Assessment and calibration of RANS turbulence models for buoyancy-driven flows using ensemble Kalman filters

Turbulence modelling of buoyancy-dominated flows is challenging due to the complex coupling of the velocity and temperature fields. Higher-order and nonlinear models have been developed to more accurately represent the underlying physics, however, they still lack universality and usually result in complicated formulations. In this paper, we show that the modelling capabilities can be significantly improved by calibrating the model coefficients in the closure equations, even with the less complex assumptions (linear eddy viscosity model and the generalised gradient diffusion hypothesis). We consider a flow in a vertical channel with differentially heated walls, with the deterministic ensemble Kalman filter chosen as our data assimilation tool to incorporate high-fidelity data from direct numerical simulation (DNS). Through variance-based sensitivity analysis, we identify the four most influential coefficients in the k − ω SST model as our adjustable parameters. We propose a residual-based adaptive filtering method that is suitable for steady parameter estimation problems and achieved convergence of parameter estimates with a cost-reduction of approximately 90%. The calibration was performed at five different Rayleigh numbers ( R a ) ranging between O ( 1 0 5 ) − O ( 1 0 9 ) . The results show a clear dependency on R a , and mathematical expressions were formulated for each parameter for a generalised solution in terms of R a . We also propose a multi-case filtering approach that produces a single, global set of coefficients applicable across multiple cases, with results that closely match with the average trends obtained from the case-by-case method. For both approaches, we show that the calibrated model yields better predictions for the quantities of interest, u ¯ , T ¯ , u ′ v ′ ¯ , v ′ T ′ ¯ , and the Nusselt number.