Week 3 - External flow simulation over an Ahmed body.

Objective :

To run the simulation of Ahmed body for the velocity of 25 m/sec with the default air properties in fluent.

In this challenge, answers to the following questions needs to be provided

Q1. Describe Ahmed's body and its importance.

Q2. Explain the reason for the negative pressure in the wake region.

Q3. Explain the significance of the point of separation.

Expected Results:

1. Velocity and pressure contours.

2. The drag coefficient plot for a refined case.

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.

Ahmed body and its significance

Ahmed body is simplified car model created by S.R. Ahmed in 1980’s to investigate the behaviour of newly developed turbulence models for complex geometry cases. The Ahmed body is made up of a round front part, a movable slant plane placed in the rear of the body to study the separation phenomena at different angles, and a rectangular box, which connects the front and rear slant plane as shown in figure below. The simple geometrical shape has a length of 1.044 meters, height of 0.288 meters, and a width of 0.389 meters. It also has 0.5-meter cylindrical legs attached to the bottom of the body.

Ahmed body is simplified model of a car body, but it demonstrates all the flow features involved in an actual case of a moving car. Due to the considerable deviation of its geometry from normal vehicles, the body represents the basic aerodynamic properties of a vehicle, especially in the rear part. Its shape is simple enough for accurate simulation and retains some important features with respect to automobile body. This model helps to calculate turbulent flow field around a simple car model.

Cad Model

The geometry loaded in Ansys Spaceclaim is as follows

A virtual wind tunnel is created using prepare-enclosure option. Another enclosure is created close to Ahmed body in order to cpature the physics near the Ahmed body region more accurately. Split body command is used to split the Ahmed body into half. Ahmed body is supressed for physics for external simualtion.

Interference check is done in order to avoid overlapping region. If there are any interference region, they are to be removed so that meshes from both region do not overlap and we can have conformal mesh. Share topolgy must be enabled for proper exchange of information.

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Creating Named Selection

Mesh Generation

Initially a baseline mesh is created which is as follows

The initial baseline mesh generated is refined in order to achieve better results of simulation. The type of mesh element used for outer enclosure used is hexa mesh as it has highest efficiency for rectangular domain.

The size of inner enclosure is futher refined to achieve better results of simulation

The cylindrical pillars of Ahmed body are refined in order to maintain its circularity.

Inflation Layer

Calculation of first layer thickness

Re = ρVL/μ

Here, V = 25m/s, ρ = 1.225 kg/m³, μ = 1.7894e-5 kg/m-s, L = 1.044m

Hence, Re = 1786772.102

C_f = 0.058/(Re)^0.2

C_f = 0.003258

𝜏_w = C_fρv²/2

𝜏_w = 1.2472

u_f = (𝜏_w/ρ)^0.5

u_f = 1.009

The value of y⁺ considered is 50

Hence, first layer thickness (y) is determined by

y = y⁺ μ/u_fρ

y = 0.73mm

Therefore, first layer thickness for y⁺ value of 50 is 0.73mm

When value of y⁺ considered is 100, the first layer thickness is 1.46mm

When value of y⁺ considered is 100, the first layer thickness is 2.92mm

Final Mesh

Setting up pre-processing physics

K-epsilon model is selected as the viscous model

The reference values for the simulation are as follows :

For setting up boundary conditions, the initial velocity is given as 25 m/s

Post Processing

Case 1

Body sizing : 0.05m

y+ 200

Inflation layer : 2.92mm

Number of Mesh elements : 91420

Case 2

Body sizing : 0.035m

y+ 100

Inflation layer : 1.46mm

Number of Mesh elements : 195185

Case 3

Body sizing : 0.025m

y+ 50

Inflation layer : 0.73mm

Number of Mesh elements : 456546

Significance of the point of separation

Flow 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. During the fluid flow over a body, shear stress caused by viscosity has a retarding effect upon the flow. This effect can however be overcome if there is a negative pressure gradient offered to the flow. A negative pressure gradient is termed a favourable pressure gradient. Such a gradient enables the flow. A positive pressure gradient has the opposite effect and is termed the adverse pressure gradient. Flowing against an increasing pressure is known as flowing in an adverse pressure gradient. The boundary layer separates when it has travelled far enough in an adverse pressure gradient that the speed of the boundary layer relative to the surface has stopped and reversed direction. One of the severe effects of an adverse pressure gradient is to separate the flow. The flow becomes detached from the surface and instead takes the forms of eddies and vortices.

Reason for negative pressure in the wake region

A wake is the region of recirculating flow immediately behind a moving or stationary blunt body caused by viscosity which may be accompanied by flow separation and turbulence. In case of Ahmed body, wake is formed by separation of air moving over the vehicle at the rear end which leaves a large low pressure turbulent region behind the vehicle. As a result, the wall shear stress and velocity becomes zero and formation of wake starts. The wake is responsible for the formation of pressure drag which impacts the overall performance of the vehicle.

Mesh Independence

Sr No	Inner Body Sizing (m)	No of Mesh Elements	Y+	1st Layer Thickness (mm)	Cd	Cl
1	0.05	91420	200	2.92	0.4064	0.2532
2	0.035	195185	100	1.46	0.3516	0.2738
3	0.025	456546	50	0.73	0.3325	0.3021

From the above table, it can be seen that the first refinement produces results which are closer to actual value. Only if high accurate results are desired then mesh should be refined further so that computation power and time require for simulation is optimized.

Conclusion

• For this simulation, the results obtained from baseline simulation deviated too much from actual results, hence appropriate mesh refinement was done.
• With increase in number of mesh elements, the value of drag coefficient decreases and reaches closer to actual value.
• Appropriate selection of y+ is important in accurately determing the value of drag coefficient.
• From the mesh independence test, it can be seen that decreasing the size of mesh element and y+ produces the results which are closer to actual value.