Uncertainty and sensitivity analysis of flow parameters for transition models on hypersonic flows

Abstract

The impossibility to reproduce the experimental conditions, which is difficult to perfectly control and inevitably fluctuate, raises the uncertainties in numerical simulation. The objective of this work is to quantify the uncertainty and sensitivity of hypersonic transition modeling due to uncertainty in the flow parameters. Two representative transition models, e.g. γ-Reθ and k-ω-γ, are considered. And five flow parameters including freesteam Mach number, pressure, temperature, turbulence intensity and wall temperature are selected as aleatory uncertain variables uniformly distributing among the bound. Then the stochastic expansions based on point-collocation non-intrusive polynomial chaos (NIPC) method is utilized to represent and propagate the uncertainties in the output quantities of interests (QoIs) for hypersonic flow over the flat plate and the straight cone. Benefiting from the efficiency of the NIPC method, accurate uncertainty results are obtained with only 42 evaluations for each problem. Furthermore, Sobol indices are utilized to provide a relative ranking of each input uncertainty to the overall uncertainty in the output. The uncertainty results quantitatively verify that the transition zone is great sensitive to changes in flow parameters. Besides, for both the heat flux and skin friction coefficient, the importance ranking of the flow parameters and their trends are roughly resemble between the γ-Reθ and k-ω-γ model. This signifies that their sensitivity with respect to the input parameters is mainly associated with flow features rather than transition models. However, the contrary is the case for uncertainty in transition onset and length whose sensitivity to uncertainties of input parameters depends strongly on transition models. The present investigation shows that the freestream pressure is the greatest contributor to uncertainty in most cases. The freestream turbulence intensity, whose effect can be nearly negligible in heat flux and Cf, plays a predominant role on transition length.