Flow Over Ahmed body

• Objective:
  
  • To simulate the flow over Ahmed body and find the aerodynamic parameters related to the same.
  • To perform a comparative study with the experimental data.
• Theory:
  • Ahmed body is an approximate shape of an automobile. Moreover, a simplified one. It is a generic bluff body(a body which when introduced in a fluid field causes flow separation to take place (or) to be specific, a body in which one of its faces doesnot interact or come in contact with the fluid) proposed to study the external aerodynamics of the vehicles.
  • It's a benchmark model used to validate new simulation tools in automotive industries. The fig.1 below, shows the image of an Ahmed body in an experimental setup(a wind tunnel).
  • As shown above, it is made-up of a parallelepiped with rounded edges at the front and a slanted face at the rear. The slant at the rear side of the vehicle causes the separation of flow and also a significant factor for drag forces of Ahmed body. The formula for various aerodynamic forces are stated below.
  • Lift Force, the force acting along the Y-axis, i.e., perpendicular to the direction of flow. The formula is as follows:
    • `L=1/2*rho*A*v^2*C_l", where "L" - Lift force in N, "``rho " - Density of the fluid in kg/"m^3", "``A" - Wing area("m^2") = Chord length"(m)" * span"(m), "``v" - Velocity of the fluid in m/s, "``C_l" - Lift coefficient"`
  • Drag Force, the force acting along the X-axis, i.e., parallel to the direction of flow.The formula is as follows:
    • `D=1/2*rho*A*v^2*C_d", where "D" - Drag force in N, "``rho " - Density of the fluid in kg/"m^3", "``A" - Wing area("m^2") = Chord length"(m)" * span"(m), "``v" - Velocity of the fluid in m/s, "``C_d" - Drag coefficient"`
• Procedure:
  1. The Ahmed body geometry is created in SolidWorks(fig.2b) using the 2D drawing data(fig.2a), shown below. (Note: The slant angle(`psi`) is taken as 35 degrees)
  2. This is saved as a STL file and imported into Converge CFD software. Then diagnosed for any surface imperfections and resolved.
  3. Then the virtual wind tunnel is created for a well-defined dimension taking the various constraints into concern as listed below:(Note: The following constraints are taken in accordance with the experimental data).
     • "Boundary layer thickness is 30mm at 400mm in front of the Ahmed body":
       • Formula for boundary layer on a flat plate: `delta~~(0.382xxx)/(Re_x)^(1/5), "where "delta-"boundary layer thickness in "m,``x-"length of the plate in "m,``Re_x-"Reynolds number at location x"`
         • `"Here, "delta=0.03m,``"Re"_x=(v*x)/nu," where " v-"velocity of the fluid"=40m"/"s, x-"length of the flat plate(to be calculated)", nu-"Kinematic viscosity in "m^2"/"s``=>Re_x=(40xxx)/(1.552xx10^-5`
         • Now, substituting the above in boundary layer equation, we get:`=>0.03=(0.382xxx)/((40xxx)/(1.552xx10^-5))^(1/5)``=>0.274=(0.382xxx)/(40xxx)^(1/5)=>0.719=x/(40x)^(1/5)=>0.1924=x^5/(40x)=>bb"x=1.6655m"`
       • The above calculated value is the length at which the boundary layer thickness reaches 30mm. So, to get the actual length in front of the Ahmed body, 400mm is added to this value as shown below:
         • `=>x+0.400=1.6655+0.400=bb"2.0655m"` (Note:This length corresponds only to the law of the wall region)
       • In addition to this length, a free-slip region is provided prior to it. This is done in order to avoid the boudary layer formation for about a length of 0.5m. Thus, the total length in front of the Ahmed body is confined.
       • Basically, in order to record the wake formation in the leeward side, the length of the wind tunnel in the leeward side is taken in the order of 5 to 10 times the length of the Ahmed body. Here, 5 times is considered.
