Oscillatory behaviors of multiple shock waves to upstream disturbances

Abstract

The oscillatory response of multiple shock waves to upstream disturbances in a supersonic flow is studied numerically in a constant area rectangular duct. The flow is accelerated through a nozzle with an exit Mach number of 1.75 and continues in the constant area duct, where multiple shock waves are formed. To investigate the effect of upstream disturbance on shock oscillations, three parameters are varied systematically: upstream turbulent intensity, frequency of upstream pressure fluctuation, and amplitude of upstream pressure fluctuation. The wall shear stress variation along the duct length provides the location of separation and reattachment points in the flow field. The wall pressure frequency spectra were used to investigate the low-frequency unsteadiness in shock oscillations. The power spectral density of the wall static pressure and the probability density function (PDF) of shock location are analyzed, and the results suggest that as the upstream turbulent intensity is increased, the dominant frequency of oscillation is increased and the shock oscillations become more symmetrical. As the upstream disturbance frequency is increased, the shock oscillations become more symmetrical and follow the Gaussian curve closely. The shock wave oscillates with the same upstream excitation frequency when the upstream disturbance amplitude is increased. At large values of upstream disturbance amplitude, the PDF shows a large deviation from the Gaussian, and the rms amplitude of shock oscillation increases monotonously. At higher amplitudes of upstream disturbance excitation, the traces of shock train leading-edge location display path-dependence characteristics.