Simulation of flow over a FSAE Car using Converge CFD

Aim:

To simulate the flow over the given geometry of the FSAE car, and find the aerodynamic properties (downforce and drag) at different car parts and compare the results obtained for different cases. 

 

Problem statement:

To perform flow a simulation over the given geometry of the FSAE car for two cases given below and compare the aerodynamic properties (downforce and drag) produced by different car components (rear tail, rear tires, rear suspension, front left-wing, front right-wing, front suspension, front tires, car body, driver helmet, underbody)

Case1:

Racing track conditions - Straights

Average lap speed - 75kmph

Case2:

Racing track conditions - Lot of turns

Average lap speeds - 45kmph

70% turns at 45 degrees

20% turns at 80 degrees

10% turns at 20 degrees

 

Geometry:

The given FSAE car dimensions in x, y, and z directions are approximately 2.5, 1.02, 0.54 meters respectively.

The given FSAE car geometry consists of the following parts where the aerodynamic properties are calculated separately:

1. Front right-wing

2. Front left-wing

3. Front suspension

4. Front tires

5. Rear tires

6. Rear suspension

7. Rear tail

8. Car body

9. Underbody

10. Driver helmet

The virtual wind tunnel dimensions are calculated as follows: 

Let the length of the given FSAE car be L

Then the length of the virtual wind tunnel aft the car (x-direction) is taken as 9L

The length of the virtual wind tunnel in front of the car (x-direction) is taken as 2L

The height of the virtual wind tunnel from the base of the tires (z-direction) is taken as 2L

The width of the virtual wind tunnel is taken as 1L in either direction (y-direction) from the car centerline

 

Case1:

Track type= stright

Average speed= 75Kmph= 20.833 m/s

Calculation of start time and end time for transient-state simulation

The inlet velocity= 20.833 m/s

The length of the virtual wind tunnel= 30m

The time taken by the air to move from inlet to outlet= 30/20.833= 1.44s

Suppose we want to simulate the flow for at least 2 times this value, then 1.44x2= 2.88s

Rounding off to the next digit= 3s

Hence the transient-state simulation must be run from 0 to 3s

 

Case setup:

1. Run parameters:

Solver= transient, time-based simulation

Simulation mode= full hydrodynamic

Gas flow solver= compressible

2. Simulation time parameters:

Start time= 0s

End time= 3s

Initial time-step= 1e-7s

Minimum time-step= 1e-7s

Maximum time-step= 1s

Maximum convection CFL limit= 1

3. Solver parameters:

Navier-Stokes solver scheme= PISO

Navier-Stokes solver type= Density-based

4. Regions and initialization:

Region0:

Velocity(x, y, z)= (20.833, 0, 0)m/s

Temperature= 300K

Pressure= 101325Pa

Species= air

5. Boundary:

a. Inlet

Inflow boundary condition

Velocity(x, y, z)= (20.833, 0, 0)m/s

Pressure= Zero normal gradient(Neumann BC)

Temperature= 300K

Species= air

b. Outlet

Outflow boundary condition

Pressure= 101325Pa

Velocity= Zero normal gradient (Neumann BC)

Species backflow= air

Temperature backflow= 300K

c. Symmetry wall

Symmetry boundary condition

d. Body, rear tail, front right-wing, front left-wing, driver helmet, rear tires, front tires, front suspension, rear suspension, underbody, road

Stationary wall boundary condition (law of wall)

Law of wall boundary condition is used rather than no-slip boundary condition since the law of wall boundary condition gives more accurate results when a coarse mesh is used, whereas, the no-slip boundary condition gives more accurate results if a finer mesh is used. This is mainly because for the no-slip boundary condition, the solver considers the first cell adjacent to the wall as zero velocity magnitude. When the law of wall boundary condition is used, the solver uses the law of the wall assumption for velocity in the log-log layer tries to estimate the flow properties near the walls. Hence it gives less error when a coarse mesh is used.

6. Turbulence modeling

Standard K-omega 2006 turbulence model

Near wall treatment= automatic wall function

7. Grid control:

Base grid size(x, y, z)= (0.25, 0.2, 0.2)m

Fixed embedding:

a. Box embedding

Entity type= box (enclosing the FSAE car)

Dimensions(x, y, z)= (8, 2, 2.4)m

Mode= permanent

Scale= 2

b. Boundary embedding

Entity type= boundary

Boundary ID= All boundaries included except inlet, outlet, road, symmetry wall

Mode= permanent

Scale= 3

Embed layers= 5

8. Output files:

Wall output= boundaries only

Time interval for writing 3D output data files= 0.03s

Time interval for writing text output= 1e-6s

Time interval for writing restarting output= 0.03s

 

Results:

Velocity contours:

The negative magnitude of velocity indicated the reverse flow of air in certain regions.

Stream tracker placed at a height of 0.1m above the tire base:

Stream tracker placed at a height of 0.25m above the tire base:

Vorticity contours:

vorticity is a pseudo-vector field that describes the local spinning motion of a continuum near some point, as would be seen by an observer located at that point and traveling along with the flow.

