Endwall contouring for a conical endwall

1. A turbine stage comprising:

an array of airfoils spaced apart circumferentially to define a flow passage therebetween for channeling a working medium, the airfoils extending radially outward from an inner endwall located at a hub side thereof,

wherein an axial position 0% Cax ID is defined as a leading edge position of the airfoils on the inner endwall in an axial direction of the stage, and an axial position 100% Cax ID is defined as a trailing edge position of the airfoils on the inner endwall in the axial direction of the stage from an upstream side to a downstream side,

wherein, at any given axial position, 0% pitch ID is defined as a first position on the inner endwall at a pressure side surface of a first airfoil, and 100% pitch ID is defined as a second position on the inner endwall at a suction side surface of a circumferentially adjacent second airfoil, which faces the first position at the pressure side surface of the first airfoil in a circumferential direction of the stage,

wherein the inner endwall is conical and inclined at an angle to an engine axis such that the flow passage is divergent from the upstream side to the downstream side,

wherein the inner endwall is non-axisymmetric about the engine axis, comprising a mid-passage bulge located between the first and second airfoils, the bulge having a peak at a position between 20-60% Cax ID and at a position between 30-70% pitch ID ,

wherein the bulge is a protrusion that extends into the flow passage in relation to the inner endwall, and

wherein the inner endwall extends from an upstream side of the inner endwall to the bulge and from the bulge to a downstream side of the inner endwall and cooperate with the bulge to define an entire portion of the inner endwall in the flow passage to increase flow acceleration in the flow passage.

2. The turbine stage according to claim 1 , wherein the peak of the bulge is located at a position between 30-50% Cax ID .

3. The turbine stage according to claim 1 , wherein the peak of the bulge is located at a position between 40-60% pitch ID .

4. The turbine stage according to claim 1 , wherein the peak of the bulge has a height in the range of 3-8% of an axial chord length, measured normal to a nominal surface of the inner endwall.

5. The turbine stage according to claim 1 , wherein the bulge is spaced from the suction side surface of the second airfoil.

6. The turbine stage according to claim 1 , wherein the inner endwall is inclined toward the engine axis in a direction from the upstream side to the downstream side, the angle of inclination of the inner endwall in relation to the engine axis is in the range between 5-25 degrees.

7. The turbine stage according to claim 1 , further comprising an outer endwall located at a tip side of the array of airfoils,

wherein an axial position 0% Cax OD is defined as a leading edge position of the airfoils on the outer endwall in the axial direction of the stage, and an axial position 100% Cax OD is defined as a trailing edge position of the airfoils on the outer endwall in the axial direction of the stage from the upstream side to the downstream side,

wherein, at any given axial position, 0% pitch OD is defined as a first position on the outer endwall at the pressure side surface of the first airfoil, and 100% pitch OD is defined as a second position on the outer endwall at the suction side surface of the second airfoil, which faces the first position at the pressure side surface of the first airfoil in the circumferential direction of the stage,

wherein the outer endwall is inclined at an angle to the engine axis such that the flow passage is divergent from the upstream side to the downstream side, and

wherein the outer endwall is non-axisymmetric about the engine axis, comprising a mid-passage depression located between the first and second airfoils, depression having a bottom point at a position between 20-60% Cax ID and at a position between 30-70% pitch ID .

8. The turbine stage according to claim 7 , wherein the depression is spaced from the pressure side surface of the first airfoil.

9. The turbine stage according to claim 7 , wherein the angle of inclination of the inner endwall in relation to the engine axis is shallower than the angle of inclination of the outer endwall in relation to the engine axis.

10. The turbine stage according to claim 7 , wherein the outer endwall is inclined away from the engine axis in a direction from the upstream side to the downstream side, the angle of inclination of the outer endwall in relation to the engine axis is in the range between 10-45 degrees.

11. The turbine stage according to claim 1 , wherein the array of airfoils is part of a row of stationary turbine vanes.

12. The turbine stage according to claim 1 , wherein the array of airfoils is part of a row of rotating turbine blades.