- Email: [email protected]
Validation of heat transfer models for PCMs with a conductivimeter
Available online at www.sciencedirect.com
Energy Procedia 30 (2012) 395 – 403
SHC 2012
Validation of heat transfer models for PCMs with a conductivimeter Aitor Urrestia,*, Jose María Salaa, Ana García-Romerob, Gonzalo Diarceb, Cesar Escuderoa a
b
University of the Basque Country UPV/EHU, Dpt. of Thermal Engines, Alda. Urquijo s/n, Bilbao, 48012, Spain University of the Basque Country UPV/EHU, Dpt. of Mining Eng, Metalurgy and Material Sciences, Beurko s/n, Barakaldo, 48902, Spain
Abstract In order to evaluate the accuracy and performance of two different heat transfer models for PCM containing systems, a thermal testing has been performed in a conductivimeter. A mixture of PCM and gypsum was submitted to a cyclic surface temperature change inside the conductivimeter, measuring heat fluxes and temperatures. The results of this test were used to validate two different heat transfer models, based on finite differences and on neural networks. Both heat transfer models were compared with the test results, showing good agreement with experimental data in both cases (mean error less than 5%) and a better performance (accuracy and calculation time) for the neural network.
© 2012 Published Publishedby byElsevier ElsevierLtd. Ltd.Selection Selection and/or peer-review responsibility of PSE and peer-review under under responsibility of the PSE AG AG Keywords: PCM; heat transfer model; finite difference; neural network
1. Introduction Buildings are great energy consumers, as seen from the statistics: 40% of energy consumption in Europe [1], and almost 36% worldwide [2]. The forthcoming energy and environmental crisis requires a call for action in two directions: energy consumption reduction, and the promotion of non-polluting renewable energy. Among these energy sources, solar energy is very advantageous, because of its wide availability.
*
Corresponding author. Tel.: +34-94-601-4402 E-mail address: [email protected].
1876-6102 © 2012 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the PSE AG doi:10.1016/j.egypro.2012.11.047
396
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
Nomenclature
h
specific enthalpy (kJ/kg)
k
conductivity (W/mK)
q
heat flux (W/m2)
T
temperature (ºC)
ȡ
Density (kg/m3)
ǻt
time interval (s)
ǻx
distance interval (m)
Phase Change Materials, or PCMs, are a promising complement to solar energy applications. Taking advantage of the high energy density provided by the latent heat of PCMs, less storage volume and mass is needed, with a more stable temperature profile in the storage system, minimizing overheating [3]. Designing an efficient thermal storage unit with PCMs requires a deep knowledge of the heat transfer processes that occur inside the PCM while it is changing phase. The simulation of heat transfer processes in PCMs is still an issue under study. There are several different approaches, as can be seen from literature [4-6]. Many of them are based on the heat diffusion equation, which is solved by the finite difference method or by the finite elements method. These are direct methods in the sense that they use the basic heat transfer equations. Indirect methods can also be used, which are based on experimental results, and use generic equations in which some parameters are adjusted to obtain the model by error minimizing. Neural networks are starting to be used for PCM heat transfer models, because of their good performance in highly non-linear systems, the speed of calculation, and their suitability for parallel computing systems[7-10]. One of the drawbacks for a wider use of latent heat storage through PCMs is the lack of standardization. The optimal type of PCM and the amount to be used depends on climatological conditions, user profile, and the objectives to achieve. From the many possible applications for PCM, the present work is focused on the modeling of wallboards with PCM. The highly non-linear thermal behavior of these materials requires an accurate simulation of their behavior, in order to optimize its benefits. The simulation methods employed need to be validated before using them, so that their accuracy is proved and evaluated. Even more, in the case of indirect methods, experimental data is needed to obtain the parameters of the models. Different testing methods have been developed to obtain the experimental data needed for the validation of the direct models, or for the training of indirect models, from small scale systems, to large scale ones. Rudd [11] compared the results from a DSC with those from a large scale room size testing, for a wallboard with PCM. The results showed that DSC underestimated by 8.7% the real scale data. The main disadvantage of large scale testing is the economical cost of the testing system, even if some standardized testing facilities could be used, such as guarded hot box systems [12] or Paslink cells [13]. On the other hand, small scale testing can be useful for homogeneous materials, but the small sample size, in the range of mg, reduces the accuracy for heterogeneous materials. Even more, the heat transfer
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
processes occurring in these small scale testing systems do not correctly represent those of real scale, mainly dominated by one-dimensional heat transfer. The present work proposes an alternative method to obtain experimental data and validate direct modeling systems or train indirect modeling systems. A standard conductivimeter has been used to test a medium-size sample, as is explained below. The design of the conductivimeter ensures a one-dimensional heat transfer, which correctly replicates the behavior of real-scale wallboards. The smaller scale of the testing facility, together with the fact of this being a standard measuring system, allow for a less expensive testing solution, without loosing accuracy. 2. Procedure A mixture of gypsum and microencapsulated PCM was used in the sample. The PCM used was Micronal 21, from BASF. The mixture is an experimental product of the company Beissier. The sample size was 600mmx600mmx70mm. The sample was tested in a Netzsch HFM 436/6/1 Lambda conductivimeter, as can be seen in Fig. 1. Different temperature and heat flux sensor were used: two surface heat flux sensors at each external surface, with an accuracy of ± 0.1 W/m2, three PT100 temperature sensors in each surface, with an accuracy of ± 0.2ºC. At three different depths, a thermocouple was placed, with an accuracy of ± 0.4ºC.
