- Email: [email protected]
Computer simulations of heat transfer in a building integrated heat storage unit made of PCM composite
Thermal Science and Engineering Progress 2 (2017) 109–118
Contents lists available at ScienceDirect
Thermal Science and Engineering Progress journal homepage: www.elsevier.com/locate/tsep
Computer simulations of heat transfer in a building integrated heat storage unit made of PCM composite Łukasz Wardziak a, Maciej Jaworski b,⇑ a b
The Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland Warsaw University of Technology, Institute of Heat Engineering, Nowowiejska 21/25, 00-665 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 31 January 2017 Received in revised form 15 May 2017 Accepted 16 May 2017
Keywords: Phase change materials (PCM) Thermal energy storage Thermal performance characteristics Building integrated PCMs
a b s t r a c t The paper presents the results of parametric study of thermal performance characteristics of thermal energy storage unit integrated in building structure being also a part of building’s ventilation system. A storage unit is in the form of a ceiling panel with internal channels through which air taken from the environment flows before it is delivered into the rooms. Thermal storage potential of the panel is thanks to phase change material (PCM) which is mixed with gypsum mortar, creating in this way a composite of high thermal capacity in the temperature range corresponding to the temperature required for thermal comfort. In order to perform the analysis of the storage unit a computer program was developed which was based on the mathematical model of complex heat transfer occurring inside the panel, inside a composite material, as well as on the boundary between the panel and air flowing through internal channels. A procedure describing variations of convective heat transfer intensity along the channel can be regarded as a unique achievement in this research. This function was validated based on measurements conducted on the experimental set-up specially prepared for this study. Using the program many computer simulations were performed. Based on the results of this analysis a detailed information on the performance of the panel for different operational parameters, e.g. air mass flow rates, were obtained. Contrary to the study reported in an earlier publication, these simulations were conducted for real environmental conditions, i.e. real ambient temperatures during summer in Central Poland. Also, important conclusions regarding selection of PCM, mainly its melting temperature range, were formulated. Ó 2017 Published by Elsevier Ltd.
1. Introduction For a long time increasing the heat capacity of buildings was combined with increasing amount of conventional building materials such as stone, bricks and concrete. By increasing wall thickness, both the strength of the building and its thermal capacity was increased. A good example are castles built during the Middle Ages. By increasing walls thickness comfortable coolness in the summer months was obtained. In this case the walls work like natural cold accumulator. During summer months thick walls of these buildings slowly accumulates heat that is then released in winter days. In Medieval period nobody thought about accumulation of thermal energy but even in this time special structures were designed and built for the purpose to accumulate and release a significant amount of heat (cold). Nowadays the construction of buildings requires much less conventional, massive building materials due to the development of ⇑ Corresponding author. E-mail address: [email protected] (M. Jaworski). http://dx.doi.org/10.1016/j.tsep.2017.05.006 2451-9049/Ó 2017 Published by Elsevier Ltd.
lightweight materials and changes in the technology of the construction. Walls thickness is limited to reduce cost of materials. Office buildings are representative and very often exterior walls are covered with glass panes. However, the idea of heat accumulation is up to date. Fortunately to increase thermal capacity of buildings it is not necessary to use a large amount of conventional materials which can accumulate relatively small amount of heat (the ratio of the amount of stored heat to its volume). It is much easier, in terms of the weight of the building structure, to use phase change materials (PCM) incorporated in the building’s envelope in order to increase its thermal inertia. Building sector belongs to the leading ones in energy consumption in the developed countries. Taking the EU as an example, the buildings sector accounts for around 40% of the total final energy consumption and produces nearly 40% of the total CO2 emissions. Most of it is due to the increase in the living standard and in occupants’ comfort demands, mainly for heating and cooling [1]. A great amount of energy can be used for other purposes. In many countries in order to reduce the demand for heat (cool) thermomodernization programs are being implemented. As a result heat
110
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
Nomenclature a dr
q qair cp cp h k
a1 a2 T0
air
thermal diffusivity [m2/s] equivalent diameter [m] density of material [kg/m3] air density [kg/m3] specific heat capacity [J/(kgK)] air specific heat capacity [J/(kgK)] enthalpy [J/kg] thermal conductivity [W/(mK)] heat transfer coefficient on the upper wall [W/(m2K)] heat transfer coefficient in the channel [W/(m2K)] a ceiling panel initial temperature [°C]
losses (or gains during summer) are substantially reduced. Thermo-modernization allows to significantly reduce demand for energy which is used for heating in winter and for cooling in summer. These operations also increase the potential for heat storage in the building structure, due to the reduction of heat transfer through the external walls. In order to efficiently use this potential thermal capacity of the building structure must also be increased. This can be easily obtained by the use of phase change materials, PCMs. The use of PCMs in buildings dates back to 1950s, however the studies on different aspects of this kind of applications intensified in last two decades. The problems related to this topic are discussed and presented in many review papers [1–5], as well as in papers focused on specific issues. In order to achieve the benefits of the use of PCMs in buildings many problems must be solved, starting from the modification of material properties to the development of the methods of incorporation of these materials in the structure of the building. The research in this area is conducted at different scales (micro/macro) and is very wide in terms of issues to be solved. On the micro scale chemical properties of individual compounds like salt hydrates, paraffin, paraffin waxes, eutectics, fatty acids and others are the subject of research. Studies identifies chemical compounds that can be used for energy storage in certain temperature ranges in practice. For example Solé et al. [6] analyzed stability of sugar alcohols as PCM for thermal energy storage. They proved that sugar alcohols as PCMs are very promising due to their high storage capacity, safety and economic reasons. Their phase change temperatures make them suitable for medium temperature storage, which is needed for solar thermal or waste heat recovery applications. Sari et al. [7] came to the conclusion that capric acid (CA)/palmitic acid (PA) mixture with eutectic composition (76.5/23.5 wt.%) was a suitable PCM for low temperature TES applications in terms of melting and freezing temperatures (around 22 °C) and latent heats (about 170 J/g). These properties make this mixture a promising PCM for LHTES systems used in heating, ventilation, and air conditioning applications [7]. Cheng Liu et al. [8] performed a research on the use of lauric-myristic-stearic acid/expanded graphite composite for thermal energy storage. The authors in detail determined wide range of thermal properties of these composites, mainly thermal capacity, thermal conductivity and stability in thousands of cycles. All the results indicated that the proposed LA–MA–SA/EG composite has suitable thermal properties for thermal energy storage applications and heat recovery in buildings. Referring to a macro scale much research has been dedicated to explore different ways of implementing the PCM material in building envelope to increase thermal capacity. Royon et al. [9] conducted research concerning optimization of PCM embedded in a
Tp Tair Tk T1 DTair
temperature of the material at a given point [°C] air temperature in the duct [°C] air temperature in the duct in ‘k’ segment [°C] ambient temperature [°C] temperature difference between inlet and outlet of the ‘k’ segment q heat flux [W/m2] w air speed [m/s] Dx, Dy, Dz dimensions of a control volume [m] mair air mass flow rate [kg/s].
