External flow Analysis of Ahmed body and Comparing the Numerical and Experimental data in STAR-CCM+.

Objective:

• Create the Ahmed Body slant for both 25⁰ and 35⁰
• Run Steady-state implicit coupled flow simulation
• Use the turbulence models K-OmegsSST and k-epsilon
• Validate the velocity profile along the Ahmed body at different points with the experimental data.
• Calculate the cd and cl using the different turbulence.

 

 

AHMED BODY

The Ahmed body is a generic car body (a simplified vehicle model). The airflow around the Ahmed body captures the essential flow features around an automobile and was first defined and characterized in the experimental work of S. R. Ahmed in 1984. Although it has a very simple shape, the Ahmed body allows us to capture characteristic features that are relevant to bodies in the automobile industry.
This model is also used to describe the turbulent flow field around a car-like geometry. Once the numerical model is validated, it is used to design new models of the car.

In this project, I am performing external flow analysis on Ahmed Body in STAR-CCM+ and comparing the numerical data with the experimental data to validate my results.

 

 

1. 3D CAD

 

Ahmed body dimensions

• The first step is to create the geometry of Ahmed body in the STAR-CCM+ 3D cad modeler.
• The coordinates of the Ahmed body is identical to the experimental data.
• Ahmed body end is at x=0. The front end of the Ahmed body is at -1442 mm in the x-direction.
• The body is symmetrical along the y-axis.
• We have to expose the slant angle to create a design parameter. Which we can later use to generate Ahmed body for 35 degrees slant angle.

 

 

 

Coordinates for legs

 

 

 

• Now we have to create a wind tunnel for external flow analysis.
• While creating a wind tunnel, we will split the road into two parts, we will use the front part of the road as the symmetry plane to achieve proper boundary layer thickness.

 

Wind tunnel dimensions

 

 

 

 

Distinguished inputs

 

2. Subtract operation

• After creating Ahmed body and the wind tunnel, we will take a CAD to subtract between Ahmed body and wind tunnel to get a nice and clean region for wind flow, without any overlapping surfaces between the Ahmed body legs and wind tunnel.
• After the subtract operation, we will define a new meshing operation.
• Now we have to assign the subtract part to the region and selecting the option to create a boundary for each part surface and create one region for each part.
• After assigning parts to region we will define the boundary types.
• Inlet: velocity inlet.
• Outlet: pressure outlet.
• The first part of the road: symmetry plane.
• Road: wall
• Sides and top of the wind tunnel: symmetry plane.
• All the surface of Ahmed body: wall.

 

3. Meshing

Default controls

• Base size: 60 mm.
• Minimum surface size: 10 %.
• Number of prism layers: 5.
• Prism layer stretching: 1.2
• Prism layer total thickness: 10 mm.
• Maximum cell size: 100 %.

Custome controls

• Ahmed body legs surface: Target Surface Size = 2 mm.
• Ahmed body legs surface: Minimum Surface Size = 0.05 mm.

• Ahmed body surface: Target Surface Size = 10 mm.
• Ahmed body surface: Minimum Surface Size = 1 mm.                                       

Volumetric control defined on a small block. This block is created for generating a finer mesh near the Ahmed body.

• Volumetric control: Cuntomize isotropic size - Enabled.
• Custome size = 50 % relative to base.

 

Surface mesh

 

Volume mesh

 

Section plane

 

 

 

 

          Case 1: External flow analysis of Ahmed body (Slant-25 degrees) with k-epsilon

                                                 turbulence model in STAR-CCM+

 

Physics setup

24 probes have been created at different locations on the x-axis to export velocity data. 

 

All the physics models selected in this case is shown below.

Inlet velocity = 40 m/s.

                 

 

 

Results

 

Residuals

 

Drag coefficient

 

Lift coefficient

 

Velocity contour

 

Pressure contour

 

• From the residual plot, we can see that the solution has converged and reached a steady-state condition.
• Coefficient of Drag: 0.3495773949278717.
• Coefficient of Lift: 0.3235535550744727.
• From the velocity contour, we can see that the velocity is high at the curved region of the Ahmed body at the front of the body. Velocity is low at the back of the Ahmed body at the wake area. Maximum velocity: 57.398 m/s.
• In the pressure contour, we can see that pressure is high at the front face of the Ahmed body. The pressure is low at the curved region of the Ahmed body where the velocity is high. Maximum pressure: 984.12 Pa.

 

 

 

      Case 2: External flow analysis of Ahmed body (Slant-25 degrees) with k-omega SST

                                                 turbulence model in STAR-CCM+

 

All the parameters will remain the same in case 2 except the turbulence model. We will use k-omega SST turbulence model in case 2.

