what way do i remove the flow

what function do i need to remove the flow .

Answer 1

[VBBV]

syms alpha beta theta
U = 8;                   % Uniform flow velocity
z0 = 0.6;                  % Center of the cylinder
R = 2;                   % Radius of the cylinder
alpha = pi/10;            % Angle of complex potential term
beta = pi/10;             % Angle for additional term
xmin = -5;
xmax = 5;
ymin = -5;
ymax = 5;
npoints = 100;
tol = +2e-2;                % geometric grid tolerance for flow visualization 
sx = 0.5;                 % displacement of circle center in  real axis. // velocity potential
sy = 0.1    ;                 % displacement of circle center in  imaginary axis.  // stream function
s = sx + i*sy;              % resultant displacement in the z plane 
[x, y] = meshgrid(linspace(xmin, xmax, npoints), linspace(ymin, ymax, npoints));


z = x + 1i*y;
% grid tolerance check for flow visualization 
for p = 1:length(x)
    for q = 1:length(y)
        if abs(z(p,q)-s) <=  R - tol
            z(p,q) = NaN;
        end
    end
end

f = U*((z-z0).*exp(-1i*alpha) + R^2.*exp(1i*alpha)./(z-z0)) + 1i*2*R*U*sin(alpha+beta)*log(z-z0);

figure;
contourf(x, y, imag(f), 40);
hold on;
theta = linspace(0, 2*pi, 100);
xc = real(z0) + R * cos(linspace(0, 2*pi, 100))-0.1;
yc = imag(z0) + R * sin(linspace(0, 2*pi, 100))+0.1;

plot(xc, yc, 'k', 'LineWidth', 2);
axis equal;

[VBBV]

Add goemetric grid tolerance as shwon above, for the streamlines flow around the cylinder defined by the Jukouskwi aerodynamic potential function.

According to Jukouskwi method, apply also the offset displacement for the cylinder along the x and y directions along the real and imaginary axis which represent the velocity potential & streamline functions.

[Matthew]

thank you very much!!