CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Wiki > A roughness-dependent model

A roughness-dependent model

From CFD-Wiki

(Difference between revisions)
Jump to: navigation, search
(→Algebraic model for the turbulent kinetic Energy)
(→Two-equation eddy viscosity model)
Line 1: Line 1:
-
==Two-equation eddy viscosity model==
+
==Two-equation <math>k</math>-<math>\epsilon</math> eddy viscosity model==
<table width="70%"><tr><td>
<table width="70%"><tr><td>
<math>  
<math>  
-
\nu _t  = C_{\mu} {{k^2 } \over \varepsilon }
+
\nu _t  = C_{\mu} {{k^2 } \over \epsilon }
</math></td><td width="5%">(1)</td></tr></table>
</math></td><td width="5%">(1)</td></tr></table>
where:  
where:  

Revision as of 20:31, 19 June 2007

Contents

Two-equation k-\epsilon eddy viscosity model

\nu _t = C_{\mu} {{k^2 } \over \epsilon } (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


This article is a stub, a short article which needs to be improved. You can help by expanding it.
Retrieved from "https://openfoam.cfd-online.com/Wiki/A_roughness-dependent_model"
My wiki