Modeling and Simulation of flow around an Ahmed Body

AHMED BODY SIMULATION

AIM:

To simulate flow around ahmed body and comparing the experimental data with the simulated data.

INTRODUCTION:

Ahmed body is a general body used for approximation of automobile bodies. In this simulation, the ahmed body is designed using CATIA V5 and the windtunnel setup and case setup is done in converge cfd. The body is simulated and the results are obtained using probe method in paraview and the results are compared with the experimental data and validated. The forces are obtained and the drag values are calculated.

CASE SETUP:

Inlet boundary condition is assigned to velocity condition as 40 m/s.

Outlet boundary condition is assigned to atmospheric pressure of 101325 Pa.

The side walls and top wall is assigned to symmetry boundary condition.

The downwall is assigned to slip for 0.7 m at the start, and then no-slip wall is assigned. The ahmed body is kept 0.4m, from the end of the slip wall.

Fixed embedding is kept around the ahmed body with a scale level of 2, to capture the flow effectively.

DESIGN OF AHMED BODY:

The design was done in Catia V5, and imported as .stl file into converge CFD.

MESH CALCULATION:

To save time, calculated grid size using y+ calculator from pointwise, but the grid size was too low and didn’t support with the license and my computer. So took the grid size , dx = 0.06 m , dy = 0.06 m ,dz = 0.06 m, and as the grid approaches near the wall, it is reduced with a fixed embedding method, box type, scaling = 2.

If we use a embedding method, the grid size near the wall is calculated by Grid size = base grid / (2 ^(embedd level)), which gives a value of 0.015 m, which is still a higher grid size value for the target set. This value is taken considering the simulation and system restrictions, so it is simulated as a less coarse simulation to understand the concept.

MESH VISUALISATION:

LINE PROBE IN PARAVIEW:

After simulating, post processed the results, and used a line probe in paraview at various y-locations to obtain the velocity data in Z direction and plotted to compare the data with the experimental data.Later,  the data was imported in Matlab to obtain the normalisation data.

ORIGIN LOCATION AND COMPARISON AT 37 MM FROM THE ORIGIN:

The experimental data had an origin near the end of the ahmed body at the ground level. So correction factors were added to compare the experimental and simulation data. Similarly, datas were taken at various x - points and the normalised data was plotted.

AHMED BODY NORMALISATION DATA PLOT:

Black Dotted lines are experimental data and red ******** lines are simulation data. Marker size is reduced for clear visibility of the change in data for simulation data.

This data is calculated by taking the data points at each x intervals and multiplying an amplification factor to observe the difference in the experimental and simulated data.

This data helps us to understand the velocity direction and the deviation between the experimental and simulated data at different x intervals.

The points aligned towards left is taken negative value of velocity and the points taken towards right is taken as positive value of velocity.

MATLAB SCRIPT USED TO PLOT FOR NORMALISATION OF VELOCITY DATA:

Wrote a simple code to plot the data by calling the excel sheet which contains both experimental and simulation data directly into matlab, as it will save time in future if any values of velocity needs to be edited.

SCRIPT:

clc;
data1 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot_-13');
data2 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot - 263');
data3 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot 37');
data4 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot87');
data5 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot - - 113');
data6 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot_minus63');
data7 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot_187');
data8 = xlsread('Data_Ahmed_body_comparison_experimental_simulation_35deg.xlsx','plot_137');
x_13 = -13;
x_263 = -263;
x_37 = 37;
x_87 = 87;
x_113 = -113;
x_63 = -63;
x_187 = 187;
x_137 = 137;
 
u_13 = data1(:,4);
y_13 = data1(:,3);
 
amp_factor = 5;
u_norm_13 = (u_13./max(u_13)).*amp_factor;
 
plot_u_13 = x_13 - u_norm_13;
%plot_u_13 = u_norm_13;
plot_y = y_13 *1000;
plot(plot_u_13,plot_y, '-r', 'MarkerSize',0.00001);
 
hold on;
%%exp
u_13_exp = data1(:,9);
y_13_exp = data1(:,8);
 
u_norm_13_exp = (u_13_exp./max(u_13_exp)).*amp_factor;
 
plot_u_13_exp = x_13 - u_norm_13_exp;
 
plot_y_exp = y_13_exp *1000;
plot(plot_u_13_exp,plot_y_exp, '.k','MarkerSize',5);
hold on;
%%%minus 263
u_263 = data2(:,4);
y_263 = data2(:,3);
 
 
u_norm_263 = (u_263./max(u_263)).*amp_factor;
 
plot_u_263 = x_263 - u_norm_263;
 
plot_y_263 = y_263 *1000;
plot(plot_u_263,plot_y_263 ,'*r','MarkerSize',0.00001);
hold on;
%%exp
u_263_exp = data2(:,9);
y_263_exp = data2(:,8);
 
 
u_norm_263_exp = (u_263_exp./max(u_263_exp)).*amp_factor;
 
plot_u_263_exp = x_263 - u_norm_263_exp;
 
plot_y_263_exp = y_263_exp *1000;
plot(plot_u_263_exp,plot_y_263_exp ,'.k','MarkerSize',5);
hold on;
%%% plus 37
u_37 = data3(:,4);
y_37 = data3(:,3);
 
 
u_norm_37 = (u_37./max(u_37)).*amp_factor;
plot_u_37 = x_37 - u_norm_37;
 
plot_y_37 = y_37 *1000;
plot(plot_u_37,plot_y_37,'*r','MarkerSize',0.00001);
hold on;
%%exp
u_37_exp = data3(:,9);
y_37_exp = data3(:,8);
 
 
u_norm_37_exp = (u_37_exp./max(u_37_exp)).*amp_factor;
plot_u_37_exp = x_37 - u_norm_37_exp;
 
plot_y_37_exp = y_37_exp *1000;
plot(plot_u_37_exp,plot_y_37_exp,'.k','MarkerSize',5);
hold on;
%%%%plus 87
u_87 = data4(:,4);
y_87 = data4(:,3);
 
 
u_norm_87 = (u_87./max(u_87)).*amp_factor;
 
plot_u_87= x_87 - u_norm_87;
 
plot_y_87 = y_87 *1000;
plot(plot_u_87,plot_y_87,'*r','MarkerSize',0.00001);
hold on;
%exp
u_87_exp = data4(:,9);
y_87_exp = data4(:,8);
 
 
u_norm_87_exp = (u_87_exp./max(u_87_exp)).*amp_factor;
 
plot_u_87_exp = x_87 - u_norm_87_exp;
 
plot_y_87_exp = y_87_exp *1000;
plot(plot_u_87_exp,plot_y_87_exp,'.k','MarkerSize',5);
hold on;
%%%% minus 113
u_113 = data5(:,4);
y_113 = data5(:,3);
 
 
u_norm_113 = (u_113./max(u_113)).*amp_factor;
 
plot_u_113 = x_113 - u_norm_113;
 
plot_y_113 = y_113 *1000;
plot(plot_u_113,plot_y_113,'*r','MarkerSize',0.00001);
hold on;
%exp
u_113_exp = data5(:,9);
y_113_exp = data5(:,8);
 
 
u_norm_113_exp = (u_113_exp./max(u_113_exp)).*amp_factor;
 
plot_u_113_exp = x_113 - u_norm_113_exp;
 
plot_y_113_exp = y_113_exp *1000;
plot(plot_u_113_exp,plot_y_113_exp,'.k','MarkerSize',5);
hold on;
%%%% minus 63
u_63 = data6(:,4);
y_63 = data6(:,3);
 
 
u_norm_63 = (u_13./max(u_63)).*amp_factor;
 
plot_u_63 = x_63 - u_norm_63;
 
plot_y_63 = y_63 *1000;
plot(plot_u_63,plot_y_63,'*r','MarkerSize',0.00001);
hold on;
%%exp
u_63_exp = data6(:,9);
y_63_exp = data6(:,8);
 
 
u_norm_63_exp = (u_13_exp./max(u_63_exp)).*amp_factor;
 
plot_u_63_exp = x_63 - u_norm_63_exp;
 