Fig. 1. (a) Sample in the conductivimeter (b) Surface sensors
The sample was submitted to a cyclic temperature change in both surfaces. Heat flux on both surfaces, and temperatures were measured during the testing, which lasted 48.5 hours. The lower and higher temperatures were selected to obtain complete fusion and solidification of the PCM in each cycle, being these 2ºC and 43ºC. These tests were also used to evaluate the conductivities of the sample, which are displayed in Table 1. Fig. 2 shows the recorded heat fluxes and surface temperatures during testing. Two different approaches have been used to model the problem. The first of them is a direct method using finite differences, in an explicit way. The second method used is a neural network that uses two neural layers combining sigmoid, and linear neurons. This architecture was used because of its versatility to accommodate a large amount of physical problems.
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Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
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3. Results 3.1. Finite difference method In order to model the heat transfer processes occurring during the test, a finite difference method has been used. In this case, a one-dimensional, explicit method has been used, using the enthalpy approach, as proposed by Shamsundar and Sparrow [14], but with some modifications. First of all, our proposal is based on an explicit differentiation scheme, which allows for a faster calculation at each timestep. Second, the exact enthalpy-calculation curve is used, instead of a linearization. And third, no dimensionless variables were used. Taking these into account, the equation for the algorithm is the following: (1)
Both conductivities appearing in equation (1) are the equivalent conductivities to the left and the right of the element, and are calculated as proposed by Patankar [15] as follows: (2)
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Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
The properties used for the equation are listed in Table 1. Table 1. Properties of the sample Property
Value
Units
Density
800
kg/m3
Conductivity PCM solid
0.131
W/(mK)
Conductivity PCM liquid
0.188
W/(mK)
These equations have been implemented in a Fortran program developed by the authors. As contour values, the surface temperature has been used. The results of the model are then compared with the experimental data. The first comparison is done with the temperature in the centre of the sample, as this is the one less influenced by the imposed surface temperature. Both, experimental and simulated temperatures are displayed in Fig. 3. ϰϱ
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The results show a good agreement between the test and the simulation. Mayor error appears in the phase change interval during heating, with a time difference of less than one minute. Mean absolute error is 0.9ºC, being the relative error 4%. The maximum time difference encountered during phase change is 52 s, which is a good result, taking into account that the algorithm is intended to be used for long time simulations (building energy consumption through a year).
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Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
Heat fluxes have also been compared in order to evaluate the accuracy of the model. Heat fluxes have been calculated on both surfaces, using the calculated temperatures, and a differentiated version of Fourier’s law: (3) Fig. 4 shows the comparison between the heat fluxes evaluated this way, from simulated data, and the heat fluxes measured during testing. As can be seen, the simulation follows the shape of the measured data, but with a certain degree of error. Absolute main error y 6.1 W/m2 and relative error is 3.3%. ϭϱϬ
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Fig. 4. Comparison of experimental and simulated heat flux with the finite difference method
Analyzing these results, an acceptable degree of accuracy has been obtained. The main disadvantage of this method is the large calculation time required even for short time periods. Stability limitation imposes a large amount of nodes and time steps to be evaluated in order to obtain an acceptable accuracy. Another important drawback of this method is that it can only be applied to homogeneous systems, in which some equivalent properties can be used for the whole system. If some kind of heterogeneity at the macro scale is present, the simulation becomes more complex. The main advantage of this method is that it is general, and can be applied to any PCM, as long as it thermophysical properties are known.
