# Two-equation turbulent models: low re airfoils

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 March 9, 2011, 16:11 #21 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 506 Rep Power: 9 Oh, I forgot to mention, the eddy viscosity at the trailing edge for Re 500,000 is about 160 times larger than the laminar viscosity.

 March 9, 2011, 17:26 #22 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 506 Rep Power: 9 Ooops, looking at my low viscous CX values for Re 500,000 I realize that I used the wrong grid, i.e. the y+=1 for Re 70,000. I was also wondering why my Re 500,000 lift result was so far from 2pi. So here are the results for the correct grid!! Geez. Full turbulent SA, unlimited (Re 500000): # Pressure # Forces: CX = -8.148592e-02 CY = 0.000000e+00 CZ = 7.283792e-01 # Moments: Cl = 0.000000e+00 Cm = -1.769565e-01 Cn = 0.000000e+00 # Viscous # Forces: CX = 1.091467e-02 CY = 0.000000e+00 CZ = 1.058283e-03 # Moments: Cl = 0.000000e+00 Cm = -4.110901e-05 Cn = 0.000000e+00 # Total # Forces: CX = -7.057125e-02 CY = 0.000000e+00 CZ = 7.294375e-01 # Moments: Cl = 0.000000e+00 Cm = -1.769976e-01 Cn = 0.000000e+00 CD = 1.88508e-2, CL=0.73260, CM (1/4 chord)=0.005362 (had to calculate these values by hand so there is the chance I messed up) The eddy viscosity above the trailing edge is about 75 times the sea level dynamic laminar viscosity. Well, that's better. OK, a recap, RANS SA results for NACA 0009 at alpha 7.0 degrees and sea level Re,Cl,Cd,Cm,Notes 50,000 0.67112 2.82293e-2 0.01192 (Limited to 10 times laminar viscosity) 50,000 0.69778 2.88194e-2 0.007793 500,000 0.73260 1.88508e-2 0.005362 The loss of lift and drag increase has been captured. How well, I'm not sure.

 March 9, 2011, 17:33 #23 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 506 Rep Power: 9 Oh, just remembered, two equation turbulence models may need less than y+=1, maybe y+=0.2. Not sure why but it has something to do with the algorithm and not physics.

March 9, 2011, 17:40
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Quote:
 Originally Posted by Martin Hegedus What were the fully turbulent Re 70000 coefficient results you obtained from Fluent and what are the WT results at that data point?
Thanks a lot Martin,

For SA I got cd around 2.7E-2 and Cl around .75, but for k-w standard Cd is about 7E-2, which is completely unacceptable.

I was directed to interesting articles that consider almost exactly the same case as here (for sd7003, which is from the same family as sd7037 I am dealing with here: wind tunnel measurement data for sd7003 are in the first article below): they saying that it is extremely difficult to get decent results for drag by using turbulence models without sophisticated transitional algorithm even for conventional airfoils, not to mention other types of airfoils I wanted to analyze afterwards.

1) Computational and experimental investigations
of low-Reynolds-number flows past an aerofoil, W. Yuan and M. Khalid, THE AERONAUTICAL JOURNAL, JANUARY 2007 http://www.raes.org.uk/pdfs/3109.pdf

Truffaldino

 March 9, 2011, 19:34 #25 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 506 Rep Power: 9 Cool. So it seems, when I look at your first paper, that our SA results are in the ball park of the experiment. Granted we don't have a bubble. Unfortunately, to even hope to get a bubble, the number of grid points will need to be upped drastically. And this does not lend itself to 3D. If your grid is fine enough, even a RANS solver may pick up on the bubble and reattachment. The key is that the recirculation of bubble itself creates eddy viscosity and that eddy viscosity then dampens out the flow downstream, thus causing reattachment. It is the same process which occurs in the wake of a blunt body or for airfoils at higher angles attack and higher Reynolds numbers, just on a finer scale. But you need a lot of grid points along the chord and a lot of CPU horse power. As for the k-w standard CD value being so large, not sure what the story is with that. One thing to check is how well the k-w standard viscous CX values compare to SA values. If they do not compare well, you probably need to up the number of points in the normal direction and have a y+ value significantly less than 1, i.e. maybe 0.2. Good Luck!

