马赫角与马赫数关系的点源推导法

本文建立了压强扰动波的点状波源模型,阐述了压强扰动波的传播机理,写出了扰动源所满足的波动方程及其推迟势的解.并采用点源的坐标变换法导出超声速物体产生的马赫波的马赫角与马赫数所满足的关系式.

New Derivation of Relationship between Mach Angle and Mach Number

The relationship between Mach angle and Mach number is well known in supersonic aerodynamics. Starting from experimentally observed facts, von Karman ingeniously employed a simple geometrical relationship to derive this basic formula. Bond et al presented in their book a derivation of relationship between Mach angle and Mach number which requires relatively advanced knowledge of physics. The author now presents a derivation that is much simpler than that of Bond et al. There are three points in which the two derivations differ, with the first two points accounting for the much greater simplicity of the author's derivation: 1. There is marked difference in the way of establishment of needed wave equation, Bond et al superimpose small disturbance on steady state flow through taking simultaneously into consideration the fundamental equation of motion for fluid flow, equation of state, and continuity equation. The author deems that an object flying in the supersonic range is a point source emitting continuously pressure disturbance wave. With this point-source model, the needed wave equation and its solution, which is called the retarded potential, are written directly. 2. Right-band side of wave equation is different. That of Bond et al is a potential function connected with the interaction between supersonic body and surrounding air. This potential function brings much complication. Such complication is bypassed in the author's derivation. 3. The author's method of solution is not the traditional method. It is what the author calls the method of coordinate transformation of point source.