---
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.'
address:
- 'Department of Applied Mathematics and Statistics, 1500 Illinois Street, Colorado School of Mines, Golden, Colorado, 80401'
- 'Center for Turbulence Research, 488 Escondido Mall, Building 500, Stanford University, Stanford, California, 94305'
- 'Department of Mechanical Engineering, 3149 Glenn L. Martin Hall, University of Maryland, College Park, MD, 20742'
author:
- 'P.G. Constantine'
- 'M. Emory'
- 'J. Larsson'
- 'G. Iaccarino'
bibliography:
- 'inflowUQ.bib'
title: 'Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the <span>H</span>y<span>S</span>hot <span>II</span> Scramjet'
---

uncertainty quantification ,active subspace ,hypersonic ,scramjet

Acknowledgments {#acknowledgments .unnumbered}
===============

This research was funded by the U.S. Department of Energy \[National Nuclear Security Administration\] under Award No. NA28614. Additional computational resources were made possible by the following award, MRI-R2: Acquisition of a Hybrid CPU/GPU and Visualization Cluster for Multidisciplinary Studies in Transport Physics with Uncertainty Quantification. This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The first author's work is supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0011077.

References {#references .unnumbered}
==========

{'source': 'arXiv_out/1408'}