Ahmed Body Challenge

For this challenge, you will have to provide answers to the following questions:

Q1. Describe Ahmed's body and its importance.

Q2. Explain the reason for the negative pressure in the wake region.

Q3. Explain the significance of the point of separation.

Ahmed body is a general car body which captures essential car body features which was firstly described experimentally by Ahmed [1]. Its a simple shape yet efficient to capture the aerodynamic features of automobile. The essential need of doing such simulation is to know the effect of drag which is one of the important parameter for efficient and smooth driving experience. The lower the drag forces the lower the fuel consumption and better the performance.

The rear part of the vehicle has a significant role in manipulating the drag forces. The Ahmed body is shown in figure 1. It has been observed that the slant angle ( ∅ ) greatly affects the drag results. This is majorly due to flow of seperation. Seperation of flow means that the flow instead of being attached or parallel to the surface gets detached from the surface and generates turbulence (by pressure gradient) which creates turbulent friction and hence creates drag force.

Step 1 :- Geometry and enclosure fomation

The dimesnions of the Ahmed body is as shown in figure. For analysis purpose the ahmed body is split into half in order to limit the number of elements during meshing and faster computation.The width of the body is 0.1945 m.

• An enclosure was generated aroud the ahmed body . Two different enclosures as shown in figure were generated. The purpose of the inner enclosure is to locally refine the meshing so that the elements count remain low and better results can be obtained. It is generally called as local refinement. The dimension of the enclosure is mentioned below.

Step 2 :- Meshing

• For meshing the outer enclosure was meshed with multizone method to get perfect hexa elements and the inner enclosure was meshed with tetra elements. The face of the ahmed body was then locally meshed to get better element quality. Four different meshing were generated in order to perform the grid independency test.
• The boundary layer becomes important for such flows and hence in ordwer to capture the physics the inflation layer were given. The parameters of the meshing independece test are given in the table.

Cases	Description	Primary mesh size (mm)	Local refined mesh size (mm)	Ahmed body mesh size (mm)	Wheel mesh size (mm)	Inflation layer	Growth Rate	Total thickness (mm)	Min mesh quality	Avg mesh quality	Total nodes	Total elements
Case A	Coarse Mesh with k Epsilon model & y+ = 300	120	80	15	10	6	1.2	10	0.137677527	0.754400827	42673	125816
Case B	Intermediate mesh with k Epsilon model & y+ = 300	100	70	12	10	6	1.2	10	0.127368705	0.770585913	71028	220825
Case C	Fine mesh with k Epsilon model & y+ = 300	80	60	10	8	6	1.2	10	0.154652863	0.780996502	102472	304076
Case D	Fine mesh with k Epsilon model & y+ = 300	60	50	8	6	6	1.2	10	0.139473029	0.788510064	168026	480383
Case E	Coarse Mesh with k Epsilon model & y+ = 200	120	80	15	10	6	1.2	7	0.16114727	0.755929095	43460	130311
Case F	Intermediate mesh with k Epsilon model & y+ = 200	100	70	12	10	6	1.2	7	0.164583632	0.769956141	72611	230253
Case G	Fine mesh with k Epsilon model & y+ = 200	80	60	10	8	6	1.2	7	0.166350841	0.781105117	104845	318084
Case H	Fine mesh with k Epsilon model & y+ = 200	60	50	8	6	6	1.2	7	0.158934985	0.789437863	172471	506654

• In every case it was ensured that the minimum orthogonal quality of the mesh was higher than 0.1 and total elements were less than 5,12,000 since student version had this limitation.

Step 3 :- Solving.

• The solving processor were mainly default setting with minor changes to it. Pressure based solver was used since the MACH number was 0.073 ( speed of body to speed of sound i.e 25/340 for this case).

The input datas are mentioned in the table and the reference values are shown in figure.

Solver	Inlet Velocity (m/s)	Outlet gauge pressure (Pa)	Material	Density (kg/m^3)	Dynamic Viscosity(kg.m/s)
Pressure based solver with realizable k epsilon model with coupled algorithm and hybrid initilization	25	0	Air	1.225	1.7894e-5

Reference values are extremely important while calculating the drag and lift coefficient.

Area was the frontal area of the ahmed body which is the height * width= 0.29*0.1945 = 0.0564 mm, Length was the total ahmed body length which is 1.044 m.

The velocity was then changed to 25 m/s.