floor panel developed for thermal management of the lightweight envelope of buildings. This component derives from an existing slab having cylindrical cavities which is used in floors/ceilings. The cavities are filled with a polymer–paraffin. The study is based on numerical simulations whose results are compared to experimental ones with the same boundary conditions in order to validate the model. Another method of increasing thermal capacity is proposed by Soares et al. [10]. They proposed incorporating PCM-drywalls in lightweight steel-framed residential buildings. The authors evaluated the impact of PCM-drywalls in the annual and monthly heating and cooling energy savings, considering real-life conditions and several European climates. Energy savings effect is more evident for the warmer climates, where the total energy savings due to PCMs can reach 46% and 62% (Seville and Coimbra). PCM-drywalls are also very attractive for colder climates (Warsaw and Kiruna), with a predominance of the heating energy demand reduction. However, the impact of PCMs in the total energy savings is not so significant for these climates (24% and 10%). Navarro et al. [11] evaluated a concrete core slab with PCMs for cooling purposes. In their study, an innovative technology for cooling application in buildings was evaluated. A prefabricated concrete slab incorporating phase change material (PCM) was used as internal separation in the active slab cubicle. The incorporated PCM was paraffin macro-encapsulated in aluminum tubes. The aim was to use the internal slab as storage unit and as an active cooling supply to replace totally or partially conventional HVAC systems. The experimental campaign showed that the cold discharged was not enough to cover the whole cooling demand of the cubicle. However, significant energy savings in the HVAC system were registered, between 30% and 55% under mild conditions, and between 15% and 20% under severe conditions, compared to the reference cubicle. Research focused on the use of PCM materials for cooling purposes were conducted also by Weinläder et al. [12]. In the Energy Efficiency Center, the new R&D building of the ZAE Bayern, two different PCM cooling ceiling types were installed and monitored in two office rooms. The ceilings were connected to a water circuit and could be used for heating and cooling. The PCM ceilings were prototypes which differ in the positioning of the PCM layer: on top of the ceiling and below the water pipes. It was found that in the second configuration thermal connection between PCM and room is much better. Although passive cooling power of the system under study was rather small as compared to active cooling solutions, efficiency of this system turned out to be quite good – it took about 7–9 h before the highly insulated test rooms reached internal temperature of 27 °C. Solgi et al. [13] presented that PCMs have a great influence on enhancing the performance of night purge ventilation and cooling
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
load reduction of office buildings in hot-arid climate of Yazd (Iran). Investigating PCMs with various melting temperatures they found the one with 27 °C melting point as the best one for those environmental conditions. They found that almost 47% reduction in cooling energy is possible when PCM is used and optimal rate of ventilation is selected. A performance of a collector storage wall system using PCMs was investigated by Zhou et al. [14]. PCM slabs were attached on the gap-side wall surface to increase the heat storage. The test was carried out for a whole day with charging period of 6.5 hours and discharging period of 17.5 h. They analyzed in details daily variations of surface temperature as well as air and indoor temperatures. The indoor temperature was found to be above 22 °C during the whole discharging period under given conditions, which indicates that the indoor thermal comfort could be kept for a long time with the use of the storage system under study. Barzin et al. [15] tested experimentally an application of PCM energy storage in combination with night ventilation for space cooling. Two identical test huts, one with PCM-impregnated gypsum boards, the other with ordinary gypsum board, were compared. They found that substantial electricity saving, up to 73%, can be obtained only when PCM storage is combined with night ventilation. Benefits of the combination of heat storage in buildings structure (in PCMs) with night ventilation was observed in the research done by Ramakrishnan et al. [16] who performed extensive analysis of building’s thermal performance in weather conditions of Melbourne, with extreme heatwave periods. Sajjadian et al. [17] conducted tests on the potential use of PCMs to reduce domestic cooling energy loads for current and future UK climates. The study used simulations of a high performance detached house model with a near Passivhaus Standard in London, where the impact of climate change effect is predicted to be significant. It was shown that appropriate levels of PCM, with a suitable incorporation mechanism into the building construction, has significant advantages for residential buildings in terms of reducing total discomfort hours. 2. The aim of the study The purpose of this paper is to present the results of the study that was focused on different issues related to the thermal performance characteristics of a ceiling panel made of gypsum-PCM composite. This panel is a special form of building integrated ther-
111
mal energy storage unit utilizing phase change material as a storage media. Its specificity consists in the fact that it contains parallel channels for the air flow, and thus it is a part of a building ventilation system. Its role in ventilation system is to cool down the air taken from the environment when it is hot (during the day) and subsequently heat it up, when it is cool (during the night). Efficiency of the absorption of heat and its release depends on the thermal capacity of the panel and heat transfer coefficient between air and the walls of channels. In this part of the research we focused on the modelling of convective heat transfer inside channels, in particular on the modelling of heat transfer coefficient variations along the channel, especially at the reversion part. In the validation of the models earlier experimental results were taken into account [18]. The experience gained in previous works on mathematical modelling of similar heat transfer process [19] were used in this study. Computational tool, based on the numerical model developed, was then used for the parametric study of the performance of the panel in different conditions. In particular the influence of the melting point of PCM on thermal behavior of the panel over a long period of time was examined. It seems that the inaccurate adjustment of the PCM material, i.e. its phase change temperature, with respect to the range of ambient air temperature variations may cause that after some time the PCM temperature will fluctuate only above (or below) the phase transition temperature. That means a continuous decrease in the degree of utilizing PCM’s thermal capacity. 3. The physical model of the heat storage unit A concept of the structure of the ceiling panel – thermal energy storage unit, dimensions of its repetitive element as well as air flow configuration inside channels are shown in Fig. 1. According to the fundamental assumption for this solution, the air taken from the environment for building ventilation first flows through internal channels in the ceiling panel. When the air temperature is higher than upper range of thermal comfort temperature (during the day) it is cooled down flowing through the channel. The material of the ceiling panel contains substantial part of phase change material, of melting point in the middle of thermal comfort range, i.e. about 23 °C. This material absorbs heat from the air, undergoing nearly isothermal phase transition (melting). During the night ambient air temperature is much lower than the lower limit of thermal comfort, and thus also lower than phase change tempera-
Fig. 1. General structure of the ceiling panel and an axonometric view of the repetitive segment of the ceiling panel.
112
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
11.7 kg 0.022 m3
transfer it was assumed that an air duct consists of two channels. The whole ceiling panel consists of several repetitive elements (see Fig. 1), their number depends on the dimensions of the room. The combination of inlets and outlets can be made using special collectors. The composite for the panel was made of gypsum mortar (produced by Knauf) with an addition of PCM, i.e. Micronal DS5008, produced by BASF. PCM content was about 34 wt.%. Thermal properties of the composite were measured using DSC calorimeter [18] and miniature plate apparatus for thermal conductivity [21]. Basic parameters of the panel and the properties of the composite are collected in Table 1.
0.016 m3 1.5 cm
4. Experimental investigation of the ceiling panel
Table 1 Basic information about the structure and properties of material used for manufacturing of the ceiling panel. Material (composite)
Gypsum mortar (Knauf) + Micronal DS5008 (BASF)
Density Thermal conductivity Heat transfer coefficient in the channel Surface area of the internal channel in the ceiling panel Mass of the ceiling panel (one segment) Total volume (material volume + air channel volume) Material volume Wall thickness
720 kg/m3 0.2 W/(mK) See Fig. 9 0.36 m2
ture of PCM. In this phase of operation PCM solidifies releasing heat to the air which is heated up. PCM in the ceiling panel is subject to a daily cycle of melting and solidification, that are charging and discharging processes of it as a storage unit. As can be seen in Fig. 1 the structure and particular dimensions of the panel were chosen so that it could be easily manufactured using typical plasterboards (e.g. SmartBoards containing PCM, produced by BASF [20]). In order to increase surface area for heat
A special experimental set-up, based on the repetitive element of the panel, was built. The main goals of an experimental study were to examine the behavior of the panel in real conditions and as well as gathering data that could be used for validation of computational tools. An experimental set-up consists of a 3 meters long repetitive element of the ceiling panel (Fig. 2), made of the PCM-composite described earlier. It is equipped with additional equipment allowing for the control of the air flow (fans, collectors, anemometer) as well as the control of air temperature (special heat exchanger supplied from thermal bath). More than 30 thermocouples were embedded in the panel and located in the internal channel. They allow for very detailed measurement of temperature variations in the panel and in the air stream. This information was useful in the evaluation of the rates of charging and discharging of the storage unit, through the comparison of temperature level in different parts of the panel with regard to the temperature range of phase change (see also Fig. 3). From the variations of air temperature along the channels and with time such information as amount of energy stored/release in the panel, heat flow during charging and discharging an intensity of heat transfer in the channel could be obtained. The scheme of an experimental set-up is shown in Fig. 2. 5. Mathematical model of the repetitive part of the ceiling panel A mathematical model and associated computational program were developed in order to get the opportunity to perform parametric study of the storage unit for wider range of operational conditions much easier and cheaper as compared to experimental investigations. The following assumptions were adopted for the model:
Fig. 2. An experimental set-up with inlet (1) and outlet (2) depicted.
transient processes for both charging and discharging of the storage unit were analyzed, a real characteristics of enthalpy vs temperature of the PCMcomposite determined with DSC was accounted in the model, this characteristics account for the hysteresis of enthalpy during heating and cooling (Fig. 4),
Fig. 3. The scheme of an experimental set-up; 1 – data acquisition station, 2 – extension cables of TCs, 3 – water–air heat exchanger, 4 – supplier of heat exchanger (thermal bath), 5 – set of fans, 6 – supplier of fans (DC supplier), 7 – rotating vane anemometer.
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
convective heat transfer coefficient in the channel, variable with the distance from the inlet and around the bend was determined and experimentally validated, heat losses for external surfaces of the model (repetitive part of the ceiling) were also validated experimentally. Temperature profiles in the structure of the ceiling panel are described by transient heat conduction equation, which can be written in the form:
q
@h ¼ kr2 T @s
ð1Þ
where enthalpy is, in general, a function of specific heat which is variable with temperature:
Z
T
hðTÞ ¼
cp ðTÞdT
ð2Þ
T0
In the study a real, i.e. based on calorimetric measurements, variations of enthalpy with temperature were taken into account. Detailed measurements conducted on DSC calorimeter revealed hysteresis on the h(T) curves for heating and cooling phases, which is shown in Fig. 4. Based on these characteristics a procedure allowing for determination of enthalpy as a function of temperature and direction of heat flow (charging or discharging of the TES unit) was developed and implemented in the computational program.
113
5.1. Boundary conditions Boundary conditions describe heat transfer on all surfaces on the cross-section of the model, different surfaces are depicted in Fig. 5. Different surfaces in the model are distinguished by different mechanisms of heat transfer with the environment. Surface A (sides and bottom surface) was assumed as adiabatic. In the experimental model these surfaces were insulated, in a real panel side parts are boundaries with similar, neighboring elements, while the lower surface is insulated. Surface B is exposed to the environment with heat transfer to the surrounding air by means of natural convection. Surface C is a contact surface between ventilation air and PCM material. Through this surface TES unit is charged (heated up with PCM melting) and discharged (cooling with PCM solidification) by means of forced convection. Since this process, i.e. forced convection inside the channel, is the most important from the point of view of operational characteristics of the TES unit, a special attention was paid on the determination of its intensity. In particular variations on heat transfer coefficient along the channel were modelled and validated experimentally. In the mathematical model the following equations were introduced as the boundary conditions for surfaces B and C:
krT ¼ a1 ðT p T 1 Þ
ð3Þ
krT ¼ a2 ðT p T air Þ
ð4Þ
where: a1 – heat transfer coefficient for natural convection, constant during the process; a2 – heat transfer coefficient for forced convection inside the channel, variable along the channel; T1 – temperature in the environment, constant, Tair – temperature of the air flowing through the channel, variable in time and along the channel. 5.2. Heat transfer coefficient along the air flow in the channel Determination of convective heat transfer coefficient (a2) variations along the channel was crucial in this study. Due to the fact that the air duct is relatively short and in addition the air flow reverse in a halfway heat transfer coefficient varies substantially along the flow. It was observed in the experimental study – Fig. 6 shows variations of measured air temperature along the channel, with distinct drop of temperature near the bend which is due to the rise of heat transfer intensity in this region [18]. Using experimental results for validation an attempt was made to deter-
Fig. 4. Enthalpy temperature dependence for the composite used in the study (gypsum/Micronal DS5008 BASF).