 

Physics setup

All the physics models selected in this case is shown below.

Inlet velocity = 40 m/s.

               

 

Results

 

Residuals

 

Coefficient of Drag

 

Coefficient of Lift

 

Velocity contour

 

Pressure contour

• From the residual plot, we can see that the solution has converged and reached a steady-state condition.
• Coefficient of Drag: 0.3457022395801299.
• Coefficient of Lift: 0.30014906126111157.
• From the velocity contour, we can see that the velocity is high at the curved region of the Ahmed body at the front of the body. Velocity is low at the back of the Ahmed body at the wake area. Maximum velocity: 57.411 m/s.
• In the pressure contour, we can see that pressure is high at the front face of the Ahmed body. The pressure is low at the curved region of the Ahmed body where the velocity is high. Maximum pressure: 984.84 Pa.

 

 

 

          Case 3: External flow analysis of Ahmed body (Slant-35 degrees) with k-epsilon

                                                  turbulence model in STAR-CCM+

 

In case 3 we will change the slant angle of Ahmed body to 35 degrees. We will use k-epsilon turbulence model in this case.

 

Physics setup

All the physics models selected in this case is shown below.

Inlet velocity = 40 m/s.

                

 

Results

 

Residuals

 

Coefficient of Drag

 

Coefficient of Lift

 

Velocity contour

 

Pressure contour

• From the residual plot, we can see that the solution has converged and reached a steady-state condition.
• Coefficient of Drag: 0.3797660816393593.
• Coefficient of Lift: 0.2130305897172416.
• From the velocity contour, we can see that the velocity is high at the curved region of the Ahmed body at the front of the body. Velocity is low at the back of the Ahmed body at the wake area. Maximum velocity: 57.373 m/s.
• In the pressure contour, we can see that pressure is high at the front face of the Ahmed body. The pressure is low at the curved region of the Ahmed body where the velocity is high. Maximum pressure: 985.97 Pa.

 

 

 

       Case 4: External flow analysis of Ahmed body (Slant-35 degrees) with k-omega SST

                                                 turbulence model in STAR-CCM+

 

All the parameters will remain the same in case 4 except the turbulence model. We will use k-omega SST turbulence model in case 4.

 

Physics setup

All the physics models selected in this case is shown below.

Inlet velocity = 40 m/s.

               

 

Results

 

Residuals

 

Coefficient of Drag

 

Coefficient of Lift

 

Velocity contour

 

Pressure contour

• From the residual plot, we can see that the solution has converged and reached a steady-state condition.
• Coefficient of Drag: 0.36121744699474156.
• Coefficient of Lift: 0.07426443298479399.
• From the velocity contour, we can see that the velocity is high at the curved region of the Ahmed body at the front of the body. Velocity is low at the back of the Ahmed body at the wake area. Maximum velocity: 57.373 m/s.
• In the pressure contour, we can see that pressure is high at the front face of the Ahmed body. The pressure is low at the curved region of the Ahmed body where the velocity is high. Maximum pressure: 985.61 Pa.
• Now we will generate normalized plots of velocity magnitude to compare the experimental and simulation data for all the cases. We will generate these plots in MATLAB.

 

 

Normalized plots for comparing the numerical and experimental data for all four cases.

 

Plot for case 1

Plot for case 2

Plot for case 3

Plot for case 4

 

Conclusion

• External flow analysis of Ahmed body of slant angle 25 degrees and 35 degrees was performed in STAR-CCM+ was performed.
• Turbulence model k-epsilon and K-omega SST was used for the analysis in both the cases, for slant angle 25 degrees and 35 degrees.
• Normalized velocity magnitude plots were created in each case using MATLAB.
• In case 1 and 2, Ahmed body with a slant angle 25 degrees was used. In both cases, we can see in the normalized velocity magnitude plot that the simulation data is very close to the experimental data.
• In case 3 and 4, Ahmed body with a slant angle 35 degrees was used. We can see that case 3 simulation data is much more deviated from the experimental data in the wake region than case 4.

