Original Article
Development and verification of an EnergyPlus-based algorithm to predict heat transfer through building walls integrated with phase change materials
Journal of Building Physics 2016, Vol. 40(1) 77–95 Ó The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1744259115591252 jen.sagepub.com
Kyoung Ok Lee1, Mario A Medina1 and Xiaoqin Sun2
Abstract A conduction finite difference algorithm developed for EnergyPlus was used to model building walls integrated with phase change materials. The model was validated by comparing it against experimental data in terms of temperatures, wall heat fluxes, and total wall heat transfer. Experimental data, using two identical test houses of conventional residential construction, were collected for the validation and further analyses. The thermal performance of walls without phase change materials (control house) and with phase change materials (retrofit house) was evaluated. The model showed that the differences between experimental and predicted total heat transfer values were under 5%. The total heat transfer reductions produced by phase change materials could be predicted accurately using the conduction finite difference algorithm in EnergyPlus.
1
Department of Civil, Environmental and Architectural Engineering, The University of Kansas, Lawrence, KS, USA
2
School of Energy and Power Engineering, Changsha University of Science & Technology, Changsha, PR China Corresponding author: Mario A Medina, Department of Civil, Environmental and Architectural Engineering, The University of Kansas, Lawrence, KS 66045, USA. Email:
[email protected]
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Keywords Phase change materials, thermal energy storage, wall heat transfer, construction materials, phase change material model, EnergyPlus
Introduction Only a few whole-building energy simulation programs account for the thermal energy storage effects of phase change materials (PCM) that are integrated in building enclosures. Some of them are the transient system simulation tool (TRNSYS; Solar Energy Laboratory, 2012), ESP-r (Hand, 2011), and EnergyPlus (2013). TRNSYS is a transient system simulation program with a modular structure. Several modules for PCM modeling have been developed (Ahmad et al., 2006; Ghoneim et al., 1991; Iba´n˜ez et al., 2005; Kuznik and Virgone, 2009; Schranzhofer et al., 2006; Stritih and Novak, 1996). One such module is a simplified PCM module that was developed and added to its commercially available version (Thermal Energy System Specialists, LLC, 2013). The module simulates PCMs as an internal layer within an enclosure system. The model is currently limited to its assumptions that materials melt and solidify isothermally and have constant specific heats in both the solid and liquid phases. In addition, in the transition state, the temperature of the solid–liquid interface of the PCM is assumed constant. ESP-r is a dynamic energy simulation tool used for modeling thermal, visual, and acoustic performance of buildings. ESP-r has the capability to model PCMs using the effective heat capacity method and the heat source method (Heim and Clarke, 2004; Schossig et al., 2005). While simulation results using ESP-r have been found in the literature, none have shown any substantial validations against experimental data. EnergyPlus is a building energy analysis and thermal energy simulation program (US Department of Energy, 2013). EnergyPlus was developed in 2001 to combine the best features and capabilities of two existing building energy simulation programs: BLAST (building energy analysis and system thermodynamics) and DOE2. BLAST was developed in the early 1970s, sponsored by the US Department of Defense (DOD), and DOE-2 was developed in the late 1960s, sponsored by the US Department of Energy (DOE). EnergyPlus was developed with the intention of making the development of the programming tool less expensive with faster periodic update releases and to allow users to make modifications and extensions. As a result, EnergyPlus consists of modular structures for adding new features and integrating it with other programs (Crawley et al., 2000). EnergyPlus was tested and validated using industry-accepted standard methods (US Department of Energy, 2013). The PCM model within EnergyPlus was validated by comparing its results with experimental data and other models such as Heating 7.3 (Tabares-Velasco et al., 2012). In this article, EnergyPlus was used to simulate the energy dynamics through the walls of conventional residential buildings with and without PCM.
