• propulsion
• parametric identification
• inducer
• cavitation-induced flow instabilities
• cavitation
• turbomachinery

Some aspects concerning unsteady flow phenomena in rocket cavitating inducers and turbopumps are still partially understood. This is mainly due to the fact that an analytical method capable of perfectly predicting the flow phenomen has not yet developed and almost all of the today's research activities in this fascinating field are based on experimental methods applied on scaled models.
An inducer is an axial flow pump located upstream of the main centrifugal pump and operating almost invariably with cavitation. The primary function of the inducer is to increase the inlet pressure by an amount such that the cavitation in the following centrifugal pump is avoided.
The main objective of this thesis consists in the formulation and subsequent demonstration of the applicability of the Maximum Likelihood Estimation Approach to the effective simultaneous identifcation and characterization of the different forms of unsteady cavitation-induced flow instabilities occurring in modern rocket axial inducers and turbopumps.
The present thesis is focused mainly in the identification of the cavitation-induced flow instabilities of the RAPDUD inducer, developed at Sital S.p.A, on behalf of the European Space Agency (ESA), according to the analitycal model developed by my advisors Professor Luca d'Agostino and his collaborators. The RAPDUD inducer is a three-bladed, high-head, axial inducer with tapered hub and variable pitch.
In order to experimentally characterize the typical flow instabilities generated by cavitation in the RAPDUD inducer, the facility has been instrumented with two different kinds of pressure transducers, which provided the measured pressure signals. These two kinds of pressure sensors, which represent the pressure data acquisition system, have been mounted both on the inducer casing and on the inducer hub, in order to allow for the simultaneous analysis of the flow-induced instabilties in the stationary and rotating reference frames. In order to detect and to identify the onset and the forms of cavitation-induced ow instabilities developing inside the inducer blade channels, Spectral Analysis has been applied to the pressure signals obtained under cavitation conditions by means of the casing-mounted (PCB) and hub-mounted (Kulite) transducers. For the identification of the onset, frequency and relative intensity of the flow instabilities is required the study of peaks of the auto-correlation spectra. For the identification of the form of the instability (axial/rotating), it is required the study of the cross-correlation phases of the signals obtained from two transducers with known azimuthal spacing. The cross-correlation, a part from the identification of the form of the instabilty, also enables the identification of the number of lobes in the case of rotating cavitation.
The identification procedure used for the analysis of the cavitation-induced flow instabilities in the RAPDUD inducer is based upon an analitycal model whose purpouse is to represent, by means of the Fouries Analysis, the pressure signals provided by the casing-mounted pressure transducer (PCB) in the rotating and stationary frame. The identification of the oscillations is performed in the stationary frame by using the time-domain pressure signal provided by the casing-mounted PCB05 transducer because it directly measures the pressure perturbations in the bade channels. The identification procedure is mainly composed by the following steps: selection of a suitable set of experimental data; selection of the most suitable location of case- mounted pressure sensors; consideration, as far as possible in reverse order of intensity, of the instabilities diagnosed from cross-correlation analyses; selection of the instability to take into consideration, based on preliminary assessment of its intensity; evaluation of the correlation coefficient of the experimental pressure power density spectrum (PDS) with the theoretical one for instability taken into consideration as a function of the assumed value of the corresponding frequency; maximum likelihood parametric identification of the most correlated frequency of the instability under consideration; subtraction of the fitted pressure power density spectrum for the identified instability from the experimental pressure power density spectrum. Selection of the next instability to take into consideration and iteration until no further instability with significant correlation coefficient is left or no further significant parametric identification is obtained. A part from the step-by-step procedure for the identification, it is important to note that the azimuthal pressure distribution in the blade channels it has been represented by means of a sequence of three trapezoidal waveforms with zero means. There are three waveforms for the fact that the RAPDUD inducer is composed by three blades. The analytical model accounts for the following instabilities: blade passage perturbation, attached blade cavitation, steady cavitation, axial surge cavitation and rotating cavitation. In order to account for frequency broadening, the arguments of the Dirac function of the theoretical spectra in the stationary frame are convolved with a Gaussian distribution with zero mean. Consequently, the different variances which appears in the theoretical spectra are evaluated by means of the Statistics.
The identification procedure is applied to different experimental spectra, each of which corresponds to a particular value of the cavitation number. The experimental spectra analyzedaccount for both design and off-design flow conditions.