Numerical study of viscous effects on centreline shock reflection in axisymmetric flow

Viscous effects on centreline shock reflection in an axisymmetric flow are studied numerically using Navier–Stokes and direct simulation Monte Carlo solvers. Computations at low Reynolds numbers have resulted in a configuration consisting of two shock waves, in contrast to the inviscid theory. On the other hand, computations at high Reynolds numbers have yielded a three-shock configuration in qualitative agreement with the inviscid theory prediction. This behaviour is explained by the presence of the so-called non-Rankine–Hugoniot zone, which accounts for the deviation of the shock structure from the inviscid paradigm. At Reynolds numbers on the verge of the transition from a two-shock to three-shock configuration, extremely high pressure that would be unattainable with the classical Rankine–Hugoniot relation for any shock configuration may occur. An analogy to the Guderley singularity in cylindrical shock implosion has been deduced for the shock behaviour from a mathematical viewpoint.