Numerical simulation of constrained melting inside spherical capsule by lattice Boltzmann method

LIN Qi1 WANG Shugang1 WANG Jihong1 SONG Shuanglin1,2

(1.Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, Liaoning, China 116024)
(2.State Key Laboratory of Coal Mine Safety Technology, CCTEG Shenyang Research Institute, Shenyang, Liaoning, China 110016)

【Abstract】Phase change materials (PCMs) are mainly used to provide high storage densities. The spherical geometry is one of the most interesting cases for heat storage applications. The present study used the lattice Boltzmann method (LBM) to investigate constrained melting process of PCMs in a spherical capsule, which can be useful for the study on phase change phenomenon of microencapsulated PCM slurry in the future. The phase interface is traced by updating the total enthalpy, while the moving interface is treated by the immersed moving boundary scheme. The computational results of the melting process of PCMs are analyzed at different scales. The numerical simulations at macro-scale are compared with the published experimental data, and the results clearly show that the thermal stratification is in the upper spherical capsule while the waviness phase front is at the bottom of the solid PCM. Quantitative analysis of the temperatures at nine points, eight points along the vertical axis and the other one near the inner shell, further indicates the existence of chaotic convective motion at the bottom of the spherical capsule. In addition, the effect of the natural convection on the melting process is reduced with the decrease of capsule sizes. When the diameter of capsule is less than 3 mm, the natural convection can be ignored.

【Keywords】 phase change; multiscale; numerical simulation; thermodynamics; lattice Boltzmann method;


【Funds】 National Natural Science Foundation of China (51678102, 51508067)

Download this article

(Translated by CAI TX)


    [1] National Energy Administration. Solar energy development “the 13th Five-year” planning [J]. Solar Energy, 2016, 12(1): 5–14 (in Chinese).

    [2] LIU M J, ZHU Z Q, XU C L, et al. Constrained melting heat transfer of composite phase change materials inside spherical container [J]. Journal of Zhejiang University (Engineering Science), 2016, 50(3): 477–484 (in Chinese).

    [3] KALNES S E, JELLEM B P. Phase change materials and products for building applications: a state-of-the-art review and future research opportunities [J]. Energy and Buildings, 2015, 94(1): 150–176.

    [4] MA Z J, LIN W Y, SOHEL M I. Nano-enhanced phase change materials for improved building performance [J]. Renewable and Sustainable Energy Reviews, 2016, 58(1): 1256–1268.

    [5] YIN H B, GAO X N, ZHANG Z G. Application of phase-change thermal control in heat shock resistance of electronic devices [J]. Journal of Chemical Engineering of Chinese Universities, 2017, 31(3): 554–560 (in Chinese).

    [6] GAO X N, LIU X, SUN T, et al. Research on the thermal management performance of electronic chip with composite phase change material [J]. Journal of Chemical Engineering of Chinese Universities, 2017, 27(2): 187–192 (in Chinese).

    [7] CHEN S T, LI W W, WANG X K, et al. Thermal management using phase change materials for proton exchange membrane fuel cell [J]. CIESC Journal, 2016, 67(S1): 1–6 (in Chinese).

    [8] SHI S, YU J Z, CHEN M D, et al. Battery thermal management system using phase change materials and foam copper [J]. CIESC Journal, 2017, 68(7): 2678–2683 (in Chinese).

    [9] DHAIDAN N S, KHODADADI J M. Melting and convection of phase change materials in different shape containers: a review [J]. Renewable and Sustainable Energy Reviews, 2015, 43(1): 449–477.

    [10] TAN F L. Constrained and unconstrained melting inside a sphere [J]. International Communications in Heat and Mass Transfer, 2008, 35(4): 466–475.

    [11] TAN F L, HOSSEINIZADEH S F, KHODADADI J M, et al. Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule [J]. International Journal of Heat and Mass Transfer, 2009, 52(15/16): 3464–3472.

    [12] ARCHIBOLD A R, RAHMAN M M, GOSWAMI D Y, et al. Analysis of heat transfer and fluid flow during melting inside a spherical container for thermal energy storage [J]. Applied Thermal Engineering, 2014, 64(1): 396–407.

    [13] LEE Y T, HONG S W, CHUNG J D. Effects of capsule conduction and capsule outside convection on the thermal storage performance of encapsulated thermal storage tanks [J]. Solar Energy, 2014, 110(1): 56–63.