       • The height and width of the wind tunnel is taken as 2 times the length of the Ahmed body in order to facilitate the 3D flow to happen in the way it should. This is done in order to avoid the top and side walls from obstructing the flow of the fluid. The fig.3 below, depicts the wind-tunnel created.
  4. Then, the boundaries are flagged accordingly, such as the inlet, outlet, top and side walls, Free-slip wall, law of the wall region, and the Ahmed body, as shown in the above figure.
  5. The input conditions are given by means of setting the case set-up:
     1. The material/ fluid medium is selected as air and various other properties of the fluid are set to their default values.
     2. Then the simulation parameters are set as follows:
        1. The transient simulation option is selected under the Run parameters as it is a time-dependant simulation.
        2. The time for simulation is found based on the flow thro' time. The flow thro' time is calculated as follows:
           • `"Flow through time"="Length of the pipe/ wind tunnel"/"Velocity of fluid"``"Here, Length of the wind tunnel=length of (free-slip+law of the wall+length of Ahmed body+length of leeward side)"``" " =0.5+2.0655+1.044+5xx1.044= bb"8.8295m"``"Velocity of fluid"=bb"40m/s""(from experimental data) "` `"So, Flow thro' time"=8.8295/40=bb"0.2207s "`
           • Generally, the time for simulation is 3 to 4 times that of the Flow thru' time; here approximately 3 times, i.e., `"Time for simulation"=3xx"flow thru' time"=3xx0.2207=0.6622s~~bb"0.7s"`
           • This time is given under the Simulation time parameters
        3. The density based solver is selected under Solver parameters.
     3. The initial values for the simulation, such as the velocity is set to 40m/s and a region is defined with air as a fluid medium.
     4. The boundary conditions for the various boundaries are given as follows(Refer fig.3 for flagged boundaries):

        S.No.	Boundary name	Boundary conditions
        1.	Inlet	Inflow boundary: Velocity along x-dir=40m/s and fluid medium air is added. Pressure-Neumann BC.
        2.	Outlet	Outflow boundary: Pressure=1atm(101325Pa) and fluid medium air is added. Velocity-Neumann BC
        3.	Free-slip region	Wall boundary: Slip wall option is selected as the boundary layer formation is not required in this region.
        4.	Law-of-the-wall region	Wall boundary: Law-of-the-wall option is selected as the boundary layer formation is required in this region.
        5.	Top and side walls	Symmetric boundary: As the boundary layer formation is not required in the top and side walls, this BC is given.
        6.	Ahmed body	Wall boundary: Law-of-the-wall option is selected as the boundary layer formation is required in this region.

     5. The `k-omega\ SST` turbulence model is selected under the Physical models. This models is a combination of `RNG\ k-epsilon` turbulence model and `"Standard " k-omega` model. This acts as `"Standard " k-omega` model near the wall boundaries and `RNG\ k-epsilon` model away from the wall. Hence, it gives an accurate prediction of the simulation both near wall and away. Moreover, it is accorded for its automatic wall treatment
     6. Basically, the mesh size is derived by determining Y+ value, here it has to be less than 1 to capture the properties of viscous sub-layer, but due to various constraints, a value of 75 is taken(Note: This falls under the turbulent layer. Though this is a coarse mesh, even this is not possible due to the same constraint. Thus, the calculation below shows how actually the mesh size is arrived and not the one used for simulation. So, the mesh size employed for the simulation is discussed at the end of this point).
        1. The website: https://www.pointwise.com/yplus/ is used to calculate the mesh size near the wall for a particular Y+ value given as input. The fig.4 below, shows how the mesh size required near the wall changes as the Y+ value changes.
        2. Now, from the above, around 0.7mm grid size is required near the wall. To refine it to this level near the wall, say a scale of 5 is used, the base grid size would be:`w.k.t.,"Base grid size"/2^n="Size of refined cell"=0.7" "=>"Base grid size"=0.7xx2^5=22.4mm=0.0224m`
        3. Since this leads to vast number of cells and is beyond the system's capacity, it is not used. After a few trials, the minimum possible and feasible base grid size is found to be 0.1m.