The vorticity magnitude is higher on certain locations of the car than at any other point of the wind tunnel. The vortices are generated as a result of flow interaction with the walls of the car.

Pressure contours:

Downforce:

The total lift generated by the car at the given conditions is found to be -5418.0864N. Hence the downforce which acts in the direction opposite to that of lift is 5418.056N.

Similarly, the downforce generated by each component can be calculated by first calculating the lift force and then multiplying the result by -1. The downforce generated by each component is given below and is calculated by taking the time average of the results obtained once the solution is converged:

Body:

Downforce= 84044.233N

Rear tail:

Downforce= 139.22126N

Front right-wing:

Downforce= 33.06109N

Front left-wing:

Downforce= 33.0524N

Driver helmet:

Downforce= 3669.7857N

Rear tires:

Downforce= 3108.07N

Front tires:

Downforce= 2287.7778N

Front suspension:

Downforce= 1.4189N

Rear suspension:

Downforce= 1.7257N

Underbody:

Downforce= -87899.548N

Drag:

The total drag force generated by the car at the given conditions is found to be 69.5644N. The downforce generated by each component is given below and is calculated by taking the time average of the results obtained once the solution is converged:

Body:

Drag force= 2032.86N

Rear tail:

Drag force= 7.4892N

Front right-wing:

Drag force= 58.5584N

Front left-wing:

Drag force= 58.56

Driver helmet:

Drag force= 2.3117N

Rear tires:

Drag force= 11.511N

Front tires:

Drag force= 16.957N

Front suspension:

Drag force= 8.38N

Rear suspension:

Drag force= -41.6N

Underbody:

Drag force= -2085.47N

Yplus:

The value of the Yplus term ranges from 10 to 5500. This term is lesser near the body of the car since a finer mesh is used (fixed embedding), but it is still higher than the recommended range. If the yplus term is higher than the recommended range (30-100 for K-omega turbulence model), the accuracy of the solution decreases. But due to lack of computation power, the case is run for coarse mesh setup.

Cell count:

As the problem is solved, there is a change in the total number of cells generated in between the solution. This is because the simulation crashed twice while solving the problem due to memory exhaustion. This happened at around the time of 1.5-1.6s. To rectify this problem, some memory was cleared out and the simulation was re-run from the point it crashed using the restart files. Once the simulation is complete, the results were stitched in Converge.

The simulation was run for 3s and towards the end of the simulation, a total of 378599 cells were generated. The problem was solved using 4 processors, and the cells were distributed between them as follows:

Rank0= 91667

Rank1= 90735

Rank2= 99643

Rank3= 96554

 

Summary of case1:

Now the obtained values of down and drag force at different car components are summarised as follows:

The body of the car is the most significant contributor to the downforce generated, whereas the underbody component generates a significant amount of lift. For a race car to be most efficient the downforce just be as high as possible and the lift must be as low as possible so that the traction between the road and tires is increased. Apart from the body and underbody, the contribution of the remaining components to the downforce is very less comparatively.

When it comes to the drag force, the underbody and the rear suspension are the only components that generate a negative drag force. The body is the main contributor to drag and the remaining components contribute significantly to the drag force generated. Even though the underbody contributes to the lift force, it contributes to the negative drag force thereby reducing the overall drag generated by the car. 

 

Case2:

Track type= Lots of turns

Average speed= 45Kmph= 12.5 m/s

Calculation of start time and end time for transient-state simulation:

The inlet velocity= 12.5 m/s

The length of the virtual wind tunnel= 30m

The time taken by the fluid to move from inlet to outlet= 30/12.5= 2.4s

Suppose we want to simulate the flow for at least 2 times this value, then 2.4x2= 4.8s

Rounding off to the next digit= 5s

Hence the transient-state simulation must be run from 0 to 5s

It is known that the track consists of the following:

• 70% turns at 45 degrees
• 20% turns at 80 degrees
• 10% turns at 20 degrees

Therefore the average turn angle of the car for the duration of the race is calculated as follows:

Average turn angle= (0.7x45)+(0.2x80)+(0.1x20)= 49.5 degrees

Hence the FSAE car is experiencing an average turn of 49.5 degrees throughout the duration of the race with an average car speed of 45Kmph. Hence, to calculate the average aerodynamic forces acting on the FSAE car during the course of the race, the car geometry needs to be tilted by 49.5 degrees. 

