Model Order Reduction of Scramjet Isolator Shock Dynamics During Unstart

Abstract

The unsteady shock dynamics occurring in a numerically simulated unstarting scramjet isolator are examined using a novel model order reduction technique. The key challenges associated with the non-stationary nature of the phenomenon are overcome by leveraging a combination of Empirical Mode Decomposition (EMD) followed by time dependent snapshot shifting. The EMD method serves two purposes: to identify the oscillation modes of the unstarting shock train and to subsequently use the calculated non-stationary residual function to invoke a translating frame of reference that is co-moving with the unstarting shock system. Each snapshot is then shifted into the determined reference frame and subsequently windowed in space, creating a smaller, subset of snapshots from the original database. The windowing is informed by the physics of pseudo-shocks, and has the benefits of ensuring that each new snapshot contains the entire unstarting shock train, while simultaneously preventing the effects of circular shifting that have plagued other model order reduction techniques based on shift operators. When applied to the unstart problem, the shifting and windowing technique presents a more statistically stationary view of the unstarting shock dynamics in the frame of reference of the moving shock train. Dynamically relevant modes associated with upstream and downstream propagating pressure waves at the peak shock oscillation frequency in the boundary layers and separation regions are further extracted from the shifted and windowed snapshots using the sparsity promoting Dynamic Mode Decomposition algorithm.