Ahmed body - Simulation and its grid independence test   (ANSYS Fluent, Skill Lync, Medium)

Aim: To simulate a case of ahmed body and check for grid independence of the solution.

Objectives:

1) To know about an ahmed body.

2) To setup a case of ahmed body.

3) To understand the effect different mesh methods and refinement techniques.

4) To post-process each feature of flow pattern observed in ahmed body.

5) To perform suitable revisions to check for grid independence of solution.

Contents:

1) About Ahmed body

2) Baseline mesh & its results

3) Revisions in mesh & their results

4) Comment on grid independence

5) Conclusion

1) About Ahmed body

      For running various simulations of today's problems, people often write their own CFD codes. This reduces the time required for computation, but there is an ambiguity. The solution given by code might be right or wrong. So to validate the results of our own code, people usually compare their solutions with standard solutions. For external flow problems, such validating is done using results from the Ahmed body.

      Ahmed body concept was invented by S.R.Ahmed in his research in 1984. He made the real life model and carried out the wind tunnel testing of the model and the data obtained from it is referred to as the standard data.

      The slant edge angle is 20 deg.

      This model, however looking simple compared to today's car design, captures salient features obtained in a basic study of external flow over a car.

Features like:

1) Recirculation region formed in the wake region of car due to seperation of flow from top surface.

2) Recirculation region formed in the wake region of car due to seperation of flow from bottom surface.

3) C-Pillar vortices formed due to seperation of flow from side and slant faces.

2) Baseline mesh & its results

Geometry:

      Baseline mesh basically means using the mesh generated by using default settings of Ansys meshing component. So, in this case setup we make a cuboidal shape and subtract the ahmed body from and then defining the remaining volume as fluid domain. This represent the geometry obtained in the wind tunnel.

The dimensions used are:

The origin is kept at the front of ahmed body and in centre of the face.

Mesh details:

Element size = 0.4036 m (system generated)

Number of elements generated =  84443

This is a cut section view of mesh, to show the mesh near ahmed body wall.

Named Selections:

1) Inlet face

2) Output face

3) Symmetry wall face (also on the other side)

4) Car wall

The quality of mesh used is good as the least quality is above 0.1

Setup Details:

Analysis type: Steady state

Solver Type: Density based (Reason stated below)

Solver used : Implicit

Inlet velocity: 50 m/s

(Since the velocity is approximately 1/6th of sound speed, we can expect the velocity to reach upto 3 times in some regions. This suggests us that we must use a density based solver)

Working Fluid: Air (Default properties in fluent database)

Viscous model: k-epsilon realizable model

Number of iterations: 1000

Results:

Velocity Contour:

Velocity contour near ahmed body:

Pressure contour on ahmed body:

Inference:

1) From velocity contours, we can see that boundary layers are not captured accurately and hence they appear irregular.

2) The formation of wake behind the body is not so uniform, so we need to refine the mesh further.

3) The pressure is high at the front face of body. This is caused by velocity reaching zero near surface, so pressure balances this and the value becomes high.

4) A negative pressure region is seen at each leg. (The reason is stated in the end of report)

Revision in mesh & its results:

       As from the inferences stated above, we need to refine the mesh. But refining whole mesh would result in large number of elements and hence would need high computational power. So the solution is to refine the mesh in a particular region where the flow physics is important. The dimension of this region can be found by looking at the velocity contour from above case. Therefore we create a smaller enclosure inside the main enclosure.

     The figures given above show the dimensions of the region of refinement. Here we revise the mesh 4 times and compare the data. The only thing that changes in each revision is the mesh, rest everything remains same.

Revision mesh details:

     The mesh diagram given below shows what are the places where refinement is done and the table below tells the values.

     (The mesh quality graph is not shown here, but the mesh quality used is good because the minimum quality was above 0.1 and average quality was near to 0.85)

Results:

Revision 1:

     The wake obtained is more clear than before and we can faintly see 2 recirculation regions (dark blue region seperated by light blue part). Since the mesh is not too fine, we can see some vectors forming recirculation region.

Revision 2:

     The vectors can be seen more clearly.

Revision 3:

     Here, the difference between 2 recirculation regions is well defined. It might seem that number of arrows are not changing much as expected. This is because the number of arrows to be plotted are reduced by me, in order to avoid crowding of arrows.

Revision 4:

      Here, the number of elements was 4 times the previous case, so the obtained wake was very realistic. The top and bottom recirculation regions were very clearly visible.

Post-Processing Results:

     These images show the C-Pillar vortex. To do this a line is made in front of a side of ahmed body and 3D streamline function is used. The line co-ordinates are: (-0.1,0,0.26), (-0.1,0.7,0.26). The following figure shows how the vortices move around the ahmed body. 12 images used here are taken at location from x = 0.6 to 5 metres.

      In this image we can see the development of bottom vortex, top vortex, their seperation from body and their final shape.

Grid dependence test:

     To check whether solution is dependent on mesh size, we perform grid independence test. It shows us the limit till which we must refine our mesh to get accurate results, since further refining the mesh would only increase computation time.

     The following graph is made by using values from a vertical line inside the wake region for all 5 cases. The line end point co-ordinates are : (1.2,0,0) , (1.2,0.5,0). A total of 100 sample points on each line are used to make the .csv file for each mesh case. The final chart is plotted using MS Excel.

     It can be seen that 1st case of baseline mesh didn't plot a smooth line. The revision 1st and 2nd results have similar form of curve but the values are still not close to each other. The 3rd and 4th revision results have similar form of curve and their results are nearly close to each other. So it can be said that solution must be reaching grid independence point at 3rd revision.

(Note: The lower limit of pressure obtained in any pressure plot of this report is negative. The resaons for this are:

1) The pressure shown here is gauge pressure. So any negative pressure is actually positive in absolute pressure terms.

2) The value is negative because of formation of vacuum. When fluid flows with high speed around any object, the layers of fluid stick to surface and get dragged along it until they seperate from the body. When they seperate, a space (wake) is left out where very few masses of fluid are present. The fluid flowing past it tries to pull it near. Since the space has a continous outward pull for particles, a vacuum is formed. This vacuum zone is present here on and near the leg surfaces.)

Conclusion:

1) The effects observed in the simulation are similar to which can be seen in real life.

2) The grid independence testing is done.