On turbulence in hydrodynamic lubrication and in ground effect

Abstract

The contribution deals with a self-consistent description of time-mean turbulent lubricant flow, i.e. flow through a wedge-shaped 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. The limit considered is conveniently approached from the typical aerodynamical problem of wing-ground interference. This then ties in with appropriate inflow and outflow conditions, which here appear quite naturally rather than form a common uncertainty in lubrication theory. As a remarkable finding, a lifting force 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 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.