Prediction of cavitation surge onset point by one-dimensional stability analysis

Cavitation instabilities such as rotating cavitation and cavitation surge often occur in high speed turbopumps. It has been shown by a stability analysis that the cause of cavitation instabilities is explained by the positive mass flow gain factor, representing the increase of cavity volume against the decrease (increase) of flow rate (incidence angle). The cavitation compliance, representing the increase of cavity volume in response to the decrease of inlet pressure, determines the frequency of instabilities. However, one-dimensional stability analysis cannot be directly used for the prediction of the onset point of cavitation surge when quasi-steady assumption is applied. In the present study, unsteady characteristics, i.e. the phase lag in the response of cavity volume against the flow rate/inlet pressure fluctuations, are taken into account in a stability analysis of cavitation surge in the form of lag element. The onset criterion considering the time lag is newly proposed for one-dimensional stability analysis, and the criterion is validated by comparisons with a two-dimensional stability analysis based on a singularity method applied to a free streamline theory.