Simulation of flow over Ahmed's Body

Aim : To perform a numerical analysis on flow over Ahmed body and to perform a grid dependence test.

Theory :

Ahmed Body and its significance:

Ahmed Body is a simplified 3 dimensional representation of a passenger car. It was first designed by S.R.Ahmed in his research \"Some Salient Features of the Time-Averaged Ground Vehicle Wake, SAE-Paper 840300, 1984\". It is a benchmarkmodel widely used in the automotive industry for validating the simulation tools based on reliable experimental data. The main aim of studying this kind of simplified body is to understand the flow process in drag production and to study the geometric effects on the wakes of the ground vehicles. By understanding the generation of various forces through these kind of simplified bodies one should be able to design a car to minimize the drag force and increase the fuel efficiency.

Ahmed Body description:

The Ahmed body basically consists of three parts. Firstly, the front curved portion of the body which adapts the flow in the inlet region. Secondly, a rectangular setion in order to stabilize the flow. Finally, at the end of the body we can find a slanted area with a particular angle,where the largest flow seperation part is located.

The dimension of Ahmed body are as follows:

The 3-Dimensional model of Ahmed Body used in this simulation is shown below:

Geometry :

We import the solid model of the ahmed body into spaceclaim graphic user interface. In order to simulate the flow around the ahmed body we need to first create a virtual wind tunnel. The dimensions of this outer enclosure is as follows:

Distance from the front end (the curved shape of the ahmed body) = 2 m

Distance from the back end (the slant angle edges of the ahmed body) = 5 m

Distance from the side walls = 0.5 m on both sides

Distance from the top wall = 1 m

Distance from the bottom wall = 0 m.

Similarly in order to capture the physics accurately around the ahmed body we create another enclosure. We will be using a finer mesh inside this enclosure compared to outer enclosure. The dimensions of this inner enclosure is as follows:

Distance from the front end (the curved shape of the ahmed body) = 0.5 m

Distance from the back end (the slant angle edges of the ahmed body) = 1 m

Distance from the side walls = 0.26 m on both sides

Distance from the top wall = 0.5 m

Distance from the bottom wall = 0 m.

Also in the spaceclaim we will be using another important command which is known as Interference. Since there are two enclosure used in this geometry, the mesh lines from each body will interfere in the domain where both enclosures coincide while meshing. To avoid interference between the mesh lines of the bodies we use interference command to create mesh without intersecting between the two bodies.

Since we will be majorly performing a grid dependency test we will be setting up various cases of different element size. The geometry and other setup parameters would be mostly the same.

Case 1:

Meshing:

A sectional view of the mesh can be seen in the above image. For the outer enclosure the meshing method chosen was Multizone resulting in hexahedral meshes. The Mesh Element Size of Outer Enclosure is 0.1 m.

We have created the inner enclosure since our interest in this case would be flow around the ahmed body. The Mesh size for the inner enclosure is selected to be 0.05 m. Also we will be doing a face sizing and its element size is set to be 0.005 m. Then we will be creating a inflation layer around the ahmed body. In total the number of Nodes is 55465 and the number of elements is 178575 is present in the domain.

We will be naming the faces of the geometry domain in order to define our boundary conditions. We will be creating the following named selections:

• Inlet.
• Outlet.
• Symmetry walls.
• wall.
• Car-walls.

Setup:

We will be using a density based solver since our inlet velocity is 50 m/s. This approximately corresponds to a mach number of 0.3. For mach number above 0.3 it is better to choose density based solver to consider compressibilty. Also we will be solving for the Energy equation and standard k-epsilon turbulence model. The matrial used would be the standard air from the ansys material libary.

Next we will be moving on to setup the boundary conditions.

• inlet: The type is set to velocity inlet and the velocity magnitude is set to 50 m/s.
• outlet: The type is set to pressure outlet and the guage pressure is to 0 pascal.
• symmetry.
• wall.
• car-walls: The boundary around ahmed body is set to stationary wall with no slip conditions.

Then we will be setting up the hybrid initializtion to initialize the solution and create some useful plots such as the velocity contours. Once these details has been set we will be proceeding to solve using steady state with 1000 iterations.

Results:

Residual Plots:

From the above plot we can see that the solution has been converged and after certain iterations the trend is repeating. Hence we can conclude that the solution is converged. The convergence criteria used in this case is 1e-03.

Pressure Contour on Ahmed Body:

From the pressure contours we can certainly see a increase in the pressure at the frontal area of the ahmed body and negative pressure in the top edge and rear slant end. This is because we can see an increase in the velocity in those specified regions. Hence to maintain the flow the pressure goes negative.

Velocity Contours along cut-plane:

Velocity Contours along cut-plane with mesh lines:

The Velocity and pressure contours are smooth compared to our base coarse mesh case.

Velocity vector along cut-plane:

Velocity distribution infront and behind the ahmed body:

Case 2:

Meshing:

A sectional view of the mesh can be seen in the above image. We can clearly see that the mesh is coarse in the outer enclosure compared to case 1, since we are interested in the physics near the ahmed body. For the outer enclosure the Mesh Element Size of Outer Enclosure is 0.2 m.

Also we can see that the mesh in the inner enclosure is more finer compared to case 1. We have refined this section since this is our area of interest. The Mesh size for the inner enclosure is selected to be 0.04 m. Also face sizing has been refined and its element size is set to be 0.003 m. The inflation layer around the ahmed body remains the same. In total the number of Nodes is 85267 and the number of elements is 349744 is present in the domain which is almost doubled compared to case 1. Also we will be looking through the mesh quality graph for this case.