 

 

Matlab code to generate the normalized plot

close all
clear all
clc

%% Plotting Ahmed body

% Plotting arc 1
a1 = -944; % x coordinate of arc
b1 = 150; % y coordinate of arc
circr = @(radius,rad_ang)  [radius*cos(rad_ang)+a1;  radius*sin(rad_ang)+b1]; % Circle Function For Angles In Radians
N1 = 500; % Number Of Points In Complete Circle
r_angl_1 = linspace(-pi, -pi/2, N1); % Angle Defining Arc Segment (radians)
radius_1 = 100; % Arc Radius
xy_r1 = circr(radius_1,r_angl_1); % Matrix (2xN) Of (x,y) Coordinates
figure(1)
hold on
p1 = plot(xy_r1(1,:), xy_r1(2,:),"color","bla","linewidth",2);

% Plotting arc 2
a2 = -944;
b2 = 238;
circr = @(radius,rad_ang)  [radius*cos(rad_ang)+a2;  radius*sin(rad_ang)+b2]; % Circle Function For Angles In Radians
N2 = 500; % Number Of Points In Complete Circle
r_angl_2 = linspace(pi, pi/2, N2); % Angle Defining Arc Segment (radians)
radius_2 = 100; % Arc Radius
xy_r2 = circr(radius_2,r_angl_2); % Matrix (2xN) Of (x,y) Coordinates
plot(xy_r2(1,:), xy_r2(2,:),"color","bla","linewidth",2); 

% plotting the straight lines in Ahmed body
plot([-944 0],[50 50],"color","bla","linewidth",2);
plot([0 0],[50 244.1787],"color","bla","linewidth",2);
plot([0 -201.2003],[244.1787 338],"color","bla","linewidth",2);
plot([-201.2003 -944],[338 338],"color","bla","linewidth",2);
plot([-1044 -1044],[150 238],"color","bla","linewidth",2);
grid minor
axis equal
axis([-1500 750 0 750])

%col1=xy_r1(1,:);
%col2=xy_r1(2,:);




% Normalized plot
alpha = 20;
inlet_velocity = 40; % m/s

%Simulation at -1442 mm
data_sim_1 = xlsread('num25ke.xlsx');
x_loc_sim_1 = data_sim_1(1:29,1);
z_loc_sim_1 = data_sim_1(1:29,2);
v_sim_1 = data_sim_1(1:29,3);
norm_sim_1 = alpha.*(v_sim_1./inlet_velocity);
x_sim_1 = x_loc_sim_1 + norm_sim_1 ; 
z_sim_1 = z_loc_sim_1;

p2= plot(x_sim_1,z_sim_1,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -1442 mm
data_exp_1 = xlsread('exp25.xlsx');
x_loc_exp_1 = data_exp_1(1:29,1);
z_loc_exp_1 = data_exp_1(1:29,3);
v_exp_1 = data_exp_1(1:29,8);
norm_exp_1 = alpha.*(v_exp_1./inlet_velocity);
x_exp_1 = x_loc_exp_1 + norm_exp_1;
z_exp_1 = z_loc_exp_1;

p3 = plot(x_exp_1,z_exp_1,"linewidth",1,"Color","b");


%Simulation at -1262 mm
data_sim_2 = xlsread('num25ke.xlsx');
x_loc_sim_2 = data_sim_2(30:58,1);
z_loc_sim_2 = data_sim_2(30:58,2);
v_sim_2 = data_sim_2(30:58,3);
norm_sim_2 = alpha.*(v_sim_2./inlet_velocity);
x_sim_2 = x_loc_sim_2 + norm_sim_2 ; 
z_sim_2 = z_loc_sim_2;

plot(x_sim_2,z_sim_2,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -1262 mm
data_exp_2 = xlsread('exp25.xlsx');
x_loc_exp_2 = data_exp_2(30:58,1);
z_loc_exp_2 = data_exp_2(30:58,3);
v_exp_2 = data_exp_2(30:58,8);
norm_exp_2 = alpha.*(v_exp_2./inlet_velocity);
x_exp_2 = x_loc_exp_2 + norm_exp_2;
z_exp_2 = z_loc_exp_2;

plot(x_exp_2,z_exp_2,"linewidth",1,"Color","b");


%Simulation at -1162 mm
data_sim_3 = xlsread('num25ke.xlsx');
x_loc_sim_3 = data_sim_3(59:87,1);
z_loc_sim_3 = data_sim_3(59:87,2);
v_sim_3 = data_sim_3(59:87,3);
norm_sim_3 = alpha.*(v_sim_3./inlet_velocity);
x_sim_3 = x_loc_sim_3 + norm_sim_3 ; 
z_sim_3 = z_loc_sim_3;

plot(x_sim_3,z_sim_3,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -1162 mm
data_exp_3 = xlsread('exp25.xlsx');
x_loc_exp_3 = data_exp_3(59:87,1);
z_loc_exp_3 = data_exp_3(59:87,3);
v_exp_3 = data_exp_3(59:87,8);
norm_exp_3 = alpha.*(v_exp_3./inlet_velocity);
x_exp_3 = x_loc_exp_3 + norm_exp_3;
z_exp_3 = z_loc_exp_3;

plot(x_exp_3,z_exp_3,"linewidth",1,"Color","b");


