Bayesian Uncertainty Quantification of Transition SST Model on Flat Plate Transition Flow

Abstract

Computational study was performed to improve the prediction of transition flow simulated with the Transition SST model. Bayesian inference was applied to calibrated and quantify the uncertainties caused by the Transition SST model coefficients, model inadequacy, and observation error using experiment data. A surrogate model based on the non-intrusive polynomial chaos (NIPC) expansion for effective posterior sampling procedure was applied to predict the skin friction coefficients (Cf ) for various coefficients of the transition SST model. Variation of transition SST model coefficients was assumed to be independent uniform distributions. Model inadequacy was modeled by a correlated additive Gaussian model with Gaussian covariance function; from the model evidence, Gaussian covariance function was more suitable than the other two covariance function(Linear, Matérn 5/2). Observation error was modeled with an independent additive Gaussian model. The affine invariant ensemble sampler (AIES) algorithm was used to sample the posterior distribution in 2,000 steps and 300 parallel chains. Posterior results showed that uncertainty due to the model inadequacy was greater in predicting Cf than due to observation error. Prediction of Cf in transition region was improved by 6% .