Assessment of RANS and LES turbulence models for natural convection in a differentially heated square cavity

Abstract

Development of computationally efficient modeling techniques for thermally driven buoyant flows remains an ongoing challenge for the computational fluid dynamics (CFD) community due to the complex interactions of buoyancy, heat transfer, and turbulence. Although several “best practice” guides are available for certain scenarios, comprehensive validation studies against benchmark-quality data must occur to ensure the accuracy and suitability of these computational models. To this end, the present study provides a robust assessment of 16 different turbulence treatments − 13 Reynolds-averaged Navier-Stokes (RANS) formulations and 3 large-eddy simulation (LES) sub-grid scale models – and their ability to predict various first- and second-order system response quantities (SRQs) in a differentially heated enclosure at a Rayleigh number of 1.58 × 109. Current ASME standards are used to quantify the latent discretization errors in the RANS predictions while a sub-grid activity parameter is used to justify the spatial resolution of the LES models. In general, most RANS models suitably replicate surface heat transfer and first-order SRQs; however, certain low-Reynolds-number formulations markedly mischaracterize the same parameters. Following a thorough comparison of turbulent statistics and turbulence kinetic energy budgets, these modeling errors are traced back to a misprediction of turbulent viscosity and direct production of turbulence from buoyancy. The LES predictions from all three sub-grid scale models are in good agreement with the corresponding experimental measurements with only minor disparities in the horizontal and vertical components of the turbulent heat flux.