Week 3 - External flow simulation over an Ahmed body.

Given data

Flow velocity of air = 25 m/sec.

The geometry of the Ahmed body along with all dimensions is as given below in the figure.

For our model slant angle is 20*.

Theory

The Ahmed body is a generic car body (a simplified vehicle model). The air flow around the Ahmed body captures the essential flow features around an automobile like wake forces, drag forces etc. and was first defined and characterized in 1984 by Ahmed et. al. the Ahmed body is designed to have smooth-edged front end with a flat roof and a flat bottom section and an angle back slant which basically acts as the rear window of a car end ending with a vertical base. The back slant angle which is commonly designed as $ is very critical to the flow patterns which are fashioned at the near wake reason and subsequently has an impact on the aerodynamic forces which act on the body. Car companies makes numerous attempts to develop modified designs to effectively reduce the aerodynamic drag force which occurs at the rear end without putting any constraints in the stability, comfort and safety of the passenger. The aerodynamic drag of road automobiles is firmly connected to the vehicles with downstream flow. The separation zone size and the drag force directly rest mainly on the position of flow separation over the Ahmed body. Subsequently, comprehensive facts regarding the wake flow characteristics and its connection with the geometry of body is essential for a successful design of upcoming future cars. The application of computational fluid dynamics in in determining fluid flow pattern has been observed to be very common among researches in the present days. CFD Modelling in determining flow line of fluid around the Ahmed body has been utilized since the early `21^(st)` century. In many open literatures the CFD application in determining air flow pattern and the changes in flow motion with altering geometry of the body have been found. Certain modifications in the and body aids researches and designers to determine the effect of modification on the resultant drag and lift force which can be calculated using CFD modelling. Purpose of automotive is reduction of drag, decreasing noise emission, increasing fuel economy and eliminating unnecessary lift force and other origin of aerodynamic unsteadiness which rises at high speed. The conventional and reference model has been considered as the standard model in this research work for carrying out numerical simulations for researching on the aerodynamic parameters the Ahmed body has a like featured like a general car and is broadly utilized for authentication of new quotes in the automobile industry. This simple geometric model has a length of 1.044 m height of 0.288m and a width of 0.389 m. It consists of cylindrical legs of 0.5 m radius attached to the bottom most part of the body. The real most surface has an inclination of 25 degree. Ahmedabad characterizes the simplified geometry of a ground vehicle as a bluff body type. Its geometry is adequate enough for precise flow simulation and returns few vital practical features relevant to cars. This model aids engineers and designers to generate turbulent flow field surrounding the simple car model by the use of K-epsilon model. In spite of neglecting quite a few numbers of features of a real car like rough underside rotating wheels, surface projection etc. Ahmed body generates the crucial feature of flow pattern around a car for instance flow impinge-mentation and the displacement around the nose, relative uniform flow of air around the middle portion and flow separation along with the wake generation at the rear. Since the Ahmed body is easy to model, it can be a place is utilized for researching various properties like turbulence, drag coefficient, wake reason, lift forces, velocity magnitude at various regions of the car. Magnitude of pressure around the car which helps in in determining what will be resistance, fuel efficiency etc. Of the car thereby providing designers a clear Idea on which reason needs to be optimized for better effectiveness. The main objective of this study being stimulation of turbulent flow within the wind tunnel and around the Ahmed body to capture the flow pattern at the rear and wake region. Are local refinement of mess inside the concerned body is done with necessary body and face sizing of the parts of the body to generate well defined plots for pressure and velocity contours and its grid dependency test is the primary focus of this project.

Case setup

Geometry

• Import Ahmed body geometry in the SpaceClaim.

• Prepare an Enclosure for the Ahmed body

Side view

Front view

• Add another Enclosure of smaller dimensions.

Side view

Front view

Final geometry after adding Enclosures is shown below:

• Add an XY plane by clicking on origin. Then use the split body so that we cut the body into 2 equal half to reduce the cell count

• View in section mode for the interference.

• In prepare section click on interference it will show interference region.

• Press on green tick and I will resolve the interference problem.

Resolved interference

• Suppress the Ahmed body for physics.

Click on share topology for FFF.

• Close SpaceClaim

Meshing

• Open meshing interface and do the named selections as shown below

inlet,outlet and car walls that are same as shown in the course video. I made changes for symmetry.

Meshing is done as shown below

The inflation layer that I added is based on y+ value. I choose y+ = 30. The calculation will be shown later

The mesh quality is shown below

The y+ value calculated is shown below.

The first cell height is added to inflation layer height

The last prism layer height is such that it is equal to mesh size

Setup

• open fluent setup and perform mesh check to ensure mesh generated is free from errors.

