A new lattice Boltzmann (LB) model to solve the phase change problem, which is based on the enthalpy-transforming model has been developed in this paper. The problems of two-region phase change, natural convection of air, and phase change by convection are solved to verify the present LB model. In two-region phase change, the results of the present LB model agree well with that of analytical solution. The benchmark solutions are applied to evaluate the present LB model in natural convection of air and phase change material (PCM) as well. The results show that the present LB model is able to simulate the temperature distribution and capture the location of solid–liquid interface in the cavity accurately. Moreover, the present LB model is effective in computing owing to the fact that no iterations are necessary during the simulations.
Issue Section:
Melting and Solidification
References
1.
Shon
, J.
, Kim
, H.
, and Lee
, K.
, 2014
, “Improved Heat Storage Rate for an Automobile Coolant Waste Heat Recovery System Using Phase-Change Material in a Fin–Tube Heat Exchanger
,” Appl. Energy
, 113
, pp. 680
–689
.2.
Mathur
, A.
, Kasetty
, R.
, Oxley
, J.
, Mendez
, J.
, and Nithyanandam
, K.
, 2014
, “Using Encapsulated Phase Change Salts for Concentrated Solar Power Plant
,” Energy Procedia
, 49
, pp. 908
–915
.3.
Rao
, Z.
, Wang
, S.
, and Zhang
, G.
, 2011
, “Simulation and Experiment of Thermal Energy Management With Phase Change Material for Ageing LiFePO4 Power Battery
,” Energy Convers. Manage.
, 52
(12
), pp. 3408
–3414
.4.
Liu
, C.
, Rao
, Z.
, Zhao
, J.
, Huo
, Y.
, and Li
, Y.
, 2015
, “Review on Nanoencapsulated Phase Change Materials: Preparation, Characterization and Heat Transfer Enhancement
,” Nano Energy
, 13
, pp. 814
–826
.5.
Yang
, J.
, Yang
, L.
, Xu
, C.
, and Du
, X.
, 2015
, “Numerical Analysis on Thermal Behavior of Solid–Liquid Phase Change Within Copper Foam With Varying Porosity
,” Int. J. Heat Mass Transfer
, 84
, pp. 1008
–1018
.6.
Rao
, Z.
, Wang
, S.
, and Peng
, F.
, 2013
, “Molecular Dynamics Simulations of Nano-Encapsulated and Nanoparticle-Enhanced Thermal Energy Storage Phase Change Materials
,” Int. J. Heat Mass Transfer
, 66
, pp. 575
–584
.7.
Rao
, Z.
, Huo
, Y.
, and Liu
, X.
, 2014
, “Dissipative Particle Dynamics and Experimental Study of Alkane-Based Nanoencapsulated Phase Change Material for Thermal Energy Storage
,” RSC Adv.
, 4
(40
), pp. 20797
–20803
.8.
Rao
, Z.
, You
, X.
, Huo
, Y.
, and Liu
, X.
, 2014
, “Dissipative Particle Dynamics Study of Nano-Encapsulated Thermal Energy Storage Phase Change Material
,” RSC Adv.
, 4
(74
), pp. 39552
–39557
.9.
Jiaung
, W.-S.
, Ho
, J.-R.
, and Kuo
, C.-P.
, 2001
, “Lattice Boltzmann Method for the Heat Conduction Problem With Phase Change
,” Numer. Heat Transfer: Part B: Fundamentals
, 39
(2
), pp. 167
–187
.10.
Guo
, Z.
, Shi
, B.
, and Wang
, N.
, 2000
, “Lattice BGK Model for Incompressible Navier–Stokes Equation
,” J. Comput. Phys.
, 165
(1
), pp. 288
–306
.11.
Peng
, Y.
, Shu
, C.
, and Chew
, Y. T.
, 2003
, “Simplified Thermal Lattice Boltzmann Model for Incompressible Thermal Flows
,” Phys. Rev. E
, 68
(2
).12.
Miller
, W.
, 2001
, “The Lattice Boltzmann Method: A New Tool for Numerical Simulation of the Interaction of Growth Kinetics and Melt Flow
,” J. Crystal Growth
, 230
(1–2
), pp. 263
–269
.13.
