Week 10: Modeling and Simulation of flow around an Ahmed Body
Aim
- Run an external flow simulation on Ahmed body
- Create the geometry file
- Extract coefficient of drag values from the paraview
- Extract the x component of velocity along a line
- Compare the experimental data and simulation data for validation
Ahmed body

Ahmed's body is a generic form of the car body that resembles all the essential flow features around a vehicle. This generic form was first defined and characterized in the experimental work of S.R.Ahmed. This body allows us to capture all the characteristics features that are relevant to bodies in the vehicle industry. This body can be used for a lot of experiments like calculating the drag and lift which are essential nowadays in the design of car bodies. Also this can be used to capture the wake regions, Flow seperation, vortices etc.. Different slant angles provide different values for Coeffecient of drag.
The reason for the negative pressure in the wake region
Wake region is formed behind the ahmed body as a result of viscous forces.The layer over the ahmed body get detatched at the rear end and a wake region is created. The velocity gradient is negetive here and the shear stresses in the flow creates a turbulent flow in wake region As the velocity of flow near to wall is almost zero due to no-slip condition the flow near to boundary layer end up in the rear side of the body through top and lower part of the body a region of low pressure relative to the pressure just outside the wake region, since there is a low pressure, the fluid has to work against adverse pressure gradient
Significance of point of seperation
The flow seperation takes place where the dv/dx or velocity gradient is zero along with pressure gradient along x-axis = 0 for the specific point.The flow seperation can be detected by a single contour and it can also be detected by ploting the velocity aliong y-axis at that region.
Flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake. Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage, for example.
Flowing against an increasing pressure is known as flowing in anadverse pressure gradient. The boundary layer separates when it has travelled far enough in an adverse pressure gradient that the speed of the boundary layer relative to the surface has stopped and reversed direction. The flow becomes detached from the surface, and instead takes the forms of eddies and vortces. The fluid exerts a constant pressure on the surface once it has separated instead of a continually increasing pressure if still attached.In aerodynamics, flow separation results in reduced lift and increased aerodynamic, caused by the pressure differential between the front and rear surfaces of the object.
Since after the separation point the flow no longer adheres the surface of the body, the skin friction drag is almost zero. At the same time, however, the pressure drops considerably due to the energy dissipation in the turbulent wake. This leads to a significant increase in pressure drag, which is far greater than the reduction in skin friction drag. In total, the parasitic drag (air resistance) thus increases very strongly in the event of a flow separation.
Geometry
- Geometry was created from Siemens solid edge
- The geometry was cut into half to reduce the amount of cells
- Then it was saved as STL file which is then opened through Converge
- Then wind tunnel is created in the converge using creating Vertices and then patching it
- To get the dimensions for the wind tunnel the following calculations were done
Formula for Boundary layer thickness on a flat plat, `delta = 0.382*x/(Re_x)^(1/5)`
Here it is given that `delta = 0.03`
`Re_x = u*x/(nu)`
`= (40x)/(1.552e-5)`
`=> 0.03 = 0.382x/((40x)/(1.552e-5))^(1/5)`
`0.274 = 0.382x/(40x^-5)`
`0.717 = x/((40x) ^(1/5))`
`0.717*(40)^(1/5) = x/(x^(1/5)`
`x^4 = 7.579`
x = 1.3 metres
- The above value is for boundary layer at the front hence with additional 0.5 metres at the front an Inlet is to be created
- This value also an additonal 0.5 is also added to the front distance from the Inlet to avoid boundary layer formation in this area hence this will be a seperate boundary (where Free slip condition is given)
- Hence a total distance of 2.3 metres is added from the front face of the geometry to the inlet
- The distance between Rear sinde of the geometry and outlet is set 5 times the length of geometry which is 5 metres itself. THe typical values industries use for this is in Between 5 times to 10 times to capture the physics effectively by avoiding the interferance of Outlet wall conditions. Since the current resources are low I will stick with the least (5 times)
- The Height is set to two times the length of the geometry
- The width is set to 0.5 metres

