Analysis of the Oscillatory Flows of Multiple Shock Waves in a Constant Area Duct

The oscillatory response of multiple shock waves to downstream perturbations in a supersonic flow is studied numerically in a rectangular duct. Multiple shock waves are formed inside the duct at a shock Mach number of 1.75. The duct has an exit height of H, and the effect of duct resonance on multiple shock oscillations is investigated by attaching exit ducts of lengths 0H, 50H, and 150H. The downstream disturbance frequency varied from 10 Hz to 200 Hz to explore the oscillation characteristics of the multiple shock waves. The oscillatory response of shock waves under self-excited and forced oscillation conditions are analyzed in terms of wall static pressure, shock train leading-edge location, shock train length, and the size of the separation bubble. The extent of the initial shock location increases with an increase in exit duct length for the self-excited oscillation condition. The analysis of the shock train leading edge and the spectral analysis of wall static pressure variations are conducted. The variation in the shock train length is analyzed using the pressure ratio method for self-excited as well as forced oscillations. The RMS amplitude of the normalized shock train length (ζST) increases with an increase in the exit duct length for the self-excited oscillation condition. When the downstream perturbation frequency is increased, ζST is decreased for exit duct configurations. For all exit duct designs and downstream forcing frequencies, the size of the separation bubble grows and shrinks during the shock oscillations, demonstrating the dependence on duct resonance and forced oscillations.