Assignment 2

Aim

We wish to learn various aspects of the implementation details of panel methods. We also wish to compare the results of the panel method with the thin airfoil theory.

Problem

Implement a vortex panel method in the language of your choice to calculate the lift over the airfoil assigned to you. Once you have a working code, we wish to compare the results of the code with the thin airfoil theory.

You are not allowed to use any inbuilt higher level funtions. That means things like numpy.linalg.solve are not allowed. You have to implement your own solver (like Gauss-Seidel, Jacobi, etc.) to solve the system of equations.

Perform following steps for the airfoil assigned to you with 100 panels each on the upper and lower surfaces.

  1. Plot the pressure distribution on the airfoil at \(\alpha = 0\) and \(\alpha = 5^\circ\).

  2. Draw a plot of \(C_l\) vs \(\alpha\) for the airfoil assingned to you.

  3. Calculate the lift curve slope and compare it with the thin airfoil theory.

  4. Calculate the zero lift angle of attack and compare it with the thin airfoil theory.

  5. Calculate the moment coefficient about the leading edge and compare it with the thin airfoil theory.

  6. Calculate the location of the center of pressure and compare it with the thin airfoil theory.

  7. Calculate the location of the aerodynamic center and compare it with the thin airfoil theory.

  8. Plot the value of the circulation \(\Gamma\) with respect to the number of panels. You should perform the calculation for 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 panels at an angle of attack of \(5^\circ\).

Deliverables

  1. A report in PDF format containing the following:
    1. Introduction
    2. Methodology
    3. Results
    4. Discussion
    5. Conclusion
    6. References
  2. The code in a zip file. If you are using a language that requires a compiler, then also provide a makefile to compile the code.

Airfoil allocation:

SC Number Airfoil
SC24M001 E1216
SC24M003 E1200
SC24M004 E1490
SC24M006 E1620
SC24M008 E1510
SC24M009 E1700
SC24M010 E1910
SC24M011 E1850
SC24M012 E1770
SC24M013 E1350
SC24M015 E1420
SC24M016 E1990
SC24M017 E1910
SC24M018 E2160
SC24M019 E1650
SC24M020 E2070
SC24M055 E2290

Airfoil coordinates can be found from any source (like here ).