Setup
- A transient simualtion is set
End time calculation ,
Length of the Wind tunnel = 8.3
Velocity of air = 40 m/s
Time required by air to travel through the wind tunnel = 8.3/40 = 0.2075 seconds
Hence End time is set to 0.36 to avoid any complications
- Energy solver is turned off
- In regions and initialisation the Velocity is set to 40 m/s and and Initial pressure is set to 101325 pascals
- Boundary conditions are shown in snap shots
- Under turbulance model K-w SST is set with enhanced wall treatment so to capture Viscous sub layer , However we need to use lower values of y+
Cell thickeness calculation at the boundary
For K-w the typical range of y+ is 0 - 10
So If y+ = 10 then the cell thickness would be 0.00009 m
Also we know that
Refined mesh = Base mesh /(2^n)
where n is the scale , for which in our case possible maximum scale is 6
`=> 9e-5 = (Base mesh) /(2^6)`
Base mesh = 64 * 9e-5 = 0.00576 m, the value cant be used in our case due to less computational resources
After some trials it was found that the allowable Base mesh size 0.5
- Hence base mesh size is set to 0.5 m
- Fixed embedding is enabled on ahmed body boundary with a scale of 6 and 5 layers
- Also rear side of the geometry is also refined using fixed embedding in order to make the values there more accurate so that it can be compared with the experimental data
- Wall output is selected to extract the lift and drag values








Outputs
- Velocity contour




- Y-plus

Observations
- The y-plus average values higher and hence the solutions are less accurate
- Inorder to obtain high accuracy the values must be smaller so as to capture the viscous sublayer
- The velocity contours defines the wake regions at the rear
Calculations using paraview
- Drag force and lift forces can be extracted from the paraview and Coefficient of drag and lift can be found using the calculator in paraview
- For extracting these forces firstly ahmbed body block is extracted and then the surface is extratcted following generating surface normals
- Calculator is turned on and then in scalars pressure and normals x is multiplied inorder to get drag force, For lift force pressure is multiplied with normals z

- Now inorder to find the Coefficient of drag we need to have frontal area which is opposing the flow, This area can be extracet from paraview.


Fd = 29.221 N
Cd = 2*29.221/(1.225*0.0166133*40^2) = 1.8
For coefficient of lift,

L = -105.26
S = 1.044*0.389 = 0.406
`C_L` = (2*-105.26)/(1.225*0.406*40^2) = -0.264
Validation
- For validation an experimental data is used to compare the extracted simulation data
- Datas are the variation of velocity at x-direction at different locations of z-directions
- eight points were used and these eight points lie at different locations of x
- The experimantal and simulated values are put together in the same excel sheet and is plotted both in the same graph
Point 1 , X = -13 mm

Point 2 , X = -263 mm

Point 3 , X = 37 mm

Point 4 , X = 87 mm

Point 5 , X = -113 mm

Point 6 , X = 63 mm

Point 7 , X = 187 mm

Point 8 , X = 137 mm

Observations
- As stated earlier the simulation data and experimented data does not match at some points and this is mainly due the coarse mesh provided
- Although the results look pretty good and the curves almost follows the same slope
- For validation we need the difference between the experimental values and the simulated values under 5% but in my case due the low computational resources the solutions are less accurate
Normalisation
- Done to visualise the change in simulation data and experimental data
- The data is calculated using the datas from each x locationscand then the differences are observed
- It is first normalised and the multiplied with an amplification factor
- It helps in determining the deviations of the simulated data from the experimented data
- The experimental data curve is coloured in black

