Linear potential theory of steady internal supersonic flow with quasi-cylindrical geometry. Part 2. Free jet flow

Abstract

By extending the methods of Part 1, the general problem of steady cylindrical supersonic free jet flow is treated in a similar manner to the flow in quasi-cylindrical ducts. It is shown that the presence of a finite pressure jump at the nozzle lip gives rise to a periodic singularity pattern in the flow field. Basic examples of free jet flows are discussed, and for the case of a nearly ideally expanded axisymmetric jet, theoretical Mach—Zehnder interferograms are calculated by analytical integration of the density field. Excellent agreement with experiment proves the validity of linear theory even close to the singularities and far downstream of the nozzle orifice. Furthermore, it is shown that Pack's formula for the wavelength of the shock cell structure is inconsistent; the correct formula is derived and excellent agreement with Emden's empirical fit is found.