I am trying use contour function in MATLAB to plot the pressure coefficient in the entire flow domain and pin the pressure coefficient at the stagnation points? Any assistance

k = 1;

Uinf = 1;

rho = 1.2;

[x y] = meshgrid ([-1:0.1:1],[-1:0.1:1]);

u = -k/(2*pi)*(x.^2 + y.^2 - 2*y.^2)./(x.^2 + y.^2).^2;

v = k/(2*pi)*(-2*x.*y)./(x.^2 + y.^2).^2;

u(find(abs(u)>5))=0;

v(find(abs(v)>5))=0;

Umag = sqrt(u.^2 + v.^2)

cp = 1-(Umag.^2/Uinf^2);

DelP = 0.5*rho*(Uinf^2 - Umag.^2);

figure

contourf(x, y, DelP, 100, 'LineStyle', 'none')

colormap('gray')

hold on

quiver(x, y, u, v, 1)

streamline(x, y, u, v, ones(1, 21)*-1,[-0.01:0.001:0.01])

Answer 1

[Abhinaya Kennedy]

Hi Kamar,

To plot the pressure coefficient “cp” in the entire flow domain and pinpoint the stagnation points, you can follow the structure you've started with and make a few adjustments.

1. Plot the pressure coefficient “cp” instead of the pressure difference “DelP”.
2. Identify and mark the stagnation points where the velocity magnitude is close to zero.

k = 1;
Uinf = 1;
rho = 1.2;
[x, y] = meshgrid([-1:0.1:1], [-1:0.1:1]);

% Velocity components
u = -k/(2*pi)*(x.^2 + y.^2 - 2*y.^2)./(x.^2 + y.^2).^2;
v = k/(2*pi)*(-2*x.*y)./(x.^2 + y.^2).^2;

% Limiting the velocity to avoid singularities/overflow
u(abs(u) > 5) = 0;
v(abs(v) > 5) = 0;

Umag = sqrt(u.^2 + v.^2);

% Pressure coefficient
cp = 1 - (Umag.^2/Uinf^2);

% Plotting the pressure coefficient
figure;
contourf(x, y, cp, 100, 'LineStyle', 'none');
colorbar; % To show the scale of Cp
colormap('jet'); % Use a more colorful colormap for better visibility
hold on;

% Velocity field
quiver(x, y, u, v, 1);

% Streamlines
streamline(x, y, u, v, ones(1, 21)*-1, [-0.01:0.001:0.01]);

% Identifying and marking stagnation points
% A simple approach: Find where velocity components are both close to zero
stagnationPointsX = x(abs(u) < 0.01 & abs(v) < 0.01);
stagnationPointsY = y(abs(u) < 0.01 & abs(v) < 0.01);

% Marking stagnation points
plot(stagnationPointsX, stagnationPointsY, 'ro', 'MarkerFaceColor', 'b');

title('Pressure Coefficient (Cp) and Flow Field');
xlabel('X Coordinate');
ylabel('Y Coordinate');

You might need to adjust the stagnation point thresholds based on your specific requirements or the characteristics of the flow you're studying.

This link will provide you with more information on plotting specific points on your figure: https://www.mathworks.com/help/matlab/ref/plot.html#bvcbkvu-1

Hope this helps!