© 1954 by Oxford University Press
COMPRESSIBLE SUBSONIC FLOW IN TWO-DIMENSIONAL CHANNELS WITH MIXED BOUNDARY CONDITIONS
( R.N.Z.A.F. Scientific Defence Corps )
Equations are given for the calculation of the subsonic compressible flow in two-dimensional channels
when the boundary conditions are ‘simply-mixed’, i.e. when the pressures are known over some contiguous
sections of the walls or bounding streamlines, and the shape of the remaining sections is assigned. Solutions to simple problems of this type in incompressible flow are occasionally met in the literature on fluid dynamics (see (1) and (2)). The method of solution is almost invariably based on an application of the Schwarz-Christoffel theorem on the conformal mapping of a polygon, an approach which is limited to problems in which the boundary conditions are specified as step functions. The general solution obtained in this paper includes as trivial examples many of the solutions obtained by separate and often lengthy applications of the Schwarz-Christoffel theorem, and, more important, provides a method of dealing with compressible subsonic flow past continuously curved walls. In this latter case the solution is given by an integral equation, which can be solved by a rapidly converging iterative process. Five examples are solved in section 5, namely
- the flow of a jet .deflected round a given curved surface (the Coanda effect, see (3));
- the design of a bend in a channel;
- the flow of a stream up a step, with boundary-layer separation;
- Helmholtz flow of a jet impinging normally on a flat plate;
- a generalization of Borda's mouthpiece.