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
3.2. Neural network method Neural networks are highly interconnected network of artificial neurons. Each one of these neurons performs a simple mathematical equation, like sigmoids or linear functions. This is a “black-box” type simulation method in which some interval parameters are adjusted so that the model replies some known experimental data. In the case of neural networks, the parameters to be adjusted are the weights linking the neurons. Due to the high interconnection between neurons, neural networks are very versatile, and suitable for complex non-linear problem simulation[16]. An example of such a network is shown in Fig. 5.
Fig. 5. A schematic image of a neural network
For the present work, a three layer network has been employed, similar to the one in Fig. 5. The first layer is the input layer. In this case the input to the network are the last three temperatures on each surface of the sample, requiring 6 neurons. The second layer, known as hidden-layer is composed of 35 neurons, each of them applying the hyperbolic tangent function to their input. The third layer, known as output layer, is composed of two neurons, applying a linear function to their inputs, and obtaining the heat fluxes at each surface as an output. The calculated heat flux obtained as an output of the network is shown in Fig. 6, together with the heat flux measured during the test. The fitting between simulated data and experimental is so close that they can hardly be distinguished. Absolute mean error is 0.34 W/m2, which is much lower than that obtained with the finite difference method. If needed, the accuracy could be adjusted adding or reducing the number of neurons in the hidden layer in order to improve or reduce the accuracy respectively. In addition to the improved accuracy, this method lacks the main drawbacks of the finite difference method. First of all the neural network is much faster to be evaluated, taking just a few seconds to to simulate the whole test, while the finite difference method takes around 5 minutes. On the other hand, the neural network method is also suitable for heterogeneous systems, as long as experimental data is available for the adjustment of the parameters in the network. The main drawback of this method is that the network is only valid for the thermophysical properties it has been adjusted for. In case a different PCM was to be simulated, new experimental data should be needed, to readjust the network’s parameters. In this case, a new testing in conductivimeter could be carried out, with the new PCM.
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Fig. 6. Comparison of experimental and calculated heat flux with neural networks
4. Conclusions A testing has been carried out in a conductivimeter in order to validate two different simulation methods for PCMs, one of them based on finite difference method, and the other based on neural networks. The simulation method based on finite differences, is less accurate, requires long calculation times, and is not suitable for heterogeneous materials, but its formulation is based on the thermophysical properties of the materials, and can be used for any homogeneous system with PCMs. On the other hand, the neural network method is more accurate, and very fast to calculate, but needs previous experimental data to adjust its internal parameters, and a different network is needed for each material.
Acknowledgements The present work is part of two research projects: MEC2007. BIA2007-65896: New materials for the envelope of the building with climatic functions and SAIOTEK 2010: GaipelBi. The authors want to thank the Spanish Government and the Government of the Basque Country, as well as the University of the Basque Country, for the funding and trust received to perform this research. Special mention should be done to the Construction Quality Control Laboratory of the Basque Government / Laboratorio de Control de Calidad en la Edificación del Gobierno Vasco (LCCE) where the conductivimeter tests were
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
carried out. The author would also like to thank the company Beissier for their mixture of PCM and gypsum, and their kind help. Besides, research efforts in this field are also coordinated through the COST TU 0802 project: Next generation cost effective phase change materials for increased energy efficiency in renewable energy systems in buildings (NeCoE-PCM).
