RE: Write a matlab code for conformal mapping of a circle to an airfoil.
Write a matlab code for conformal mapping of a circle to an airfoil.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | clear;clc% Step 1: Select the parameters that define the airfoil of interest.% (1) Select the a == angle of attack alphaa = -3; % in degreesa = a*pi/180; % Conversion to radians% (2) Select the parameter related to thichkness of the airfoil:e = .1;% (3) Select the shift of y-axis related to camber of the airfoil:f = .1;% (4) Select the trailing edge angle parameter:te = .06; % 0 < te < 1 (0 ==> cusped trailing edge)n = 2 - te; % Number related to trailing edge angle.tea = (n^2-1)/3; % This is a Karman-Trefftz extension.% Step 2: Compute the coordinates of points on circle in zp-plane:R = 1 + e;theta = 0:pi/200:2*pi;yp = R * sin(theta);xp = R * cos(theta);% Step 3: Transform coordinates of circle from zp-plane to z-plane:z = (xp - e) + 1i.*(yp + f);% Step 4: Transform circle from z-plane to airfoil in w-plane% (the w-plane is the "physical" plane of the airfoil):rot = exp(1i*a); % Application of angle of attack.w = rot .* (z + tea*1./z); % Joukowski transformation.% Step 5: Plot of circle in z-plane on top of airfoil in w-planeplot(xp,yp), hold onplot(real(w),imag(w),'r'),axis image, hold off |
