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

Abstract

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.

The World's First Test Facility That Enables the Experimental Visualization of Cavitation on a Rotating Inducer in Both Cryogenic and Ordinary Fluids

“…In addition, there are two types of cavitations on a rotating inducer in both water and liquid nitrogen, as mentioned in Refs. [7][8][9][10][11].…”

“…The movement and position of the backflow vortices were theoretically explained and experimentally validated in Ref. [11] in detail; the backflow vortices' movement depends on the flow coefficient / and is independent of the cavitation number r. In the same manner as the tip vortex cavitation, the pressure along the axis of each backflow vortex is lower than that of the surroundings. Where this pressure is less than the local saturation pressure, liquid is vaporized; then, backflow vortex cavitation occurs.…”

“…(1) As mentioned in Ref. [11], overall flow structures (e.g., the number, size, direction of cavitation) can be determined by / and are independent of the working fluid. (2) The overall flow structures are similar between liquid nitrogen and water.…”

“…Then, the author and colleagues successfully visualized backflow vortex cavitation on a rotating inducer in both cryogenic and ordinary fluids in the same flow channel under the same values of r and /, and the visualized cavitation was analyzed. Using this test facility version 3, the author and colleagues [11] published their results of the visualization experiment to validate the theoretical analyses performed by the author.…”

“…In this paper, the structures of the cavitation tunnel that enable the visualization of cavitation on a rotating inducer in both cryogenic and ordinary fluids are first introduced; then, the features of cryogenic cavitation, which strongly exhibit the thermodynamic effect, are expounded based on the visualization results of cavitation compared with water cavitation under the same geometric and hydrodynamic conditions using test facility versions 2 and 3. [10], and the lower panel shows the improved cavitation tunnel version 3 used from 2017 to 2020 [11]. These two tunnels were located at Tokyo Institute of Technology.…”