Gamma Theta model and underpredicted lift
 

Hi All,

I've been trying to simulate incomressible flow over a thick airfoil NACA0020 at transitional reynolds numbers using the gamma theta model.
Although the transition onset and pressure distribution over the top foil is in good agreement with experiments and xfoil, the pressure distribution on the bottom side past an 8 degree aoa is not correct. The airfoil undergoes early stall and a large portion of the underside of the foil is under suction which accounts for the loss of lift.

My yplus is below 1, boundaries are also quite far. I would very much appreciate any comments and suggestions to improve the results.
Nick

I do not understand your comment - Can you post some images of pressure distribution and velocities?

Also is your incoming turbulence levels correct? What about foil roughness?

Any luck solving this problem?

If it is still an issue can you post your Cl and Cd vs AoA for your results and data? Also, can you give a reference from where your data comes from?

Hi

Is there a chance I could have an email address. I'm using this simulation for my graduate degree so it may be best not to post results here. Thanks for your attention. You may wish to send a private message with your email if that is convenient.

cheers,
Nick

Hi Nick,

Sorry, I like working on these topics in a forum where everyone can later learn from the results and answers. Likewise, I depend on seeing other peoples questions and answers. I learn the most from seeing what doesn't work, fixes, and work arounds. I also hope that others will use this forum more. Especially the professionals at agencies like NASA, DLR, etc.

Hi Nick -

What is your Reynolds number?

We simulated the NACA 0012 with the gamma-theta model from Re = 48k to 250k and found that it almost consistently under-predicted lift due to the too-large separation region/bubble. Like you, we found good pressure curve and transition onset data. The problem was with the prediction of the reattachment points, which were too far downstream compared to published results. It seems that the transition onset correlations work well for external aerodynamics while the transition length and reattachment correlations need to be calibrated specifically for this regime.

We have a paper being released soon online in the International Journal for Numerical Methods in Fluids (authors: Counsil and Boulama) on this topic; our work will also be in the proceedings of the 20th AIAA CFD Conference from June 2011 (same authors).

Hi Josh

I'm looking forward to the paper. The issue I'm struggling with is that the foil goes into stall a few degrees too early and at lower lift coefficient values than experiments. It's a thick airfoil so I assume it would be hard to simulate as well. Convergence of steady state often doesn't happen and I switch to the unsteady model when lift and drag begin to oscillate.

In our case, steady state was only achievable for higher Reynolds numbers and turbulence intensities. Stall occurs too early in our simulations, as well, and we also base our convergence on lift and drag oscillations.

Thanks for the feedback. I wonder whether other solvers perform better with the model than cfx.

Let's step back. How does your comparison look at 4 degrees AoA?

It could be that the top and bottom walls (which I assume are solid) of the WT are affecting the results. But, since I don't have knowledge about the data, not sure. It will depend on the 0.5*height/chord ratio.

I would suggest that you do a run with the top and bottom WT walls. Neglect the B.L. by setting the walls to slip.

When I ran SA on the S809 my slope with the walls was higher than without. The half height vs. chord ratio TU Delft data is about 1.5. So, it is not surprising, in this case, that the walls affect the results.

Hi Martin,

I ran the simulation using slip walls and convergence was problematic (residuals oscillated a lot) plus the pressure distribution on the foil was wrong.
At 4 deg AOA using no-slip walls the pressure distribution reasonably agrees with experiments hence good lift coefficient. However in the wall shear curve on foil in the region where separation bubble occurs and wall shear is supposed to be nearly constant, the wall shear value starts off nearly straight but dips before reattachment. I've seen this dip at other attack angles as well. I haven't seen this dip in xfoil and don't have experimental results for wall shear.

Cheers,
Nick

Not sure why your case with slip wind tunnel walls would have trouble converging when your case with no slip does converge. But, I don't have experience with the gamma theta turbulence model.

BTW, does this mean your prediction improved by including the wind tunnel walls in your model?

If you would like to pin down the skin friction, you may need to decrease your y+ spacing. The boundary layer next to the airfoil on the inside of the separation bubble can get thin. Also, the boundary layer towards a separation and reattachment point can get thinish too. So try cutting your y+ by 1/2. If you see a difference, try cutting by another 1/2. Keep doing this until the changes become unimportant to your solution.

I would also suggest that you run SA and SST to baseline your results. In general, for thin airfoils, SA and SST give similar results. However, for thick airfoils that may not be true for all cases. In regards to lift curve slopes, my experience is very limited with this, but it may be that SA gives a result with characteristics that are more laminar than turbulent, at least when compared to SST. This would mean that the boundary layer thickness as predicted by SA is more representative of laminar boundary layer thickness than SST. Again, I've done minimal work with this and the results are of course Reynolds number dependent. So your results could be totally different.

