| Abstract: | Growth of the turbulent boundary layer over a flat plate rotating about an axis parallel to the leading edge is considered in which the axial length (or span) is contained between rotating radial end-plates (the hub and shroud, in effect, of a centrifugal impeller). The problem of the influence of the cross-flows in the boundary layers on the end-plates as they affect the blade boundary layer is considered. The latter is treated as a three-dimensional problem and the dependence of the solution on the boundary conditions is discussed. The integral equations of this boundary layer reduce to a pair of quasi-linear partial differential equations which are weakly elliptic, parabolic, or weakly hyperbolic according to the rotation number. When the equations are exactly parabolic and the boundary layers remain thin it is shown that the end-plate boundary layers can have no influence upon the blade boundary layer if the flow is initially radial; separation of the end-plate cross flows takes place in the corners. |
