Two-Dimensional, Laminar, Compressible Boundary-Layer Calculations in Turbomachines

Theme I N radial compressor flow one usually can observe a flowfield at the impeller tip, which separates into a jet area and a wake area. As the wake area is attached to the suction side, it is assumed that separation occurs first on the suction side. This phenomenon was discussed experimentally and theoretically in an early paper by G. Jungclaus for the case of the boundary-layer flow along a rotating, radial standing flat plate. He found that coriolis acceleration induces separation on the suction side earlier than on the pressure side. In the present paper, a solution is given for the laminar, boundary layer on far more complicated blade surfaces as present for instance in high-speed turbomachinery, especially in radial compressors. First, we outline the sort of simplifications which can be introduced in the general fluid mechanical equations to make a boundary-layer concept practicable for machine computation, while still providing reliable information on the boundary-layer behavior in such flows. 1) Second-order boundary-layer theory has to be applied, which means curvature terms, and coriolis and centrifugal acceleration terms of higher order are to be included. 2) The boundary layer is laminar, which may be acceptable for preliminary studies. The turbulent boundary layer is more energetic and therefore should lead to separation further downstream. 3) The boundary layer is compressible, because of the high relative speeds and the high temperatures in turbomachinery. 4) The boundary layer is assumed to be two-dimensional along a curve in space on the blade surface neglecting cross flow. Although this assumption is very crucial with respect to the calculation of the separation behavior, it has been made in order to simplify the effort to study the influences of the curvature, coriolis, and centrifugal effects which are the essentials considered in this investigation. 5) Since the boundary layer is nonsimilar no similarity assumption has been made, so that the boundary-layer profiles can develop continuously from the stagnation to the separation point. A further problem is to find a natural blade orientated orthogonal coordinate system, which is able to represent the near wall region more easily than a Cartesian coordinate system. For this new coordinate system, the governing