Handbook of Compressible Aerodynamics

Chapter 25

Some Properties of Transonic Flows

25.1. Introduction

A flow is called transonic if the field contains both subsonic and supersonic regions. If the flow is retarded (undergoes a compression), these regions are usually separated by a normal or nearly-normal shock wave, whereas in the case of an expansion, the transition from subsonic to supersonic happens continuously with as boundary a sonic line which is a locus of points where the critical velocity is reached (Mach number equal to 1). Transonic flows are met:

– at the throat of a convergent-divergent nozzle accelerating the flow to supersonic velocities (see Figure 25.1a),

– in a channel or interblade passage, where a counter pressure causes the formation of a shock wave (see Figure 25.1b),

– before the nose of a projectile where a detached shock wave forms downstream of which the subsonic flow accelerates and becomes supersonic (see Figure 25 .1c),

– on a wing profile where, at high subsonic flight Mach numbers, the acceleration created by the shape of the airfoil causes the supersonic passage of the flow, the supersonic pocket being ended by a shock wave (see Figure 25.1d).

The prediction of transonic flow in a non-viscous fluid has long faced the difficulty of the coexistence of subsonic regions, governed by elliptic equations, and supersonic regions where the equations are hyperbolic. This raises difficult theoretical problems due to the change of the disturbance propagation mechanisms which, in the first case, ...