Investigation on the relative performance of various low-Reynolds number turbulence models for buoyancy-driven flow in a tall cavity

Abstract

The present study deals with the numerical investigation of turbulent buoyancy driven flow in a differentially heated rectangular cavity with adiabatic horizontal walls. The aspect ratio of cavity is 5 and the Rayleigh number based on the cavity height is 4.56 × 1010. The computations have been carried out using the finite volume method on a staggered grid and SIMPLEC algorithm for pressure–velocity coupling. The low-Reynolds number \(k-\epsilon\) model proposed by Yang and Shih (YS), low-Reynolds number \(k-\omega\) model proposed by Wilcox, and \(k-\omega\) shear stress transport (SST) model of Menter have been applied for turbulence closure. The performance comparison of different models have been carried out using the experimental, LES and various RANS results available in the literature. The computation of turbulent natural convection flow is numerically challenging due to complex flow involving laminar, transition and turbulent regions, coupling of velocity with the energy equation, and some other problems reported in literature e.g. grid dependency of solution, numerical stability problem, etc. The flux Richardson number is calculated to get an estimate of relative importance of buoyancy and shear force in different regions of flow. The shearing and swirling zones have been identified in the entire flow domain using the \(\lambda _{2}\) criterion. Based on the comparison of mean flow, heat transfer and turbulence characteristics with the available results, it has been found that YS model performs better. The better performance obtained from YS model may be due to peculiarity of model that takes into account the Kolmogorov time scale near the wall and the conventional time scale \((k/\epsilon )\) away from the wall.