Final project - Linear vortex panel method

[ncclementi]

Here is my final project : Linear vortex panel method.
Open to suggestions 👍

[labarba]

Nice job, overall. What I missed was a concluding section where you explain what you gained from this project. It would have been easy to run the vortex-source panel method and compare it with the experimental data you have, and say something about how the two methods compare in the number of panels needed to achieve a certain percentage error.

On the other hand, it would've been nice to have a brief discussion of the fact that a panel method is never expected to really match experimental data. It's potential theory, after all! And I would have expected significant deviation from potential theory at 10º angle of attack. What is the stall angle of this airfoil? I'm actually surprised that the difference is only 3.5%.

It would be satisfying to have some final commentary on the pros and cons of this version of the panel method, instead of simply leaving it as an exercise for the reader!

Typos, grammar, etc.

how to apply panel method—> methods
(Lesson10) —> missing space
Source panel method gives as a solution—> The source panel method

Then, to get a solution with circulation we add, to the constant source panel method, vortices to our panels and that allows us to may have lift force.—> Then, to get a solution with circulation, we add vortices to the constant-source panel method, allowing us to obtain an lift force. (…check commas, wording and ordering)

(Lesson11)—> missing space

However, in this case we need to use linear elements instead of use constant ones—> instead of using
(and why is this so? )

What does linear elements mean? —> This is awkward: "elements" is a plural noun, so there is a verb mis-match with "does." But this also sounds a bit awkward: "What do linear elements mean?" (although it's grammatically correct)
Perhaps it's better to just say: "What are linear elements?"
But then … why "elements"? (confuses with finite elements)
I would replace "elements" with "panels" everywhere.

singularities distribution —> singularity distributions
stregth—> strenth
linear varying varying —> repeated word, and it should be "linearly"
add this two solutions —> these
So now, using the powers of —> delete "So now," (superfluous)
Notice that this passage is a fragment, not a sentence. You need to think of the equations as part of your sentences, and check that you have subject/verb/object in each case. For example, this passage could read: "Using the powers of superposition, and remembering that the potential at a location (x,y) in this case is (2), we explicitly write the potential function as (3)."
Subject: we; verb: write; object: the potential function (all missing from your original).

If we discretize into N panels—> If we discretize the geometry into N panels (or "the airfoil" or whatever: missing object of the verb)
preious—> previous
Again, this passage is a fragment, not a complete sentence. Perhaps you need to remove the period after "lessons," make that a comma, and combine the fragment with the next sentence.

I think you need to add a line break after the text underneath equation (5), so that next equation is rendered correctly. Or maybe a missing underdash for gamma?

the length of the panel j —> the length of panel j
and βj is the angle —> delete "is" (parallel construction: with L the length and B the angle…)
we already fight with the math—> we already had to fight with the math

After equation (7), you have three sentences beginning with "then." Most of the time, this word is superfluous and can be deleted without any loss.

the strength singularities—> the singularity strengths?
to be ensure panels follow—> to ensure that panels follow
the equation we mention before—> mentioned

So for the flow-tangency—> do you really need "so"?
So, after we integrate,—> do you really need "so"?

we are gonna use—> Nooooooo!!!!!! Never again. Promise?

So following the same idea—> do you really need "so"?

define two integrate functions on to solve—>define two functions to compute
depending the case—> depending on the case
Now we can use this functions—> these

There is a floating period after the equation for the linear system.

So we will call—> do you really need "so"?

A2 correspond to γj and A3 correspond to γj+1 —> corresponds
coefficintes—> coefficients

This is the moment, where you should—> This is the moment when you should (no comma)
After writing couple—> After writing a couple

• For $ 0 —> huh?

So yes, our matrix will have—> do you really need "so yes"?
remember Kutta condition—> remember the Kutta condition
Then, the final matrix A will have this contributions—> The final matrix A will have these contributions

Now we have the solution of our system we can get—> Now that we have the solution of our system, we can get (note the comma

So, we have to compute the tangential velocity—> do you really need "so"?
we have to do some integral,—> integrals (plural?)
remember?. —> no period after question mark
So, after we integrate, —> do you really need "so"?
So, following the same idea —> do you really need "so"?

B1 the term related—> B1, the term related (comma)
and B2 the term related—> and B2, the term related (comma)
and B3=B2 the term related—> and B3=B2, the term related (comma)

(you left quotes for writing docstring on A_tangential(panels,B1,B2,B3), but didn't write it?)

From Lesson 10 we kow—> know
so let copy that —> let's
our solution match with the theoretical one—> Our … matches (capitalize "Our" and verb/noun agreement)
However the purpouse of use vortices—> However, the purpose of using vortices (comma, spelling, verb tense)

So let's calculate solve the problem—> do you really need "so"? Delete "calculate."
Gregory & O'Reilly pressure data.—> Add "See" in front, to make it a sentence.
As we mention before—> As we mentioned before, (verb tense and comma)
was obtain from reference 4 —> obtained
with this value as a reference—> Capitalize "With" and add comma after "reference"

less than 5% what is an acceptable value. —> less than 5%, which is an acceptable value. (Better: "which may be an acceptable value," because "acceptable" is not an absolute.)

it is not worthy to solve—> it is not worthwhile to solve
for all this panels—> with all these panels
get a similar performance—> get a similar result
for a smaller Np.—> with smaller Np.

[ncclementi]

Thank you for the feedback, I'm going to work on that!

About the 3.5% . I've just found the original paper, and they said that the experimental data is from "low-speed wind tunnel on a two-dimensional model of NACA 0012 aerofoil. "
(http://naca.central.cranfield.ac.uk/reports/arc/rm/3726.pdf) First sentence of introduction. Then, that's the reason why the match well. I will include this paper, and make comments on this fact.

[labarba]

I don't understand what you mean with "that's the reason they match well." There's no such thing as a two-dimensional model in experiments. There will always be 3D effects! Besides, you can't get rid of viscosity in real life …

[anushkrish]

Panel methods should actually work pretty well for calculating the lift of thin airfoils with attached flow. 3D effects are low for thin airfoils, and the pressure distribution around the airfoil is approximately the same even with a boundary layer (dp/dn is approximately zero, and boundary layers are very thin at high Re). And it looks like the NACA 0012 stalls at 16 deg AoA, so the good match is not surprising.