Mach-disk formation and shock-structure transitions in underexpanded coflowing jets

Abstract

The near-field shock structures of underexpanded sonic jets exiting into a subsonic coflow are investigated over a range of nozzle pressure ratio (NPR) and coflow-to-nozzle-exit velocity ratio ($U_c$), representative of a propulsive nozzle in subsonic flight. Time-averaged statistics from fully-resolved axisymmetric simulations and inviscid method-of-characteristics (MOC) analysis are used to understand how coflow alters the shock-cell structures, in particular the Mach-disk formation. It is well established that increasing NPR transitions the centerline reflection from regular (characterized by oblique shocks) to Mach reflection (characterized by a near-normal Mach disk). We find that coflow has the opposite influence: a strong coflow shrinks the Mach disk until it vanishes, reverting Mach reflection to regular reflection, so the NPR for this transition increases with $U_c$. This effect has previously been attributed to a reduction in the jet-boundary inclination at the nozzle lip, which confines the lip Prandtl-Meyer fan to a smaller angle and weakens the embedded shock. We show instead that this inclination is determined by the non-uniform pressure the coflow imposes along the jet boundary, which is the primary driver of the shock-structure transitions in coflowing jets. The non-uniform pressure weakens the boundary-reflected compression waves and orients them at shallower angles, so the embedded shock reflects regularly or fails to form. A simulation-informed MOC analysis with this non-uniform pressure boundary condition reproduces the transition behavior with increasing coflow. Coflow also lengthens the first shock cell linearly, which is accurately estimated by a simple correction to Prandtl classical shock-cell length scaling.