Week 10: Modeling and Simulation of flow around an Ahmed Body

AIM:

Modeling and Simulation of flow around an Ahmed Body

objcetives:

• Create the CAD model using your any CAD package
• Setup a Coarse CFD simulation
  • Setup the virtual wind tunnel
  • 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 on a cutplane. This cutplane should cut the ahmed body model in two symmetric pieces.
    • You need to show an animation of the pressure distribution on a cutplane. This cutplane 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

Theory:

Ahmed body and its importance:

As the burning of fossil fuels becomes a more pressing issue, manufacturers are introducing more fuel efficient cars to the market. One main contributor to fuel burn is the car’s aerodynamic drag. Complexly shaped, cars are very challenging to model and it’s difficult to quantify the aerodynamic drag computationally. The Ahmed body is a benchmark model widely used in the automotive industry for validating simulation tools. The Ahmed body shape is simple enough to model, while maintaining car-like geometry features.

          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, 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 40 degrees.

geometry:

 firstly i have created the ahmed body using the above dimensions in the CAD software. then i have taken the half part of the ahmed body which is symmetrical to other half, so that we can reduce the number of the cells to reduce the simulation time.

now i have created the wind tunnel around the ahmed body. we need to take the length between inlet wind tunnel and front portion of the ahmed body is smaller than the length between outlet wind tunnel and rear portion of the ahmed body so that we can see the wake properly at the rear part of the body. to measurethe distance between inlet wind tunnel and front portion of the ahmed body we have taken the data from experimental values that the there is a boundary layer thickness of 30 mm is obtained at a distance of 400mm from the front of the ahmed body.

the fluid is flowing with velocity of 40 m/s. we have the below formulae to calculate where the boundary layer is formed from the inlet of wind tunnel. 

                                                                                   `deltaL = (0.385x)/((rho.v.x/mu)^0.2)` 

we know that `deltaL=0.03m`

density of air, rho = 1.225 kg/m^3

v = 40 m/s

mu = 1.81*10^(-5) kg/(m·s)

from tese values we can find the value of 'x' at where the boundary layer thickness is formed from the wind tunnel inlet.

the obtained value of x is 1.68m. here i have given a slip region at the inlet with the length of 1m because to meake sure that upto 1m length, the fluid is flowing with 40m/s without forming any boundary layer in that region. so that we are going to give slip wall boundary condition to that region. also we have a distance of 0.4 m from the boundary layer thickness of 0.03m region to front face of the body. so the final distance between the inlet of wind tunnel to front of ahmed body is 1+0.68+0.4 = 2.08m , 

the distance betweent the rear part of body to outlet  of wind tunnel is taken as 5 times the length of the ahmed body. after creating of the wind tunnel, the final obtained geometry is 

now check the normals of all the faces are facing inside or not by using normal toggle tool and then buid case setup.then i have used boundary tool in the geometry.  here i have named the boundaries. i have named them as below

in the above figure, sum represents the number of triangles selected at the each boundary. now use normal toggle tool. in the converge,the normals are always directed to outside of the box faces as a default. but here the fluid is inward flow. so eliminate them, click on transform in geometry and slect of triangle and click apply. to check whethere the geometry is correct or not(ie open edges errors, overlap errors), click on the diagnosis which is shown at the bottem left of the display and click findings. now buid the case setup.

case setup:

application type: time beased

materials: air

click on gas simulation as the air is gaseous state and click on species to calcuate how the mass fraction of N2 and O2 are changing along the flow.

species-

simulation parameters:

run parameters-

i am running the somulation using transient state solver. full hydrodynamic simulation mode is used for simple geometries.

we have click on steady state monitor only for the steady state problems only.

simulation time parameters-

the maximum convection cfl number should always be less than or equal to 1. so that solution would converge otherwise solution gets blown up.to calculate the end time, i have used the following procedure.

to calcumate the time we need velocity flow and length of the elbow. here the length of the wind tunnel is 8.3m. the inlet velocity of fluid i have taken is 40m/s. so we can say that time taken by the fluid to move out of the wind tunnel is 0.2075 s. we need to take the simulation end time as two to five times of the time taken by fluid to come out of tunnel, so that we can see the wake region and how the primitive variables reached to steady state. 

solver parameters-

density based solver is used here 

initial conditions and events:

regions and initialization-

here i have named the entire box region as volumetric region. the velocity i have taken in negative value because here the fluid flows along the negative x direction.

boundary conditions:

boundary-

• inlet- the inlet velocity i have taken is 40m/s.

