Study of the kinematic radial work flow of a well jet pump
DOI:
https://doi.org/10.31471/1993-9965-2022-2(53)-23-30Keywords:
borehole jet pump, ejection system, potential flows, hydrodynamic functions, complex potential, analytical function.Abstract
The paper analyzes the possibility of applying the characteristic function of the working flow, obtained using the spatial leakage function of a complex variable, to study the process of working jet propagation in the mixing chamber of a downhole jet pump. The existence of continuous partial derivatives of the characteristic function for both variables, the velocity potential and the flow function, is shown, indicating that the Cauchy-Riemann conditions are satisfied. The existence of analytical conditions allowed the determination of the absolute value of the working flow velocity vector in the form of the modulus of the derivative of the characteristic function. The distribution of the working fluid velocities in the inlet section of the mixing chamber is characterized by an axisymmetric parabolic dependence. The horizontal projection of the working fluid velocity decreases with increasing distance between the working nozzle and the mixing chamber of the jet pump. Generalized velocity profiles are defined as the ratio of the horizontal projections of the working fluid velocities to their axial value. The working fluid velocity reaches its maximum value on the axis of the mixing chamber of the jet pump. The value of the working fluid velocity decreases towards the walls of the mixing chamber. The coincidence of the generalized dimensionless velocity profiles obtained for any distance between the working nozzle and the mixing chamber indicates their similarity. The coefficient of unevenness of the velocity distribution in the inlet section of the mixing chamber was determined in the form of the ratio of the average and maximum velocity of the working flow. The influence of the main design parameters of the jet pump on the unevenness of the working fluid velocity profile is analyzed. The coefficient of unevenness of the distribution of the working fluid velocities increases with the increasing distance between the working nozzle and the mixing chamber and decreases with the increasing of the main geometric parameters of the jet pump.
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