• analytical modeling
• Cavitation
• cavitation compliance
• cavitation dynamics
• Cavitation Instabilities
• Inducer
• mass flow gain factor
• matrix stacking method
• modular multi-actuator disk
• Rotating Cavitation
• Rotating Stall
• transmission matrix
• Turbomachines Flow Instabilities

The present thesis represents the prosecution of the project of the past joint collaboration between Pisa University and Massachusetts Institute of Technology named "Dynamic Characterization of POGO Instabilities in Cavitating Turbopumps". The work is based on the mathematical framework defined during the mentioned past project, characterized by modular approach known as "Matrix Stacking Method", in which each system component is cast into a transmission matrix that can be linked to any other component of the system. A simple hydraulic system is considered, composed of an inducer placed between two infinite axial ducts with constant cross section. The unsteady system dynamic is studied by means of a linear approximated two-dimensional mathematical model in the axial and azimuthal directions, assuming incompressible, inviscid and adiabatic flow. The unsteady disturbances are treated in the Laplace domain which, assuming periodic solution in tangential direction, are decomposed into spatial harmonics in the azimuthal direction. The first objective is the mathematical framework validation, that is accomplished by reproducing the results of a different framework modeling approach. Then, the attention is shifted on the cavitating inducer semi-actuator disk modeling and its transmission matrix definition. Based on the different inertial inducer pressure modeling, three generalized cavitating inducer models are defined, adaptable to different hypotheses and perturbative modeling. The cavitating volume behavior is modeled through the cavitation compliance and the mass flow gain factor. Varying the combinations of these two factors, the role of inertial pressure term is highlighted by means of trend analyses. Three system natural modes for each analyzed inducer models are predicted: rotating stall (RS), supersynchronous forward rotating cavitation (FRC) and backward rotating cavitation (BRC). Two of the inducer modeling procedures result coherent with literature while, for the third one, unexpected supersynchronous RS mode and unusual flow coefficient and mass flow gain factor effect on the FRC mode are obtained. Moreover, for many of the cases, a globally stabilizing cavitating effect is observed for the RS mode. Then, the eigenvalues stability analysis is performed both in non cavitating and cavitating conditions. In the former case, a RS mode is predicted which behavior satisfies the expected head curve slope effect, while in the latter a flow coefficient effect on the FRC onset condition curve is investigated. This last analysis leads to put into question a simplified linear RC onset condition reported in literature which, even if it is still a good tool, is considered not universally valid, too generic and of low practical use.