An Axial Compressor End-Wall Boundary Layer Calculation Method

Abstract

An axial compressor end-wall boundary layer theory which requires the introduction of three-dimensional velocity profile models is described. The method is based on pitch-averaged boundary layer equations and contains blade force-defect terms for which a new expression in function of transverse momentum thickness is introduced. In presence of tip clearance a component of the defect force proportional to the clearance over blade height ratio is also introduced. In this way two constants enter the model. It is also shown that all three-dimensional velocity profile models present inherent limitations with regard to the range of boundary layer momentum thicknesses they are able to represent. Therefore a new heuristic velocity profile model is introduced, giving higher flexibility. The end-wall boundary layer calculation allows a correction of the efficiency due to end-wall losses as well as calculation of blockage. The two constants entering the model are calibrated and compared with experimental data allowing a good prediction of overall efficiency including clearance effects and aspect ratio. Besides, the method allows a prediction of radial distribution of velocities and flow angles including the end-wall region and examples are shown compared to experimental data.

A Fast Numerical Procedure to Solve the Meridional Equations of Motion in a Multistage Axial Flow Turbomachine

“…They can be determined by interpolation on streamsurfaces in the z-r plane. However, the shape of the streamsurfaces is represented by the quantity of functions u (s) which themselves are results of (2) respectively (5). Hence an iterative computation procedure is necessary.…”

“…The static state here always is considered as a function of the total state and the velocity. -in equation (5). 8(S) is given as input.…”

“…They determine the radial boundaries of the compution field. Several theories for their computation are known, particularly for compressors (5). For turbine flows their influence is often neglected.…”

“…The integration of the differential equations (2) or (5) in each new station is started by setting the slope angle y (s) and the curvature X (s) as linear functions in s. In further passes, spline functions on streamsurfaces of the given values ri^ (about 10 values) yield some points of the functions y (s) and X (s). These points are fitted with small errors by third order polynoms in s. To perform the given geometry of hub and shroud, the following formulation is reasonable.…”

“…u(S + 6HUB . cos (e+yHUB)) = 0 (20) u(SSHROUD-6 SHROUD cos(e+Y SHROUD )) = M (21) This cycle is a step within a larger cycle, where some parameters of the differential equations are adapted to the latest values of p(S) and c m (S).These parameters are:-T*(S) and Q(S) in equations (2) and T**(S) in equations(5). They are conserved on streamsurfaces and can be taken from the previous station upstream, if the coordinates of the intersection S L of the streamsurface with the station are known.…”