Week 3 - External flow simulation over an Ahmed body.
External Flow Simulation over an Ahmed Body
Aim:
External flow simulation over an Ahmed body.
Objective:
The objective of this project is to determine the aerodynamic forces on the Ahmed body such as drag and lift coefficient and to perform the grid independence test.
- Velocity and pressure contours.
- The drag coefficient plot for a refined case. (For a velocity of 25m/sec, the drag coefficient should be around 0.33).
- The vector plot clearly showing the wake region.
- Perform the grid independence test and provide the values of drag and lift with each case.
Introduction:
The Ahmed body was first created by S.R Ahmed. It’s an important benchmark for aerodynamic simulation tools. It will be clearly shown in the sketch below that it has a length of 1.044 meters, the height of 0.288 m and width of 0.389m. it also has a 50 mm cylindrical legs attached to the bottom of the body and the rear surfaces which has a slant that falls of at 35 degrees.
The flow for the model is turbulent which is based on velocity and body length. For the default mesh size in ANSYS FLUENT we will use k-ɛ model and for the later stage k- ὡSST model is used.
Importance of Ahmed body:
The drag force is an important factor considering fuel consumption. As the drag increases the fuel consumption also increases which in turn becomes expensive for the car owners. As the burning of fossil fuels becomes an issues, the manufactures are fuel efficient cars. One of the main factors considering the car is fuel efficient or not is the car’s geometry.
Complex shaped cars are very challenging to model and it’s difficult to quantify the aerodynamic drag computationally. The Ahmed body is a validating simulation tools.
Negative pressure in the wake region:
When the air moving over the vehicle is separated at the rear end, it leaves a large low-pressure turbulent region behind the vehicle which is known as the wake. This contributes to the formation of pressure drag which affects the vehicle performance.
When the vehicle is moving at a certain velocity the fluid imparts viscous force to the vehicle as long as it is viscous sub layer 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.
The point of separation will occur when there is a discontinuity in the surface or a region of the negative pressure gradient (a sharp end or rear portion of the car).
When the flow is attached to the body of the vehicle the viscous force will increase which will increase the pressure and a decrease in velocity before the rear end of the vehicle. As soon as the air encounters the sharp turn causing the velocity to decrease resulting in the negative pressure region which is in the wake region. The recirculating 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.
In order 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.
Modeling approach:
Baseline simulation approach using k- ɛ model:
- Ahmed body is loaded into the space claim.
- A single enclosure is drawn across Ahmed body.
- Now the geometry is loaded for meshing.
- A baseline simulation is set up with the default element size of ANSYS (413.6mm).
- A named selection is created for the enclosure inlet, outlet, and symmetry.
- To create the named selection for the car the enclosure faces are hidden and box select is selected from the meshing toolbar and (car wall) name is given to it.
- ANSYS fluent window is opened and the geometry is loaded.
- Steady – state, the density – based solver is selected.
- Reference values are updated as per the prescribed conditions.
- In the inlet boundary condition, inlet velocity is 25 m/sec and 300K temperature are set.
- Drag – coefficient plot and lift – coefficient plot is created by setting the reference as (car walls).
- Hybrid initialization is selected.
- The solution is initialized by hitting t=0.
- The cut – plane –z is created along Ahmed body.
- The velocity contour, pressure contour is created along the cut – plane –z.
- The animation video is created for the velocity contour.
- The simulation is executed for 1000 iteration.
Simulation with a finer mesh using k - ὡ SST:
- The first simulation ran successfully.
- The geometry is loaded into the space Claim.
- The region of local refinement is created along Ahmed’s body.
- As the body is perfectly symmetry, the simulation is executed by considering the only half body. This is the best practice where we can save on the number of cells and get the results faster as well.
- The geometry is loaded for meshing. The multi zone method is selected for the outer enclosure to provide hexahedral mesh which provides accurate results in simulation.
- The element size for the first enclosure will vary as (100mm, 90mm, 80mm) the element size for the second enclosure will vary as (50mm, 45mm, 40mm) the element size of the leg of Ahmed body will be 5mm, the first layer thickness, inflation layer, and the maximum thickness will be varied accordingly to imitate the experimental results.
- The rest procedure is the same as above, the necessary contour plot and graphs have been upload respectively.
Case 1:
Turbulence model k - ɛ:
- The three planes are normal to the x, y, z axis respectively.
- As the body is perfectly symmetry, we can simulate by considering only half body. This is the best practice where we can save on the number of cells and get the results faster as well.
- To get half of Ahmed body the section mode is selected in space claim and the front view plain is selected to yield the desired results accordingly.
