Drawing Wired Closed Objects Using Rankine Oval

[x,y] = meshgrid(-10:0.01:10);

Here is my code and picture

m=5;
a=2;
U=1;
psi = U*y-m*atan2(2*a*y,x.^2+y.^2-a.^2);
contour(x,y,psi,100);
grid on;

I want to represent a closed object by wire in Rankin Oval code.

The picture you want is:

How should I change my code?

Answer 1

[suen]

% Parameters for the Rankine Oval
V_inf = 10; % Uniform flow velocity (m/s)
b = 1; % Distance of source and sink from origin (m)
Lambda = 20; % Source strength (m^2/s)
% Define grid for plotting
[x, y] = meshgrid(linspace(-5, 5, 200), linspace(-5, 5, 200));
% Uniform flow stream function
psi_uniform = V_inf * y;
% Stream function for the source at (-b, 0)
r_source = sqrt((x + b).^2 + y.^2); % Distance to the source
theta_source = atan2(y, x + b); % Angle to the source
psi_source = (Lambda / (2 * pi)) * theta_source;
% Stream function for the sink at (b, 0)
r_sink = sqrt((x - b).^2 + y.^2); % Distance to the sink
theta_sink = atan2(y, x - b); % Angle to the sink
psi_sink = -(Lambda / (2 * pi)) * theta_sink;
% Total stream function
psi_total = psi_uniform + psi_source + psi_sink;
% Adjust streamline density
num_contours = 30; % Change this value to adjust streamline intensity
min_psi = min(psi_total(:)); % Minimum value of the stream function
max_psi = max(psi_total(:)); % Maximum value of the stream function
contour_levels = linspace(min_psi, max_psi, num_contours); % Custom contour levels
% Plot the streamlines
figure;
contour(x, y, psi_total, contour_levels, 'LineColor', 'blue', 'LineWidth', 1); % Draw streamlines
hold on;
% Mark the source and sink locations
plot(-b, 0, 'ro', 'MarkerSize', 8, 'MarkerFaceColor', 'r'); % Source
plot(b, 0, 'ko', 'MarkerSize', 8, 'MarkerFaceColor', 'k'); % Sink
% Plot the Rankine Oval shape
% The oval corresponds to a specific streamline (e.g., psi = 0)
contour(x, y, psi_total, [0 0], 'r-', 'LineWidth', 2); % Extract the oval shape
% Add labels and title
title('Streamlines and Rankine Oval Shape');
xlabel('x (m)');
ylabel('y (m)');
axis equal;
grid on;
% Add a legend
legend('Streamlines', 'Source', 'Sink', 'Rankine Oval', 'Location', 'Best');
% Close hold state
hold off;

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% you can adjust the velocity and the strength yourself