Transonic Controversy and Regular Perturbation Methods for Subcritical Flows

Part 1: Transonic Controversy. The flow of an inviscid, irrotational and compressible perfect gas in the upper half plane is used as a model to investigate the transonic controversy. The solution of the complete potential equation for the velocity potential (phi)(x,y), with boundary condition: (phi) + c (phi)(,y) = U sin x on y = 0, is developed as a regular perturbation series. 36 terms of the series are determined by computer. The effective boundary condition is varied with the choice of c; and for each of the velocity series, its nature and the location of the singularity nearest to the origin are investigated using the ratio method of Domb and Sykes and Pade approximants. The result of the analysis shows that the phenomenon of shockless transonic flow is dependent on the imposed boundary condition. Part 2: Regular Perturbation Methods for Subcritical Flows. Regular perturbation methods, namely the Jansen -Rayleigh expansion and the Prandtl-Glauert expansion, are used to solve steady, inviscid, irrotational, subcritical flow field over arbitrary two-dimensional bodies. To facilitate the computation, the particular integrals of successive order equations are found by Macsyma. The literal operations of routine algebra of extending the series are then performed by Fortran. These perturbation methods provide an alternative approach to solution of two dimensional flow field other than usual numerical methods of finite difference, finite volume, finite element and integral equation method. As compared with other numerical methods, these methods are easier to implement, use much less computation time and less computer storage. The order of accuracy is generally highly than most approximation methods.