Journal of Building Performance Simulation ISSN: 1940-1493 (Print) 1940-1507 (Online) Journal homepage: https://www.tandfonline.com/loi/tbps20 Phenomenological modelling of phase transitions with hysteresis in solid/liquid PCM Tilman Barz, Johannn Emhofer, Klemens Marx, Gabriel Zsembinszki & Luisa F. Cabeza To cite this article: Tilman Barz, Johannn Emhofer, Klemens Marx, Gabriel Zsembinszki & Luisa F. Cabeza (2019): Phenomenological modelling of phase transitions with hysteresis in solid/liquid PCM, Journal of Building Performance Simulation, DOI: 10.1080/19401493.2019.1657953 To link to this article: https://doi.org/10.1080/19401493.2019.1657953 © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group Published online: 05 Sep 2019. Submit your article to this journal Article views: 114 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=tbps20 JOURNAL OF BUILDING PERFORMANCE SIMULATION https://doi.org/10.1080/19401493.2019.1657953 Phenomenological modelling of phase transitions with hysteresis in solid/liquid PCM Tilman Barz a, Johannn Emhofera, Klemens Marxa, Gabriel Zsembinszkib and Luisa F. Cabezab aAIT Austrian Institute of Technology GmbH, Giefingasse 2, 1210 Vienna, Austria; bGREiA Research Group, INSPIRES Research Centre, University of Lleida, Pere de Cabrera s/n, 25001 Lleida, Spain ABSTRACT ARTICLE HISTORY Technical-grade and mixed solid/liquid phase change materials (PCM) typically melt and solidify over a Received 17 January 2019 temperature range, sometimes exhibiting thermal hysteresis. Three phenomenological phase transition Accepted 15 August 2019 models are presented which are directly parametrized using data from complete melting and solidification KEYWORDS experiments. They predict hysteresis phenomena and are used to calculate effective PCM properties. Two Solid/liquid phase transition; models have already been implemented in commercial building simulation and/or multiphysics software, static hysteresis models; but not the third novel model. Applications are presented for two commercial PCM: a paraffin, and a salt identification of PCM water mixture with additives. Numerical implementation aspects are discussed, and significant differences properties; incomplete in the predicted absorbed and released heat are highlighted when simulating consecutive incomplete melting and solidification; phase transitions. The models are linked with energy balance equations to predict recorded PCM temper- enthalpy–temperature atures of a thermal energy storage. The cross-validation with data from 26 partial load conditions clearly curves indicate a superior predictive performance of the novel hysteresis model. 1. Introduction (data-based) approach without consideration of physical pro- The performance of a latent heat thermal energy storage (LHTES) cesses inside the PCM. Accordingly, the following definition is with solid/liquid phase change material (PCM) critically depends used (Barz and Sommer 2018): on the thermo-physical PCM properties and its phase transi- tion behaviour. Established building performance simulation Definition: (Hysteresis during temperature-induced phase tools mostly ignore complex phase transition characteristics, transitions of solid/liquid PCM) The term hysteresis is used to indi- relevant for many commercial PCM used in real applications cate that different PCM state parameters, i.e. values of enthalpy h (Al-Saadi and Zhai 2013). A major shortcoming of these simu- or phase fraction ξ, can be found for the same temperature value lation tools is the lack of suitable models for the description of T, depending on the direction of change of T, and possibly also thermal hysteresis (Goia, Chaudhary, and Fantucci 2018). Ther- on the rate of change of T. mal hysteresis effects are complex in nature. They are normally induced by supercooling which is caused by complex nucle- Following the phenomenological approach for modelling ation and crystal growth mechanisms. Corresponding mecha- thermal hysteresis, Goia, Chaudhary, and Fantucci (2018) used nistic macroscopic modelling approaches for PCM can be found two different building simulation software (EnergyPlusTM:and e.g. in Ziskind (2014) and Uzan et al. (2017). Experimental analy- WufiPro/Plus), to implement different phenomenological sis of hysteresis effects are presented e.g. in Diaconu, Varga, and phase transition models which are defined by enthalpy– Oliveira (2010). temperature curves. These curves are derived from the PCM heat In contrast to the mechanistic modelling approach for the capacity and phase transition data obtained from various calori- analysis of hysteresis in the solid/liquid phase transition of metric methods, including differential scanning calorimetry PCM, this contribution follows a purely phenomenological (DSC) for complete melting and solidification (Goia, Chaudhary, CONTACT Tilman Barz [email protected] AIT Austrian Institute of Technology GmbH, Giefingasse 2, 1210 Vienna, Austria © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. 