Global Sensitivity Analysis and Uncertainty Quantification for a Hypersonic Shock Interaction Flow

Abstract

Hypersonic gas flows over concentric double-cone configurations are commonly used to investigate shock-shock and shock wave/boundary-layer interaction phenomena, and are characterized by the formation of interacting flow structures that are highly sensitive to models used in flow simulation. The work presented here is intended to clarify the influence of several modeling parameters and approximations on simulation output quantities through a more general and systematic approach than has previously been employed for this type of flow, with the ultimate goal of improved model validation for simulation of hypersonic shock interactions. Global sensitivity analysis and uncertainty quantification techniques are integrated with a direct simulation Monte Carlo gas flow simulation code, and a large number of these Monte Carlo simulations are performed for a representative hypersonic double-cone flow. Aleatory and epistemic uncertainties are considered in sensitivity analysis/uncertainty quantification calculations, both independently and in combination, through a variety of probabilistic sampling procedures. These procedures include a novel uncertainty quantification technique that combines elements of importance sampling sensitivity analysis with Latin hypercube sampling, as an efficient surrogate-free means of simultaneously considering mixed uncertainty types. Following a strong engineering interest in surface heating augmentation due to hypersonic shock wave/boundary-layer interaction, this paper focuses on surface heat flux at a shock impingement point as an output quantity in sensitivity analysis/uncertainty quantification calculations; other output quantities of interest include impingement point pressure and the integrated force and heat transfer rate over the model surface. Nomenclature a = local speed of sound f = Gaussian probability density function K = number of postprocessing Monte Carlo samples for target input parameter distributions Kn max = maximum gradient length local Knudsen number M = sample size (or number of simulations) used for uncertainty quantification N= number of input parameters associated with uncertainty n = number density P = cumulative probability corresponding to a given output quantity value R i = Pearson product-moment correlation coefficient between quantities x i and y r = random number within specified domain for Latin hypercube sampling S = N × M matrix of input value combinations based on Latin hypercube sampling s ij = element in matrix S T = temperature V = bulk velocity magnitude x i = value for input parameter i ∈ 1; N y = output quantity value ϑ = uniformly distributed random number in [0, 1] λ = mean free path μ i = mean value for distribution of input parameter i ∈ 1; N ρ = mass density σ i = standard deviation for distribution of input parameter i ∈ 1; N

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