Flow over a finite-span circular cylinder rolling along a plane wall: forces and moments

This study obtains expressions for the force and moment coefficients for a finite-span circular cylinder rolling on a plane wall. It is assumed that a small, but finite, gap exists between the cylinder and the wall, as a result of, for example, surface roughness. Using the method of matched asymptotic expansions, the flow is decomposed into an inner solution, valid in the narrow interstice between the cylinder and the wall, and an outer solution, valid far from the interstice. Then, the force and moment coefficients are expressed as the sum of a gap-dependent term, which is computed from the inner solution, and a gap-independent term, which is computed from the outer solution. Solutions to the inner flow are obtained by solving numerically the two-dimensional Reynolds equation for the lubrication flow in the interstice. The inner solution depends only on a single parameter, the cylinder aspect ratio divided by the gap-diameter ratio, and the effects of this parameter on the gap-dependent force and moment coefficients are deduced. Solutions to the outer flow are obtained using thee-dimensional numerical simulations for a range of Reynolds numbers, cylinder aspect ratios and cylinder rotation rates. Then, the variation of the force and moment coefficients against each of these terms is obtained.