Multi-fidelity numerical simulations of shock/turbulent-boundary-layer interaction in a duct with uncertainty quantification

The interaction between shock waves and turbulent boundary layers (STBLI) plays a fundamental role in the operation of (sc)ramjet engines utilized in supersonic/hypersonic flight vehicles. In particular, the isolator part of such engines is often designed to contain a series of shock waves (shock-train) that sets the flow of incoming, atmospheric air in the optimal conditions for its subsequent mixing and combustion with the injected fuel. Robust design of isolators (and other engineering components) requires an assessment of their response to deviations with respect to operating nominal conditions, resulting, for example, from aleatory uncertainties in the flight conditions as well as from fabrication or operational tolerances in the engine geometry. Numerical simulations can potentially be used to exhaustively map such response at a reduced cost and time compared with experiments, but the validation of the computational models in the range of conditions considered is a prerequisite before the predictive capabilities of the simulations can be trusted. This validation includes the evaluation of numerical errors due to the computational formulation (e.g., numerical discretization) as well as the quantification of epistemic uncertainties due to simplifying or erroneous modeling assumptions. The objectives of the present work are multifold: first, experimental results of a nominal STBLI in a low-aspect ratio duct (Helmer et al. 2012) are used to validate the use of an equilibrium wall-model in high-fidelity, large-eddy simulations (WMLES) of this flow type, representative of the first interaction occurring in an isolator (see Section 2 for a description of the flow conditions and numerical setup). Second, 2D and 3D ReynoldsAveraged Navier-Stokes (RANS) simulations are performed to evaluate the suitability of lower fidelity computations to predict flow features and derived quantities of interest relevant in the design of such engine isolators, by comparing their results with both experiments and WMLES (see Section 3 for a four-way comparison of experimental and simulation results). Third, these lower fidelity computations are used to quantify the importance of different sources of uncertainty: geometric perturbations (Section 4) that replicate the experimental work of Campo et al. (2012) and inflow variations (Section 5) are considered as aleatory uncertainties, whereas the turbulence model form is taken as a source of epistemic uncertainty (Section 6). Fourth, the effect of those aleatory and epistemic uncertainties is balanced (Section 7).