• outlet- the outlet pressure is atmospheric i have taken is 101325 pascals

• symmetry- i have taken this boundary condition to all the walls of the wing tunnel except bottem of the wind tunnel

• slip-wall - 

• bottem-

• ahmed body-

physical models:

turbulence modelling-

grid control:

base grid-

fixed embedding- i have enabled fixed embedding because to scale the cells at walls of the geometry. it means to to capture the turbulence in the turbulence boundary layer region, we have to provide cells with small size at the walls of the boundary. embedded layers represents the number of layers of cells we are going to take. scale represnts at what factot of base size is taken for first layer thickness. here i have determined the scale from the below formula

                             first layer thickness = base size/2^n, where n represents the scale.

• here i have reduced the scale that i have got from the above formula because by increaing the scale, there will be more refinement in the box whicj increases the cell count. i have limited access for the cell count for the simulation. so that i have reduced the scale so that my software can start simulation.

output/post-processing:

post variable selection-  here i have enabled y+ value along with default variables.

output-

time interval for writing the 3d output data files is 0.001 seconds. it means , the output values of the proble gets stored for every 0.001 seconds . for every 0.001 seconds, we can see the values of primitive variables in the paraview.  and also i have enbles boundary only wall output to calculate the drag and lift foces acting on the body.

solution:

now export all the input files in a folder. so from this we can see that converge is used to create the input files for the simulation. now insert the two application files from the converge folder to the folder where i have exported all the input files.

for the simulation i have used cygwin64 terminal. in cygwin termpinal open the folder where you have pasted all the input and application files.

now for the simulation write mpiexec.exe -n 4 converge.exe restricted and click enter. here 4 represents the number of processors used at a time.

post processing of results:

for this copy post convert application from converge folder to output folder which is generated in the input files folder. we are doing this because we are goingto convert all the output files into a vtk file which can be easily read by paraview software. toconvert the files we have to use post conver application as shown in the figure. there we can see the results that are obtained. now in cygwin open the output folder and write mpiexec.exe -n 4 post_convert.exe and click enter. now the below figure will appear

after naming the case and choosing 10, hit enter. now click yes for boundary output surface. now all the output files will appear and then write 'all' to convert all the output files. now select 'all' at cell variable selection menu. now all the files gets converted into paraview vtk files.

now open paraview. in paraview, open file and select case name .. vtm file which is present in the output files. finally we see the geometry in the paraview. now choose slice tool to select the axis along which all the primitive variables are same. as we know that, along z axis the primitive varibles are equal. so select  axis and click apply. 

velocity contour-

pressure contour-

animation of velocity flow-

animation of pressure contour-

drag force plot-

average drag force acting ont he body is 22.5N

lift froce plot-

the average lift force acting on the body is 134N. negative sign represnts the force acting towards the ground which is beneficial for the object moving on the road to increase the traction. 

y+ plot-

here the value of the y+ is greater than 300 which indicates that we got the wrong simulation outputs. this is obtained because we have taken the coarse mesh here because we have limited license for the cell count to run the simulation. 

i have validated my results with experimental data by seeing the velocity profiles at dfferent points of x axis. the experimental data is obtained from the refined mesh. so we can say that we can conclude that we can;t get the results as same as experimental data. below are the velocity profiles at different x positions. i have saved the details of the plot in paraview in excel format. i have validated those details with experimental details and plotted the graphs in excel.  below the different velocity profiles at different x locations. red color line represents the data obtained from experimental data where as blue color represents the data obtained from my results.

velocity profiles at different locations of x:

now to calculate the drag coefficent we need to have the projected area of the ahmed body. to calculate the projected are, open paraview and then select the ahmed body by extraxting the geometry. then use 'select cells on' tool and select the aera which we wanted to select and then extract the selection. no use delaynay tool and take alpa value as 0.05 and then click apply. now finally use integrated variables tool and in that select cell data. now we can see the values of projected area. theprojected are normal to the x axis obtained is 0.0535 m^2.  below is the formula used to calclulate the drag coefficent.

                                                       drag force = Cd*0.5*rho*projected area*v^2 

 where v is the free stream velocity of flow, 40 m/s

by substituting all the values, the final drag coefficent is 0.429

conclusion:

• by seeing the pressure contour,we are seeing that there is a increase in pressure at front face of body because of suddden drop of velocity of air and there is a decrease in pressure at rear face of the body.
• the wake region is created at the back bace and there is revrsal of flow alos occured at the rear portion of ahmed body.
• by doing validation, we can say that by using the coarse mesh, we will get the results wrong.
• we have also observed that thwre is a negative lift force generated here, which should be necessary for a moving body traveling on roads. by increasing of negative lift fore, there will be more traction, so that the wheels of vehicles always attaches to the road.