US Patent 7465155 Non-axisymmetric end wall contouring for a turbomachine blade row

A turbomachine blade row is provided having a hub that includes a non-axisymmetric end wall modified by a transformation function. The blade row further includes a circumferential row of a plurality of airfoil members radially extending from the non-axisymmetric end wall of the hub and forming a plurality of sectoral passages therebetween. A radius of the non-axisymmetric end wall is determined by a transformation function including a plurality of geometric parameters defined by a user based on flow conditions. The plurality of geometric parameters provide for modification of the end wall in both an axial and a tangential direction to include a plurality of concave profiled regions and convex profiled regions.