Thanks for the suggestions. I've done yplus sensitivity study but it hasn't changed the cf distribution. I'll do it again just to double check. If gamma theta is available as an option for SA in cfx or fluent I'll do that as well and get back to you.

The intent was to run fully turbulent SA and SST, i.e. without the gamma theta transition model. This is to insure that the gamma theta transition model is working correctly and providing value added for your case, i.e. it is not giving oddball results. I assume it is working, but one never knows.

Do you have a reference for the data? Or is it something that was specifically generated for your work?

I know it's working reasonably well up to 7 degrees AOA based on my own wind tunnel experiments, literature and also xfoil but past this angle it goes into stall which it's not supposed to-stall should happen about a few degrees higher and at larger lift coefficients. The main source of lift loss from my observations is the fact that pressure on the suction side is supposed to be lower according to experiments towards the leading edge at higher AOAs which is not the case in the simulation. I've changed the domain size..mesh density etc already to no avail

What Reynolds number are you at?

In my opinion, there is two areas to focus on. Modeling the experiment correctly and the turbulence model.

In the experiment, what was the aspect ratio of the wing, i.e. span/chord and how was the lift calculated? Were the pressures integrated along a row of pressure taps, or was there a balance on the wing?

Were any of the WT results tripped?

When you get a chance, run the fully turbulent SA and SST and see where that stalls.

As far as my CFD calculations went, here is the story with the S809, another fat airfoil. If one runs the S809 in 2D mode with the SA model, the CFD stall is high. However, if one includes the side walls of the wind tunnel, the stall comes down and one gets the two humps as seen in the cl data. This is because a vortex is generated at the junction of the wing and wall. The vortex is also a function of the wind tunnel side wall boundary layer thickness. The simulation is tough and uncertain. And, I'm not sure how much of this experience applies to a 0020.

BTW, do you see two humps in your experimental cl data as with the S809? http://www.osti.gov/bridge/purl.cove...9/webviewable/

Reynolds is 122000. Span/chord = 8 no trips were used...no two bumps is observed in lift diagram ...force measurements and pressure measurements were both done and in good agreement in terms of lift coefficient curve

Here is the article I referenced earlier:

Counsil, J. and Goni Boulama, K. (2011), Validating the URANS shear stress transport γ −Reθ model for low-Reynolds-number external aerodynamics. International Journal for Numerical Methods in Fluids. doi: 10.1002/fld.2651

http://onlinelibrary.wiley.com/doi/1....2651/abstract

Sounds like the experiment is ok. So that leaves the turbulence model. Sorry, I don't have a specific idea about how to make the solutions better. I gather, somehow, more eddy viscosity has to be added to stabilize/damp the flow so that the airfoil stalls later. I'm also not sure if this transition model was meant for transitioning flow on top of a bubble thus helping to reattach the flow.

Sorry, I'm confused. The abstract states

"The current model was shown to reproduce the complex flow phenomena, including the laminar separation bubble dynamics and aerodynamic performance, with a very good degree of accuracy."

and

"In view of the results obtained, the proposed model is deemed appropriate for modelling low-Reynolds-number external aerodynamics and provides a framework for future studies for the better understanding of this complex flow regime."

Yet above you stated

"We simulated the NACA 0012 with the gamma-theta model from Re = 48k to 250k and found that it almost consistently under-predicted lift due to the too-large separation region/bubble. Like you, we found good pressure curve and transition onset data. The problem was with the prediction of the reattachment points, which were too far downstream compared to published results. It seems that the transition onset correlations work well for external aerodynamics while the transition length and reattachment correlations need to be calibrated specifically for this regime."

Does the statement immediately above refer to the results presented in the paper? The statements don't seem to match. The first two give the sense of all around thumbs up and the last gives a sense of "so-so.".

I'm not sure of the various turbulence models that CFX has, but is there one which provides a dial so that you can tailor it to your case? For example, and this is complete speculation on my part, one of the SA models out in literature has a trip term. One might be able to use such a term to trip the flow at a certain location. Of course that location would be a function of Reynolds number.

Edit: Just wanted to add that the trip term, as far as I understand, does not trip the flow in the sense of rapidly ramping up the eddy viscosity in the region the trip is set.

