Elliptic-blending k - ε model
Elliptic-blending k - ε model
Elliptic-blending k - ε model
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Formulation<br />
Equation-by-equation modifications<br />
Turbulent dissipation rate <strong>ε</strong>:<br />
Dρ<strong>ε</strong><br />
Dt<br />
Modifications:<br />
1 <br />
= C<strong>ε</strong>1<br />
τ<br />
(fcPk +Pb)−ρC ∗ <strong>ε</strong>2<strong>ε</strong> + ∂<br />
∂xj<br />
◮ Adding buoyancy source term Pb,<br />
<br />
µ µt ∂<strong>ε</strong><br />
+<br />
2 σ<strong>ε</strong> ∂xj<br />
◮ Testing curvature correction fc, as suggested by Durbin for<br />
k −ω <strong>model</strong>s:<br />
◮ Option for C ∗ <strong>ε</strong>2 :<br />
fc = 1+α1|η3|+3α1|η3|<br />
C ∗ <strong>ε</strong>2 =<br />
⎧<br />
⎨ C<strong>ε</strong>2<br />
⎩ C<strong>ε</strong>2 +α3 (0.4−C<strong>ε</strong>2 )tanh<br />
<br />
∂ νt ∂k<br />
∂xj σk ∂xj<br />
<strong>ε</strong>−1 <br />
<br />
3/2