On the Fully Turbulent Regime in Hydrodynamic Lubrication

The long-standing classical theory of lubrication in the fully hydrodynamic regime is essentially traced back on the assumptions of (i) a relatively slender gap formed by two rigid surfaces that exhibit a (counter-)sliding (and “squeezing”) motion in the specific reference frame, (ii) a Newtonian lubricant, (iii) the neglect of inertia terms in the Navier-Stokes equations, and (iv) strictly laminar flow. Issues (i)(iv) prove sufficient for a rigorous derivation of the well-known Reynolds equation (in the most general form) governing the pressure distribution in the gap. In engineering applications as e.g. thrust bearings for oilor steam-lubricated high-speed rotors, however, the Reynolds number Re formed with a typical gap height may take on rather large values, thus rendering prerequisite (iii) questionable. It is pointed out on the basis of quantitative results relevant for the global stability bounds of internal flows that relaxing assumption (iii) also involves a critical review of supposition (iv), which finally suggests the inclusion of turbulence. Here we restrict the investigation to incompressible fully developed turbulent flow between smooth surfaces.