On Turbulence in Hydrodynamic Lubrication

The contribution deals with a self-consistent description of time-mean turbulent lubricant flow, i.e. flow through a wedgeshaped gap confined by counter-sliding solid surfaces. The methods adopted are matched asymptotic expansions, where the slenderness or aspect ratio of the gap and the accordingly defined Reynolds number represent the perturbation parameters. As a remarkable finding, a load-bearing capacity as a consequence of the resultant pressure distribution can only be maintained for fully developed turbulent flow provided its asymptotic structure flow differs distinctly to that known from other turbulent internal flows as pipe flows or channel flows or classical turbulent boundary layers. The basic analysis is carried out without resorting to a specific Reynolds shear stress closure. However, the resulting requirements for asymptotically correct turbulence models are discussed. The theoretical study is accompanied by a numerical study of the boundary layer equations governing the fully turbulent core flow. Finally, the impact of cavitation, a phenomenon highly relevant in lubrication theory, on the novel flow structure is addressed.