Modeling and Simulation of Airflow around an Ahmed Body for a 35-degree slat using converge studio

Objective:

• Create the CAD model using CATIA as per dimensions (35-degree slant)
• Setup a Coarse CFD simulation
  • Setup the virtual wind tunnel as shown in the video
  • Apply the right boundary conditions and solver settings
  • Use a coarse mesh to demonstrate that your setup runs successfully
    • You need to show an animation of the velocity distribution and pressure distribution on a cut plane. This cut plane should cut the Ahmed body model in two symmetric pieces.
    • Post-process the coarse mesh results and extract the x component of velocity along a line(Here, I am assuming that the normal of the intake boundary is along the +x direction)
    • The line should be perpendicular to the ground plane.
  • Enable wall-averaged outputs to measure the drag and lift forces
    
    • Calculate the steady-state drag force value and explain your calculation procedure.
    • Calculate the drag co-efficient using ParaView and explain your calculation process in detail

Ahmed Body:

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 become a benchmark for aerodynamic simulation tools. The simple geometrical shape has a length of 1.044 meters, the 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 and the rear surface has a slant that falls off at 35 degrees.

The simple geometry of an Ahmed body.

Geometry

The geometry is created based on the simplified aerodynamic body used by Ahmed body. The slant angle is set to 35 degrees.

Fig.1 Dimensions of the Ahmed Body

There are certain ways to modify a car to optimize its aerodynamics and decrease the drag coefficient. To streamline the exterior, you can remove certain aftermarket items such as the roof rack, mud flaps, spoilers, and radio antenna. Professional car racers also take off their windshield wipers and side mirrors, but this isn’t recommended for the average driver! You can also add wheel covers, a partial grille block, an undertray, fender skirts, and a modified front bumper to improve the drag coefficient and make your car stand out in the process.

PHASE 2: CASE SET UP FOR PRE PROCESSING

Model created in CATIA (.STL file) and then imported in converge studio for simulation set up

VIRTUAL WIND TUNNEL SET UP FOR AHMED BODY

BOUNDARY CONDITIONS:

General flow

RUN PARAMETERS:

Transient solver with full hydrodynamic mode was chosen

SIMULATION TIME PARAMETERS:

The end time was calculated using the flow-through time formula for Ahmed body the value is around 1.25s.

NOTE: (5 times greater than flow through time )

REGIONS AND INITIALIZATION:

The region created here is named as Region 0. The inlet velocity is the same as inlet flow velocity.

oxygen with a concentration of 0.23

nitrogen with a concentration of 0.77

Temperature- 300K,

Pressure- 101325 Pascal

If we specified velocity in regions will take a shorter time to compute the simulation process.

TURBULENCE MODEL:

For the purpose of this project, I have chosen standard k-ω SST because it solves two transport equations to resolve Reynolds stress tensor. In addition, it addresses some additional issues namely poor predictions of swirling and rotating flows. It has an automatic enhanced wall treatment function. For this case the Y+ value should be 0.5 -300 otherwise it goes below 10 or 1 it will use enhanced wall treatment.

CASE SET UP:

The turbulence model used is k -ω\">ω SST because it has automatic wall function and also used for external flow simulations. PISO (pressure implicit with splitting of operator) is used for pressure- velocity coupling it converts non-linear to linear systems. SOR ( Successive over-relaxation) is used for solving algebraic equations.

Flow Inlet Parameters

μ=1.789 x 10-5 kg/m.s

ρ= 1.225 kg/m3.
V = 40m/s.
Re =768,000 (based on object’s length).
ν=15 × 10−6

The base grid sizes are calculated using the below-Mentioned terms free stream velocity, density, characteristic length, dynamic viscosity, and desired (Y+).

Website name: http://www.pointwise.com/yplus/. The following equations are also used to finding the wall spacing value:

1. Reynolds Number:

Reynolds number is a dimensionless value which is applied in fluid mechanics to represent whether the fluid flow in a duct or pat a body is steady or turbulent. This value is obtained by comparing the inertial force with the viscous force.