        4. As the Ahmed body and the wake region are the areas of interest, Fixed Embedding feature is used to refine these regions. The fixed embedding of box type is used in order to refine the cells in 3D as the wake is three-dimensional. The maximum possible embed scale, based on the system capacity is found to be 2, so it is applied with the number of layers being 2.
     7. In the Outputs/Post-processing, the Y+ is included, so that it could be observed at various points of time. The wall boundary output option is enabled so as to compute the lift and drag forces in wall boundary. Then the time interval for writing the 3D and text outputs are given as 0.01s and 0.001s respectively based on number of outputs required.
     8. Thus all the required inputs for the simulation are given by setting up the case set-up.
  6. Now, the input files are generated and exported to a folder. The converge executable file is run and the output files are generated.
  7. These outputs are converted into a form Paraview can interpret, by means of the option available in converge studio to run the post-convert executable.
  8. Then the outputs are post-processed using Paraview software and the simulation results are analysed.

(Note: The simulation is run with higher degree of refinement in a system with higher capacity once the coarse simulation results are found valid. This simulation is run with half Ahmed body(i.e., Ahmed body is cut into 2 symmetric halves) to reduce the number of cells, which doesnot affect the simulation results in anyway. So, the results of the this simulation are also included in the below section along with the coarse simulation results)

• Observations and inferences:
  • Depiction of flow using Stream tracer:
    • • Observations:
        • The flow is obstructed by the Ahmed body to a greater extent. The flow is diverted to the upper and lower part of the body as it strikes the front surface.
        • The flow in the leeward side undergoes drastic changes in its characteristics.
      • Inference:
        • The flow is diverted to a greater extent by the front surface as its corners are rounded(i.e. filleted to higher radius)
        • The nature of flow in the leeward side is due to the wake formation, which is due to the flow separation and recirculation.
        • The flow separation is accorded to the geometry of the Ahmed body, i.e., the slant angle, which is discussed in detail in the following plots.
  • Velocity Contour:
  • Velocity variation over the surface(front & back side):
    • Refined Simulation:
  • Velocity Contour Animation:
    • • Observations:
        • The velocity is very low(indicated dark blue) in the wind-ward side at the point of incidence and in the leeward side too.
        • The velocity is quite higher in the top & bottom sides of the Ahmed body, and the top-rear edge indicated red
        • As the flow furthers there is a formation of low velocity region along the trailing edge, which seems to show motion.
      • Inference:
        • The velocity is very low in the wind-ward side because the air strikes the front part and loses its kinetic energy.
        • Unlike the above case, the velocity is low in the leeward side due to the flow separation taking place at that location, which causes flow-reversal or recirculation. Due to this a partial vacuum is created, thus leading to low velocity in this region.
        • The velocity is higher in the top and bottom part of the body because the deflected air, due to its encounter with the body flows over the top and bottom surface. This adds up to the flow of air already existing in this location.
        • The higher velocity in the top-rear edge denotes the arrival of the point of flow separation. Due to this fact, the velocity is higher(Note: The velocity is higher just at the point which is proximity to the point of flow-separation and not in the region of flow separation!)
        • The low velocity region(as explained earlier) along the trailing edge is called the wake region, which is due to the slant angle of the Ahmed body(35deg), i.e. it is accorded to the geometry. This seems to move because of the nature of the vortices formed in the region due to recirculation of air. This contributes to the majority of the drag force on the body as it causes suction to take place in this location(i.e., a negative pressure) which ultimately adds up to the drag on the body.
    • Velocity Vector and Stream tracer:
    • Refined Simulation:
    • • Observation:
        • Evidence of detached flow in the areas proximity to the trailing edge.
        • The velocity vector shown above, depicts the recirculation(or flow-reversal) of air. This can be verified by some arrows in the leeward side pointing to a direction opposite to that of flow.
