A hybrid scheme of single relaxation time lattice Boltzmann and finite volume methods coupled with discrete ordinates method for combined natural convection and volumetric radiation in an enclosure

Document Type: Research Paper

Authors

1 Laboratory of Petroleum Equipments Reliability and Materials, Université M'Hamed Bougara, Boumerdés, Algerie.

2 Institut Pprime, CNRS, ENSMA, University of Poitiers, Poitiers, 86961 Chasseneuil Futuroscope, France.

Abstract

This paper is focused on the application of hybrid Single relaxation time lattice Boltzmann and finite volume methods in conjunction with discrete ordinates method to simulate coupled natural convection and volumetric radiation in differentially heated enclosure, filled with an absorbing, emitting and non-scattering gray medium. In this work, the velocity and temperature fields are calculated using lattice Boltzmann and finite volume methods respectively, whereas the radiative term is computed by the discrete ordinates method. This study is carried out for Pr = 0.71, a Rayleigh number range of 103 ≤ Ra ≤ 106, an optical thickness with values 0 ≤ τ ≤ 100, a Planck number ranging in 0.001≤ Pl ≤ 100 and an aspect ratio varying between 0.5 ≤ Ar ≤ 2. Results are presented in terms of streamlines, isotherms, velocity profiles and average Nusselt number. Based on the obtained results, it can be concluded that the presence of volumetric radiation is noteworthy. Its effect, as a function of Rayleigh number and the radiative properties, yields significant changes on the behavior of streamlines and isotherms. In the taller enclosure, the increase of average total Nusselt number with increasing Rayleigh number is less significant than that in the case of the shallow enclosure.

