Transpiration Boundary Conditions for a Steady Inverse Method

Abstract

Computational fluid dynamics has been widely used in the analysis of turbomachinery blades, however, its use as a design tool is far from sophisticated. The inverse method is such a design approach, which lends it self to the latter category. One application of the inverse method is the so called “pure inverse methd”, which differs from common analysis solver mainly in the boundary conditions on the blade surfaces. For this application, the usual non-penetration boundary conditions on the blade surfaces are aborted, instead, some aerodynamic constraints are imposed, and the flow is allowed to transpire through the actual solid wall. A camber line generation equation is added to periodically re-generate the blade camber line and drive the normal velocities on the blade surfaces to zero. When converged, the inverse method should obtain the blade shapes which satisfy the specified aerodynamic performance. In the present paper, three transpiration boundary conditions for turbomachinery blades design are compared in terms of time cost, robustness, capability of coping separation flow etc. The first inverse boundary condition is based on the flow-tangency condition on the blade surfaces, the second relys on the propagating characteristics in the flow field, and the third is a hybrid version of the first and the second. The computation is validated for 2D Navier-Stokes equation. Two compressor cascades are taken as examples to compare the performance of the three transpiration boundary conditions. Finally some conclusions are drawn.