A Time-Marching Method for the Calculation of Nonsimilar 3D Boundary Layers on Turbomachinery Blades

Abstract

A method is presented for the computation of three-dimensional boundary layers on turbomachinery blades. The method is based on a finite difference approach on a body-fitted curvilinear coordinate system, in which the time-dependent 3D boundary layer equations are marched in time until the steady-state solution is found. The method does not employ a similarity law and can therefore be applied to nonsimilar boundary layers. The method not only enables one to compute the skin friction and displacement of the boundary, but also provides information on the sources of entropy generation on the blades. The entropy generation is in fact split into three main components, which correspond to heat conduction, streamwise shear stress, and cross-flow shear stress. By considering each of the components of shear stress, at the design stage considerable insight can be found on the best way of modifying the blade geometry in order to reduce blade losses. The method is validated by comparison with analytical data for a laminar flat plate, experimental results for a helical blade in turbulent flow, and an axial compressor blade. Finally, the method is applied to the prediction of boundary layers on a subsonic centrifugal compressor impeller blade.