×

Comparison of the finite volume and lattice Boltzmann methods for solving natural convection heat transfer problems inside cavities and enclosures. (English) Zbl 1474.80013

Summary: Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. A laterally heated square enclosure, filled with air, was studied. A FORTRAN code based on the lattice Boltzmann method (LBM) was developed for this purpose. The finite difference method was applied to discretize the LBM equations. Furthermore, for comparison purpose, the commercially available CFD package FLUENT, which uses finite volume Method (FVM), was also used to simulate the same problem. Different discretization schemes, being the first order upwind, second order upwind, power law, and QUICK, were used with the finite volume solver where the SIMPLE and SIMPLEC algorithms linked the velocity-pressure terms. The results were also compared with existing experimental and numerical data. It was observed that the finite volume method requires less CPU usage time and yields more accurate results compared to the LBM. It has been noted that the 1st order upwind/SIMPLEC combination converges comparatively quickly with a very high accuracy especially at the boundaries. Interestingly, all variants of FVM discretization/pressure-velocity linking methods lead to almost the same number of iterations to converge but higher-order schemes ask for longer iterations.

MSC:

80M12 Finite volume methods applied to problems in thermodynamics and heat transfer
65N08 Finite volume methods for boundary value problems involving PDEs
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
80A19 Diffusive and convective heat and mass transfer, heat flow

Software:

