Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-18T15:46:35.610Z Has data issue: false hasContentIssue false

Numerical Simulation of Melting with Natural Convection Based on Lattice Boltzmann Method and Performed with CUDA Enabled GPU

Published online by Cambridge University Press:  03 June 2015

Wei Gong*
Affiliation:
INSA-Lyon, CETHIL, UMR5008, F-69621, Villeurbanne, France Université de Lyon, CNRS, France
Kévyn Johannes
Affiliation:
Université Lyon 1, F-69621, France Université de Lyon, CNRS, France
Frédéric Kuznik
Affiliation:
INSA-Lyon, CETHIL, UMR5008, F-69621, Villeurbanne, France Université de Lyon, CNRS, France
*
*Corresponding author. Email addresses: [email protected] (W. Gong), [email protected] (K. Johannes), [email protected] (F. Kuznik)
Get access

Abstract

A new solver is developed to numerically simulate the melting phase change with natural convection. This solver was implemented on a single Nvidia GPU based on the CUDA technology in order to simulate the melting phase change in a 2D rectangular enclosure. The Rayleigh number is of the order of magnitude of 108 and Prandlt is 50. The hybrid thermal lattice Boltzmann method (HTLBM) is employed to simulate the natural convection in the liquid phase, and the enthalpy formulation is used to simulate the phase change aspect. The model is validated by experimental data and published analytic results. The simulation results manifest a strong convection in the melted phase and a different flow pattern from the reference results with low Rayleigh number. In addition, the computational performance is estimated for single precision arithmetic, and this solver yields 703.31MLUPS and 61.89GB/s device to device data throughput on a Nvidia Tesla C2050 GPU.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Hasnain, S. Review on sustainable thermal energy storage technologies, Part I: heat storage materials and techniques, Energy Conversion and Management, 1998, 39, 11271138.Google Scholar
[2]Burch, S. D.; Keyser, M. A.; Colucci, C. P.; Potter, T. F.; Benson, D. K. & Biel, J. P.Applications and benefits of catalytic converter thermal management. Presented at SAE Fuels & Lubricants Spring Meeting (Dearborn, MI), 1996, 961134.Google Scholar
[3]Gumus, M.Reducing cold-start emission from internal combustion engines by means of thermal energy storage system, Applied Thermal Engineering, 2009, 29, 652660.Google Scholar
[4]Weinlader, H.; Beck, A. & Fricke, J.PCM-facade-panel for daylighting and room heating, Solar Energy, 2005, 78, 177186.Google Scholar
[5]EsamM, A. M, A.Using phase change materials in window shutter to reduce the solar heat gain, Energy and Buildings, 2012, 47, 421429.Google Scholar
[6]Comparison of theoretical models of phase-change and sensible heat storage for air and water-based solar heating systems, Solar Energy, 42(1989), 209–202.Google Scholar
[7]Bertrand, O.; Binet, B.; Combeau, H.; Couturier, S.; Delannoy, Y.; Gobin, D.; Lacroix, M.; Quéré, P. L.; Médale, M.; Mencinger, J.; Sadat, H. & Vieira, G.Melting driven by natural convection A comparison exercise: first results.Google Scholar
[8]Benard, C.; Gobin, D. and Zanoli, A.Moving boundary problem: heat conduction in the solid phase of a phase-change material during melting driven by natural convection in the liquid, International Journal of Heat and Mass Transfer, 1986, 29, 16691681.CrossRefGoogle Scholar
[9]Mencinger, J.Numerical simulation of melting in two-dimensional cavity using adaptive grid, Journal of Computational Physics, 2004, 198, 243264.Google Scholar
[10]Chatterjee, D. and Chakraborty, S.An enthalpy-based lattice Boltzmann model for diffusion dominated solidliquid phase transformation, Physics Letters A, 2005, 341, 320330.Google Scholar
[11]Semma, E.; El Ganaoui, M.; Bennacer, R. and Mohamad, A. A.Investigation of flows in solidification by using the lattice Boltzmann method, International Journal of Thermal Sciences, 2008, 47, 201208.Google Scholar
[12]Miller, W.The lattice Boltzmann method: a new tool for numerical simulation of the interaction of growth kinetics and melt flow, Journal of Crystal Growth, 2001, 230, 263269.Google Scholar
[13]Miller, W.; Rasin, I. and Succi, S.Lattice Boltzmann phase-field modelling of binary-alloy solidification, Physica A: Statistical Mechanics and its Applications, 2006, 362, 7883.Google Scholar
