# Aerospace Engineering: Predicting Airfoil Drag in 2D Potential Flow

#### lordvon

Hi,

My other post got deleted because it was flagged for spam, but it was just a link to a pdf. So I'm uploading the pdf instead.

I am working on a model to predict drag on airfoils in 2D potential flow (e.g. vortex panel methods). Currently, XFOIL uses a semi-empirical wake-momentum-thickness method to estimate drag, but I think there is a more elegant explanation for drag.

My physical model seems to show some promise but has one loose end: a parameter for which I am not sure how to estimate. Any critiques or other assistance would be greatly appreciated.

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#### berkeman

Mentor
My other post got deleted because it was flagged for spam, but it was just a link to a pdf. So I'm uploading the pdf instead.

I've moved your thread to the ME / Aero forum for better replies. Is this paper for a senior project? Or are you intending on publishing it in a journal? If so, which journals were you considering submitting it to?

#### lordvon

Thanks berkeman. If I can come up with a physical way to estimate the last parameter, and it compares well with experimental data, then I would like to submit it for publication (AIAA SciTech maybe). I am no longer a student or academic professional.

Gold Member
Your first step ought to be making sure you adequately describe all of your variables and what they mean. You haven't really defined $\gamma$ or $C_N$, for example.

Second, a potential flow is governed by Laplace's equation, which is elliptic. That means its region of influence in the flow domain is infinite, so there isn't some finite $\dot{m}$ that interacts with the flow. If you wanted to get that physically correct, you'd have to choose an $\dot{m}$ and $A_{\infty}$ that correspond to a streamtube whose boundaries are located far enough from the surface that the effect has died down to a value suitably close to zero.

Otherwise, as it stands now, your idea seems to me to be based initially on sound physics, but then makes an arbitrary cut through the flow, rendering your $A_{\infty}/A_w$ term as an empirical tuning parameter rather than something based on first principles.

The other issue I have here is that solving this really ought to warrant at least a discussion of co-author credit, and that is a difficult conversation when no one has any idea with whom they are working.

#### lordvon

1. I will add a glossary of terms.
2. Note that the equations deals with an averaged effect on the flow. Of course, velocity isn't V_infinity everywhere in the expression (m_dot * V_infinity).
3. I don't think it is merely an empirical tuning parameter; I believe it has physical meaning (important to remember that all of the developed equations are dealing with flow interactions in an averaged sense), and there might be a physical basis to estimate this parameter.
4. I would be happy to add anyone who helps with this paper as a co-author. I am not a professional academic in any way, so I think that would imply I don't have an incentive to hog all of the credit. I am assuming good faith from myself and others (e.g. by putting this draft out there I am not too afraid of someone stealing my ideas). If we ever get to the point of good results from a complete model, we can go into more personal introductions among prospective co-authors. Most importantly I want future aerodynamicists to be able to clearly answer the question "What is lift and drag?".

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#### lordvon

Your first step ought to be making sure you adequately describe all of your variables and what they mean. You haven't really defined $\gamma$ or $C_N$, for example.

Second, a potential flow is governed by Laplace's equation, which is elliptic. That means its region of influence in the flow domain is infinite, so there isn't some finite $\dot{m}$ that interacts with the flow. If you wanted to get that physically correct, you'd have to choose an $\dot{m}$ and $A_{\infty}$ that correspond to a streamtube whose boundaries are located far enough from the surface that the effect has died down to a value suitably close to zero.

Otherwise, as it stands now, your idea seems to me to be based initially on sound physics, but then makes an arbitrary cut through the flow, rendering your $A_{\infty}/A_w$ term as an empirical tuning parameter rather than something based on first principles.

The other issue I have here is that solving this really ought to warrant at least a discussion of co-author credit, and that is a difficult conversation when no one has any idea with whom they are working.
Regarding your first point, after looking at my draft again I actually did explain gamma and C_N inline. I guess you missed it.

Gold Member
I didn't miss it. You defined $\gamma$, for example, as the induced flow angle. You never made it clear what that physically means. Draw a diagram or something to make it more clear. Just calling it induced flow angle is not at all clear, because that sounds to me a lot like "deflection," which you have already defined as $\phi$.

#### lordvon

I didn't miss it. You defined $\gamma$, for example, as the induced flow angle. You never made it clear what that physically means. Draw a diagram or something to make it more clear. Just calling it induced flow angle is not at all clear, because that sounds to me a lot like "deflection," which you have already defined as $\phi$.
Are you familiar with lift-induced drag? https://en.wikipedia.org/wiki/Lift-induced_drag
I thought it would be straightforward for someone familiar with this to get it. Also, I explain what it is in context (it is half of the deflection angle far downstream, and what the airfoil sees), along with a visual diagram (Figure 1).
But it seems like you get it now, would you like to propose a more explicit explanation that makes sense for you?

Is C_N defined to your satisfaction?

#### lordvon

I've enhanced the description of gamma / induced flow angle (pdf attached). Please let me know what you think.

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