 March 10, 2011, 18:01 #26 Senior Member   Joshua Counsil Join Date: Jul 2009 Location: Halifax, Nova Scotia, Canada Posts: 366 Rep Power: 9 Does the latest version of Fluent not include the gamma-Re_theta (intermittency and momentum thickness Reynolds number) transition model?

March 11, 2011, 02:50
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 Originally Posted by Josh Does the latest version of Fluent not include the gamma-Re_theta (intermittency and momentum thickness Reynolds number) transition model?
I have access to fluent 6.3.26 and it has s-a, k-e, k-w, k-w sst, k-w sst transitional, and Reynolds Stress: I could not get decent results with k-w sst transitional for sd7037 at RE=70000.

I know that γ-Reθ t-transition model is purely based on local variables, will it give reliable results at Re=10^4-10^5? Is it suited for geometries other than conventional airfoils, say an airfoil with a step on a suction side?

As far as I understood from the the first reference given in the post 24 local-based predictions will not work for such reynolds numbers.

Last edited by truffaldino; March 11, 2011 at 03:49.

 March 11, 2011, 13:24 #28 New Member   Rambod Mojgani Join Date: Jun 2010 Posts: 9 Rep Power: 7 I have the same problem as yours, I want to know that your problem get solved? the gamma R theta seems to be good enough for the problem, but it is not in fluent 6.3.26 I use. Does anybody know that if Ansys 12 has this model or not? http://hiliftpw.larc.nasa.gov/Worksh...-2011-0864.pdf

 March 11, 2011, 18:34 #29 Senior Member   Joshua Counsil Join Date: Jul 2009 Location: Halifax, Nova Scotia, Canada Posts: 366 Rep Power: 9 Truffal - I have used the k-w (SST) γ-Reθ transition model with excellent results on the NACA 0012 airfoil at 5E4 <= Re <= 2.5E5. I have recently modeled the SD7003, as well, though I haven't checked the results. I have seen validation studies with the model on flat plates, turbine blades, and airfoils. The airfoils were pretty complex in shape. Here are some studies: Malan, P., Suluksna, K., and Juntasaro, K., Calibrating the γ‐Reθ Transition Model for Commercial CFD, AIAA paper 2009‐1142 (2009). Sørensen, N.N., Airfoil Computations using the γ‐Reθ Model, Technical University of Denmark, Report Number Risø‐R‐1693 (2009). http://130.226.56.153/rispubl/reports/ris‐r‐1693.pdf Alam, M., and Suzen, Y.B., Numerical Investigation of Transitional Flows over a NACA0012 Airfoil, SAE Paper 2008‐01‐2250, (2008). (Be on the lookout soon for a paper from Counsil and Boulama using the SST γ-Reθ model!) Your Yuan and Khalid paper did not discuss the SST γ-Reθ. In their paper, they used fully turbulent models coupled with the e^N method with moderate success. Rambod - The k-w SST transitional model is the SST γ-Reθ model. rmojgani likes this.

March 11, 2011, 19:22
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Quote:
 Originally Posted by Josh Truffal - I have used the k-w (SST) γ-Reθ transition model with excellent results on the NACA 0012 airfoil at 5E4 <= Re <= 2.5E5.
Thanks for Info: Did you do steady or unstedy simulations, if unsteady/transient what was the timestep? What was the resolution of grid (in direction of normal and along airfoil surface) and boundary conditions for turbulence parameters. Did it model the bubble size and location of transition correctly?

I tried k-omega transitional steady and then unsteady and I have strongly oscillating residuals and messy flow in both cases. I understand that it is due to instabilityof the bubble. What is the way to get accurate results?