Fig. 5. Cross section of the ceiling panel. Inlet on the left, outlet on the right. Boundary conditions are marked using different lines (description in the text).
Fig. 6. Air temperature distribution along the channel for a specified time in a heating phase.
114
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
mine the relationship between a2 and z coordinate (along pathway) with a particular focus on an inlet to the channel (where boundary layers are developing) and the area around the bend of the channel. A following correlation for convective heat transfer in case of internal flow through non-circular channels was taken as a starting point in the research for particular relationship [22]:
a2 ¼ f ðx; wÞ ¼
e20 kair 2dr
þ
dr wcpair dair e2 ln 0 4x 8G0
ð5Þ
Heat transfer coefficient is a function of a distance from the inlet of the duct (x) and speed of a fluid (w). Parameters e20 and G0 are constants and depend on the shape of the channel. For ducts of square cross-section: e20 ¼ 5:96, G0 = 0.598. The shape of the curve described by this correlation is shown in Fig. 7 (solid line). It is seen that close to the inlet this correlation overestimates intensity of heat transfer. In experimental set-up a nozzle was used at the inlet to the ceiling panel to stabilize an air flow into a duct (Fig. 2 & Fig. 3). As a result heat transfer coefficient (a2) at the inlet was reduced. Taking into account experimental results this function was modified so that maximum value of a2 tends to 35 W/(m2K) at the inlet – corrected shape of the curve is shown in Fig. 7 (dashed line). Much attention was paid on the variations of a2 near the bend of the channel. Several distributions of heat transfer coefficient along the length of the channel were investigated. Fig. 8 shows six versions of heat transfer coefficient along the length of the channel are shown, in fact there were still more, but only slightly different from those shown. After many trials heat transfer coefficient variations along the whole channel were determined on the basis of experimental results – it is shown in Fig. 9. It is a unique achievement of the research, because we have determined heat transfer coefficient distribution for a given geometry of a channel for which theoretically predicted air temperature variations in a channel to a great extent matches results of measurements, i.e. the curves shown in Fig. 6. It is practically not possible to determine accurate distribution of heat transfer coefficient, since it would require detailed measurement of this property. The main goal of this part of the research was to find rather simple mathematical function (in fact a set of functions merged) describing variations of this coefficient, in order to be implemented in a computational code used for the analysis of overall performance characteristics of this specific heat storage unit. The best match with experimental results were obtained for very steep function in the vicinity of the bend of the
Fig. 8. Selected heat transfer coefficient variations along the channel considered in the study; mean air velocity in the channel w = 2.0 m/s.
Fig. 9. The most appropriate heat transfer coefficient variations along the length of the channel; whole length of the channel – 6 m, w = 2.0 m/s.
Fig. 7. Heat transfer coefficient (HTC) along the straight part channel (3 m length); solid line – HTC according to the formula (5), dashed line – corrected HTC; w = 2 m/ s.
channel with extremely high (as for air) local value of heat transfer coefficient, up to 140 W/(m2K). Other functions, shown in Fig. 8, with lower local extremum were much more unphysical since they introduced disturbance in heat transfer coefficient in much extended region around the bend. The final choice was a combination of different variants that partially overlapped, which is particularly evident in the second graph in Fig. 8. All the heat transfer coefficient characteristics shown in Figures from 7 to 9 correspond to the air velocity on the channel equal to 2 m/s (the same as in the experimental procedure used for validation). For other air velocities the level of this characteristic is scaled using the formula (5), that was used as a base for heat transfer
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
115
coefficient determination. The model characteristics (Fig. 9) was digitized and appropriate procedure developed, that was incorporated in the program used in this research (including scaling due to air velocity changes). 6. Numerical model of heat transfer in the ceiling panel A problem of determination of temperature profile in the part of energy storage unit, briefly described in a mathematical form by Eqs. (1)–(4), was solved numerically with an explicit scheme for time depending term of heat conduction equation. 6.1. Spatial discretization The ceiling panel has been divided into cuboid control volumes (84,000 elements). The division of the control volume was applied only to the material of which the heat exchanger was built (Fig. 10). Air temperature distribution was determined in a different way. It was assumed, that air temperature is uniform in the cross-section (although it changes with time), spatial variations occur only along the channel as a result of heat transfer between air stream and internal walls of the panel. 6.2. Discretization of heat conduction equation In order to determine the temperature of a cell marked as ‘P’ after time Ds, the following equation was used. It is a finite difference equation approach to transient heat conduction process.
qcp
T T 0 T 0w T 0 T 0P xyz ¼ P kyz þ E kyz s x x 0 0 0 0 T TS T TP kxz þ N kxz P y y
T 0P T 0T T 0 T 0P kxy þ B kxy z z
Fig. 11. Location of adjacent cells and their symbols. Cells called T and B were not drawn because the drawing would become unreadable. Arrows symbolize heat flow.
time (is cooled during charging of the panel and heated during discharging) as well as with the distance from the inlet to the channel. The channel was divided into n control volumes – the same as the number of control volumes along z coordinate in case of the panel. In each control volume air temperature is assumed to be uniform, but variable with time. These temperatures were determined based on the energy balance, i.e. the balance of heat flow rate on the air side and heat flow rate on the panel side in the PCM composite. A heat absorbed by cells that are in contact with the air flow has been described by the formula (see also Fig. 12):
ð6Þ
This equation describes enthalpy change of a control element as a result of heat fluxes imbalance between the element and adjacent elements or environment (in case of boundary elements). Location of adjacent cells and their symbols are shown in Fig. 11. Time step Ds was determined based on the criterion for convergent solution when explicit scheme is applied:
Ds 6
1 1 2a ðDxÞ2 þ ðD1yÞ2 þ ðD1zÞ2
ð7Þ
6.3. Air temperature determination along the channel One of the main tasks was to calculate a temperature of the flowing air inside the ceiling panel. Air temperature changes with
Fig. 12. Cells which contact directly with the air flow was marked by thick lines.
Fig. 10. Control volumes in the cross-section of the ceiling panel; dimensions of a single control volume: Dx = 1.5 mm, Dy = 1.5 mm, Dz = 10 cm.
116
Q_ k1 ¼
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
X
a2 ðT k T pi ÞSpi
ð8Þ
i
The sum on the right hand side of Eq. (8) represents the total heat flow rate on internal surface of the channel of the length corresponding to the control volume. Tk is the air temperature in the control volume, Tpi is a temperature of the surface of control volumes in the panel, i – number of control volumes in the panel adjacent to the channel. The same heat flow rate can be described form the point of view of the change of enthalpy of air flowing through the control volume:
Q_ k2 ¼ mair cpair DT air ¼ qair wSk cpair DT air
ð9Þ
P where Sk ¼ i Spi . Given the equality of heat flows Q_ k1 and Q_ k2 , the air temperature change along the control volume T air can be determined from the formula:
X
a2 ðT k T pi ÞSpi
DT air ¼ T kþ1 T k ¼
i
qair wSk cpair
ð10Þ
Repeating the above sequence of computations for all n control volumes (k = 1. . .n) temperature profile of the air along the channel for a given time can be determined.
convective heat exchange between the air and the walls of the panel. As a result of the validation some assumptions in the model were modified. For example, it turned out that an assumption about the lack of heat transfer on insulated walls was not true with regard to the experimental model. Much better numerical results (as compared to the experimental ones) were obtained when convective heat transfer to the environment was taken into account on all external surfaces (a3 for side surfaces and a4 for bottom surface), with heat transfer coefficient equals to 5 W/(m2K). 7. Parametric study of the ceiling panel A computational tool, developed in the framework of the research, after successful validation was used in parametric study of operational behavior of the ceiling panel designed for heat/cool storage in building. An influence of selected parameters on the storage potential, as well as outlet air temporal characteristics was investigated. Experiments were performed for boundary conditions that were simplified mainly due to the limitations of control devices.
6.4. Computer program validation Validation process was performed to verify results generated by the computer program with results obtained in an experimental way. Some experiments performed at a set-up described before, were also simulated computationally using the code developed in the study. One test as an example is presented in the paper. It is related to the charging of the panel by hot air stream of constant temperature and subsequent discharging by cool air. Inlet air temperature to the ceiling panel during the first phase was equal to 29.7 °C for 9 h and then was decreased to 15.5 °C for the next 15 h. The air temperature was controlled by using a heat exchanger connected to a digital thermostat. The experiment was conducted for 72 h and consisted of three cycles of 24 h. Average ambient temperature was equal to 21.4 °C. Air temperatures at the inlet and at the outlet from the channel obtained experimentally and numerically were compared. Results are shown in Fig. 13. Good agreement of the results obtained by two methods confirms the correctness of the modelling of heat transfer process, in particular
Fig. 14. Daily air temperature in Warsaw (central Poland) in July averaged based on meteorological data.