2 T. BARZ ET AL. and Fantucci 2018). The models implement enthalpy– transitions, was applied recently to model hysteresis phenom- temperature curves which correspond to the curve for complete ena in PCM for thermal energy storages by Barz and Som- melting, complete solidification, or an average between both mer (2018). To take up the naming convention established in the curves. The experimental validation of these models with tem- documentation of NRGsim, in the following this model is referred perature data from various PCM during consecutive complete to as ‘curve scale’ model. The ‘curve scale’ model accounts for and incomplete phase transitions revealed adequate simulation different hysteresis magnitudes for cycles within the phase tran- results for PCM with low hysteresis during complete phase tran- sition temperature range and makes use of the temperature sitions. However, high inaccuracies were found for incomplete history. A variant of the ‘curve scale’ model was also proposed transitions and PCM showing significant hysteresis effects (Goia, by Delcroix (2015); Delcroix, Kummert, and Daoud (2017)and Chaudhary, and Fantucci 2018). The same approach for identifi- implemented in TRNSYS. First studies with the ‘curve scale’ cation of complete transition models and their use for modelling model, and comparison with experimental temperature data of complete phase transitions was followed by Frei (2016), Vir- recorded in a LHTES showed convincing results in terms of pre- gone and Trabelsi (2016), Michel et al. (2017), Biswas et al. (2018) diction of hysteresis effects during partial charging and discharg- and Hu and Heiselberg (2018) using COMSOL MultiphysicsR , ing operation (Barz and Sommer 2018). and by Diaconu and Cruceru (2010), Moreles, Huelsz, and Bar- This contribution continues the work started by Barz and rios (2018), and Gasia et al. (2018) using in-house simulation Sommer (2018) on the application of the ‘curve scale’ model code. for PCM and presents a systematic comparative analysis of the An alternative phenomenological modelling approach for three different hysteresis models, namely the ‘curve track’, ‘curve the consideration of hysteresis and varying enthalpy– switch’ and the ‘curve scale’ models. The models are applied temperature relationship was proposed by Gowreesunker, Tas- to predict temperature-induced phase transitions in technical- sou, and Kolokotroni (2012), Gowreesunker and Tassou (2013) grade solid/liquid PCM mixtures. They are rate-independent and and Kumarasamy et al. (2016, 2017). The so called ‘source term’ thus, predict equilibrium states of the PCM. These states charac- approach uses a heat source term in the PCM energy bal- terize the PCM solid, liquid or mushy state.1 The phase transition ance equation model to represent the latent heat during phase models might be used to predict thermo-physical properties, change. This modelling technique corresponds to the default e.g. PCM enthalpies. They can be applied for the numerical solu- solidification/melting model in ANSYS Fluent (Kumarasamy tion of heat transfer problems in PCM. et al. 2017). The authors use DSC heat capacity data obtained for For the ‘curve track’ and ‘curve switch’ hysteresis models complete melting and for complete solidification. From this data implementations are available in commercial building simula- two different models for the latent heat evolution with temper- tion and/or multiphysics software. For the ‘curve scale’ hysteresis ature are derived. This approach is also restricted to the analy- model proposed in this contribution no such implementation sis of hysteresis effects for complete melting and solidification exists. The purpose of this contribution is firstly, to provide a experiments. detailed analysis on the numerical implementation and perfor- All mentioned models realize (or track) enthalpy– mance of all three models, and secondly, to present a quanti- temperature transition curves identified either for complete tative assessment