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Numerical model PCM model in EnergyPlus In general, EnergyPlus uses a conduction finite difference (CondFD) solution algorithm to model the heat transfer in the presence of PCMs. This algorithm is known as CondFD (Tabares-Velasco et al., 2012). In addition, EnergyPlus includes two schemes for the solution of the finite difference model. One is the Crank–Nicholson and the other is referred to as fully implicit. The Crank–Nicholson and the fully implicit schemes are finite difference methods used to solve partial differential equations (e.g. heat conduction equation) numerically. Both schemes approximate the solution of the heat conduction equation on finite grids with discretization in space and time (Ames, 1992). The Crank–Nicholson scheme has advantages when dealing with time-accurate solutions because its truncation error is significantly smaller than the truncation error of other schemes. The fully implicit scheme happens to be very stable when dealing with relatively large time steps (Hoffman, 1992). For this research, the Crank–Nicholson scheme was selected because it offered a higher accuracy (Ames, 1992). The Crank–Nicholson scheme was coupled with an enthalpy–temperature function (HTF) to model the heat conduction through the PCM-integrated enclosure components. The formulation for the Crank–Nicholson scheme is shown in equation (1) (EnergyPlus, 2013) " ! +1 j+1 j+1 j+1 Tij + 1 Tij 1 (Tij+ T ) (T T ) i i 1 kW + kE i1 = Cp rDx 2 Dx Dx Dt !# ð1Þ j (Tij+ 1 Tij ) (Ti1 Tij ) + kE + kW Dx Dx where Cp was the specific heat of the material; r was the density of the material; Dx was the finite difference layer thickness; T represents the temperature of a node; Dt was the calculation time step; i was the node being modeled; i + 1 and i 2 1 were adjacent nodes to interior and exterior of a material layer, respectively; j + 1 and j were new and previous time steps, respectively; and kW and kE were the thermal conductivities. Equation (1) was coupled with the HTF, which was given by hi (Ti ) = HTF(Ti )
ð2Þ
where h(T) was the enthalpy node as a function of temperature and T was the temperature node. The HTF was specified from in-house differential scanning calorimeter (DSC) experimental data for the PCM used in the building enclosure. The HTF was then used to develop an equivalent specific heat (Cp) for each time step.
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Table 1. Experimental temperature and corresponding enthalpy for the PCM used in the building enclosure. Temperature (°C)
Enthalpy (kJ/kg)
210.0 0.1 11.6 18.0 23.6 26.0 26.9 29.0 30.4 31.4 31.7 32.1 33.2 35.7 40.7 60.0
0.001 14.8 30.4 39.9 51.7 61.6 68.4 101.5 142.1 189.0 201.2 208.3 212.5 215.9 222.6 245.0
PCM inputs in EnergyPlus In addition to the standard data required by EnergyPlus (e.g. weather data, indoor conditions, enclosure materials geometry and dimensions, operating schedules, and so on) for the case of simulating PCMs, PCM enthalpy and thermal conductivity as functions of temperature were also required by CondFD. Enthalpy of PCM as a function of temperature. Because the enthalpy of the PCM varies as a function of temperature, several values of enthalpy were input based on PCM temperature. A two column table of temperature with its corresponding enthalpy was constructed based on the in-house DSC experiments. This is shown in Table 1 for the PCM used in the building enclosure of this research. The values of Table 1 covered the entire temperature range that the PCM would experience during the simulations. Once the enthalpy–temperature inputs were set, EnergyPlus calculated the enthalpy in a linear fashion based on any two temperature points from the given enthalpy–temperature curve shown in Figure 1. An equivalent specific heat as a function of temperature, Cp(T), at each time step, was developed by the HTF of Figure 1 for the PCM contained in the building enclosure. The Cp(T) was formulated by Cp (T ) =
hji hj1 i Tij Tij1
ð3Þ
where Cp(T) was the specific heat as a function of temperature, h was the enthalpy node, and T was the temperature node.
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Figure 1. Calculated enthalpy as a function of temperature for the PCM contained in the building enclosure and used by CondFD from Table 1.
Table 2. Conductivity of the PCM contained in the building enclosure (Mehling and Cabeza, 2008). Temperature (°C)
Conductivity (W/m°C)
\18 (Solid) .33 (Liquid)
1.088 0.540
Thermal conductivity of PCM as a function of temperature. The thermal conductivity of a PCM varies with its phase (e.g. solid and liquid). In other words, the thermal conductivity of a PCM is dependent on its temperature. In EnergyPlus, one of two input fields was required to provide variable thermal conductivities: variable thermal conductivity (VTC) or temperature coefficient for thermal conductivity (TCTC) (EnergyPlus, 2013). In this article, the VTC was specified by entering the thermal conductivities that corresponded to the temperatures as indicated in Table 2, which shows the conductivities for the PCM. The temperature range of phase transition of Table 2 and Figure 2 was derived from the DSC experimental data. Based on Table 2 and Figure 2, CondFD calculated the thermal conductivity of the PCM as a function of temperature. According to Figure 2, the value of the conductivity of the PCM in its solid state was 1.088 W/m°C. Similarly, the value of the conductivity in its
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Figure 2. Calculated conductivity as a function of temperature for the PCM contained in the building enclosure and used by CondFD from Table 2.
liquid state was 0.540 W/m°C. When the PCM was undergoing phase transition, its conductivity was calculated based on the linear function between its solid and liquid states.
Model validation Experiments were carried out under real weather conditions with the purpose of validating the model presented in the previous section.