Fig. 13. A results of the computer program validation. Input data for the tests performed: q = 720 kg/m3, k = 0.2 W/(mK), a1 = a3 = a4 = 5 W/(m2K), w = 2.0 m/s, T1 = 21.4 °C.
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
Among others, temporal characteristics of inlet air temperature were far from reality – see Fig. 13. Fig. 14 shows averaged daily variations of ambient air temperature in the region of Central Poland. For this characteristics a simulation of thermal behavior of the panel were performed. Simulation were done also for different air flow rates, i.e. different air velocity in the channel: 1.0, 2.0, 3.0 and 4.0 m/s. Outlet air temperatures were analyzed, as an important property influencing thermal comfort in the room to which ventilation air is delivered. Results of the simulations are shown in Fig. 15. Daily variations of air temperature, which equal to 14.6 °C (from 15.9 °C to 30.5 °C), are substantially attenuated in the panel due to absorption and release of heat by PCM in the composite. Attenuation, of course, depends on the mass flow rate of the air, increases with the decrease of mass flow rate because of decreasing thermal capacity of the air stream. The aim of this study was to give quantitative, not qualitative, information about the potential for air conditioning by this kind of heat storage unit. For a case when air velocity equals to
117
1 m/s, temperature oscillation at the outlet from the ceiling panel was below 1 °C. For the highest velocity in the range under study, i.e. 4 m/s, a range of temperature variations increased to 5.9 °C, but even in this case temperature oscillations were about 2.5 times smaller than for outside temperature. It can be also noticed that outlet air temperature from a ceiling panel for all studied cases was kept in the thermal comfort range (19–25 °C). It was confirmed that using of ceiling panels made of composite containing phase change material is reasonable to maintain a proper temperature in rooms. Detailed results of the simulations were also used to determine the amount of heat stored in the panel. For the same characteristics of ambient air temperature as in Fig. 15, energy accumulated (and released, depending on the phase of the cycle) in the ceiling panel during three subsequent days is shown in Fig. 16. Initially an amount of heat accumulated decreases, i.e. heat is released form the storage unit because of low air temperature. Then a phase of accumulation of heat starts and lasts for about 15 h. Subsequent
Fig. 15. Air inlet temperature to the ceiling panel and air outlet temperatures for different air speeds (1 m/s, 2 m/s, 3 m/s, 4 m/s). Data using in the numerical simulation: q = 720 kg/m3, k = 0.2 W/(mK), a1 = a3 = a4 = 5 W/(m2K), T1 = 21.4 °C, T0 = 21.9 °C.
Fig. 16. Energy accumulated in a ceiling panel from the beginning to specify time for a different air speed (1 m/s, 2 m/s, 3 m/s, 4 m/s).
118
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
phase of the release of heat is shorter and as a result not all heat accumulated is taken back by the air stream. So that an increase of average temperature of the panel is observed during this (rather short) time of operation. The main reason for such thermal behavior of the ceiling panel (storage unit) is the fact, that PCM was not properly selected for the characteristics of ambient air temperature. Melting point of PCM is a little too low, it is lower than the mean temperature of the air in this period. Because of this heating period (melting of PCM n the composite) is much longer than cooling phase (solidification of PCM) and, as a consequence the panel is heated up. After long time, longer than 3 days, the panel, in terms of its mean temperature, would reach quasi-steady state. These results show that appropriate selection of phase change temperature is crucial for the proper operation of the storage unit.
8. Conclusions There were two main goals of the study presented in this paper. The first one was related to the development of numerical model (and computational code) of heat transfer occurring during operation of the special thermal energy storage unit integrated with building structure and building ventilation system that was based on the use of phase change material (PCM). A particular attention was paid on the modelling of convective heat transfer between air stream and the walls of the panel. A specific function describing the variations of heat transfer coefficient along the channel was determined and validated by experimental results. Other boundary conditions, of minor significance, were also modified during validation of the whole mathematical model of the process. The other goal of the study was related to the parametric analysis of the thermal behavior of the panel (storage unit) in different operational conditions, that couldn’t be investigated experimentally due to limitations of experimental set-up. This analysis revealed some specific features of the unit. The main one is the importance of the proper selection of phase change material, in terms of its melting point, with regard to environmental conditions, here, the daily variations of ambient air temperature. Mismatch of PCM properties to the characteristics of daily ambient temperature changes in a given region may be the reason of incorrect operation of heat storage unit or incomplete utilization of its potential. Quantitative information of the operational characteristics of the unit, e.g. attenuation of air temperature variations as a function of air mass flow rate, were also determined.
Acknowledgments This project has received funding from the Warsaw University of Technology in the framework of statutory activity as well as from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 657466 (INPATH-TES).
References [1] N. Soares, J.J. Costa, A.R. Gaspar, P. Santos, Review of passive PCM latent heat thermal energy storage systems towards buildings’ energy efficiency, Energy Build. 59 (2013) 82–103. [2] M. Pomianowski, P. Heiselberg, Y. Zhang, Review of thermal energy storage technologies based on PCM application in buildings, Energy Build. 67 (2013) 56–69. [3] A. Waqas, Z.U. Din, Phase change material (PCM) storage for free cooling of buildings. A review, Renewable Sustainable Energy Rev. 18 (2013) 607–625. [4] L.F. Cabeza, A. Castell, C. Barreneche, A. de Gracia, A.I. Fernández, Materials used as PCM in thermal energy storage in buildings: A review, Renew. Sustain. Energy Rev. 15 (2011) 1675–1695. [5] C. Veerakumar, A. Sreekumar, Phase change material based cold thermal energy storage: materials, techniques and applications. A review, Int. J. Refrigeration 67 (2016) 271–289, http://dx.doi.org/10.1016/j.ijrefrig.2015. 12.005. [6] A. Solé, H. Neumann, S. Niedermaier, I. Martorell, P. Schossig, L.F. Cabeza, Stability of sugar alcohols as PCM for thermal energy storage, Sol. Energy Mater. Sol. Cells 126 (2014) 125–134. [7] A. Sari, A. Karaipekli, Preparation and thermal properties of capric acid/palmitic acid eutectic mixture as a phase change energy storage material, Mater. Lett. 62 (2008) 903–906. [8] C. Liu, Y. Yuan, N. Zhang, X. Cao, X. Yang, A novel PCM of lauric-myristic-stearic acid/ expanded graphite composite for thermal energy storage, Mater. Lett. 120 (2014) 43–46. [9] L. Royon, L. Karim, A. Bontemp, Optimization of PCM embedded in a floor panel developed for thermal management of the lightweight envelope of buildings, Energy Build. 82 (2014) 385–390. [10] N. Soares, A.R. Gaspar, P. Santos, J.J. Costa, Multi-dimensional optimization of the incorporation of PCM-drywalls in lightweight steel-framed residential buildings in different climates, Energy Build. 70 (2014) 411–421. [11] L. Navarro, A. de Gracia, A. Castell, L.F. Cabeza, Experimental evaluation of a concrete core slab with phase change materials for cooling purposes, Energy Build. 116 (2016) 411–419. [12] H. Weinläder, F. Klinker, M. Yasin, PCM cooling ceilings in the Energy Efficiency Center – passive cooling potential of two different system designs, Energy Build. 119 (2016) 93–100. [13] E. Solgi, R. Fayaz, B.M. Kari, Cooling load reduction in office buildings of hotarid climate, combining phase change materials and night purge ventilation, Renewable Energy 85 (2016) 725–731. [14] G. Zhou, M. Mengmeng Pang, Experimental investigations on the performance of a collector–storage wall system using phase change materials, Energy Convers. Manage. 105 (2015) 178–188. [15] R. Barzin, J. Chen, B. Young, M. Farid, Application of PCM energy storage in combination with night ventilation for space cooling, Appl. Energy 158 (2015) 412–421. [16] S. Ramakrishnan, X. Wang, J. Sanjayan, J. Wilson, Thermal performance of buildings integrated with phase change materials to reduce heat stress risks during extreme heatwave events, Appl. Energy 194 (2017) 410–421, http://dx. doi.org/10.1016/j.apenergy.2016.04.084. [17] S.M. Sajjadian, J. Lewis, S. Sharples, The potential of phase change materials to reduce domestic cooling energy loads for current and for future UK climates, Energy Build. 93 (2015) 83–89. [18] M. Jaworski, Thermal performance of building element containing phase change material (PCM) integrated with ventilation system – an experimental study, Appl. Therm. Eng. 70 (2014) 665–674. [19] M. Jaworski, P. Łapka, P. Furman´ski, Numerical modelling and experimental studies of thermal behavior of building integrated thermal energy storage unit in a form of a ceiling panel, Appl. Energy 113 (2014) 548–557. [20] http://www.micronal.de/portal/basf, (access on November, 2016). [21] M. Jaworski, S. Abeid, Thermal conductivity of gypsum containing phase change material (PCM) for building applications, J. Power Technol. 91 (2) (2011) 49–53. [22] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, Wiley, 2011.