      • Inference:
        • Due to the geometry of the Ahmed body there is flow separation which leads to detached flow. It is the slant angle(35deg) that causes this phenomenon.
        • The observation of recirculation(or flow-reversal) of air ascertains the formation of vortices and wake in the leeward side. The above observations upholds the inferences made earlier.
  • Pressure Contour:
  • Pressure variation over the surface(front & back):
    • Refined Simulation:
  • Pressure Contour Animation:
    • • Observations:
        
        • The pressure is very high(indicated dark red) in the wind-ward side at the point of incidence and the surrounding areas.
        • The pressure is a bit lower in the top & bottom sides of the Ahmed body and the top-rear edge indicated dark blue.
      • Inference:
        • As the air strikes the front surface, the kinetic energy is converted into pressure energy, which leads to the drastic increase in pressure in this area, this pressure is known as stagnation pressure as the fluid stagnates here. Even this contributes to some amount of drag.
        • The lower pressure in the top & bottom sides, and the top-rear edge is accorded to the high velocity in these regions. As the velocity increases the pressure decreases.
  • Drag Force Vs time Plot:
    • • Observations:
        • The drag force(Pressure Force X) has attained a steady state as the simulation reaches its end.
        • The drag force converges to a value of about 52.58N
      • Inference:
        • The drag force is caused due to 2 reasons as listed below:
          
          • Skin Friction drag- due to the friction in the surface over which the fluid flows
          • Pressure drag- due to the pressure difference between the front and the rear side of the body.
        • Of these, the major amount of total drag is accorded to the pressure drag, and the friction drag is comparatively less, hence, neglected.
        • The pressure drag is contributed by 2 regions, namely, the forebody and the afterbody(or the base body).
        • Forebody is the front part of the body which is stricken by the incident air.(Note: The high pressure in the front part of the body as depicted in the pressure plot relates to the drag contributed by forebody)
        • Afterbody or base body is the rear part of the body interacting with the wake region.(Note: The low velocity wake region in the rear part of the body as depicted in the velocity plot relates to the drag contributed by the afterbody)
        • Hence, the cause of the drag has been dealt in brief.
        • Now, using the formula for drag, stated previously, the drag coefficient is computed:
          • `w.k.t, "Drag Force(D)"=(C_d xxrhoxxAxxv^2)/2 =>C_d=(2xxD)/(rhoxxAxxv^2)`
          • Here, `D=52.58N," "rho=1.1765 kg"/"m^3," " A="Frontal Area"=0.288xx0.398=0.112m^2," " v=40m"/"s`
          • `=>C_d=(2xx52.58)/(1.1765xx0.112xx40^2)=bb"0.498"`
          • Thus the drag coefficient value has been computed.
  • Lift Force Vs time Plot:
    • • Observations:
        • The lift force(Pressure Force Y) has attained a steady state as the simulation reaches its end.
        • The lift force converges to a value of about -240.64N
      • Inference:
        • As the lift force turns out to be negative, it is called as negative lift or down force.
        • This force plays a crucial role in keeping the vehicle in contact with the ground and avoid lifting of vehicles. Thus, it is an essential force!
        • The lift coefficient is calculated by:
          • `w.k.t," Lift Force(L)"=(C_lxxrhoxxAxxv^2)/2=>C_l=(2xxL)/(rhoxxAxxv^2)`
          • Here, again, `L=-240.64N," "rho=1.1765 kg"/"m^3," " A="Frontal Area"=0.288xx0.398=0.112m^2," " v=40m"/"s`
          • `=>C_l=(2xx(-240.64))/(1.1765xx0.112xx40^2)=bb"-2.283"`
          • Thus the negative lift coefficient is calculated.
  • Mesh Generation:
    • • Observations:
        • The cells are refined near the Ahmed body and the region surrounding the wake.
        • The total number of cells is about 3,50,000 cells.
      • Inference:
        • As the area around the Ahmed body and the wake region are the areas of concern(critical to variation in flow characteristics), these regions are refined using fixed embedding using a scale of 2.
