function wing_flow_conformal clear all;close all; R=0.8; U=10; alpha_deg = 20; alpha = alpha_deg/180*pi; gamma = -4*pi*R*U*sin(alpha); rho = 10; x=-2:0.05:2; y=-2:0.05:2; [X,Y] = meshgrid(x,y); Xi= X +i*Y; xi0 = -0.12; eta0 = 0.52; Rdash = R*sqrt((1-xi0/R)^2+(eta0/R)^2); % W = U*(Xi + R^2./Xi*exp(-2*i*alpha)); W = U*(Xi + R^2./Xi*exp(-2*i*alpha)) -i*gamma/(2*pi)*log(Xi); % Wdash = (R'/R*W + xi0 + R^2./((Rdash/R)*W+xi0))*exp(-i*alpha); Phi = real(W); Psi = imag(W); subplot(1,2,1); axis equal; hold on; contour(X,Y,Phi,100,'LineColor','red'); contour(X,Y,Psi,100,'LineColor','blue'); ncount=1; drawWing(); %% subplot(1,2,2); axis equal; hold on; % return; %not working.......................... z = (R'/R.*Xi + xi0 + R^2./((Rdash/R).*Xi+xi0))*exp(-i*alpha); w = (U*(exp(-i*alpha)-R^2./(z.^2)*exp(i*alpha))-i*gamma./(2*pi*z))./... (Rdash/R-R^2*(Rdash/R).*((Rdash/R)*z+xi0).^2*exp(-2*i*alpha)); WX = real(w); WY = -imag(w); % w2 = w.*(abs(w)>8); % w2X = real(w); % w2Y = -imag(w); % vmax = max(w(w<max(w))); % [ii,ii] = sort(w); % vmax = w(ii([2,end-1])); % vmax = abs(max(w)); % p = 1-(abs(w)/max(abs(vmax)))^2; thresh = 0.00001 w2 = w.*(abs(w)>thresh*10e+3); X2 = X.*(abs(w)>thresh*10e+3); Y2 = Y.*(abs(w)>thresh*10e+3); p = 1-1/2*rho*abs(w2).^2; p = p./1e+7; p(isinf(p))=0; p = p.*(p>-0.0002); [cv,ch]=contourf(X2,Y2,p); % colorbar; colormap(winter); set(ch,'edgecolor','none'); ncount=1; drawWing(); Un=WX./sqrt(WX.^2+WY.^2); Vn=WY./sqrt(WX.^2+WY.^2); width=7; q = quiver(X(1:width:end),Y(1:width:end),Un(1:width:end),Vn(1:width:end)); function drawWing() for theta=linspace(0,2*pi,30) cylinder(ncount) = R*exp(i*theta); ncount=ncount+1; end hold on; wing = (R'/R*cylinder + xi0 + R^2./((Rdash/R)*cylinder+xi0))*exp(-i*alpha); h = plot(wing,'r'); set(h,'linewidth',2); end end
