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

Authors

Reinhard Willinger  - Technische Universität Wien, Austria

Abstract

The preliminary design of radial flow fans (centrifugal fans) is usually performed by the theory of fluid-flow machinery, based on the change of moment of momentum between impeller inlet and exit. Mainly due to the Coriolis forces in the rotating frame of reference (impeller), the streamlines of the relative flow are not identical to the blade shape. As a result, the relative flow at impeller exit does not follow the blade exit angle and a so-called slip velocity appears. The slip velocity is induced by a relative eddy in the blade channel and, therefore, the effect depends on the number of impeller blades. For an infinite number of blades, the slip velocity will diminish. The relative effect of the slip velocity is described by 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. Without claim of completeness, the slip factors of Stodola (1924), Busemann (1928), Pfleiderer (1961), Wiesner (1967) and Eck (1972) can be mentioned. Depending on the theoretical or experimental background, the slip factors are provided as equations or in diagrams. The present paper extends the slip factor theory of Stodola to the case of constant meridional velocity (b · r = const.). Furthermore, it is shown that under some assumptions and simplifications, the slip factor equations of Eck and Stodola are identical. In a first step, a simplified velocity triangle (β2∞+=β1) is used to transform the equation of Stodola to a form similar to the equation of Eck. In the next step, a theoretical approach is presented to derive a slip factor equation based on the theory of Stodola for impellers with constant meridional velocity. The model is based on Kelvin’s Theorem on the convective transport of the relative eddy in the impeller blade channel. As can be seen, the slip factors from both theories depend on the same physical parameters. In the next step, a Taylor series expansion is applied to the original slip factor equations of Eck. It will be shown that the linearized equations of Eck are identical to the (extended) equations of Stodola. It is planned to extend this approach to a wider range of slip factor equations in a future work.