Determination of the axisymmetric potential flow in the passages of turbomachines using the method of singularities

The method of singularities is applied to the problem of axisymmetric flow in fluid passages, and newly developed numerical techniques are used to achieve a highly accurate solution. The fluid passages are considered to be infinite at both entrance and exit. For example, in the case of a Francis turbine, the fluid passage at the entrance goes to infinity between two planes perpendicular to the turbine axis and the fluid passage at the exit goes to infinity inside of the cylinder parallel to the turbine axis. The gamma distribution along the infinite surfaces of revolution is determined as a solution of a Fredholm integral equation of the second kind.