Maximum Likelihood Identification of Flow Instabilities in Cavitating Inducers

The article illustrates the application of Bayesian estimation to the identification of flow instabilities, with special reference to rotating cavitation, in a three-bladed axial inducer using the unsteady pressure readings of a single transducer mounted on the casing just behind the leading edges of the impeller blades. The typical trapezoidal pressure distribution in the blade channels is parametrized and modulated in time and space for theoretically reproducing the expected pressure generated by known forms of cavitation instabilities (cavitation auto-oscillations and higher-order surge cavitation modes, n-lobed subsynchronous/synchronous/super-synchronous rotating cavitation). The Fourier spectra of the theoretical pressure so obtained in the rotating frame are transformed in the stationary frame, frequency broadened to better approximate the experimental results, and parametrically fitted by maximum likelihood estimation to the measured auto-correlation spectra. Each form of instability generates a characteristic distribution of sidebands in addition to its fundamental frequency. The identification makes use of this information for effective detection and characterization of multiple simultaneous flow instabilities with intensities spanning over about 20 db down to about 4 db signal-to-noise ratios. The same information also allows for effectively bypassing the aliasing limitations of traditional cross-correlation methods in the discrimination of multiple-lobed azimuthal instabilities from the measurements returned by arrays of equally spaced sensors. The method returns both the estimates of the model parameters and their standard deviations, providing the information needed for the assessment of the statistical significance of the results. The proposed approach represents therefore a promising tool for experimental research on flow instabilities in high-performance turbopumps.