Unified Equation of Motion (UEM) Approach as Applied to S1 Turbomachinery Problems

Abstract

Incompressible, blade-to-blade (SI surface) flow solutions for stators and rotors of turbomachines are obtained utilizing an approach which combines the equations of motion into a single elliptic, second-order partial differential equation for the streamline field. This Unified Equation of Motion (UEM) is obtained from the momentum equation which is modified by using a stream function that satisfies the continuity equation identically. The unified equation is solved numerically by use of a finite difference technique. The velocity field is determined by differentiation of the stream function field and use of the computed streamlines. The pressure field is then determined from an energy relation along the streamlines. The present method is similar to the classical Streamline Curvature Method (SLCM) in that a computation grid is not required; however, the ellipticity of the flow field is preserved directly by the unified equation of motion. The UEM solution is substantially more stable than the SLC method and yields the periodic stagnation streamlines directly. Body-fitted curvilinear coordinates (quasi-orthogonals and streamlines) are generated naturally by the UEM solution. A number of comparisons of the results of the present method are made with experimental data and results of other numerical methods. These comparisons are made for incompressible two dimensional and quasi-three dimensional stationary and rotating blade sections. There is general agreement with accepted analysis procedures.