Errors trying to get the right plots
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I'm trying to get the plots shown in the enclosed image. Not sure how to fix the code. Attached the .txt data file. Any help will be appreciated. Thanks
close all
clear all
clc
% Inputs
A = 10;
m = 0.06;
L = 1;
nu = 2e-5; % Kinematic viscosity of the fluid
rho = 10; % Fluid density
x_start = 0.2;
x_end = 1;
dx = 0.001;
y_start = 0;
VelN = load('posm_profiles.txt');
y_high = round(max(VelN(:,1)),2);
y_end = y_high;
dy = 0.0001;
N = (x_end - x_start) / dx + 1
M = (y_end - y_start) / dy + 1
Re_x = A * L / nu;
% Initialize arrays
U = zeros(M, N);
Ue = zeros(1, N);
Theta = zeros(1, N);
cf = zeros(1, N);
y = linspace(y_start, y_end, M);
x = linspace(x_start, x_end, N);
%Inital Data Interpolation
Uef = @(XX)A*(XX/L).^m;
u = interp1(VelN(:,1),VelN(:,2),y)*Uef(x_start);
% Boundary conditions
U(1, :) = 0;
U(M, :) = 1;
% Solve for velocity profile using an explicit finite method
for i = 1:N
Ue(i) = (x(i) / L)^m * A;
theta = zeros(1, M);
for j = 2:M-1
F = [U(j-1, i), U(j, i), U(j+1, i)];
Uy = (F(3) - F(1)) / (2 * dy);
Uyy = (F(3) - 2 * F(2) + F(1)) / dy^2;
theta(j) = theta(j-1) + U(j, i) * dy / Ue(i);
cf(i) = 2 * nu * Uy / Ue(i)^2;
U(j, i+1) = U(j, i) + (U(j, i) * (F(3) - F(1)) - U(j, i)^2 * theta(j) + nu * Uyy) * dx / Ue(i)^2;
end
Theta(i) = trapz(y, 1 - U(:, i));
end
% Plot results
figure
plot(x, Theta,'o-')
title('Momentum thickness as a function of x')
xlabel('x')
ylabel('\theta')
figure
semilogy(x, cf,'o-')
title('Skin friction coefficient as a function of x')
xlabel('x')
ylabel('C_f')
% figure
% plot(y,u)
%
% title('Velocity Profile')
% xlabel('u [m/s]')
% ylabel('y [mm]')
%axis([-.001 .05 0 y_end])
figure
for i = 1:100:N
plot(U(:, i), y,'-')
hold on
end
title('Velocity profiles')
xlabel('u [m/s]')
ylabel('y [mm]')
%axis([-.001 .05 0 y_end])
legend('x = 0.2 m', 'x = 0.3 m', 'x = 0.4 m', 'x = 0.5 m', 'x = 0.6 m', 'x = 0.7 m', 'x = 0.8 m', 'x = 0.9 m', 'x = 1.0 m')
figure
for i = 1:100:N
U_over_Ue = U(:, i) / Ue(i);
y_over_theta = y / Theta(i);
plot(U_over_Ue, y_over_theta,'o-')
hold on
end
title('Velocity profiles normalized by momentum thickness')
xlabel('u/U_e')
ylabel('y/\theta')
axis([-0.001 .125 0 1.01])
legend('x = 0.2 m', 'x = 0.3 m', 'x = 0.4 m', 'x = 0.5 m', 'x = 0.6 m', 'x = 0.7 m', 'x = 0.8 m', 'x = 0.9 m', 'x = 1.0 m')
5 个评论
VBBV
2023-3-30
When vector U are all zeros, its less likely, that velocity profile can be evaluated correctly,
There needs to be a condition where the vector U needs to be updated with right values
theta(j) = theta(j-1) + U(j, i) * dy / Ue(i);
% ------------------->>> theta vector are all zeros, conisder u(j) or some
% input taken from VelN variable or combination of both u(j) & VelN
% Recheck whether this equation is correctly formulated
U(j, i+1) = U(j, i) + (U(j, i) * (F(3) - F(1)) - U(j, i)^2 * theta(j) + nu * Uyy) * dx / Ue(i)^2;
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