USE OF CONFORMAL REPRESENTATION METHOD FOR JET PUMP CAVITATION CHARACTERISTICS CONTROL
DOI:
https://doi.org/10.31471/1993-9981-2022-1(48)-18-26Keywords:
downhole jet pump, circulating flows, cavitation, hydrodynamic functions, complex potentialAbstract
Modern methods of studying the cavitation modes of operation of the downhole ejection system do not take into account the possibility of its rotation in the well, resulting in reduced efficiency of forecasting the mode of operation of the jet pump. The paper proposes a mechanism for determining the effect of jet pump rotation on the configuration of mixed flow lines using the theory of flat potential flows. To construct the configuration of flow lines for a given velocity field, the conformal mapping method is used, which consists in mapping a region with a known complex potential to a flow region with given boundaries. The boundaries of the working and injected flow areas are determined according to the theory of jets: on solid surfaces that limit the flow, the normal velocity component is zero, and on free surfaces, the velocity modulus takes constant values. According to the mathematical model developed by the author, the presence of circulating flow can be taken into account by using the coefficient of non-uniformity of the distribution of longitudinal velocities in the cross section of the working jet. The rotation of the flow due to the action of viscous friction changes the plot of longitudinal velocities, which can be taken into account by introducing into the known method of calculating the coefficient of non-uniformity. Using the known procedures for determining the form of functions in the planes of the complex variable and the Zhukovsky variable, a system of equations of jet coordinates in parametric form is obtained. The solution of the obtained system of equations allowed to obtain a direct connection between the coordinates of the jet. The coordinates of the trajectory of the working jet are determined by the diameter of the working nozzle of the jet pump, the distance to the mixing chamber and the uneven distribution of velocities in the flow caused by the rotation of the ejection system in the well. Increasing the distance between the working nozzle and the mixing chamber of the jet pump causes a decrease in the radius of propagation of the jet of the workflow.
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