%Simulation at -1062 mm
data_sim_4 = xlsread('num25ke.xlsx');
x_loc_sim_4 = data_sim_4(88:116,1);
z_loc_sim_4 = data_sim_4(88:116,2);
v_sim_4 = data_sim_4(88:116,3);
norm_sim_4 = alpha.*(v_sim_4./inlet_velocity);
x_sim_4 = x_loc_sim_4 + norm_sim_4 ; 
z_sim_4 = z_loc_sim_4;

plot(x_sim_4,z_sim_4,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -1062 mm
data_exp_4 = xlsread('exp25.xlsx');
x_loc_exp_4 = data_exp_4(88:116,1);
z_loc_exp_4 = data_exp_4(88:116,3);
v_exp_4 = data_exp_4(88:116,8);
norm_exp_4 = alpha.*(v_exp_4./inlet_velocity);
x_exp_4 = x_loc_exp_4 + norm_exp_4;
z_exp_4 = z_loc_exp_4;

plot(x_exp_4,z_exp_4,"linewidth",1,"Color","b");


%Simulation at -962 mm
data_sim_5 = xlsread('num25ke.xlsx');
x_loc_sim_5 = data_sim_5(117:131,1);
z_loc_sim_5 = data_sim_5(117:131,2);
v_sim_5 = data_sim_5(117:131,3);
norm_sim_5 = alpha.*(v_sim_5./inlet_velocity);
x_sim_5 = x_loc_sim_5 + norm_sim_5 ; 
z_sim_5 = z_loc_sim_5;

plot(x_sim_5,z_sim_5,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -962 mm
data_exp_5 = xlsread('exp25.xlsx');
x_loc_exp_5 = data_exp_5(117:131,1);
z_loc_exp_5 = data_exp_5(117:131,3);
v_exp_5 = data_exp_5(117:131,8);
norm_exp_5 = alpha.*(v_exp_5./inlet_velocity);
x_exp_5 = x_loc_exp_5 + norm_exp_5;
z_exp_5 = z_loc_exp_5;

plot(x_exp_5,z_exp_5,"linewidth",1,"Color","b");


%Simulation at -862 mm
data_sim_6 = xlsread('num25ke.xlsx');
x_loc_sim_6 = data_sim_6(132:146,1);
z_loc_sim_6 = data_sim_6(132:146,2);
v_sim_6 = data_sim_6(132:146,3);
norm_sim_6 = alpha.*(v_sim_6./inlet_velocity);
x_sim_6 = x_loc_sim_6 + norm_sim_6 ; 
z_sim_6 = z_loc_sim_6;

plot(x_sim_6,z_sim_6,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -862 mm
data_exp_6 = xlsread('exp25.xlsx');
x_loc_exp_6 = data_exp_6(132:146,1);
z_loc_exp_6 = data_exp_6(132:146,3);
v_exp_6 = data_exp_6(132:146,8);
norm_exp_6 = alpha.*(v_exp_6./inlet_velocity);
x_exp_6 = x_loc_exp_6 + norm_exp_6;
z_exp_6 = z_loc_exp_6;

plot(x_exp_6,z_exp_6,"linewidth",1,"Color","b");


%Simulation at -562 mm
data_sim_7 = xlsread('num25ke.xlsx');
x_loc_sim_7 = data_sim_7(147:161,1);
z_loc_sim_7 = data_sim_7(147:161,2);
v_sim_7 = data_sim_7(147:161,3);
norm_sim_7 = alpha.*(v_sim_7./inlet_velocity);
x_sim_7 = x_loc_sim_7 + norm_sim_7 ; 
z_sim_7 = z_loc_sim_7;

plot(x_sim_7,z_sim_7,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -562 mm
data_exp_7 = xlsread('exp25.xlsx');
x_loc_exp_7 = data_exp_7(147:161,1);
z_loc_exp_7 = data_exp_7(147:161,3);
v_exp_7 = data_exp_7(147:161,8);
norm_exp_7 = alpha.*(v_exp_7./inlet_velocity);
x_exp_7 = x_loc_exp_7 + norm_exp_7;
z_exp_7 = z_loc_exp_7;

plot(x_exp_7,z_exp_7,"linewidth",1,"Color","b");


