Simulation of the Flow over Ahmed Body

OBJECTIVE:-

• To run the steady-state simulation of the flow over Ahmed body.
• To perform the grid independent test.
• To plot the velocity contour & pressure contour and to calculate the coefficient of drag & lift.
• To study the significance of point of separation and negative pressure in the wake region.

GEOMETRY - AHMED BODY:-

• Ahmed Body is used to run all the steady-state simulations in this project.
• It is a 3D model of a standard passenger car.
• It has a blunt front side (left side of the below images), downward slanting backside (right side of the below images) and four small cylinders representing four wheels of the vehicle (bottom part of the below images).
• This model was physically constructed and a lot of experiments have been conducted on the same. The database with huge amount of experimental data is available for the flow over Ahmed body. Hence, this is intensively used as a validation model in the automotive research field.
• Once the numerical method or solution is figured out, it can be validated with Ahmed body. By comparing the simulation result with the available experimental data, the correctness of the new code/solution can be checked. If it gives the needed accuracy with Ahmed body, it can be applied to other cases and can be used to design new car models.
• Since the geometry is symmetric, only half of the body has been used to run the simulations. It was done in SpaceClaim by using split body tool. After splitting the model into half, it will look like the below.
• The front view with dimension of the model in this project has been shown below. It is 0.194m wide along z axis.
• Two enclosures have been created around the Ahmed body to accodomate the air flow field. The boundary conditions will be given to the faces of these enclosures while setting up the case.
• The cushion distances of large and small enclosures from Ahmed Body in all axes are given below.
• Share topology has been enabled to remove the interferences between the enclosures with the Ahmed body & themselves and to facilitate the smooth information transfer along the common edges and/or faces. After enabling the share topology and removing the interference, the sectional view of the geometry will look like the below.
• For this simulation, we are interested only in the flow outside of the Ahmed body and hence the Ahmed body is suppressed for physics.

MESHING DETAILS:-

• Following named selections have been provided for the geometry.
• Since outer enclosure is made up of perfect straight lines, MultiZone method has been applied for the same. The element size has been given as 0.06 m. The maximum size was also given as 0.06 m so that we will get a perfect looking mesh for the outer enclosure as shown below.
• Body sizing has been given for the inner enclosure with element size, 0.032 m.
• Face sizing has been given for the Ahmed body faces with element size, 0.01 m.
• We are more interested in capturing the physics of the flow near the Ahmed body. To capture the same with more accuracy, more nodes and cells are needed. That's why we have reduced the element size as we approach towards the Ahmed body from outer enclosure.
• Six Inflation layers have been provided for the Ahmed body (car_wall) with maximum thickness as 7.0178e-3 m and growth rate, 1.1. This has been given to retain the shape of the Ahmed body which other wise may get distored when different mesh conditions are applied. When we preserve the original shape of the Ahmed body, we will get better results. The calculation of the total thickness is on the basis of the target y+ which will be explained in detail later.
• Five Inflation layers have been provided for the bottom wall with smooth transition option and growth rate, 1.2. This has been given to capture the the flow more accuately as we will give a wall boundary condition for the bottom face when we set up the case.
• Edge sizing has been given for the wheels with 18 number of divisions. This has been given to retain circular/cylindrical shape which other wise might get distorted and reduce the accuracy of the result.
• The below images will show how the final mesh of the geometry will look like. 2D views have been given for better visualization.
  
• Mesh Element Quality Metrics is shown below. There are no cells which has less than 5% quality which is an indication of good mesh.
• Overall, the geometry has 157152 nodes and 496957 elements.

