How is wall shear stress defined on complex 3D surfaces?

AI Thread Summary
Wall shear stress on complex 3D surfaces, like a golf ball, can be straightforward to calculate on smooth areas, where tangential velocity aligns with the azimuthal plane. However, challenges arise in the dimples due to the infinite tangents and the difficulty in selecting a single tangential velocity. The flow behavior in these dimples may lead to slip conditions, complicating shear stress calculations. It is suggested that shear stress may not exist at the deepest points of some dimples. Understanding these dynamics is crucial for accurate modeling of flow past complex geometries.
nikosb
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I have computed the flow past a golfball and I am trying to calculate the shear stress on the surface of the golfball but I am having trouble figuring out how the wall shear stress is defined on 3D complex surfaces.
When I am on the main part of the golfball that it is similar to that of the sphere the calculation of the wall shear stress is straightforward. From the surface I move a distance "h" along the normal and compute the tangential velocity. In this case I choose the tangential velocity to be aligned with the azimuthal plane.
However when I am in the dimples, it is hard to choose a single tangential velocity as there are infinite number of tangents and not anyone of them is necessarily aligned with an azimuthal plane. How do I choose the tangential velocity in such a case?

Thanks
 
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Not sure how you do that as the flow across the dimples slip (or break off). You probably don't have any shear stress at the deepest point in the some of the dimples
 
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