Ahmed Body Challenge
Objective: Grid Independence study on Ahmed Body
Describe about Ahmed body and its importance.
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. Although it has a very simple shape, Ahmed body allows us to capture characteristic features that are relevant to bodies in the automobile industry.
ANSYS is a general purpose FEA and CFD simulation software. It gives numerical prediction of the behavior of a system. These numerical predictions need to be validated by experimental data.
People working in vehicle aerodynamics use Ahmed body to validate their numerical model because the experimental data from wind tunnel testing is available for Ahmed body. Once the numerical model in validated, it is used to design new models of the car.
The Ahmed body was described originally by S. R. Ahmed in 1984. Three main features were seen in the wake:
- Recirculation region that is formed as the flow separates at the top of the vertical back surface of the model
- Recirculation region that is formed due to the separation at the base of the model.
- Pillar vortices that form as the vorticity in the side boundary layers roll up over the slant edges.
Description of the test case: The Ahmed body was first defined and its characteristics described in the experimental work of S. R. Ahmed. Two configurations with slant angles of 25°and 35°are considered as a test case. For this configurations detailed LDA Measurements have been performed by Becker, Lienhart and Stoots in the LSTM low-speed wind-tunnel with a cross-section of 1.87x1.4 square metre (width x height) with a bulk velocity of 40 m/s. The test-section of the wind-tunnel was 3/4 open (only ground plate present). The distance between the body and the plate representing the ground is 50 mm. In the experiment perform by S. R. Ahmed, flow velocity was taken 60 m/s, Reynolds number was 4.29 million based on model length.
In our test , we are giving inlet velocity of 25 m/s and outlet has 0 pascal as gauge pressure.
Geometry:
(Dimensions are in mm)
Fig Ahmed Body Model
Modeling airflow over an Ahmed Body-
Computational domain and boundary conditions for the fluid flow simulation.
The front of the body is placed at a distance of 2 car lengths (2L) from the flow inlet. To reduce the computational cost, the asymmetry plane is introduced to model half of the model.
The flow for this model is turbulent, which is based on the Reynolds number determined by the body length and inlet velocity. The simulation solves for the turbulent kinetic energy in addition to the velocity field. For this simulation, we need a larger mesh size than what is usually common to resolve the turbulent flow. More specifically, we use a finer mesh downstream of the model to capture the wake zone.
Mesh:
Since the boundaries of our domain are rectangular it is better to use Hexahedral mesh because of highest quality. For the inner enclosure Tetrahedral Meshes were used. Inflation layer was created around the wall of Ahmed Body to accurately capture the boundary phenomenon. In all the cases the elements size of both meshes were varied to increase the number of elements.
Inflation first layer height = 4.65 mm with 6 layers and growth of 1.2 was kept fixed as wall y+ was lying range of 30-300.
Results:
Base setup
No. of elements = 272393
Convergence residual plot:
Wall y+:
As K epsilon with standard wall function is used so y+ value is lying almost in between 30-300.
Drag coefficient:
Drag coefficient = 0.39
Lift coefficient:
Lift coefficient = 0.328
Velocity contour:
Velocity Vector contour:
Velocity Streamline contour:
Pressure contour:
Pressure Vector contour:
Pressure Streamline contour:
Refine mesh 1
No. of elements = 343736
Convergence residual plot:
Wall y+:
As K epsilon with standard wall function is used so y+ value is lying almost in between 30-300.
Drag coefficient:
Drag coefficient = 0.38
Lift coefficient:
Lift coefficient = 0.304
Velocity contour:
Velocity Vector contour:
Velocity Streamline contour:
Pressure contour:
Pressure Vector contour:
Pressure Streamline contour:
Refine mesh 2
No. of elements = 478198
Convergence residual plot:
Wall y+:
As K epsilon with standard wall function is used so y+ value is lying almost in between 30-300.
Drag coefficient:
Drag coefficient = 0.37
Lift coefficient:
Lift coefficient = 0.290
Velocity contour:
Velocity Vector contour:
Velocity Streamline contour:
Pressure contour:
Pressure Vector contour:
Pressure Streamline contour:
Refine mesh 3
No. of elements = 949411
Convergence residual plot:
Wall y+:
As K epsilon with standard wall function is used so y+ value is lying almost in between 30-300.
Drag coefficient:
Drag coefficient = 0.35
Lift coefficient:
Lift coefficient = 0.293
Velocity contour:
Velocity Vector contour:
Velocity Streamline contour:
Pressure contour:
Pressure Vector contour:
Pressure Streamline contour:
Refine mesh 4
No. of elements = 1521570
Convergence residual plot:
Wall y+:
As K epsilon with standard wall function is used so y+ value is lying almost in between 30-300.
Drag coefficient:
Drag coefficient = 0.35
Lift coefficient:
Lift coefficient = 0.293
Velocity contour:
Velocity Vector contour:
Velocity Streamline contour:
Pressure contour:
Pressure Vector contour:
Pressure Streamline contour:
Table for Ahmed body grid dependency study with drag coefficient:
|
Mesh setup |
No. of Cells |
Lift Coefficient |
Drag Coefficient Experimental for velocity 25 m/s |
Drag coefficient of simualtion |
Error % |
|
Base mesh |
99082 |
0.328 |
0.33 |
0.39 |
18.18 |
|
Refine 1 |
155493 |
0.304 |
0.38 |
15.15 |
|
|
Refine 2 |
309354 |
0.290 |
0.37 |
12.12 |
|
|
Refine 3 |
382703 |
0.293 |
0.35 |
6.060 |
|
|
Refine 4 |
503443 |
0.293 |
0.35 |
6.060 |
Grid dependency was achieved as further refinement of mesh provided similar results.
Negative pressure in the wake region
From the velocity vector diagram we can see that there is a wake region formed behind the vehicle. This is due to sudden change in the boundary on rear side of the body. If the body was streamlined there will be no seperation as in case of airfoils. Due to formation of wake there is a decrease in velocity and we should expect an increase in pressure according to Bernoulli's theorem but that is not the case here. The pressure also decreases and in this case it is negative.
First of all the flow is highly viscous so we cannot apply Bernoulli's theorem. There is loss of energy due to formation of wake and that happens in the expense of both pressure and velocity. This negative pressure pulls the body and causes in increase in pressure drag.
Significance of Point of Seperation
The major aerodynamic problem is at the rear. The flow over the upper rear surface is interesting. The slant angle is an important parameter which decides the point of seperation. For slant angle of less than 30 deg the flow remains attached in the upper rear surface and the seperation occurs in the rear surface. This vortices generated are drag producing due to negative pressure. For 30 deg slant angle the drag is maximum and seperation happens at the rear end of top surface and in that case vortices generated are higher in number and causes additional negative pressure there by increasing the drag value.
Conclusion:
Pressure goes negative to maintain the flow when the velocity increases. This results in the contionous flow. Separation bubbles are produced at the presure region.Pressure goes neagtive to balance the shear stress developed. Flow recirculation also results in negative pressure. Decrease in pressure results in increase in velocity and vice-versa.
By performing the grid dependency test it was clear that as we go on reducing the mesh size we are getting the good results and smooth curve for velocity at both the base lines created. Also the velocity variation and pressure variation are changing across the refined meshed region.