FLUENT
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Mirhashemi, F. S.; Hashemabadi, S. H., Experimental and CFD study of wall effects on orderly stacked cylindrical particles heat transfer in a tube channel, International Communications in Heat and Mass Transfer, 39, 3, 449-455 (2012) · doi:10.1016/j.icheatmasstransfer.2012.01.007
[2] Bellecci, C.; Gaudio, P.; Lupelli, I.; Malizia, A.; Porfiri, M. T.; Quaranta, R.; Richetta, M., Loss of vacuum accident (LOVA): comparison of computational fluid dynamics (CFD) flow velocities against experimental data for the model validation, Fusion Engineering and Design, 86, 4-5, 330-340 (2011) · doi:10.1016/j.fusengdes.2011.02.057
[3] Selmi, M.; Al-Khawaja, M. J.; Marafia, A., Validation of CFD simulation for flat plate solar energy collector, Renewable Energy, 33, 3, 383-387 (2008) · doi:10.1016/j.renene.2007.02.003
[4] Dixon, A. G.; Walls, G.; Stanness, H.; Nijemeisland, M.; Stitt, E. H., Experimental validation of high Reynolds number CFD simulations of heat transfer in a pilot-scale fixed bed tube, Chemical Engineering Journal, 200, 344-356 (2012)
[5] Zhang, Z.; Zhang, X., Direct simulation of low-re flow around a square cylinder by numerical manifold method for Navier-Stokes equations, Journal of Applied Mathematics, 2012 (2012) · Zbl 1251.76046 · doi:10.1155/2012/465972
[6] Nordström, J.; Gong, J.; van der Weide, E.; Svärd, M., A stable and conservative high order multi-block method for the compressible Navier-Stokes equations, Journal of Computational Physics, 228, 24, 9020-9035 (2009) · Zbl 1375.76036 · doi:10.1016/j.jcp.2009.09.005
[7] Chen, Z.; Zhang, L., A stabilized mixed finite element method for single-phase compressible flow, Journal of Applied Mathematics, 2011 (2011) · Zbl 1204.76022 · doi:10.1155/2011/129724
[8] Boivin, S.; Cayré, F.; Hérard, J., A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes, International Journal of Thermal Sciences, 39, 8, 806-821 (2000)
[9] Liu, X.; Liu, H.; Liu, Y., Simulation of magnetorheological fluids based on Lattice Boltzmann method with double meshes, Journal of Applied Mathematics, 2012 (2012) · Zbl 1251.76047 · doi:10.1155/2012/567208
[10] Mohamad, A. A., Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes (2011), Springer · Zbl 1247.80003
[11] Shi, Y.; Zhao, T. S.; Guo, Z. L., Lattice Boltzmann method for incompressible flows with large pressure gradients, Physical Review E, 73, 2 (2006) · doi:10.1103/PhysRevE.73.026704
[12] Karimipour, A.; Nezhad, A. H.; D’Orazio, A.; Shirani, E., The effects of inclination angle and prandtl number on the mixed convection in the inclined lid driven cavity using lattice boltzmann method, Journal of Theoretical and Applied Mechanics, 51, 2, 447-462 (2013)
[13] Rouboa, A.; Monteiro, E., Heat transfer in multi-block grid during solidification: performance of finite differences and finite volume methods, Journal of Materials Processing Technology, 204, 1-3, 451-458 (2008) · doi:10.1016/j.jmatprotec.2007.11.125
[14] Karimipour, A.; Afrand, M.; Akbari, M.; Safaei, M. R., Simulation of fluid flow and heat transfer in the inclined enclosure, Proceedings of the World Academy of Science, Engineering and Technology, World Academy of Science, Engineering and Technology
[15] Garoosi, F.; Bagheri, G.; Talebi, F., Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers (HACs) inside, International Journal of Heat and Mass Transfer, 67, 362-376 (2013)
[16] Bararnia, H.; Hooman, K.; Ganji, D. D., Natural convection in a nanofluids-filled portioned cavity: the lattice-boltzmann method, Numerical Heat Transfer A, 59, 6, 487-502 (2011) · doi:10.1080/10407782.2011.541195
[17] Imani, G.; Maerefat, M.; Hooman, K., Lattice Boltzmann simulation of conjugate heat transfer from multiple heated obstacles mounted in a walled parallel plate channel, Numerical Heat Transfer A, 62, 10, 798-821 (2012)
[18] Tian, Z.; Zou, C.; Liu, H. J.; Liu, Z. H.; Guo, Z. L.; Zheng, C. G., Thermal lattice boltzmann model with viscous heat dissipation in the incompressible limit, International Journal of Modern Physics C, 17, 8, 1131-1139 (2006) · Zbl 1121.82339 · doi:10.1142/S0129183106009631
[19] Zou, Q.; He, X., On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, 9, 6, 1591-1596 (1997) · Zbl 1185.76873
[20] Patankar, S. V., Numerical Heat Transfer and Fluid Flow (1980), Taylor & Francis · Zbl 0521.76003
[21] Safaei, M. R.; Rahmanian, B.; Goodarzi, M., Numerical study of laminar mixed convection heat transfer of power-law non-Newtonian fluids in square enclosures by finite volume method, International Journal of Physical Sciences, 6, 33, 7456-7470 (2011) · doi:10.5897/ijps11.1092
