Skin friction coefficient
From CFD-Wiki
(Difference between revisions)
| Line 13: | Line 13: | ||
1/7 power law with experimental calibration (equation 21.12 in [1]): | 1/7 power law with experimental calibration (equation 21.12 in [1]): | ||
| - | <math>C_f = 0.0592 \, Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7</math> | + | <math>C_f = 0.0592 \, Re_x^{-1/5} \quad \mbox{for} \quad 5 \cdot 10^5 < Re_x < 10^7</math> |
Schlichting (equation 21.16 footnote in [1]) | Schlichting (equation 21.16 footnote in [1]) | ||
| - | <math>C_f = [ 2 \, log(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad | + | <math>C_f = [ 2 \, log(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad Re_x < 10^9 </math> |
Schultz-Grunov (equation 21.19a in [1]): | Schultz-Grunov (equation 21.19a in [1]): | ||
Revision as of 14:59, 25 February 2011
The skin friction coefficient, 
, is defined by:
Where 
is the local wall shear stress, 
is the fluid density and 
is the free-stream velocity (usually taken ouside of the boundary layer or at the inlet).
For a turbulent boundary layer several approximation formulas for the local skin friction can be used:
1/7 power law:
1/7 power law with experimental calibration (equation 21.12 in [1]):
Schlichting (equation 21.16 footnote in [1])
![C_f = [ 2 \, log(Re_x) - 0.65 ] ^{-2.3} \quad \mbox{for} \quad Re_x < 10^9](/W/images/math/7/1/3/713d49c9c76550f69eab8db83a189b82.png)
Schultz-Grunov (equation 21.19a in [1]):
![C_f = 0.370 \, [ log(Re_x) ]^{-2.584}](/W/images/math/4/f/f/4ff34a9bfeb1c9a8869f9a7e297b3d57.png)
References
- Schlichting, Hermann (1979), Boundary Layer Theory, ISBN 0-07-055334-3, 7th Edition.
To do
Someone should add more data about total skin friction approximations, Prandtl-Schlichting skin-friction formula, and the Karman-Schoenherr equation.
