Assignment 2

Published

September 6, 2024

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 panel method in the language of your choice and compare the results with the thin airfoil theory. You are not allowed to use any inbuilt linear algebra solver to solve the system of equations. Implement your own solver (like Gauss-Seidel, Jacobi, etc.) to solve the system of equations.

Once you are certain that the your code works, then perform following steps for the airfoil assigned to you with 100 panels each on the upper and lower surfaces.

  1. Plot \(C_L\) vs \(\alpha\) for the airfoil assingned to you.

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

  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 moment coefficient about the quarter chord and compare it with the thin airfoil theory.

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

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

  9. Plot the value of the circulation \(\Gamma\) with respect to the number of panels. You should perform the calculation for 10 to 100 panels in the increment of 10 panels. Take \(\alpha = 5^\circ\).

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 E1098
SC24M003 E1210
SC24M004 E1950
SC24M005 E1620
SC24M006 E1350
SC24M008 E1400
SC24M009 E1980
SC24M010 E1560
SC24M011 E1740
SC24M012 E1810
SC24M013 E2070
SC24M015 E1360
SC24M016 E2150
SC24M017 E2190
SC24M018 E2200
SC24M019 E2320
SC24M020 E1200
SC24M055 E1510

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

Deadline

By 2:00PM on 08th November 2024 via email to devendra.ghate at iist.ac.in.