Twist and Lift Distribution of an A320

[fabian peter]

Hi,

first: a very big THANK YOU to all people working on openVSP and VSPAERO and making it available. It is a great tool and I very much enjoy working with it. This thread is not meant as criticism but an honest neutral question from my side. I am trying to get a feeling of the suitability of openVSP's VLM and panel method for determining the lift distribution for a given transonic airliner wing geometry. For this I set up a simplified A320 Geometry:

• Main component geometries (i.e. wing plan form, fuselage, empennage, nacelles and belly fairing) from the Aircraft Characteristics document
  (https://www.airbus.com/aircraft/support-services/airport-operations-and-technical-data/aircraft-characteristics.html)
• Twist and thickness distribution from Obert 2009 "Aerodynamic Design of Transport Aircraft"
  which I simplified to (twist;thickness2chord_ratio)
  root: 3.5°; 14%
  kink: 0.5°; 12%
  tip: -0.5°; 12%
• I adjusted the tessellation to yield roughly equal elements and took airfoils (i.e. NASA SC2 0614 and 0712) from the NASA super critical family (cf. Harris 1990) and closed the trailing edge in order to avoid problems with the panel method.

The result looks like this and the openVSP file is attached (A320.zip). 

I would say that this is a reasonable realistic wing geometry. For all further calculations (VSPAERO in openVSP 3.23.0) I only used the wing and the fuselage.

I want to judge the lift distribution on its shape (goal: elliptical) and the oswald factor. For the oswald factor I would expect a result above 0.9 (cf.  Sun 2019 https://www.sesarju.eu/sites/default/files/documents/sid/2018/papers/SIDs_2018_paper_75.pdf).

Now I ran the VLM, with only the wing and fuselage and with the Karman-Thisen Mach correction at Re 1e7 and Ma 0.78. The wake and pressure distribution look like this:

The lift distribution plot looks like this:

The lift distribution is far from elliptic.
oswald factor (capital E) is (for AoA 0°,3°,6°): 0.81,0.86, 0.86
LoD (only FYI) not very good with: 12, 12, 11

For the panel method (with the Karman-Thisen Mach correction at Re 1e7 and Ma 0.78) the pressure distribution looks like this:

No plot for lift distribution is available afaik. But in the .fem file there are data and one column is called "CL"... so here is the respective plot over y:

If this is the lift distribution, it is also far from elliptic.
oswald factor (capital E) is (for AoA 0°,3°,6°): 0.64,0.64, 0.64
LoD (only FYI) high with, but OK I thin for being inviscid: 130,40, 25

So that are my results. In my opinion I did not achieve a satisfactory result. This can have several cause:

• Geometry is unrealistic (even if I tried)
• I configured VSPAERO settings wrong
• VLM and panel method are not suited for this task
• ... your suggestion ... ;-)

Thank you for your support I am looking forward for your feedback!

Cheers

Fabian

[Rob McDonald]

You mention that you used NASA SC family airfoils, but did you have a reference that guided the specific choice of airfoils?  In particular, the design lift coefficient / camber of the foils?

You found a reference that documented the geometric twist of the wing.  That is a great start.

Wings also have 'aerodynamic twist' -- which is caused by the camber distribution.  Say lots of camber at the root, less at the tip or similar.  It is called twist because it has the same aerodynamic effects as geometric twist.

So, if your camber distribution choice was arbitrary -- it is just like if your twist distribution was arbitrary.

Even with the right twist and camber distribution, you also need to know what x/c the wing was twisted about.  The aerodynamically elementary answer is to twist about c/4.  However, some aircraft will twist about the aft spar -- that makes the structure more simple in particular at the hinge line for control surfaces, etc.  Other aircraft have reasons to twist about the leading edge.

In the end, it is very difficult to actually match an aircraft's lift distribution without very detailed geometry information.  All the required information is seldom available outside the manufacturer.

On the other hand, we also know that any wing can be twisted to match any desired load distribution at one CL.  So, if you want it elliptical, you can match that.  If you want triangular, you can match that, etc.

VSPAERO - including the thin surface formulation - should be appropriate for these kinds of studies.  

I have not read the Sun, Hoekstra, Ellerbroek paper in depth, but at a quick glance, their approach is to back the drag polar out of flight data.  I would not treat this as a great source of the oswald factor.  I certainly would not have reported it to three sig figs.

Rob

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[fabian peter]

Dear Rob,

thank you very much for the quick and helpful reply. Many of the aspects were not yet aware to me, but of course are very feasible.

