Exact solutions of compressible plane potential flows - a new approach
The paper presents a new method for finding exact closed-form solutions of steady plane irrotational flow of compressible fluids when the pressure is a single-valued function of density only. A short description of two existing methods for finding exact solution can be found in the introduction. The authors' method is based on introducing a streamfunction \(\psi\) and then on treatment the plane variables \(x,y\), velocities \(u,v\), pressure \(p\) and density \(\rho\) as functions of \(\beta, \psi\) instead of independent variables \(x,y.\) Here \(\beta,\psi\) form curvilinear coordinates in the physical plane in which the curves \(\psi=\)const are the streamlines. It is shown that this approach delivers infinitely many solutions for the full potential equation. Vortex and spiral flows are re-discovered, too.
scientific article; zbMATH DE number 1045413
scientific article