Effect of cross-sectional anisotropy on shock train dynamics in supersonic internal flows

TL;DR

This paper examines how the shape of an elliptical duct influences shock train behavior in supersonic flows, revealing that duct aspect ratio alters shock morphology but not overall flow efficiency due to boundary layer effects.

Contribution

It provides new insights into the impact of duct cross-sectional shape on shock train structure and flow dynamics in supersonic internal flows, isolating shape effects from boundary layer influences.

Findings

Increasing aspect ratio reduces shock cell count.

Shock front elongates along the major axis with higher aspect ratio.

Flow efficiency remains unaffected by aspect ratio changes.

Abstract

This study investigates the effect of duct aspect ratio ($AR$), defined as the ratio of major to minor axis in an elliptical duct, on shock train dynamics for a freestream Mach number of 2.1. The aspect ratio $AR$ is varied from 1.0 to 3.0 while maintaining a constant cross-sectional area and identical upstream conditions, thereby ensuring the same inlet mass flow and nearly constant boundary-layer-induced blockage across all $AR$. This isolates shape-induced confinement effects. Simulations are performed using an embedded-boundary method with adaptive mesh refinement which enabled a finest resolution of 48$\mu$m resolving the shocks in the shock train. The results show that increasing $AR$ significantly modifies the shock train morphology. The number of discrete shock cells decreases, and the leading shock front elongates along the major axis while contracting along the minor axis. The normal shock stem prominent in the circular duct (AR=1.0) nearly disappears at AR=3.0. Despite these morphological changes, the wall-pressure trace and stagnation-pressure loss remain largely insensitive to $AR$. These results indicate that while duct cross-section governs the detailed shock train structure, the overall efficiency of flow deceleration and pressure recovery is dictated primarily by the effective blockage imposed by the turbulent boundary layer, rather than the aspect ratio itself for a given mass flow rate and pressure ratio across the pseudo shock.