Reynolds number is given by,

Reynolds Number = Inertial Force / Viscous Force

The Reynolds number formula is expressed by,

where:

• ρ is the density of the fluid ( kg/m³)
• u is the velocity of the fluid with respect to the object (m/s)
• L is a characteristic linear dimension (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/m·s)
• ν is the kinematic viscosity of the fluid (m²/s).

The Kind of flow is based on the value of Re

1. If Re < 2000, the flow is called Laminar
2. If Re > 4000, the flow is called turbulent
3. If 2000 < Re < 4000, the flow is called transition.

2.SKIN FRICTION COEFFICIENT:

3. WALL SHEAR STRESS:

The wall shear stress, is given by:

`τ_ω = (C_f.ρ.V^2)/2`

Where is the dynamic viscosity, is the flow velocity parallel to the wall and is the distance to the wall.

The SI unit of wall shear stress is pascal ().

4.FRICTION VELOCITY:

5.WALL SPACING:

A non-dimensional wall distance for a wall-bounded flow can be defined in the following way:

Where is the friction velocity at the nearest wall, is the distance to the nearest wall and is the local kinematic viscosity of the fluid.

is often referred to simply as y plus and is commonly used in boundary layer theory and in defining the law of the wall.

To resolve the bpoundary layer on the body I need more cells so I have side fixed embedding. For capturing accurate wake and flow behind the body, the box embedding is used. The box size should be at least 2 or 3 times the length of the Ahmed body.

Based on these calculations, the wall spacing value is found out to be 0.31. So it will take a long time for simulation because of finer mesh. For this reason, im taking a base mesh size of 0.09 to run the simulation.

SIMULATION SETUP:

The virtual wind tunnel created with the dimension of 16.57 in length and height is 1.5 and the width is 1.556 on both sides. The outlet distance is above 10 times the characteristic length then only it will easy to visualize flow data accurately.

Calculation the slip region:

where

is the density

is the freestream velocity

is the kinematic viscosity

is the overall thickness (or height) of the boundary layer

is the Reynolds number

is the distance downstream from the start of the boundary layer

μ is the dynamic viscosity

By substituting these values

μ=1.789 x 10-5 kg/m.s

ρ= 1.225 kg/m3.
V = 40m/s.
Re =768,000 (based on object’s length).
ν=15 × 10−6

The value of X will be 1.18 m. This is the place where the slip region ends. The body is kept at a distance of (2+ 1.18 + 0.4 ) from the inlet

DRAG AND LIFT COEFFICIENT CALCULATIONS:

DRAG COEFFICIENT:

The drag coefficient (C_d) is defined as the aerodynamic drag coefficient is a measure of the effectiveness of streamlined aerodynamic body shape in reducing the air resistance to the forward motion of a vehicle. A low drag coefficient implies that the streamline shape of the vehicle\'s body is such as to enable it to move easily through the surrounding viscous air with the minimum of resistance; conversely a high drag coefficient is caused by poor streamlining of the body profile so that there is a high air resistance when the vehicle is in motion.

C_d= 2.D / ρ.A.V2

where:

d is the drag force,

ρ is the mass density of the fluid,

V is the flow speed of the object relative to the fluid,

A is the reference area.

LIFT COEFFICIENT:

The lift coefficient (C_L) is a dimensionless coefficient that relates the lift generated by a lifting body to the fluid density around the body, the fluid velocity and an associated reference area A lifting body is a foil or a complete foil-bearing body such as a fixed-wing aircraft. C_L is a function of the angle of the body to the flow, its Reynolds number and its Mach number. The lift coefficient c_l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord.

C_d= 2.L /ρ.A.V2

where:

L is the lift force,

ρ is the mass density of the fluid,

V is the flow speed of the object relative to the fluid,

A is the reference area.

