Numerical solution of two- and three-dimensional rotor tip leakage models

Abstract

Blade tip losses represent a major efficiency penalty in a turbine or compressor rotor. These losses are presently controlled by maintaining close tolerances on tip clearances. This paper initially focuses on the control of tip leakage flow through minimization of the discharge coefficient to control the normal leakage flow component. A detailed numerical study of rotor-tip winglets, using a two-dimensional (2-D) turbulent flow formulation in primitive variables, is reported. Long and short winglets on the pressure, suction, and both sides (partial shroud) of the blade tip are analyzed. The results of the viscous analysis indicate superior performance with a partial shroud. The numerical technique is extended further to incorporate the axial flow effects by solving the full three-dimensional (3-D) Navier-Stokes equations with tip clearance effects included in the analysis. The 3-D model is validated by comparing it with the experimental results of the double-sided discharge rig of an earlier investigation. In addition, the variations in the specification of the boundary conditions at the inlet and exit of the pressure and suction side channels are investigated in detail. Comparison of the numerical and experimental results suggests an improvement in the predictive capability of the 3-D model over the 2-D analysis. Nomenclature b = height of the channel CD = discharge coefficient Ckn = discharge coefficient for 2-D model (Ref. 9) D — dilation term du dv dw dx dy Lc = axial length of tip clearance slot (3-D model) Ld = axial length of blade downstream of tip clearance (3-D model) Lg =tip clearance, gap height (3-D model) Lp = width of pressure side channel (3-D model) Ls - width of suction side channel (3-D model)