%Simulation at -362 mm
data_sim_8 = xlsread('num25ke.xlsx');
x_loc_sim_8 = data_sim_8(162:176,1);
z_loc_sim_8 = data_sim_8(162:176,2);
v_sim_8 = data_sim_8(162:176,3);
norm_sim_8 = alpha.*(v_sim_8./inlet_velocity);
x_sim_8 = x_loc_sim_8 + norm_sim_8 ; 
z_sim_8 = z_loc_sim_8;

plot(x_sim_8,z_sim_8,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -362 mm
data_exp_8 = xlsread('exp25.xlsx');
x_loc_exp_8 = data_exp_8(162:176,1);
z_loc_exp_8 = data_exp_8(162:176,3);
v_exp_8 = data_exp_8(162:176,8);
norm_exp_8 = alpha.*(v_exp_8./inlet_velocity);
x_exp_8 = x_loc_exp_8 + norm_exp_8;
z_exp_8 = z_loc_exp_8;

plot(x_exp_8,z_exp_8,"linewidth",1,"Color","b");


%Simulation at -262 mm
data_sim_9 = xlsread('num25ke.xlsx');
x_loc_sim_9 = data_sim_9(177:191,1);
z_loc_sim_9 = data_sim_9(177:191,2);
v_sim_9 = data_sim_9(177:191,3);
norm_sim_9 = alpha.*(v_sim_9./inlet_velocity);
x_sim_9 = x_loc_sim_9 + norm_sim_9 ; 
z_sim_9 = z_loc_sim_9;

plot(x_sim_9,z_sim_9,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -262 mm
data_exp_9 = xlsread('exp25.xlsx');
x_loc_exp_9 = data_exp_9(177:191,1);
z_loc_exp_9 = data_exp_9(177:191,3);
v_exp_9 = data_exp_9(177:191,8);
norm_exp_9 = alpha.*(v_exp_9./inlet_velocity);
x_exp_9 = x_loc_exp_9 + norm_exp_9;
z_exp_9 = z_loc_exp_9;

plot(x_exp_9,z_exp_9,"linewidth",1,"Color","b");


%Simulation at -212 mm
data_sim_10 = xlsread('num25ke.xlsx');
x_loc_sim_10 = data_sim_10(192:206,1);
z_loc_sim_10 = data_sim_10(192:206,2);
v_sim_10 = data_sim_10(192:206,3);
norm_sim_10 = alpha.*(v_sim_10./inlet_velocity);
x_sim_10 = x_loc_sim_10 + norm_sim_10 ; 
z_sim_10 = z_loc_sim_10;

plot(x_sim_10,z_sim_10,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -212 mm
data_exp_10 = xlsread('exp25.xlsx');
x_loc_exp_10 = data_exp_10(192:204,1);
z_loc_exp_10 = data_exp_10(192:204,3);
v_exp_10 = data_exp_10(192:204,8);
norm_exp_10 = alpha.*(v_exp_10./inlet_velocity);
x_exp_10 = x_loc_exp_10 + norm_exp_10;
z_exp_10 = z_loc_exp_10;

plot(x_exp_10,z_exp_10,"linewidth",1,"Color","b");


%Simulation at -162 mm
data_sim_11 = xlsread('num25ke.xlsx');
x_loc_sim_11 = data_sim_11(207:221,1);
z_loc_sim_11 = data_sim_11(207:221,2);
v_sim_11 = data_sim_11(207:221,3);
norm_sim_11 = alpha.*(v_sim_11./inlet_velocity);
x_sim_11 = x_loc_sim_11 + norm_sim_11 ; 
z_sim_11 = z_loc_sim_11;

plot(x_sim_11,z_sim_11,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -162 mm
data_exp_11 = xlsread('exp25.xlsx');
x_loc_exp_11 = data_exp_11(205:219,1);
z_loc_exp_11 = data_exp_11(205:219,3);
v_exp_11 = data_exp_11(205:219,8);
norm_exp_11 = alpha.*(v_exp_11./inlet_velocity);
x_exp_11 = x_loc_exp_11 + norm_exp_11;
z_exp_11 = z_loc_exp_11;

plot(x_exp_11,z_exp_11,"linewidth",1,"Color","b");


