Robust Bayesian Calibration of a RANS Model for Jet-in-Crossflow Simulations

Abstract

Compressible jet-in-crossflow interactions are poorly simulated using Reynolds-Averaged Navier Stokes (RANS) equations. This is due to model-form errors (physical approximations) in RANS as well as the use of parameter values simply picked from literature (henceforth, the nominal values of the parameters). Previous work on the Bayesian calibration of RANS models has yielded joint probability densities of C = (Cµ, C 2, C 1), the most influential parameters of the RANS equations. The calibrated values were far more predictive than the nominal parameter values and the advantage held across a range of freestream Mach numbers and jet strengths. In this work we perform Bayesian calibration across a range of Mach numbers and jet strengths and compare the joint densities, with a view of determining whether compressible jet-in-crossflow could be simulated with either a single joint probability density or a point estimate for C. We find that probability densities for C 2 agree and also indicate that the range typically used in aerodynamic simulations should be extended. The densities for C 1 agree, approximately, with the nominal value. The densities for Cµ do not show any clear trend, indicating that they are not strongly constrained by the calibration observables, and in turn, do not affect them much. We also compare the calibrated results to a recently developed analytical model of a jet-in-crossflow interaction. We find that the values of C estimated by the analytical model delivers prediction accuracies comparable to the calibrated joint densities of the parameters across a range of Mach numbers and jet strengths. Nomenclature(u e , v e ) Experimental counterpart of (u m , v m ) (u m , v m ) Modeled streamwise velocity deficit and normalized vertical velocities at probes (C µ , C 2 , C 1 ) Parameters in the k − RANS model requiring calibration C a Analytical estimates of (C µ , C 2 , C 1 ) C nom Nominal value of (C µ , C 2 , C 1 ) R Physically realistic part of the parameter space CVP Counter-rotating vortex pair JIC Jet-in-crossflow