RNG k-epsilon model
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(Difference between revisions)
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- | <math> | + | :<math> |
\frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left(\alpha_k \mu_{\rm eff} \frac{\partial k}{\partial x_j}\right) + P_k + P_b - \rho \epsilon | \frac{\partial}{\partial t} (\rho k) + \frac{\partial}{\partial x_i} (\rho k u_i) = \frac{\partial}{\partial x_j} \left(\alpha_k \mu_{\rm eff} \frac{\partial k}{\partial x_j}\right) + P_k + P_b - \rho \epsilon | ||
</math> | </math> | ||
- | <math> | + | :<math> |
\frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_i} (\rho \epsilon u_i) = \frac{\partial}{\partial x_j} \left(\alpha_{\epsilon} \mu_{\rm eff} \frac{\partial \epsilon}{\partial x_j}\right) + C_{1 \epsilon}\frac{\epsilon}{k} \left( G_k + C_{3 \epsilon} G_b \right) - C_{2\epsilon} \rho \frac{\epsilon^2}{k} - R_{\epsilon} | \frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_i} (\rho \epsilon u_i) = \frac{\partial}{\partial x_j} \left(\alpha_{\epsilon} \mu_{\rm eff} \frac{\partial \epsilon}{\partial x_j}\right) + C_{1 \epsilon}\frac{\epsilon}{k} \left( G_k + C_{3 \epsilon} G_b \right) - C_{2\epsilon} \rho \frac{\epsilon^2}{k} - R_{\epsilon} | ||
</math> | </math> | ||
- | <math> | + | :<math> |
d \left(\frac{\rho^2 k}{\sqrt{\epsilon \mu}} \right) = 1.72 \frac{\hat{\nu}}{\sqrt{{\hat{\nu}}^3-1+C_\nu}} d{\hat{\nu}} | d \left(\frac{\rho^2 k}{\sqrt{\epsilon \mu}} \right) = 1.72 \frac{\hat{\nu}}{\sqrt{{\hat{\nu}}^3-1+C_\nu}} d{\hat{\nu}} | ||
</math> | </math> | ||
- | <math> | + | :<math> |
\hat{\nu} = \mu_{\rm eff}/\mu | \hat{\nu} = \mu_{\rm eff}/\mu | ||
</math> | </math> | ||
and | and | ||
- | <math> | + | :<math> |
C_\nu \approx 100 | C_\nu \approx 100 | ||
- | + | </math> | |
+ | |||
+ | |||
+ | :<math> | ||
+ | R_{\epsilon} = \frac{C_\mu \rho \eta^3 (1-\eta/\eta_0)}{1+\beta\eta^3} \frac{\epsilon^2}{k} | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \eta \equiv Sk/\epsilon | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \eta_0 = 4.38 | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | \beta = 0.012 | ||
+ | </math> | ||
+ | |||
+ | |||
+ | :<math> | ||
+ | \frac{\partial}{\partial t} (\rho \epsilon) + \frac{\partial}{\partial x_i} (\rho \epsilon u_i) = \frac{\partial}{\partial x_j} \left(\alpha_{\epsilon} \mu_{\rm eff} \frac{\partial \epsilon}{\partial x_j}\right) + C_{1 \epsilon}\frac{\epsilon}{k} \left( G_k + C_{3 \epsilon} G_b \right) - C_{2\epsilon}^* \rho \frac{\epsilon^2}{k} | ||
+ | </math> | ||
+ | |||
+ | :<math> | ||
+ | C_{2\epsilon}^* \equiv C_{2\epsilon} + {C_\mu \eta^3 (1-\eta/\eta_0)\over 1+\beta\eta^3} | ||
+ | </math> | ||
+ | |||
+ | |||
+ | :<math> | ||
+ | C_{1\epsilon} = 1.42, \; \; C_{2\epsilon} = 1.68 | ||
+ | </math> |
Revision as of 13:04, 14 September 2005
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