Triple-deck analysis of the steady flow over a rotating disk with surface roughness

The effect of surface roughness on the steady laminar flow induced by a rotating disk submerged by fluid otherwise at rest is investigated here theoretically and numerically. A theory is proposed where a triple-deck analysis is applied leading to a fast evaluation of the steady-flow modification due to the rough surface. The theory assumes that the roughness is much smaller than the boundary-layer height and is characterized by a significantly longer length scale (slender roughness). Only the leading-order correction is developed here, corresponding to a velocity-field correction that is linear with the roughness height. The proposed theory neglects some curvature terms (here partially accounted by means of a stretching of the radial coordinate and of a scaling of the dependent variables). Numerical simulations performed with different roughness geometries (axisymmetric roughness, radial grooves, and localized bumps) have been used to validate the theory. Results indicate that the proposed theory leads to a good quantification of the flow modifications due to surface roughness at a very low computational cost. A demonstration of the capabilities of the theory is finally proposed where the statistical effects on the flow due to a random (but statistically known) roughness distributed on the surface of a rotating disk are characterized.