2D Potential Flow Around a Cylinder

Consider the 2-D potential flow around a circular cylinder as described by the velocity components.

𝑣𝑟 = 𝑈∞ (1 −𝑅2/𝑟2 ) cos⁡(𝜃)

𝑣𝜃 = −𝑈∞ (1 +𝑅2/𝑟2 ) sin⁡(𝜃)

 Make a contour plot of the static pressure field, p(r,𝜃).

Solution:

MATLAB Code:

%% This code solves the static pressure field around a cylinder

% Author: Arif Hossain

clear all

close all

Radius = input('Radius of the cylinder : ');

theta = (0:1:360)*pi/180;

r = Radius:0.1:10*Radius;

for i = 1:length(r)

p(i,:) = 2*(Radius.^2/r(i).^2).*cos(2.*theta)-(Radius.^4/r(i).^4);

end

[TH,R] = meshgrid(theta,r);

[X,Y] = pol2cart(TH,R);

contourf(X,Y,p,30);

colorbar

axis image

xlim([-3*Radius 3*Radius])

ylim([-3*Radius 3*Radius])

xlabel('x/R','fontsize',14)

ylabel('y/R','fontsize',14)

set(gca,'fontsize',14)

title(sprintf('Static pressure field (R = %.1f)',Radius))