Prediction of shock wave configurations in compression ramp flows

TL;DR

This paper introduces a theoretical framework based on the least action principle to predict shock wave configurations and pressure peaks in compression ramp flows, aligning well with experimental and numerical data.

Contribution

The study develops a novel theoretical approach to predict shock wave shapes and pressure peaks in compression ramp flows, independent of Reynolds number and wall temperature.

Findings

Theoretical predictions match experimental and numerical data.

Shock configuration depends on Mach number and ramp angle, not on Reynolds number or wall temperature.

The framework can be applied to other shock-dominated flow systems.

Abstract

Here, we provide a theoretical framework revealing that a steady compression ramp flow must have the minimal dissipation of kinetic energy, and can be demonstrated using the least action principle. For a given inflow Mach number $M_{0}$ and ramp angle $\alpha$, the separation angle $\theta_{s}$ manifesting flow system states can be determined based on this theory. Thus, both the shapes of shock wave configurations and pressure peak $p_{peak}$ behind reattachment shock waves are predictable. These theoretical predictions agree excellently with both experimental data and numerical simulations, covering a wide range of $M_{0}$ and $\alpha$. In addition, for a large separation, the theory indicates that $\theta_{s}$ only depends on $M_{0}$ and $\alpha$, but is independent of the Reynolds number $Re$ and wall temperature $T_{w}$. These facts suggest that the proposed theoretical framework can be applied to other flow systems dominated by shock waves, which are ubiquitous in aerospace engineering.