% 1st point
x_13 = [186 -1.805 186 -4.6827
188 -1.98 186.5 -4.6827
193 -2.496 187 -4.6827
198 -2.972 187.51 -4.6827
203 -3.171 188.01 -4.6827
208 -3.537 188.51 -4.6827
213 -3.793 189.01 -4.6827
218 -4.082 189.51 -4.6827
223 -4.328 190.02 -4.6827
228 -4.455 190.52 -4.6827
233 -4.489 191.02 -4.6827
238 -4.213 191.52 -4.6827
243 -3.4 192.02 -4.6827
248 -1.505 192.53 -4.6827
253 1.595 193.03 -4.6827
258 5.916 193.53 -4.6827
263 11.234 194.03 -4.5647
268 16.528 194.53 -4.5647
273 22.544 195.04 -4.5647
278 28.866 195.54 -4.5647
288 39.688 196.04 -4.5647
298 43.742 196.54 -4.5647
308 43.892 197.04 -4.5647
318 43.753 197.55 -4.5647
328 43.61 198.05 -4.5647
338 43.484 198.55 -4.5647
358 43.212 199.05 -4.5647
378 43.004 199.55 -4.5647
408 42.692 200.06 -4.5647
438 42.398 200.56 -4.5647
468 42.15 201.06 -4.5647
508 41.865 201.56 -4.5647
548 41.606 202.06 -4.357
588 41.553 202.57 -4.357
638 41.482 203.07 -4.357
688 41.316 203.57 -4.357
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0 0 536.4 43.22
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0 0 537.9 43.178
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0 0 569.03 42.832
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0 0 584.59 42.851
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0 0 586.09 42.851
0 0 586.6 42.851
0 0 587.1 42.851
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0 0 588.1 42.851
0 0 588.6 42.851
0 0 589.11 42.851
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0 0 591.11 42.851
0 0 591.62 42.851
0 0 592.12 42.851
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0 0 593.62 42.851
0 0 594.13 42.851
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0 0 596.64 42.851
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0 0 599.15 42.851
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0 0 600.15 42.939
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0 0 686.49 42.432
0 0 687 42.432
0 0 687.5 42.432
0 0 688 42.432
]
% 2nd point
x_263 = [313 42.904 313 44.836
318 42.894 313.37 44.836
328 42.831 313.75 44.836
338 42.77 314.13 44.836
348 42.747 314.5 44.836
358 42.699 314.88 44.836
378 42.601 315.25 44.836
408 42.494 315.63 44.836
438 42.34 316 44.836
468 42.187 316.37 44.836
508 41.964 316.75 44.836
548 41.771 317.12 44.836
588 41.701 317.5 44.836
638 41.663 317.87 44.836
688 41.477 318.25 44.836
0 0 318.63 44.836
0 0 319 46.074
0 0 319.38 46.074
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0 0 323.13 46.074
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0 0 365.13 47.021
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0 0 365.88 46.866
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0 0 379 46.866
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0 0 394 46.93
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0 0 397 46.573
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0 0 416.88 46.355
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0 0 422.13 46.355
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0 0 423.25 46.355
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0 0 426.25 46.355
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0 0 427.37 46.355
0 0 427.75 46.355
0 0 428.12 46.355
