Help with a contour graph

I've been trying (and failing to plot) this graph (Fig 1) for a week, but the closest I've gotten is Fig 2. It seems weirdly stretched out and I can't figure out what's wrong.

This is my code:

clear all
close all
clc
%Constant
rho = 4420; %kg/m^3
Cp = 550; %J/kg?K
T0 = 303.15; %K
A = 0.5; %[Absorbtivity]
k = 7.2; %W/m/K
alpha = 2.96*10^-6; %m^2/s
D = alpha;
P = 100; %W
v = 1; %m/s
u = v;
Tm = 1933; %K
d_laser = 0.01; %mm
r_laser = d_laser/2; %mm
a = r_laser;
p = D/(u*a);
%Define
x = linspace(-0.05,0.125,100);
y = linspace(-0.025,0.025,100);
z = linspace(0,0.05,100);
%Normalize
x_nor = x/a;
y_nor = y/a;
z_nor = z/sqrt((D*a/u))
[x_mesh,y_mesh,z_mesh] = ndgrid(x_nor,y_nor,z_nor);
% fun = @(t) exp((-z_mesh.^2/(4*t)-((y_mesh.^2.+(x_mesh-t).^2)./(4*p.*t+1)))./((4*p*t)+1)*sqrt(t));
fun = @(t) exp((-z_mesh.^2/(4*t))-((y_mesh.^2+(x_mesh-t).^2)/((4*p*t)+1)))/(((4*p*t)+1)*sqrt(t));
g = integral(fun,0,Inf,'ArrayValued',true);
squeeze(g(:,:,1))

figure(1)
iz = 1;
contourf(x_mesh(:,:,iz), y_mesh(:,:,iz),squeeze(g(:,:,iz)))
axis([-5 25 -5 5])
% xlim([5 25])
% ylim([-10 0])
colorbar

% figure(2)
% iy =1;
% contourf(x_mesh,z_mesh,transpose(squeeze(g(:,iy,:))))
% axis([-5 25 -10 0])
% colorbar

[KSSV]

Check the constants you have used...we don't know the reference, so it is tough to find out why there is a difference.

[Sarinya]

Oh, my bad. This is the paper I'm referencing: Promoppatum, P., Yao, SC. Analytical evaluation of defect generation for selective laser melting of metals. Int J Adv Manuf Technol 103, 1185–1198 (2019). https://doi.org/10.1007/s00170-019-03500-z

I'm just trying to recreate the graphs in the paper, starting with Figure 4, which is what I'm having trouble with.

[Sargondjani]

You can set the levels at which a contour should appear. Did you try setting that?

(Sorry, it was too much code for me to fnd it quickly)

[cdawg]

The paper says 0.1 mm and it looks like you have D = 0.01 mm. Not sure if this helps

Answer 1

[akshatsood]

Hi Sarinya,

I thoroughly investigated the code script attached and have concluded that the weirdly stretch visible in the graph is due to improper scaling of the dimensions. For instance, consider the following line from the code snippet.

p = D/(u*a) 

D has units m^2/s, u has units m/s but a has units mm. So, for the expression to be evaluated in a correct manner, uniformity in dimensions has to be maintained. To correct this, a simple modification shown below can be performed.

p = 1000*D/(u*a)

On similar lines, a modification while computing z_nor needs to be done

z_nor = z/sqrt((1000*D*a/u)) 

I also went through the research paper attached and noticed that diameter of the laser is stated to be 0.1 mm as highlighted in the comments as well. Performing the following changes would be sufficient to replicate the required results.

d_laser = 0.1; %mm 

%Define 
x = linspace(-0.5,1.25,100); 
y = linspace(-0.25,0.25,100); 
z = linspace(0,0.5,100); 

I hope this helps.