Ahmed Body Challenge

Objective:

1. Significance of a Ahmed Body.
2. To simulate the Ahmed Body and calculate the lift and drag coefficients and perform the grid impedence test.

Introduction:

Importance of Ahmed Body:

Ahmed Body is a benchmark model widely used in the automotive industry for validating the simulation tools. The ahmed body shape is simple enough to model with the car like geometry features. The Ahmed Body was first created by S.R. Ahmed in his research “Some Salient Features of the Time-Averaged Ground Vehicle Wake” in 1984. Since then, it has become a benchmark for aerodynamic simulation tools. The simple geometrical shape has a length of 1.044 meters, height of 0.288 meters, and a width of 0.389 meters. It also has 0.5-meter cylindrical legs attached to the bottom of the body and the rear surface has a slant that falls off at 40 degrees.

During the air flow in the car, There are basically two regions created during the air flow over any car or ahmed body:

1. High pressure under the vehicle
2. Low pressure on the top

When the air flows over the body, at the rear end of the vehicle the two pressure zones collide with each other and at the rear ends of the vehicle the thus resulting in the formation of the vortex at the rear end of the body which result in the negative the direction of the air flow. These vortexes result in the drag force formation and thus the car engine has to compensate these losses as the result of drag.

In the automotive industries, the main goal is to reduce the drag, preventing the unwanted lift and other instabilities that can occour at the high speeds. To reduce the drag forces the shape of the body is made more streamilned and aerodynamic to prevent the aerodynamic drag.

Methodology:

1. Modeling of Ahmed Body
2. Setting up Body
3. Meshing
4. Preprocessing and Boundary Conditions
5. Post Processing

Modeling of Ahmed Body

The Ahmed Body is first modeled in any CAD Software (i prefer Solidworks) according to the dimensions shown below:

After modeling of the body rthe body can be exported into any readable format for ANSYS Spaceclaim such as stp, igs, x_t, etc.

Setting Up Body

After modeling the body it is then imported in ANSYS Spaceclaim where the fluid domain for the body is then prepared using the enclosure command and the dimensions for the enclosure command can be seen below:

As our body is symmetric from the center plain we will split the body into half as it would decrease the number of elements and also save our computational time and resources. For splitting the body the split command will be used and from the center plane the body will be split into two and the one half of the body will be deleted or removed. The split body can be seen below:

Meshing

Once we are done with setting up our body we will import the geometry into ANSYS meshing module for the meshing. We will forst start with the baseline meshing to check the wake region generated in the body for this body and accordingly in that region we could define our mesh.

For baseline meshing we will be using the default settings provided by the mesh module and we will simply generate the mesh. The base line generated mesh can be seen below:

Once the mesh is generated we will create the named selection and name the different boundaries as front of enclosure as inlet, back of enclosure as outlet, base of enclosure as wall and the side walls will be given as symmetry boundary condition such that the symmetry is maintained in the half cut body. The rest of the faces of the car will be named as the car wall.

Preprocessing and Boundary Conditions:

For the fluent we will be using the density based solver because the velocity with which we will be working is 25m/s which is almost 7% of the velocity of sound. So while working with such high speeds the commpressibity has to be taken in consideration. Apart from that we will turn on the energy equation to monitor the change in temperature and we will working with the turbulence model .i.e. k-epsilon model with standard wall function. After setting up the basic physics we will check for the domain given to zone should be fluid and teh material is air. After that we will setup the bounday conditions giving the inlet boundary as velocity inlet with the temperature of 25m/s and the temperature of 300K at the inlet. We will set outlet as the pressure outlet with the output of zero gauge pressure. We will set the side walls to the symmetry boundary condition and all the walls are set to noslip boundary condition. After that we will set up the drag and lift monitors on the car wal and start solving the solution under the hybrin initialisation to give the initial values for the solver. Further then the solver is solved for about 1000 iterations.

After 1000 iterations the residuals plot can be seen below:

Here the stable residuals around the value of 1e-3 can be seen thus concluding that the solution has converged. Further we can check the drag and lift plots over the car wall can be seen below:

The constant steady state drag value of 0.22 can be seen in this body further the lift plot can be observed below:

The lift coefficient over the body can be 0.15.

