Generalised similarity solutions for 3-D laminar compressible boundary layer flows on swept profiled cylinders

Summary

The method of generalised similarity allows us to derive solutions for the laminar steady, compressible three-dimensional boundary layer equations for flows over swept wings. The model configuration is that of an infinitely long swept profiled cylinder in an ideal gas flow whose dynamic viscosity is a linear function of temperature. A universal mathematical model is derived by successively introducing three transformations: Stewartson’s, Saljnikov’s Generalized Similarity [2] and Loitsianskii’s Group of Parameters [7]. It can be integrated numerically by the finite difference iterative method — Tridiagonal Algorithm (TDA) — with an arbitrary choice of pressure distribution, Pr and Ma numbers, as well as of the angle of sweep and the temperature boundary condition. In the article, however, an interesting practical problem of transonic swept wing with air flowing around it is considered for two cases of: a) isothermal and b) adiabatic wall. The obtained results are presented graphically and analysed.