[22] Safaei, M. R.; Goshayeshi, H. R.; Razavi, B. S.; Goodarzi, M., Numerical investigation of laminar and turbulent mixed convection in a shallow water-filled enclosure by various turbulence methods, Scientific Research and Essays, 6, 22, 4826-4838 (2011)
[23] Goodarzi, M.; Safaei, M. R.; Vafai, K.; Ahmadi, G.; Dahari, M.; Kazi, S. N.; Jomhari, N., Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model, International Journal of Thermal Sciences, 75, 204-220 (2014)
[24] Mousavi, S. S.; Hooman, K., Heat and fluid flow in entrance region of a channel with staggered baffles, Energy Conversion and Management, 47, 15-16, 2011-2019 (2006) · doi:10.1016/j.enconman.2005.12.018
[25] Tao, W. Q.; He, Y. L.; Li, Z. Y.; Qu, Z. G., Some recent advances in finite volume approach and their applications in the study of heat transfer enhancement, International Journal of Thermal Sciences, 44, 7, 623-643 (2005) · doi:10.1016/j.ijthermalsci.2005.02.007
[26] Forooghi, P.; Hooman, K., Numerical study of turbulent convection in inclined pipes with significant buoyancy influence, International Journal of Heat and Mass Transfer, 61, 1, 310-322 (2013)
[27] Safaei, M. R.; Goodarzi, M.; Mohammadi, M., Numerical modeling of turbulence mixed convection heat transfer in air filled enclosures by finite volume method, International Journal of Multiphysics, 5, 4, 307-324 (2011) · doi:10.1260/1750-9548.5.4.307
[28] Goshayeshi, H.; Safaei, M. R.; Maghmoumi, Y., Numerical simulation of unsteady turbulent and laminar mixed convection in rectangular enclosure with hot upper moving wall by finite volume method, Proceedings of the 6th International Chemical Engineering Congress and Exhibition (IChEC ’09)
[29] Lancial, N.; Beaubert, F.; Harmand, S.; Rolland, G., Effects of a turbulent wall jet on heat transfer over a non-confined backward-facing step, International Journal of Heat and Fluid Flow, 44, 336-347 (2013)
[30] Hou, S.; Zou, Q.; Chen, S.; Doolen, G.; Cogley, A. C., Simulation of cavity flow by the lattice Boltzmann method, Journal of Computational Physics, 118, 2, 329-347 (1995) · Zbl 0821.76060 · doi:10.1006/jcph.1995.1103
[31] D’Orazio, A.; Arrighetti, C.; Succi, S., Kinetic Scheme for Fluid Flows with Heat Transfer (2003), Roma, Italy: University of Rome “La Sapienza”, Roma, Italy · Zbl 1186.76148
[32] Krane, R.; Jessee, J., Some detailed field measurements for a natural convection flow in a vertical square enclosure, Proceedings of the 1st ASME-JSME Thermal Engineering Joint Conference
[33] Bakhshan, Y.; Emrani, S. H., Investigating the behavior of nanofluids in a rectangular enclosure in order to enhance the heat transfer coefficient, Journal of Basic and Applied Scientific Research and Essays, 3, 1, 976-986 (2013)
[34] Khanafer, K.; Vafai, K.; Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, International Journal of Heat and Mass Transfer, 46, 19, 3639-3653 (2003) · Zbl 1042.76586 · doi:10.1016/S0017-9310(03)00156-X
[35] Oztop, H. F.; Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29, 5, 1326-1336 (2008) · doi:10.1016/j.ijheatfluidflow.2008.04.009
[36] Buick, J. M.; Created, C. A., Gravity in a lattice Boltzmann model, Physical Review E, 61, 5 A, 5307-5320 (2000)
[37] He, X.; Luo, L., Lattice Boltzmann model for the incompressible Navier-Stokes equation, Journal of Statistical Physics, 88, 3-4, 927-944 (1997) · Zbl 0939.82042
[38] Tao, W., Recent Advances in Computational Heat Transfer (2000), Beijing, China: Science Press, Beijing, China
[39] Barakos, G.; Mitsoulis, E.; Assimacopoulos, D., Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions, International Journal for Numerical Methods in Fluids, 18, 7, 695-719 (1994) · Zbl 0806.76055
[40] Markatos, N. C.; Pericleous, K. A., Laminar and turbulent natural convection in an enclosed cavity, International Journal of Heat and Mass Transfer, 27, 5, 755-772 (1984) · Zbl 0542.76112
[41] de Vahl Davis, G., Natural convection of air in a square cavity: a bench mark numerical solution, International Journal for Numerical Methods in Fluids, 3, 3, 249-264 (1983) · Zbl 0538.76075
[42] Fusegi, T.; Hyun, J. M.; Kuwahara, K.; Farouk, B., A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure, International Journal of Heat and Mass Transfer, 34, 6, 1543-1557 (1991)
[43] Karimipour, A.; Nezhad, A. H.; D’Orazio, A.; Shirani, E., Investigation of the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method, International Journal of Thermal Sciences, 54, 142-152 (2012) · doi:10.1016/j.ijthermalsci.2011.11.015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.