Week 3 - External flow simulation over an Ahmed body.

OBJECTIVE OF THE PROJECT:

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. 

 

TO PLOT:

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 independence test and provide the values of drag and lift with each case. 

 

Most modern automobiles utilize fossil fuels since fossil fuels are finite resources and sustainable usage of fossil fuels has become a necessity in the modern-day, making our automobiles more fuel-efficient has become a need for the day, for the modern automobile designers. Aerodynamic drag is proportional to the square of velocity, and hence the power needed to overcome drag is proportional to the cube of velocity. This means that there is a very strong relationship between the speed at which a vehicle is traveling and the proportion of the fuel used to overcome drag.

For passenger cars, this means that aerodynamics is responsible for a much higher proportion of the fuel used in the highway cycle than the city cycle: 50% for highway; versus 20% for the city. This means that if you make a 10% reduction in aerodynamic drag your highway fuel economy will improve by approximately 5%, and your city fuel economy by approximately 2%.

On looking into this passage we can clearly see those improved aerodynamics give rise to better fuel efficiency, hence sustainable fuel usage.

 

THEORY:

 THE IMPORTANCE OF AHMED BODY:

The Ahmed body was created by S.R Ahmed in his research, "Some salient features of the Time- Average Ground Vehicle Wake". The length of the body is 1.044m, with a height of 0.288m and a width of 0.389m. The Ahmed body is the simplest base shape of a car, whose sole purpose is to validate CFD codes. A lot of experimental data and wind tunnel tests are available for the Ahmed Body. The CFD codes with the least divergence with experimental data are selected for use.

On closely looking at the Ahmed body, we see that it vaguely represents the chassis of a automobile since the aerodynamics of vehicles is greatly affected by body shape, we get a base line understanding of the flow over an automobile body so that it can tailored according to the problem statement.

THE IMPORTANCE OF POINT OF SEPERATION

The point of separation is a very important concept in external flow's. Flow's tend to separate when they encounter adverse pressure gradients, mathematically it can represented as dp/dx>0. Due to an increase in pressure in the direction of flow, the flow velocity reduces.(We can see this as the fluids mechanism to follow the body contours). At a molecular level we know that there is region of fluid flow close to surface called the boundary layer. In this region the movement of the flow is governed by viscous forces and energy is required to overcome the viscous effects. On the onset of an adverse pressure gradient, the flow is no longer able to stay attached to the body surface and follow the contours, gets detached from the surface tangentially, this point is called the point of separation. This has more rigorous mathematical definitions which can be described as the point where the skin friction coefficient is zero, or we can say that the point where the spatial derivative of velocity (du/dx) is zero. 

The information about the point of separation has numerous applications, it has an important role in determining the 'wake width', which is very important factor when considering low drag designs. Also this information is crucial in determination of the size of the laminar separation bubble, whose stability, size and integrity plays a very important role in making aerodynamically stable designs.

 

NEGATIVE PRESSURE IN THE WAKE REGION

We very well know that fluid when moving over the surface exerts pressure on the surface. When there is fluid boundary layer separation, due to an adverse pressure gradient, the pressure exerted by the fluid on the surface cease to exist, which causes a region of low pressure. In order to fill this void, the free stream fluid since at a higher pressure, attaches to the body, causing recircualtory flow within this region, with different pressure distributions hence called the wake region. Due to variation in pressure distribution, this might cause vibrations and loss of kinetic energy. In a turbulent boundary layer energy is dissipated due to friction, slowing the air velocity which causes an increase in pressure. If the increase in pressure is gradual, then the mixing process causes an energy transfer from a faster eddie to a slower one.

If the pressure change is very sharp, like that of a sharp corner, the mixing is not able to move the slower moving molecules ( the ones moving slow due to viscosity), which results in sepration of flow. The detached flow if the Reynolds number of the flow is high, gains energy from the turbulent flow and reattaches to the surface at a point called the point of reattachement.  

Due lack of fluid flow over the surface, due to adverse pressure there is low pressure region with recirculatory flow called the wake region, due to different pressure distributions there is a increase in drag. Also since there is a reduced pressure region, there is net force acting opposite to the motion of the body, which contributes as drag. 

MODEL AND SETUP

We start by importing the Ahmed Body model in Space claim.

