Numerical modeling of buoyancy-driven turbulent flows in enclosures

Modeling turbulent natural convection in enclosures with differentially heated vertical walls is numerically challenging, in particular, when low-Reynolds-number (low-Re) models are adopted. When the turbulence level in the core region of cavity is low, most low-Re models, particular those showing good performance for bypass transitional flows, tend to relaminarize the flow and, as a consequence, significantly underpredict the near-wall turbulence intensities and boundary-layer thickness. Another challenge associated with low-turbulence buoyancy-driven flows in enclosures is its inherent unsteadiness, which can pose convergence problems when a steady Reynolds-averaged Navier–Stokes (RANS) equation is solved. In the present study, an unsteady RANS approach in conjunction with the low-Re k–ϵ model of Lien and Leschziner [Int. J. Comput. Fluid Dyn. 12 (1999) 1] is initially adopted and the predicted flow field is found effectively relaminarized. To overcome this difficulty, likely caused by the low-Re functions in the ϵ-equation, the two-layer approach is attempted, in which ϵ is prescribed algebraically using the one-equation k–l model of Wolfshtein [Int. J. Heat Mass Transfer 12 (1969) 301]. The two-layer approach combined with a quadratic stress–strain relation gives overall the best performance in terms of mean velocities, temperature and turbulence quantities.