Keywords

[1]           A.A. Mohamad, 2011, Lattice Boltzmann Method: Fundamentals and Engineering Applications with Computer Codes, Springer London .
[2]           S. Succi, 2011, The lattice Boltzmann equation: for fluid dynamics and beyond, Oxford university press.
[3]           A.A. Mohamad, A. Kuzmin, 2010, A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International Journal of Heat and Mass Transfer, (53) 990-996.
[4]           H.N. Dixit, V. Babu, 2006, Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, (49) 727-739.
[5]           F. Kuznik, J. Vareilles, G. Rusaouen, G. Krauss, 2007, A double-population lattice Boltzmann method with non-uniform mesh for the simulation of natural convection in a square cavity, International Journal of Heat and Fluid Flow, (28) 862-870.
[6]           Y. Peng, C. Shu, Y.T. Chew, 2004, A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity, Journal of Computational Physics, (193) 260-274.
[7]           Z. Li, M. Yang, Y. Zhang, 2016, Lattice Boltzmann method simulation of 3-D natural convection with double MRT model, International Journal of Heat and Mass Transfer,( 94) 222-238.
[8]           P. Asinari, S. Mishra, R. Borchiellini, 2010, A Lattice Boltzmann Formulation for the Analysis of Radiative Heat Transfer Problems in a Participating Medium, Numerical Heat Transfer, Part B: Fundamentals, (57)126-146.
[9]           Z. Li, M. Yang, Y. Zhang, 2014, Hybrid Lattice Boltzmann and Finite Volume Method for Natural Convection, Journal of Thermophysics and Heat Transfer, (28) 68-77.
[10]         M. Jami, A. Mezrhab, M. Bouzidi, P. Lallemand, 2007, Lattice Boltzmann method applied to the laminar natural convection in an enclosure with a heat-generating cylinder conducting body, International Journal of Thermal Sciences, (46) 38-47.
[11]         A. Yücel, S. Acharya, M.L. Williams, 1989, Natural Convection and Radiation in a Square Enclosure, Numerical Heat Transfer, Part A: Applications, (15) 261-278.
[12]         G. Lauriat, 1982, Combined Radiation-Convection in Gray Fluids Enclosed in Vertical Cavities, Journal of Heat Transfer, (104) 609-615.
[13]         G. Colomer, M. Costa, R. Cònsul, A. Oliva, 2004, Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method, International Journal of Heat and Mass Transfer, (47) 257-269.
[14]         X. Liu, G. Gong, H. Cheng, 2015, Combined Natural Convection and Radiation Heat Transfer of Various Absorbing-Emitting-Scattering Media in a Square Cavity, Advances in Mechanical Engineering, (6).
[15]         S. Laouar-Meftah, D. Lemonnier, D. Saury, A. Benbrik, M. Cherifi, 2015, Comparative Study of Radiative Effects on Double Diffusive Convection in Nongray Air-CO2Mixtures in Cooperating and Opposing Flow, Mathematical Problems in Engineering, DOI 10.1155/2015/586913 (1-17).
[16]         M. Cherifi, S. Laouar-Meftah, A. Benbrik, D. Lemonnier, D. Saury, 2015, Interaction of radiation with double-diffusive natural convection in a three-dimensional cubic cavity filled with a non-gray gas mixture in cooperating cases, Numerical Heat Transfer, Part A: Applications, (69)  479-496.
[17]         S. Hamimid, M. Guellal, 2014, Numerical Study of Combined Natural Convection-Surface Radiation in a Square Cavity, Journal of Thermophysics and Heat Transfer, (10) 377-393.
[18]         M.A. Ramankutty, A.L. Crosbie, 1997, Modified discrete ordinates solution of radiative transfer in two-dimensional rectangular enclosures, Journal of Quantitative Spectroscopy and Radiative Transfer, (57) 107-140.
[19]         M.M. Keshtkar, P. Talebizadehsardari, 2018, Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM, Sādhanā, (43).
[20]         Y. Sun, X. Zhang, 2016, Analysis of transient conduction and radiation problems using lattice Boltzmann and finite volume methods, International Journal of Heat and Mass Transfer, (97) 611-617.
[21]         S. Derfoufi, F. Moufekkir, A. Mezrhab, 2018, Numerical assessment of the mixed convection and volumetric radiation in a vertical channel with MRT-LBM, International Journal of Numerical Methods for Heat & Fluid Flow, (28) 745-762.
[22]         H. Ahmadi Tighchi, J.A. Esfahani, 2017, Combined Radiation/Natural Convection in a Participating Medium Using Novel Lattice Boltzmann Method, Journal of Thermophysics and Heat Transfer, (31) 563-574.
[23]         H.A. Tighchi, M. Sobhani, J.A. Esfahani, 2018, Effect of volumetric radiation on natural convection in a cavity with a horizontal fin using the lattice Boltzmann method, The European Physical Journal Plus, (133).
[24]         S. Nataraj, K.S. Reddy, S.P. Thampi, 2017, Lattice Boltzmann simulations of a radiatively participating fluid in Rayleigh–Benard convection, Numerical Heat Transfer, Part A: Applications, (72) 313-329.
[25]         B. Mondal, S.C. Mishra, 2008, Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method, Numerical Heat Transfer, Part A: Applications, (55) 18-41.
[26]         B. Mondal, X. Li, 2010, Effect of volumetric radiation on natural convection in a square cavity using lattice Boltzmann method with non-uniform lattices, International Journal of Heat and Mass Transfer, (53) 4935-4948.
[27]         S.C. Mishra, A. Akhtar, A. Garg, 2013, Numerical Analysis of Rayleigh-Bénard Convection with and Without Volumetric Radiation, Numerical Heat Transfer, Part A: Applications, (65) 144-164.
[28]         R. Chaabane, F. Askri, A. Jemni, S. Ben Nasrallah,2017, Numerical Study of Transient Convection With Volumetric Radiation Using an Hybrid Lattice Boltzmann Bhatnagar–Gross–Krook–Control Volume Finite Element Method, Journal of Heat Transfer, (139).
[29]      F. Moufekkir, M.A. Moussaoui, A. Mezrhab, H. Naji, D. Lemonnier, 2012, Numerical prediction of heat transfer by natural convection and radiation in an enclosure filled with an isotropic scattering medium, Journal of Quantitative Spectroscopy and Radiative Transfer, (113) 1689-1704.

Volume 51, Issue 2
December 2020
Pages 389-402
  • Receive Date: 12 June 2020
  • Revise Date: 11 July 2020
  • Accept Date: 12 July 2020