PFEM; Thermal energy storage; Phase change material; Adaptive mesh refinement
Abstract :
[en] Purpose
The purpose of this study is to improve the numerical simulation of thermal energy storage systems based on phase change materials (TES–PCM). These systems involve strong nonlinearities due to phase change and natural convection, which makes their design challenging. This study focuses on enhancing computational efficiency and accuracy in modeling the phase transition process through an adaptive mesh strategy within the particle finite element method (PFEM).
Design/methodology/approach
The authors implement PFEM for the simulation of TES–PCM, allowing dynamic remeshing during computation. A new mesh adaptation strategy is proposed to optimize spatial discretization in the mushy zone, based on thermal gradients rather than distance fields. The methodology is validated using experimental data from the literature and verified through a fin-placement optimization problem.
Findings
The proposed method accurately reproduces experimental melting fronts for lauric acid and gallium while reducing computational time by up to 25% compared to classical mesh adaptation. The approach captures the influence of natural convection and fin placement, confirming its robustness and predictive capability for TES–PCM applications.
Originality/value
To the best of the authors’ knowledge, this is the first application of PFEM to TES–PCM problems. The new mesh adaptation criterion enhances efficiency without compromising accuracy, offering a promising alternative to classical fixed-mesh CFD methods. The findings highlight the potential of PFEM as a flexible and efficient tool for simulating phase change problems and guiding the design of TES devices.
Research Center/Unit :
LTAS-MN2L
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Claeskens, Maxence; University of Liège Aerospace and Mechanical Engineering Department, , Liège,
Bogucki, Dorian ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Février, Simon ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Lacroix, Martin ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Boman, Romain ; Université de Liège - ULiège > Département d'aérospatiale et mécanique
Ponthot, Jean-Philippe ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > LTAS-Mécanique numérique non linéaire
Fernández, Eduardo; University of Liège Aerospace and Mechanical Engineering Department, , Liège,
Language :
English
Title :
Thermo-fluid simulation of latent heat thermal energy storage devices using the particle finite element method
Publication date :
19 March 2026
Journal title :
International Journal of Numerical Methods for Heat and Fluid Flow
E. Fernández and M. Lacroix acknowledge the research project TiNTHyN, as part of the
Win4Excellence program − convention 2310142, Walloon Region of Belgium.
Agrawal, S., Sutheesh, P., Kirankumar, L. and Rohinikumar, B. (2025), “Numerical investigations on thermal performance of latent heat thermal energy storage system with novel corrugated annular fins in PCM”, Journal of Energy Storage, Vol. 125, p. 116902.
Akhmetov, B., Navarro, M., Seitov, A., Kaltayev, A., Bakenov, Z. and Ding, Y. (2019), “Numerical study of integrated latent heat thermal energy storage devices using nanoparticle-enhanced phase change materials”, Solar Energy, Vol. 194, pp. 724-741.
Bobach, B.-J., Boman, R., Celentano, D., Terrapon, V.E. and Ponthot, J.-P. (2021), “Simulation of the Marangoni effect and phase change using the particle finite element method”, Applied Sciences, Vol. 11 No. 24, p. 11893.
Bouckaert, S., Pales, A.F., McGlade, C., Remme, U., Wanner, B., Varro, L., D’Ambrosio, D. and Spencer, T. (2021), “Net zero by 2050: a roadmap for the global energy sector”.
Cabeza, L.F. (2021), “Advances in thermal energy storage systems: methods and applications”, Advances in Thermal Energy Storage Systems, Elsevier, pp. 37-54.
Carman, P.C. (1997), “Fluid flow through granular beds”, Chemical Engineering Research and Design, Vol. 75, pp. S32-S48.
Cerquaglia, M.L. (2019), “Development of a fully-partitioned PFEM-FEM approach for fluid-structure interaction problems characterized by free surfaces, large solid deformations, and strong added-mass effects”, PhD thesis, University of Liège, Liège, Belgium.
Çolak, E., Öztop, H.F. and Ekici, Ö. (2022), “Analysis of the gallium melting problem with different heating configurations”, Journal of Energy Storage, Vol. 50, p. 104651.
Cremonesi, M., Franci, A., Idelsohn, S. and Oñate, E. (2020), “A state of the art review of the particle finite element method (PFEM)”, Archives of Computational Methods in Engineering, Vol. 27 No. 5, pp. 1709-1735.
Edelsbrunner, H. and Mücke, E.P. (1994), “Three-dimensional alpha shapes”, ACM Transactions On Graphics (TOG), Vol. 13 No. 1, pp. 43-72.
Falla, R., Bobach, B.-J., Boman, R., Ponthot, J.-P. and Terrapon, V.E. (2023), “Mesh adaption for two-dimensional bounded and free-surface flows with the particle finite element method”, Computational Particle Mechanics, Vol. 10 No. 5, pp. 1049-1076.
