Week 3 - External flow simulation over an Ahmed body.

Aim: To perform the external flow simulation over Ahmed's body.

Objective:

1. To determine the aerodynamic forces on the Ahmed body such as drag and lift coefficient.
2. To perform the grid dependency test.

Introduction:

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 SR Ahmed in his research Some salient features of time average ground vehicle wake. Although it has a very simple shape, the Ahmed body allows 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 is invalidated, it is used to design new models of the car. The rear part of Ahmed's body called as 'slant angle' which influences drag and lift with its critical slant angle which is around 0-30 degrees.
• It is used for testing new CFD solvers or testing one's ability to perform simulations as there is a plethora of experimental data available about the Ahmed body to compare simulation data to.
• In this project, I will be performing analysis on an Ahmed Body in ANSYS using the Fluent solver.

Importance of Ahmed's Body:

• Ahmed's Body plays a vital role in testing the aerodynamic properties of vehicles.
• It is also used to describe the turbulent flow field around a car-like geometry and later to design new car models with validated results.

Theory:

1) Y+ Concept:

When any viscous flow flows over a surface, a region of slow-moving flow called the boundary layer develops. Inside the boundary layer, there is a strong velocity gradient and U varies non-linearly. It is important to distinguish these layers to model the boundary physics correctly and use an appropriate turbulence model. Hence, Y+ is a non-dimensional distance normal from the wall. It is applicable to all flows. For a CFD simulation, we can compute the first layer height for a desired Y+ value with the following formula:

Where,

ρ is fluid density ;

µ is fluid viscosity ;

U is the free stream velocity ;

L is characteristic length ;

U_τ is frictional velocity ;

τ_ω is wall stress ;

C_f is the skin friction coefficient

2) Boundary Layer:

The boundary layer is a thin layer of a real fluid along the surface of an object in which viscosity affects fluid dynamics. When fluid flows over a plate, velocity near the surface is much lower and vorticity is present. The no-slip condition accounts for zero relative velocity at the plate and keeps on increasing until it reaches the free stream velocity. The thickness of the boundary layer increases along the length of the plate. In a narrow boundary layer adjacent to the plate, the shear forces and inertia forces are equally important in determining the motion of the fluid element and outside of the region, shear stresses can be neglected. The fluid deceleration is transferred from one fluid layer to another fluid layer by viscosity and it forms the velocity gradient in the boundary layer. The thickness of the boundary layer is often described as the distance from the plate until the velocity reaches 99 % of the free stream velocity.

The gradient of the velocity normal to the wall (∂u/∂y) times the viscosity (μ) is the wall skin friction or shear stress. The greater the velocity gradient normal the wall, the greater the shear stress. As the velocity gradient goes on decreasing along the flow direction, the shear stress also decreases. The growth of the boundary layer thickness along the plate can be explained by considering the time history of the vorticity within the boundary layer. The viscosity acts through the mechanism of molecular diffusion to spread out the vorticity as it is convected downstream. The local boundary layer thickness is the measure of the distance for vorticity diffused away from the plate.
Since we are dealing with the turbulent boundary layer and related phenomena, let us not get into the laminar boundary layer. From the above figure, it can be seen that in the turbulent boundary layer region flow near the wall has been analyzed in terms of three layers. The inner layer, or sublayer (where viscous shear dominates), The outer layer or defect layer (where large-scale turbulent eddy shear dominates), The overlap layer or log layer (where velocity profiles exhibit a logarithmic variation)

3) Flow Separation:

When a fluid is forced to flow over a curved surface at high velocities. A fluid follows the front portion of the curved surface with no problem, but it has difficulty remaining attached to the surface on the backside. At sufficiently high velocities, the fluid stream detaches itself from the surface of the body. This is called flow separation. The location of the separation point depends on several factors such as the Reynolds number, the surface roughness, and the level of fluctuations in the free stream, and it is usually difficult to predict exactly where separation will occur unless there are sharp corners or abrupt changes in the shape of the solid surface. This contributes to the formation of pressure drag which affects the vehicle's performance.

• Negative pressure near the wake region:

When the vehicle is moving at a certain velocity the fluid imparts viscous force to the vehicle as long as it is in the viscous sublayer of the boundary. When the fluid reaches the rear end of the vehicle it gets detached from the surface of the body causing negative pressure in the wake region. The movement of the fluid around the vehicles depends on the geometry of the car and the Reynolds number.

When the flow is attached to the body of the vehicle the viscous force will increase which will increase the pressure and decrease in velocity before the rear end of the vehicle. As soon as the air encounters the sharp turn causing the velocity decreases resulting in the negative pressure region which is in the wake region. The recirculation region happens beyond the point of separation.

If the rate of change of pressure is large the mixing process will not occur and the boundary layer flow stops. The above figure shows that at the point of turning the flow gets separated from the boundary layer and there is a region of recirculation after which the flow attaches itself to the boundary layer. To reduce the separation of fluid from the boundary layer, it is advisable to have a smooth edge to reduce the effect of drag on the vehicle.

Solving & Modeling approach:

Geometry:

• Import the Geometry.

• Provide Enclosures to Ahmed's body (Inner and outer) according to the given dimensions.

• Suppress Ahmed's body.
• Input Planes & select XY plane and view the interference range.

• Now, go to prepare and check for interference and correct it.

• Now, split the body in half using the split body command.

• Then, Set the topology to share. This completes the geometry step.

Meshing:

• Start the mesh section.
• Name the boundaries, which are Inlet, Outlet, Symmetry, Wall, and Car-wall.

• Then, provide a specific element size and generate the base mesh.
• First, we have to provide the mesh method for the outer enclosure & set the multizone method so it creates Hexagonal mesh elements over that enclosure.

• Then, we have to add Body sizing for the inner enclosure to make it more refined.
• Now, add face sizing to the legs of Ahmed's body so they become completely circular while making their mesh element size smaller.
• Finally, add inflation layers according to correct y+ values. This completes the Mesh section.

Setup:

• First, we need to check the mesh from the Domain section.
• Now, provide the reference values according to the problem.

• Here no need to turn on the energy equation option since we are not interested in dealing with the heat transfer, temperature, etc, and also set the turbulence model according to the problem.

• Select the solver according to the problem.

• Now, set in the boundary conditions like inlet velocity, guage pressure, etc.

• In the solution, section creates drag and lift reports and plots, and also set the solution method.

• Now, go to the results section and create a plane at some distance normal to the x,y, and z axis which will be used to examine the velocity and pressure along it.
• Initialize the problem with Hybrid Initialization.
• Go back to result section and add velocity and pressure contours along a plane. Also, add velocity animation.
• Finally simulate the problem for some amount of iteration and observe the Drag, Lift, and Residual plots.
• This completes the setup section.

Results :

1. Select the wall volume to make it visible. Also, color it with the variable needed to be observed.
2. After that, insert the plane and color it with variables like Pressure and Velocity which shows the Pressure and Velocity flow on the plane.
3. Edit the legend according to requirement. This completes the results and hence the entire simulation.

Note:

1. We will be performing 3 cases in which we will keep refining the mesh from default size up to 0.5 million elements size.
2. Geometry and the solver setup will remain the same for all the cases.

Case 1: External flow simulation over Ahmed's body with

Geometry:

In this case, we will add an inner enclosure for more accuracy near Ahmed's body simulation. Also, we will add body sizing and inflation layers for more precision.

Meshing:

Outer enclosure element size (Base Mesh)	100 mm
Inner enclosure element size (Body Mesh)	50 mm
Ahmed's body legs element size (Face Mesh)	8 mm
Inflation First Layer thickness	1.5 mm
No. of Elements	78,074

Results:

1) Residuals

2) Drag coefficient

Drag coefficient = 0.37

3) Lift Coefficient

Lift Coefficient = 0.29

4) Velocity contour

5) Pressure contour

6) Velocity vector (XY Plane)

7) Velocity vector (YZ Plane)

Case 2: External flow simulation over Ahmedys body with

Geometry:

In this case, we will add an inner enclosure for more accuracy near Ahmed's body simulation. Also, we will add body sizing and inflation layers for more precision.

Meshing:

Outer enclosure element size (Base Mesh)	80 mm
Inner enclosure element size (Body Mesh)	30 mm
Ahmed's body legs element size (Face Mesh)	5 mm
Inflation First Layer thickness	1.5 mm
No. of Elements	2,84,689

Results:

1) Residuals

2) Drag coefficient

Drag coefficient = 0.33

3) Lift Coefficient

Lift Coefficient = 0.26

4) Velocity contour

5) Pressure contour

6) Velocity vector (XY Plane)

7) Velocity vector (YZ Plane)

Case 3: External flow simulation over Ahmed's body with

Geometry:

In this case, we will add an inner enclosure for more accuracy near Ahmed's body simulation. Also, we will add body sizing and inflation layers for more precision.

Meshing:

Outer enclosure element size (Base Mesh)	80 mm
Inner enclosure element size (Body Mesh)	25 mm
Ahmed's body legs element size (Face Mesh)	3 mm
Inflation First Layer thickness	1.5 mm
No. of Elements	4,72,213

Results:

1) Residuals

2) Drag coefficient

Drag coefficient = 0.31

3) Lift Coefficient

Lift Coefficient = 0.25

4) Velocity contour

5) Pressure contour

6) Velocity vector (XY Plane)

7) Velocity vector (YZ Plane)

Conclusion:

• From the velocity contours, we can see that there is a formation of a recirculation region at the back of ahmed's body.
• Also, we can see that as the mesh gets refined, drag values lower as we are refining it near walls.
• The negative lift can also be seen which means the creation of downforce. Also, the lift values are decreasing.
• Y+ values are essential for correct values of drag and lift.
• There is a variation of pressure across Ahmed's body. The pressure in front of the body is positive because that's the location where the flow first comes in contact with the body and comes to rest. At the corner, the flow accelerates, thereby decreasing the pressure.
• The reason behind negative pressure in the wake region is due to flow separation, and recirculating flow. It's a phenomenon that generally happens as the air moving past the body isn't able to pass through the immediate backside of the body creating a region, where there is no movement of air and thereby creating a pressure gradient.
• As the wake flow is the main contributor to the drag force(pressure drag), the point of separation is an important aspect of the flow. The more attached the flow is to the body the recirculation zone will be smaller and hence reduce the adverse effect of pressure drag, improving the fuel efficiency of the body.