OBSERVATIONS:

Mesh:

Y- Plus :

Fig 1. Y PLUS

Video 2. Y PLUS animation ( FRONT)

Video 3. Y PLUS animation ( BACK)

Video 1. Y PLUS animation

VELOCITY CONTOUR:

Fig 1. Velocity profile ( Front)

Fig 2. Velocity profile ( Back)

Fig 3. Velocity on cylindrical legs

Video 1. Velocity animation

Video 2. Velocity animation

Video 3. Velocity animation

PRESSURE :

Fig 1. PRESSURE ( CUT SECTION )

Fig 2. PRESSURE

Video 1. Pressure ( cut section ) animation

Video 2. Pressure animation

CALCULATING LIFT AND DRAG FORCES:

1. open the (test.vtm file case) and then go to filters and select Extract block. then choose the Ahmed body and wheels as the block to calculate the lift and drag.

2. Next, generate the surface on block. go to filter select Extract Surface.

3. After that genrate the surface normals. Again go to filter, select the generate surface normals and check the box \' compute cell normals \'.

4. To calculate lift. Select the calculator and choose Pressure from the scalar drop-down menu then multiply it with Normals Z In the Result Array name box writes down as lift.

5. To calculate Drag. Select the calculator and choose Pressure from the scalar drop-down menu then multiply it with Normals X. In the Result Array name box writes down as Drag.

6. finally, we choose to integrate variables to get the lift and drag force value in the paraview. For calculation drag and lift coefficients we need area, it can be measured using the converge studio with the help of area measuring Tool.

LIFT:

Fig 1. LIFT ( CUT SECTION )

Video 1. LIFT animation

DRAG:

Fig 1. DRAG ( CUT SECTION )

Video 1. Drag animation

GLYPH VECTOR MAGNITUDE:

Fig 1. GLYPH VECTOR MAGNITUDE

Video 1. GLYPH animation

GRAPHS ( Line Probe):

RESULTS:

The Y plus value here used between 30-100 because if we use low value then the cell is in the viscous layer. Indeed, the Y plus is uniform throughout the Ahmed body with reduced value.

The pressure and velocity visualization of the front face of the Ahmed body it shows an increase in pressure and decreases in pressure which is known as Bernoulli\'s effect. the pressure and velocity visualization on the rear side of the slant edge there decrease is decrease pressure so it created circulation which is known as wake region. Also, the bottom of Ahmed body near cylindrical legs showing the circulation which is known as Von Karman vortex sheet.

Most of the drag appears on the rear side of the Ahmed body which can be visualized in a cut section of body. This type of drag is known as pressure drag ( Body drag ). Here Coanda effect and suction peak appeared but not uniformly so visualizing will be difficult. suction peak is nothing but a sudden increase in velocity and a drop in pressure.

The flow strikes the Ahmed body divided into two higher pressure on the front surface and lower pressure on the lower surface. Then the flow leaving the slant edge makes pressure drop.

The wake structure can be visualized with the help of glyph the flow detached from the bottom surface of the body and the flow splitting on the leg will eventually join and form the single flow circulation.

The line probe was drawn by using the plot over the line and the X, Y, Z coordinates were used. Points Z was selected to lie on X-axis and Velocity X was selected to lie on Y-axis. Then the graphs were created in the excel with the help of data from paraview and the experimental data already given in the challenge. The line probe each situated at a distance of 0.03 metres and Ahmed body height 288 mm with free stream velocity of 40 m/s. In the beginning, I have to measure the region and I have to set up origin with respect to the experimental data origin. So it will be easy to compare both data.

-13 mm was created at the slant edge in that we can get negative velocity after 0.28 m away from the Ahmed body the flow increases. Then -63 mm was created before the surface starts slanting and - 113 mm was created in the middle section of Ahmed body were both probes we can get negative velocity and more than 5% error. Then the -263 mm was created near the front side of the Ahmed body.

Then the positive line probes the 37 mm created where the strongest recirculation zone occurs and the flow appears almost similar to -63 mm and -113 mm. Then the 187 mm was created below the recirculation zone and it is also far away from the Ahmed body with positive velocity.

REFERENCES :

1. NPTEL

2. Skill lync youtube videos

3. Experimental data are available from Dr s. Becker, H. Lienhart, C. Stoots, ERCOFTAC Workshop (9.4 )

4. Wikipedia