Maximum likelihood identification of cavitation instabilities in axial inducers

The article illustrates the application of maximum likelihood estimation to the identification of cavitation instabilities in axial inducers from the unsteady pressure readings measured on the impeller casing. The typical triangular pressure distribution in the blade channels of the impeller is parametrized and modulated in time and space in order to theoretically reproduce the expected pressure generated by known forms of cavitation instabilities (cavitation auto-oscillations, n-lobed sub/super-synchronous rotating cavitation, higher-order surge/rotating cavitation modes). The Fourier spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame and fitted by maximum likelihood estimation to the auto-correlation of the pressure measurements on the inducer casing. Each form of instability generates a characteristic spectral distribution of side bands in addition to its fundamental frequency. The identification makes use of this information for effective discrimination of simultaneous flow oscillations with significantly different intensities and partially overlapping frequencies. The method returns the estimates of the model parameters and their standard errors, allowing for both recognition of the forms of instabilities occurring in the inducer and assessment of the statistical significance of the results.