 

 

This is the isometric model of the imported Ahmed Body. We then begin by preparing the geometry, by creating an enclosure over the model, in the prepare option the following steps were used for this simulation:

1. Symmetric options were turned off for better control over enclosure, units were set in 'm'.

2. Two sets of enclosure's were created for this simulation an 'outer one' and an 'inner one'.

3. The enclosures act here as the wind tunnel an their dimensions are given as:

    Outer: 4m(aft), 2m(front), 1m(high), 0.5m wide in both sides (All distances are from the body)

     Inner: 1m(aft), 0.8m(front), 0.5m(high), 0.25m wide from both sides.

4. Interference check and resolution was performed.

5. The share topology option was switched on for both enclosures, so the information passing and mesh overlapping can be avoided.

The finished geometry looks like this:

 

 

The check for interference can be checked through a section plane like this:

 

The lines appear to be in proper coherence.

Once the geometry preparation is done we process towards meshing, the steps followed for meshing is as follows:

1. Named selections were created like the inlet, outlet, symmetry and wall ( using box select)

2.Once this done we proceed towards body meshing for the outer enclosure since there are four cases here, sizes of the elements were:

CASE-1	CASE-2	CASE-3	CASE-4
0.2m	0.1m	0.1m	0.1m

3. Then we select 'method', and apply multizone meshing, keeping Hex elements as dominant, since they have good quality.

4. Then we use body meshing for the inner enclosure, the element sizes are as follows:

CASE-1	CASE-2	CASE-3	CASE-4
0.07m	0.06m	0.04m	0.035m

We can use additional face meshing for the bottom face, as if we observe it closely the circular legs, appear as polygons. This would increase element numbers it is better to perform edge sizing, with No of divisions as 36.

5. Then the most important part of meshing here is the inflation layer, if we oberserve the wall-mesh interface, we see that the cell- centers are spaced unevenly, this becomes an issue, because the viscous layers are so thin, if we have to capture all the phenomenon, then body fit mesh's have to be used, so that cell-centers are evenly spaced. For this we need to do the Y+ calculation's which are as follows:

The Re can be calculated, as Re=rho*V*D/mu, on substituting values we get Re= 1.8*10^6.

Cf= 0.057*(Re)^2= 0.00323

Tou=1/2*Cf*rho*V^2=1.236

Ut=1.0056

y.=1.4524*10^(-5)*Y+

For, Y+=30, Y+=40, Y+=50 is 1.766*10^-3, 1.418*10^-3, 1.7667*10^-3.

The total thickness comes out as 8e-4.

We would be entering a value of total thickness of 8e-4, with total layers as 11, and with growth rate of 1.2.

Case-I 

Case-II

Case-III

Case-IV

The inflation layer is shown:

Now the Setup in Fluent is as follows:

1. General- Pressure based, Steady state (Velocity, is still below Mach 0.3, hence incompressible.)

2. Models- k-omega SST (shear stress transport) & k-epsilon models both used.

3. Materials- The fluid is air, with standard properties.

4. Boundary conditions- Inlet=25m/s, with outlet with gauge pressure zero, with other faces with symmetry and the car wall with no slip cinditions.

5. Refrence Values- Area=0.1123m^2, length=1.044m, other conditions as set for inlet.

6. SIMPLE Method used, Hybrid initilization.

7. Monitors unchecked for convergence,  solution to run for 500 iterations.

8. Plot report for lift and drag are generated, with contours of velocity & pressure  setup.

9. The plots, contours and vector plots attached below are obtained from post processing.

PLOTS AND CONTOURS

Case-I

 

 

 

 

 

 

 

 

Case-II

 

 

 

 

 

Case-III

 

 

 

 

 

 

 

Case-IV

 

 

 

 

 

RESULTS & DISCUSSIONS

 

	RESIDUAL	ELEMENTS	NODES	CL	CD
CASE-1	345	81846	20560	0.3934	0.496623
CASE-2	375	116793	36883	0.40418	0.4845
CASE-3	385	289619	65060	0.3545	0.46194
CASE-4	430	423534	95755	0.2461	0.37806

 

The first three case's k-epsilon model was used and the last case k-omega SST was used.

1. It is very clear from the simulations that the theory is evident in the vector plots, and contours.

2. The reason why k-omega is preferred over the k-epsilon is that SST version has a blending function where it utilizes the wall functions of the k-omega model and uses the k-epsilon model at the free stream. So for this problem statement k-omega is a better model.

3. k-omega takes a longer time to converge than k-epsilon.

4. As we see there is grid dependency, finer the mesh more reasonable the coefficients value, as we are able to capture the flow phenomenon better. The recirculating region is more clear in a finer mesh. ( Academic liscnese restrictions are 5Million cells).