Standard k-epsilon model
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(Add a value for C_{3 \epsilon}, typically = -0.33) |
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== Transport equations for standard k-epsilon model == | == Transport equations for standard k-epsilon model == | ||
- | For k <br> | + | For turbulent kinetic energy <math> k </math> <br> |
:<math> \frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j}\right] + P_k + P_b - \rho \epsilon - Y_M + S_k </math> | :<math> \frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_k} \right) \frac{\partial k}{\partial x_j}\right] + P_k + P_b - \rho \epsilon - Y_M + S_k </math> | ||
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:<math> | :<math> | ||
- | C_{1 \epsilon} = 1.44, \;\; C_{2 \epsilon} = 1.92, \;\; C_{\mu} = 0.09, \;\; \sigma_k = 1.0, \;\; \sigma_{\epsilon} = 1.3 | + | C_{1 \epsilon} = 1.44, \;\;\; C_{2 \epsilon} = 1.92,\;\;\; C_{3 \epsilon} = -0.33, \;\; \; C_{\mu} = 0.09, \;\;\; \sigma_k = 1.0, \;\;\; \sigma_{\epsilon} = 1.3 |
</math> | </math> | ||
[[Category:Turbulence models]] | [[Category:Turbulence models]] |
Revision as of 14:55, 22 August 2013
Contents |
Transport equations for standard k-epsilon model
For turbulent kinetic energy
For dissipation
Modeling turbulent viscosity
Turbulent viscosity is modelled as:
Production of k
Where is the modulus of the mean rate-of-strain tensor, defined as :
Effect of buoyancy
where Prt is the turbulent Prandtl number for energy and gi is the component of the gravitational vector in the ith direction. For the standard and realizable - models, the default value of Prt is 0.85.
The coefficient of thermal expansion, , is defined as