plot_y_63_exp = y_63_exp *1000;
plot(plot_u_63_exp,plot_y_63_exp,'.k','MarkerSize',5);
hold on;
%%%%% plus 187
u_187 = data7(:,4);
y_187 = data7(:,3);
 
 
u_norm_187 = (u_187./max(u_187)).*amp_factor;
 
plot_u_187 = x_187 - u_norm_187;
 
plot_y_187 = y_187 *1000;
plot(plot_u_187,plot_y_187,'*r','MarkerSize',0.00001);
hold on;
%%%exp
u_187_exp = data7(:,9);
y_187_exp = data7(:,8);
 
 
u_norm_187_exp = (u_187_exp./max(u_187_exp)).*amp_factor;
 
plot_u_187_exp = x_187 - u_norm_187_exp;
 
plot_y_187_exp = y_187_exp *1000;
plot(plot_u_187_exp,plot_y_187_exp,'.k','MarkerSize',5);
hold on;
%%%%137
u_137 = data8(:,4);
y_137 = data8(:,3);
 
 
u_norm_137 = (u_137./max(u_137)).*amp_factor;
 
plot_u_137 = x_137 - u_norm_137;
 
plot_y_137 = y_137 *1000;
plot(plot_u_137,plot_y_137,'*r','MarkerSize',0.0001);
hold on;
%%%exp
u_137_exp = data8(:,9);
y_137_exp = data8(:,8);
 
 
u_norm_137_exp = (u_137_exp./max(u_137_exp)).*amp_factor;
 
plot_u_137_exp = x_137 - u_norm_137_exp;
 
plot_y_137_exp = y_137_exp *1000;
plot(plot_u_137_exp,plot_y_137_exp,'.k','MarkerSize',5);
hold on;

DRAG AND LIFT CALCULATION :

DRAG CALCULATION FOR AHMED BODY:

Drag is the opposite force which is generated when air is made to flow over an object. The simulation results can be used to obtain the drag force acting on the ahmed body.

SIMULATION RESULTS:

The drag force is converged to around 98 N. This value is obtained by averaging the last 1000 cycles of the simulation in Matlab.

PROJECTED FRONTAL AREA CALCULATION IN CATIA V5:

To calculate the drag coefficient, we use,

Where F_d = Drag force,

 Is the density of air (1.184 kg/m³) at 26 degree C,

Cd is the drag coefficient,

A – Frontal Projected area (0.112 m²)

V – Inlet velocity (40 m/s),

By using this, the values of Cd is found to be 0.92

LIFT CALCULATION FOR AHMED BODY:

Lift is the force which is acting perpendicular to the body and the value of the force determines whether the body is lifted upwards or pushed downwards..

The simulation results can be used to obtain the lift force acting on the Ahmed body.

SIMULATION RESULTS:

The lift force is converged to around 215 N. This value is obtained by  averaging the last 1000 cycles of the simulation in Matlab.

PROJECTED AREA CALCULATION IN CATIA V5:

To calculate the lift coefficient, we use,

Where F_l = Lift force,

 ρ is the density of air (1.184 kg/m³) at 26 degree C,

Cl is the lift coefficient,

A – Projected Area in top view ( 0.402 m²)

V – Inlet velocity (40 m/s),

By using this, the values of Cl is found to be 0.56

 CONCLUSION:

Thus, the ahmed body is simulated, by designing in Catia V5, and then, the results are compared with the experimental data and validated. Validation with the experimental data provides us with the assurance, that the setup and the simulation done in converge cfd is correct. Although there will be a difference in values, since the conditions might change during actual experimentation compared with the cfd results, this simulation provides us with the accuracy of the solver, and the method of approach to solve a CFD problem.

ANIMATION LINK :

VELOCITY ANIMATION WITH STREAM TRACER:

https://drive.google.com/file/d/1NqK2XqJs-djcl0hTxDFa6qi_II9H6WL-/view?usp=sharing

PRESSURE DISTRIBUTION ANIMATION: https://drive.google.com/file/d/1WT3tI-pIktl3bRIBomBPYQqDB1n8JmXw/view?usp=sharing