[14]Safari, H.; Rahimian, M. H. & Krafczyk, M.Extended lattice Boltzmann method for numerical simulation of thermal phase change in two-phase fluid flow, Phys. Rev. E, American Physical Society, 2013, 88, 013304.CrossRefGoogle ScholarPubMed
[15]Fan, Z.; Qiu, F.; Kaufman, A. & Yoakum-Stover, S.GPU Cluster for High Performance Computing, Proceedings of the 2004 ACM/IEEE Conference on Supercomputing, IEEE Computer Society, 2004, 47.Google Scholar
[16]Kuznik, F.; Obrecht, C.; Rusaouen, G. and Roux, J.-J.LBM based flow simulation using GPU computing processor, Computers and Mathematics with Applications, 2010, 59, 23802392.Google Scholar
[17]Obrecht, C.; Kuznik, F.; Tourancheau, B. and Roux, J.-J.Scalable lattice Boltzmann solvers for CUDA GPU clusters, Parallel Computing, 2013, 39, 259270.CrossRefGoogle Scholar
[18]Banari, A.; Janen, C.; Grilli, S. T. & Krafczyk, M.Efficient GPGPU implementation of a lattice Boltzmann model for multiphase flows with high density ratios, Computers & Fluids, 2014, 93, 117.Google Scholar
[19]Brent, A. D.; Voller, V. R. & Reid, K. J.Enthalpy-porosity Technique For Modeling Convection-diffusion Phase Change: Application To The Melting Of A Pure Metal, Numerical Heat Transfer, 1988, 13, 297318.Google Scholar
[20]Jany, P. & Bejan, A.Scaling theory of melting with natural convection in an enclosure, International Journal of Heat and Mass Transfer, 1988, 31, 12211235.Google Scholar
[21]d’Humieres, D.Multiplerelaxationtime lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002, 360, 437451.Google Scholar
[22]Crouse, B.; Krafczyk, M.; Khner, S.; Rank, E. & van Treeck, C.Indoor air flow analysis based on lattice Boltzmann methods, Energy and Buildings, 2002, 34, 941949.Google Scholar
[23]Van Treeck, C.; Rank, E.; Krafczyk, M.; Toelke, J. & Nachtwey, B.Extension of a hybrid thermal LBE scheme for large-eddy simulations of turbulent convective flows, Computers & Fluids, 2006, 35, 863871.CrossRefGoogle Scholar
[24]Lallemand, P. & Luo, L.-S.Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E, American Physical Society, 2000, 61, 65466562.Google Scholar
[25]Wang, J.; Wang, D.; Lallemand, P. & Luo, L.-S. Lattice Boltzmann simulations of thermal convective flows in two dimensions, Computers & Mathematics with Applications, 2013, 65, 262286.Google Scholar
[26]Contrino, D.; Lallemand, P.; Asinari, P. & Luo, L.-S.Lattice-Boltzmann simulations of the thermally driven 2D square cavity at high Rayleigh numbers, Journal of Computational Physics, 2014, 275, 257272.Google Scholar
[27]Okada, M.Analysis of heat transfer during melting from a vertical wall, International Journal of Heat and Mass Transfer, 1984, 27, 20572066.Google Scholar
[28]Tolke, J. & Krafczyk, M.TeraFLOP computing on a desktop PC with GPUs for 3D CFD, International Journal of Computational Fluid Dynamics, 2008, 22, 443456.CrossRefGoogle Scholar
[29]Cuda, C.Programming guide NVIDIA Corporation, July, 2013.Google Scholar
[30]Obrecht, C.; Kuznik, F.; Tourancheau, B. & Roux, J.-J.The TheLMA project: A thermal lattice Boltzmann solver for the GPU, Computers &; Fluids, 2012, 54, 118126.Google Scholar
[31]Mbaye, M. & Bilgen, E.Phase change process by natural convectiondiffusion in rectangular enclosures Heat and Mass Transfer, Springer-Verlag, 2001, 37, 3542.Google Scholar
[32]Lim, J. & Bejan, A.The Prandtl number effect on melting dominated by natural convection, Journal Name: Journal of Heat Transfer, (Transactions of the ASME (American Society of Mechanical Engineers), Series C), 1992.CrossRefGoogle Scholar
[33]Voller, V. & Prakash, C.A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems, International Journal of Heat and Mass Transfer, 1987, 30, 17091719.CrossRefGoogle Scholar
[34]Fuents, J. Miranda, Développement dun modéle de Boltzmann sur gaz réseau pour létude du changement de phase en présence de convection naturelle et de rayonnement, PhD. Thesis, 2013.Google Scholar
[35]He, X. & Luo, L.-S.A priori derivation of the lattice Boltzmann equation, Phys. Rev. E, American Physical Society, 1997, 55.CrossRefGoogle Scholar
[36]Lallemand, P. & Luo, L.-S.Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Phys. Rev. E, American Physical Society, 2003, 68, 036706.Google Scholar
[37]Chen, Y.; Ohashi, H. & Akiyama, M.Prandtl number of lattice BhatnagarGrossKrook fluid, Physics of Fluids (1994-present), 1995, 7, 22802282.Google Scholar