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

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 = ۰.۷۱, a Rayleigh number range of ۱۰۳ ≤ Ra ≤ ۱۰۶, an optical thickness with values ۰ ≤ τ ≤ ۱۰۰, a Planck number ranging in ۰.۰۰۱≤ Pl ≤ ۱۰۰ and an aspect ratio varying between ۰.۵ ≤ Ar ≤ ۲. 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:

Natural convection , volumetric radiation , single relaxation time lattice Boltzmann method , Aspect ratio , discrete ordinates method