Rotordynamic Fluid Forces on Whirling and Cavitating Radial Impellers

This paper investigates the linearized dynamics of the rotordynamic forces exerted by the fluid on the rotor in whirling and cavitating radial impellers with thin logarithmic blades and constant eccentricity and whirl speed. The flow is modeled as an incompressible, inviscid, fully-guided liquid except on the suction sides of the blades, where attached cavitation occurs in a small layer of given acoustic admittance depending on the assumed values of the layer thickness and void fraction. Constant boundary conditions for the total pressure are imposed at the inlet and outlet sections. The three-dimensional unsteady governing equations are written in rotating orthonormal logarithmic spiral coordinates, linearized for small-amplitude whirl perturbations of the mean steady flow, and solved by modal decomposition. Rotordynamic fluid forces in centrifugal pumps are found to be almost insensitive to cavitation; also, they do not undergo the internal flow resonances in the blade channels predicted by similar flow models and observed in whirling and cavitating axial inducers. Comparison with the available experimental results shows that the present theory underestimates the intensity of rotordynamic impeller forces, but correctly captures their observed parabolic trend as functions of the whirl frequency, thus indicating that it can usefully contribute to identify the main physical phenomena involved and provide useful practical indications on their dependence on the relevant flow conditions and parameters.