%Simulation at -112 mm
data_sim_12 = xlsread('num25ke.xlsx');
x_loc_sim_12 = data_sim_12(222:240,1);
z_loc_sim_12 = data_sim_12(222:240,2);
v_sim_12 = data_sim_12(222:240,3);
norm_sim_12 = alpha.*(v_sim_12./inlet_velocity);
x_sim_12 = x_loc_sim_12 + norm_sim_12 ; 
z_sim_12 = z_loc_sim_12;

plot(x_sim_12,z_sim_12,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -112 mm
data_exp_12 = xlsread('exp25.xlsx');
x_loc_exp_12 = data_exp_12(220:238,1);
z_loc_exp_12 = data_exp_12(220:238,3);
v_exp_12 = data_exp_12(220:238,8);
norm_exp_12 = alpha.*(v_exp_12./inlet_velocity);
x_exp_12 = x_loc_exp_12 + norm_exp_12;
z_exp_12 = z_loc_exp_12;

plot(x_exp_12,z_exp_12,"linewidth",1,"Color","b");


%Simulation at -62 mm
data_sim_13 = xlsread('num25ke.xlsx');
x_loc_sim_13 = data_sim_13(241:263,1);
z_loc_sim_13 = data_sim_13(241:263,2);
v_sim_13 = data_sim_13(241:263,3);
norm_sim_13 = alpha.*(v_sim_13./inlet_velocity);
x_sim_13 = x_loc_sim_13 + norm_sim_13 ; 
z_sim_13 = z_loc_sim_13;

plot(x_sim_13,z_sim_13,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -62 mm
data_exp_13 = xlsread('exp25.xlsx');
x_loc_exp_13 = data_exp_13(239:261,1);
z_loc_exp_13 = data_exp_13(239:261,3);
v_exp_13 = data_exp_13(239:261,8);
norm_exp_13 = alpha.*(v_exp_13./inlet_velocity);
x_exp_13 = x_loc_exp_13 + norm_exp_13;
z_exp_13 = z_loc_exp_13;

plot(x_exp_13,z_exp_13,"linewidth",1,"Color","b");


%Simulation at -12 mm
data_sim_14 = xlsread('num25ke.xlsx');
x_loc_sim_14 = data_sim_14(264:290,1);
z_loc_sim_14 = data_sim_14(264:290,2);
v_sim_14 = data_sim_14(264:290,3);
norm_sim_14 = alpha.*(v_sim_14./inlet_velocity);
x_sim_14 = x_loc_sim_14 + norm_sim_14 ; 
z_sim_14 = z_loc_sim_14;

plot(x_sim_14,z_sim_14,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at -12 mm
data_exp_14 = xlsread('exp25.xlsx');
x_loc_exp_14 = data_exp_14(262:288,1);
z_loc_exp_14 = data_exp_14(262:288,3);
v_exp_14 = data_exp_14(262:288,8);
norm_exp_14 = alpha.*(v_exp_14./inlet_velocity);
x_exp_14 = x_loc_exp_14 + norm_exp_14;
z_exp_14 = z_loc_exp_14;

plot(x_exp_14,z_exp_14,"linewidth",1,"Color","b");


%Simulation at 38 mm
data_sim_15 = xlsread('num25ke.xlsx');
x_loc_sim_15 = data_sim_15(291:335,1);
z_loc_sim_15 = data_sim_15(291:335,2);
v_sim_15 = data_sim_15(291:335,3);
norm_sim_15 = alpha.*(v_sim_15./inlet_velocity);
x_sim_15 = x_loc_sim_15 + norm_sim_15 ; 
z_sim_15 = z_loc_sim_15;

plot(x_sim_15,z_sim_15,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 38 mm
data_exp_15 = xlsread('exp25.xlsx');
x_loc_exp_15 = data_exp_15(289:333,1);
z_loc_exp_15 = data_exp_15(289:333,3);
v_exp_15 = data_exp_15(289:333,8);
norm_exp_15 = alpha.*(v_exp_15./inlet_velocity);
x_exp_15 = x_loc_exp_15 + norm_exp_15;
z_exp_15 = z_loc_exp_15;

plot(x_exp_15,z_exp_15,"linewidth",1,"Color","b");


%Simulation at 88 mm
data_sim_16 = xlsread('num25ke.xlsx');
x_loc_sim_16 = data_sim_16(336:380,1);
z_loc_sim_16 = data_sim_16(336:380,2);
v_sim_16 = data_sim_16(336:380,3);
norm_sim_16 = alpha.*(v_sim_16./inlet_velocity);
x_sim_16 = x_loc_sim_16 + norm_sim_16 ; 
z_sim_16 = z_loc_sim_16;

plot(x_sim_16,z_sim_16,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 88 mm
data_exp_16 = xlsread('exp25.xlsx');
x_loc_exp_16 = data_exp_16(334:378,1);
z_loc_exp_16 = data_exp_16(334:378,3);
v_exp_16 = data_exp_16(334:378,8);
norm_exp_16 = alpha.*(v_exp_16./inlet_velocity);
x_exp_16 = x_loc_exp_16 + norm_exp_16;
z_exp_16 = z_loc_exp_16;

plot(x_exp_16,z_exp_16,"linewidth",1,"Color","b");


