Grid independence test on ahmed body

GRID INDEPENDENCE TEST ON AHMED BODY:

OBJECTIVE:

To perform a grid independence test on the ahmed body and to compare the results.

ABOUT AHMED BODY:

Ahmed Body is a generic bluff body model built to study the external flow and its characteristics over automobile bodies with the help of computational fluid dynamics.The ahmed body actually replicates a passenger car and it helps to capture all the relevant flow physics that are needed to design the body of a car.The Ahmed Body was first created by S.R Ahmed in his research "Some Salient Features of the Time-Averaged Ground Vehicle Wake" in 1984.Since then,it has became an important benchmark for aerodynamics simulation tools.This model is also used to describe the turbulent flow field around a car like geometry.Once the numerical model is validated,it is used to design the new model of car.

The figure shown above is the geometric model of Ahmed Body having standard dimensions.The simple geometric shape has a length of 1.044 metres,height of 0.288 metres,and a width of 0.389 metres.It also has 0.5 metre cylindrical legs attached to the bottom of the body and at the rear surface the slant angle is `20^o`.

MODELLING OF AIRFLOW OVER THE AHMED BODY:

The modelling of the flow of air over the Ahmed Body have been performed in two parts and they are described below:

• PART I: Here the air flow is simulated by making an enclosure over the Ahmed Body and the numerical simulation is carried on.

• PART II : Whereas in this case another enclosure have also been provided as a region of refinement to capture the flow around the Ahmed Body more accurately than the previous case.

As the Ahmed body is perfectly symmetric,a symmetry plan has been created and only the one half of the Ahmed Body has been utilised for the study in order to reduce the computational cost.The split part of the Ahmed Body has been provided below.

The flow for this model is turbulent,which is based on the Reynolds number determined by the body length and the inlet velocity.The simulation solves the turbulent kinetic enrgy in addition to the velocity field.

PART I: SINGLE ENCLOSURE

GEOMETRY:

The geometry has been modified in spaceclaim and an enclosure is provided around the body to capture the flow as per the required dimensions.

MESHING:

• Mesh Element size: 100 mm
• Type of element: Terahedral
• Number of Elements: 5,10,624
• Orthogonal Quality: 0.79

A Body sizing of 100 mm element size has been provided to the enclosure.The meshed geoemtry has been shown below:

No infalation layer has been provided to the model.The mesh metric obtained is shown:

• Most of the elements are having an orthogonal quality near to 0.88,so the mesh is considered to be good.

• Mesh metric for the element quality has been shown above.

SETUP:

• Pressure based solver has been used to solve the problem as only the inlet velocity is 25m/s.
• Steady states was employed.

Model: Turbulence Model- k- omega SST

Material : Fluid - Air

Solid - Aluminium.

Boundary Conditions: inlet - velocity inlet (25m/s)

outlet - Pressure outlet ( Guage pressure = 0 atm )

car-wall - No slip Boundary condition

symmetry - symmetry boundary

domain-wall - No slip Boundary.

Solver : Pressure-velocity coupling - SIMPLE

I.1 Residual Plot:

I.2 Velocity Contour:

• The wake region behind the Ahmed body can be seen above.

I.3 Pressure Contour:

I.4 Velocity Vector Plot:

• From the above plots we can see that the wake regions and the regions where there is a reduction in pressure is not much clearly visible.So inorder to capture the flow correctly and to get a body fitted mesh,we have to provide inflation layers around the Ahmed Body and add another enclosure which can be regarded as the region of refinement.Thus by varying the meshing in this area, we can compare the diferent results obtained.By refining the mesh size only around that enclosure near the Ahmed Body the computational cost of providing much refined grid around the large enclosure can be reduced.

PART II: AHMED BODY WITH REGION OF REFINEMENT

GEOMETRY:

The goemetry of the Ahmed body placed within the enclosure is given below:

• Due to the symmetry of the geometry only the half of the geometry has been studied for the simulation

MESHING:

The meshing has been done by applying multizone meshing method to the outer enclosure

• Type of meshing element : Outer enclosure - Hexa dominant mesh

Inner enclosure - Tetrahedral

• Named selection for the geometry

Different element size for the body sizing has been provided to vary the number of elements and to perform the grid independence test.