Contents lists available at ScienceDirect
Thermal Science and Engineering Progress journal homepage: www.elsevier.com/locate/tsep
Computer simulations of heat transfer in a building integrated heat storage unit made of PCM composite Łukasz Wardziak a, Maciej Jaworski b,⇑ a b
The Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland Warsaw University of Technology, Institute of Heat Engineering, Nowowiejska 21/25, 00-665 Warsaw, Poland
a r t i c l e
i n f o
Article history: Received 31 January 2017 Received in revised form 15 May 2017 Accepted 16 May 2017
Keywords: Phase change materials (PCM) Thermal energy storage Thermal performance characteristics Building integrated PCMs
a b s t r a c t The paper presents the results of parametric study of thermal performance characteristics of thermal energy storage unit integrated in building structure being also a part of building’s ventilation system. A storage unit is in the form of a ceiling panel with internal channels through which air taken from the environment flows before it is delivered into the rooms. Thermal storage potential of the panel is thanks to phase change material (PCM) which is mixed with gypsum mortar, creating in this way a composite of high thermal capacity in the temperature range corresponding to the temperature required for thermal comfort. In order to perform the analysis of the storage unit a computer program was developed which was based on the mathematical model of complex heat transfer occurring inside the panel, inside a composite material, as well as on the boundary between the panel and air flowing through internal channels. A procedure describing variations of convective heat transfer intensity along the channel can be regarded as a unique achievement in this research. This function was validated based on measurements conducted on the experimental set-up specially prepared for this study. Using the program many computer simulations were performed. Based on the results of this analysis a detailed information on the performance of the panel for different operational parameters, e.g. air mass flow rates, were obtained. Contrary to the study reported in an earlier publication, these simulations were conducted for real environmental conditions, i.e. real ambient temperatures during summer in Central Poland. Also, important conclusions regarding selection of PCM, mainly its melting temperature range, were formulated. Ó 2017 Published by Elsevier Ltd.
1. Introduction For a long time increasing the heat capacity of buildings was combined with increasing amount of conventional building materials such as stone, bricks and concrete. By increasing wall thickness, both the strength of the building and its thermal capacity was increased. A good example are castles built during the Middle Ages. By increasing walls thickness comfortable coolness in the summer months was obtained. In this case the walls work like natural cold accumulator. During summer months thick walls of these buildings slowly accumulates heat that is then released in winter days. In Medieval period nobody thought about accumulation of thermal energy but even in this time special structures were designed and built for the purpose to accumulate and release a significant amount of heat (cold). Nowadays the construction of buildings requires much less conventional, massive building materials due to the development of ⇑ Corresponding author. E-mail address: [email protected] (M. Jaworski). http://dx.doi.org/10.1016/j.tsep.2017.05.006 2451-9049/Ó 2017 Published by Elsevier Ltd.
lightweight materials and changes in the technology of the construction. Walls thickness is limited to reduce cost of materials. Office buildings are representative and very often exterior walls are covered with glass panes. However, the idea of heat accumulation is up to date. Fortunately to increase thermal capacity of buildings it is not necessary to use a large amount of conventional materials which can accumulate relatively small amount of heat (the ratio of the amount of stored heat to its volume). It is much easier, in terms of the weight of the building structure, to use phase change materials (PCM) incorporated in the building’s envelope in order to increase its thermal inertia. Building sector belongs to the leading ones in energy consumption in the developed countries. Taking the EU as an example, the buildings sector accounts for around 40% of the total final energy consumption and produces nearly 40% of the total CO2 emissions. Most of it is due to the increase in the living standard and in occupants’ comfort demands, mainly for heating and cooling [1]. A great amount of energy can be used for other purposes. In many countries in order to reduce the demand for heat (cool) thermomodernization programs are being implemented. As a result heat
110
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
Nomenclature a dr
q qair cp cp h k
a1 a2 T0
air
thermal diffusivity [m2/s] equivalent diameter [m] density of material [kg/m3] air density [kg/m3] specific heat capacity [J/(kgK)] air specific heat capacity [J/(kgK)] enthalpy [J/kg] thermal conductivity [W/(mK)] heat transfer coefficient on the upper wall [W/(m2K)] heat transfer coefficient in the channel [W/(m2K)] a ceiling panel initial temperature [°C]
losses (or gains during summer) are substantially reduced. Thermo-modernization allows to significantly reduce demand for energy which is used for heating in winter and for cooling in summer. These operations also increase the potential for heat storage in the building structure, due to the reduction of heat transfer through the external walls. In order to efficiently use this potential thermal capacity of the building structure must also be increased. This can be easily obtained by the use of phase change materials, PCMs. The use of PCMs in buildings dates back to 1950s, however the studies on different aspects of this kind of applications intensified in last two decades. The problems related to this topic are discussed and presented in many review papers [1–5], as well as in papers focused on specific issues. In order to achieve the benefits of the use of PCMs in buildings many problems must be solved, starting from the modification of material properties to the development of the methods of incorporation of these materials in the structure of the building. The research in this area is conducted at different scales (micro/macro) and is very wide in terms of issues to be solved. On the micro scale chemical properties of individual compounds like salt hydrates, paraffin, paraffin waxes, eutectics, fatty acids and others are the subject of research. Studies identifies chemical compounds that can be used for energy storage in certain temperature ranges in practice. For example Solé et al. [6] analyzed stability of sugar alcohols as PCM for thermal energy storage. They proved that sugar alcohols as PCMs are very promising due to their high storage capacity, safety and economic reasons. Their phase change temperatures make them suitable for medium temperature storage, which is needed for solar thermal or waste heat recovery applications. Sari et al. [7] came to the conclusion that capric acid (CA)/palmitic acid (PA) mixture with eutectic composition (76.5/23.5 wt.%) was a suitable PCM for low temperature TES applications in terms of melting and freezing temperatures (around 22 °C) and latent heats (about 170 J/g). These properties make this mixture a promising PCM for LHTES systems used in heating, ventilation, and air conditioning applications [7]. Cheng Liu et al. [8] performed a research on the use of lauric-myristic-stearic acid/expanded graphite composite for thermal energy storage. The authors in detail determined wide range of thermal properties of these composites, mainly thermal capacity, thermal conductivity and stability in thousands of cycles. All the results indicated that the proposed LA–MA–SA/EG composite has suitable thermal properties for thermal energy storage applications and heat recovery in buildings. Referring to a macro scale much research has been dedicated to explore different ways of implementing the PCM material in building envelope to increase thermal capacity. Royon et al. [9] conducted research concerning optimization of PCM embedded in a
Tp Tair Tk T1 DTair
temperature of the material at a given point [°C] air temperature in the duct [°C] air temperature in the duct in ‘k’ segment [°C] ambient temperature [°C] temperature difference between inlet and outlet of the ‘k’ segment q heat flux [W/m2] w air speed [m/s] Dx, Dy, Dz dimensions of a control volume [m] mair air mass flow rate [kg/s].
