The Different Role of Cavitation on Rotordynamic Whirl Forces in Axial Inducers and Centrifugal Impellers

The linearized dynamics of the flow in cavitating axial helical inducers and centrifugal turbopomp impellers is investigated with the purpose of illustrating the impact of the dynamic response of cavitation on the rotordynamic forces exerted by the fluid on the rotors of whirling turbopumps. The flow in the impellers is modeled as a fully-guided, incompressible and inviscid liquid. Cavitation is included through the boundary conditions on the suction sides of the blades, where it is assumed to occur uniformly in a small layer of given thickness and complex acoustic admittance, whose value depends on the void fraction of the vapor phase and the phase-shift damping coefficient used to account for the energy dissipation. Constant boundary conditions for the total pressure are imposed at the inlet and outlet sections of the impeller blade channels. The unsteady governing equations are written in rotating “body fitted” orthogonal coordinates, linearized for small-amplitude whirl perturbations of the mean steady flow, and solved by modal decomposition. In helical turbopump inducers the whirl excitation and the boundary conditions generate internal flow resonances in the blade channels, leading to a complex dependence of the lateral rotordynamic fluid forces on the whirl speed, the dynamic properties of the cavitation region and the flow coefficient of the machine. Multiple subsynchronous and supersynchronous resonances are predicted. At higher levels of cavitation the amplitudes of these resonances decrease and their frequencies approach the rotational speed (synchronous conditions). On the other hand, application of the same approach indicates that no such resonances occur in whirling and cavitating centrifugal impellers and that the rotordynamic fluid forces are almost insensitive to cavitation, consistently with the available experimental evidence. Comparison with the scant data from the literature indicates that the present theory correctly captures the observed features and parametric trends of rotordynamic forces on whirling and cavitating turbopump impellers. Hence there are reasons to believe that it can usefully contribute to shed some light on the main physical phenomena involved and provide practical indications on their dependence on the relevant flow conditions and parameters.