References [1] Eurostat. Epp.Eurostat.Ec.Europa.Eu n.d. [2] IEA. Key World Energy Statistics 2011. IEA; 2011. [3] Zalba B, Marin J, Cabeza LF, Mehling H. Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Applied Thermal Engineering 2003;23:251–83. [4] Dutil Y, Rousse DR, Salah NB, Lassue S, Zalewski L. A review on phase-change materials: Mathematical modeling and simulations. Renew Sust Energ Rev 2011;15:112–30. [5] Myers T. Optimal exponent heat balance and refined integral methods applied to Stefan problems. International Journal of Heat and Mass Transfer 2010;53:1119–27. [6] Kuznik F, David D, Johannes K, Roux J-J. A review on phase change materials integrated in building walls. Renew Sust Energ Rev 2011;15:379–91. [7] Varol Y, Koca A, Oztop HF, Avci E. Forecasting of thermal energy storage performance of Phase Change Material in a solar collector using soft computing techniques. Expert Systems with Applications 2009;37:2724–32. [8] Ermis K, Erek A, Dincer I. Heat transfer analysis of phase change process in a finned-tube thermal energy storage system using artificial neural network. International Journal of Heat and Mass Transfer 2007;50:3163–75. [9] Kanesan J, Arunasalam P, Seetharamu KNN, Azid IA. Artificial neural network trained, genetic algorithms optimized thermal energy storage heatsinks for electronics cooling, IPACK2005, ASME InterPACK'05, 2005, pp. 1389–95. [10].Kovacecic I, Poredos A, Šarler B. Solving the Stefan Problem with the Radial Basis Function Collocation Method. Numerical Heat Transfer, Part B 2003;44:575–99. [11] Rudd A. Phase-Change Material Wallboard for Distributed Thermal Storage in Buildings. ASHRAE Transactions 1993;99:339–46. [12] Brown W, Stephenson D. A Guarded Hot Box Procedure for Determining the Dynamic Response of Full-Scale Wall Specimens. Part I. ASHRAE Transactions 1993;99:632–42. [13] Urresti Gonzalez A, Diarce G, García-Romero A, Delgado A, Erkoreka A, Escudero C, Campos Celador A. Ventilated active façades with PCM, Innostock Conference Proceedings, 2012. [14] Shamsundar N, Sparrow E. Analysis of multi-dimensional conduction phase change via the enthalpy model. Journal of Heat Transfer 1975;97:333–40. [15] Patankar S. Numerical Heat Transfer and Fluid Flow. Taylor & Francis; 1980. [16] Hagan MT, Demuth HB, Beale M. Neural Network Design. PWS Publishing Company; 1996.
403
Energy Procedia 30 (2012) 395 – 403
SHC 2012
Validation of heat transfer models for PCMs with a conductivimeter Aitor Urrestia,*, Jose María Salaa, Ana García-Romerob, Gonzalo Diarceb, Cesar Escuderoa a
b
University of the Basque Country UPV/EHU, Dpt. of Thermal Engines, Alda. Urquijo s/n, Bilbao, 48012, Spain University of the Basque Country UPV/EHU, Dpt. of Mining Eng, Metalurgy and Material Sciences, Beurko s/n, Barakaldo, 48902, Spain
Abstract In order to evaluate the accuracy and performance of two different heat transfer models for PCM containing systems, a thermal testing has been performed in a conductivimeter. A mixture of PCM and gypsum was submitted to a cyclic surface temperature change inside the conductivimeter, measuring heat fluxes and temperatures. The results of this test were used to validate two different heat transfer models, based on finite differences and on neural networks. Both heat transfer models were compared with the test results, showing good agreement with experimental data in both cases (mean error less than 5%) and a better performance (accuracy and calculation time) for the neural network.
© 2012 Published Publishedby byElsevier ElsevierLtd. Ltd.Selection Selection and/or peer-review responsibility of PSE and peer-review under under responsibility of the PSE AG AG Keywords: PCM; heat transfer model; finite difference; neural network
1. Introduction Buildings are great energy consumers, as seen from the statistics: 40% of energy consumption in Europe [1], and almost 36% worldwide [2]. The forthcoming energy and environmental crisis requires a call for action in two directions: energy consumption reduction, and the promotion of non-polluting renewable energy. Among these energy sources, solar energy is very advantageous, because of its wide availability.
*
Corresponding author. Tel.: +34-94-601-4402 E-mail address: [email protected].
