We investigate the onset of three-dimensionality in a Mach 5 slender-double-wedge flow as the turn angle at the compression corner increases. Beyond a critical angle, the two-dimensional flow destabilizes to three-dimensional perturbations and results in growth of spanwise periodic flow structures. We carry out global linear stability analysis to identify the critical turn angle and the nature of the associated three-dimensional instability. At the critical angle, an unstable mode is present in the separation bubble and the reattached boundary layer. The mode is associated with streamwise streaks in wall temperature downstream of the corner. The existence of the unstable mode and its growth rate are confirmed with direct numerical simulations. It is found from budget analysis that streamwise deceleration of the recirculating flow plays a dominant role in the three-dimensional instability. Wave-maker analysis suggests that the instability does not have a centrifugal origin. Linear stability analysis of the steady-state flow at an angle beyond bifurcation is also carried out. The spanwise wavelength of the most unstable mode obtained at this turn angle compares well with experimental observations.
Bibliographical noteFunding Information:
We acknowledge support from the Office of Naval Research (Grant No. N00014-15-1-2522).
We acknowledge support from the Office of Naval Research (Grant No. N00014-15-1-2522). We thank John Thome for help with the grids and Anthony Knutson for careful reading of the equations.
© 2018 American Physical Society.