Summary: | An attempt to validate the use of the Riegels-factor and to obtain the camber line velocity near the nose of a rounded profile is made. Three methods for replacing profile thickness by a source distribution along the straight camber line of NACA-4-digit profiles 'by are described, the first/taking account of the induced velocity (method 2), the second by taking account of its derivative also (method 3), while the "methodl" refers to the previous simplification which uses the free stream velocity only. A new "source-correction-factor Rf " is presented and used in connection with each of the above methods (referred to here as method lA, 2A and 3A). The velocity distributions on the blade surfaces obtained by these methods together with the use of the Riegels~factor are compared with the surface velocity distributions obtained by the method of Martensen. Method 2 "is applied to an ellipse, and an analytical solution for the source distribution is derived. The numerical solution of the integral equation resulting is compared with the analytical solution and the difficulties arising in the numerical treatment are resolved. The modified numerical solution is applied also to the NACA-profiles, and in addition suggestion on the basis of the above numerical solution using method 3 is presented. In order to assess the validity of correction factors for obtaining surface velocities from camber line velocities on which source sheets are imposed the "Bounding Stream Lines" around arbitrary - x - linear source distributions are found iteratively after determination of the velocity components along the "camber line" and in the flow above it by exact numerical integration. Finally the stagnation points of the dividing stream line are also found by integration.
|