Computation of the Potential Flow through Cascades using the Conformal Mapping and the Singularity Method

抄録

A new procedure for a numerical analysis of a two-dimensional incompressible potential flow through cascades of airfoils with arbitrary profiles has been presented. The procedure consists of three steps. At first, a cascade of airfoils in a physical plane are transformed into a near-circle row using a simple mapping function; then the flow field through near circles in the mapped plane is calculated with the singularity method. Finally, the flow in the mapped plane is transformed back into the physical plane. The method for determination of parameters of the mapping function to obtain near-circles with sufficiently smooth contours in the mapped plane, which is indispensable in achieving the highest numerical accuracy in the singularity method, has been proposed. The validity of the procedure is demonstrated by comparing the present results with exact solutions, which indicates that the present procedure is very useful for the computation of the cascade flow with simple thin airfoils as well as many practical airfoils with a camber and thickness.