Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations

Abstract

The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the systems stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. These methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

“…The most dominating coefficients, in decreasing magnitude, correspond to the linear terms in M 0 , p 0 , δ i , and L i . This is consistent with the global sensitivity analysis performed in [27], where the leading total sensitivity Sobol indices for P stag were {M 0 : 0.904}, {p 0 : 0.033}, {δ i : 0.032}, and {L i : 0.031}. While the Sobol indices are not exactly equal to the linear coefficients (Sobol indices also include sum of coefficientssquared from higher order orthnormal basis terms), they are dominated by the linear coefficients in this case.…”

“…In this paper we focus on a setup that corresponds to the HiFiRE program [25]. This configuration is relevant for the design of supersonic combusting ramjet (scramjet) engines [27]. Having a fundamental understanding of this physical behavior is thus extremely valuable for producing accurate simulations and high-performing designs.…”

Embedded Model Error Representation for Bayesian Model Calibration

“…Specifically, we employed independent-normal approximation to the likelihood function and ABC-inspired likelihoods that compare the first two moments of the data and the embedded model. In principle, both are found to be viable options, and the choice should mostly be driven by the goals of the modeler (see, e.g., [58,32,54] for ABC, and [38,74,54] for independent-normal). Different approaches do typically lead to different posterior distributions.…”

Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds

“…The objective of the present paper is to use the recent approach devoted to probabilistic learning on manifolds [1] to the challenges presented by large-eddy simulations (LES) of reactive flows inside a scramjet combustor. While investigations adopting probabilistic approaches for scramjet applications are growing in recent years [2][3][4][5][6][7][8], substantial challenges remain in characterizing and predicting combustion properties for turbulent flows under extreme conditions especially in conjunction with uncertainty quantification. We are particularly interested in employing and enabling probabilistic methods with LES, since these simulations, while computationally more demanding, can allow us to access some turbulence details and features often not available through models involving additional simplifications, such as with Reynolds-averaged Navier-Stokes (RANS).…”