A Contribution to the Theory of Slip Factor for Radial Flow Fans

Abstract

The preliminary design of radial flow (centrifugal) fans is usually performed by the theory of fluid-flow machinery, based on the change of angular momentum between impeller inlet and exit. As a consequence of the rotation of the impeller, the relative flow at impeller exit does not follow the blade exit angle. This effect is modeled by a so-called slip velocity, induced by a relative eddy in the blade channel. The nondimensional slip velocity characterizes the so-called slip factor. A number of empirical correlations, semi-empirical and theoretical equations are available to calculate the slip factor for impellers of radial flow fans: Stodola, Busemann, Wiesner, Eck, and others. The present paper extends the slip factor model of Stodola for parallel hub and shroud walls (b = const.) to impellers with contoured shroud wall (b · r = const.). The model is based on Helmholtz’ vorticity theorem on the convective transport of the relative eddy through the impeller blade channel. Using simplified velocity triangles, a transformation of the equations of Stodola is performed to make them sensitive to the impeller inlet to exit diameter ratio. Finally, a linearization of the original slip factor equations of Eck for high blade solidities is performed using a Taylor series expansion.