Leakage Threshold of a Saddle Point

Abstract

The threshold condition for leakage inception is of great interest to many engineering applications, and it is essential for seal design. In the current study, the leakage threshold is studied by means of a numerical method for a mechanical contact problem between an elastic bi-sinusoidal surface and a rigid flat surface. The coalesce process of the contact patches is first investigated, and a generalized form of solution for the relation between the contact area ratio and the average applied pressure is acquired. The current study shows that the critical value of the average applied pressure and the corresponding contact area required to close the percolation path can be represented as a power law of a shape parameter, if the effect of the hydrostatic load from the pressurized fluid is ignored. With contact patches merged under a constant applied load, the contact breakup process is investigated with elevated sealed fluid pressure condition, and it is shown that the leakage threshold is a function of the excess pressure, which is defined as a ratio between the average applied pressure and the critical pressure under dry contact conditions. Graphical abstract

Significance of Elastic Coupling for Stresses and Leakage in Frictional Contacts

“…The flow patterns depicted in Fig. 3 are in line with the idea that fluid-flow is impeded predominantly by a few constrictions [43,44], where current densities are high and which become critical just before they block fluid flow completely. The average effect of coupling on the fluid flow suffers from large statistical uncertainties near the percolation threshold, since the number of relevant constrictions per unit area is minuscule.…”