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Old   October 19, 2012, 10:02
Default Turbulence model parameters and equations
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Dear CFD users,

Right now Im working on a CFD computation for external flow around a very streamlined car.
I have some questions regarding the turbulence parameters. Ill first specify what formulas I used to calculate some parameters. FYI, I use FineOpen of Numeca. I will either use the SA or Mentor-SST k omega (Extended wall) model.

Description of the stream: A free steam around a car driving in the open i.e. on the road. So it is an external flow. The free stream velocity V_{\infty} is 25 m/s.

There are a couple parameters I have to specify in the CFD software program which im not complete sure about, being:

Boundary conditions:
for the k-omega model: k and \varepsilon
for the Spalart-Allmaras model: turbulent viscosity

Initial conditions:
for the k-omega model: k and \varepsilon
for the Spalart-Allmaras model: ratio \frac{\tilde{\nu}}{\nu} (taken as 1)
So it comes down to calculating/guestimating these parameters. I used the following formulas (all in SI units) to calculate these parameters:

U_{\tau}=\sqrt{\frac{\tau_{wall}}{\rho}}=\sqrt{0.5*V_{ref}^2*C_f} (From Numeca FineOpen manual)
C_f=\frac{0.027}{Re_x^{1/7}} (Also from FineOpen manual)
Re_x=\frac{\rho_{ref}*V_{ref}*L_{ref}}{\mu} with \mu being the dynamic (molecular) viscosity
k=\frac{\tau_{wall}}{\rho}*\frac{1}{C_{\mu}} with C_{\mu}=0.09 and \frac{\tau_{wall}}{\rho}=0.5*V_{ref}^2*C_f
\varepsilon=C_{\mu}*(\frac{\mu_t}{\mu})^{-1}*\frac{\rho_{ref}*k^2}{\mu} I took \frac{\mu_t}{\mu}=1 (Numeca specifies in the manual that a typical value for this ratio is 1 for external flows). So before I can calculate \varepsilon, I first calculate k.

Turbulent (eddy) viscosity \mu_t=C_{\mu}*\rho*\frac{k^2}{\varepsilon} (So before calculating this parameter, I first calculate k, then \varepsilon and then \mu_t)

Using the above mentioned formulas, I was able to calculate all the needed parameters. Still Im not sure if these formulas are correct or maybe are not valid in every case.

However, when I just assume these formulas are correct I calculated k, \varepsilon=3075 and \mu_t. This yielded
k = 0.718, \varepsilon=3075 and \mu_t=1.85*10^-5. Do these values make sense in anyway, or are they completely out of range?

The actual reason Im posting this question is to validate our computation. One year ago, a group performed the same computation for the exact same car. This yielded a drag force of about 40N. The problem we are having now is that the drag force is in the order of 10^4 Newton. Obviously this does not make sense. Right now the mesh I runned in FineOpen contains about 18 million cells with refinements near the car itself, behind the car, beneath the car etc. etc.

So what Im specifically asking:
1) Can someone verify the method I use, especially the formulas I use
2) What may cause the problem of a way too high drag value?
3) Do the values of k and epsilon make sense?

I know these are a lot of questions, but any help is much appreciated.
Thank you in advance,

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Old   October 24, 2012, 13:20
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