    [14] SATTARI H, MOHEBBI A, AFSAHI M M, et al. CFD simulation of melting process of phase change materials (PCMs) in a spherical capsule [J]. International Journal of Refrigeration, 2017, 73(1): 209–218.

    [15] ZHU Z Q, XIAO S L, SHI S H, et al. Constrained melting heat transfer of a phase change material in a finned spherical capsule [J]. Chinese Science Bulletin, 2015, 60(12): 1125–1131 (in Chinese).

    [16] DARZI A R, JOURABIAN M, FARHADI M. Melting and solidification of PCM enhanced by radial conductive fins and nanoparticles in cylindrical annulus [J]. Energy Conversion and Management, 2016, 118(1): 253–263.

    [17] FAN L W, ZHU Z Q, ZENG Y, et al. Unconstrained melting heat transfer in a spherical container revisited in the presence of nano-enhanced phase change materials (NePCM) [J]. International Journal of Heat and Mass Transfer, 2016, 95(1): 1057–1069.

    [18] LIU L K, ALVA G, HUANG X, et al. Preparation, heat transfer and flow properties of microencapsulated phase change materials for thermal energy storage [J]. Renewable and Sustainable Energy Reviews, 2016, 66(1): 399–414.

    [19] FANG Y T, XIE H Z, LIANG X H, et al. Characterization of polystyrene-silica@n-tetradecane composite nano-encapsulated phase change material and its emulsion performance [J]. CIESC Journal, 2015, 66(2): 800–805 (in Chinese).

    [20] FANG Y T, WAN W J. Review on latent functionally thermal fluid [J]. Materials Review, 2009, 23(8): 108–116 (in Chinese).

    [21] LI J L, LIU L. Research progress in mechanical properties of microencapsulated phase change materials used as functional thermal fluid [J]. Chemical Industry and Engineering Progress, 2015, 34(7): 1928–1932 (in Chinese).

    [22] QIU Z Z, MA X L, LI P, et al. Micro-encapsulated phase change material (MPCM) slurries: characterization and building applications [J]. Renewable and Sustainable Energy Reviews, 2017, 77(1): 246–262.

    [23] XIE J C, TANG Y L, ZHANG Z F, et al. Optimum heat storage performance of building envelope under coupling condition of ventilation and phase change [J]. CIESC Journal, 2017, 68(7): 2684–2695 (in Chinese).

    [24] MONDAL S. Phase change materials for smart textiles—an overview [J]. Applied Thermal Engineering, 2008, 28(11): 1536–1550.

    [25] GIRO-PALOMA J, MARTÍNEZ M, CABEZA L F, et al. Types, methods, techniques, and applications for microencapsulated phase change materials (MPCM): a review [J]. Renewable and Sustainable Energy Reviews, 2016, 53(1): 1059–1075.

    [26] HUANG R Z, WU H Y, CHENG P. A new lattice Boltzmann model for solid-liquid phase change [J]. International Journal of Heat and Mass Transfer, 2013, 59(1): 295–301.

    [27] GUO Z L, ZHENG C G, SHI B C. Discrete lattice effects on the forcing term in the lattice Boltzmann method [J]. Physical Review E, 2002, 65(4): 046308.

    [28] KRÜGER T, KUSUMAATMAJA H, KUZMIN A, et al. The Lattice Boltzmann Method: Principles and Practice [M]. Switzerland: Springer International Publishing, 2017: 240–243.

    [29] MOHAMAD A A. Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes [M]. Dordrecht, Netherlands: Springer Science & Business Media, 2011: 54–56.

    [30] HUANG R Z, WU H Y. Total enthalpy-based lattice Boltzmann method with adaptive mesh refinement for solid-liquid phase change [J]. Journal of Computational Physics, 2016, 315(1): 65–83.

    [31] HUANG R Z, WU H Y. Phase interface effects in the total enthalpy-based lattice Boltzmann model for solid-liquid phase change [J]. Journal of Computational Physics, 2015, 294(1): 346–362.

    [32] COOK B K, NOBLE D R, WILLIAMS J R. A direct simulation method for particle-fluid systems [J]. Engineering Computations, 2004, 21(2/3/4): 151–168.

This Article


CN: 11-1946/TQ

Vol 69, No. 06, Pages 2373-2379+2807

June 2018


Article Outline


  • Introduction
  • 1 Numerical model
  • 2 Simulation analysis and discussion
  • 3 Conclusion
  • References