floor panel developed for thermal management of the lightweight envelope of buildings. This component derives from an existing slab having cylindrical cavities which is used in floors/ceilings. The cavities are filled with a polymer–paraffin. The study is based on numerical simulations whose results are compared to experimental ones with the same boundary conditions in order to validate the model. Another method of increasing thermal capacity is proposed by Soares et al. [10]. They proposed incorporating PCM-drywalls in lightweight steel-framed residential buildings. The authors evaluated the impact of PCM-drywalls in the annual and monthly heating and cooling energy savings, considering real-life conditions and several European climates. Energy savings effect is more evident for the warmer climates, where the total energy savings due to PCMs can reach 46% and 62% (Seville and Coimbra). PCM-drywalls are also very attractive for colder climates (Warsaw and Kiruna), with a predominance of the heating energy demand reduction. However, the impact of PCMs in the total energy savings is not so significant for these climates (24% and 10%). Navarro et al. [11] evaluated a concrete core slab with PCMs for cooling purposes. In their study, an innovative technology for cooling application in buildings was evaluated. A prefabricated concrete slab incorporating phase change material (PCM) was used as internal separation in the active slab cubicle. The incorporated PCM was paraffin macro-encapsulated in aluminum tubes. The aim was to use the internal slab as storage unit and as an active cooling supply to replace totally or partially conventional HVAC systems. The experimental campaign showed that the cold discharged was not enough to cover the whole cooling demand of the cubicle. However, significant energy savings in the HVAC system were registered, between 30% and 55% under mild conditions, and between 15% and 20% under severe conditions, compared to the reference cubicle. Research focused on the use of PCM materials for cooling purposes were conducted also by Weinläder et al. [12]. In the Energy Efficiency Center, the new R&D building of the ZAE Bayern, two different PCM cooling ceiling types were installed and monitored in two office rooms. The ceilings were connected to a water circuit and could be used for heating and cooling. The PCM ceilings were prototypes which differ in the positioning of the PCM layer: on top of the ceiling and below the water pipes. It was found that in the second configuration thermal connection between PCM and room is much better. Although passive cooling power of the system under study was rather small as compared to active cooling solutions, efficiency of this system turned out to be quite good – it took about 7–9 h before the highly insulated test rooms reached internal temperature of 27 °C. Solgi et al. [13] presented that PCMs have a great influence on enhancing the performance of night purge ventilation and cooling
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
load reduction of office buildings in hot-arid climate of Yazd (Iran). Investigating PCMs with various melting temperatures they found the one with 27 °C melting point as the best one for those environmental conditions. They found that almost 47% reduction in cooling energy is possible when PCM is used and optimal rate of ventilation is selected. A performance of a collector storage wall system using PCMs was investigated by Zhou et al. [14]. PCM slabs were attached on the gap-side wall surface to increase the heat storage. The test was carried out for a whole day with charging period of 6.5 hours and discharging period of 17.5 h. They analyzed in details daily variations of surface temperature as well as air and indoor temperatures. The indoor temperature was found to be above 22 °C during the whole discharging period under given conditions, which indicates that the indoor thermal comfort could be kept for a long time with the use of the storage system under study. Barzin et al. [15] tested experimentally an application of PCM energy storage in combination with night ventilation for space cooling. Two identical test huts, one with PCM-impregnated gypsum boards, the other with ordinary gypsum board, were compared. They found that substantial electricity saving, up to 73%, can be obtained only when PCM storage is combined with night ventilation. Benefits of the combination of heat storage in buildings structure (in PCMs) with night ventilation was observed in the research done by Ramakrishnan et al. [16] who performed extensive analysis of building’s thermal performance in weather conditions of Melbourne, with extreme heatwave periods. Sajjadian et al. [17] conducted tests on the potential use of PCMs to reduce domestic cooling energy loads for current and future UK climates. The study used simulations of a high performance detached house model with a near Passivhaus Standard in London, where the impact of climate change effect is predicted to be significant. It was shown that appropriate levels of PCM, with a suitable incorporation mechanism into the building construction, has significant advantages for residential buildings in terms of reducing total discomfort hours. 2. The aim of the study The purpose of this paper is to present the results of the study that was focused on different issues related to the thermal performance characteristics of a ceiling panel made of gypsum-PCM composite. This panel is a special form of building integrated ther-
111
mal energy storage unit utilizing phase change material as a storage media. Its specificity consists in the fact that it contains parallel channels for the air flow, and thus it is a part of a building ventilation system. Its role in ventilation system is to cool down the air taken from the environment when it is hot (during the day) and subsequently heat it up, when it is cool (during the night). Efficiency of the absorption of heat and its release depends on the thermal capacity of the panel and heat transfer coefficient between air and the walls of channels. In this part of the research we focused on the modelling of convective heat transfer inside channels, in particular on the modelling of heat transfer coefficient variations along the channel, especially at the reversion part. In the validation of the models earlier experimental results were taken into account [18]. The experience gained in previous works on mathematical modelling of similar heat transfer process [19] were used in this study. Computational tool, based on the numerical model developed, was then used for the parametric study of the performance of the panel in different conditions. In particular the influence of the melting point of PCM on thermal behavior of the panel over a long period of time was examined. It seems that the inaccurate adjustment of the PCM material, i.e. its phase change temperature, with respect to the range of ambient air temperature variations may cause that after some time the PCM temperature will fluctuate only above (or below) the phase transition temperature. That means a continuous decrease in the degree of utilizing PCM’s thermal capacity. 3. The physical model of the heat storage unit A concept of the structure of the ceiling panel – thermal energy storage unit, dimensions of its repetitive element as well as air flow configuration inside channels are shown in Fig. 1. According to the fundamental assumption for this solution, the air taken from the environment for building ventilation first flows through internal channels in the ceiling panel. When the air temperature is higher than upper range of thermal comfort temperature (during the day) it is cooled down flowing through the channel. The material of the ceiling panel contains substantial part of phase change material, of melting point in the middle of thermal comfort range, i.e. about 23 °C. This material absorbs heat from the air, undergoing nearly isothermal phase transition (melting). During the night ambient air temperature is much lower than the lower limit of thermal comfort, and thus also lower than phase change tempera-
Fig. 1. General structure of the ceiling panel and an axonometric view of the repetitive segment of the ceiling panel.
112
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
11.7 kg 0.022 m3
transfer it was assumed that an air duct consists of two channels. The whole ceiling panel consists of several repetitive elements (see Fig. 1), their number depends on the dimensions of the room. The combination of inlets and outlets can be made using special collectors. The composite for the panel was made of gypsum mortar (produced by Knauf) with an addition of PCM, i.e. Micronal DS5008, produced by BASF. PCM content was about 34 wt.%. Thermal properties of the composite were measured using DSC calorimeter [18] and miniature plate apparatus for thermal conductivity [21]. Basic parameters of the panel and the properties of the composite are collected in Table 1.
0.016 m3 1.5 cm
4. Experimental investigation of the ceiling panel
Table 1 Basic information about the structure and properties of material used for manufacturing of the ceiling panel. Material (composite)
Gypsum mortar (Knauf) + Micronal DS5008 (BASF)
Density Thermal conductivity Heat transfer coefficient in the channel Surface area of the internal channel in the ceiling panel Mass of the ceiling panel (one segment) Total volume (material volume + air channel volume) Material volume Wall thickness
720 kg/m3 0.2 W/(mK) See Fig. 9 0.36 m2
ture of PCM. In this phase of operation PCM solidifies releasing heat to the air which is heated up. PCM in the ceiling panel is subject to a daily cycle of melting and solidification, that are charging and discharging processes of it as a storage unit. As can be seen in Fig. 1 the structure and particular dimensions of the panel were chosen so that it could be easily manufactured using typical plasterboards (e.g. SmartBoards containing PCM, produced by BASF [20]). In order to increase surface area for heat
A special experimental set-up, based on the repetitive element of the panel, was built. The main goals of an experimental study were to examine the behavior of the panel in real conditions and as well as gathering data that could be used for validation of computational tools. An experimental set-up consists of a 3 meters long repetitive element of the ceiling panel (Fig. 2), made of the PCM-composite described earlier. It is equipped with additional equipment allowing for the control of the air flow (fans, collectors, anemometer) as well as the control of air temperature (special heat exchanger supplied from thermal bath). More than 30 thermocouples were embedded in the panel and located in the internal channel. They allow for very detailed measurement of temperature variations in the panel and in the air stream. This information was useful in the evaluation of the rates of charging and discharging of the storage unit, through the comparison of temperature level in different parts of the panel with regard to the temperature range of phase change (see also Fig. 3). From the variations of air temperature along the channels and with time such information as amount of energy stored/release in the panel, heat flow during charging and discharging an intensity of heat transfer in the channel could be obtained. The scheme of an experimental set-up is shown in Fig. 2. 5. Mathematical model of the repetitive part of the ceiling panel A mathematical model and associated computational program were developed in order to get the opportunity to perform parametric study of the storage unit for wider range of operational conditions much easier and cheaper as compared to experimental investigations. The following assumptions were adopted for the model:
Fig. 2. An experimental set-up with inlet (1) and outlet (2) depicted.
transient processes for both charging and discharging of the storage unit were analyzed, a real characteristics of enthalpy vs temperature of the PCMcomposite determined with DSC was accounted in the model, this characteristics account for the hysteresis of enthalpy during heating and cooling (Fig. 4),
Fig. 3. The scheme of an experimental set-up; 1 – data acquisition station, 2 – extension cables of TCs, 3 – water–air heat exchanger, 4 – supplier of heat exchanger (thermal bath), 5 – set of fans, 6 – supplier of fans (DC supplier), 7 – rotating vane anemometer.
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
convective heat transfer coefficient in the channel, variable with the distance from the inlet and around the bend was determined and experimentally validated, heat losses for external surfaces of the model (repetitive part of the ceiling) were also validated experimentally. Temperature profiles in the structure of the ceiling panel are described by transient heat conduction equation, which can be written in the form:
q
@h ¼ kr2 T @s
ð1Þ
where enthalpy is, in general, a function of specific heat which is variable with temperature:
Z
T
hðTÞ ¼
cp ðTÞdT
ð2Þ
T0
In the study a real, i.e. based on calorimetric measurements, variations of enthalpy with temperature were taken into account. Detailed measurements conducted on DSC calorimeter revealed hysteresis on the h(T) curves for heating and cooling phases, which is shown in Fig. 4. Based on these characteristics a procedure allowing for determination of enthalpy as a function of temperature and direction of heat flow (charging or discharging of the TES unit) was developed and implemented in the computational program.
113
5.1. Boundary conditions Boundary conditions describe heat transfer on all surfaces on the cross-section of the model, different surfaces are depicted in Fig. 5. Different surfaces in the model are distinguished by different mechanisms of heat transfer with the environment. Surface A (sides and bottom surface) was assumed as adiabatic. In the experimental model these surfaces were insulated, in a real panel side parts are boundaries with similar, neighboring elements, while the lower surface is insulated. Surface B is exposed to the environment with heat transfer to the surrounding air by means of natural convection. Surface C is a contact surface between ventilation air and PCM material. Through this surface TES unit is charged (heated up with PCM melting) and discharged (cooling with PCM solidification) by means of forced convection. Since this process, i.e. forced convection inside the channel, is the most important from the point of view of operational characteristics of the TES unit, a special attention was paid on the determination of its intensity. In particular variations on heat transfer coefficient along the channel were modelled and validated experimentally. In the mathematical model the following equations were introduced as the boundary conditions for surfaces B and C:
krT ¼ a1 ðT p T 1 Þ
ð3Þ
krT ¼ a2 ðT p T air Þ
ð4Þ
where: a1 – heat transfer coefficient for natural convection, constant during the process; a2 – heat transfer coefficient for forced convection inside the channel, variable along the channel; T1 – temperature in the environment, constant, Tair – temperature of the air flowing through the channel, variable in time and along the channel. 5.2. Heat transfer coefficient along the air flow in the channel Determination of convective heat transfer coefficient (a2) variations along the channel was crucial in this study. Due to the fact that the air duct is relatively short and in addition the air flow reverse in a halfway heat transfer coefficient varies substantially along the flow. It was observed in the experimental study – Fig. 6 shows variations of measured air temperature along the channel, with distinct drop of temperature near the bend which is due to the rise of heat transfer intensity in this region [18]. Using experimental results for validation an attempt was made to deter-
Fig. 4. Enthalpy temperature dependence for the composite used in the study (gypsum/Micronal DS5008 BASF).
