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Backflow vortices occasionally occur in the annular mixing zone between the main and axially reverse whirling flows from the impeller tip clearance on an axial pump or compressor. A number (N) of tornado-like backflow vortices rotate around themselves and revolve around the casing axis with a diameter (d) and a revolving angular velocity (ω). To investigate the factors determining N and the movement of the backflow vortices, theoretical analyses are performed. Each backflow vortex is generated in the mixing zone; the core region of each backflow vortex is considered to be a forced vortex, while the outer region is considered to be a free vortex. The ratio (f) of the forced vortex to the distance between the backflow-vortex center and the casing is defined. Each backflow vortex has a circulation and induces movements of all the other backflow vortices depending on the distance between the vortices. The casing restricts the movements of all the backflow vortices, and imaginary image vortices are considered on the other side of the casing. Consequently, for d, ω, N, and f, any parameter can be determined if the other three parameters are specified. As an application of the present theory to an inducer representing an axial pump or compressor, the number (Ncav) of “backflow-vortex cavitations,” which occur around the backflow-vortex center, is predicted. Cavitation is visible; therefore, Ncav is quantitatively measurable. In the parameter ranges studied for the tested inducer, the predicted value of N accurately agrees with the experimentally measured value of Ncav.

Theoretical Analyses of the Number of Backflow Vortices on an Axial Pump or Compressor