Improved RANS Turbulence Models for Buoyancy-Driven Flows

Abstract: Turbulence modelling of buoyancy-dominated flows are challenging due to the coupling of the velocity and temperature fields. Nonlinear algebraic models can be used to overcome some concerns, however they are usually not easily generalizable. In this paper, we show that the modelling capabilities can be significantly improved through the calibration of coefficients in the closure equations even with the simpler assumptions (linear eddy viscosity model and the generalized gradient diffusion hypothesis). We focus on the flow in an infinite vertical channel with differentially heated walls, using the deterministic ensemble Kalman filter as our approach for data assimilation. We identify the four most influential coefficients in the k -w SST model as our adjustable parameters, and perform the calibration at five different Rayleigh numbers ranging from O(10^5)?O(10^9). The mathematical expressions are then formulated for each parameter to provide a generalized solution. Using these functions, we show that the test case (not used in the calibration) yields better predicted quantities for u', u'v', v'T' and the Nusselt number. Keywords: Turbulence modelling, RANS, Natural convection, Parameter estimation, Kalman filter