Investigations of Transonic Diffusers : 2nd Report, Theoretical Study on Stability of a Shock Wave

Abstract

The response of a normal shock wave in a transonic diffuser to small-amplitude pressure disturbances introduced downstream of the shock wave is analyzed with the method of small perturbations. The subsequent shock wave motion is classified into a stable oscillation about the initial steady flow shock position and an unstable case where the shock wave moves upstream of the throat, depending on the initial shock position and the pressure recovery in the subsonic region downstream of the shock wave. The stability criterion of the shock wave is presented as a function of the Mach number where the shock is initially located and the diffuser efficiency of the subsonic region downstream of the shock, and it is shown that the criterion agrees well with the previous experimental results.