Fernández, E., Février, S., Lacroix, M., Boman, R. and Ponthot, J.-P. (2023b), “Generalized-α scheme in the PFEM for velocity-pressure and displacement-pressure formulations of the incompressible Navier–Stokes equations”, International Journal for Numerical Methods in Engineering, Vol. 124 No. 1, pp. 40-79.
Fernández, E., Février, S., Lacroix, M., Boman, R., Papeleux, L. and Ponthot, J.-P. (2023a), “A particle finite element method based on level–set functions”, Journal of Computational Physics, Vol. 487, p. 112187.
Fernández, E., Lacroix, M., Février, S., Zhang, T., Papeleux, L., Bobach, B.-J., Boman, R., Ryelandt, S., Simar, A. and Ponthot, J.-P. (2024), “Modelling melt pool dynamics in aluminium-to-steel welds performed by friction melt bonding: a challenge addressed with the particle finite element method”, Computational Particle Mechanics, Vol. 12 No. 6, pp. 1-17.
Février, S. (2020), Travail de Fin D’etudes: Development of a Compressible Flow Solver for PFEM Fluid Simulations, University of Liège, Liège, Belgium.
Février, S., Fernández, E., Lacroix, M., Boman, R. and Ponthot, J.-P. (2025), “Simulation of melt pool dynamics including vaporization using the particle finite element method”, Computational Mechanics, Vol. 75 No. 6, pp. 1787-1815.
Fritts, M. and Boris, J. (1979), “The Lagrangian solution of transient problems in hydrodynamics using a triangular mesh”, Journal of Computational Physics, Vol. 31 No. 2, pp. 173-215.
Garoosi, F., Kantzas, A. and Irani, M. (2025), “Numerical analysis of thermal performance in phase change material (PCM) melting within rectangular and square enclosures: impact of design parameters”, Energy, Vol. 326, p. 136185.
Gau, C. and Viskanta, R. (1986), “Melting and solidification of a pure metal on a vertical wall”.
Idelsohn, S.R., Oñate, E. and Pin, F.D. (2004), “The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves”, International Journal for Numerical Methods in Engineering, Vol. 61 No. 7, pp. 964-989.
Idelsohn, S.R., Nigro, N.M., Gimenez, J.M., Rossi, R. and Marti, J.M. (2013), “A fast and accurate method to solve the incompressible Navier-Stokes equations”, Engineering Computations, Vol. 30 No. 2, pp. 197-222.
Ismail, M., Dincer, I. and Bicer, Y. (2024), “Modeling and simulation of nano-enriched latent heat thermal storage system for concentrated solar energy”, Journal of Energy Storage, Vol. 78, p. 110071.
Joshi, V. and Rathod, M.K. (2020), “Experimental and numerical assessments of thermal transport in fins and metal foam infused latent heat thermal energy storage systems: a comparative evaluation”, Applied Thermal Engineering, Vol. 178, p. 115518.
Kalapala, L. and Devanuri, J.K. (2021), “Effect of orientation on thermal performance of a latent heat storage system equipped with annular fins–an experimental and numerical investigation”, Applied Thermal Engineering, Vol. 183, p. 116244.
Kamkari, B. and Shokouhmand, H. (2014), “Experimental investigation of phase change material melting in rectangular enclosures with horizontal partial fins”, International Journal of Heat and Mass Transfer, Vol. 78, pp. 839-851.
Kang, Z., Tan, R., Yao, Q., Zhang, J., Zhang, S. and Wei, Y. (2025), “Numerical simulation of energy storage radiant floor heating systems with phase change materials having different thermophysical properties”, Construction and Building Materials, Vol. 463, p. 140010.
Kiros, A.K., Zeru, B.A., Desisa, D.G. and Tewolde, D.G. (2025), “Fin geometry optimization for enhanced PCM solidification in solar cooking thermal storage system: numerical simulation and experimental validation”, International Journal of Thermofluids, Vol. 27, p. 101243.
Kozeny, J. (1927), “Ueber kapillare Leitung des Wassers im Boden”, Sitzungsberichte Der Akademie Der Wissenschaften in Wien, Vol. 136, p. 271.
Kumar, R. and Verma, P. (2020), “An experimental and numerical study on effect of longitudinal finned tube eccentric configuration on melting behaviour of lauric acid in a horizontal tube-in-shell storage unit”, Journal of Energy Storage, Vol. 30, p. 101396.
Lacroix, M. (2025), “Robust PFEM-FEM partitioned coupling framework for the simulation of solids under complex flow-induced loads”.
Lacroix, M., Fernández, E., Février, S., Papeleux, L., Boman, R. and Ponthot, J.-P. (2026), “An efficient level set-based mesh adaptation for the particle finite element method”, Computer Methods in Applied Mechanics and Engineering, Vol. 450, p. 118644.