Fig. 5. Cross section of the ceiling panel. Inlet on the left, outlet on the right. Boundary conditions are marked using different lines (description in the text).
Fig. 6. Air temperature distribution along the channel for a specified time in a heating phase.
114
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
mine the relationship between a2 and z coordinate (along pathway) with a particular focus on an inlet to the channel (where boundary layers are developing) and the area around the bend of the channel. A following correlation for convective heat transfer in case of internal flow through non-circular channels was taken as a starting point in the research for particular relationship [22]:
a2 ¼ f ðx; wÞ ¼
e20 kair 2dr
þ
dr wcpair dair e2 ln 0 4x 8G0
ð5Þ
Heat transfer coefficient is a function of a distance from the inlet of the duct (x) and speed of a fluid (w). Parameters e20 and G0 are constants and depend on the shape of the channel. For ducts of square cross-section: e20 ¼ 5:96, G0 = 0.598. The shape of the curve described by this correlation is shown in Fig. 7 (solid line). It is seen that close to the inlet this correlation overestimates intensity of heat transfer. In experimental set-up a nozzle was used at the inlet to the ceiling panel to stabilize an air flow into a duct (Fig. 2 & Fig. 3). As a result heat transfer coefficient (a2) at the inlet was reduced. Taking into account experimental results this function was modified so that maximum value of a2 tends to 35 W/(m2K) at the inlet – corrected shape of the curve is shown in Fig. 7 (dashed line). Much attention was paid on the variations of a2 near the bend of the channel. Several distributions of heat transfer coefficient along the length of the channel were investigated. Fig. 8 shows six versions of heat transfer coefficient along the length of the channel are shown, in fact there were still more, but only slightly different from those shown. After many trials heat transfer coefficient variations along the whole channel were determined on the basis of experimental results – it is shown in Fig. 9. It is a unique achievement of the research, because we have determined heat transfer coefficient distribution for a given geometry of a channel for which theoretically predicted air temperature variations in a channel to a great extent matches results of measurements, i.e. the curves shown in Fig. 6. It is practically not possible to determine accurate distribution of heat transfer coefficient, since it would require detailed measurement of this property. The main goal of this part of the research was to find rather simple mathematical function (in fact a set of functions merged) describing variations of this coefficient, in order to be implemented in a computational code used for the analysis of overall performance characteristics of this specific heat storage unit. The best match with experimental results were obtained for very steep function in the vicinity of the bend of the
Fig. 8. Selected heat transfer coefficient variations along the channel considered in the study; mean air velocity in the channel w = 2.0 m/s.
Fig. 9. The most appropriate heat transfer coefficient variations along the length of the channel; whole length of the channel – 6 m, w = 2.0 m/s.
Fig. 7. Heat transfer coefficient (HTC) along the straight part channel (3 m length); solid line – HTC according to the formula (5), dashed line – corrected HTC; w = 2 m/ s.
channel with extremely high (as for air) local value of heat transfer coefficient, up to 140 W/(m2K). Other functions, shown in Fig. 8, with lower local extremum were much more unphysical since they introduced disturbance in heat transfer coefficient in much extended region around the bend. The final choice was a combination of different variants that partially overlapped, which is particularly evident in the second graph in Fig. 8. All the heat transfer coefficient characteristics shown in Figures from 7 to 9 correspond to the air velocity on the channel equal to 2 m/s (the same as in the experimental procedure used for validation). For other air velocities the level of this characteristic is scaled using the formula (5), that was used as a base for heat transfer
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
115
coefficient determination. The model characteristics (Fig. 9) was digitized and appropriate procedure developed, that was incorporated in the program used in this research (including scaling due to air velocity changes). 6. Numerical model of heat transfer in the ceiling panel A problem of determination of temperature profile in the part of energy storage unit, briefly described in a mathematical form by Eqs. (1)–(4), was solved numerically with an explicit scheme for time depending term of heat conduction equation. 6.1. Spatial discretization The ceiling panel has been divided into cuboid control volumes (84,000 elements). The division of the control volume was applied only to the material of which the heat exchanger was built (Fig. 10). Air temperature distribution was determined in a different way. It was assumed, that air temperature is uniform in the cross-section (although it changes with time), spatial variations occur only along the channel as a result of heat transfer between air stream and internal walls of the panel. 6.2. Discretization of heat conduction equation In order to determine the temperature of a cell marked as ‘P’ after time Ds, the following equation was used. It is a finite difference equation approach to transient heat conduction process.
qcp
T T 0 T 0w T 0 T 0P xyz ¼ P kyz þ E kyz s x x 0 0 0 0 T TS T TP kxz þ N kxz P y y
T 0P T 0T T 0 T 0P kxy þ B kxy z z
Fig. 11. Location of adjacent cells and their symbols. Cells called T and B were not drawn because the drawing would become unreadable. Arrows symbolize heat flow.
time (is cooled during charging of the panel and heated during discharging) as well as with the distance from the inlet to the channel. The channel was divided into n control volumes – the same as the number of control volumes along z coordinate in case of the panel. In each control volume air temperature is assumed to be uniform, but variable with time. These temperatures were determined based on the energy balance, i.e. the balance of heat flow rate on the air side and heat flow rate on the panel side in the PCM composite. A heat absorbed by cells that are in contact with the air flow has been described by the formula (see also Fig. 12):
ð6Þ
This equation describes enthalpy change of a control element as a result of heat fluxes imbalance between the element and adjacent elements or environment (in case of boundary elements). Location of adjacent cells and their symbols are shown in Fig. 11. Time step Ds was determined based on the criterion for convergent solution when explicit scheme is applied:
Ds 6
1 1 2a ðDxÞ2 þ ðD1yÞ2 þ ðD1zÞ2
ð7Þ
6.3. Air temperature determination along the channel One of the main tasks was to calculate a temperature of the flowing air inside the ceiling panel. Air temperature changes with
Fig. 12. Cells which contact directly with the air flow was marked by thick lines.
Fig. 10. Control volumes in the cross-section of the ceiling panel; dimensions of a single control volume: Dx = 1.5 mm, Dy = 1.5 mm, Dz = 10 cm.
116
Q_ k1 ¼
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
X
a2 ðT k T pi ÞSpi
ð8Þ
i
The sum on the right hand side of Eq. (8) represents the total heat flow rate on internal surface of the channel of the length corresponding to the control volume. Tk is the air temperature in the control volume, Tpi is a temperature of the surface of control volumes in the panel, i – number of control volumes in the panel adjacent to the channel. The same heat flow rate can be described form the point of view of the change of enthalpy of air flowing through the control volume:
Q_ k2 ¼ mair cpair DT air ¼ qair wSk cpair DT air
ð9Þ
P where Sk ¼ i Spi . Given the equality of heat flows Q_ k1 and Q_ k2 , the air temperature change along the control volume T air can be determined from the formula:
X
a2 ðT k T pi ÞSpi
DT air ¼ T kþ1 T k ¼
i
qair wSk cpair
ð10Þ
Repeating the above sequence of computations for all n control volumes (k = 1. . .n) temperature profile of the air along the channel for a given time can be determined.
convective heat exchange between the air and the walls of the panel. As a result of the validation some assumptions in the model were modified. For example, it turned out that an assumption about the lack of heat transfer on insulated walls was not true with regard to the experimental model. Much better numerical results (as compared to the experimental ones) were obtained when convective heat transfer to the environment was taken into account on all external surfaces (a3 for side surfaces and a4 for bottom surface), with heat transfer coefficient equals to 5 W/(m2K). 7. Parametric study of the ceiling panel A computational tool, developed in the framework of the research, after successful validation was used in parametric study of operational behavior of the ceiling panel designed for heat/cool storage in building. An influence of selected parameters on the storage potential, as well as outlet air temporal characteristics was investigated. Experiments were performed for boundary conditions that were simplified mainly due to the limitations of control devices.
6.4. Computer program validation Validation process was performed to verify results generated by the computer program with results obtained in an experimental way. Some experiments performed at a set-up described before, were also simulated computationally using the code developed in the study. One test as an example is presented in the paper. It is related to the charging of the panel by hot air stream of constant temperature and subsequent discharging by cool air. Inlet air temperature to the ceiling panel during the first phase was equal to 29.7 °C for 9 h and then was decreased to 15.5 °C for the next 15 h. The air temperature was controlled by using a heat exchanger connected to a digital thermostat. The experiment was conducted for 72 h and consisted of three cycles of 24 h. Average ambient temperature was equal to 21.4 °C. Air temperatures at the inlet and at the outlet from the channel obtained experimentally and numerically were compared. Results are shown in Fig. 13. Good agreement of the results obtained by two methods confirms the correctness of the modelling of heat transfer process, in particular
Fig. 14. Daily air temperature in Warsaw (central Poland) in July averaged based on meteorological data.
