Week 3 - External flow simulation over an Ahmed body.

AHMED BODY SIMULATION

 

Introduction 

As the burning of fossil fuels and conventional resources of energy becomes an issue of great importance, manufacturers are focusing on the introduction of more fuel efficient cars in the market. When a car is in motion, the aerodynamic drag on the car is the main contributor to the fuel burn. Complexly shaped, cars are very challenging to model and it’s difficult to quantify the aerodynamic drag computationally. The Ahmed body is a benchmark model widely used in the automotive industry for validating simulation tools. The Ahmed body shape is simple enough to model, while maintaining car-like geometry features.

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 Ahmed.
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 different angles depending on the requirements of the simulation (40, 30, 25 degrees).
The flow for this model is turbulent, which is based on the Reynolds number determined by the body length and inlet velocity.

Importance of Ahmed Body

Although it has a very simple shape, Ahmed body helps 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 in validated, it is used to design new models of the car. 
The drag coefficient (Cd) quantifies the resistance of an object in a fluid environment. It is not an absolute constant for a body’s shape because it varies with the speed and direction of flow, object shape and size, and the density and viscosity of the fluid. The lower the drag coefficient of an object, the less aerodynamic or hydrodynamic drag occurs. In terms of a car, the lower the drag coefficient, the more efficient the car is. As well as affecting the top speed of a vehicle, the drag coefficient also affects the handling. Cars with a low drag coefficient are sought after, but decreasing the drag drastically can reduce the downforce and lead to loss in road traction and a higher chance of car accidents. 
Thus, it is important to analyze and predict the drag coefficient and various other parameters for better performance and handling of the car.

For the above mentioned reasons, an Ahmed body simulation is important and may be looked at as the first step in aerodynamic analysis of a car, as it has a simplified shape which makes it easier to capture the salient features of aerodynamic flow around an automobile.

 

Objectives

The main objective of this project is to validate the following parameters of aerodynamic flow for an Ahmed body

- Drag coefficient

- Aerodynamic drag

-Velocity and pressure profile

-Vector plots of velocity

 

Baseline simulation

A baseline simulation was conducted using a simply generated mesh to check if the setup was accurate.

Geometry

The entire Ahmed body was considered for the baseline simulation, as the cell count of the mesh was fairly low.

Length - 1.04m

Height - 0.34m

Width - 0.39m

 

   

Meshing

A basic mesh was generated to determine whether the physics was being captured accurately and expected results were obtained. There were no refinement zones or meshing methods used in this meshing process. 

 

Setup

The k-epsilon model with standard wall functions was used to conduct this simulation. 
Inlet velocity was set to be 25m/s. Thus, due to a low Mach number of 0.07, a pressure based solver was used for neglecting compressibility effects of air.
Outlet was set to be a pressure outlet with 0 pascal gauge pressure. The fluid used was air, having standard properties.

 

 

Results

 

Desirable results were obtained and physics was captured as expected. Thus, we can refine the mesh and carry on the simulation to further determine the values of drag and lift coefficient.

 

 

Simulation after refining the mesh

Geometry

Since the body was symmetric about the XY plane, it was split in half about the plane using the split command in SpaceClaim. This was done to reduce the cell count of the mesh and get faster results. Only half of the Ahmed body was considered for the further simulations due to its symmetry. 
For refinement of the mesh, in addition to the main enclosure for fluid flow, another inner enclosure was made to capture the physics around the Ahmed body as accurately as possible. Share topology was also enabled to keep the mesh from both the enclosures consistent with each other.

  

 

Meshing

Different meshing methods were used to optimize the mesh and keep the cell count to minimum, at the same time, also high enough to capture the physics accurately.

 

Minimum mesh quality is more than 5% with most of the cells in the range of 40-100%.
Thus, mesh quality is acceptable.

 

The different methods used were: 

Multizone

Body Sizing - 30mm

Face Sizing 1 - 10mm

Face Sizing 2 - 

Inflation -

5 inflation layers were used around the Ahmed body. The thickness of these layers were controlled using only the First Layer Thickness, with a growth rate of 1.2.

The thickness of the first layer depends on the value of y+.
Since the k-epsilon turbulent model with standard wall functions was used in this simulation, the y+ value would vary between 30 - 300.
Thus, 3 different values of y+ were considered and the drag coefficient was monitored to chose the most approximately accurate value, that gave the least error as compared to the validated results.

Case 1: y+ 70

 

Case 2: y+ 100

 

Case 3: y+ 250

 

Setup

The setup in these simulations was same as that of the baseline simulation. The wall along the cut-plane was now given symmetry boundary condition.

