任意夹角交叉封闭边界内平面流线计算及应用

目前以解析法求解交叉封闭边界内的复势函数需要满足边界夹角等于π/n（n为正整数）的条件。为将n拓展到任意范围（正实数），提出先保角变换再镜像反映的思路。将原始平面内任意夹角的封闭边界利用保角变换映射到目标平面，使得映射后封闭边界的夹角在目标平面内满足n为正整数的条件，根据保角变换前后平面内对应点的复势函数和点源（汇）流量值不变的性质，利用镜像反映法求解原始平面内场点在目标平面内对应点的复势函数值即为原始平面内场点复势函数值，并推导了流场内任意点流速的计算公式。采用等分等值线方法，利用计算机对流场内流线分布进行了绘制，并指出了解析法计算流场存在的缺陷及相应的改进方法。结果表明，越靠近边界夹角的顶点，流线密度越低流速越慢，则该区域的含油饱和度相对越高。

Method for Computing In-plane Streamlines in Cross-sealed Boundaries of Any Angle of Tip and Its Applications

At present, to solve the function of complex potentials in cross-sealed boundaries with an analytic method requires the condition that the boundary angle of the dip equals π/n (where n is a positive integer). To extend the application of n to any real number, performing conformal transformation followed by mirror imaging is proposed. Specifically, the idea is to mirror a sealed boundary of any angle of the tip in the original plane onto a target plane by performing conformal transformation, thereby enabling the angle of the tip of the sealed boundary after mirroring to satisfy the condition that n is a positive integer. According to the property that the values of the complex potential and current of the point source (convergence) of a point in the original plane remain unchanged after conformal transformation, the complex-potential function of the corresponding point in the target plane of the point in the original plane is solved, and the resulting value is the value of the complex-potential function of the point in the original plane. An equation for computing the flow velocity of any point in flow fields was also derived. The streamline distribution in flow fields was rendered graphically by employing the contours method. In addition, the shortage of flow fields computed with the analytic method was reviewed and, correspondingly, improvements were proposed. The field application results show that an area closer to the vertex of the boundary angle of the tip has a higher streamline density, lower flow velocity, and higher degree of oil saturation.