• blades
• dynamic matrix
• Eurler number
• experimental validation
• flow coefficient
• impedances
• numerical
• rocket engine turbopumps
• space
• temperature
• theory of inducer cavitation instabilities

A linear perturbation analysis is applied to the study of cavitation instabilities in typical inducers and turbopumps, aiming to improve the understanding of these potentially critical phenomena in liquid propellant rocket (LPR) engine turbomachinery. This work presents a novel model developed specifically within the scope of this thesis, which overcomes the limitations of traditional approaches by employing dynamic transfer matrices to describe the unsteady behavior of cavitating inducers and turbopumps. The flow in the (cylindrical) suction line is assumed ideal, with uniform unperturbed axial velocity, impermeability at the duct wall, constant total pressure at the inlet, and a parametrically defined cavitation impedance at the impeller inlet cross-section. The resulting 3D boundary value problem (BVP) for the perturbation velocity potential is solved using a separable solution, yielding natural modes and frequencies of unstable harmonic flow oscillations as functions of the suction line geometry, unperturbed flowrate, and impeller cavitation impedance. In agreement with experimental evidence, the predicted instabilities include 1D axial, 2D meridional, and fully 3D azimuthal rotating modes.
By comparing theoretical predictions with experimentally observed instability frequencies from various inducer tests in water under different operating conditions, the corresponding impeller cavitation impedance values are extracted. The results reveal how flow coefficient, cavitation number, liquid temperature, impeller radial clearance, and unstable frequency affect cavitation impedance. Specifically, the real part of the impedance decreases with increasing flow coefficient, while the imaginary part increases with instability frequency due to the growing influence of inertial effects. However, in this thesis, the focus is placed on analyzing the imaginary part of the cavitation impedance, which is particularly relevant to the onset and characterization of cavitation phenomena.
Order-of-magnitude estimates correctly suggest that both subsynchronous and supersynchronous rotating cavitation frequencies correspond to similar values of nondimensional cavitation impedance. The study further confirms that the impedance is relatively insensitive to the Euler number. The agreement with experimental observations supports both the validity of the proposed approach and the conclusion that this newly developed model offers a valuable tool for analyzing and interpreting cavitation-induced flow instabilities.