液膜润滑机械端面密封流体动压沟槽侧壁效应研究

针对非接触机械密封端面开槽后所出现的膜厚不连续处存在的侧壁效应，在沟槽边界处将广义伯努利方程引入传统润滑方程，建立了考虑动压沟槽侧壁效应的液膜润滑螺旋槽端面机械密封数值分析模型. 采用有限单元法结合拉格朗日乘子法求解润滑方程，研究了不同螺旋槽几何参数和工况条件下沟槽侧壁效应对密封性能的影响. 结果表明:数值模型可方便捕捉沟槽边界处的压力跃变，侧壁效应在不同螺旋槽深度下表现出截然不同的影响规律，高转速、大螺旋角和小密封间隙下动压沟槽的侧壁效应较为显著. 理论模型和计算方法可为超高速工况螺旋槽机械密封的设计和局部惯性效应的研究提供指导. 

Sidewall Effect of Hydrodynamic Grooves of Liquid Film Lubricated Mechanical Face Seals

In order to improve the performance of the mechanical face seals, the hydrodynamic grooves are often etched on the face of one seal ring, which will produce the hydrodynamic effect and make the seal faces run in non-contacting states. By this, the wear of the seal faces can be probably avoided. The existence of these grooves leads to the sudden variation of the flow channel, which has influences the pressure distribution of the lubricant film and the sealing performance of the mechanical seal, especially under the high speed conditions. This is called “the sidewall effect”. In this paper, aiming at the sidewall effect due to the film thickness discontinuity at the hydrodynamic grooves boundaries on the non-contacting spiral-grooved mechanical seal face, a numerical analysis model of the spiral-grooved mechanical seal lubricated with the liquid film was established. The generalized Bernoulli equations was introduced and coupled with the Reynolds equations. The computational domain of grooved and non-grooved zone fluid film between seal faces was meshed into triangular grids. The domain decomposition finite element method was used to solve the control equations and the Lagrange multiplier method was applied to deal with the pressure constraints at the groove boundaries introduced by the Bernoulli equations. The numerical method was validated by comparing the present results with the theoretical results and literature data. Then the model was used to analyze the influence of groove sidewall effect on the lubrication film pressure between the seal faces and sealing performance under the different spiral groove geometrical parameters and operating conditions. The results showed that the proposed theoretical model and numerical method can effectively capture the sudden film pressure rise in the divergent region of the liquid film and the sudden pressure drop at the convergent boundary of the liquid film caused by groove sidewall effect. With the proposed model, the local fluid film pressure distribution at the groove boundaries can be numerically predicted. The film pressure jump can be attributed to the local inertia effect of the fluid film at the groove boundaries. The sidewall effect of the spiral groove boundary was closely dependent on the rotational speeds, sealing clearances, spiral angle and the groove depth. Compared with the calculation results without considering the groove sidewall effect, the sidewall effect of hydrodynamic grooves improved the hydrodynamic effect of the spiral grooved face seals. Meanwhile, it was found that there was a critical spiral groove depth for a specific sealing clearance. When the groove depth was less than this value, the sidewall effect increased the opening force and leakage rate; however, when the groove depth was greater than this value, the sidewall effect decreased these parameters. The sidewall effect due to the film discontinuity greatly affected the hydrodynamic effect of the fluid film and further affected the lubrication performance and sealing characteristics of mechanical face seal. The optimal spiral groove depth and spiral angle were obtained when considering the sidewall effect. For the practical application, the high rotational speed and large groove depth conditions will lead to the obvious sidewall effect of spiral grooves, and the influence cannot be ignored. The present theoretical model and numerical method of this paper can provide guidance for the design of spiral groove mechanical seal and the investigation on the local inertia effect at the ultra-high speed conditions.