1876-6102 © 2012 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the PSE AG doi:10.1016/j.egypro.2012.11.047
396
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
Nomenclature
h
specific enthalpy (kJ/kg)
k
conductivity (W/mK)
q
heat flux (W/m2)
T
temperature (ºC)
ȡ
Density (kg/m3)
ǻt
time interval (s)
ǻx
distance interval (m)
Phase Change Materials, or PCMs, are a promising complement to solar energy applications. Taking advantage of the high energy density provided by the latent heat of PCMs, less storage volume and mass is needed, with a more stable temperature profile in the storage system, minimizing overheating [3]. Designing an efficient thermal storage unit with PCMs requires a deep knowledge of the heat transfer processes that occur inside the PCM while it is changing phase. The simulation of heat transfer processes in PCMs is still an issue under study. There are several different approaches, as can be seen from literature [4-6]. Many of them are based on the heat diffusion equation, which is solved by the finite difference method or by the finite elements method. These are direct methods in the sense that they use the basic heat transfer equations. Indirect methods can also be used, which are based on experimental results, and use generic equations in which some parameters are adjusted to obtain the model by error minimizing. Neural networks are starting to be used for PCM heat transfer models, because of their good performance in highly non-linear systems, the speed of calculation, and their suitability for parallel computing systems[7-10]. One of the drawbacks for a wider use of latent heat storage through PCMs is the lack of standardization. The optimal type of PCM and the amount to be used depends on climatological conditions, user profile, and the objectives to achieve. From the many possible applications for PCM, the present work is focused on the modeling of wallboards with PCM. The highly non-linear thermal behavior of these materials requires an accurate simulation of their behavior, in order to optimize its benefits. The simulation methods employed need to be validated before using them, so that their accuracy is proved and evaluated. Even more, in the case of indirect methods, experimental data is needed to obtain the parameters of the models. Different testing methods have been developed to obtain the experimental data needed for the validation of the direct models, or for the training of indirect models, from small scale systems, to large scale ones. Rudd [11] compared the results from a DSC with those from a large scale room size testing, for a wallboard with PCM. The results showed that DSC underestimated by 8.7% the real scale data. The main disadvantage of large scale testing is the economical cost of the testing system, even if some standardized testing facilities could be used, such as guarded hot box systems [12] or Paslink cells [13]. On the other hand, small scale testing can be useful for homogeneous materials, but the small sample size, in the range of mg, reduces the accuracy for heterogeneous materials. Even more, the heat transfer
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
processes occurring in these small scale testing systems do not correctly represent those of real scale, mainly dominated by one-dimensional heat transfer. The present work proposes an alternative method to obtain experimental data and validate direct modeling systems or train indirect modeling systems. A standard conductivimeter has been used to test a medium-size sample, as is explained below. The design of the conductivimeter ensures a one-dimensional heat transfer, which correctly replicates the behavior of real-scale wallboards. The smaller scale of the testing facility, together with the fact of this being a standard measuring system, allow for a less expensive testing solution, without loosing accuracy. 2. Procedure A mixture of gypsum and microencapsulated PCM was used in the sample. The PCM used was Micronal 21, from BASF. The mixture is an experimental product of the company Beissier. The sample size was 600mmx600mmx70mm. The sample was tested in a Netzsch HFM 436/6/1 Lambda conductivimeter, as can be seen in Fig. 1. Different temperature and heat flux sensor were used: two surface heat flux sensors at each external surface, with an accuracy of ± 0.1 W/m2, three PT100 temperature sensors in each surface, with an accuracy of ± 0.2ºC. At three different depths, a thermocouple was placed, with an accuracy of ± 0.4ºC.
Fig. 1. (a) Sample in the conductivimeter (b) Surface sensors
The sample was submitted to a cyclic temperature change in both surfaces. Heat flux on both surfaces, and temperatures were measured during the testing, which lasted 48.5 hours. The lower and higher temperatures were selected to obtain complete fusion and solidification of the PCM in each cycle, being these 2ºC and 43ºC. These tests were also used to evaluate the conductivities of the sample, which are displayed in Table 1. Fig. 2 shows the recorded heat fluxes and surface temperatures during testing. Two different approaches have been used to model the problem. The first of them is a direct method using finite differences, in an explicit way. The second method used is a neural network that uses two neural layers combining sigmoid, and linear neurons. This architecture was used because of its versatility to accommodate a large amount of physical problems.
