The occurence and removal of indeterminacy from flow calculations in turbomachines

The flow physics for inviscid flow on an arbitrary two-dimensional streamsurface for application to turbomachines were re-examined without specializing to a particular type of surface. This re-examination introduces stream function as a function of three space dimensions which is two dimensional in the locality of the prescribed stream surface and does not involve the concept of a force normal to the surface. An equation of motion was developed which is applicable to any stream surface. This equation has several advantages over the principal equations formerly used, one being that rotation of axes is no longer necessary and solutions become possible for annular ducting of increased geometrical complexity including flow around a toroidal surface as in a fluid coupling. The coordinate form of the n bar principal equation is developed for application to hub-to-shroud stream surfaces and for blade-to-blade streamsurfaces of revolution. The n bar principal form of equator gains its advantage chiefly by its freedom from indeterminacy. Other forms of indeterminacy and computational failure may arise from the choice of coordinate system used to express the derivatives and the manner in which the molecule grid points are chosen. Other failures or restrictions relate to the way in which the grid is set up.