k-omega SST: what is the Reference length scale?

steddy · February 19, 2020, 14:18

Hi all,
I'm trying to investigate the flow of air around a car with the RAS k-omega SST.
The OpenFOAM guide: https://www.openfoam.com/documentati...omega-sst.html says that the following formula can be used to estimate omega, that is the turbulence specific dissipation rate:
$\omega = \frac{k^{0.5}}{C_\mu L}$
where L is the reference length scale,
and cmu is equal to 0.09
I wanted to ask: what exactly is L? In my case, would it be the length of the car?

I saw that OpenFOAM has a motorbike scenario and tutorial.

The motorbike has a length of 1.42 m (this value is lRef and can be found in the system/forceCoeffs dict.
The value of k is 0.24, and can be found in the 0/include/initialConditions file.
The value of omega is 1.78 (again, it is is located in the initialConditions file).

If we isolate the L in the previous formula, we get:
$L = \frac{k^{0.5}}{C_\mu \omega}$
If we substitute for k, omega and Cmu, we get 3.058 m, which is different than the valur of lRef (the length of the motorbike). Therefore, I'm not anymore convinced that L is the length of the vehicle.

Can anyone help me?
Regards,
Andrea

sapujapu · February 20, 2020, 10:27

The exact reference length is not that important afaik. The important thing is that your nu/nu_t ratio (laminar viscosity to turbulent viscosity) is small enough. This paper by Spalart & Rumsey gives some recommendations in Section C for external aerodynamics: https://ntrs.nasa.gov/archive/nasa/c...0070035069.pdf

LuckyTran · February 20, 2020, 11:55

It's not the same length scale.

The length scale in forceCoeffs is related to the definition of your force coefficients like lift, and that one is a geometric length scale.

The length scale in the formula for omega is a turbulent length scale for your boundary. Say if your oncoming flow comes from a fully developed flow in a duct with diameter D is a small fraction of D (usually estimated to be about L~0.07D). It's a boundary condition, you need to "know" what it is. It could be anything because not all flows come from fully developed ducts.

steddy · February 20, 2020, 12:26

Quote:

It's not the same length scale.

I agree; and it makes sense.
Do you have any idea on how to estimate the turbulent length scale for my case,
which concerns the study of the air flow around a car, or even many cars?
Can I use a value similar to the one used for the flow around the motorbike?
If I do so, the yielded results seem convincing and reasonable.
But I am wondering if there is a more "scientifical" sound way to do it.

Also, do you know why the OpenFOAM developers have specifically chosen 3.058 as a value for the turbulent length scale? I can't seem to find the reason anywhere on the web.

JoaoRoque · September 11, 2020, 14:39

Hi everybody.
I'm studying the flow around a circular cylinder in the drag crisis region, using the kOmegaSST turbulence model. I'm struggling to find a plausible estimation for the turbulence lenght scale in the literature. What would be a good option?

Thanks.

Edgar Alejandro Martínez · September 27, 2021, 12:50

I made a tutorial on YT.

Here's the meshing part: https://www.youtube.com/watch?v=zWCPRhWHPqs

And here is the case setup: https://www.youtube.com/watch?v=3yw6nf-bN20

Go to the video's description to get the link to the files.

Mazze[ITA] · December 2, 2022, 10:48

Quote:

Originally Posted by steddy

Hi all,
I'm trying to investigate the flow of air around a car with the RAS k-omega SST.
The OpenFOAM guide: https://www.openfoam.com/documentati...omega-sst.html says that the following formula can be used to estimate omega, that is the turbulence specific dissipation rate:
$\omega = \frac{k^{0.5}}{C_\mu L}$
where L is the reference length scale,
and cmu is equal to 0.09
I wanted to ask: what exactly is L? In my case, would it be the length of the car?

I saw that OpenFOAM has a motorbike scenario and tutorial.

The motorbike has a length of 1.42 m (this value is lRef and can be found in the system/forceCoeffs dict.
The value of k is 0.24, and can be found in the 0/include/initialConditions file.
The value of omega is 1.78 (again, it is is located in the initialConditions file).

If we isolate the L in the previous formula, we get:
$L = \frac{k^{0.5}}{C_\mu \omega}$
If we substitute for k, omega and Cmu, we get 3.058 m, which is different than the valur of lRef (the length of the motorbike). Therefore, I'm not anymore convinced that L is the length of the vehicle.

Can anyone help me?
Regards,
Andrea

The c_mu should be c_mu^0.25?

farzadmech · April 6, 2023, 20:34

Dear Steddy
did you find any answer for

Code:

Do you have any idea on how to estimate the turbulent length scale for my case

I have the same problem. How should I define it?

Thanks,
Farzad

Quote:

Originally Posted by steddy

I agree; and it makes sense.
Do you have any idea on how to estimate the turbulent length scale for my case,
which concerns the study of the air flow around a car, or even many cars?
Can I use a value similar to the one used for the flow around the motorbike?
If I do so, the yielded results seem convincing and reasonable.
But I am wondering if there is a more "scientifical" sound way to do it.