• Element sizes :CASE A. 50 mm

CASE B. 40 mm

CASE C. 30 mm

CASE D. 20 mm

CASE E. 15 mm

• For the Reynolds number calculated with the inlet velocity and the body length of the Ahmed Body , the target Y+ value was 100. Hence to obtain this target Y+ value, the height of the first cell from the wall was calcuated to be 2 mm.

Infaltion: Number of inflation layer - 5

First layer height - 2 mm

Growth rate - 1.2

• Meshing profile showing the inflation layers for a body sizing for inner enclosure element size 20 mm.

• Meshing profile with the hexa dominant meshes in the outer enclosure.

SETUP:

• Pressure based solver
• Steady-state simulation

Model :Turbulence Model - k - epsilon Realizable with scalable wall functions.

Material : Fluid - Air

Solid - Aluminium

Boundary Condition : inlet - velocity inlet (25 m/s)

outlet - Pressure outlet ( Guage Pressure - 0 atm)

car-wall - No slip condition

bottom-wall- No slip condition

domain-wall - No slip condition

symmetry - symmetry boundary

Solver: Pressure- velocity coulping- SIMPLE

Number of Iterations : 600

CASE A.

A.1 Residual Plot:

• The flow converged at about 122 iterations.

A.2 Coefficient of drag:

• Coefficient of drag at car-wall Cd is 0.358

A.3 Coefficient of lift:

• Coefficient of lift,Cl is 0.272

A.4 Velocity Contour:

A.5 Pressure Contour:

A.6 Vector plot of velocity:

• The wake regon behind the car is visible

CASE B:

B.1 Residual Plot :

• The flow converged at about 200 iterations as the residual plot are appearing to be in a repeating pattern.

B.2 Coefficient of Drag:

• Coefficient of Drag,Cd = 0.335

B.3 Coefficient of lift:

• Coefficient of lift,Cl = 0.276

B.4 Velocity contour:

B.5 Pressure contour:

B.6 Vector plot for velocity:

CASE C:

C.1 Residual Plot:

C.2 Coefficient of Drag:

• Coefficient of drag at car-wall,Cd=0.3278

C.3 Coefficient of Lift:

• Coefficeint of lift at car-wall,C= 0.2846

C.4 Velocity contour:

C.5 Pressure conotur:

C.6 Vector plot for velocity:

CASE D:

D.1 Residual Plot:

D.2 Coefficient of Drag Plot:

• Coefficient of drag at the car-wall ,Cd=0.3276

D.3 Coefficient of Lift Plot:

• Coefficient of lift at the car-wall,Cl=0.272

D.4 Velocity contour:

D.5 Pressure contour:

D.6 Vector plot for velocity:

CASE E:

E.1 Residual Plot:

• The flow havent converged within the 600 iterations , but the residual plot appears to be the same over a number of iterations.

E.2 Coefficient of Drag Plot:

• Coefficient of Drag at the car-wall,Cd= 0.3275

E.3 Coefficient of lift plot;

• Ceofficient of lift at the car-wall,Cl= 0.2677

E.4 Velocity Contour;

E.5 Pressure contour:

E.6 Vector plot for velocity:

• Clearly the wake region is visible in this case and the it can be seen that the velocity vectors avoiding the wake region.

GRID INDEPENDENCE TEST:

Number of Elements Coefficient of Drag,Cd Coefficient of list,Cl

88,514 0.358 0.272

1,37,377 0.335 0.2846

2,75,313 0.3278 0.276

8,20,555 0.3276 0.272

18,48,157 0.3275 0.26677

• The datas obtained from the various simulations has been tabulated above.

• From the plot for the coeffcient of drag it is clearly visible that the value of Cd,becomes almost the same at a particular number of grid.Thus,instead of increasing the number of grid,which inturn increase the computational cost,we can use lesser number of grid which will give the same result.
• Here as shown above,we can see that for grid number almost near to 5,00,000 the value of the Cd becomes constant.

RESULTS & CONCLUSIONS:

• There is a variation in the pressure along the ahmed body from the front to the rear side,one of the reason for the negative pressure at the rear is due to the seperation of flow at at the rear and the other reasons are as follows

- Due to the recirculation of the air

- To counter the shear stress effects

- When the velocity is increased over the bodyto maintain the flow,pressure becomes negative.

• For a lower number of grid points also,we will be able to obtain required results,but the regions of the wake is clearly visible when the meshing profile with higher number of grud points are higher.

Thankyou

Arjun Vs