Non-linearity in VSPAERO

[Danilo Ciliberti]

Dear all,

I would like to ask if non-linearities in the lift curve are due to something recently added to VSPAERO or there is something I am missing. I navigated through this group and watched the last video from the 2020 workshop by Dr. Kinney, but I did not find an explanation. As far as I know, the VLM is a linear solver, hence by doubling the angle of attack the CL should double its value. Eventual non-linearities in the lift curve could derive from complex geometries or numerical issues, especially at high angles of attack, say higher than 15°, on multi-components wing-bodies.

The original file where I was working is about a two-panels, tapered wing, with distributed propulsion and flaps modelled as subsurfaces. However, I found that the non-linearities do happen earlier than 10° even for simple geometries. So, I'm uploading here the VSP3 files of a simple, straight, untapered, unswept wing made up of a single NACA 0010 airfoil at different aspect ratios.

The same geometries have been analyzed with AVL for comparison. As you can see from the attached pictures, the deviation becomes significant at AoA > 10°. The results for an infinite flat plate are added as reference. Both AVL and VSPAERO run at M=0.0. I understand that it makes little sense to use a VLM above 15-20 degrees, but I would like to know what is the reason of this non-linear deviation. The curvature of the mean line is excluded: the enclosed files are with a symmetric profile. There is no compressibility correction. Maybe the simple drag estimation with wetted area included in the solver (CD0 in the polar file) do provide this effect?

[Brandon Litherland]

I'll relay some information that was very recently passed on to me that helped.

In Abbott and Von Doenhoff, "Theory of Wing Sections", on page 4 Figure 2, you'll see plots of CL vs Alpha for various aspect ratio wings.  Note how the AR is basically altering the slope of the line.  

Now to the differences between the models.  The linear approximation of lift is true for "common" angles of attack, that is between about -5 and 15 or so as you've stated.  This is partly because linear theory CL actually trends approximately as sin(alpha) rather than linearly so the small angle approximation works.

In fact, if you plot the CL vs Alpha from 0 to 90 degrees, you'll end up with something that looks a lot like sin(2*alpha).  I show this for the benefit of the forum but assume that you've seen this as well.  The difference between these models may lie in the wake behavior.  This is where I get a bit fuzzy so if I make a misstatement, forgive me.  Linear theory assumes flat wakes and I *think* that AVL uses this assumption based on the user document.  VSPAERO allows the wakes to deform over several wake iterations.  Usually, the result is converged for simple geometries by about ITER 2 or 3.  More complex interactions such as multiple lifting surfaces or wing + propellers need more iterations to capture the wake deformation.  

I think the assumptions here are mostly correct but maybe Dave Kinney or Rob McDonald will call me out on something.  That's how we learn.

From the AVL User Documentation text file:

Vortex-Lattice Modeling Principles

==================================

Like any computational method, AVL has limitations on what it can do.

These must be kept in mind in any given application.

Configurations

--------------

A vortex-lattice model like AVL is best suited for aerodynamic configurations

which consist mainly of thin lifting surfaces at small angles of attack

and sideslip.  These surfaces and their trailing wakes are represented 

as single-layer vortex sheets, discretized into horseshoe vortex filaments, 

whose trailing legs are assumed to be parallel to the x-axis.  AVL provides 

the capability to also model slender bodies such as fuselages and nacelles 

via source+doublet filaments.  The resulting force and moment predictions 

are consistent with slender-body theory, but the experience with this model 

is relatively limited, and hence modeling of bodies should be done with 

caution.  If a fuselage is expected to have little influence on the 

aerodynamic loads, it's simplest to just leave it out of the AVL model.

However, the two wings should be connected by a fictitious wing portion

which spans the omitted fuselage.