Analysis of Flow over an Ahmed Body

Objective:

To simulate the flow across an Ahmed body and find the drag coefficient.

Introduction:

Ahmed body is a bluff body that represents a generic car body. It has a simplistic shape and has the basic aerodynamic properties of a vehicle and has been used as a reference in many aerodynamic studies. Optimization of external aerodynamics of a car is necessary in order to achieve efficient vehicles with minimum fuel consumption.

A lot of experimental wind tunnel testing has been carried out for the Ahmed body and the same can be used for validation of CFD models.

The geometrical shape of the Ahmed body can be seen in the figure below. The front of the Ahmed body has filleted edges and the back has a slant thus roughly representing a car.

Computational Domain:

The computational domain for the given simulation is prepared using space claim.

As the Ahmed body is symmetrical along its length, the body can be split and only one half of it is used for analysis in order to limit the number of computational cells.

The inside of the body is not a part of the analysis and hence the Ahmed body is suppressed for physics. The Enclose Option is created and the dimensions of the cuboidal domain is set accordingly.

This is used as the base case setup.

The next case a smaller enclosure is used and a refined region around the Ahmed body is used in order to capture the wake region correctly. The computational domain used in the refined cases can be seen below.

Meshing:

Tetra mesh is used for the base case with the mesh size 0.1m. the names selections include an inlet, outlet, car walls, bottom wall, and the car symmetry wall. The named selections used and the base mesh can be seen in the figure below.

For the refined mesh case, the outer body is cuboidal in shape and hence the multizone method of meshing is used to mesh the outer body. Body sizing is applied in the inner rectangle and the size is set. Edge sizing is set on the circular legs of the Ahmed body. The size is set up with respect to number of elements which is set to 36. Inflation is applied to the inner body and the car walls are chosen as the inflation boundary. The total thickness of the layers is chosen as the parameter.

The y+ has to be above 30. The assumed value of y+ is taken to be 250 and the first cell thickness is maintained at 40mm.

Different cases are run for different sizes of mesh. The details of the mesh are tabulated below:

Base Grid Size(m)	Body Size (m)	Inflation FLT(m)	No of Elements
Base	NA	NA	140603
0.1	0.05	0.04	140412
0.1	0.04	0.04	227175
0.1	0.03	0.04	503448

The named selections and mesh can be seen in the figure below:

Case Setup:

The case is setup in fluent.

The density-based solver is used and so the energy equation is employed in the computation.

The viscous k-epsilon is used for turbulence modelling with scalable wall functions

Air is the fluid used for simulation.

Boundary conditions:

Inlet: Velocity Inlet

Outlet: Pressure Outlet

Symmetry: Symmetry

Car Symmetry: Symmetry

Bottom_wall= wall with no slip condition

Car_Wall= wall with no slip condition

Reference Values:

Reference values are setup as compute from the inlet and the dimensions are edited as below:

Reference Length:1.044m

Reference Area: 0.112 m²

Surface Monitors:

The surface forces option is used to plot the drag coefficient on the car walls.

Solution Initialization: Hybrid

Contours:

The velocity contour is setup at the midplane of the computational domain. The contour is used to setup a solution animation.

Results:

Simulations are carried out for various cases. The base grid simulation gives a rough idea of the contours formed. The velocity contours obtained are seen in the figure below followed by the pressure contours and the vector representation.

The contours can be observed to be very diffusive and hence arises the requirement for mesh refinement in order to obtain better results.

Different cases are run for different mesh resolution and the drag coefficient is noted, tabulated below.

The velocity contours of the simulations can be seen below.

Velocity contours Body Size 0.05m:

Velocity contours Body Size 0.04m:

Velocity contours Body Size 0.03m:

The Pressure Contours are seen below

Pressure contours Body Size 0.05m:

Pressure contours Body Size 0.04m:

Pressure contours Body Size 0.03m:

Velocity monitors are places downstream of the flow and the velocity along the line is compared in each case.

The mesh with body size 0.05m is used for further analysis.

From the velocity contours it is seen that the velocity is zero at the walls and increases. Line plots are placed in order to monitor the velocity downstream of the Ahmed Body.

The following image show the velocity vectors and it can be seen that recirculation zones are formed at the back of the Ahmed Body. The velocity becomes zero at the front face of the Ahmed body. As the fluid passes over the inclined plane at the back it rejoins the main flow stream. Although recirculation zones are formed behind the body. This is the wake region.

The boundary layer formed on the bottom wall can be seen and it can be observed that the boundary layer is more refined in the central refined enclosure.

The velocity plots at three different line monitors downstream of the Ahed body can be seen below. It can be observed that the boundary layer on the ground is disturbed in the wake region as the line monitor at 1.5m lies in the wake region.

The velocity profiles can be seen to be taking a increasing profile as the line monitor moves away from the Ahmed body with the velocity being zero at 0m and attaining the free stream value as moved away from the bottom wall.

Below is the pressure contour obtained:

The pressure if maximum at the front face showing that all the kinetic energy of the flow has been converted into pressure energy. The pressure reduces along the curve of the front face and increases again along the walls of the body.

Given below is the Pressure distribution along the wall of the car. The stagnation point where the pressure is maximum is seen on the front face.

The velocity is zero at the stagnation point and the pressure is maximum as the velocity or kinetic energy gets converted to pressure energy.

The flow velocity is now changed within a range from 10m/s to 40m/s and the drag coefficient for each is noted. The details of the flow are tabulated below

Flow Velocity(m/s)	Reynolds Number	Drag Coefficient.
10	714708	0.291
17.5	1250740	0.291
25	1786772	0.2886
32.5	2322803	0.284
40	2858835	0.2876

The drag coefficient can be observed to be reducing with increase in the flow velocity. This is because the flow velocity is low. At higher velocities the relation between the drag coefficient and the Reynolds number may be different.

Conclusion:

Flow is simulated along an Ahmed body and the velocity and pressure contours are observed.

The simulation is conducted for different mesh resolution.

The drag coefficient is computed and its variation with respect to flow velocity is noted.