Flow Analysis Over Ahmed Body

INTRODUCTION:

Ahmed Body: Ahmed body is simplified model of an automobile or generic car ,first defined and studied by S.R.Ahmed in his research work called \"Some Salient Features of the Time- Averaged Ground Vehicle\" in 1984. It is now used as a reference model for the external flow analysis of automobile.

Significance:

• The airflow over Ahmed body captures the crucial flow field characteristics around an automobile.
• It\'s experimental data forms the basis for the validation of CFD codes or results of CFD simulation on vehicle aerodynamics
• It also helps to determine the influence of flow condition like air velocity on the Auotmobile.
• It is used for studying vehicle aerodynamics parameters like drag coefficient, lift coefficent and turbulences.
• There are lots of datas available on Ahmed body.

1.Problem Specifications:

3 dimensional simulation of Ahmed body is performed which is subjected to the free stream velocity of 50m/s. The fuid taken is air and the main objective is to perform grid independency test .The simulation is performed for three different setup with differnt element sizes in addition to baseline setup.Velocity profiles and pressure distributions are obtained.

2.Mathematical Model:

The simulation is governed by the conituinty, momentum and energy equation. Since the flow is turbulent ,we will be using Reynolds Average version of these equations. The turbulence model used is standard k-ε turbulence model.

These differential equations are converted into large set of algebraic equations which is then inverted using iterative process to get values of variables(u,v,w,ρ,T,p) at cell centres.Then everthing else is derived from these cell centred values.

3.Geometry:

The external geometry file of Ahmed body is imported. The flow domain is created around it using rectangular enclosure in SpaceClaim. Two rectangular enclosures is created, outer and inner enclosures, of the dimensions as shown in the figure below. The inner enclosure is created for local mesh refinement around Ahmed body.

Fig 3.1 Isometric View of Outer Enclosure

Fig 3.2 Side View of inner enclosure

Fig-3.3 Back View of an inner enclosure

4.Mesh Generation:

At first the baseline mesh is genrated and numerical simulation is performed.Then, the mesh refinement is done with 3 different setup containing different element sizes.

BaseLine Mesh:

The number of nodes and elements in the flow domain is 16696 and 84641 respectively.

The mesh parameters are as follows:

Element Type: Tetrahedral

Element Size: 0.4123m

No. of Element: 84641

Fig 4.1-The outer isometric view of Mesh

Fig 4.2- Mesh inside the flow domain

Fig 4.3: Closeup view of mesh near the Ahmed body\'s wall

The element quality of mesh is shown in the figure below and it is good and accetable for further processing.

Fig 4.4: Element quality of baseline mesh

5.Solver Setup:

Solution modelling: 3dimensional - Steady - Density based - Energy on - Standard k-ε

Material: Air density, ρ = 1.225 kg/m3

dynmaic viscosity, μ =1.789 x 10−5 kg/m-s

Specific heat capacity, Cp=1006.43 J/kg-k

Boundary conditions:

6. Numerical Results:

6.1 Residual plot

Residuals are allowed to drop as low as possible until the convergence is achieved.

Fig 6.2- Velocity distribution over a cutplane (xy plane, z=0)

Fig 6.3 - Streamlines on a midplane

The above figures shows the velocity distribution and streamlines over the midplane (XY plae, Z=0) for the BaseLine setup. To capture the flow field parameters nicely in the flow domain and for more accurrate results, fine mesh is needed . Therefore, Meshrefinement is done next.

7. Mesh Refinement:

7.1 Case1:

As I have shown earlier in the Geometry section that inner enclosure is created for the local mesh refinement around the Ahmed body. Outer enclosure consists of hexahedral mesh and inner enclosure is made up of tetrahedral mesh.

Mesh parameters are as follows:

Type of Element : Outer enclosure - hexahedral

Inner enclosure - tetrahedral

Element Size : Outer enclosure - 0.1m

Inner enclosure - 0.05m

Inflation Layer : Car wall

No of layers : 5

Maximum thickness : 0.012m

Growth rate :1.2

No of nodes : 63183

Cell count : 207897

Fig 7.1- The Outer isometric view of Mesh

Fig 7.2- Mesh Inside the Flow Domain

Fig 7.3- Closeup view showing inflation layers

Nice and beautiful mesh shown above have good element quality and it is shown in the graph below.