Results

Case 1: y+ 70

Drag and drag co-efficient

 

Lift and lift coefficient

 

Pressure contour on Ahmed body

 

Velocity contour XY Plane -1 (Coinciding with origin)

Pressure contour XY Plane -1 (Coinciding with origin)

Velocity contour XY Plane -2 (Cutting through legs of Ahmed Body)

Vector plot XY Plane -1

Vector plot YZ Plane (Behind the Ahmed Body)

 

Case 2: y+ 100

Drag and drag co-efficient

 

Lift and lift coefficient

 

Pressure contour on Ahmed body

 

Velocity contour XY Plane -1 (Coinciding with origin)

Pressure contour XY Plane -1 (Coinciding with origin)

Velocity contour XY Plane -2 (Cutting through legs of Ahmed Body)

Vector plot XY Plane -1

Vector plot YZ Plane (Behind the Ahmed Body)

 

Case 3: y+ 250

Drag and drag co-efficient

 

Lift and lift coefficient

 

Pressure contour on Ahmed body

 

Velocity contour XY Plane -1 (Coinciding with origin)

Pressure contour XY Plane -1 (Coinciding with origin)

Velocity contour XY Plane -2 (Cutting through legs of Ahmed Body)

 

Vector plot XY Plane -1

Vector plot YZ Plane (Behind the Ahmed Body)

Comments:

The y+ value plays an important role in getting a solution that is most accurate. Changing the y+ value changes the first layer thickness. From the y+ values used in the above 3 cases, a y+ of 250 i.e. First layer thickness of 3.5814mm give a drag coefficient of 0.292, which is approximately accurate as compared to the expected value of 0.3. The error in the computed value is only of 2.6%, which is acceptable.

So, a y+ value of 250 was used to conduct the mesh independency test.

 

Mesh independency test

Since the inner enclosure is critical to the simulation, the body sizing of the inner enclosure was modified to check whether the results deviate from the correct values. 3 such cases were considered.

1. Body sizing - 30mm

 

 

2. Body sizing - 33mm

  

 

3. Body sizing - 36mm

 

 

Comments: There was negligible deviation in the values of Cd and Cl with change in the element size of the inner enclosure.

 

Negative pressure in the wake region

The wake region is the low pressure region having disturbed flow (often turbulent) found downstream of a bluff body moving through a fluid. The recirculation of flow can be seen in the wake region. This is due to the viscous effects of the flow and may be accompanied by flow separation.
As the body is a bluff body, the flow is obstructed and thus, we can say that initially there is no air flow behind the body. This causes the pressure to drop. The pressure is negative in the sense that the gauge pressure is lower than the atmospheric pressure. As a consequence of this low pressure, 2 recirculation zones can be observed near the top and bottom portion of the trailing end of the Ahmed Body.

 

  

Significance of point of separation

When a solid body is immersed in a flowing fluid, a thin layer of fluid called boundary layer is formed adjacent to the surface of the body. The velocity in this layer varies from 0 to free stream velocity. The thickness of this layer increases as the fluid flows along the body, as the fluid layer has to do work against the skin friction at the expense of its kinetic energy. This kinetic energy is compensated for by immediately next fluid layer. Along the length of the solid body, at a certain point, a stage may come when the boundary layer may not be able to keep sticking to the solid body if it cannot provide kinetic energy to overcome the resistance offered by the body. Thus, the boundary layer will separate from the body. This is called as boundary layer separation.
The point on the body at which the boundary layer is on the verge of separation from the surface is called point of separation.

Now, as the fluid flows along the rear end of the Ahmed body, the area of flow increases, causing a decrease in the velocity of flow. This increases the flow pressure and the pressure gradient for the flow becomes positive, i.e. dp/dx >0. 
As the pressure increases, the kinetic energy of the flow decreases. Due to the combined effect of the increased pressure and decreased kinetic energy, the momentum of the fluid is unable to overcome the surface resistance, the boundary layer starts separating.

The point of separation is determined by the following condition: 

 

Conclusion

The simulation was carried out for different values of y+. 
A y+ value of 250 gave fairly accurate results. The computed value of coefficient of drag was found to be 0.292, which deviates from the validated value (0.3) by only 2.6%.

The wake region is the low pressure region of flow behind a bluff body. This low pressure region is responsible for the aerodynamic pressure drag acting on the body. Thus, a longer wake gives more aerodynamic drag. So, it is advisable to design automobiles in a way that the wake region is as small as possible.

It is better to delay the separation of flow and have the separation point as downstream of the body as possible. This is because flow separation generated wake and recirculation zones, contribute a lot to generating pressure drag on the body flowing through the fluid.

 

References

https://www.comsol.com/blogs/studying-the-airflow-over-a-car-using-an-ahmed-body/

https://www.simscale.com/forum/t/ahmed-body/64235

https://www.simscale.com/docs/validation-cases/aerodynamics-flow-around-the-ahmed-body/