Patent ID: 7465155

Claim:
A turbomachine blade row comprising: a hub including a non-axisymmetric end wall modified by a transformation function; and a circumferential row of spaced apart airfoil members radially extending from the non-axisymmetric end wall of the hub, each airfoil member having a base, a tip, a pressure surface and a suction surface; wherein a radius (R 2 ) of the non-axisymmetric end wall is determined by the transformation function: R 2 ( x )= R 1 ( x )+Δ R ( x ) where R 2 (x) is the radius of the non-axisymmetric end wall; R 1 (x) is a radius of an original axisymmetric hub end wall; and ΔR(x)=K(x)[cos (θ+φ)+2 sin φ/π]; where coefficient K(x) is a function of a local pressure gradient in a circumferential direction at a specific axial location: K ( x )=αΔ P =α( P ps −P ss ) where P ps is a pressure exerted on the pressure surface of one of the plurality of airfoil members and P ss is a pressure exerted on the suction surface of an adjacent one of the plurality of airfoil members; where θ is a circumferential location along the non-axisymmetric end wall; and φ and α are geometric parameters defined by a designer based on a specific flow condition.