Bow shock stand-off distance for subsonic decelerating bodies

Abstract

Projectile accelerations above $$500~\hbox {ms}^{-2}$$ are commonly encountered in aerodynamic applications, but suitable validation data are rare in this regime. Experimental transonic velocity range data for a sphere decelerating under its own drag have been used to validate a numerical model for decelerating objects. The validated model is then used to explore the flow field ahead of objects decelerating from supersonic to subsonic Mach numbers. To model the non-inertial frame of the projectile, source terms were included in the momentum and energy equations in a computational fluid dynamics model. In decelerating cases, the bow shock formed in supersonic flight persists in the subsonic regime. The differences in the flow field between the steady and unsteady cases are explained using the concept of flow history. In the experiment, a tubular insert was present near the observation window in the ballistic range. The insert was numerically modelled, and it is shown that the resulting bow shock behaviour can be explained in terms of the Kantrowitz criterion, in conjunction with flow history. The RAE2822 aerofoil was used to explore the effects of shock overtaking and propagation during deceleration from supersonic to low subsonic Mach numbers. In this case, the bow shock wave persists from the initial supersonic speed to projectile Mach numbers lower than 0.4. The expansion wave and tail shock are shown to overtake the decelerating projectile and propagate forward, behind the bow shock.