0 0 428.5 45.76
0 0 428.87 45.76
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0 0 436 45.76
0 0 436.37 45.76
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0 0 442.75 45.76
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0 0 445.75 45.322
0 0 446.13 45.322
0 0 446.5 45.322
0 0 446.88 45.322
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]
% 3rd point
x_37 = [-22 43.102 -22 34.738
-12 37.219 -21.29 34.738
-2 14.176 -20.58 34.738
8 -6.139 -19.87 34.738
18 -7.4 -19.16 34.738
28 -7.706 -18.45 34.738
38 -7.687 -17.74 34.738
48 -7.641 -17.03 29.875
58 -7.589 -16.32 29.875
68 -7.457 -15.61 29.875
78 -7.055 -14.9 29.875
88 -6.755 -14.19 29.875
98 -6.284 -13.48 29.875
108 -5.819 -12.77 29.875
118 -5.221 -12.06 29.875
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178 -1.802 -7.8 21.95
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198 -0.709 -6.38 21.95
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248 9.118 -2.83 21.95
258 15.708 -2.12 21.95
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278 35.061 -0.7 7.8537
288 42.402 1.00E-02 7.8537
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0 0 553.81 42.08
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0 0 688 41.807
]
% 5th point
x_113 = [256 -2.858 256 5.7163
258 -2.967 256.43 12.012
263 -3.021 256.86 12.012
268 -2.596 257.3 12.012
273 1.796 257.73 12.012
278 11.262 258.16 12.012
283 23.088 258.59 12.012
288 34.692 259.02 12.012
298 42.333 259.46 12.012
308 44.254 259.89 12.012
318 44.098 260.32 12.012
328 43.928 260.75 12.012
338 43.771 261.18 12.012
358 43.481 261.62 12.012
378 43.208 262.05 12.012
408 42.924 262.48 12.012
438 42.593 262.91 12.012
468 42.343 263.34 12.012
508 42.032 263.78 12.012
548 41.776 264.21 21.221
588 41.698 264.64 21.221
638 41.621 265.07 21.221
688 41.425 265.5 21.221
0 0 265.94 21.221
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]
% 6th point
x_63 = [221 -1.897 221 -3.8234
223 -2.396 221.47 -3.8234
228 -3.507 221.93 -3.8234
233 -4.319 222.4 -3.8234
238 -4.957 222.87 -3.8234
243 -5.287 223.33 -3.8234
248 -5.313 223.8 -3.8234
253 -4.575 224.27 -3.8234
258 -2.771 224.74 -3.8234
263 1.409 225.2 -2.9233
268 7.689 225.67 -2.9233
273 14.498 226.14 -2.9233
278 21.978 226.6 -2.9233
288 37.297 227.07 -2.9233
298 43.33 227.54 -2.9233
308 44.19 228.01 -2.9233
318 44.005 228.47 -2.9233
328 43.857 228.94 -2.9233
338 43.702 229.41 -2.9233
358 43.404 229.87 -2.9233
378 43.183 230.34 -2.9233
408 42.868 230.81 -2.9233
438 42.532 231.27 -2.9233
468 42.283 231.74 -2.9233
508 41.989 232.21 -2.9233
548 41.718 232.68 -2.9233
588 41.642 233.14 -1.4334
638 41.569 233.61 -1.4334
688 41.385 234.08 -1.4334
0 0 234.54 -1.4334
0 0 235.01 -1.4334
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0 0 271.9 39.215
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0 0 287.78 40.399
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0 0 303.19 41.695
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0 0 319.07 43.328
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0 0 320 43.328
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% 7th point
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]
% Normalisation
Amp = 5 % amplification factor