Concerning the airfoil choice and camber distribution, my approach would be to first determine a local lift distribution with the chord distribution and an assumed elliptical lift distribution. With that I would have a local lift then for the specific wing sections. My guess would be that airfoils designed for a specific lift will probably have a similar camber. I did not apply this process in the example above, but for a previous study. There, I chose the mentioned NASA SC airfoils (NASA SC2 0614 and 0712) with this process for a A350 wing. In that study I determined the optimum lift coefficient with MSES. In that study I noticed that the L/D optimum determined by MSES was at a different Cl, as the design lift coefficient indicated by the nomenclature (06 and 07 respectively). This could however be due to different flow conditions, since the design flow conditions are not specifically mentioned for the NASA SC family. Also it should be mentioned that in A350 study I applied simple sweep theory to transform the flow conditions to 2D.

I see your point with the chord position of the twist execution. I guess there is no way to obtain such data for a real aircraft in the public domain, as you already said. Also I agree that the Oswald factor is not sensible to be given with such an accuracy from derived data. However I would expect a value above 0.9 for an A320. Do you think that is too high?

I would like to continue a bit with this experiment and therefore try to modify twist and twist position somewhat. As stated in your publication with Lane (“Lift Superposition and Aerodynamic Twist Optimization for Achieving Desired Lift Distributions”) every VLM neglects the thickness of the airfoil, which is of course correct. Would you suggest to use the panel method or the VLM (which I deduct from your comment regarding the “thin surface formulation”) in VSPEAERO?

Ultimately, my goal is not to achieve the A320’S twist distribution. There are simply not enough geometric data available. However, I would like to achieve a twist distribution that would produce a well performing lift distribution also if later analysed with higher order methods (e.g. RANS). Do you think that is an achievable goal?

 Thank you very much again for your very much appreciated help.

 Fabian

[Rob McDonald]

The VLM method in VSPAERO is not technically a VLM in the purest sense.  However, we refer to it as that is the kind of thin surface method people are most familiar with -- and it is based on Vortex loops.  So, it is extremely similar to a VLM, but to some people, VLM is a more specific term vs. Panel code which is a fairly general term...

VSPAERO actually uses the same method for both thick surfaces and thin surfaces with very few changes between them.  Dave Kinney and I are working to allow cases with both thick and thin surfaces.  So, I'm trending away from calling the thin surface mode a VLM...

I think your goal of obtaining a rational lift distribution before carrying a design forward for further analysis is achievable and appropriate.

Rob

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[Felix Finger]

A couple of general points regarding the aerodynamic design of airliners, that might be helpful to consider:

 

The wings are not designed to give minimum induced drag, but rather to give the aircraft the best possible performance. The design is a tradeoff between aero performance and wing mass. An elliptic lift distribution might save a few drag counts, but that doesn't help if the structure is heavier to deal with the loads. Every extra kilo needs to be carried the entire life of the aircraft. Naturally, this is a multidisciplinary optimization problem. Most of the time, the resulting lift distribution is much closer to a triangle, than to an ellipse.

 

If you look at the aircraft efficiency factor, you need to look at the entire aircraft. Assume that the wing lifts and the horizontal stab carries a download. This will be reflected in the far field downwash distribution. It's not coincidence that the horizontal tail extends right to the kink (extra area = extra lift at the wing root). The Horizontal evens out the far field downwash distribution.

 

In the transonic regime, shocks can significantly alter the loading of wings. Thin surface methods reach their limits in this regime. Especially, if the interaction with close coupled nacelles is part of the problem.

 

-Felix

[Neal Pfeiffer]

To the group in general,

One needs to understand that an "optimum" elliptical distribution will only be maximum at one CL / Mach combination for a transonic transport.  So what is the condition for optimization?  Is it at 35,000, 37,000, 39,000, or 41,000 feet?  Is it at the max start-of-cruise weight, mid-cruise weight, or something else?  Is it at a long-range-cruise speed (99% max-specific-range speed) that is much slower than max-cruise speed?  Since the airplane will fly all of these conditions, the aerodynamic solution should be acceptable for all of them

And then, as mentioned below, transport wings are designed to "optimize" structural efficiency as well.  There is always a tradeoff between aerodynamics and structure.  This is an active area of research with abundant AIAA papers on the topic.

It's one thing to use a specific case to study the use of a computational tool(s), but it is quite another to make a commercially-viable wing design.

Good Luck!

..... Neal

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