397
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Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
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3. Results 3.1. Finite difference method In order to model the heat transfer processes occurring during the test, a finite difference method has been used. In this case, a one-dimensional, explicit method has been used, using the enthalpy approach, as proposed by Shamsundar and Sparrow [14], but with some modifications. First of all, our proposal is based on an explicit differentiation scheme, which allows for a faster calculation at each timestep. Second, the exact enthalpy-calculation curve is used, instead of a linearization. And third, no dimensionless variables were used. Taking these into account, the equation for the algorithm is the following: (1)
Both conductivities appearing in equation (1) are the equivalent conductivities to the left and the right of the element, and are calculated as proposed by Patankar [15] as follows: (2)
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Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
The properties used for the equation are listed in Table 1. Table 1. Properties of the sample Property
Value
Units
Density
800
kg/m3
Conductivity PCM solid
0.131
W/(mK)
Conductivity PCM liquid
0.188
W/(mK)
These equations have been implemented in a Fortran program developed by the authors. As contour values, the surface temperature has been used. The results of the model are then compared with the experimental data. The first comparison is done with the temperature in the centre of the sample, as this is the one less influenced by the imposed surface temperature. Both, experimental and simulated temperatures are displayed in Fig. 3. ϰϱ
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The results show a good agreement between the test and the simulation. Mayor error appears in the phase change interval during heating, with a time difference of less than one minute. Mean absolute error is 0.9ºC, being the relative error 4%. The maximum time difference encountered during phase change is 52 s, which is a good result, taking into account that the algorithm is intended to be used for long time simulations (building energy consumption through a year).
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Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
Heat fluxes have also been compared in order to evaluate the accuracy of the model. Heat fluxes have been calculated on both surfaces, using the calculated temperatures, and a differentiated version of Fourier’s law: (3) Fig. 4 shows the comparison between the heat fluxes evaluated this way, from simulated data, and the heat fluxes measured during testing. As can be seen, the simulation follows the shape of the measured data, but with a certain degree of error. Absolute main error y 6.1 W/m2 and relative error is 3.3%. ϭϱϬ
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Fig. 4. Comparison of experimental and simulated heat flux with the finite difference method
Analyzing these results, an acceptable degree of accuracy has been obtained. The main disadvantage of this method is the large calculation time required even for short time periods. Stability limitation imposes a large amount of nodes and time steps to be evaluated in order to obtain an acceptable accuracy. Another important drawback of this method is that it can only be applied to homogeneous systems, in which some equivalent properties can be used for the whole system. If some kind of heterogeneity at the macro scale is present, the simulation becomes more complex. The main advantage of this method is that it is general, and can be applied to any PCM, as long as it thermophysical properties are known.
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
3.2. Neural network method Neural networks are highly interconnected network of artificial neurons. Each one of these neurons performs a simple mathematical equation, like sigmoids or linear functions. This is a “black-box” type simulation method in which some interval parameters are adjusted so that the model replies some known experimental data. In the case of neural networks, the parameters to be adjusted are the weights linking the neurons. Due to the high interconnection between neurons, neural networks are very versatile, and suitable for complex non-linear problem simulation[16]. An example of such a network is shown in Fig. 5.
Fig. 5. A schematic image of a neural network
For the present work, a three layer network has been employed, similar to the one in Fig. 5. The first layer is the input layer. In this case the input to the network are the last three temperatures on each surface of the sample, requiring 6 neurons. The second layer, known as hidden-layer is composed of 35 neurons, each of them applying the hyperbolic tangent function to their input. The third layer, known as output layer, is composed of two neurons, applying a linear function to their inputs, and obtaining the heat fluxes at each surface as an output. The calculated heat flux obtained as an output of the network is shown in Fig. 6, together with the heat flux measured during the test. The fitting between simulated data and experimental is so close that they can hardly be distinguished. Absolute mean error is 0.34 W/m2, which is much lower than that obtained with the finite difference method. If needed, the accuracy could be adjusted adding or reducing the number of neurons in the hidden layer in order to improve or reduce the accuracy respectively. In addition to the improved accuracy, this method lacks the main drawbacks of the finite difference method. First of all the neural network is much faster to be evaluated, taking just a few seconds to to simulate the whole test, while the finite difference method takes around 5 minutes. On the other hand, the neural network method is also suitable for heterogeneous systems, as long as experimental data is available for the adjustment of the parameters in the network. The main drawback of this method is that the network is only valid for the thermophysical properties it has been adjusted for. In case a different PCM was to be simulated, new experimental data should be needed, to readjust the network’s parameters. In this case, a new testing in conductivimeter could be carried out, with the new PCM.
