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How to calculate viscous part of aerodynamic coefficients in 3D NS-flow

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Old   October 13, 2010, 04:40
Post How to calculate viscous part of aerodynamic coefficients in 3D NS-flow
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hmd
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jack
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I appreciate if someone tell me how to callculate forces due to viscous stress tensor in 3D viscous external flow.
i mean:
Txx Txy Txz
Tyx Tyy Tyz
Tzx Tzy Tzz
I have writen a 3d navier-stokes code and want to calculate aerodynamic forces and CL ,CD, CM by viscous part . and how to calculate Cf, too.

Thanks alot.
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Old   October 15, 2010, 07:27
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Dynampally Pavitran
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\mu
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Originally Posted by hmd View Post
I appreciate if someone tell me how to callculate forces due to viscous stress tensor in 3D viscous external flow.
i mean:
Txx Txy Txz
Tyx Tyy Tyz
Tzx Tzy Tzz
I have writen a 3d navier-stokes code and want to calculate aerodynamic forces and CL ,CD, CM by viscous part . and how to calculate Cf, too.

Thanks alot.
Hi,

you can find this in any advance fluid mechanics text book (Panton; White), but below is the general method to calculate Force contribution due to viscosity.


Fx = T11 x dAx + T12 x dAy + T13 x dAz
Fy = T21 x dAx + T22 x dAy + T23 x dAz
Fz = T31 x dAx + T32 x dAy + T33 x dAz


viscous stress is given as T_{ij} = 2\mu \times \frac {1}{2}\left(\frac {\partial{u_{i}}}{\partial{x_{j}}} + \frac {\partial{u_{j}}}{\partial{x_{i}}}\right)

where i & j take valeus 1,2,3

to calculated Cf cf = \frac {F_{x}}{\frac{1}{2} \times density \times U^{2}_{\infty}}
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aerodynamics, friction coefficient, viscous flow

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