Theoretical Study of Fluid Forces

Along with the developments of high-speed and highperformance turbomachines, there has been increasing occurrence of rotational speeds higher than the first critical speed. Under these circumstances, turbomachines may suffer from severe vibration and rotor whirl caused by fluid-dynamic forces. As possible causes of whirling instabilities, fluid forces on journal bearings and seals are well known and extensive studies have been made of these effects. Recently, experiments have shown that the fluid forces on the impeller itself can be a cause of the whirl instabilities. Ohashi and Shoji (1984) measured unsteady fluid forces on two-dimensional centrifugal impellers whirling in a vaneless diffuser, for various whirl ratios and flow coefficients. Their purpose was to obtain fundamental data for rotor whirl and to compare the results with their theoretical estimates of the effect. They found that, in most cases, the fluid forces have a damping effect on the whirling motion but they observed destabilizing fluid forces for forward whirling motion at lower flow coefficients near shut off and in a range of small whirl speed ratio. At nearly the same time, experiments on three-dimensional impellers with a volute were made at Caltch for direct use in design. Fluid forces were measured quasistatically (Chamieh et a]., 1982) and dynamically (Jery et a]., 1984). In the first of these it was shown that the quasisteady fluid forces have a destabilizing effect for forward whirl and in the second that the region of instability is similar to that observed by Ohashi and Shoji (1984). The major differences from Ohashi and Shoji's results were that: ( i ) measured forces are much larger, and (ii) destabilizing forces are also observed near the design flow coefficient. More recently, experimental results on a strictly two-dimensional radial impeller in the same volute have become available (Arndt and Franz, 1986). The magnitudes of the impeller forces are significantly reduced but the contrast with Ohashi and Shoji's results without volutes still remain. It has been shown (Adkins, 1986) that the large difference between the forces on the 3-D and 2-D impellers in the volute is on a Centrifugal Impeller Rotating and Whirling in a Volute