Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the HyShot II Scramjet

TL;DR

This paper introduces a novel active subspace methodology to efficiently quantify uncertainty in hypersonic scramjet simulations, reducing input parameters from seven to one and enabling comprehensive analysis with limited computational resources.

Contribution

The study applies active subspaces to hypersonic scramjet modeling, demonstrating dimension reduction and uncertainty quantification with significantly fewer simulations than traditional methods.

Findings

Identified key parameters influencing scramjet performance.

Estimated bounds and distributions of the quantity of interest.

Classified operating conditions as safe or unsafe.

Abstract

We present a computational analysis of the reactive flow in a hypersonic scramjet engine with focus on effects of uncertainties in the operating conditions. We employ a novel methodology based on active subspaces to characterize the effects of the input uncertainty on the scramjet performance. The active subspace identifies one-dimensional structure in the map from simulation inputs to quantity of interest that allows us to reparameterize the operating conditions; instead of seven physical parameters, we can use a single derived active variable. This dimension reduction enables otherwise infeasible uncertainty quantification, considering the simulation cost of roughly 9500 CPU-hours per run. For two values of the fuel injection rate, we use a total of 68 simulations to (i) identify the parameters that contribute the most to the variation in the output quantity of interest, (ii) estimate upper and lower bounds on the quantity of interest, (iii) classify sets of operating conditions as safe or unsafe corresponding to a threshold on the output quantity of interest, and (iv) estimate a cumulative distribution function for the quantity of interest.