Patterns of steady axisymmetric supersonic compression flows with a Mach disk

Abstract

Results of a numerical simulation of steady axisymmetric supersonic flows in convergent conical ducts and in overexpanded jets are presented. The characteristic feature of these compression flows is the formation of an initial longitudinally curved shock wave with intensity increasing downstream and toward the flow axis, which is finalized by the generation of a central Mach disk. Computations have demonstrated patterns of an irregular interaction of these shocks followed by the formation of a triple-shock configuration, including a reflected shock and a shear layer with entropy varying across the layer. The formation of triple-shock configurations is analogous to the configurations known for the steady inviscid two-dimensional flows where the irregular reflection of a wedge-generated shock from a wall with Mach stem formation occurs. Either a single triple-shock Mach configuration occurs or a triple-shock configuration corresponding to the von Neumann paradox condition is formed at the considered flow Mach numbers and initial angles of deflection to the axis of the flow behind the longitudinally curved shock wave.

An investigation of starting processes and flow patterns occurring in hypersonic axisymmetric inlets of internal compression

“…The results obtained in [7] has shown that the triple-shock configurations forming in the axisymmetric flows with the Mach disc are analogous to the configurations known for the steady inviscid two-dimensional flows where the irregular reflection of a wedge-generated shock from a wall with the Mach stem formation occurs. Either the single triple-shock Mach configuration occurred or the triple-shock configuration corresponding to the von Neumann paradox conditions formed, depending on the considered flow Mach numbers and initial angles of deflection to the axis of the flow behind the longitudinally-curved shock wave.…”

“…The numerical solution of the problem on steadying the flow yields a particular irregular triple-shock configuration and its parameters, including a Mach disk position. Examples of computed occurring triple-shock configurations are presented in [7].…”

“…The types of triple-shock configurations possible in the axisymmetric flows were established in [7] basing on the shock polars and triple-shock theory developed by von Neumann and basing on the Rankine-Hugoniot jump relations. Note that this theory is valid for the two-dimensional flows of ideal gas.…”

“…A numerical simulation of the steady axisymmetric supersonic flows occurring in the considered funnel-shaped inlets was performed in the work [7] in order to study the peculiarities of these flows associating with the Mach disc formation depending on the free-stream Mach number and the conical wall angle. The flow structure in such an inlet schematically shown in Fig.…”

Numerical study of thermochemical effects on the flowfield structure near the triple point at irregular reflection of shock waves

“…Shock wave reflection and interaction are interesting from both fundamental [1,2] and applied [3,4] points of view. Traditionally the parameters around the point of shock intersection were predicted with the gas being considered as an inviscid fluid, for example, by using t three-shock theory [5].…”