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 bentmol July 1, 2011 17:18

Wall coordinates and boundary layer thickness

Is there a simple scaling between wall coordinates and the boundary layer thickness?

The only book that I have read that even attempts to relate wall coordinate y+ with the boundary layer thickness [BLT] is "Applied Fluid Dynamics Handbook" by Blevins. He suggests that 0.005 x BLT = y+ = 10, 0.1 x BLT = y+ = 300 and BLT = y+ = 3000, pertaining only to turbulent flow over flat plate.

Blevins says that these relationships are highly approximate. After plugging in the formulas involving friction factor, wall coordinates and BLT, I find that the relationship between wall coordinates and boundary layer coordinates depends on the local Reynolds number Re = Ux/[kinematic viscosity]. I get

y/BLT = 60.9 x [y+] times Re^-0.7857

based on the friction factor formulas that I found in Blevins' book, for flow over a flat plate. Other formulas in other books will result in a somewhat different Reynolds number dependence and the numerical constants will vary too.

But, there seems to be no simple conversion between the 2 coordinate systems.

Is this the right conclusion?

Ben

 RossFS July 3, 2011 20:44

I'd say that your conclusion is correct as you can set the y+ value arbitrarily as it's value is a function of the distance from the wall to the first node (in the mesh you have) off the wall. Hence you can make this any value you like and thus won't have any connection with the boundary layer height.

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