Centreline shock reflection phenomena for Supersonic Internal Flows in the non-Rankine-Hugoniot zone: Overexpanded Supersonic Microjets

TL;DR

This study numerically investigates how viscosity and rarefaction effects influence centreline shock reflection in overexpanded microjets, revealing transitions in shock configurations and providing insights into shock reflection phenomena in low-Reynolds-number, rarefied gas flows.

Contribution

It introduces a coupled Navier-Stokes and slip boundary condition model to analyze shock reflection in microjets, highlighting viscosity-induced shock configuration transitions not predicted by inviscid theory.

Findings

Viscosity causes a transition from three-shock to two-shock configurations.

Transition from Mach reflection to regular-like reflection is similar to dual-solution domain transition.

Mathematical prediction of incident shock curvature was achieved.

Abstract

The viscous and rarefaction effects on centreline shock reflection occurring in an overexpanded axisymmetric microjet have been investigated numerically by means of a fully coupled pressure-based shock capturing scheme. Due to the low free-stream Reynolds number (Re $\approx$ 7), the Navier-Stokes equations were coupled with slip velocity and temperature jump boundary conditions to account for rarefied gas effects in the Knudsen layer. It has been found that pronounced viscosity levels can cause a transition from a three-shock to a two-shock configuration, which is impermissible by inviscid theory. This provides novel evidence that supports recent observations for axisymmetric ring wedge intakes. Analysis of the von Neumann and detachment criteria indicates that the transition from Mach reflection to regular-like reflection is analogous to the dual-solution domain transition for planar shocks. In addition, prediction of the longitudinal curvature of the incident shock has been conducted from a mathematical standpoint.