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A roughness-dependent model

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(the algebraic eddy viscosity model is therefore)
(the algebraic eddy viscosity model is therefore)
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\nu _t(y)  = \kappa  A  \left( 1 - e^{\frac{-y}{A}} \right)
\nu _t(y)  = \kappa  A  \left( 1 - e^{\frac{-y}{A}} \right)
  u_\tau  e^{\frac{-y}{A}}   
  u_\tau  e^{\frac{-y}{A}}   
-
</math></td><td width="5%">(6)</td></tr></table>
+
</math></td><td width="5%">(7)</td></tr></table>
== References ==
== References ==

Revision as of 15:29, 19 June 2007

Contents

Two-equation eddy viscosity model

 
\nu _t  = C_{\mu} {{k^2 } \over \varepsilon }
(1)

where:  C_{\mu} = 0.09

One-equation eddy viscosity model

 
\nu _t  = k^{{1 \over 2}}  l 
(2)

Algebraic eddy viscosity model

 
\nu _t(y)  = {C_{\mu}}^{{1 \over 4}} l_m(y) k^{{1 \over 2}}(y) 
(3)

l_m is the mixing length.

Algebraic model for the turbulent kinetic Energy


k^{{1 \over 2}}(y) = {1 \over {C_{\mu}}^{{1 \over 4}}}  u_\tau  e^{\frac{-y}{A}} 
(4)

u_\tau is the shear velocity and A a model parameter.

Algebraic model for the mixing length, based on (4) [Absi (2006)]


l_m(y) = \kappa \left( A - \left(A - y_0\right) e^{\frac{-(y-y_0)}{A}} \right)
(5)

\kappa = 0.4, y_0 is the hydrodynamic roughness

the algebraic eddy viscosity model is therefore

 
\nu _t(y)  = \kappa \left( A - \left(A - y_0\right) e^{\frac{-(y-y_0)}{A}} \right)
 u_\tau  e^{\frac{-y}{A}}  
(6)

for a smooth wall (y_0 = 0):

 
\nu _t(y)  = \kappa  A  \left( 1 - e^{\frac{-y}{A}} \right)
 u_\tau  e^{\frac{-y}{A}}  
(7)

References


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