Fig. 13. A results of the computer program validation. Input data for the tests performed: q = 720 kg/m3, k = 0.2 W/(mK), a1 = a3 = a4 = 5 W/(m2K), w = 2.0 m/s, T1 = 21.4 °C.
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
Among others, temporal characteristics of inlet air temperature were far from reality – see Fig. 13. Fig. 14 shows averaged daily variations of ambient air temperature in the region of Central Poland. For this characteristics a simulation of thermal behavior of the panel were performed. Simulation were done also for different air flow rates, i.e. different air velocity in the channel: 1.0, 2.0, 3.0 and 4.0 m/s. Outlet air temperatures were analyzed, as an important property influencing thermal comfort in the room to which ventilation air is delivered. Results of the simulations are shown in Fig. 15. Daily variations of air temperature, which equal to 14.6 °C (from 15.9 °C to 30.5 °C), are substantially attenuated in the panel due to absorption and release of heat by PCM in the composite. Attenuation, of course, depends on the mass flow rate of the air, increases with the decrease of mass flow rate because of decreasing thermal capacity of the air stream. The aim of this study was to give quantitative, not qualitative, information about the potential for air conditioning by this kind of heat storage unit. For a case when air velocity equals to
117
1 m/s, temperature oscillation at the outlet from the ceiling panel was below 1 °C. For the highest velocity in the range under study, i.e. 4 m/s, a range of temperature variations increased to 5.9 °C, but even in this case temperature oscillations were about 2.5 times smaller than for outside temperature. It can be also noticed that outlet air temperature from a ceiling panel for all studied cases was kept in the thermal comfort range (19–25 °C). It was confirmed that using of ceiling panels made of composite containing phase change material is reasonable to maintain a proper temperature in rooms. Detailed results of the simulations were also used to determine the amount of heat stored in the panel. For the same characteristics of ambient air temperature as in Fig. 15, energy accumulated (and released, depending on the phase of the cycle) in the ceiling panel during three subsequent days is shown in Fig. 16. Initially an amount of heat accumulated decreases, i.e. heat is released form the storage unit because of low air temperature. Then a phase of accumulation of heat starts and lasts for about 15 h. Subsequent
Fig. 15. Air inlet temperature to the ceiling panel and air outlet temperatures for different air speeds (1 m/s, 2 m/s, 3 m/s, 4 m/s). Data using in the numerical simulation: q = 720 kg/m3, k = 0.2 W/(mK), a1 = a3 = a4 = 5 W/(m2K), T1 = 21.4 °C, T0 = 21.9 °C.
Fig. 16. Energy accumulated in a ceiling panel from the beginning to specify time for a different air speed (1 m/s, 2 m/s, 3 m/s, 4 m/s).
118
Ł. Wardziak, M. Jaworski / Thermal Science and Engineering Progress 2 (2017) 109–118
phase of the release of heat is shorter and as a result not all heat accumulated is taken back by the air stream. So that an increase of average temperature of the panel is observed during this (rather short) time of operation. The main reason for such thermal behavior of the ceiling panel (storage unit) is the fact, that PCM was not properly selected for the characteristics of ambient air temperature. Melting point of PCM is a little too low, it is lower than the mean temperature of the air in this period. Because of this heating period (melting of PCM n the composite) is much longer than cooling phase (solidification of PCM) and, as a consequence the panel is heated up. After long time, longer than 3 days, the panel, in terms of its mean temperature, would reach quasi-steady state. These results show that appropriate selection of phase change temperature is crucial for the proper operation of the storage unit.
8. Conclusions There were two main goals of the study presented in this paper. The first one was related to the development of numerical model (and computational code) of heat transfer occurring during operation of the special thermal energy storage unit integrated with building structure and building ventilation system that was based on the use of phase change material (PCM). A particular attention was paid on the modelling of convective heat transfer between air stream and the walls of the panel. A specific function describing the variations of heat transfer coefficient along the channel was determined and validated by experimental results. Other boundary conditions, of minor significance, were also modified during validation of the whole mathematical model of the process. The other goal of the study was related to the parametric analysis of the thermal behavior of the panel (storage unit) in different operational conditions, that couldn’t be investigated experimentally due to limitations of experimental set-up. This analysis revealed some specific features of the unit. The main one is the importance of the proper selection of phase change material, in terms of its melting point, with regard to environmental conditions, here, the daily variations of ambient air temperature. Mismatch of PCM properties to the characteristics of daily ambient temperature changes in a given region may be the reason of incorrect operation of heat storage unit or incomplete utilization of its potential. Quantitative information of the operational characteristics of the unit, e.g. attenuation of air temperature variations as a function of air mass flow rate, were also determined.
Acknowledgments This project has received funding from the Warsaw University of Technology in the framework of statutory activity as well as from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 657466 (INPATH-TES).
References [1] N. Soares, J.J. Costa, A.R. Gaspar, P. Santos, Review of passive PCM latent heat thermal energy storage systems towards buildings’ energy efficiency, Energy Build. 59 (2013) 82–103. [2] M. Pomianowski, P. Heiselberg, Y. Zhang, Review of thermal energy storage technologies based on PCM application in buildings, Energy Build. 67 (2013) 56–69. [3] A. Waqas, Z.U. Din, Phase change material (PCM) storage for free cooling of buildings. A review, Renewable Sustainable Energy Rev. 18 (2013) 607–625. [4] L.F. Cabeza, A. Castell, C. Barreneche, A. de Gracia, A.I. Fernández, Materials used as PCM in thermal energy storage in buildings: A review, Renew. Sustain. Energy Rev. 15 (2011) 1675–1695. [5] C. Veerakumar, A. Sreekumar, Phase change material based cold thermal energy storage: materials, techniques and applications. A review, Int. J. Refrigeration 67 (2016) 271–289, http://dx.doi.org/10.1016/j.ijrefrig.2015. 12.005. [6] A. Solé, H. Neumann, S. Niedermaier, I. Martorell, P. Schossig, L.F. Cabeza, Stability of sugar alcohols as PCM for thermal energy storage, Sol. Energy Mater. Sol. Cells 126 (2014) 125–134. [7] A. Sari, A. Karaipekli, Preparation and thermal properties of capric acid/palmitic acid eutectic mixture as a phase change energy storage material, Mater. Lett. 62 (2008) 903–906. [8] C. Liu, Y. Yuan, N. Zhang, X. Cao, X. Yang, A novel PCM of lauric-myristic-stearic acid/ expanded graphite composite for thermal energy storage, Mater. Lett. 120 (2014) 43–46. [9] L. Royon, L. Karim, A. Bontemp, Optimization of PCM embedded in a floor panel developed for thermal management of the lightweight envelope of buildings, Energy Build. 82 (2014) 385–390. [10] N. Soares, A.R. Gaspar, P. Santos, J.J. Costa, Multi-dimensional optimization of the incorporation of PCM-drywalls in lightweight steel-framed residential buildings in different climates, Energy Build. 70 (2014) 411–421. [11] L. Navarro, A. de Gracia, A. Castell, L.F. Cabeza, Experimental evaluation of a concrete core slab with phase change materials for cooling purposes, Energy Build. 116 (2016) 411–419. [12] H. Weinläder, F. Klinker, M. Yasin, PCM cooling ceilings in the Energy Efficiency Center – passive cooling potential of two different system designs, Energy Build. 119 (2016) 93–100. [13] E. Solgi, R. Fayaz, B.M. Kari, Cooling load reduction in office buildings of hotarid climate, combining phase change materials and night purge ventilation, Renewable Energy 85 (2016) 725–731. [14] G. Zhou, M. Mengmeng Pang, Experimental investigations on the performance of a collector–storage wall system using phase change materials, Energy Convers. Manage. 105 (2015) 178–188. [15] R. Barzin, J. Chen, B. Young, M. Farid, Application of PCM energy storage in combination with night ventilation for space cooling, Appl. Energy 158 (2015) 412–421. [16] S. Ramakrishnan, X. Wang, J. Sanjayan, J. Wilson, Thermal performance of buildings integrated with phase change materials to reduce heat stress risks during extreme heatwave events, Appl. Energy 194 (2017) 410–421, http://dx. doi.org/10.1016/j.apenergy.2016.04.084. [17] S.M. Sajjadian, J. Lewis, S. Sharples, The potential of phase change materials to reduce domestic cooling energy loads for current and for future UK climates, Energy Build. 93 (2015) 83–89. [18] M. Jaworski, Thermal performance of building element containing phase change material (PCM) integrated with ventilation system – an experimental study, Appl. Therm. Eng. 70 (2014) 665–674. [19] M. Jaworski, P. Łapka, P. Furman´ski, Numerical modelling and experimental studies of thermal behavior of building integrated thermal energy storage unit in a form of a ceiling panel, Appl. Energy 113 (2014) 548–557. [20] http://www.micronal.de/portal/basf, (access on November, 2016). [21] M. Jaworski, S. Abeid, Thermal conductivity of gypsum containing phase change material (PCM) for building applications, J. Power Technol. 91 (2) (2011) 49–53. [22] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. Dewitt, Fundamentals of Heat and Mass Transfer, Wiley, 2011.