Mathematical modeling of fluid flow during the closure of distribution ports in a straight-tooth rotary pump

   The study examines transient flow in a straight-tooth rotary pump when a rotor tooth progressively covers the suction and discharge ports.

   The aim is to improve prediction of instantaneous pressure in the working chamber by representing the actual variation in the open flow area instead of assuming instantaneous port closure.

   The formulation combines the Bernoulli and continuity equations with relations for frictional and local hydraulic losses. The changing port area is described as a circular segment whose dimensions depend on rotor position. The authors establish analytical relations between rotor angle, tooth position, effective flow area and the corresponding local resistance coefficient. Moreover, the research presents a calculation procedure that continuously accounts for changes in the suction and discharge flow areas during tooth passage. The derived expressions allow determining how hydraulic resistance and head losses vary with rotor position and pump geometry. Therefore, the model identifies angular regions associated with the greatest additional losses and provides a more detailed estimate of pressure variation within the working chamber. Explicit representation of partial port closure removes a simplifying assumption used in earlier models and improves the physical description of the transient process. The method can support optimization of tooth geometry and port dimensions and can be adapted to other positive-displacement hydraulic machines in which flow is controlled by moving elements. Further development should include experimental validation over a wider operating range and extensions accounting for liquid compressibility and cavitation.

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