I have calculated CP(pressure coefficient) and CL(Lift coefficient) for a NACA2412 airfoil using the panel method but as it only allows us to calculate the same for inviscid flow, I could not get the CL vs alpha(angle of attack) curve to stall. How do I utilize my panel method velocities and datas to calculate CL for an actual viscous flow? My final aim is to get the CL vs alpha curve to stall. I have used MS Excel for the panel method calculation. Please find the attachment below to see and observe my calculations. You can also edit it on your own for adding the viscous calculation and attach it in the comments, that would be very helpful. Otherwise, please give me suggestions of how to do it.

Thank you!

( You can change the angle of attack value in P1129 cell and the calculations will show you the resulting inviscid lift coefficient in N1129 cell)

Note: I know I have to couple boundary layer equations(like Von-Karman, Thwaites equations) with panel method tangential velocities but I don't know how to do it. I have read so many books, all they are showing is the equations and formulas but there is not a single example of how to couple velocity datas with those equations to calculate viscous CL and CP. Please help.


  • 1
    $\begingroup$ The problem you are trying to solve can be tackled with a viscous-inviscid interaction technique. I believe you have asked a similar question on a sister site (aviation.stackexchange.com/a/89523/16331) and the same approach can be taken here too. However, I would suggest using an existing code such as xfoil or viiflow If you are interested in creating your own, Flight Vehicle Aerodynamics by Mark Drela has some excellent points. $\endgroup$
    – Alwin
    Commented Dec 2, 2021 at 1:52

1 Answer 1


Hi Mate please see the HFLR5 Site and software that includes also calls to xfoil. As we know what you are asking is not an easy task. The following example is for an airplane with NACA 2410 airfoil, pretty similar to your 2412 (10% instead of 12%) wing with a 0 degree elevator:

enter image description here

The bottom left graph shows L/Alpha graph, with the software you can get also Cl/Alpha as you are asking.

enter image description here

Please check the following link for free software download, documentation and tutorials, that will solve all your problems http://www.xflr5.tech/xflr5.htm Happy to support further if you may need it.

  • $\begingroup$ I don't want to use any software, I have Xfoil in my system, I can use it but I won't as I only want the results of it to compare my calculated data. I have already compared my non-viscous Cp vs x/c data and graphs that came pretty close to Xfoil. I want add viscosity into it for the flow separation, boundary layer and etc. And I want to calculate the viscous Cl vs alpha graph that will stall at higher aoa. I just don't know how to couple my non-viscous panel data with integral methods like Thwaites and Head to achieve the viscous Cl vs graph. $\endgroup$ Commented Dec 5, 2021 at 9:53
  • $\begingroup$ Please send me a connection request in my linkedin profile - linkedin.com/in/twisampati-roy-chowdhury or this is my number 8961002511(whatsapp number) in case you don't have a linkedin profile. $\endgroup$ Commented Dec 5, 2021 at 9:56

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