Elementary propeller theories in compressible inviscid fluids

Abstract

The existing propeller theories are valid for an incompressible inviscid fluids range. In the present paper, the known Glauert's propeller theories are transferred into the compressible inviscid fluids region. All the discontinuity phenomena are excluded from the considerations. Four elementary theories will be discussed: axial momentum-, general momentum-, improved general momentum-, and vortex theory. The application of some approximate methods of solution, like Pistolesi's method, to compressible range will be shown. In a first approximation, Betz's theory of propellers of highest efficiency may be applied to propellers moving in a compressible medium, with the assumption that the conditions existing in the propeller's wake are invariable and that the compressibility phenomena are restricted to the close neighbourhood of the propeller with the density in the propeller's plane differing from that one in the wake. There are indications, however, that Betz's theorem should be revised for compressible range since the Froude-Finsterwalder theorem, on which the previous one is based, breaks down for compressible fluids as Frankl had shown.