM) or even up to ten times (in case of inorganic PCM) storage capacity or decrease storage space accordingly [2]. The optimum building energy management based on the startling developments of technology requires changes in building design, which often lead to objectionable constructions, from the aesthetics and architectural point of view. Here, PCM may offer an excellent solution as they are invisible, hidden within construction elements, from where they may absorb or release considerable amount of heat. Other PCM applications in buildings are related to the non-inphase thermal needs among various building departments, arising from their different use, orientation or construction. Thermal energy released or absorbed from such departments may be used, after storage in PCM, for heating or cooling other parts of the building, thus providing considerable energy savings. Purpose of the present study is the development of a prediction procedure for passive PCM solar applications in buildings and the use of results in solar energy management along the typical year in the Athens area. The solar radiation and ambient temperature values used were obtained by statistical processing of related hourly measurements corresponding to more than 20 years [3-4]. The required thermal properties of PCM employed in our calculations were measured using a developed technique [5], which is an improved version of the wellknown T-history Method [6]. The effect of the main PCM parameters is examined, i.e. phase change temperature range, phase change heat, PCM location, quantity and way of embodiment into construction elements, etc. In all cases the hourly, daily, monthly and yearly energy savings are calculated. Such information was not so far available for the Athens area. Therefore, the engineer has now more data for obtaining the optimum result. The conclusions of the study may be applied to any region with climate similar to that of Athens and, because of their generality, most of them may be useful to any climate. Classifications of inorganic (salt hydrates) and organic (paraffins, microcrystalline waxes, fatty acids, esters, fatty alcohols) PCM together with their advantages and disadvantages may be found in [7,8] among others. Related reviews of PCM applications in buildings, starting from 1920, may be found in [1, 8, 9], among others.
Thermal Behavior Prediction off Buildings Containing PCM General Heat transfer prediction in PCM is considerably more complicated than that in materials remaining in the same phase during the process of interest, for the following reasons: a. Phase change is not a linear problem. b. Mushy zone, in which phase change takes place, does not have distinct boundaries, with the exception of some materials with phase change under practically constant temperature. c. During melting, natural convection may cause detachment and then movement of solid material within the liquid phase, while during solidification, cavities may result within solid phase, owing to volume changes. d. Convection heat transfer may take place within liquid and mushy regions. However, the estimation of convection coefficient is difficult. Int J Mech Syst Eng ISSN: 2455-7412
To overcome the above difficulties, the following main assumptions and approximations are made in the present study, which simplify the simulation procedure considerably: a.
b. c.
Relations for the calculation of convection coefficients have been proposed in some basic or very simple cases, as for example for PCM contained between two parallel plates [10]. However, in the present work convection heat transfer is neglected,as it happens in most related studies [11-12]. PCM properties are accurately known in the solid and liquid phases. For the mushy region various functions have been tested, based on our measurements [5], as described later. Volume change and possible cavity formations are neglected.
Numerical techniques are good tools for heat transfer predictions in buildings with embodied PCM. In the present work the Finite Difference Method has been selected. However, a model for the simulation of phase change is needed. The main models developed for this purpose include: a.
b.
The Enthalpy Method [10], which is based on a numerical solution of the enthalpy transport differential equation. It is suitable for predicting details of the phase change process, as for example is the movement of the solid-liquid interface. The Effective Thermal Capacity Method [11-12], which is the most easily applied, as it follows the usual numerical solution process of the energy transport differential equation, with PCM thermal capacity during phase change being a function of temperature usually called “the effective thermal capacity function Cp,eff (T). The only difficulty of the method is the choice of the proper function Cp,eff (T).
In the thermal behavior analysis of buildings containing PCM, phase change is interesting only as a macroscopic phenomenon, i.e. details like movement of the liquid-solid interface or the spreading of the mushy zone, are not a primary interest. Therefore, in the present study, the effective thermal capacitance model has been selected, as the simplest way for the simulation of phase change in conjunction with the finite-difference method. The Cp,eff(T) functions for the PCM used have been derived as described in the following section. Measurements and estimation of effective thermal capacity function Cp,eff(T) The data needed for deriving simple Cp,eff(T) functions are the PCM phase change heat, H, and the solid and liquid PCM temperatures, Ts and Tl, as well as the corresponding heat capacities Cps and Cpl, respectively, at the ends of PCM two phase region. The following four different Cp,eff(T) functions of simple geometrical shape have been tested: (a) Triangular function The analytical expression for line segment 12 (Figure 1a) may be written [Cp,eff(T) - Cps] / (T - Ts) = (Cpmax- Cps) / (Tc – Ts)
(1)
where Tc = (Tl+Ts)/2 is the temperature at the middle of the PCM phase change temperature width and Cpmax is the value of Cp,eff at T=Tc. The area H/2 below line segment 1 2 may be expressed as: H/2 = (Cpmax + Cps) (Tc - Ts)/2
(2)
IJMSE, an open access journal Volume 1. 2015. 102
Citation: Kravvaritis ED, Antonopoulos KA, Tzivanidis C, Bellos E (2015) Solar Energy Management Using Phase Change Materials Passive Systems in the Athens Area Buildings. Int J Mech Syst Eng 1: 102. doi: http://dx.doi.org/10.15344/2455-7412/2015/102 Page 3 of 3
Substitution of Cpmax from Eq.(2) to Eq.(1) gives the Cp,eff(T) function for Ts ≤T ≤Tc, i.e. Cp,eff(T) = 4(H - bCps)(T - Ts)/b2 + Cps
(3)
where b = Tl – Ts is the temperature width of PCM phase change. The Cp,eff(T) function for Tc T Tl is derived similarly, i.e. : Cp,eff(T) = 4(bCpl- H)(T -Ts - b/2)/b2 + 2H/b - Cpl
(4)
(b) Ramp function The expression for Cp,eff(T) function of a ramp shape (Figure 1b), which is derived in a similar way as above, is Cp,eff(T) = 2 (H - bCps) (T - Ts)/b2 + Cps, Ts ≤T≤Tl
(5) Figure 1.1: Comparison of experimental data (Ref.11, Figure 7b) with numerical solution.
(c) Reversed ramp function Here, the Cp,eff(T) function becomes (Figure 1(c)) Cp,eff(T) = 2(bCpl - H) (T - Ts) / b2 + (2H/b - Cpl), Ts ≤T ≤Tl
Cp,eff(T)=M (Tr,k-Tr,k+1)(Tm,k+Tm,k+1-2Ta)/ (Tm,k-Tm,k+1)(Tr,k+Tr,k+1-2Ta) – N
(6)
where,
(d) Step function
M = (mtrCptr + mrCpr)Stm/ mmStr
Here, it is obvious that (Figure 1d)
N = mtmCptm / mm
Cp,eff(T) = H/b,
Ts ≤T ≤Tl
(7)
(8)
(9) (10)
In the above equations mtm, Cptm and Stm are the mass, heat capacity and exterior surface of the tube containing PCM, while mtr, Cptr and
Figure 1:Effective thermal capacity functionsCp,eff(T) of simple geometrical shape for PCM.
For the experimental derivation of the effective heat capacity function Cp,eff(T) for PCM suitable for passive building applications, measurements have been performed using a developed and constructed measurement arrangement with a corresponding measuring procedure, as described in detail in [5]. The whole system is an improved version of the well-known and widely used T-history method [6]. Briefly, two glass tubes containing liquid PCM and reference fluid, respectively, are cooled within a controlled environment test chamber of constant temperature Ta
