Realisable k-epsilon model
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:<math> \frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_j} (\rho \epsilon u_j) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_{\epsilon}}\right) \frac{\partial \epsilon}{\partial x_j} \right ] + \rho \, C_1 S \epsilon - \rho \, C_2 \frac{{\epsilon}^2} {k + \sqrt{\nu \epsilon}} + C_{1 \epsilon}\frac{\epsilon}{k} C_{3 \epsilon} P_b + S_{\epsilon} </math> | :<math> \frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_j} (\rho \epsilon u_j) = \frac{\partial}{\partial x_j} \left[ \left(\mu + \frac{\mu_t}{\sigma_{\epsilon}}\right) \frac{\partial \epsilon}{\partial x_j} \right ] + \rho \, C_1 S \epsilon - \rho \, C_2 \frac{{\epsilon}^2} {k + \sqrt{\nu \epsilon}} + C_{1 \epsilon}\frac{\epsilon}{k} C_{3 \epsilon} P_b + S_{\epsilon} </math> | ||
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+ | Where <br> | ||
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+ | <math> C_1 = \max\left[0.43, \frac{\eta}{\eta + 5}\right] , \;\;\;\;\; \eta = S \frac{k}{\epsilon}, \;\;\;\;\; S =\sqrt{2 S_{ij} S_{ij}} </math> <br> | ||
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+ | In these equations, <math> P_k </math> represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated in same manner as standard k-epsilon model. <math> P_b </math> is the generation of turbulence kinetic energy due to buoyancy, calculated in same way as standard k-epsilon model. |
Revision as of 22:52, 18 September 2005
Transport Equations
Where
In these equations, represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated in same manner as standard k-epsilon model. is the generation of turbulence kinetic energy due to buoyancy, calculated in same way as standard k-epsilon model.