%point 1 x = -13
%experimental
z_13_exp = x_13(:,1);
u_13_exp = x_13(:,2);
u_norm_13 = Amp.*(u_13_exp./(max(u_13_exp)));
x1 = (-13) - (u_norm_13);
%simulated
z_13_sim = x_13(:,3);
u_13_sim = x_13(:,4);
u_norm_13_s = Amp.*(u_13_sim./(max(u_13_sim)));
x1_s = (-13) - (u_norm_13_s);
%point 2 x = -263
%experimented
z_263_exp = x_263(:,1);
u_263_exp = x_263(:,2);
u_norm_263 = Amp.*(u_263_exp./(max(u_263_exp)));
x2 = (-263) - (u_norm_263);
%Simulated
z_263_sim = x_263(:,3);
u_263_sim = x_263(:,4);
u_norm_263_s = Amp.*(u_263_sim./(max(u_263_sim)));
x2_s = (-263) - (u_norm_263_s);
%point 3 x = 37
%experimented
z_37_exp = x_37(:,1);
u_37_exp = x_37(:,2);
u_norm_37 = Amp.*(u_37_exp./(max(u_37_exp)));
x3 = (37) - (u_norm_37);
%Simulated
z_37_sim = x_37(:,3);
u_37_sim = x_37(:,4);
u_norm_37_s = Amp.*(u_37_sim./(max(u_37_sim)));
x3_s = (37) - (u_norm_37_s);
%point 4 x = 87
%experimented
z_87_exp = x_87(:,1);
u_87_exp = x_87(:,2);
u_norm_87 = Amp.*(u_87_exp./(max(u_87_exp)));
x4 = (87) - (u_norm_87);
%Simulated
z_87_sim = x_87(:,3);
u_87_sim = x_87(:,4);
u_norm_87_s = Amp.*(u_87_sim./(max(u_87_sim)));
x4_s = (87) - (u_norm_87_s);
%point 5 x = -113
%experimented
z_113_exp = x_113(:,1);
u_113_exp = x_113(:,2);
u_norm_113 = Amp.*(u_113_exp./(max(u_113_exp)));
x5 = (-113) - (u_norm_113);
%Simulated
z_113_sim = x_113(:,3);
u_113_sim = x_113(:,4);
u_norm_113_s = Amp.*(u_113_sim./(max(u_113_sim)));
x5_s = (-113) - (u_norm_113_s);
%point 6 x = -63
%experimented
z_63_exp = x_63(:,1);
u_63_exp = x_63(:,2);
u_norm_63 = Amp.*(u_63_exp./(max(u_63_exp)));
x6 = (-63) - (u_norm_63);
%Simulated
z_63_sim = x_63(:,3);
u_63_sim = x_63(:,4);
u_norm_63_s = Amp.*(u_63_sim./(max(u_63_sim)));
x6_s = (-63) - (u_norm_63_s);
%point 7 x = 187
%experimented
z_187_exp = x_187(:,1);
u_187_exp = x_187(:,2);
u_norm_187 = Amp.*(u_187_exp./(max(u_187_exp)));
x7 = (187) - (u_norm_87);
%Simulated
z_187_sim = x_187(:,3);
u_187_sim = x_187(:,4);
u_norm_187_s = Amp.*(u_187_sim./(max(u_187_sim)));
x7_s = (187) - (u_norm_187_s);
%point 8 x = 137
%experimented
z_137_exp = x_137(:,1);
u_137_exp = x_137(:,2);
u_norm_137 = Amp.*(u_137_exp./(max(u_137_exp)));
x8 = (137) - (u_norm_137);
%Simulated
z_137_sim = x_137(:,3);
u_137_sim = x_137(:,4);
u_norm_137_s = Amp.*(u_137_sim./(max(u_137_sim)));
x8_s = (137) - (u_norm_137_s);
%plot point 1
plot(x1,z_13_exp,'k');
hold on
plot(x1_s,z_13_sim);
%plot point 2
hold on
plot(x2,z_263_exp,'k');
hold on
plot(x2_s,z_263_sim);
%plot point 3
hold on
plot(x3,z_37_exp,'k');
hold on
plot(x3_s,z_37_sim);
%plot point 4
hold on
plot(x4,z_87_exp,'k');
hold on
plot(x4_s,z_87_sim);
%plot point 5
hold on
plot(x5,z_113_exp,'k');
hold on
plot(x5_s,z_113_sim);
%plot point 6
hold on
plot(x6,z_63_exp,'k');
hold on
plot(x6_s,z_63_sim);
%plot point 7
hold on
plot(x7,z_187_exp,'k');
hold on
plot(x7_s,z_187_sim);
%plot point 8
hold on
plot(x8,z_137_exp,'k');
hold on
plot(x8_s,z_137_sim);
Conclusions
- Created the cad model
- Simulated external flow over Ahmed body through transient simulation
- Post processed and extracted Drag and lift force values
- Extracted velocity contours
- Validated with experimental data by visualising the variation of velocity in x direction at different z locations