Quantification of parametric uncertainty in k–ω–γ transition model for hypersonic flow heat transfer

Abstract

The uncertain empirical values of closure coefficients in k–ω–γ transition model flaws the predictive capability. The current work aims to examine the uncertainty of k–ω–γ transition model due to uncertain closure coefficients for hypersonic flow over a flat plate and a straight cone, with introducing the stochastic expansions based on the point-collocation non-intrusive polynomial chaos method into computational fluid dynamics simulations for efficient and accurate uncertainty propagation. Specifically, five model coefficients are regarded as epistemic uncertain probabilistic variables on intervals. The output quantities of interests include the surface heat flux, skin friction coefficient, transition onsets and transition lengths. To better identify the key uncertainty contributor, Sobol indices are utilized as a variable-based global sensitivity analysis approach. Results show that the performance of the k–ω–γ transition model is highly susceptible to its closure coefficients evidenced by that small changes (10%) of model coefficients could yield more than 30% uncertainty in the transition onsets and roughly 17% uncertainty in the transition lengths. The largest uncertainty source contributing to the uncertainty in heat flux, Cf and transition onsets is C3 for hypersonic transitional flows. Besides, C4 dominates the uncertainty in transition lengths. In the future model improvement, attention should be paid to improve apprehension of rational values or constitutions of C2, C3 and C4.