On the influence of co-flow on the shocks and vortex rings in the starting phases of under-expanded jets

Abstract

In the starting phases of continuously blowing under-expanded jets, this numerical study investigates the effect of co-flow (UaUj) (a) on the circulation and evolution of primary vortex ring (PVR) and (b) on the occurrence of Mach reflection, slipstream generation, and subsequent formation of counter rotating vortex rings (CRVRs). With increase in co-flow (UaUj), the PVR circulation gradually decreases. The size of supersonic PVR gradually decreases with increase in co-flow (UaUj), and at high magnitudes of co-flow (UaUj≳0.3), the supersonic PVR attains a circular shape. The strengths of embedded shock (ES) and vortex-induced shock are found to decrease with increase in co-flow (UaUj), and at high magnitudes of co-flow (UaUj≳0.3), these shocks may even cease to form inside the supersonic PVR. An increase in co-flow (UaUj) causes the expansion fan to become more and more narrow. This reduces the acceleration of the supersonic flow inside the inviscid core, thereby weakening the incident oblique shock (IOS), which in turn increases the pressure prevailing downstream of this shock inside the inviscid core. The increase in co-flow (UaUj) also leads to a simultaneous decrease in the pressures prevailing in front of the downstream marching PVR and Mach disk (MD) of the inviscid core due to the reduction in the strength of precursor shock. As the magnitudes of pressures prevailing in the upstream and downstream of Mach disk approach each other, hence, MD also weakens. This shows that with the increase in co-flow (UaUj), there is weakening of the different shocks (i.e., ES, IOS, and MD) involved in Mach reflection. This causes a reduction in the strength of the resulting slipstream, thereby affecting the formation of CRVR patterns.