Three-Dimensional Unsteadiness of a Shock Train in a Low Aspect Ratio Rectangular Duct

The unsteady dynamics of a shock train in a low aspect ratio, rectangular duct are investigated using large eddy simulations. Flow conditions are defined by the incoming Mach number (M∞ = 2.0) and the ratio of mean outlet to inlet pressures (pb/pi = 2.5), whereas geometric conditions are defined by the aspect ratio of duct width to height (w:h = 0.82). Significant differences between the statistics of the lateral (side) and vertical (top/bottom) walls are noted, with the side wall experiencing elevated pressure fluctuations. These differences are explained by examining the band isolated dynamics of side and bottom wall pressure fields and the oscillatory motion of the shock feet interacting with the boundary layers lining each wall. Low-frequency shock motions manifest as an essentially rigid body motion of the entire shock column, whose signature manifests as low-frequency pressure oscillations on all duct walls. Mid-band dynamics are dominated by tonal shock oscillations, driven by a combined hydrodynamic-acoustic feedback loop between adjacent shock-boundary layer interactions within the train. These tones, characterized by a dominant fundamental frequency and its first two harmonics, leave a significantly larger pressure signature on the side wall than the bottom wall. Large differences in pressure variance between the lateral and vertical walls are attributed to this phenomenon. However, high-frequency dynamics, such as those associated with eddying motions of the turbulent boundary layer and associate local shock responses, remain similar between the two walls.