Simulation of asymmetrical rotational flow in the flow part of a well jet pump
Keywords:ejection system, jet pump rotation, potential flows, complex potential, equipotential surfaces, flow line, asymmetric vorticity function
In order to improve the mathematical model of the working process of the above-bit ejection system for the conditions of its asymmetric rotation in the well, a method of modeling the circulating injected flow using a hydrodynamic vortex function, the center of which is shifted relative to the axis of the mixing chamber of the jet pump, has been developed. In the process of modeling the rotating asymmetric movement of the injected flow, the concept of circulation of the vector of the translational velocity of the liquid along a closed circuit is used. With the help of the components of the complex potential of the hydrodynamic circulation function, a graphical interpretation of the equipotential lines and flow lines of the spatial vortex with one-sided and two-sided displacement of the coordinate center was obtained. Using analytical relations for the velocity potential and stream function, the components of the circulation velocity are determined and the analyticity of the function of the complex potential with a shifted vortex center is proven. The fulfillment of the Cauchy-Riemann conditions allowed us to present the resulting velocity of the circulating current with the coordinate center shifted along the vertical axis in the form of a partial derivative of the complex potential. In contrast to the complex potential for a symmetric vortex, the ratio for determining the circulation speed in case of misalignment of the working nozzle and the mixing chamber of the jet pump contains an additional component in the form of the displacement of the vortex center.In the process of analyzing the results of using the proposed mathematical model, it was established that the resulting speed of the circulation current and the relative displacement of the spatial vortex center are directly proportional. The conducted studies proved that the ratio of the velocities of the symmetric and asymmetric circulation flow is a function of the displacement of the center of the vortex flow coordinates and varies from 1 to zero. The magnitude of the relative speed of the circulation flow is inversely proportional to the displacement of the coordinate center and the distance to the mixing chamber of the jet pump. The developed mathematical model can be used to predict the influence of the rotation of the ejection system on its pressure characteristic in the case of radial relative displacement of the working nozzle and the mixing chamber of the jet pump.
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