Relationship between Geometric Convergent Point and Leakage Rate of Mechanical Seal with Elliptical Dimples

The orientation angle alters the geometric characteristic of ellipse, and then leads to the change of leakage rate in mechanical seal with elliptical dimples. The numerical calculation and analytical method were employed to explain this phenomenon. Firstly, the analytical solution for the geometric convergent point of ellipse in the sliding direction was worked out. Secondly, based on the mass-conservative JFO cavitation boundary condition, a numerical calculation model was developed. The coordinates of maximum pressure point represented the position of high pressure region. Thereafter, the relationship between the coordinates of maximum pressure points and orientation angles was obtained after analyzing the fluid pressure distributions. Thirdly, comparing the locations of the geometric convergent points and the maximum pressure points, two types of points were nearly overlapped, and the possible reason was discussed. Finally, the influence of orientation angle on the leakage rate was studied at various structural and operating parameters. The locations of high/low pressure regions varied because the locations of geometric convergent points changed with the orientation angles. Moreover, the leakage rate became smaller as the high pressure region moved away from the leakage outlet.