401
402
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
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Fig. 6. Comparison of experimental and calculated heat flux with neural networks
4. Conclusions A testing has been carried out in a conductivimeter in order to validate two different simulation methods for PCMs, one of them based on finite difference method, and the other based on neural networks. The simulation method based on finite differences, is less accurate, requires long calculation times, and is not suitable for heterogeneous materials, but its formulation is based on the thermophysical properties of the materials, and can be used for any homogeneous system with PCMs. On the other hand, the neural network method is more accurate, and very fast to calculate, but needs previous experimental data to adjust its internal parameters, and a different network is needed for each material.
Acknowledgements The present work is part of two research projects: MEC2007. BIA2007-65896: New materials for the envelope of the building with climatic functions and SAIOTEK 2010: GaipelBi. The authors want to thank the Spanish Government and the Government of the Basque Country, as well as the University of the Basque Country, for the funding and trust received to perform this research. Special mention should be done to the Construction Quality Control Laboratory of the Basque Government / Laboratorio de Control de Calidad en la Edificación del Gobierno Vasco (LCCE) where the conductivimeter tests were
Aitor Urresti et al. / Energy Procedia 30 (2012) 395 – 403
carried out. The author would also like to thank the company Beissier for their mixture of PCM and gypsum, and their kind help. Besides, research efforts in this field are also coordinated through the COST TU 0802 project: Next generation cost effective phase change materials for increased energy efficiency in renewable energy systems in buildings (NeCoE-PCM).
References [1] Eurostat. Epp.Eurostat.Ec.Europa.Eu n.d. [2] IEA. Key World Energy Statistics 2011. IEA; 2011. [3] Zalba B, Marin J, Cabeza LF, Mehling H. Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Applied Thermal Engineering 2003;23:251–83. [4] Dutil Y, Rousse DR, Salah NB, Lassue S, Zalewski L. A review on phase-change materials: Mathematical modeling and simulations. Renew Sust Energ Rev 2011;15:112–30. [5] Myers T. Optimal exponent heat balance and refined integral methods applied to Stefan problems. International Journal of Heat and Mass Transfer 2010;53:1119–27. [6] Kuznik F, David D, Johannes K, Roux J-J. A review on phase change materials integrated in building walls. Renew Sust Energ Rev 2011;15:379–91. [7] Varol Y, Koca A, Oztop HF, Avci E. Forecasting of thermal energy storage performance of Phase Change Material in a solar collector using soft computing techniques. Expert Systems with Applications 2009;37:2724–32. [8] Ermis K, Erek A, Dincer I. Heat transfer analysis of phase change process in a finned-tube thermal energy storage system using artificial neural network. International Journal of Heat and Mass Transfer 2007;50:3163–75. [9] Kanesan J, Arunasalam P, Seetharamu KNN, Azid IA. Artificial neural network trained, genetic algorithms optimized thermal energy storage heatsinks for electronics cooling, IPACK2005, ASME InterPACK'05, 2005, pp. 1389–95. [10].Kovacecic I, Poredos A, Šarler B. Solving the Stefan Problem with the Radial Basis Function Collocation Method. Numerical Heat Transfer, Part B 2003;44:575–99. [11] Rudd A. Phase-Change Material Wallboard for Distributed Thermal Storage in Buildings. ASHRAE Transactions 1993;99:339–46. [12] Brown W, Stephenson D. A Guarded Hot Box Procedure for Determining the Dynamic Response of Full-Scale Wall Specimens. Part I. ASHRAE Transactions 1993;99:632–42. [13] Urresti Gonzalez A, Diarce G, García-Romero A, Delgado A, Erkoreka A, Escudero C, Campos Celador A. Ventilated active façades with PCM, Innostock Conference Proceedings, 2012. [14] Shamsundar N, Sparrow E. Analysis of multi-dimensional conduction phase change via the enthalpy model. Journal of Heat Transfer 1975;97:333–40. [15] Patankar S. Numerical Heat Transfer and Fluid Flow. Taylor & Francis; 1980. [16] Hagan MT, Demuth HB, Beale M. Neural Network Design. PWS Publishing Company; 1996.
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