Huang
, R.
, and Wu
, H.
, 2014
, “An Immersed Boundary-Thermal Lattice Boltzmann Method for Solid–Liquid Phase Change
,” J. Comput. Phys.
, 277
(0
), pp. 305
–319
.14.
De Fabritiis
, G.
, Mancini
, A.
, Mansutti
, D.
, and Succi
, S.
, 1998
, “Mesoscopic Models of Liquid/Solid Phase Transitions
,” Int. J. Mod. Phys. C
, 9
(08
), pp. 1405
–1415
.15.
Miller
, W.
, Succi
, S.
, and Mansutti
, D.
, 2001
, “Lattice Boltzmann Model for Anisotropic Liquid-Solid Phase Transition
,” Phys. Rev. Lett.
, 86
(16
), pp. 3578
–3581
.16.
Miller
, W.
, and Succi
, S.
, 2002
, “A Lattice Boltzmann Model for Anisotropic Crystal Growth From Melt
,” J. Stat. Phys.
, 107
(1/2
), pp. 173
–186
.17.
Miller
, W.
, Rasin
, I.
, and Pimentel
, F.
, 2004
, “Growth Kinetics and Melt Convection
,” J. Crystal Growth
, 266
(1–3
), pp. 283
–288
.18.
Miller
, W.
, Rasin
, I.
, and Succi
, S.
, 2006
, “Lattice Boltzmann Phase-Field Modelling of Binary-Alloy Solidification
,” Phys. A: Stat. Mech. Appl.
, 362
(1
), pp. 78
–83
.19.
Brent
, A.
, Voller
, V.
, and Reid
, K. J.
, 1988
, “Enthalpy-Porosity Technique for Modeling Convection-Diffusion Phase Change: Application to the Melting of a Pure Metal
,” Numer. Heat Transfer, Part A Appl.
, 13
(3
), pp. 297
–318
.20.
Chatterjee
, D.
, 2010
, “Lattice Boltzmann Simulation of Incompressible Transport Phenomena in Macroscopic Solidification Processes
,” Numer. Heat Transfer, Part B: Fundam.
, 58
(1
), pp. 55
–72
.21.
Chatterjee
, D.
, 2009
, “An Enthalpy-Based Thermal Lattice Boltzmann Model for Non-Isothermal Systems
,” EPL (Europhys. Lett.)
, 86
(1
), p. 14004
.22.
Semma
, E. A.
, El Ganaoui
, M.
, and Bennacer
, R.
, 2007
, “Lattice Boltzmann Method for Melting/Solidification Problems
,” C. R. Méc.
, 335
(5–6
), pp. 295
–303
.23.
Semma
, E.
, El Ganaoui
, M.
, Bennacer
, R.
, and Mohamad
, A. A.
, 2008
, “Investigation of Flows in Solidification by Using the Lattice Boltzmann Method
,” Int. J. Therm. Sci.
, 47
(3
), pp. 201
–208
.24.
Huber
, C.
, Parmigiani
, A.
, Chopard
, B.
, Manga
, M.
, and Bachmann
, O.
, 2008
, “Lattice Boltzmann Model for Melting With Natural Convection
,” Int. J. Heat Fluid Flow
, 29
(5
), pp. 1469
–1480
.25.
Gao
, D.
, and Chen
, Z.
, 2011
, “Lattice Boltzmann Simulation of Natural Convection Dominated Melting in a Rectangular Cavity Filled With Porous Media
,” Int. J. Therm. Sci.
, 50
(4
), pp. 493
–501
.26.
Chen
, Z.
, Gao
, D.
, and Shi
, J.
, 2014
, “Experimental and Numerical Study on Melting of Phase Change Materials in Metal Foams at Pore Scale
,” Int. J. Heat Mass Transfer
, 72
, pp. 646
–655
.27.
Song
, W.
, Zhang
, Y.
, Li
, B.
, and Fan
, X.