Experimental set-up—test houses The experiments to obtain data for the validation of the model were performed using two identical 1.83 3 1.83 3 1.22 m test houses located in the central zone of the United States, with coordinates of 38.97 °N and 95.24 °W, where the climate includes hot and humid summers and cold and dry winters. The houses were constructed using conventional North American residential construction and were space conditioned using instrumented scaled down space cooling and heating systems. The test houses are shown in Figure 3. One house was kept as the control and the other house was modified to include the retrofits. Within the retrofit house, only the south and west walls were outfitted with the PCM. The walls were constructed of 0.95-cm plywood siding, 5.08- by 10.16-cm studs, and 0.95-cm wallboards. Five layers of rigid polystyrene foam board, each with a thermal resistance of 0.53 m2°C/W and thickness of 1.27 cm, were installed in the cavities of the walls.
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Figure 3. Test houses (southwest view).
To collect surface and air temperature data, type T thermocouples (T/C) were used. For each surface or air temperature, T/C grids were assembled in parallel, where the measured temperatures represented the average temperature of the T/Cs grids. The measurement error of the T/Cs was 60.6 °C. In addition, heat flux meters (HFMs), with dimension of 5.08 3 5.08 3 0.48 cm, were installed on the interior surfaces of the walls to collect heat fluxes through both the south and west walls. The measurement error of the HFMs was 62%. A weather station collected weather data, which included outdoor air temperature, outdoor air relative humidity, wind speed and direction, rainfall, and solar irradiation.
Phase change material thermal shields The PCM was integrated into the walls via aluminized sheets lined with a polymeric film on both inside surfaces where PCM-carrying pouches were held in place. That is, the PCM was contained within these sealed polymer pouches. In this article, this PCM integration method is referred to as phase change material thermal shield (PCMTS). Figure 4 shows a sample sheet of PCMTS. Figure 5 shows an example of how the PCMTS would be installed, in a wall cavity, next to the wallboard; however, in this validation, the PCMTS was installed at a distance of 2.54 cm from the wallboard. This is shown in Figure 6. This location (2.54 cm from the wallboard) was selected because the experimental data indicated that a PCMTS installed at this location would produce optimal heat flux reductions (Lee et al., 2015).
PCM properties The PCMTS carried a hydrated salt-based PCM. In-house DSC experiments with a heating rate of 0.5 °C/min were conducted to obtain thermal properties of this PCM. These included specific heat, latent and total heat storage capacities, latent heat of fusion, enthalpy, melting temperature, and onset of melting temperature.
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Figure 4. A sheet of PCMTS.
Figure 5. Example of an installed PCMTS inside the wall cavities.
These measured properties were the inputs to the model. Figure 7 shows the endotherm process of the PCM. The melting temperature range was 18.0 °C–38.0 °C, the melting peak temperature was 31.36 °C, the onset of melting temperature was 24.79 °C, and the latent heat of fusion was 149.9 J/g.
Results and discussion Model validation for the control case The heat transfer through the south and west walls of the test house (Figure 3) was modeled using the same materials and dimensions as described in the previous
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Figure 6. Schematic of a wall section showing the selected location of the PCMTS for the model validation.
Figure 7. Endotherm process of the PCM contained in the PCMTS.
section. A modeling schematic of the test house is shown in Figure 8. Model predictions without the PCMTS were obtained to verify the accuracy of the inputs of the wall components. Model predictions were then compared against the experimental
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Figure 8. Modeling schematic of the test house.
data of the control house to verify the accuracy of the model. The weather data that were collected during the experiments were used for this modeling. Figures 9 and 10 show heat flux and temperature comparisons of the model predictions against experimental data for the south and west walls, respectively. From the temperature graphs of Figures 9 and 10, the average outdoor air temperatures were between 24.03 °C and 41.90 °C while the indoor air temperatures were maintained at an average of 21.34 °C. The average exterior surface temperature ranges of the south and west walls were 22.49 °C–56.65 °C and 23.24 °C–66.12 °C, respectively. The model predictions of the heat fluxes through the south wall as well as exterior surface temperatures, shown in Figure 9, were relatively close to the experimental values including peaks and valleys. The discrepancies in the comparison of these values were the result of several factors, including (1) the differences in indoor air temperatures between the experimental data and the simulation data, (2) measurement errors, and (3) the use of published values for the thermal properties of the construction materials. For example, the model assumed that the indoor air temperature values were constant; however, keeping these values constant during the experiments proved impossible because the summer in which these experiments were carried out was unusually hot. In terms of experimental errors, the sudden and short-duration peaks observed in the heat flux data at the beginning of the peak periods were the result of a blast of cold air blowing over the heat flux sensors when the fan coil units initially started. As expected, sudden experimental events were not modeled. Therefore, when comparing peaks, only those values that were sustained for longer periods of time were used. The average difference between predicted and experimental peaks of the heat fluxes was 24.5%. The difference between predicted and experimental
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Figure 9. Model prediction and experimental heat fluxes through the south wall (top) and temperatures (bottom).
total heat transfer was 210.9%. The average difference in exterior surface temperature peaks was 21.04 °C and the temperature difference between averaged predicted and experimental values of surface temperatures was 20.40 °C.
