Dynamics study of shock wave intersection under high-frequency sine oscillation incoming flow

Abstract

This paper numerically studies the dynamics of symmetrical wedge shock intersection under sinusoidal supersonic oscillation conditions. The 15° symmetrical wedges are used as the shock generator, and the sinusoidal oscillation is used as the inflow condition. Two forms are considered: (I) The fluctuation amplitude is kept constant ( A = 1.4), and the influence of the fluctuation frequency from 4 kHz with a step of 2–10 kHz in the shock wave system is considered. (II) Keeping the frequency constant ( f = 10 kHz), the effect of three amplitudes ( A = 1.0, 1.4, 1.8) on shock waves is considered. A detailed analysis of unsteady flow features, including the Mach stem growth, the swing of slip lines, pressure evolution, and peculiar pressure wave phenomenon are presented with a focus on the bi-directional regular intersection (RI ↔ MI) Mach intersection transition process. The study found that: RI ↔ MI always occurs near the von Neumann solution, and there are premature transformation and hysteresis. The higher the frequency, the more noticeable the hysteresis and premature transformation are, the more obvious the swing of slip lines is. The lower the frequency, the longer the bi-directional transition time of the RI ↔ MI, the greater the maximum height of the Mach stem, the more frequent the triple points' pressure fluctuation. In addition, the oscillating flow will cause the propagation of pressure waves in the slip line channel and the transition from transverse waves to longitudinal waves. Under the condition of different amplitudes, the greater the amplitude is, the greater the height of the Mach stem is. When the amplitude is maximum, the Mach number of partial incoming flow is less than the minimum Mach number of the attached oblique shock wave. The evolution of the detached shock wave will lead to the complexity of the system. As the amplitude increases, the greater the pressure difference of the triple points, the greater the curvature of the incident shocks. The research of the unsteady shock wave intersection under the oscillating flow is useful to the study of supersonic flow, loss control, and heat and mass transfer of detonation engines and intake ducts.