Computational aspects of the prediction of multidimensional transonic flows in turbomachinery

The analytical prediction and description of transonic flow in turbomachinery is complicated by three fundamental effects: (1) the fluid equations describing the transonic regime are inherently nonlinear, (2) shock waves may be present in the flow, and (3) turbomachine blading is geometrically complex, possessing large amounts of curvature, stagger, and twist. A three-dimensional computation procedure for the study of transonic turbomachine fluid mechanics is described. The fluid differential equations and corresponding difference operators are presented, the boundary conditions for complex blade shapes are described, and the computational implementation and mapping procedures are developed. Illustrative results of a typical unthrottled transonic rotor are also presented.