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 (Cμ,Ce2,Ce1), 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 (Cμ,Ce2,Ce1) space R supports realistic flow simulations. R is used as a prior belief when formulating the inverse problem. ...