Bayesian Parameter Estimation of a k-ε Model for Accurate Jet-in-Crossflow Simulations

Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this work, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow. A Bayesian inverse problem is formulated to estimate three Reynolds-averaged Navier–Stokes parameters , and a Markov chain Monte Carlo method is used to develop a probability density function for them. The cost of the Markov chain Monte Carlo is addressed by developing statistical surrogates for the Reynolds-averaged Navier–Stokes model. It is found that only a subset of the space supports realistic flow simulations. is used as a prior belief when formulating the inverse problem. It is enforced with a classifier in the current Markov chain Monte Carlo solution. It is found that the calibrated parameters improve predictions of the entire flowfield substantially when compared to the nominal/literature values of ; furthermore, this improvement is seen to hold for interactions at other Mach numbers and jet strengths for which the experimental data are available to provide a comparison. The residual error is quantifies, which is an approximation of the model-form error; it is most easily measured in terms of turbulent stresses.