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plucas April 4, 2013 12:15

Initial Turbulence Conditions
 
I am doing an automotive analysis using the k-omega SST turbulence model and I have a question on initial conditions.

The two values:
turbulentKE
turbulentOmega

So to calculate these first I calculated Reynolds Number:
Re = U * L / nu = 45 * 4.16 / 1.5e-5 = 12.5 E6

Then initial turbulence %:
I = 0.16 Re ^-1/8 = 0.0208

Now to turbulentKE:
k = 1.5 * (UI)^2 = 1.5 * (45 * 0.0208)^2 = 1.309

Now is the real question. I found 2 equations for epsilon with one being an approximation. After calculating both a get a big difference in numbers and wonder which one I should use to calculate omega.

epsilon ~ (k^1.5) / L = (1.309^1.5) / 4.16 = 0.360

epsilon = (cmu^.75) * (k^1.5) * (l^-1)
cmu = 0.09 (seems to be most commonly used)
l = 0.07 * L = 0.07 * 4.16 = 0.2912
epsilon = (0.09^0.75) * (1.309^1.5) * (0.2912^-1)
epsilon = 0.845

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epsilon = 0.360
epsilon = 0.845

So am I doing this right? If so, which epsilon value should I be using?

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turbulentOmega = k / epsilon

fumiya April 6, 2013 00:09

Hi plucas,

For external flows the freestream effective viscosity will be on the order of laminar viscosity
so small values of \beta are appropriate, say \beta = 0.1 0.2:
\beta = \frac{\nu _t}{\nu}
For k-omega SST turbulence model, the turbulent eddy viscosity \nu _t is computed from:
\nu _t = \frac{k}{\omega}
You can estimate \omega value using the above equations.

References:
Hope this helps,
Fumiya


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