Uncertainty Quantification of GEKO Model Coefficients on Compressible Flows

Abstract

In the present work, supersonic flows over an axisymmetric base and a 24-deg compression ramp are investigated using the generalized k-ω (GEKO) model implemented in the commercial software, ANSYS FLUENT. GEKO is a two-equation model based on the k-ω formulation, and some specified model coefficients can be tuned depending on the flow characteristics. Uncertainty quantification (UQ) analysis is incorporated to quantify the uncertainty of the model coefficients and to calibrate the coefficients. The Latin hypercube sampling (LHS) method is used for sampling independent input parameters as a uniform distribution. A metamodel is constructed based on general polynomial chaos expansion (gPCE) using ordinary least squares (OLS). The influential coefficient closure is obtained by using Sobol indices. The affine invariant ensemble algorithm (AIES) is selected to characterize the posterior distribution via Markov chain Monte Carlo sampling. Calibrated model coefficients are extracted from posterior distributions obtained through Bayesian inference, which is based on the point-collocation nonintrusive polynomial chaos (NIPC) method. Results obtained through calibrated model coefficients by Bayesian inference show superior prediction with available experimental measurements than those from original model ones.