Compressible Subsonic Impinging Flows

This paper establishes the existence and the uniqueness of two dimensional steady compressible subsonic impinging flows. It is demonstrated that there exists a critical value mcr > 0 such that when the mass flux m0 of the incoming flow is less than mcr, a subsonic irrotational impinging flow also exists, but such a subsonic impinging flow does not exist if m0 > mcr. The impinging flows possess a positive horizontal velocity, except on the wall, and a unique stagnation point on the plate. It is also shown that there exists a smooth streamline which separates the fluids flowing out of the different outlets of the nozzle. Several results on the uniqueness of the subsonic impinging flow are provided. The asymptotic behaviors of the impinging flows both in the upstream and the downstream are also described. Finally, some examples and comparison results are given for special nozzles.