The velocity contour can be seen below:

The pressure contour can be seen below:

The vector plot can be seen below for the velocity profile over the car body:

The velocity along the lines shown in velocity plot can be seen below:

In the velocity contour the boundary layer formation is low and low mixing can be seen near the car wall boundary can be seen, thus a much finer mesh is required near the car wall to study the wake region and the formation of the negative velocity in the wake region. Thus a redefined mesh will be created to observe and study the wake region for the ahmed body.

Case 2 Refining the mesh:

In this case we will make two enclosures and refine the mesh accordingily in the inner enclosure such that the number of elements remain less in the body and we could accuratly capture the wake region in the body and get the exzct values of lift and drag coefficient. The enclosures can be seen below:

The two enclosures are first defined and the inner enclosure is then subtracted from the outer enclosure using the interference command and the enclosures are set to the share topology such that the physical quantities is shared between the enclosures. As the body is symmetric we split the body into two along the mid plane to study it while reducing the number of elements as well as the computational resources.

Meshing

After preparing the body we open the mesh module of the fluent and create the meshing as shown:

In the outer enclosure we change the mesh method to the multizone such that the quaddominant mesh is created in the outer zone. The quaddominant method should be used wherever possible because they are in shape of square and they are simpler and better to solve along both the axis while sharing the data. Further in the inner enclosure the mesh sizing was set as 60mm as it is the wake region so the mesh needed to be refined so that the boundary layer could be captured accurately. Also the mesh at the boundary can be seen sharing properly due to the share topology command. Further for the legs of the ahmed body the face sizing was given as 3mm because they need to be considered fine in sizing or they will take the shape of a polygon thus changing the shape and results of the simulation.

Apart from the face sizing we provide the inflation layer for the car wall and legs. For provinding the inflation layer we use the y+ value of 100 because we are using teh k epsilon method with standard wall function in which we solve for the turbulent layer where we could use the value in between 30-300. So for the y+ of 100 we get the first layer sizing of 1.4 mm and can be seen below:

The inflation layer and the face sizing for the legs can be seen below:

Further the mesh quality can be seen for the above mesh below:

Here we can se that the tetrahedral have achieved the best mesh quality and the maximum number of mesh elements around have 85% of the quality. Futher the number of elements for this mesh are 95530 and the number of nodes are 34311 which are quite low with this mesh and this is due to splitting the body into the half and using the symmetry boundary condition.

Setting up Physics

Further after meshing we will open fluent setup and start setting up the physics after checking the mesh. We will be using the density based solver for this program as explained above apart from this we will be using energy equation to monitor temperature and k epsilon method with standard wall function. Further the both enclosure zones will be checked weather they are set as fluid and set teh material as air with the properties shown below:

Further the boundary conditions were set as

1. Inlet (velocity Inlet at 25m/s and 300k)
2. Outlet (Pressure Outlet at 0gauge pressure)
3. Top and Side Walls (Symmetry)
4. Bottom (wall)
5. Car Body (car wall)

After setting these boundary conditions the solution was initialised under hybrid initialisation and wsa solved for 2200 iterations. The residuals plots and other results can be seen below:

1. Residuals

2. Velocity Contour

3. Lift Coefficient Plot

The average coefficient of lift is about 0.16

4. Drag Coefficient Plot

The average coefficient of drag is about 0.225

Further in the ANSYS post processing the following results were taken:

1. Velocity Contour

2. Pressure Plot

3. Vector Representation of velocity:

4. Velocity plot along the line

Conclusions:

1. The solution converged at about 1200 iterations.
2. Here in this case the bottom wall was defined as the no slip boundary condition so that the velocity at the bottom wall van be seen zero. Further the velocity can be seen very low under the Ahmed body this is due to the boundary layer phenomenon and the viscosity of the air.
3. The coefficient of lift is about 0.16 whereas the coefficient of drag comes out to be 0.225 (about 30% of the error).
4. In the vector plot for the velocity the velocity can be seen dropping behind the body and can even be seen in the negative direction. the region o fthe negative velocity and pressure is called as the wake region.
5. In the velocity plot along the line as shown in the baseline mesh the velocity can be seen first increasing then decreasing this id due to the velocity in the wake region and negative velocity in wake region. Further when we move the line away from the body we cannot see the negative velocity in the wake region.

