Design Problem Relating to a Profile or a Cascade of Profiles and Construction of Orthogonal Networks Using the Riemann Surfaces for the Multiform Singularities

Summary

The complex potential induced by the source-vortex distribution is a multi-values function. In order to treat the field problem defined by the Dirichlet type boundary condition, it is necessary to get its correct value which has to be taken from an appropriate sheet of the Riemann surface. For the analytical formulations of a homogenous density distribution over a segment or a cascade of segments, it can be done that the multi-value part is located at one of the end points of each segment. An algorithm is proposed to get the appropriate definition according to the relative positions of the induction element with the reception point.

The construction of an orthogonal network inside a domain by solving the Dirichlet problem is shown. The simple layer distributions on the boundaries of the domain are used to generate the field in this example.

The turbomachine blading design in connection with the flow field problem is described. The proposed method admits the thickness distribution and the bound vortex distribution as the initial data. In the case of the 2D cascade, we show how to define the boundary conditions in order to obtain a properly posed field problem.