Secondary Flow in Cascades: Two Simple Derivations for the Components of Vorticity

Abstract

By considering a many-bladed cascade, two simple theories are developed for secondary flow m cascades. Following the work of Hawthorne (1)#, three components of vorticity are identified at exit from the cascade. An expression is obtained for the difference in the time taken for fluid particles to travel over the two surfaces of the blade, and this is used to derive the governing equations for the distributed secondary, trailing fdament and trailing shed vorticities. It is shown that, for a many-bladed cascade, the total secondaly circulation in the downstream flow is zero. The calculation of secondary flow for a real cascade is discussed, and it is shown that earlier calculations of secondary flow at exit fromcascades are consistent with this new approach.

The sensitivity of turbine cascade endwall loss to inlet boundary layer thickness

“…Assuming inviscid flow, these methods predict the exit streamwise vorticity by considering the convection and reorientation of the inlet boundary layer vorticity as it convects through the blade row. For incompressible flow, Hawthorne (1955) used a vortex-filament analysis and applied Helmholtz's theorems, while Came and Marsh (1974) presented an alternative approach based on Kelvin's Circulation theorem. Both approaches give the same expression for the distributed vorticity associated with the passage vortex and bulk secondary flow.…”

A Simple Method for Estimating Secondary Losses in Turbines at the Preliminary Design Stage

“…In this work the three component model proposed by Gregory-Smith (1982) is used and the total of these three components, each calculated separately, will provide the secondary loss. It must be noted here that no attempt has been made to model tip Classical secondary flow theory assumes that the convection of the primary streamlines are negligible and the secondary vorticity, as in Came and Marsh (1974), can be calculated analytically. The secondary velocity field is then calculated from a stream function which is the solution of a Poisson equation, see Glynn and Marsh (1981).…”

Secondary Loss Generation in a Linear Cascade of High-Turning Turbine Blades

“…Results are also presented from work done by Camus, Starling and Lam (1988) as part of an undergraduate project. Their method was based on the oil drop viscosity balance method of Tanner and Blows (1969).…”

“…The passage vortex is clearly visible and some of the trailing filament vorticity is concentrated in a discrete vortex above this. (Trailing filament vorticity is defined by Hawthorne (1955) and Came and Marsh (1974) but may crudely be regarded as resulting in the wake because there is a large component of spanwise flow near the suction surface but hardly any near the pressure surface). These two vortices coincide with the two loss peaks at x/Cx=1.23 seen in fig.4.…”