Set Reference values

• change viscous model to realizable K-Omega SST model.

• Add material type as fluid and material air.

• Change boundary conditions:
  • Car wall = wall
  • Outlet = pressure outlet
  • Symmetry = symmetry
  • Inlet = velocity

• Now perform hybrid initialization.

• Create a velocity contour at symmetry plane

• Similarly create a pressure contour

• Create animation for velocity contour.

• Create a definition for drag coefficient.

• Similarly create definition for lift coefficient.
• Run calculation, iteration is 300 nos

Now the mesh independent study takes place

----------------------------------------------------------------------------------------------------------------------------

1) Case – 1

For bigger Enclosure

y+ = 30;

Mesh element size = 0.1 mm

Maximum size = 0.1 mm

Inflation (car wall) no. of layers = 21

Growth rate = 1.2

Inflation option = first layer thickness

First layer thickness = 0.0004342706789630705 m

For smaller Enclosure

Body sizing

Element size = 0.016648895549016197 m

Face sizing bottom leg

Element size = 0.001 m

No. of nodes = 374546

No. of elements = 1546355

Residuals

Coefficient of drag

Value = 0.30963158;

Coefficient of lift

Value = 0.30286695;

Velocity contour

Pressure contour

a)Static pressure

b)Dynamic pressure

c)Total Pressure

Total Pressure at any pont is defined below

Total Pressure = Static Pressure + Dynamic Pressure

Vector plot

Zoomed view showing the wake region

The velocity animation video from Fluent is shown below

2) Case – 2

In order to capture the wake region better, I m using sphere of influence. y+ = 100

For bigger Enclosure

Mesh element size = 0.1 m

Maximum size = 0.1 m

Inflation (car wall) no. of layers = 10

Growth rate = 1.2

Inflation option = first layer thickness

First layer thickness = 0.0014475689298769016 m

For smaller Enclosure

Body sizing

Element size = 0.03 m

For 2 faces at rear side, sphere of influence is used

Edge sizing bottom leg

Element size = 0.001 m

No. of nodes = 426991

No. of elements = 2113786

Residuals

Coefficient of drag

Value = 0.30630111;

Coefficient of lift

Value = 0.27962795;

Velocity contour

Pressure contour

a)Static pressure

b)Dynamic pressure

c)Total pressure

Vector plot

Wake region

3) Case – 3

Here my aim is to find the more accurate value of drag coefficient only. So the mesh near to all area needs to be more refined

a)y+ = 100

The sphere of influence is in the region shown below

By doing this, I m focussing more on pressure drag, the frictional drag values are not properly captured here

The mesh parameters are shown below

Residuals

Coefficient of drag

Value = 0.33915673;

Coefficient of lift

Value = 0.28171271;(The lift values are oscilating)

Velocity vector

The velocity features are not captured properly because my area of interest is drag. Here the frictional drag is not captured properly

Case

b) y+ = 30

Cell count is higher.

Mesh quality is not good

Drag coefficient = 0.29727931

Lift coefficient = 0.29918764

As the mesh quality is not good, there may be chance of error in final result

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

c) y+=180

OPTIMISED MODEL FOR INDUSTRY

The values put appropriately

The mesh elements are reduced the mesh is shown below

Here the mesh quality is good, because standard deviation is less

Residuals

Coefficient of drag

Value = 0.32405637;

Coefficient of lift

Value = 0.27912245;

Velocity vector

OBSERVATIONS

Cd=0.32405637;

Cl=0.27912245;

INFERENCE for this model

This case is the optimised model suitable for industry to reduce computational cost and predict accurate values of coefficient of drag and lift. The computational cost can be further reduced by adding some small changes in this model, it is easy for anyone to make small changes to my model. The value of coefficient of drag is calculated by considering pressure drag, viscous drag, reduction of drag due to negative pressure, negative pressure at slant of the Ahmed body at wake region by making use of K-Omega SST model. The characteristics length is taken based on the reference from the journals. The values are then compared with standard journal in journal, where Cd=0.33 at slant angle=25*. but in our case, the slant angle is 20*.

So, the slant angle of a surface behind the have high influence in determining the coefficient of drag as it plays an important role in negative pressure behind the Ahmed body. The design of backside of the vehicle is to be made in such a way to generate maximum negative pressure behind slanting region of Ahmed body. If negative pressure increases, the coefficient of drag decreases due to equipotential or inviscid flow theory.

