Effective boundary conditions for creeping flow along a periodic rough surface
The creeping flow along a periodic rough surface is calculated as a series in the slope of the roughness grooves. On a scale much larger than the grooves, this flow is equivalent to that over a smooth plane which is shifted from the top of the riblets. The convergence of the series for the shift distance in term of the slope is accelerated by use of Euler transformation and of the existence of a limit for large slope. The case of a flow along the grooves is presented in detail. The result for the shift is typically valid for a slope up to 2. A flow perpendicular to grooves can be treated in a similar way. Asymptotic behaviour for large slope depends on the profile shape.
KeywordsConformal Mapping Large Slope Normalise Shift Smooth Plane Collocation Technique
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