From the above graph we can see that the mesh quality is pretty good as most of the elemnts are in the range of 75 ~ 95%. Also we can see that the graph represents all types of elemnts present in the geometry such as tetrahedral, hexahedral etc.

We will be naming the faces of the geometry domain in order to define our boundary conditions. We will be creating the following named selections:

• Inlet.
• Outlet.
• Symmetry walls.
• wall.
• Car-walls.

Setup:

We will be using a density based solver since our inlet velocity is 50 m/s. This approximately corresponds to a mach number of 0.3. For mach number above 0.3 it is better to choose density based solver to consider compressibilty. Also we will be solving for the Energy equation and standard k-epsilon turbulence model. The matrial used would be the standard air from the ansys material libary. The boundary conditions are similar to the case 1.

Then we will be setting up the hybrid initializtion to initialize the solution and create some useful plots such as the velocity contours. Once these small details has been set we will be proceeding to solve using steady state with 1000 iterations.

Results:

Residual Plots:

From the above plot we can see that the solution has been converged and after certain iterations the trend is repeating. Hence we can conclude that the solution is converged. The convergence criteria used in this case is 1e-03. It takes around 700 iterations to converge for the above case.

Pressure Contour on Ahmed Body:

From the pressure contours we can see a increase in the pressure at the frontal area of the ahmed body and negative pressure in the top edge and rear slant end. This is because we can see an increase in the velocity in those specified regions. Hence to maintain the flow the pressure goes negative. The results are almost similar to case 1.

Velocity Contours along cut-plane:

Velocity Contours along cut-plane with mesh lines:

The Velocity and pressure contours are smooth compared to our base coarse mesh case.

Velocity vector along cut-plane:

Velocity distribution infront and behind the ahmed body:

Case 3:

Meshing:

A sectional view of the mesh can be seen in the above image. We can clearly see that the mesh is refined in the outer enclosure compared to case 2 but the mesh size of the outer enclosure is similar to case 1. For the outer enclosure the Mesh Element Size of Outer Enclosure is 0.1 m.

Also we can see that the mesh in the inner encloser is more finer compared to case 1 and case 2. We have refined this section since this is our area of interest. The Mesh size for the inner enclosure is selected to be 0.035 m. The face sizing has been kept similar to case 1 and its element size is set to be 0.003 m. The inflation layer around the ahmed body remains the same. In total the number of Nodes is 119765 and the number of elements is 479113 is present in the domain which is almost closer to number of elements which can be solved using a student license. Also we will be looking through the mesh quality graph for this case.

From the above graph we can see that the mesh quality is pretty good as most of the elements are in the range of 75 ~ 95%. Also we can see that the graph represents all types of elements present in the geometry such as tetrahedral, hexahedral etc.

We will be naming the faces of the geometry domain in order to define our boundary conditions. We will be creating the following named selections:

• Inlet.
• Outlet.
• Symmetry walls.
• wall.
• Car-walls.

Setup:

We will be using a density based solver since our inlet velocity is 50 m/s. This approximately corresponds to a mach number of 0.3. For mach number above 0.3 it is better to choose density based solver to consider compressibilty. Also we will be solving for the Energy equation and standard k-epsilon turbulence model. The matrial used would be the standard air from the ansys material libary. The boundary conditions are similar tothe case 1.

Then we will be setting up the hybrid initializtion to initialize the solution and create some useful plots such as the velocity contours. Once these small details has been set we will be proceeding to solve using steady state with 1000 iterations.

Results:

Residual Plots:

From the above plot we can see that the solution has been converged and after certain iterations the trend is repeating. Hence we can conclude that the solution is converged. The convergence criteria used in this case is 1e-03.

Pressure Contour on Ahmed Body:

From the pressure contours we can certainly see a increase in the pressure at the frontal area of the ahmed body and negative pressure in the top edge and rear slant end. This is because we can see an increase in the velocity in those specified regions. Hence to maintain the flow the pressure goes negative.

Velocity Contours along cut-plane:

Velocity Contours along cut-plane with mesh lines:

The Velocity and pressure contours are smooth compared to case 1 and case 2.

Velocity vector along cut-plane:

Velocity distribution infront and behind the ahmed body:

Grid Dependency Test:

Four different locations was selected as shown in the figure below x= -0.02, 0.5, 1.1 & 2.

Velocity Distribution at each location for 3 cases is compared below.

For all the locations and three different cases the velocity distribution is almost similar with the increase of refinement.

In the graph of line 1 we can see that initially the velocity drops. This is because of the increase in the pressure since the ahmed body blocks the flow of air. For the graph of line 2 we can observe that the velocity is not recorded at some points due to the presence of body. For the graph of line 3 we can see that the velocity is negative next to the body, as there is wake and due to recirculation of air moving in opposite direction which can be seen in the vector images.

From the grid dependency test we can conclude that a smoother mesh results in accurate results. But smoother mesh increases the computational time, hence a trade off needs to be made. Also the flow is less diffused if we use finer mesh.

Why does the variation in pressure goes negative?

In most of the area closer to the ahmed body, we can see that the pressure is negative. The reasons for this are:

• To maintain the flow when there is an increase in velocity of the flow.
• Due to flow seperation at the surface.
• Seperation bubbles are produced due to flow seperation which also contributes to the negative pressure.
• Due to recirculation effect or presence of wake.
• Due to the formation of vortex.
• To counterbalance the effect of shear stress.