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

4) Case 4

OPTIMISED MODEL TO STUDY VELOCITY AND PRESSURE VARIATION IN WAKE REGION

y+ = 180;

For wake region

The mesh is shown below

The values given as per below calculation

Residuals

Coefficient of drag

Value = 0.37160131;

Coefficient of lift

Value = 0.32925761;

Velocity vector

The velocity features are captured properly because my area of interest is velocity is wake region. There is change in the value of drag and lift from standard journal because the mesh is not refined in the areas of ahmed body where forces of drag and lift acting.

INFERENCE

The case 3c and case 4 models are the best suited optimised models.

a) The case 3c model, is one of the optimum model for industrial applications in order to capture the drag and lift coefficients such that the computational cost is minimum and to get the accurate values of drag and lift coefficients. The cost is minimum because of less cell count.

b) The case 4 model is suitable for the study of pressure and velocity variation in wake region. Here also the computational cost is minimum due to less cell count and it is the optimum model for study of wake region. After that apply the case 4 model to case 3 model so that computational cost can be minimised. We can do both the models in parallel for industrial application and then apply case 4 to case 3c model .

REASON FOR NEGATIVE PRESSURE in wake region

For this explanation, we have to simplify it using inviscid fluid and then apply to viscous fluid.

Inviscid flow is the flow of an inviscid fluid, in which the viscosity of the fluid is equal to zero.

Let us take an example of inviscid fluid fluid flow over a cylinder.

See the figure below

The fluid moves from point A to point B with accelaration. So, velocity at point B is higher. Thus the region between A to b is favourable pressure gradient. The change in velocity is the reason for the favourable pressure gradient.

The fluid move from point B. In this case, the fluid will decelarate because it has to stagnate at point C. So, the velocity at point C will be zero. Then the pressure at point C = pressure at point A (Equal in magnitude and opposite in direction). The pressure along the red stagnation streamline is same everywhere. This creates a positive or adverse pressure gradient.

Just try to understand dP/d(theta) and dU/d(theta) as pressure and velocity gradient in polar cordinates.

Let's define a parameter called CP, so coefficient of pressure

where P_infinity is the free stream pressure, P is the pressure at any point on the surface of cylinder

See the image for theta here

Theta is equal to 0 to 180 degree, so from the forward stagnation point to the rear stagnation point, that is Theta is equal to 0 to 180 degree.

If we plot CP, okay, so this particular, it will essentially give me the variation of pressure, because of the quantities P infinity, rho and U all are constant. This is a nondimensional way of plotting(figure below) this particular variable. If we plot this, it will from the inviscid flow theory or the potential flow theory,we can get this kind of a variation of pressure

basically this region if you go through the pressure is reducing and then the pressure is increasing

And in an inviscid flow you will see that the pressure recovery is complete, that means pressure reduces as it comes to 90 degrees. That means Theta is equal to 90 degrees that means this top of the cylinder but it again recovers to the same value of pressure which was here as it, as it approach the forward stagnation point.

So forward stagnation point and rear stagnation point, the pressures are same.So there is a complete pressure recovery.

Now we can use this pressure information to get the drag force on this particular cylinder. So this drag actually results from 2 things, one is the friction drag, that means due to viscosity the flow decelerates, of course this is an inviscid flow, so that is not important here, the friction drag. Another is the pressure drag, pressure drag

is, we know that if we have to find out the net force acting on a control volume we have to find out what is the pressure around that control volume.

See the expression for frictional drag below

so R dTheta is basically the arc length. Arc length multiplied by 1 gives the area.

Tow_w is the wall shear stress, R is basically the radius of this cylinder.

Friction drag = 0 due to inviscid fluid

Pressure drag is shown below

See the figure below for a cylinder

This is how the pressure is acting at the front and the rear part of the cylinder.

So this integration from the symmetry of this pressure, as we see from this CP variation of from this particular representation of the pressure on the surface of the cylinder we can say this is also zero. So what it means is the drag force on this particular cylinder is zero. This is of course contradictory to our understanding that is as we know that if we place a cylinder on a flow, it will experience some drag.

But what this inviscid flow theory is telling me is that there is no drag because there is a full pressure recovery.

So, see the figure below

Here flow seperation is not considered.

See the laminar flow seperation figure below. Here the full pressure recovery is not happening. So, the pressure around the wake region is very low

Let's look at pressure drag and frictional drag equation below

Look at the figure below and see the blue line, which is basically the coefficient of pressure plot in laminar region.

From the graph,

laminar curve follows the inviscid curve up to some point but after that there is a adverse pressure gradient even before theta is equal to 90 degree. The reason for that is basically the viscosity of the fluid and makes it to separate or the adverse pressure gradient to exist even before Theta is equal to 90 degree.

