A Perspective of Shock Waves for Gasdynamical and Granular Flows

Abstract

Shock waves are an important phenomenon observed in supersonic gasdynamical flows and also in granular free-surface flows at a supercritical speed when the flow is deflected by an obstacle. Between these two types of flows there exist both strong analogies and distinctions, and we here intend to discuss a few aspects on the difference between the gasdynamical and granular flows. We first compare the oblique shock relations between them, where weak, strong and detached shock waves can be generated in both conditions. If the upstream Froude number of granular flow becomes infinitely large, however, a granular shock wave would still remain attached and oblique around a wedge at a deflection angle of 90°, while an attached gasdynamical shock wave is limited by a maximum wedge angle of, say, 45.6°. On the other hand, the shock standoff distance for a detached granular shock wave tends to become infinitely small with the increase of the upstream Froude number since it is associated with the flow height ratio across the shock wave, whilst that of a detached gasdynamical shock approaches a constant value due to the limitation in the compressibility. Finally, an example of shock interaction is discussed to suggest that a complex shock system could lead to some instability effect in the flow.