Turbulence model parameters and equations

Maximus91 · October 19, 2012, 10:02

Dear CFD users,

Right now I´m working on a CFD computation for external flow around a very streamlined car.
I have some questions regarding the turbulence parameters. I´ll 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 I’m 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 I’m 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 I’m 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,

Maximus

Maximus91 · October 24, 2012, 13:20

Anyone any suggestions?

October 19, 2012, 10:02	Turbulence model parameters and equations	#1
Maximus91 New Member Maarten Join Date: Sep 2012 Posts: 3 Rep Power: 13	Dear CFD users, Right now I´m working on a CFD computation for external flow around a very streamlined car. I have some questions regarding the turbulence parameters. I´ll 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: $U_{\tau}=\sqrt{\frac{\tau_{wall}}{\rho}}=\sqrt{0.5V_{ref}^2C_f}$ (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 $\frac{\tau_{wall}}{\rho}=0.5V_{ref}^2C_f$ $\varepsilon=C_{\mu}(\frac{\mu_t}{\mu})^{-1}\frac{\rho_{ref}k^2}{\mu}$ 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 I’m 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 I’m 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 I’m 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, Maximus

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October 24, 2012, 13:20		#2
Maximus91 New Member Maarten Join Date: Sep 2012 Posts: 3 Rep Power: 13	Anyone any suggestions?