*************************

Example: Pass a ball through a control volume full of water. Then observe what happening. We can clearly see the boundary layer.

Let's do the same experiment with highly viscous fluid. See what happening.

The boundary layer seperation happens early in the case of highly viscous fluid. Here Reynold's number is less. So laminar seperation

*************************

So, for laminar seperation, the pressure recovery path does not exist. So the pressure is very low in the wake region.

See the image below

So now if we find the pressure drag, in region A you have a positive pressure region, a positive pressure force, force arising due to the pressure acting in the positive X direction. In the region B you have a force acting due to pressure in the negative X direction but the force arising due to pressure in the negative X direction is much less because the pressure itself is very small as compared to the pressure on the front side. So this negative force is less and the net force will be in the positive X direction.

It is clear that the reason for negative pressure is simply due to sign convention that we are taking. If we say the pressure at A is positive, we have to say the pressure at B is negative as per cartesian sign convention.

If the flow is turbulent, the seperation is delayed, the seperation angle will be around 120*.

See the graph below

The pressure drag will be lesser in the case of a turbulent flow because A portion of the cylinder will have very similar pressure as to this B portion of the cylinder

See the figure below

The portion C have much lower pressure than portion B. But the sign of pressure force at portion B and portion C is negative due to sign convention taken from inviscid flow or potential flow theory. This is the case for turbulent flow.

So, it means if the point of seperation is delayed, the drag force acting on the body will be reduced because the area of negative pressure acting on portion B in increased

The similar theory can be applied to Ahmed body as it is a blunt body, but the Ahmed body is not symmetrical like cylinder. So, the wake region is created in a circular manner and the negative pressure region is very small.

This negative pressure wake region here depends upon the slant angle. If the slant angle is 30*, we can find a different pattern of wake region, which is available in open literature.

The slant angle of the car body can be varied to find out the variation of drag values and negative pressure values.

Explain the significance of the point of separation??

If the point of seperation is delayed, the drag force acting on the body will be reduced because the area upon which negative pressure acting will be increased.This is as per the inviscid or equipotential flow theory for fluid flow where turbulent flow try to behave closer to inviscid flow upto some extend(See the figure below, where black line almost overlap the inviscid flow upto 120* in case of a cylinder). The turbulent seperation increases the area of negative pressure acting on the body as it delays the flow seperation. The turbulent flow have higher energy to resist the shear force from the wall because du/dy is steeper near to the wall for turbulent boundary layer (Shear force = µ x (du/dy)).

Reason for flow seperation and wake formation

The reason for flow seperation on a simply external flow is still unclear to me. I m not sure what is the basic reason for flow seperation

Let's look at some reasons available in open sources

1) Due to adverse pressure gradient, du/dy = 0. Then wall shear stress is zero. du/dy = 0 means, there is zero velocity gradient in y direction for the fluid flow, this basically means there is no fluid motion in y direction and thus the flow seperates.This is a case of critical adverse pressure gradient.During weak adverse pressure gradient, flow seperation does not happens.

When there is a strong adverse pressure gradient, the fluid near to the wall starts decelarating in the reverse direction because the point of inflection of the velocity profile shifts to some vertical height away from the wall. The reverse flow happens between point of inflection and wall. This is called recirculation of flow and thus wake is generated. Here eddy formation takes place.

Also, the flow seperation happens due to

a) shape of the geometry(as we seen in Ahmed body)

b) viscosity of the fluid determines the flow seperation (as we seen in inviscid or potential flow theory)

2) It is still unclear on the fact that the reason for pressure gradient is the to fluid motion OR fluid motion causes pressure gradient

As per the inviscid fluid flow theory, the accelaration or decelaration of fluid flow causes pressure gradient. But in other cases, the pressure gradient causes the accelaration or decelaration of the fluid as in the case of converging diverging section.

So, the question arises which comes first.

REFERENCE

Nptel videos: https://www.youtube.com/watch?v=x2_wkrv8j3s

ATTACHMENT

The velocity colour animation and stream line animation file is attached

LEARNING OUTCOME or GAPS

The study of inviscid flow or potential flow theory helped in doing the challenge in a better way. After studying this theory, the case 3a is modified to case 3c. The case 4 should come ahead of case 3c because after studying the effect of negative pressure, then only it is possible to implement it on industrial approach.

In this case I made case 3c without considering the negative pressure, then after studying the effect of inviscid flow or potential flow theory, I made changes to Case 3c and do it to find the better value for coefficient of drag.

The study for coefficient of lift is not done by me. The NPTEL video helped me in studying the effect of negative pressure and the journal provided by skill lync helped me to understand the effect of slant angle of the car body.