A new similarity law for transonic-supersonic flow

TL;DR

This paper introduces a new similarity law for steady transonic-supersonic flow that improves the prediction of aerodynamic forces by incorporating local Mach number and specific heat ratio, validated through numerical simulations.

Contribution

It proposes a novel similarity law based on the local Mach number frozen principle, enabling more accurate aerodynamic force predictions in high-speed flows.

Findings

Excellent agreement with numerical simulations of airfoil flows

Effective in predicting lift and drag coefficients

Applicable to both 2D and 3D high-speed flows

Abstract

How to determine accurately and efficiently the aerodynamic forces of the aircraft in high-speed flow is one of great challenges in modern aerodynamics. In this Letter we propose a new similarity law for steady transonic-supersonic flow over thin bodies. The new similarity law is based on the local Mach number frozen principle. It depends on both the specific heat ratio and the free-stream Mach number. The new similarity law enables one to determine the lift and drag coefficients of the aircraft from that of a reference state which is more reachable. The validity of the new similarity law has been confirmed by the excellent agreement with numerical simulations of both two-dimensional airfoil flows and three-dimensional wing flows.