Bayesian uncertainty quantification applied to RANS turbulence models

A Bayesian uncertainty quantification approach is developed and applied to RANS turbulence models of fully-developed channel flow. The approach aims to capture uncertainty due to both uncertain parameters and model inadequacy. Parameter uncertainty is represented by treating the parameters of the turbulence model as random variables. To capture model uncertainty, four stochastic extensions of four eddy viscosity turbulence models are developed. The sixteen coupled models are calibrated using DNS data according to Bayes' theorem, producing posterior probability density functions. In addition, the competing models are compared in terms of two items: posterior plausibility and predictions of a quantity of interest. The posterior plausibility indicates which model is preferred by the data according to Bayes' theorem, while the predictions allow assessment of how strongly the model differences impact the quantity of interest. Results for the channel flow case show that both the stochastic model and the turbulence model affect the predicted quantity of interest. The posterior plausibility favors an inhomogeneous stochastic model coupled with the Chien k-ϵ model. After calibration with data at Reτ = 944 and Reτ = 2003, this model gives a prediction of the centerline velocity at Reτ = 5000 with uncertainty of approximately ± 4%.