• The required output were Drag coefficient and lift coefficient . The convergence criteria was not kept limited to any values so that the iterations won't stop even after reaching minimum default values.
• In order to calculate the y+ value which plays a major role in capturing the boundary layer details here, following calculations were done and the total thickness was calculated.

• Toatl 6 layers were taken with Growth rate of 1.2 which gave a total thickness of 7 mm. (1.2^(6-1) * 0.00436). Note here y* is the thickness of the first layer which has to be captured. Hence an inflation layer with the above mentioned parameters were given. A lower growth rate was giving rise to lesser nodes but the orthogonal quality was affected hence the growth rate was limited to 1.2.
• Based on the above mentioned physics and boundary conditions applied the solution was obtained.

Step 4 :- Results and Post processing

Case A:- Coarse Mesh (1.2 lakh) with k Epsilon model & y+ = 300

Case B:- Intermediate Mesh (2.2 lakh) with k Epsilon model & y+ = 300

Case C:- Fine Mesh (3.0 lakh) with k Epsilon model & y+ = 300

Case D:-Fine Mesh (4.8 lakh) with k Epsilon model & y+ = 300

Case E:- Coarse Mesh (1.2 lakh) with k Epsilon model & y+ = 200

Case F:- Intermediate Mesh (2.3 lakh) with k Epsilon model & y+ = 200

Case G:- Fine Mesh (3.3 lakh) with k Epsilon model & y+ = 200

Case H:- Fine Mesh (5 lakh) with k Epsilon model & y+ = 200

Cases	Description	Drag Coefficient	Lift Coefficient	Error percentage
Case A	Coarse Mesh with k Epsilon model & y+ = 300	0.35935685	0.30164448	8.896015152
Case B	Intermediate mesh with k Epsilon model & y+ = 300	0.3502	0.30538938	6.121212121
Case C	Fine mesh with k Epsilon model & y+ = 300	0.33549993	0.28249514	1.666645455
Case D	Fine mesh with k Epsilon model & y+ = 300	0.31735634	0.28797621	3.831412121
Case E	Coarse Mesh with k Epsilon model & y+ = 200	0.35163485	0.3138578	6.556015152
Case F	Intermediate mesh with k Epsilon model & y+ = 200	0.34329022	0.30230387	4.027339394
Case G	Fine mesh with k Epsilon model & y+ = 200	0.32956883	0.29699846	0.130657576
Case H	Fine mesh with k Epsilon model & y+ = 200	0.3250308	0.27277282	1.505818182

Discussion:-

• As seen from the figures and tables the iterations required to converge the data were approximately 200 to 250 for most of the cases.
• The drag coefficent was found to be reducing and approaching expected value with finer mesh size.
• An important conclusion can be seen that with reduction in the y+ value the error percentage was reducing and the values were closely approaching towards the expected value. However the residual plots shows that it may take some more iterations to converge .
• In order to analyze the results better the post processing was done which shows the contour of velocity and pressure.

POST PROCESSING PRESSURE AND VELOCITY CONTOURS:-

Figure :- Comparision of the result with the literature [2] result indicating the effect of slant angle on back pressure

DISCUSSION:-

• As it can be seen that the negative pressure region is created at the region where sharp or smooth change in shape can be seen. When the fluid flows over the body the shearing starts occuring at the surface and due to which there comes a point where the boundary layer seperates which is called the transition region to turbulent from the laminar region.
• This seperation of the boundary layer creates a pressure gradient which results into eddy velocities or a region of negative pressure. The slant angle plays a major role in this phenomena . With increase in the slant angle (i.e it starts becoming vertical) the point of seperation of the boundary layer increases which results into formation of higher eddies and negative pressure. This results in increase in drag forces.
• As mentioned by H. Lienhart [2] it can be seen from the figure that with increase in the slant angle the back velocity or the region of negative pressure is created which increases as per the above mentioned effect.
• A better understanding can be seen from here.
• https://www.youtube.com/watch?v=SiOiVHUEYao
• The generation of the vortices for CASE 3 can also be seen from the figure.This kind of similar vortices were observed for all the cases .

References:-

[1]Ahmed, S. R., et al. “Some Salient Features of the Time -Averaged Ground Vehicle Wake.” SAE Transactions, vol. 93, 1984, pp. 473–503. JSTOR, www.jstor.org/stable/44434262. Accessed 17 May 2020.

[2] Lienhart, H., Stoots, C. and Becker, S., 2002. Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Modell). New Results in Numerical and Experimental Fluid Mechanics III, pp.323-330.