Best practice for modeling bi-directional endplates (up and down) for VLM stability derivatives?

[Esther Barros Gomes]

Hi everyone,

I'm working on a flying wing design for an AeroDesign competition, and I am currently using VSPAero (VLM solver) to extract lateral-directional stability derivatives, specifically Cn_beta and Cy_beta, through a Beta sweep.

I want to add wingtip endplates that extend both upwards and downwards to maximize directional stability. However, when trying to model this, I am running into a few aerodynamic and solver issues:

1. Mesh Intersections: If I try to model the endplate as a single continuous surface that crosses the wingtip, the solver struggles with the intersecting meshes, resulting in singular matrix errors or unrealistic spikes in the pressure distribution.

2. Wake Leakage: When using a Fixed Wake, the wake shedding from the main wing cuts directly through the vertical endplate surface. This destroys the pressure gradient and results in a Cn_beta that is near zero.

3. Reference Area Corruption: If the geometry isn't isolated properly, the solver adds the vertical plate to the reference span (bref) and area (Sref), artificially shrinking the stability coefficients.

To solve this, I am planning to adopt the following setup:

• Split the endplate into two separate child geometries attached to the main wing tip.

• Set the "Upper Endplate" to a 90-degree dihedral and the "Lower Endplate" to a -90-degree dihedral.

• Switch from Fixed Wake to Relaxed Wake (with around 5 iterations) so the wake naturally bypasses the vertical surfaces.

• Manually lock the Reference Area and Span to the main wing only.

My question is: Is splitting the endplate into two separate child components and using a Relaxed Wake the official "best practice" in OpenVSP to handle this kind of geometry in VLM? Are there any hidden limitations I should be aware of, or would switching to the Panel Method be strictly necessary for this specific setup?

Thanks in advance for your help and insights!

[Rob McDonald]

Instead of using dihedral, I would rotate the end plates by 90 degrees about X.

I would use thin surfaces for the wing and the endplate.

I would move the endplate slightly in from the wingtip -- and I would make the wingtip chord slightly smaller than the intersecting endplate chord.  Something like this:

Then, I would turn on the option 'Cull Orphans'.  'Orphans' are those isolated panels at the tip of the wing.  They are topologically isolated from the rest of the wing.  This option was developed with truss braced wings in mind (which have multiple such sets of orphans), but it works well here too.  This results in the following:

Which runs well and gives a reasonable solution (run with a relaxed wake, but would likely work fine with a fixed wake too):

Rob

[Esther Barros Gomes]

Hi Rob,

Thank you for the advice. In our current design, the endplate is relatively small compared to the main wing chord. Because of this size proportion, adjusting the endplate chord to cover the wingtip as suggested causes some geometric constraints. Should we proceed using the previous setup where the endplate dimensions are kept as they are without modifying the chords, or is there a specific adjustment recommended for smaller endplates?

[Rob McDonald]

Ok, the Cull Orphans flag is not going to be useful for you.

I'm not sure -- I would try aligning the end plates perfectly with the end of the wing -- and then also in slightly moving them inboard.

When you have the NGonMesh in the Geom Browser, you can click on 'Other' and then 'Show Manifold Edges'.

That mode will color the edges of the mesh.  Any edge with exactly two faces will not be highlighted.  Edges with exactly one face will be highlighted blue.  Edges with more than two faces will be highlighted red.

Red is not bad.  Here is an example of a wing with a vertical in the middle of the wing...

Along the intersection, those edges have four faces (as expected).  All the boundaries, the edges have one face.  In the interior, everything has two.

You're looking for things that don't make sense -- perhaps a blue/red dashed line along an intersection.  You want to find an approach that looks good in this view.

You might be able to use the 'Cull Orphans' approach with two separate endplates (upper/lower).  Possibly offsetting them slightly...

You'll have to experiment with things.

Rob