Analysis of Natural Convection in the Presence of Volumetric Radiation in a Square Cavity with Non-Uniform Lattices Using the Lattice Boltzmann Method

ABSTRACT

This article deals with the analysis of natural convection in the presence of volumetric radiation in a square cavity containing an absorbing, emitting and scattering medium. Numerical simulation has been carried out by using lattice Boltzmann method (LBM). To enhance the computational efficiency and capture sharp gradients, non-uniform lattices/control volumes have been implemented. Separate equations dealing with different particle distribution functions in the LBM are used to calculate the density and velocity fields and the thermal field. The finite volume method is used to compute the radiative term of the energy equation. Without effects of volumetric radiation, the maximum vertical velocity on horizontal mid-plane and maximum horizontal velocity on the vertical mid-plane and Nusselt numbers are compared with the results available in the literature. With volumetric radiation, the results for present numerical code are validated with the results available in the literature. Streamlines and isotherms are analyzed for different parameters such as Rayleigh number, conduction-radiation parameter, extinction coefficient and scattering albedo. The results obtained by using the non-uniform lattices-based LBM are compared with the results for uniform lattice based-LBM. It is found that the non-uniform lattice-based LBM provides accurate results and it is computationally more efficient.

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