• analytical model
• cavitation
• fluid dynamics instabilities
• inducer
• liquid rocket turbopumps
• rotating cavitation
• two dimensional model

Liquid rocket turbopumps commonly employ axial inducers to avoid the occurrence of cavitation in the main stages of the pump, typically radial impellers. On the contrary, axial inducers often work in conditions leading to cavitation, whose intrinsically unstable nature creates a variety of unsteady phenomena. Inducers, in turn, result prone to flow instabilities, especially to those initiated and supported by cavitation.
The present thesis develops an analytical dynamic model of a pumping system for assessment of cavitation dynamics in axial inducers. The mathematical model is linear and two-dimensional in the axial and azimuthal direction, and it is based on the incompressible, inviscid, and adiabatic flow approximation. Each component of the system is modeled by means of a transmission matrix, such that many components may be stacked together easily and efficiently. The inducer is considered as a semi-actuator disk, and the effect of a strongly tapered hub is taken into account to derive the governing equations. The cavitation is modeled by taking into account its dependence on the blade incidence angle (through the parameter commonly called "mass flow gain factor") and on the inlet pressure (usually assessed by means of the cavitation compliance). The aim of the analytical dynamic method is to predict the onset of unstable conditions, and system eigenvalues analysis leads to identify both the growth rate and the frequency of the various instabilities.
The dynamic system model is applied to the inducer designed by Massachusetts Institute of Technology (MIT). In non cavitaing conditions, dynamic instability analyses correctly predict a rotating stall mode for positive value of the head characteristic slope. The analyses also identify a stabilizing effect of the time lag associated with pressure losses. Eigenvalues analyses in cavitating conditions predict three system natural modes: rotating stall, supersynchronous forward rotating cavitation, and backward rotating cavitation. Several trend analyses are performed, showing that rotating stall mode is not affected by cavitation, and that the direct effect of the cavitation number on both the cavitation modes is negligible. Frequency and growth rate maps are presented as result of the trend analyses, proving that backward rotating cavitation is unaffected by the flow coefficient. Therefore, the onset condition for that mode is a function only of the mass flow gain factor and of the cavitation compliance. Concerning forward rotating cavitation, an instability onset function for the mass flow gain factor is derived, which doesn't depend linearly on the cavitation compliance. This function is unaffected by the cavitation number, but it shows an approximately linear dependence on the flow coefficient. Values of the mass flow gain factor and of the cavitation compliance for MIT inducer are calculated by means of experimental dynamic data fitting. Results depict that cavitation compliance may be the discriminating factor to understand which type of instability may appear.