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Figure 10. Model prediction and experimental heat fluxes through the west wall (top) and temperatures (bottom).
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Figure 10 shows the comparisons between the predicted and experimental values for the west wall. Similar to Figure 9, as explained in the case of the south wall, the heat flux curves of the model predictions show highly comparable trends. The average difference between predicted and experimental peaks of the heat fluxes was 24.4%. The difference between predicted and experimental total heat transfer was 11.9%. The average difference in exterior surface temperature peaks was 23.19 °C and the temperature difference between averaged predicted and experimental values of surface temperatures was 20.20 °C. Sudden, short-duration peaks were also observed in the west wall data. Again, these were the results of cold air flowing over the heat flux sensors once the fan coil unit started. From the model predictions of the control cases for the south and west walls, it was observed that the peak heat fluxes and the average exterior surface temperatures were similar to the experimental values. The predicted total heat transfer for the south wall was slightly underestimated, while the predicted total heat transfer for the west wall was slightly overestimated.
Model validation for the retrofit case The test house south and west walls with the PCMTSs were modeled and the results were compared against the experimental data to verify the accuracy of both the PCM inputs obtained in the previous section and the ability of CondFD to model the phase transition aspects of the PCM. It is recommended that time steps should be equal to or less than 3 min, and a space discretization constant should be between 0.3 and 0.5 for hourly performance analysis (Tabares-Velasco et al., 2012). In this research, 1 min for the time steps and 0.3 for the space discretization constant were used. For the phase transition aspects of the PCM, the enthalpy as a function of temperature in Table 1 and the thermal conductivity as a function of temperature in Table 2 were used. In addition, other necessary inputs related to the PCM had to be provided. These are shown in Table 3. Figures 11 and 13 show the comparisons between the predicted and experimental values for the south and west walls of the retrofit test house, respectively. Figures 12 and 14 show the comparisons between the experimental and predicted heat fluxes for the control and retrofit south and west walls, respectively.
Table 3. PCMTS thickness and PCM density. Input value PCM shield thickness PCM density PCM: phase change material; PCMTS: phase change material thermal shields. a ConFD used a single density value.
0.001 m 3266 kg/m3a
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Figure 11. Predicted heat fluxes through the retrofit south wall compared with the experimental data.
Figure 12. Heat flux comparisons for the south wall: (a) experiment and (b) model prediction.
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Figure 13. Predicted heat fluxes through the retrofit west wall compared with the experimental data.
Figure 14. Heat flux comparisons for the west wall: (a) experiment and (b) model prediction.
The average difference between predicted and experimental peaks of the heat fluxes was 9.2% for the retrofit south wall. This is shown in Figure 11. The difference between predicted and experimental total heat transfer was 26.6%. When the PCMTS were added to the wall and modeled, the model predictions (model vs experimental data) show that the model was able to follow the trend of
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the heat fluxes relatively well including peaks and valleys. But, the comparisons were not as close as these were for the control case. This was expected because of the following reasons: (1) although the thin PCM layer was at the same location for both, model and experiments, the shield created extra air spaces between the shield and the insulation, which were not modeled; (2) the PCMTS was constructed of aluminum foil, which created a reduction in radiation heat transfer between the PCMTS and the insulation, which was also not modeled; (3) the model assumed that the PCM was evenly and symmetrically distributed within the thin PCM layer, which was not the case in the actual experiments; (4) CondFD assumed a constant PCM density regardless of whether the PCM state was solid or liquid; and (5) CondFD was limited to inputs of single enthalpy curve for either the melting process or solidification process. The enthalpy–temperature curve of PCM during solidification process was different with that of the curve for the melting process. This caused discrepancies between the model predictions and the experimental data, especially during the nighttime. In other words, although CondFD is the latest and state-of-the-art algorithm for modeling PCMs in enclosure components, there are still several shortcomings within the existing algorithm. Nevertheless, comparisons of heat flux reductions between predicted control and retrofit cases were within 5.0% (Figure 12) of actual comparisons of control and retrofit cases. This would allow the predictions to be accurate to within an acceptable margin. That is, the predicted heat transfer reductions of the retrofit south wall would be close to the experimental heat transfer reductions. For the west wall, the average difference between predicted and experimental retrofit peaks of the heat fluxes was 7.9%. This is