Non-unique regimes of oscillatory transonic flow in bent channels

Abstract

The turbulent transonic two-dimensional airflow in 9°-bent channels is studied numerically on the basis of the Reynolds-averaged Navier–Stokes equations. The flow is supersonic at the entrance of channels and subsonic at the exit. Numerical solutions reveal non-uniqueness of flow regimes in certain ranges of boundary conditions. The location of a formed shock wave exhibits hysteresis with changes in the inflow Mach number M_∞, or the angle of attack, or pressure given at the exit p_exit. The existence of hysteresis is caused by an interaction of the shock wave with an expansion flow region over the convex wall of channel. Shock wave behavior under forced oscillations of the Mach number M_∞ or pressure p_exit is discussed. Dependencies of hysteresis and non-unique regimes on the amplitude and period of the oscillations of M_∞, p_exit are studied. It is shown that hysteresis in a long channel is essentially wider than that in a short one.