Flow around a Ahmed Body

FLOW AROUND THE AHMED BODY

The Ahmed body as shown in fig.1, has the form of a highly simplified car, consisting of a blunt nose with rounded edges fixed onto a box-like middle section and a rear end that has an upper slanted surface, the angle of which can be varied. The model is supported on circular-sectioned legs or stilts, rather than wheels. Despite neglecting the number of features of a
real car (rotating wheels, rough underside, surface projections etc.) the Ahmed body generates the essential features of flow around a car, namely the flow impingement and displacement around the nose, relatively uniform flow around the middle and flow separation and wake generation at the rear.
The principal aim of studying such a simplified car body is to understand the flow processes involved in drag production. Through understanding the phenomena involved in generating drag one should be able to design a car to minimize drag and therefore minimize fuel consumption which inturn maximizes the performance. The principal contribution to drag experienced by a car is pressure drag. The rear end of the vehicle is responsible for the major contribution to pressure drag and, in particular, the angle of rear slant is critical in determining the mode of the wake flow and hence the drag experienced by the vehicle.

Fig. 1: Ahmed Body

In the present case, the flow around the ahmed body was studied with an aim to find out the velocity profiles at the mid plane. Initially, the ahmed body as shown in fig.1 was imported into the spaceclaim module with an encloure i.e. fluid domain of appropriate dimensions around it. Then, whole geometry is taken into the meshing module where the default mesh has been generated with the appropriate name selection to suitable boundaries i.e inlet, oulet, symmetry and car wall as shown in fig 2.

Fig 2: Baseline Mesh

The default mesh contains tetrahedral mesh elements size of 0.4136 m and 83882 mesh elements in the fluid domain. In fig. 2 , the mesh appears only on the fluid domain i.e. the around the Ahmed body not inside the Ahmed body since flow around the Ahmed body is main objective for this study. The area around the circular-sectioned legs gets refined due to adaptive nature of mesh module. The minimum quality of tetrahedral mesh element is of the order of 33.8 % which is quite accpetable for this case as shown in fig.3.

Fig 3: Baseline Mesh Quality

Furthermore, the geometry was taken to a Fluent module for setting up the physics i.e. steady, density based, K-epsilon turbulence model and velocity formulation under the solver setting with a energy equation option enabled. The appropriate boundary conditions to Ahmed body has been aasigned such as air inlet velocity of 50 m/s while the temperature of the air at the inlet as 298 K . Here, the hybrid method of initialization is used instead of standard initialization. After this, the case has been run for 500 iterations with residuals keep dropping after each iteration and flow gets converged after certain iterations as shown in fig 4.

Fig 4: Baseline Residuals

The pressure and velocity contours at the mid-section plane for the baseline mesh case are as shown in fig 5 & fig 6. The flow that passes from the curved front end of the body to the flat top, bottom and side surfaces of the body remains attached as it passes through a strong local adverse pressure gradient due to the curvature. This pressure variation can be seen over the front end of the body shown in fig. 5. This figure also gives an indication of the vortices present in the wake region during which the whole of the rear end becomes separated, leaving a vacuum or low pressure region. The resulting lower pressure creates lift which then acts upon the surface of the rear slant.The velocity contours extending behind the body indicate the low velocity wake region, which causes the form drag. As the wake area is reduced, the drag-causing eddies (vortices), generated due to the pressure difference between the top and bottom of the Ahmed body at the rear trailing end, come closer together. This result in less kinetic energy being dissipated due to these smaller eddies and consequently less compensation power required by the engine to propel the vehicle forward. It additionally results in higher pressure being applied at the rear surface of the body and consequently less form drag. In fig 7, the velocity vectors near the front end of the body predominant compared to rear slant end.

In order to capture the intended physics i.e. wake formation region that we looking for, there is need of mesh refinement in fluid domain. Hence the mesh has been refined as per the requirement.

Fig 5(a): Baseline Pressure Contour (Front end) Fig 5(b): Baseline Pressure Contour (Rear end)

Fig 6: Baseline Velocity Contour Fig 7: Baseline Velocity Vector Plot

As the y-distance increases i.e. far away from the body in particular y=0.8 m, the velocity remains constant irrespective of the data points chosen from the sets of line which is clearly shown in the graph of variation of velocity,u(m/s) and distance, y(m).

Graph 1 : Variation of Velocity,u(m/s) & distance,y(m) for Baseline case

Here, the second enclosure of appropriate size has been chosen within the larger enclsoure. The larger enclosure consists of hexahedral structural mesh while the smaller enclosure contains tetrahedral mesh of size 0.1m. The inflation layer and face sizing mesh method were adapted to refine mesh locally around the Ahmed body as shown in fig 8. The quality of different mesh element are as shown in fig 9 and the number of elements counts to be 106352.

Fig 8: Refined Mesh for Case-I

Fig 9: Refined Mesh Quality for Case-I

After the mesh refinement around the Ahmed body, the geometry was loaded to Fluent solver with other settings remains unchanged.This time, the case has been run for larger iterations say 700 iterations for the flow to get converged as shown in fig 10.

Fig 10: Refined Residuals for Case-I

The respective pressure and velocity contours of refined mesh are as shown in fig 11 & 12. After, the mesh refinement the wake formation region in velocity contour seems to be smooth and distinct. The vector plot in fig 13 also depicts the same phenomena of wake formation.

Fig 11(a): Refined Pressure Contour (Front end) for Case-I Fig 11(b): Refined Pressure Contour (Rear end) for Case-I

Fig 12: Refined Velocity Contour for Case-I Fig 13: Refined Velocity Vector Plot for Case-I

As the y-distance increases i.e. far away from the body in particular y=0.7 m, the velocity remains constant irrespective of the data points chosen from the sets of line which is clearly shown in the graph of variation of velocity,u(m/s) and distance, y(m).

Graph 2 : Variation of Velocity,u(m/s) & distance,y(m) for Refined Case-I

Again, the second enclosure has been refined as compared to the previous case consists of hexa structure mesh while the smaller enclosure contains tetrahedral mesh of size 0.05 m. The inflation layer and face sizing mesh element size was further reduced to refine mesh locally around the Ahmed body as shown in fig 14. The quality of different mesh element are as shown in fig 15 and the number of elements counts to be 496822.

Fig 14: Refined Mesh for Case-II

Fig 15: Refined Mesh Quality for Case-II

After the mesh refinement around the Ahmed body, the geometry was loaded to Fluent solver with other settings remains unchanged.This time again, the case has been run for larger iterations say 1200 iterations for the flow to get converged as shown in fig 16.

Fig 16: Refined Residuals for Case-II

Hence, the respective pressure and velocity contours for the refined mesh are shown in fig 17 & 18. In this mesh refinement case, the velocity and pressure contours around the body hardly any variation was observed from the previous case which inturn clearly indicates the results were independent of the grid size. Hence, the grid independent test were recorded for this case. The vector plots indicates the larger amount of vectors follows the Ahmed body surface contour except near the rearer slant edge region because of wake formation as shown in fig 19.

Fig 17(a): Refined Pressure Contour (Front end) for Case-II Fig 17(b): Refined Pressure Contour (Rear end) for Case-II

Fig 18: Refined Velocity Contour for Case-II Fig 19: Refined Velocity Vector Plot for Case-II

As the y-distance increases i.e. far away from the body in particular y=0.7 m, the velocity remains constant irrespective of the data points chosen from the sets of line which is clearly shown in the graph of variation of velocity,u(m/s) and distance, y(m).

Graph 3 : Variation of Velocity,u(m/s) & distance,y(m) for Refined Case-II