Global and local modal characteristics of supersonic open cavity flows

Abstract

Flows past cavities at high-speeds have become increasingly important in applications such as flame-holding and propulsion unstart control. Recently maturated linear techniques have helped discern the underlying mechanisms in the subsonic and low supersonic speed regime (M∞<1.4). Here, we combine these linear methods with fully non-linear two- and three-dimensional simulations to assimilate the significant changes observed when the Mach number is increased further to the 1.4≤M∞≤3 range. The resolvent method is first employed to analyze cavity-shear layer coupled oscillations and modal characteristics, which are found to differ in key respects from those reported at lower Mach numbers. At higher speeds, more 2D coupled modes are obtained with the dominant modes containing secondary waves displaying elaborate patterns. The role of the shear layer on the cavity dynamics is then examined with local spatial stability analyses. In addition to the well-known Kelvin–Helmholtz instability encountered in the subsonic and transonic regimes, forward-propagating (k+) supersonic shear layer instabilities are detected at higher speeds. These are associated with Mach wave reflections between the shear layer and the cavity floor and may introduce higher order coupled modes. Furthermore, 3D modal analysis indicates a shift toward the dominance of 3D modes compared to 2D modes; although consistent with compressible free shear layer observations, 2D cavity modes remain significant to higher convective Mach number. When the Reynolds number is increased, resolvent-based mode shapes and frequencies continue to compare favorably with Dynamic Mode Decomposition of large-eddy simulations because of inviscid instability dominance.