Fig 7.4: Element quality

Solver setup and results:

The solution modelling done is similar to the one done in the Baseline setup. The boundary conditions given are also same.

Fig 7.4- Residual plot

As you see from the above graph that residual value fell below 0.001 at 621th iteration.

Fig 7.5- Velocity distribution over the mid plane

Fig 7.6- Streamlines on the midplane

The above figures show the velocity distribution and streamlines over the midplane (XY plane, Z=0). It is observed that there is high velocity region at the fillet on the leading edge of the body which is due to acceleration of flow as explained by conservation of mass and energy when fluid flows in a streamtube. Disturbance in the uniform flow due to presence of Ahmed body can be seen from the streamlines, the flow separation and wake formation at the back of the body is also observed.

7.2 Case2:

Further mesh refinement is done here. The grids in the outer and inner enclosure is refined to a smaller sizes. The mesh parameters are as follows,

Type of Element : Outer enclosure - hexahedral

Inner enclosure - tetrahedral

Element Size : Outer enclosure - 0.08m

Inner enclosure - 0.04m

Inflation Layer : Car wall

No of layers : 5

Maximum thickness : 0.012m

Growth rate :1.2

No of nodes : 99033

Cell count : 338021

Fig 7.7 - Outermesh

Fig 7.8- Inside mesh

Fig 7.9- Closeup view showing inflation layers

The mesh qualities are good and accetable as shown below.

Fig 7.9- Element quality

Solver Setup and Results:

The solution modelling done is similar to the one done in the previous setup and also the same boundary conditions are given.

Fig 7.10 - Residual plot

As you can see the residuals are allowed to drop as low as possible.

Fig 7.11- Velocity distribution over midplane

Fig 7.12- Streamline on the midplane

7.3 Case3:

Here meshes in outer and inner domain are further refined.The mesh parameters are as follows:

Type of Element : Outer enclosure - hexahedral

Inner enclosure - tetrahedral

Element Size : Outer enclosure - 0.08m

Inner enclosure - 0.04m

Inflation Layer : Car wall

No of layers : 5

Maximum thickness : 0.012m

Growth rate :1.2

No of nodes : 99033

Cell count : 338021

Fig 7.13- Outer isometric view of Mesh

Fig 7.14- Mesh inside the Flow Domain

Fig 7.15- Closeup view showing inflation layers

Fig 7.16 - Element quality

The quality of mesh is shown in the above figure and it is good and accetable for further processing.

Solver Setup and Results:

The solution modelling done is similar to the one done in all the setups and also same boundary conditions are given.

Fig 7.17- Residual plot

The convergence criteria of 0.001 residual value is attained at 758th iteration and it was allowed to drop further for around 100 more iterations.

Fig 7.18 - Velocity distribution over the midplane

Fig 7.19- Streamlines on the Midplane

Flow acceleration, flow separation and formation of wake as flow takes place is observed.

Grid Dependency Test:

Fig 7.20 - Monitor lines in a midplane

Fig 7.21- Velocity profile at vertical line 1.5m from the origin

Fig 7.22- Velocity profile at vertical line 2m from the origin

In order to determine the optimum mesh model, 2 vertical monitor lines are considered on a mid plane at a distance of 1.5m and 2 m from the origin and the velociy profile at these lines are obtained from all three cases and compared.

As it can be seen from above graphs, there is big deviation between Baseline setup and Case1. But as we go from the Case1 to Case2 , the deviation gets smaller. The velocity profiles of Case 2 and Case 3 almost concides at most of the points. So, I would use Case2 for further simulation considering computational time and cost.

Pressure Distribution(explaination for negative pressure value):

Fig 7.23- Pressure distribution on a midplane

Fig 7.24- Pressure distribution over a car surface

Fig 7.25 - Pressure distribution over a car surface

Pressure distribution on the surface of Ahmed Body is shown above. It is clear that frontal area has the highest value of pressure this is due to the air molecules striking the frontal area and converting the dynamic pressure into static pressure.

It is also observed that the pressure value goes negative which implies that pressure in those region is less than the operating pressure which we have set to 101325 pascal. At the leading edge curves pressure is low because flow accelerating at that region as the mass flow rate and total energy of fluid molecules remains constant as it flows through the streamtube.

At the back of the Ahmed body, wake region is formed, therefore there is a low pressure region over there.