Reviewing Theoretical and Numerical Models for PCM-embedded Cementitious Composites
Abstract
:1. Introduction
2. Review on Thermal Energy Storage Using PCM
3. Experimental Investigations on PCM-Concretes
4. Phase Change Materials: Stefan Problem
- Fixed grid method: In this approach, a grid of spatial nodes used for discretizing the problem remains fixed during time, while the problem is studied with auxiliary constitutive formulations and state functions, which help to trace the phase change phenomena governed by solidification and/or melting. These models are mostly employed and several examples can be found in the scientific literature. Pioneer contributions in this fixed grid method can be found in [94,111,112,113].
- Deformed grid method: In this approach, the nodes forming the grid may move to follow the sharp fronts and interfaces occurring during melting and solidification. These models are thus able to solve the Stefan problem and to follow, by deforming the grid, i.e., the Stefan condition, as the solution evolves [114,115].
5. Fixed Grid Numerical Method
5.1. Enthalpy-Based Method
5.2. Apparent Calorific Capacity Method (ACCM)
5.3. Heat Source Method (HSM)
5.4. Concluding Remarks on Fixed Grid Method
6. Cementitious Porous Materials with PCM: Numerical Models and Scales
6.1. Structural-Scale Models
6.2. Macro-Scale Models
6.3. Meso-Scale Models
7. Concluding Remarks
- A large number of studies on various PCM-related topics are available in the literature. Some of them referring to specific topics from a material point of view (i.e., micro- and macro-encapsulation of PCM, thermal conductivity enhancements, thermal stability), while others refer to the possible field of application of PCMs, like thermal energy storages, high temperature applications, solar water heaters, cold applications, and building accumulation solutions;
- numerical solutions for analyzing the so-called Stefan problem in phase change materials were reviewed and discussed. The literature on different solution approaches was presented discussed;
- fixed grid method, representing the simplest approach for solving thermal problems involving PCMs, were reviewed and the basic equations behind this approach were outlined and discussed;
- in the framework of the fixed grid method, three different approaches were recognized, namely the “enthalpy-based method (EM)”, the “apparent calorific capacity method (ACCM)”, and the “heat source method (HSM)”. All these methods have in common that they are capable of determining a posteriori the movement of the melting/solidification front according to the Stefan problem. The different methods and corresponding models associated with the EM, ACCM, and HSM approach were briefly described and discussed; and
- the available models for PCM-concrete composites, focusing on the different length scales, i.e., micro, meso, macro, and possible multiscale approaches, are being reviewed and discussed. Many articles on PCM-concretes followed a macroscopic and building scale approach, while only few contributions are available in the literature that deal with the meso- to micro-scale level.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Authors | Apparent Heat Capacity—Ceff |
---|---|
Lamberg et al. (2004) [127] Bonacina et al. (1973) [134] Idelsohn et al. (1994) [135] Voller (1997) [136] Pasupathy et al. (2008) [137,138] Zang et al. (2008) [139] Fang and Medina (2009) [140] Thiele et al. (2015) [141] Šavija and Schlangen (2016) [142] | |
Hu and Argyropoulos (1996) [143] | |
Samarskii and Vabishchevivh (1995) [144] Heim and Clarke (2004) [145] Heim (2010) [146] | |
Zukowski (2007) [147] Mankel et al. (2019) [148] | tabular data from DSC tests |
Evola et al. (2013) [149] | |
Thiele et al. (2015) [141,150] (for composite applications: i.e., cementitious ones) | |
Tittelein et al. (2015) [151] Kheradmand et al. (2016) [152] (for composite applications: i.e., cementitious ones) | |
Yao et al. (2018) [153] | melting solidification |
Young et al. (2018) [154] | |
Singh and Bhat (2018) [155] | |
Han et al. (2018) [156] |
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Caggiano, A.; Mankel, C.; Koenders, E. Reviewing Theoretical and Numerical Models for PCM-embedded Cementitious Composites. Buildings 2019, 9, 3. https://doi.org/10.3390/buildings9010003
Caggiano A, Mankel C, Koenders E. Reviewing Theoretical and Numerical Models for PCM-embedded Cementitious Composites. Buildings. 2019; 9(1):3. https://doi.org/10.3390/buildings9010003
Chicago/Turabian StyleCaggiano, Antonio, Christoph Mankel, and Eddie Koenders. 2019. "Reviewing Theoretical and Numerical Models for PCM-embedded Cementitious Composites" Buildings 9, no. 1: 3. https://doi.org/10.3390/buildings9010003