%Simulation at 138 mm
data_sim_17 = xlsread('num25ke.xlsx');
x_loc_sim_17 = data_sim_17(381:425,1);
z_loc_sim_17 = data_sim_17(381:425,2);
v_sim_17 = data_sim_17(381:425,3);
norm_sim_17 = alpha.*(v_sim_17./inlet_velocity);
x_sim_17 = x_loc_sim_17 + norm_sim_17 ; 
z_sim_17 = z_loc_sim_17;

plot(x_sim_17,z_sim_17,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 138 mm
data_exp_17 = xlsread('exp25.xlsx');
x_loc_exp_17 = data_exp_17(379:423,1);
z_loc_exp_17 = data_exp_17(379:423,3);
v_exp_17 = data_exp_17(379:423,8);
norm_exp_17 = alpha.*(v_exp_17./inlet_velocity);
x_exp_17 = x_loc_exp_17 + norm_exp_17;
z_exp_17 = z_loc_exp_17;

plot(x_exp_17,z_exp_17,"linewidth",1,"Color","b");


%Simulation at 188 mm
data_sim_18 = xlsread('num25ke.xlsx');
x_loc_sim_18 = data_sim_18(426:470,1);
z_loc_sim_18 = data_sim_18(426:470,2);
v_sim_18 = data_sim_18(426:470,3);
norm_sim_18 = alpha.*(v_sim_18./inlet_velocity);
x_sim_18 = x_loc_sim_18 + norm_sim_18 ; 
z_sim_18 = z_loc_sim_18;

plot(x_sim_18,z_sim_18,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 188 mm
data_exp_18 = xlsread('exp25.xlsx');
x_loc_exp_18 = data_exp_18(424:468,1);
z_loc_exp_18 = data_exp_18(424:468,3);
v_exp_18 = data_exp_18(424:468,8);
norm_exp_18 = alpha.*(v_exp_18./inlet_velocity);
x_exp_18 = x_loc_exp_18 + norm_exp_18;
z_exp_18 = z_loc_exp_18;

plot(x_exp_18,z_exp_18,"linewidth",1,"Color","b");


%Simulation at 238 mm
data_sim_19 = xlsread('num25ke.xlsx');
x_loc_sim_19 = data_sim_19(471:515,1);
z_loc_sim_19 = data_sim_19(471:515,2);
v_sim_19 = data_sim_19(471:515,3);
norm_sim_19 = alpha.*(v_sim_19./inlet_velocity);
x_sim_19 = x_loc_sim_19 + norm_sim_19 ; 
z_sim_19 = z_loc_sim_19;

plot(x_sim_19,z_sim_19,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 238 mm
data_exp_19 = xlsread('exp25.xlsx');
x_loc_exp_19 = data_exp_19(469:513,1);
z_loc_exp_19 = data_exp_19(469:513,3);
v_exp_19 = data_exp_19(469:513,8);
norm_exp_19 = alpha.*(v_exp_19./inlet_velocity);
x_exp_19 = x_loc_exp_19 + norm_exp_19;
z_exp_19 = z_loc_exp_19;

plot(x_exp_19,z_exp_19,"linewidth",1,"Color","b");


%Simulation at 288 mm
data_sim_20 = xlsread('num25ke.xlsx');
x_loc_sim_20 = data_sim_20(516:560,1);
z_loc_sim_20 = data_sim_20(516:560,2);
v_sim_20 = data_sim_20(516:560,3);
norm_sim_20 = alpha.*(v_sim_20./inlet_velocity);
x_sim_20 = x_loc_sim_20 + norm_sim_20 ; 
z_sim_20 = z_loc_sim_20;

plot(x_sim_20,z_sim_20,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 288 mm
data_exp_20 = xlsread('exp25.xlsx');
x_loc_exp_20 = data_exp_20(514:558,1);
z_loc_exp_20 = data_exp_20(514:558,3);
v_exp_20 = data_exp_20(514:558,8);
norm_exp_20 = alpha.*(v_exp_20./inlet_velocity);
x_exp_20 = x_loc_exp_20 + norm_exp_20;
z_exp_20 = z_loc_exp_20;

plot(x_exp_20,z_exp_20,"linewidth",1,"Color","b");


