  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.