Grid Independence Test

After finding the results we will recheck the results again by refining the mesh and using the lower values of y+.

Refine 1:

1. Multizone and quadominant elements.

For the multizone and quadominant method the mesh size was reduced to 80mm. and can be seen below:

2. Tetrahedral elements

For the tetrahedral elements the mesh size was reduced to 50mm and teh face sizing was reduced to 2mm. Further the y+ was also reduced to 80 and teh inflation size was further changed and can be seen below:

Y+ value

Inflation Size:

Face Sizing:

Mesh Quality:

Further the boundaries were given the named selection as in the above cases and the boundary conditions were given the same as in the above cases. The mesh quality can be seen that it is maximum at about 85% and the maximum number of elements are good quality. Further residuals velocity lift and drag plots can be seen below:

1.Residuals

2. Velocity Plot

3. Drag

The average value of drag is about 0.225

4. Lift

The average value of lift is about 0.165

Post-Processing

1. Velocity Plot

2. Pressure Plot

3.Vector plot for Velocity

4. The velocity plot along the line as shown in baseline mesh can be seen below:

2.Refine 2

1. Multizone and quadominant elements.

For the multizone and quadominant method the mesh size was reduced to 70mm and can be seen below:

2. Tetrahedral elements

For the tetrahedral elements the mesh size was reduced to 40mm and the face sizing was reduced to 1mm. Further the y+ was also reduced to 70 and the inflation size was further changed and can be seen below:

Y+ value

Inflation Size:

Face Sizing:

Mesh Quality:

Further the boundaries were given the named selection as in the above cases and the boundary conditions were given the same as in the above cases. The mesh quality can be seen that it is maximum at about 85% and the maximum number of elements are good quality. The number elements are 421287 and the number of nodes are 145439. Further residuals velocity lift and drag plots can be seen below:

1.Residuals

2. Velocity Plot

3. Drag

The average value of drag is about 0.225

4. Lift

The average value of lift is about 0.165

Post-Processing

1. Velocity Plot

2. Pressure Plot

3.Vector plot for Velocity

4. The velocity plot along the line as shown in baseline mesh can be seen below:

The observations made from the above refinement can be seen in the tabulated form below:

	Main Case	Refinement 1	Refinement 2
Enclosure 1 element size	100	80	70
Enclosure 2 element size	60	50	40
Leg Sizing	3	2	1
Y+	100	80	70
Inflation Layers	5	5	5
Nodes	34311	59656	145439
Elements	95530	168201	421287
Coefficient of Lift	0.15	0.165	0.165
Coefficient of Drag	0.22	0.225	0.225

Explainantion

Negative Pressure in wake Region

Theoritically when the velocity is high the pressure is very low but in the case of Ahmed Body the pressure is high enough to detach layer from the body and the velocity and the shear stress becomes zero thus resulting in creation of vorteces in the region thus resulting in the wake region. There is negative velocity gradient and shear stress due to the negative flow circulation which results in high turbulent flow as shown in velocity vector plot. As fluid moves in negative direction in the high pressure gradient it results in low pressure region in wake region resulting in drag force.

Point of seperation

The point of seperation in the turbulent flow is reffered to as the point from which the boundary layer starts to seperate from the surface in the external flow problem. Due to teh increasing frictional forces the velocity and the shear stress starts decreasing and the pressure starts increasing. When the fluid flows through high pressure gradient along the boundary layer the velocity along the boundary layer starts to slow down and reverse its direction. The point at which the velocity along the boundary layer becomes zero and starts to reverse its direction is known as the point of seperation. The point of seperation can be seen in the figure below:

Conclusions:

1. Ahmed Body is used as an automative proptotype used to calibrate the simulation tools from the experimental data thus to run the simulation on the complex structures.
2. Mesh refinement plays a major rols in the results and thus gives the close results in drag and lift plots. Further the mesh refinment should be justified as the finer mesh require more computational resources and time.
3. A proper model for solvingfg the problem should be used according to the expected output results. The Y+ values should also be chosen accordingly. Changing the values of y+ in the admirable range can lead to the much accurate results.
4. The rise in negative pressure in the wake regions gives rise to the drag forces generated in the body.