The incompressible two-dimensional potential flow through blades of a rotating radial impeller

The Busemann coefficients for the performance of a rotating impeller in 2-dimensional potential flow are computed by means of Fourier series applied to general smooth shapes of blades. Busemann’s results for the logarithmic blade are reviewed historically from Wagenbach to Acosta. The relative steady flow is analyzed by the method of Muskhelishvili. The analysis in terms of Fourier series is directly carried out in Convolution Algebra of Taylor and Laurent series. Busemann’s coefficients are re-computed with Busemann’s exact analytic equations for logarithmic shaped blades, as reference for the Fourier series method, except the theoretical asymptotic case of infinitely long blades. The convergence of series in three possible mapping planes is explored. The logarithmic blade is then used as the basis for analytic variations. Examples are given of general non-logarithmic shapes combined with the Theodorsen iteration method in DDFT. The Wislicenus coefficient and Busemann’s coefficients are re-defined for the general blade and its connection with the slip factor, and an inner slip velocity is introduced. Some results are given in the graphical form of streamlines. The alternative velocity boundary value method with Convolution Algebra is given in an Appendix.