%Simulation at 338 mm
data_sim_21 = xlsread('num25ke.xlsx');
x_loc_sim_21 = data_sim_21(561:605,1);
z_loc_sim_21 = data_sim_21(561:605,2);
v_sim_21 = data_sim_21(561:605,3);
norm_sim_21 = alpha.*(v_sim_21./inlet_velocity);
x_sim_21 = x_loc_sim_21 + norm_sim_21 ; 
z_sim_21 = z_loc_sim_21;

plot(x_sim_21,z_sim_21,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 338 mm
data_exp_21 = xlsread('exp25.xlsx');
x_loc_exp_21 = data_exp_21(559:603,1);
z_loc_exp_21 = data_exp_21(559:603,3);
v_exp_21 = data_exp_21(559:603,8);
norm_exp_21 = alpha.*(v_exp_21./inlet_velocity);
x_exp_21 = x_loc_exp_21 + norm_exp_21;
z_exp_21 = z_loc_exp_21;

plot(x_exp_21,z_exp_21,"linewidth",1,"Color","b");


%Simulation at 438 mm
data_sim_22 = xlsread('num25ke.xlsx');
x_loc_sim_22 = data_sim_22(606:650,1);
z_loc_sim_22 = data_sim_22(606:650,2);
v_sim_22 = data_sim_22(606:650,3);
norm_sim_22 = alpha.*(v_sim_22./inlet_velocity);
x_sim_22 = x_loc_sim_22 + norm_sim_22 ; 
z_sim_22 = z_loc_sim_22;

plot(x_sim_22,z_sim_22,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 438 mm
data_exp_22 = xlsread('exp25.xlsx');
x_loc_exp_22 = data_exp_22(604:648,1);
z_loc_exp_22 = data_exp_22(604:648,3);
v_exp_22 = data_exp_22(604:648,8);
norm_exp_22 = alpha.*(v_exp_22./inlet_velocity);
x_exp_22 = x_loc_exp_22 + norm_exp_22;
z_exp_22 = z_loc_exp_22;

plot(x_exp_22,z_exp_22,"linewidth",1,"Color","b");


%Simulation at 538 mm
data_sim_23 = xlsread('num25ke.xlsx');
x_loc_sim_23 = data_sim_23(651:695,1);
z_loc_sim_23 = data_sim_23(651:695,2);
v_sim_23 = data_sim_23(651:695,3);
norm_sim_23 = alpha.*(v_sim_23./inlet_velocity);
x_sim_23 = x_loc_sim_23 + norm_sim_23 ; 
z_sim_23 = z_loc_sim_23;

plot(x_sim_23,z_sim_23,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 538 mm
data_exp_23 = xlsread('exp25.xlsx');
x_loc_exp_23 = data_exp_23(649:693,1);
z_loc_exp_23 = data_exp_23(649:693,3);
v_exp_23 = data_exp_23(649:693,8);
norm_exp_23 = alpha.*(v_exp_23./inlet_velocity);
x_exp_23 = x_loc_exp_23 + norm_exp_23;
z_exp_23 = z_loc_exp_23;

plot(x_exp_23,z_exp_23,"linewidth",1,"Color","b");


%Simulation at 638 mm
data_sim_24 = xlsread('num25ke.xlsx');
x_loc_sim_24 = data_sim_24(696:740,1);
z_loc_sim_24 = data_sim_24(696:740,2);
v_sim_24 = data_sim_24(696:740,3);
norm_sim_24 = alpha.*(v_sim_24./inlet_velocity);
x_sim_24 = x_loc_sim_24 + norm_sim_24 ; 
z_sim_24 = z_loc_sim_24;

plot(x_sim_24,z_sim_24,"Marker","o","MarkerSize",5,"Color","r");

%Experimental at 638 mm
data_exp_24 = xlsread('exp25.xlsx');
x_loc_exp_24 = data_exp_24(694:738,1);
z_loc_exp_24 = data_exp_24(694:738,3);
v_exp_24 = data_exp_24(694:738,8);
norm_exp_24 = alpha.*(v_exp_24./inlet_velocity);
x_exp_24 = x_loc_exp_24 + norm_exp_24;
z_exp_24 = z_loc_exp_24;

plot(x_exp_24,z_exp_24,"linewidth",1,"Color","b");


h = [p1;p2;p3];
legend(h,"Ahmed body","Normalized Velocity Magnitude (U) - Simulation","Normalized Velocity Magnitude (U) - Experimantal","Location","best");
title("Comparison of Numerical and Experimantal Data of Ahmed body (Slant-25^{o}) for K-epsilon Turbulence Model in STAR-CCM+","FontSize",15);
xlabel("X-axis (mm)");
ylabel("Z-axis (mm)");