shown in Figure 13. The difference between predicted and experimental total heat transfer was 12.0%. For the case of the control west wall in Figure 10, the difference between predicted and experimental total heat transfer was 11.9%. This implied that the predicted total heat transfer reductions of the retrofit west wall would be within 1% of the experimental results. In other words, with all of its shortcomings, the total heat transfer reductions produced by a PCMTS could be predicted accurately using CondFD. This is in line with the conclusion of Tabares-Velasco et al. (2012) who were members of CondFD development team. The PCM model also did not predict the time delay for the case of retrofit west wall. Figure 14 shows the comparisons between the experimental and predicted heat fluxes for the control and retrofit west walls. Based on the model predictions with the PCM contained in the PCMTS, the predicted heat flux curves were not as similar to the experimental results as in the control cases. In addition to the reasons given above for the differences between model prediction and experimental values, the following reasons also contributed to the discrepancy. The average melting speeds of the PCM during the test periods were 0.009 °C/min and 0.017 °C/min, for the cases of the south and west walls, respectively. The average solidification speeds of the PCM during the same periods were 0.006 and 0.015 °C/min. These were much lower than the minimum time discretization of 1 min allowed by the PCM model in CondFD. Another reason for the discrepancy between model prediction and experimental data was the fact that
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the produced PCM enthalpy as a function of temperature curve of Table 1 and Figure 1 resulted from a DSC heating rate of 0.5 °C/min, while the actual heating and cooling rates were much lower than these values. Therefore, the PCM model could not predict the delays in heat transfer when the PCM was melting or solidifying. This implied that the predicted hourly heat fluxes would not compare favorably to those of the experimental data. However, the model predictions would be comparable to the experimental results on a basis of the total heat transfer reduction comparisons between the retrofit and control south and west walls. It is recommended to validate the PCM model against the experimental data using different types of PCM applications. In addition, model validations for different testing periods would be required. The accuracy of the PCM model in EnergyPlus would be improved if the time steps could be less than 1 min. In addition, it is recommended that the PCM model uses PCM input from the enthalpy– temperature curves for both melting and solidification processes. Furthermore, the PCM model could be improved if variable density of the PCM for its liquid, mixed with liquid and solid, and solid phases was used. The PCM input of VTC requires further study.
Conclusion For modeling, a public-domain building energy simulation software, known as EnergyPlus, that included an open-source algorithm, known as CondFD, was used. CondFD was used for handling the transient heat transfer with phase transition which is characteristic of PCM-outfitted walls. To be able to use the CondFD algorithm, actual values of the enthalpy as a function of temperature and thermal conductivity as a function of temperature had to be determined. These were determined via DSC tests using the PCM contained in the PCMTS. With this information, together with standard modeling information (e.g. building material properties, building dimensions, and climates), the thermal performance of the walls, for both the control and retrofit cases, was evaluated. Comparisons between predicted and experimental heat fluxes and temperatures were carried out for the south and west walls of the test houses. For the pre-retrofit cases, the average differences between predicted and experimental peaks of the heat fluxes were 24.5% and 24.4% for the south and west walls, respectively. The differences between predicted and experimental total heat transfer were 210.9% and 11.9% for the south and west walls, respectively. For the retrofit cases, the average differences between predicted and experimental peaks of the heat fluxes were 9.2% and 7.9% for the south and west walls, respectively. The differences between predicted and experimental total heat transfer were 26.6% and 12% for the south and west walls, respectively. These implied that the predicted total heat transfer reductions of the retrofit south and west walls would be within 5% and 1% of the experimental results, respectively. In other words, with all of its deficiencies, the total heat transfer reductions produced by a PCMTS could be predicted accurately using CondFD.
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Declaration of Conflicting Interests The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.
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Appendix 1 Nomenclature Cp Cp(T) h h(T) k T Dt Dx
specific heat (kJ/kg°C) specific heat as a function of temperature (kJ/kg°C) enthalpy (kJ/kg) enthalpy as a function of temperature (kJ/kg) thermal conductivity (W/m°C) temperature node (°C) calculation time step (s) finite difference layer thickness (m)
Greek symbols r
density (kg/m3)
Subscripts E i i+1 i21 W
interface between i node and i 2 1 node node being modeled adjacent node to interior of construction adjacent node to exterior of construction interface between i node and i + 1 node
Superscripts j j+1
previous time step (s) new time step (s)
