井喷泵流动部分不对称旋转流动的模拟

Denys Panevnik
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引用次数: 0

摘要

为了改进钻头上顶喷射系统在井内不对称旋转情况下工作过程的数学模型,提出了一种利用流体动力旋涡函数来模拟循环注入流动的方法,该旋涡函数的中心相对于喷射泵混合室的轴向发生了位移。在模拟注入流体旋转不对称运动的过程中,采用了液体平移速度矢量沿闭合回路循环的概念。借助水动力环流函数的复势分量,得到了坐标中心单向和双向位移的空间涡旋等势线和流动线的图形化解释。利用速度势和流函数的解析关系,确定了环流速度的分量,证明了旋涡中心移位时复势函数的解析性。柯西-黎曼条件的满足使我们能够以复势的偏导数的形式,表示出坐标中心沿垂直轴移动的循环电流的最终速度。与对称涡的复势相反,在工作喷嘴与喷射泵混合室不对准的情况下,用于确定循环速度的比率包含了涡中心位移形式的附加分量。在对数学模型计算结果进行分析的过程中,发现环流速度与空间涡旋中心的相对位移成正比关系。研究证明,对称环流和非对称环流的速度之比是涡旋流坐标中心位移的函数,其变化范围为1 ~ 0。循环流动相对速度的大小与坐标中心的位移和喷射泵到混合室的距离成反比。所建立的数学模型可用于预测喷射泵工作喷嘴与混合室径向相对位移情况下,喷射系统旋转对其压力特性的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simulation of asymmetrical rotational flow in the flow part of a well jet pump
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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