Three-Dimensional Analysis of Rotordynamic Fluid Forces on Whirling and Cavitating Finite-Length Inducers

The paper investigates the linearized dynamics of the threedimensional flow in finite-length helical inducers with attached blade cavitation, with the purpose of understanding the impact of the cavitation response on the rotordynamic forces exerted by the fluid on the impeller of whirling turbopumps. The flow in the inducer annulus is modelled 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 depending on the void fraction of the vapor phase and the parametric value of the phase-shift damping used to account for the energy dissipation in the dynamics of the cavitating layer. Constant boundary conditions for the total pressure are imposed at the inlet and outlet sections of the inducer blade channels. The three-dimensional unsteady governing equations are written in rotating "body fitted" orthogonal helical coordinates, linearized for small-amplitude whirl perturbations of the mean steady flow, and solved by modal decomposition. The whirl excitation and the boundary conditions generate internal flow resonances in the blade channels of the inducer, leading to a complex dependence of the lateral rotordynamic fluid forces on the whirl speed, the properties of the cavitating layer and the flow coefficient of the machine. Multiple subsynchronous and supersynchronous resonances are predicted. At higher levels of cavitation the amplitudes of the resonances decrease and their frequencies approach the rotational speed (synchronous conditions). Comparison with available experimental data indicates that the present theory correctly evaluates the observed magnitude of the rotordynamic forces as functions of the whirl frequency and their stabilizing or destabilizing effects on the whirl motion. The results may help understanding the origin and sustain of some of the most critical and destructive instabilities of whirling and cavitating turbopumps.