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

By considering a many-bladed cascade, two simple theories are developed for secondary flow in 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 filament and trailing shed vorticities. It is shown that, for a many-bladed cascade, the total secondary 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 from cascades are consistent with this new approach.