 

Case setup:

1. Run parameters:

Solver= transient, time-based simulation

Simulation mode= full hydrodynamic

Gas flow solver= compressible

2. Simulation time parameters:

Start time= 0s

End time= 5s

Initial time-step= 1e-7s

Minimum time-step= 1e-7s

Maximum time-step= 1s

Maximum convection CFL limit= 1

3. Solver parameters:

Navier-Stokes solver scheme= PISO

Navier-Stokes solver type= Density-based

4. Regions and initialization:

Region0:

Velocity(x, y, z)= (12.5, 0, 0)m/s

Temperature= 300K

Pressure= 101325Pa

Species= air

5. Boundary:

a. Inlet

Inflow boundary condition

Velocity(x, y, z)= (12.5, 0, 0)m/s

Pressure= Zero normal gradient(Neumann BC)

Temperature= 300K

Species= air

b. Outlet

Outflow boundary condition

Pressure= 101325Pa

Velocity= Zero normal gradient (Neumann BC)

Species backflow= air

Temperature backflow= 300K

c. Symmetry wall

Symmetry boundary condition

d. Body, rear tail, front right-wing, front left-wing, driver helmet, rear tires, front tires, front suspension, rear suspension, underbody, road

Stationary wall boundary condition (law of wall)

Law of wall boundary condition is used rather than no-slip boundary condition since the law of wall boundary condition gives more accurate results when a coarse mesh is used, whereas, the no-slip boundary condition gives more accurate results if a finer mesh is used. This is mainly because for the no-slip boundary condition, the solver considers the first cell adjacent to the wall as zero velocity magnitude. When the law of wall boundary condition is used, the solver uses the law of the wall assumption for velocity in the log-log layer tries to estimate the flow properties near the walls. Hence it gives less error when a coarse mesh is used.

6. Turbulence modeling

Standard K-omega 2006 turbulence model

Near wall treatment= automatic wall function

7. Grid control:

Base grid size(x, y, z)= (0.25, 0.2, 0.2)m

Fixed embedding:

a. Box embedding

Entity type= box (enclosing the FSAE car)

Dimensions(x, y, z)= (8, 3, 2.4)m

Mode= permanent

Scale= 2

b. Boundary embedding

Entity type= boundary

Boundary ID= All boundaries included except inlet, outlet, road, symmetry wall

Mode= permanent

Scale= 3

Embed layers= 5

8. Output files:

Wall output= boundaries only

Time interval for writing 3D output data files= 0.05s

Time interval for writing text output= 1e-6s

Time interval for writing restarting output= 0.05s

 

Results:

Velocity contours:

The negative magnitude of velocity indicated the reverse flow of air in certain regions.

Stream tracker placed at a height of 0.1m above the tire base:

Vorticity:

The vorticity magnitude is higher on certain locations of the car than at any other point of the wind tunnel. The vortices are generated as a result of flow interaction with the walls of the car.

Pressure:

Downforce:

The total lift generated by the car at the given conditions is found to be -5397.97N. Hence the downforce which acts in the direction opposite to that of lift is 5397.97N.

Similarly, the downforce generated by each component can be calculated by first calculating the lift force and then multiplying the result by -1. The downforce generated by each component is given below and is calculated by taking the time average of the results obtained once the solution is converged:

Body:

Downforce= 84067.294N

Rear tail:

Downforce= 96.963N

Front right-wing:

Downforce= 31.0565N

Front left-wing:

Downforce= 31.25N

Driver helmet:

Downforce= 3670.26N

Rear tires:

Downforce= 3111.6961N

Front tires:

Downforce= 2296.3298N

Front suspension:

Downforce= 1.5491

Rear suspension:

Downforce= 1.6984

Underbody:

Downforce= -87910.131N

Drag:

The total drag force generated by the car at the given conditions is found to be 54.0864N. The downforce generated by each component is given below and is calculated by taking the time average of the results obtained once the solution is converged:

Body:

Drag force= 1330.68N

Rear tail:

Drag force= 3.4618N

Front right-wing:

Drag force= -116.922N

Front left-wing:

Drag force= 193.7263N

Driver helmet:

Drag force= 1.69N

Rear tires:

Drag force= 8.4422N

Front tires:

Drag force= 8.3174N

Front suspension:

Drag force= 5.108N

Rear suspension:

Drag force= -27.076N

Underbody:

Drag force= -1353.3467N

Yplus:

The value of the Yplus term ranges from 10 to 3400. This term is lower near the body of the car since a finer mesh is used (fixed embedding), but it is still higher than the recommended range. If the yplus term is higher than the recommended range (30-100 for K-omega turbulence model), the accuracy of the solution decreases. But due to lack of computation power, the case is run for coarse mesh setup.

Cell count:

The simulation was run for 5s and a total of 498621 cells were generated. The problem was solved using 4 processors, and the cells were distributed between them as follows:

Rank0= 113596

Rank1= 131395

Rank2= 131126

Rank3= 122504

 

Summary of case2:

The body of the car is the most significant contributor to the downforce generated, whereas the underbody component generates a significant amount of lift. For a race car to be most efficient the downforce just be as high as possible and the lift must be as low as possible so that the traction between the road and tires is increased. Apart from the body and underbody, the contribution of the remaining components to the downforce is very less comparatively.

When it comes to the drag force, the underbody, rear suspension, and front right-wing are the only components that generate a negative drag force. The body is the main contributor to drag and the front left-wing significantly to the drag force generated. Even though the underbody contributes to the lift force, it contributes to the negative drag force thereby reducing the overall drag generated by the car. 

 

Conclusions:

From the above comparison chart, we can say that the downforce is more or less the same for both the cases.

From the above comparison chart, we can say that there is a substantial difference in the drag force generated in the two cases at different car components. The aerodynamic forces acting on different car components depend on the race track conditions.