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Code for finding the lift coefficient of NACA

  1. May 4, 2012 #1
    I'm trying to code a method to find the lift coefficient of a NACA airfoil using panel method.
    (Coding mentioned below is MATLAB)
    There are two things I am stuck at:

    1) Finding the coordinates of NACA
    Usually we use the given general formula for camber. However as we all know, if we compute the equation, the "actual" calculated coordinates do not meet at the trailing edge.
    In other words, if the camber is 1, the trailing edge is located at slightly beyond 1 and the y-axis is smaller than 0.
    Would I have to re-scale the output airfoil so that the trailing edge is located at x=1? If so, should I assume that the trailing edge is less than 0 for more accurate analysis?
    So is there any method to accurately compute out the coordinates of NACA airfoil?

    2) Finding the Cl from Cp
    If I divide the airfoil as following:
    12 panels. Starting point from trailing edge, then through the lower edge, then the leading edge, then the upper edge and the 13th point being back at point 1.
    Then I obtained the values:
    I X Y THETA S GAMA V CP
    1.0000 0.9665 -0.0025 -3.0656 0.0672 0.0145 -0.8445 0.2868
    2.0000 0.8415 -0.0115 -3.0713 0.1835 -0.1411 -0.9612 0.0761
    3.0000 0.6250 -0.0257 -3.0800 0.2505 -0.1548 -1.0071 -0.0143
    4.0000 0.3750 -0.0378 -3.1065 0.2502 -0.1635 -1.0525 -0.1077
    5.0000 0.1585 -0.0380 3.0962 0.1832 -0.1720 -1.1071 -0.2256
    6.0000 0.0335 -0.0169 2.6735 0.0751 -0.1850 -0.8112 0.3420
    7.0000 0.0335 0.0231 0.6032 0.0813 -0.0042 0.8040 0.3536
    8.0000 0.1585 0.0613 0.1647 0.1855 0.1947 1.2136 -0.4729
    9.0000 0.3750 0.0744 -0.0170 0.2500 0.1989 1.2014 -0.4434
    10.0000 0.6250 0.0583 -0.1112 0.2516 0.1873 1.1309 -0.2789
    11.0000 0.8415 0.0290 -0.1670 0.1856 0.1722 1.0423 -0.0863
    12.0000 0.9665 0.0068 -0.1993 0.0683 0.1505 0.8674 0.2477
    13.0000 0 0 0 0 -0.0145 0 0

    how would I find the lift coefficient?
    For the Area, do I need the area of the airfoil or the area surrounded by panels?

    This is my MATLAB code (gives highly strange values...)
    The angle of attack was 0 degrees
    x,y,theta,s... are all vectors
    x= x coordinates of panels
    y= y coordinates of panels
    theta=angles in radians
    s= panel lengths
    v= dimensionless velocity at control panel
    cp= pressure coefficient at control panel
    ρ,μ,v were arbitrary values I gave.
    The lift comes out as 3.2365, Although from what I know that it should be around 0.2

    Code (Text):
    l=sum(cp.*s.*sin(theta)); %Lift
    ro=1.225;
    A=0;
    for jjj=1:m
        if jjj==1
            A=A+abs((x(jjj)-x(end))*(y(jjj)+y(end)));
        else
            A=A+abs((x(jjj)-x(jjj-1))*(y(jjj)+y(jjj-1)));
        end
    end
    A=A/2;
    c=1; %camber length
    mu=1.78*10^-5;
    Re=25000;
    v=Re*mu/(ro*c);
    cl=l/(0.5*ro*v^2*A)
    Where did go wrong? What should I have done? I'm completely lost...
     
  2. jcsd
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