Prediction of destabilizing blade tip forces for shrouded and unshrouded turbines

The effect of a nonuniform flow field on the Alford force calculation is investigated. The ideas used here are based on those developed by Horlock and Greitzer. It is shown that the nonuniformity of the flow field does contribute to the Alford force calculation. An attempt is also made to include the effect of whirl speed. The values predicted by the model are compared with those obtained experimentally by Urlicks and Wohlrab. The possibility of using existing turbine tip loss correlations to predict beta is also exploited. The nonuniform flow field induced by the tip clearnance variation tends to increase the resultant destabilizing force over and above what would be predicted on the basis of the local variation of efficiency. On the one hand, the pressure force due to the nonuniform inlet and exit pressure also plays a part even for unshrouded blades, and this counteracts the flow field effects, so that the simple Alford prediction remains a reasonable approximation. Once the efficiency variation with clearance is known, the presented model gives a slightly overpredicted, but reasonably accurate destabilizing force. In the absence of efficiency vs. clearance data, an empirical tip loss coefficient can be used to give a reasonable prediction of destabilizing force. To a first approximation, the whirl does have a damping effect, but only of small magnitude, and thus it can be ignored for some purposes.