Lacroix, M., Février, S., Fernández, E., Papeleux, L., Boman, R. and Ponthot, J.-P. (2024), “A comparative study of interpolation algorithms on non-matching meshes for PFEM-FEM fluid-structure interactions”, Computers and Mathematics with Applications, Vol. 155, pp. 51-65.
Liu, X., Huang, Y., Zhang, X., Zhang, C. and Zhou, B. (2020), “Investigation on charging enhancement of a latent thermal energy storage device with uneven tree-like fins”, Applied Thermal Engineering, Vol. 179, p. 115749.
Liu, W., Mokhtari, M., Hussein, M.A., Kumar, A., Albayati, T.M., Bains, P.S., Abdul-Redha, H.K., Salahshour, S. and Hekmatifar, M. (2024), “Investigation of the arrangement of aluminum fins on the thermal behavior of lauric acid as a phase change material in a two-pipe heat exchanger by CFD simulation”, Case Studies in Thermal Engineering, Vol. 64, p. 105469.
Meng, E., Xia, T., Zhao, J., Song, Y., Li, J. and Zhao, H. (2025), “Numerical study on thermal environment of plastic greenhouse with high absorption latent heat storage plate (LHSP)”, Applied Thermal Engineering, Vol. 278, p. 127376.
Nandi, A. and Biswas, N. (2025), “Melting dynamics and energy efficiency of nano-enhanced phase change material (NePCM) with graphene, Al2O3, and CuO for superior thermal energy storage (TES)”, Journal of Energy Storage, Vol. 109, p. 115076.
Pourakabar, A. and Darzi, A.A.R. (2019), “Enhancement of phase change rate of PCM in cylindrical thermal energy storage”, Applied Thermal Engineering, Vol. 150, pp. 132-142.
Rodriguez, J., Carbonell, J.M., Cante, J. and Oliver, J. (2016), “The particle finite element method (PFEM) in thermo-mechanical problems”, International Journal for Numerical Methods in Engineering, Vol. 107 No. 9, pp. 733-785.
Rodríguez, J.M., Carbonell, J.M., Cante, J. and Oliver, J. (2017), “Continuous chip formation in metal cutting processes using the particle finite element method (PFEM)”, International Journal of Solids and Structures, Vol. 120, pp. 81-102.
Rozenfeld, A., Kozak, Y., Rozenfeld, T. and Ziskind, G. (2017), “Experimental demonstration, modeling and analysis of a novel latent-heat thermal energy storage unit with a helical fin”, International Journal of Heat and Mass Transfer, Vol. 110, pp. 692-709.
Sadaka, G., Rakotondrandisa, A., Tournier, P.-H., Luddens, F., Lothodé, C. and Danaila, I. (2020), “Parallel finite-element codes for the simulation of two-dimensional and three-dimensional solid–liquid phase-change systems with natural convection”, Computer Physics Communications, Vol. 257, p. 107492.
Safari, V., Abolghasemi, H. and Kamkari, B. (2021), “Experimental and numerical investigations of thermal performance enhancement in a latent heat storage heat exchanger using bifurcated and straight fins”, Renewable Energy, Vol. 174, pp. 102-121.
Shokouhmand, H. and Kamkari, B. (2013), “Experimental investigation on melting heat transfer characteristics of lauric acid in a rectangular thermal storage unit”, Experimental Thermal and Fluid Science, Vol. 50, pp. 201-212.
Singh, R.P., Xu, H., Kaushik, S., Rakshit, D. and Romagnoli, A. (2019), “Effective utilization of natural convection via novel fin design and influence of enhanced viscosity due to carbon nano-particles in a solar cooling thermal storage system”, Solar Energy, Vol. 183, pp. 105-119.
Tiari, S., Hockins, A. and Mahdavi, M. (2021), “Numerical study of a latent heat thermal energy storage system enhanced by varying fin configurations”.
Xu, Y., Zheng, Z.-J., Yang, C. and Cai, X. (2021), “Intelligent optimization of horizontal fins to improve the melting performance of phase change materials in a square cavity with isothermal vertical wall”, Journal of Energy Storage, Vol. 44, p. 103334.
Zhang, S., Mancin, S. and Pu, L. (2023), “A review and prospective of fin design to improve heat transfer performance of latent thermal energy storage”, Journal of Energy Storage, Vol. 62, p. 106825.
Zhang, W., Zhong, Z-h., Peng, C., Yuan, W-h. and Wu, W. (2021), “GPU-accelerated smoothed particle finite element method for large deformation analysis in geomechanics”, Computers and Geotechnics, Vol. 129, p. 103856.
Zhang, L., Ahmad, S.F., Nutakki, T.U.K., Agrawal, M.K., Ghfar, A.A., Chauhdary, S.T. and Youshanlouei, H.M. (2024), “Charging an inclined PCM storage exposed to time-varying solar radiation: latent heat thermal energy storage”, Journal of Energy Storage, Vol. 90, p. 111911.