CASE SET-UP DETAILS:-

• Since we are interested in final velocity and pressure contours, we will be running a steady state simulation for this case.
• Viscous Model: k-epsilon Realizable model with Standard Wall Functions.
• Material: Air (Density = 1.225 kg/m3 and Viscosity = 1.7894e-5 kg/m-s)
• Boundary Conditions:
  • inlet: velocity-inlet type, 25 m/s
  • outlet: pressure-outlet type, zero gauge pressure
  • car_wall: wall type
  • bottom_wall: wall type
  • symmetry1: symmetry type
  • symmetry2: symmetry type
• Since velocity is less, we would use Pressure based solver.
• Since we are interested to calculate the drag and lift, we need to give reference values as shown below.
  • Area: It is the projected area of the front face of the Ahmed body
    • `Area = l * b = 0.288*0.1945 = 0.056016 m^2`
  • Length: It is the length of the Ahmed body in x-axis which is 1.044 m
  • Velocity: It is the freenstream velocity which is 25 m/s
  • Temperature: We assume the whole phenomenon takes place at 300K
• Initialization: Hybrid Initialization
• Definitions: Coefficient of Drag and Coefficient of Lift at car_wall boundary
• Number of Iterations: 500
• Solution Method: Coupled (Default settings)

DETERMINATION OF FIRST CELL THICKNESS:-

• We have provided inflation layers to the car_wall to retain its shape to get more accurate simulation results. We have provided six inflation layers over there with growth rate of 1.1.
• The first cell thickness and total thickness of the inflation layers have been calculated on the basis of Y+. For this sumlation, the target Y+ was given as 300.
• The calculation of first cell height and thereby the total thickness of inflation layers have been explained below.
  • Let `rho` = Density of Air, `mu` = Viscosity of Air, `U` = Free Stream Velocity of Air, `L` = Length of car_wall or Ahmed Body, `Re` = Reynolds Number, `Cf` = Coefficient of Friction, `tauw` = Wall Shear Stress, `ut` = Frictional Velocity, `nu` = Kinematic Viscosity, `y+` = Desired y+ and `y**` = First Cell Thickness
  • `Re = (rhoxxUxxL)/mu = (1.225 xx25xx1.044)/(1.7894xx10^-5) = 1786772`
  • `Cf = 0.0576xxRe^(-1/5) = 0.0576 xx 1786772^(-1/5) = 0.003236`
  • `tauw = 1/2xxCfxxrhoxxU^2=1/2xx0.003236xx1.225xx25^2=1.23878`
  • `ut=sqrt((tauw)/rho) = sqrt(1.23878/1.225)=1.0056`
  • `nu = mu/rho = (1.7894xx10^(-5))/1.225 = 1.4607xx10^-5`
  • `y**=(nuxx(y+))/(ut) = (1.4607xx10^-5xx(y+))/1.0056=1.4525xx10^-5xx(y+)`
  • `y**=1.4525xx10^-5xx300=0.004358`
• In all equations, we have used SI unit system and hence the first cell thickness obtained is in meters ie `0.004358 m`.
• We have provided six inflation layers with 1.1 growth rate. Hence, the total thickness will be `0.004358xx1.1^(6-1) = 0.007018 m`