Also, do you know why the OpenFOAM developers have specifically chosen 3.058 as a value for the turbulent length scale? I can't seem to find the reason anywhere on the web.

farzadmech · April 6, 2023, 20:39

Using the correct formula form here, I reversely solved motorBike problem and I got

Code:

Turbulent intensity = 0.02
turbulent length scale = 0.14 which is the 10% of Lref

Thanks,
Farzad

Quote:

Originally Posted by steddy

Hi all,
I'm trying to investigate the flow of air around a car with the RAS k-omega SST.
The OpenFOAM guide: https://www.openfoam.com/documentati...omega-sst.html says that the following formula can be used to estimate omega, that is the turbulence specific dissipation rate:
$\omega = \frac{k^{0.5}}{C_\mu L}$
where L is the reference length scale,
and cmu is equal to 0.09
I wanted to ask: what exactly is L? In my case, would it be the length of the car?

I saw that OpenFOAM has a motorbike scenario and tutorial.

The motorbike has a length of 1.42 m (this value is lRef and can be found in the system/forceCoeffs dict.
The value of k is 0.24, and can be found in the 0/include/initialConditions file.
The value of omega is 1.78 (again, it is is located in the initialConditions file).

If we isolate the L in the previous formula, we get:
$L = \frac{k^{0.5}}{C_\mu \omega}$
If we substitute for k, omega and Cmu, we get 3.058 m, which is different than the valur of lRef (the length of the motorbike). Therefore, I'm not anymore convinced that L is the length of the vehicle.

Can anyone help me?
Regards,
Andrea

manuelffonseca · December 6, 2025, 05:48

Quote:

Originally Posted by Edgar Alejandro Martínez

I made a tutorial on YT.

Here's the meshing part: https://www.youtube.com/watch?v=zWCPRhWHPqs

And here is the case setup: https://www.youtube.com/watch?v=3yw6nf-bN20

Go to the video's description to get the link to the files.

Hello Alejandro, I was checking, but those videos are not available on YouTube.

https://www.youtube.com/watch?v=zWCPRhWHPqs
https://www.youtube.com/watch?v=3yw6nf-bN20

Could you share it again

Thanks

February 19, 2020, 14:18	k-omega SST: what is the Reference length scale?	#1
steddy New Member Andrea Stedile Join Date: Feb 2020 Posts: 11 Rep Power: 7	Hi all, I'm trying to investigate the flow of air around a car with the RAS k-omega SST. The OpenFOAM guide: https://www.openfoam.com/documentati...omega-sst.html says that the following formula can be used to estimate omega, that is the turbulence specific dissipation rate: $\omega = \frac{k^{0.5}}{C_\mu L}$ where L is the reference length scale, and cmu is equal to 0.09 I wanted to ask: what exactly is L? In my case, would it be the length of the car? I saw that OpenFOAM has a motorbike scenario and tutorial. The motorbike has a length of 1.42 m (this value is lRef and can be found in the system/forceCoeffs dict. The value of k is 0.24, and can be found in the 0/include/initialConditions file. The value of omega is 1.78 (again, it is is located in the initialConditions file). If we isolate the L in the previous formula, we get: $L = \frac{k^{0.5}}{C_\mu \omega}$ If we substitute for k, omega and Cmu, we get 3.058 m, which is different than the valur of lRef (the length of the motorbike). Therefore, I'm not anymore convinced that L is the length of the vehicle. Can anyone help me? Regards, Andrea

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February 20, 2020, 10:27		#2
sapujapu New Member Join Date: Feb 2020 Posts: 10 Rep Power: 7	The exact reference length is not that important afaik. The important thing is that your nu/nu_t ratio (laminar viscosity to turbulent viscosity) is small enough. This paper by Spalart & Rumsey gives some recommendations in Section C for external aerodynamics: https://ntrs.nasa.gov/archive/nasa/c...0070035069.pdf

February 20, 2020, 11:55		#3
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,846 Rep Power: 68	It's not the same length scale. The length scale in forceCoeffs is related to the definition of your force coefficients like lift, and that one is a geometric length scale. The length scale in the formula for omega is a turbulent length scale for your boundary. Say if your oncoming flow comes from a fully developed flow in a duct with diameter D is a small fraction of D (usually estimated to be about L~0.07D). It's a boundary condition, you need to "know" what it is. It could be anything because not all flows come from fully developed ducts.

September 11, 2020, 14:39		#5
JoaoRoque New Member João Join Date: Aug 2020 Posts: 3 Rep Power: 7	Hi everybody. I'm studying the flow around a circular cylinder in the drag crisis region, using the kOmegaSST turbulence model. I'm struggling to find a plausible estimation for the turbulence lenght scale in the literature. What would be a good option? Thanks.

September 27, 2021, 12:50		#6
Edgar Alejandro Martínez New Member Edgar Alejandro Martínez Ojeda Join Date: Jul 2019 Posts: 20 Rep Power: 8	I made a tutorial on YT. Here's the meshing part: https://www.youtube.com/watch?v=zWCPRhWHPqs And here is the case setup: https://www.youtube.com/watch?v=3yw6nf-bN20 Go to the video's description to get the link to the files.