        • The total number of cells are quite optimal in accordance with the system configuration, hence the obtained simulation is approximate one.
  • Y-Plus:
    • • Observations:
        • The Y+ value converges to around 2000, which is quite high.
      • Inference:
        • As the maximum possible refinement, due to system constraints, is coarse, the Y+ value is very high. Hence, the simulation is an approximate one.
  • Comparative study with the Experimental data:
    • After the simulation has run, it is post-processed using Paraview software. In Paraview, the plot over line feature is used to plot the required variable along a line, whose end points are specified. Here, the velocity along x-direction is plotted w.r.t. the y-position, for that the lines are drawn as shown below.
    • These are drawn one by one, at stated locations, using the plot over line tool and the data is extracted and saved in an Excel file. Then the experimental data provided is compared with it by plotting. (Note: The origin stated in the below figure(the experimental origin) and the origin of the wind tunnel are different so, in order to plot the lines at the exact locations as that of experimental data, the points are mappped from the experimental origin to the wind tunnel origin by adding the difference between x-coordinates of the origins, here 3.1095m to the corresponding x-coordinates as the origins are collinear here).
    • As shown above, 4 lines in the wake section and another 4 at various locations near the surface of the Ahmed body are plotted.
    • As the probe is near the rear end, there is reduction in velocity for some length. The experimental data and the simulation data have a similar trend, though don't coincide which is accorded to the coarse meshing due to the system constraints.
    • As this one is quite away from the rear end, the velocity is a bit steady. The experimental data and simulation data coincide to a greater extent, as this area is not critical to changes.
    • This is placed in the wake region, so the velocity is negative at certain locations. Again, both the data possess a similar curve trend, which suggests that the simulation is valid.
    • Similar to the previous one, even this is placed in the wake region, as the velocity is negative. Again, both the data possess a similar curve trend, which suggests that the simulation is valid.
    • This is closer to the rear end, where flow separation takes place, hence the above plot is got. Though the curves have a similar trend, the velocity near the walls don't coincide.
    • Similar to the previous one, even this is plsce in the flow separation region. Though the curves have a similar trend, the velocity near the walls don't coincide.
    • It is placed in the wake region, which results in the above plot. The data possess a similar trend, hence the simulation is valid.
    • This is again similar to the previous plot. The data possess a similar trend, hence the simulation is valid.
    • Therefore, the overall simulation is found to be valid as the trends of the curves match eachother. The deviation in a certain curves are accorded to the coarse meshing.
    • The below are the plots made from the simulation with high degree of refinement.
    • The above plots coincide well with the experimental data as the refinement is higher.
  • Normalised Velocity Plot:
    • Normalisation is done to visualise the velocity profile and compare it a bit easily. In order to normalise, for each line probe (both experimental and simulation data), the velocity at each point in the line probe is divided by the maximum velocity along the line and multiplied by an amplification factor, here 5. Then this value is subtracted from the x-coordinate value of the line, so that it could be plotted for comparison. The below plot shows the normalised velocity plot, which suggests that the simulation and experimental data coincide to a greater extent. This shows that the simulation is valid. (Note: For verification, the results of simulation run in a high configuration system have been included in the last)
    • Link for the Excel file containing all the data including normalisation: https://drive.google.com/file/d/1HBaZQ4zJ4MqaQFTK-EwseNIoNEqQkqwy/view?usp=sharing
    • The Normalised plot obtained from the simulation with higher degree of refinement is shown below. The link for Excel file containing data and calculation pertaining to the refined simulation: https://drive.google.com/file/d/1_J53O3C77Ky9EdLDoQFZzWH8RhmN8bmt/view?usp=sharing
• Result:
  • Thus the flow over the Ahmed body is simulated and the aerodynamic parameters derived. It is infered that the major amount of drag is produced by the rear part(wake region) of the Ahmed body.
  • The comparative study with the experimental data has been performed and it turns out that the simulation is valid.