, 2016
, “A Lattice Boltzmann Model for Heat and Mass Transfer Phenomena With Phase Transformations in Unsaturated Soil During Freezing Process
,” Int. J. Heat Mass Transfer
, 94
, pp. 29
–38
.28.
Eshraghi
, M.
, and Felicelli
, S. D.
, 2012
, “An Implicit Lattice Boltzmann Model for Heat Conduction With Phase Change
,” Int. J. Heat Mass Transfer
, 55
(9–10
), pp. 2420
–2428
.29.
Feng
, Y.
, Li
, H.
, Li
, L.
, Bu
, L.
, and Wang
, T.
, 2015
, “Numerical Investigation on the Melting of Nanoparticle-Enhanced Phase Change Materials (NEPCM) in a Bottom-Heated Rectangular Cavity Using Lattice Boltzmann Method
,” Int. J. Heat Mass Transfer
, 81
, pp. 415
–425
.30.
Huang
, R.
, Wu
, H.
, and Cheng
, P.
, 2013
, “A New Lattice Boltzmann Model for Solid–Liquid Phase Change
,” Int. J. Heat Mass Transfer
, 59
, pp. 295
–301
.31.
Huang
, R.
, and Wu
, H.
, 2015
, “Phase Interface Effects in the Total Enthalpy-Based Lattice Boltzmann Model for Solid–Liquid Phase Change
,” J. Comput. Phys.
, 294
, pp. 346
–362
.32.
Huang
, R.
, and Wu
, H.
, 2016
, “Total Enthalpy-Based Lattice Boltzmann Method With Adaptive Mesh Refinement for Solid-Liquid Phase Change
,” J. Comput. Phys.
, 315
, pp. 65
–83
.33.
Huo
, Y.
, and Rao
, Z.
, 2015
, “Lattice Boltzmann Simulation for Solid–Liquid Phase Change Phenomenon of Phase Change Material Under Constant Heat Flux
,” Int. J. Heat Mass Transfer
, 86
, pp. 197
–206
.34.
Huo
, Y.
, and Rao
, Z.
, 2017
, “Investigation of Phase Change Material Based Battery Thermal Management at Cold Temperature Using Lattice Boltzmann Method
,” Energy Convers. Manage.
, 133
, pp. 204
–215
.35.
Cao
, Y.
, Faghri
, A.
, and Chang
, W. S.
, 1989
, “A Numerical Analysis of Stefan Problems for Generalized Multi-Dimensional Phase-Change Structures Using the Enthalpy Transforming Model
,” Int. J. Heat Mass Transfer
, 32
(7
), pp. 1289
–1298
.36.
Cao
, Y.
, and Faghri
, A.
, 1990
, “A Numerical Analysis of Phase-Change Problems Including Natural Convection
,” ASME J. Heat Transfer
, 112
(3
), pp. 812
–816
.37.
Guo
, Z.
, Zheng
, C.
, and Shi
, B.
, 2002
, “Discrete Lattice Effects on the Forcing Term in the Lattice Boltzmann Method
,” Phys. Rev. E
, 65
(4
), p. 046308
.38.
Danaila
, I.
, Moglan
, R.
, Hecht
, F.
, and Le Masson
, S.
, 2014
, “A Newton Method With Adaptive Finite Elements for Solving Phase-Change Problems With Natural Convection
,” J. Comput. Phys.
, 274
, pp. 826
–840
.39.
Hu
, H.
, and Argyropoulos
, S. A.
, 1996
, “Mathematical Modelling of Solidification and Melting: A Review
,” Modell. Simul. Mater. Sci. Eng.
, 4
(4
), p. 371
.40.
Hortmann
, M.
, Perić
, M.
, and Scheuerer
, G.
, 1990
, “Finite Volume Multigrid Prediction of Laminar Natural Convection: Bench‐Mark Solutions
,” Int. J. Numer. Methods Fluids
, 11
(2
), pp. 189
–207
.41.
Mencinger
, J.
, 2004
, “Numerical Simulation of Melting in Two-Dimensional Cavity Using Adaptive Grid
,” J. Comput. Phys.
, 198
(1
), pp. 243
–264
.Copyright © 2018 by ASME
You do not currently have access to this content.
