Turbopump inducers often have swirling backflow under a wide range of flow rates because they are designed with a certain angle of attack even at the design point in order to attain high cavitation performance. When the flow rate is decreased, the backflow region extends upstream and may cause various problems by interacting with upstream elements. It is also known that the backflow vortex structure occurs in the shear layer between the main flow and the swirling backflow. Experimental studies on the backflow from an inducer have given us insight into the characteristics of backflow vortex structure, but the limited information has not lead to the complete understanding of the phenomena. Numerical studies based on Reynolds-averaged Navier-Stokes (RANS) computations usually deteriorate when the flow field of interest involves large-scale separations, as shown by a previous study by Tsujimoto et al. (2005). On the other hand, the numerical approach using the Large Eddy Simulation (LES) technique has the potential to predict unsteady flows and/or flow fields that include regions of large-scale separation much more accurately than RANS computations does in general. The present paper describes the application of the LES code developed by one of the authors (Kato) to further understand the backflow vortex structure at the inlet of an inducer. First, the internal flow of the inducer was simulated, as a way to evaluate the validity of the proposed method, under a wide range of inlet flow coefficients. The static pressure peformance and the length of the backflow region was compared with measured values, and good agreement was obtained. Second, using the validated LES code, the fundamental characteristics of the backflow vortex was investigated in detail. It was found that the backflow vortices are formed in a circumferentially twisted manner at the boundary between the swirling backflow and the straight inlet flow. Also, the backflow vortices rotate in the same direction as the inducer, but with half of the circumferential flow velocity in the backflow region. Another finding was that the backflow region expands toward the center of the flow field and the number of vortices decrease, as the flow coefficient decreases. To the best of our knowledge, this is the first computation of the backflow at the inducer inlet to achieve quantitative agreement with measured results, and give new findings to the complicated three-dimensional structure of the backflow, which was very limited under experimental studies.

The response of backflow at the inlet of an inducer to the flow rate fluctuation is studied by using three-dimensional numerical calculations based on the k-ϵ turbulence model for the discussion of its effect on cavitation instabilities. It is first shown that the size of the backflow region can be correlated with the angular momentum in the upstream and the phase of the backflow significantly delays behind the quasi-steady response even at a very low frequency. It is then shown that the conservation relation of angular momentum is satisfied with minor effects of the shear stress on the boundary. The supply of the angular momentum by the negative flow is shown to be quasi-steady due to the fact that the pressure difference across the blade causing the backflow is quasi-steady at those frequencies examined. A response function of the angular momentum in the upstream to flow rate fluctuation is derived from the balance of the angular momentum and the results of the numerical calculations. This clearly shows that the backflow responds to the flow rate fluctuation as a first-order lag element. The effects of the backflow cavitation on cavitation instabilities are discussed assuming that the delay of cavity development is much smaller than the delay of the backflow. It was found that the backflow cavitation would destabilize low frequency disturbances due to the effects of the positive mass flow gain factor but stabilize high frequency disturbances due to the effect of the cavitation compliance.

The present paper summarizes recent studies on the dynamics of backflow vortex structure associated with cavitation instabilities in turbopump inducers. First, the cause of cavitation instabilities is discussed. Various methods for the suppression of cavitation instabilities are then reviewed to illustrate the importance of backflow vortex cavitation on instabilities. The characteristics of backflow vortices are described based on experimental observations. Calculations based on the k-ε turbulence model are used for clarifying the mechanisms of inlet backflow and its response to flow rate fluctuations. Backflow vortex structure is simulated by LES calculations on a simplified geometry. Cavity volume is estimated from the volume of the regions with the pressure lower than the vapour pressure and its response to flow rate fluctuation is clarified. From the results obtained, the effects of backflow vortex cavitation on cavitation instabilities are discussed.

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