A new similarity law for transonic–supersonic flow

Abstract

Similarity laws of aerodynamics are of crucial importance in both pre-computer time and the modern era, since they can greatly facilitate relevant aerodynamic analyses, wind tunnel experiments, and aircraft designs. In this Letter, we present a new similarity law for steady transonic–supersonic flow over thin bodies at a small angle of attack. The new similarity law is based on the extrapolation of the lift and drag coefficient slopes at a sonic point, which are obtained from the single longitudinal process. The effect of transverse process on the drag coefficient is accounted for afterwards by introducing a dimensionless wake width, which can be theoretically estimated. The remarkable feature of the new similarity law is that it depends on both the free-stream Mach number and the specific heat ratio. The validity of the new similarity law is confirmed by the excellent agreement with numerical data of the flow over a two-dimensional airfoil with the free-stream Mach number between 0.9 and 2.