RESULTS:-

• Scaled Residuals Graph:-
• After about 250 iterations, the plot repeats the pattern therefore we can say that the solution has been converged.
• Coefficient of Drag Plot:-
• After about 150 iterations, the Coefficient of Drag started to give a constant value of 0.32117.
• The value of Coefficient of Drag obtained by conducting an experiment with the similar condition is 0.33. If we compare the value obtained as a result of our CFD simulation, we can see that the error is only 2.67% which is acceptable.
• Coefficient of Lift Plot:-
• After about 125 iterations, the Coefficient of Lift started to give a constant value of 0.30878.
• Velocity Contour:-
• Pressure Contour:-
• Stream Lines:-
• Vector Plot:-
• By analyzing all the above plots, following observations and deductions have been made.
  • The boundary condition of the inlet was given as 25 m/s velocity. It implies that the air has 25 m/s free stream velocity. As evident from the velocity plot, this is truely replicated.
  • As the air comes towards the right hand side, there is an obstruction for the flow field due to Ahmed Body (car_wall). The air molecules will strike the front face of the Ahmed body and will slow down. That is why a reduction in the velocity is visible in the velocity contours.
  • As air molecules strike on the Ahmed body front face wall, the pressure over there will also increase. This is also visible in the pressure contours.
  • However, since there is a continous flow of air from left hand side towards the right hand side, the air molecules will be forced to flow over the Ahmed body. Hence, the straight line path of the flow will get diverted to upward and downward. This is evident in the vector plot.
  • A small flow separation can also be observed in the top and bottom part of the front face of the Ahmed body. This is due to the curved shape of the front face. As the flow separates, the velocity very near the wall be reduced and pressure will be increased. But away from the boundary, the molecules will gain the momentum. This can be clearly observed in the velocity and pressure contours. But the scope for air recirculation in this region is less as the molecules will join with the free stream velocity soon after the separation.
  • After the occurance of the flow separation near the front face, the molecules will again have a straight line path as the top and bottom faces of the Ahmed body are flat.
  • Due to the downward slant shape, the flow again separate. As seen near the front face region, the velocity will reduce and pressure will increase. However, the space is more empty here in the back face region of the Ahmed body. Thus the velocity reduction will be significant and there is a huge scope for the recirculation of the air. The recirulation is clearly visible in the stream lines plot and in the vector plot.
  • The negative pressure caused by the flow separation will in turn cause the the air molecules to reverse its flow direction thus will cause flow recirculation leading to bubble formation. This phenomenon will eventually help the flow to re-attach with the main stream flow. This is evident in the vector plot and stream lines near the wake region. After re-attaching, the flow will gain the velocity and continue in the straight line path.
  • Due to the flow separation past the separation point at the slant region, flow reversal phenomenon and recirculation, the drag will increase. More drag will cause more energy loss. Thus the designers will try to reduce the drag by changing the design on the body. In this case, if the slant angle was more, there would have been more empty space past the separation point which would have caused more drag. Thus such a design will not stand as a good one. From this same concept, we can say that the box shaped car will have more drag than aerodynamically designed new type of car models and thus will cause more energy loss in box shaped cars. Hence, the location at which the flow separates determines the size of the separation zone and consequently the drag force. This is the significance of point of separation.

GRID INDEPENDENCE TEST:-

• Four cases have been used to conduct the grid independence test.
• Above indicated geometry and case set-up details are used in all the four cases but the meshing details are changed. Below table will show the meshing details of each case.
• In all the below given figures and/or plots, the first one will be of case-1, second one will be of case-2, third one will be of case-3 and the last one will be of case-4.
• 2D View of Final Mesh:-
• Scaled Residual Graph:-
• Coefficient of Drag Plot:-
• Coefficient of Lift Plot:-
  
• Final Vales of Cd and Cl:-
• Velocity Contour near Ahmed Body:-
• Comparative Study:-
  • From the mesh plots, it is evident that the mesh becomes finer and finer as moves from case-1 to case-4. This is because we have reduced various elements sizes which in turn increased the total number of cells.
  • Per scaled residuals graphs, it was observed that all the cases have attained convergence after about 250-300 iterations.
  • From the coefficient of drag plots and the final values obtained, it was found that the Coefficient of Drag value tends to reduce and becomes close to the experimentally obtained value (0.33) as the mesh becomes finer. The below table and graph will indicate the trend in more clarity.
  • Per velocity contours, it was observed that the accuracy of the physics captured by case - 1 set up is very poor. From case - 2 onwards, it started to show realistic plots. Also, as the mesh becomes finer and finer, the contour gave mare clarity.

CONCLUSIONS:-

• The flow over Ahmed Body has been successfully simulated and the results were analyzed.
• The flow separation, negative pressure, flow reversal, recirculation phenomenon, bubble formation and re-attachment are observed especially in the wake region with the help of pressure contour, velocity contour, stream lines and vector plots.
• The point of separation is an important factor which decides the extent of the flow separation zone and hence the drag. By changing the point of separation such as changing the slant angle, the drag produced can be controlled and new design models can be experimented.
• Reference values and y+ value are important factors in the CFD simulations involving the drag and lift calculations.
• Different meshing techniques such as body sizing, face sizing, edge sizing and inflation layers have been used to accurately capture the physics.
• The obtained value of the Coefficient of Drag as a result of CFD simulation has only 2.67% error compared to the actual experimentally obtained value which is acceptable.
• The grid independent test has been conducted with four different cases. Three out of four cases gave almost similar contours though the most finer mesh has given the most accurate and clear contour.
• The importance of Ahmed body in the automotive research and how it helps to design more efficient car models have been studied and understood.