Sorry. I did word that rather confusingly. Our under-prediction of lift occurred for the SD7003, not the NACA 0012. The NACA 0012 results in the above paper were quite good compared to certain published experimental and DNS data. I specify "certain" because there are large discrepancies between high-fidelity experimental and DNS studies despite having nominally identical setups. As evidenced by this topic, proper prediction of aerodynamic performance criteria, among other parameters, is difficult to achieve in this regime. Experimentally, wind tunnel effects, such as noise and vibration, can cause premature transition, delayed separation, etc. Experimental measurement tools like Pitot tubes and hot wires also cause problems. Numerically, nominally identical DNS setups can produce different results due to discretization errors, averaging techniques, etc. etc. etc. Therefore, slight underestimation of lift by a URANS model for this regime can still be considered as good agreement.

Thanks for the clarification. Do you have a hypothesis of why the SD7003 results did not fair as well as the 0012?

Do you think it is atributed to the wind tunnel test, airfoil geometry, or something else? When I say geometry, I mean that the geometry causes the separation bubble and turbulence to behave differently than the 0012. I'm curious if this is related to the SD7003 being a thinner airfoil. I guess that at some point there may be two separation bubbles, one up front and one in back.

I am no expert on airfoil modelling but for a thick-ish foil at Re=122000 that sounds like a case when the SST model with turbulence transition model is ideally suited.

We haven't looked too in-depth as to this reasoning, but certain results have led us to propose certain hypotheses. The pressure and friction curve magnitudes of the SD7003 match published DNS and LES data very well, though the reattachment points are too far downstream. Similarly, the velocity profiles are excellently matched in terms of shape, though the separated flow and reversal regions are too thick downstream of transition. These trends seem to indicate proper resolution of the separation and transition onset locations but mediocre transitional flow and reattachment regions. Increasing the turbulence intensity to near-bypass levels (~ 1%) drastically improves the results compared to data with nominally acquiescent conditions. It seems as though the empirical correlations defining transition length and reattachment, e.g., the Re_theta correlation (which is a function of turbulence intensity), require calibration for this regime. The NACA 0012 results, as well, also showed delayed reattachment for most cases.

The exact reason for the SD7003 results being poorer is unknown. However, we have some ideas. For one, the SD7003 seems to have a much more physically complex flow regime at the Reynolds numbers and angles of attack of interest. Even high-fidelity experiments with nominally identical setups show varying physical phenomena, e.g., one study indicated vortex pairing while another witnessed no vortex interactions. The LSB on the SD7003 is also long, thin, and highly unsteady, making it quite difficult to capture either experimentally or numerically.

Other errors abound. We used the same grid resolution, timestepping scheme, etc. on the SD7003 that we used on the NACA 0012, so it's possible that the modelling was insufficient.

Agreed! This may allude to the mystery behind our superior NACA 0012 results over our SD7003 results.

Thanks for the paper and the comments. It must have been a lot of hard work. So from what I understand your NACA 0012 stalled past 8, is that why you didn't include the results from that point onwards?

It stalled at about 8 degrees for the Re = 50k case with Tu = 0.25%. What should happen for this case, according to published DNS and LES results of Jones et al. and Almutairi et al., is continual bursting (complete separation) and re-formation (reattachment) of the laminar separation bubble. In other words, it's not fully stalled, but it's close. They also witnessed additional trailing edge separation.

For our case, we saw a laminar separation bubble form at the beginning of the simulation, which produced the proper lift and drag results. A few thousand timesteps later, the reattachment point of the bubble slowly moved toward the trailing edge and eventually merged with the trailing edge separation region, forming completely separated flow. This is good - this is supposed to happen, according to the DNS. Next, the bubble should re-form and move upstream toward the leading edge, but it doesn't. The flow remained fully stalled in our simulation, producing too-low lift.

The DNS and LES authors also experienced the above problem (bursting without re-forming) between 8 and 10 degrees when their domain was too thin (~0.2c, I believe). When they widened the domain (~0.5c), the proper behaviour (continual bursting and re-forming) was captured. So it seems that the shortcoming at Re = 50k, AoA = 8 deg. is caused by 2D modelling.

Our simulations did not stall at 8 deg. for the higher Re cases (100k and 250k).

The choice of angles of attack was fairly arbitrary. We chose 4 degrees because almost every published study seemed to include a 4 deg. angle of attack study. We weren't looking to capture stall. We just wanted to see how the model performed for moderate, i.e., practical angles of attack.

Sounds very interesting and quite complicated. Kudos to you! How did the unstalled naca0012 past 8 (100k) fair in terms of lift coefficient at higher angles compared to experiments?

We only studied the 0, 4, and 8 degree angles. The agreement at 8 degrees, Re = 100k is excellent compared to the experiments at the same conditions (Fig. 21b in the paper).

For the record, we're currently reformatting the pictures to make them better in quality, so the figure quality will improve in the published paper. If you would like an updated copy, remind me in two weeks.

I see. Excellent. I'll contact you.