Will be grateful for useful info

March 11, 2011, 19:47
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Martin Hegedus
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Quote:
 Originally Posted by Josh Truffal - I have used the k-w (SST) γ-Reθ transition model with excellent results on the NACA 0012 airfoil at 5E4 <= Re <= 2.5E5. I have recently modeled the SD7003, as well, though I haven't checked the results. .... Rambod -
What angles of attack did you run and did you get a bubble at the lower Re number?

March 13, 2011, 04:05
#32
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Quote:
 Originally Posted by Josh Malan, P., Suluksna, K., and Juntasaro, K., Calibrating the γ‐Reθ Transition Model for Commercial CFD, AIAA paper 2009‐1142 (2009). Sørensen, N.N., Airfoil Computations using the γ‐Reθ Model, Technical University of Denmark, Report Number Risø‐R‐1693 (2009). http://130.226.56.153/rispubl/reports/ris‐r‐1693.pdf Alam, M., and Suzen, Y.B., Numerical Investigation of Transitional Flows over a NACA0012 Airfoil, SAE Paper 2008‐01‐2250, (2008). (Be on the lookout soon for a paper from Counsil and Boulama using the SST γ-Reθ model!)
Joshua,

The published papers you gave (I do not have access to one by Alam) seem to discuss flows at re of several millions (perhaps your coming paper will present results on smaller re).

Do you know other references that discuss gamma-re-theta at re=10^4-10^5? Will be grateful for informattion

Truffaldino

March 13, 2011, 16:17
#33
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Rambod Mojgani
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Quote:
 Originally Posted by Josh Truffal - Rambod - The k-w SST transitional model is the SST γ-Reθ model.

I have encountered several names similar to the named model, do U know (preferably by introducing reference ) which one is most suited for external flows of Rey=10e5 to 10e6 , and what y+ should be reached for answer:
Fluent in Ansys 12 :
k-Omega (2 eqn) => Standard/SST (low-Re Corrections)
transition k-kl-omega (3 eqn)
Transition SST (4 eqn)

in Fluent 6.3.26
k-Omega (2 eqn) => Standard/SST (Transitional Flow)

 March 13, 2011, 19:42 #34 Senior Member   Joshua Counsil Join Date: Jul 2009 Location: Halifax, Nova Scotia, Canada Posts: 366 Rep Power: 9 Truffal - It was unsteady, but I'm afraid I can't give you the grid, timestep, parameter, etc. details because we're publishing the paper! The residuals do oscillate rather strongly, but should be oscillating at an appropriately low residual order. Monitoring another parameter of interest, like lift, is a good idea. And yes, our paper is the only one we know of using the model at lower Re for airfoils. Martin - We ran from approximately 0 to 8 degrees. A bubble was seen at the nonzero angles of attack. Laminar separation without reattachment was seen at zero degrees. Rambod - Not familiar with Fluent. Only CFX. SST Gamma-Theta model is the one I used.

March 14, 2011, 08:58
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Quote:
 Originally Posted by rmojgani I have encountered several names similar to the named model, Fluent in Ansys 12 : k-Omega (2 eqn) => Standard/SST (low-Re Corrections) transition k-kl-omega (3 eqn) Transition SST (4 eqn) in Fluent 6.3.26 k-Omega (2 eqn) => Standard/SST (Transitional Flow)
There is quite a confusion with the names of models in Ansys/Fluent.

I found another reference that has comparison different models with gamma re theta and sst-for transitional flows among them (see figure 4 there) http://stc.fs.cvut.cz/pdf/DurisMiroslav-313777.pdf

gamma-re-theta which is a 4eqn model, performs better, but unfortunately it is not in fluent 6.3. Although there is a sst transitional model in Fluent 6.3, it is basically 2eqn sst model with one coefficient algebraically depending on flow variables and is of a little use in our case.

Last edited by truffaldino; March 14, 2011 at 13:56.

 March 14, 2011, 14:06 #36 Senior Member   Joshua Counsil Join Date: Jul 2009 Location: Halifax, Nova Scotia, Canada Posts: 366 Rep Power: 9 In the link Truffal provided, they compare the classic (standard) SST model with the SST transition model (i.e., gamma-Re_theta). The SST transition model is the same thing as the gamma-Re_theta model. It has 4 equations - the 2 for the classic SST (k and w), plus the intermittency factor (gamma) and momentum thickness Reynolds number (Re_theta).

March 14, 2011, 15:04
#37
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Martin Hegedus
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What is one looking for when choosing a good turbulence model for low Reynolds number flow?

For example, I've attached a SA (fully turbulent) run for Mach 0.10, alpha=7, and Re=5000 over a NACA0009 airfoil. My off wall spacing is 4.0E-6 (my airfoil chord is 1.0). The spacing is small and is based on having a y+=1 at 1/4 chord for a Re number of 5.0e6. The result is steady and has been converged to machine zero.

If I was looking to improve this, what would give me the most bang for the buck?

Screen shots
1) Cp and grid
2) U velocity
3) U velocity limited to negative values. Shows reversed flow, thus a bubble exists.
4) Eddy viscosity as a ratio to laminar viscosity
5) Eddy viscosity limited to 0.01. The blue areas shows the regions which are basically unaffected by eddy viscosity.
Attached Images
 NACA0009.jpg (98.7 KB, 55 views) NACA0009_A.jpg (45.4 KB, 52 views) NACA0009_B.jpg (17.5 KB, 47 views) NACA0009_C.jpg (17.1 KB, 53 views) NACA0009_D.jpg (20.2 KB, 44 views)

March 14, 2011, 16:02
#38
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Joshua Counsil
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Quote:
 Originally Posted by Martin Hegedus What is one looking for when choosing a good turbulence model for low Reynolds number flow?
Well, truthfully, a turbulence model is not ideal for low-Reynolds-number flow. The physics is very complex, so modeling the physics is tough. Namely, RANS methods can predict neither the Tollmien-Schlichting waves nor the Kelvin-Helmholtz instabilities associated with separation-induced transition.

Certain turbulence models can predict some aspects of the flow. The SST model can predict some flows under adverse pressure gradients with possible small laminar separation bubbles, though most fully turbulent models are too dissipative to sustain the LSB. The SA model has shown some success as you have noted below.

The SST gamma-Re_theta model has built-in correlations for better transition prediction, namely equations based on the intermittency (the fraction of the likelihood of turbulence, 0 - laminar, 1 - fully turbulent) and momentum thickness Reynolds number. This model also has a built-in correlation for separation-induced transition, which is highly useful and unique. The 2 extra transport equations will cause the solution to take longer to converge. Further, the solution must be unsteady. I've had success using the models for Reynolds numbers as low as 50000, but Re = 5000 may require something more physics-based, like the e^N, LES, or DNS methods.

March 14, 2011, 16:37
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 Originally Posted by Josh In the link Truffal provided, they compare the classic (standard) SST model with the SST transition model (i.e., gamma-Re_theta). The SST transition model is the same thing as the gamma-Re_theta model.
I am still confused: At figure 4 of that reference they list k-w sst, k-w sst trans., gamma-re-theta. So it sems that they distinguish between k-w sst trans and gamma-re-theta. At that figure k-w SST is close to k-w SST trans, which is drastically different from gamma-re-theta. It seems what they call k-w sst trans. is not SST transitional, but SST with k-omega options "Transitional Flows" from Fluent 6.3.

March 14, 2011, 17:05
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Quote:
 Originally Posted by Martin Hegedus For example, I've attached a SA (fully turbulent) run for Mach 0.10, alpha=7, and Re=5000 over a NACA0009 airfoil.
Martin,

Have you tried to run laminar? Is it really turbulent at RE=5000 and alpha=7? At such a low speed the transition can be delayed up to the trailing edge.

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