EXTERNAL FLOW SIMULATION OVER AHMED BODY

OBJECTIVE :

To perform external flow simulation over Ahmed Body.

To perform the grid dependency test and to provide the values of the coefficient of drag for each case.

THEORY :

The Ahmed body is a generic car body (a simplified vehicle model). The airflow around the Ahmed body captures the essential flow features around an automobile and was first defined and characterized in the experimental work of SR Ahmed in his research Some salient features of time average ground vehicle wake. Although it has a very simple shape , the Ahmed body allows us to capture characteristics features that are relevant to bodies in the automobile industry.

The simple geometrical shape has a Length of 1.044 m , Height of 0.288 m , and a width of 0.389 m . It also has 0.5 m cylindrical legs attached to the bottom of the body and the rear surface has a slant that falls off at 40 degrees.

IMPORTANCE OF AHMED'S BODY :

• The three-dimensional flow around a vehicle has become a subject of significant importance in the automotive industry . One apparent technique of improving the fuel efficiency of a vehicle is to reduce aerodynamic drag force by optimizing the body shape .

• Execution of fine aerodynamic design under stylistic constraints requires an immense understanding of the flow pattern phenomena and how the aerodynamics are impacted by changes in body shape.

• The flow area which is presents the major contribution to a cars drag is the wake flow backing the vehicle . The point at which the flow seperates directs the size of the separation zone , and as a result the drag force . Clearly,a more accurate simulation of the wake flow.

• Most cars have an average drag coefficient between 0.30 and 0.35 . Boxy cars have a higher number , like the HUMMER H2 vehicle at 0.57 , while more streamlined and agile cars have a lower number , like the Mercedes-Benz vehicle at 0.24 . Again , this is just an average measurement . The exact drag coefficient of a car varies with the Reynolds number and various other factors.

Y⁺ Concept :

The behaviour of the flow near the wall is a complicated phenomenon and to distinguish the different regions near the wall the concept of wall Y⁺ has been formulated. Thus Y⁺ is a dimensionless quantity, and is distance from the wall measured in terms of viscous lengths.

Where ,

ρ , µ are fluid density and viscosity ;

U is the free stream velocity ;

L is characteristic length ;

U_τ is frictional velocity ;

τ_ω is wall stress , C_f is skin friction coefficient

In this case , we take Y⁺=200 ;

From the calculation ,

We got first layer thickness is found to be 3 mm(0.003m)

Thus , Total thickness =3 * (1.2)^(6-1) =7.4645 mm ≈ 7.5 mm

PROCEDURE :

STEP 1 : GEOMETRY USED

The geometry is taken from the modelling software into the space claim

BASELINE ENCLOSURE REFINED ENCLOSURE

SECTIONAL VIEW

STEP 2 : MESHING

For this analysis , a baseline mesh along with 3 refinements has been done with the following features. Only baseline mesh and the finest refinement of the meshings are included in this report for the reference.

BASELINE MESHING

BASELINE mesh of the Computational Domain : SECTION VIEW :

REFINED MESHING

REFINED mesh of the Computational Domain : SECTION VIEW :

NAMED SELECTIONS of Domain :

STEP 3 : SET UP & SOLUTION

Fluent Setup

- Solver type : Pressure based

- Check the Energy equation

- Turblent Model : K-Epsilon – standard (Range of Y⁺ value is 30 - 300)

- Fluid Material : Air

Boundary conditions

- Inlet velocity : 25 m/s

- Outlet pressure : 0 pa

- Symmetry : For side walls

- Wall : Bottom

Reference Values :

- Create a surface plane to see the contours.

- Create a Cd plot for Ahmed wall.

Expected Results:

1. Velocity and pressure contours.

2. The drag coefficient plot for a refined case. ( For velocity of 25m/sec )

3. The vector plot clearly showing the wake region.

4. Perform the grid independency test and provide the values of drag and lift with each case.

The Following are the various details of the mesh used in this simulation run :

NOTE : Further refinement cannot be done because the cell count exceeds 500000 cells which cannot be solved in the academic version.

STEP 4 : RESULTS

BASE LINE SETUP RESULTS

Residual plot :

Velocity Contour : Pressure Contour :

Drag Coefficient for baseline : Velocity Vector :

REFINED CASE RESULTS

(Most Refined Case)

Residual Plot : Drag Coefficient for the refind case ( 3rd refinement) :

Velocity Contour for finest refinement : Pressure Contour for finest refinement :

Velocity Contour showing Mesh lines : Velocity vector for refined case :

GRID INDEPENDENCY TEST :

Following table shows the tends of Drag Coefficient vs Refinement :

Graphical Analysis :

The following table represents the values of Drag force and Lift force :

Drag Coefficient :

In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

Negative -ve Pressure at Wake :

The moment the flow hits the front of the pressure gets increased , then accordings to Bernoulli’s theorem that flow gets divided between the upstream and downstream of Ahmed body having high and low velocity respectively.

As the flow gets unable to navigate the surface , the upper layer i.e free velocity goes straight . The boundary layer experience a disruption making some of particle get goes straight some gets separated and takes reverse direction , only few particles cope up with contour of the body . this creates a low pressure region that has negative pressure at the back.

On the other hand at the base side , the pressure is high compared to the overhead side of Ahmed body but the pressure keeps on increasing as it can seem to from the contour . The already created low pressure region by the upstream flow causes the flow to move straight.

The pressure region also causes the some air molecules to get reattached to the Ahmed body which makes a recirculation region . The low pressure region at the rear cause a pressure drag . As the flow from the front get heavily attracted gets attracted toward low pressure.

Significance of the Point of Separation :

• A flow separates as soon as it detaches from a surface into a wake . It occurs when the flow slows and there is an increase in the pressure after passing a bluff or streamlined body.

• The position at which the boundary layer leaves the surface of a solid body. It may occur with the laminar flow (laminar separation) or when the boundary layer is turbulent (turbulent separation). Separation is sometimes followed by reattachment of the flow.

• Flow separation or boundary layer separation is the detachment of a boundary layer from a surface into a wake.Separation occurs in flow that is slowing down, with pressure increasing, after passing the thickest part of a streamline body or passing through a widening passage. For example , Flowing against an increasing pressure is known as flowing in an adverse pressure gradient.

References :

https://www.researchgate.net/publication/266883948_Flow_and_Turbulence_Structures_in_the_Wake_of_a_Simplified_Car_Model_Ahmed_Model

https://www.researchgate.net/publication/330383775_Experiments_and_numerical_simulations_on_the_aerodynamics_of_the_Ahmed_body