Week 3 - 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.
The expected results will include
1. Velocity and pressure contours.
2. The drag coefficient plot for a refined case. ( For a velocity of 25m/sec, the drag coefficient should be around 0.33).
3. The vector plot clearly shows the wake region.
4. Perform the grid independence test and provide the values of drag and lift with each case.
Abstract
Ahmed body: The Ahmed body was first created by S.R. Ahmed. It is 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, a height of 0.288 meters, and a width of 0.389 meters. It also has 50 mm cylindrical legs attached to the bottom of the body and the rear surface which has a slant that falls off 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 the `k-epsilon` model and for the later stage `k-omega`SST model is used.
Importance of Ahmed's body
The drag force is an important factor considering fuel consumption. As the drag force increases the fuel consumption also increases which in turn becomes expensive for the car owners. As the burning of fossil fuels becomes an issue, manufacturers are pressing for fuel-efficient cars. One of the main factors considering whether the car is fuel-efficient or not is the car's geometry.
Complex-shaped cars are very challenging to model and its difficult to quantify the aerodynamic drag computationally. The Ahmed body is a benchmark model widely used in the automotive industry for 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 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.
Significance of point of separation
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 decrease in velocity before the rear end of the vehicle. As soon as the air encounters the sharp turn causing the velocity decrease 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.
Modeling approach
Creating enclosure:
In the Ahmed body provided is imported to the SpaceClaim and two enclosures are created as shown in the figures below
And then the interference between two enclosures is removed
and the topology is shared between two enclosures for uniformity
And then to save the simulation time the symmetrical body is cut into half using spilt body command
For performing the mesh independent study different sizes of the mesh are tried to find the optimum quality of mesh which can be used for the simulation and provide the best results in lesser time.
Case 1:
In this case, the outer enclosure mesh element size is set to 250mm with hexahedron type elements and the inner enclosure mesh element size is set to 100mm and the legs faces mesh element size is set to 5mm to capture the finer details
and for inflation, the Yplus calculator is used to calculate the first layer thickness with the desired y plus value of 30 and inflation layers are created around the car wall to capture the no-slip boundary layer conditions
The number of faces and nodes are as shown in the figure below
and then all the boundary parts are named according to their functionality
In the setup of k-epsilon turbulence with enhanced wall treatment is selected and the solver is pressure-based and steady state
And the reference values are as shown in the figure below
For the inlet boundary conditions, inlet velocity is updated to 25m/s and the working fluid is kept as air with default values and definitions for calculating the drag-coefficient, lift-coefficient, and skin friction-coefficient is created to calculate the desired values
The number of iterations required to converge all the discrete equations are as shown in the figure below:
Residuals while solving the equations:
Drag-coefficient:
Lift coefficient:
Skin Friction-coefficient:
Pressure contour:
Velocity vector and contour:
As it can be seen from the figure tube to the turbulence bubble behind Ahmed's body a vacuum is created and in this, the velocity is almost equal to zero but due to coarse mesh the contour is not properly visible in this case
Results:
It can be seen that the results obtained in this case don't match the analytical solution accurately.
So the mesh element sizes are further reduced to capture the results perfectly
Case 2:
In this case, the outer enclosure mesh element size is set to 100mm with hexahedron type elements and the inner enclosure mesh element size is set to 50mm, and the legs face mesh element size is set to 2mm to capture the finer details
and for inflation, the Yplus calculator is used to calculate the first layer thickness with the desired y plus value of 30 and inflation layers are created around the car wall to capture the no-slip boundary layer conditions
The number of faces and nodes are as shown in the figure below
and then all the boundary parts are named according to their functionality
In the setup k-epsilon turbulence with enhanced wall treatment is selected and the solver is pressure-based and steady state
And the reference values are as shown in the figure below
For the inlet boundary conditions, inlet velocity is updated to 25m/s and the working fluid is kept as air with default values and definitions for calculating the drag-coefficient, lift-coefficient, and skin friction-coefficient is created to calculate the desired values
The number of iterations required to converge all the discrete equations are as shown in the figure below:
Residual while converging the equations:
Drag-coefficient:
Lift-coefficient:
Friction-Coefficient:
Pressure contour:
Velocity contour and vector:
From the velocity and pressure contour, it can be observed that at the separation point due to wake region formation there is low pressure and velocity. On the rear end of Ahmed's body, negative pressure and low velocity can be observed due to the separation of the flow which will pull the body in the opposite direction of the body's movement.
Results:
In this case, the results obtained match accurately with the analytical solution and so this mesh can be referred to as the optimum size for the calculation there is no need to further reduce the element size of the mesh but for more validation, the element size is reduced and this deduction is verified.
Case 3:
In this case, the outer enclosure mesh element size is set to 50mm with hexahedron type elements and the inner enclosure mesh element size is set to 25mm, and the legs face mesh element size is set to 1mm to capture the finer details
and for inflation, the Yplus calculator is used to calculate the first layer thickness with the desired y plus value of 30 and inflation layers are created around the car wall to capture the no-slip boundary layer conditions
The number of faces and nodes are as shown in the figure below
and then all the boundary parts are named according to their functionality
In the setup k-epsilon turbulence with enhanced wall treatment is selected and the solver is pressure-based and steady state
And the reference values are as shown in the figure below
For the inlet boundary conditions, inlet velocity is updated to 25m/s and the working fluid is kept as air with default values and definitions for calculating the drag-coefficient, lift-coefficient, and skin friction-coefficient is created to calculate the desired values
The number of iterations required to converge all the discrete equations are as shown in the figure below:
Residual while converging the equations:
Drag-coefficient:
Lift-coefficient:
Friction-Coefficient:
Pressure contour:
Velocity contour and vector:
From the velocity and pressure contour, it can be observed that at the separation point due to wake region formation there is low pressure and velocity. On the rear end of Ahmed's body, negative pressure and low velocity can be observed due to the separation of the flow which will pull the body in the opposite direction of the body's movement.
Results:
Here it can be observed that the results don't match the analytical solution so it can be validated that the mesh element size in case 2 is the optimum size.
So it can be concluded from this grid independent study that the mesh element size of 100mm for the outer enclosure and 50mm for the inner enclosure and 2mm for other finer details in Ahmed's body is the optimum mesh elements sizes for a given size of Ahmed's body which would optimally save the simulation time and provide accurate results from the k-epsilon model with enhanced wall treatment.