- Once the geometry part is complete, it is loaded in the meshing window to perform the baseline meshing.
Mesh size of ANSYS – FLUENT:
- Creating named selection to set up physics and boundary conditions. Inlet boundary conditions (velocity inlet), Outlet boundary conditions (Pressure Outlet), symmetry boundary condition, car wall boundary condition.
- Then performing meshing with default mesh size in ANSYS FLUENT.
- Thus the mesh is created inside Ahmed body which is not good for simulation because the flow outside Ahmed body is taken into account. It can be fixed by going back to space claim, one of the copies should be suppressed for physics.
Results:
Residuals plot:
Drag coefficient:
Lift coefficient;
Velocity plane:
Velocity vector plot:
Pressure plane:
Pressure vector:
Drag coefficient = 0.3092.
Lift coefficient = 0.19117.
- It can be inferred from the following figure that the results of the base simulation are distorted and do not capture the turbulent flow behind the body perfectly. This simulation captures the wake length, high velocity, and low – velocity areas which can be used to further refine the mesh value around the Ahmed body and add a local refinement around.
Case 2:
External flow simulation over Ahmed body with finer mesh in a double enclosure:
Turbulence model k- ὡ SST:
First refinement
- A region of local refinement is add to the Ahmed body.
Share topology:
- It is set to share. It is used for sharing the information between the two enclosures and also to make the mesh uniform.
Method:
- Outside the box, the hexahedral mesh is used. The mesh is of the highest quality and gives higher accuracy.
Multi zone method:
- It is used to create hexahedral meshes wherever possible and for other regions where different mesh types are used it will connect it properly.
Sizing:
- It is defined as increasing the number of elements by decreasing the elements size. The elements size of the second closure is 0.05m.
- Element size for the first enclosure: 100mm or 0.1m.
- Maximum size for the first enclosure: 100mm or 0.1m.
- Element size for the second enclosure: 50mm or 0.05m.
- Element size of pillars of Ahmed body: 5mm.
Inflation layer:
- It is the process of add layers to the boundary to cover the boundary layer thickness fully.
- The first cell height value: 5mm.
- Inflation layer: 5.
- Last layer of thickness: 15mm.
Results:
Residuals plots:
Drag coefficient:
Lift coefficient:
Velocity plane:
Velocity vector plot:
Pressure plane:
Pressure vector plot:
Drag coefficient: 0.38361.
Lift coefficient: 0.30305.
Case 3:
External flow simulation over Ahmed body with finer mesh in a double enclosure:
Turbulence model k- ὡ SST:
- Element size for the first enclosure: 90mm or 0.09m.
- Maximum size for the first enclosure: 90mm or 0.09m.
- Element size for the second enclosure: 45mm or 0.045m.
- Element size of pillars of Ahmed body: 5mm.
Inflation layer:
- It is the process of add layers to the boundary to cover the boundary layer thickness fully.
- The first cell height value: 3mm.
- Inflation layer: 10.
- Last layer of thickness: 15mm.
Results:
Residual plot:
Drag coefficient:
Lift coefficient;
Velocity plane:
Pressure plane:
Drag coefficient: 0.3512.
Lift coefficient: 0.2889.
Case 3:
External flow simulation over Ahmed body with finer mesh in a double enclosure:
Turbulence model k- ὡ SST:
- Element size for the first enclosure: 80mm or 0.08m.
- Maximum size for the first enclosure: 80mm or 0.08m.
- Element size for the second enclosure: 40mm or 0.04m.
- Element size of pillars of Ahmed body: 5mm.
Inflation layer:
- It is the process of add layers to the boundary to cover the boundary layer thickness fully.
- The first cell height value: 5mm.
- Inflation layer: 10.
- Last layer of thickness: 15mm.
Results:
Residual plot:
Drag coefficient:
Lift coefficient;
Velocity plane:
Velocity vector plot:
Pressure plane:
Pressure vector plot:
Drag coefficient: 0.3498.
Lift coefficient: 0.2884.
Conclusion:
- It can be inferred that the grid independence test is performed to know the smaller cell size for convergence.
- Apart from mesh refinement, convergence depends on the Y+ value, inflation layer, it is advisable to use k- ὡ SST as the turbulence value because it calculates the values well near the wall.
- As the setup is refined drag coefficient, lift coefficient decreases.
- Y+ plays an important role in determining the value of drag.
- The negative pressure in the wake region is primarily because there is no flow in that region. This can be further attributed to various factors such as separation and recirculation which is evident from the vector plot near the wake region.
- The point of separation occurs at the rear end of the vehicle, the separation occurs beyond this point where it can be observed that the flow recirculates and attaches it to the boundary layer.
References: