Maximum Likelihood Identification of Backflow Vortex Instability in Rocket Engine Inducers

Bayesian estimation is applied to the analysis of backflow vortex instabilities in typical three- and four-bladed liquid propellant rocket engine inducers. The flow in the impeller eye is modeled as a set of equally intense and evenly spaced 2D axial vortices, located at the same radial distance from the axis and rotating at a fraction of the impeller speed. The circle theorem is used to predict the flow pressure in terms of the vortex number, intensity, rotational speed, and radial position. The theoretical spectra so obtained are frequency broadened to mimic the dispersion of the experimental results and parametrically fitted to the measured data by maximum likelihood estimation with equal and independent Gaussian errors. The method is applied to three inducers, tested in water at room temperature and different operating conditions. It successfully characterizes backflow instabilities using the signals of a single pressure transducer flush-mounted in the impeller eye, effectively bypassing the aliasing limitations and the data acquisition/reduction complexities of traditional multiple-sensor cross-correlation methods. The identification returns the estimates of the model parameters and their standard deviations, providing the information necessary for assessing the accuracy and statistical significance of the results. The flowrate is found to be the major factor affecting the backflow vortex instability, which, on the other hand, is rather insensitive to the occurrence of cavitation. The results are consistent with the data reported in the literature, as well as with those generated by the auxiliary models specifically developed for initializing the maximum likelihood searches and supporting the identification procedure.