Analysis of Aerodynamic Forces over Forumla SAE Car
Introduction:
Formula SAE, commonly known as FSAE, is a student design competition organized by Society of Automotive Engineers (SAE). In the growing technology and engineering process, Computational Fluid Dynamics (CFD) has played a huge role in the design of such aerodynamic cars. CFD analysis on an FSAE car can give vital information as to where the maximum drag occurs, or vorticity of the space behind the car. This information can help design the best FSAE car and beat the competition.
Objective:
The main objective of this project is to perform a full-fledged virtual wind tunnel analysis on an FSAE car using ParaView (post-processing software).
Method:
The geometry of the car was provided for analysis. However, the geometry had some error which needed to be fixed and cleaned up before doing the simulation. Figure 1 shows the triangles and the corresponding error.
FIGURE 1 Geometry with the error shown in Converge Studio.
Using the Repair tool, along with the Patch tool, the errors were resolved and geometry was cleaned up as shown in Figure 2.
FIGURE 2 Geometry cleaned up without any errors
Boundary Flagging
Since this is a full-fledged FSAE car, and suspension team is interested in finding the components and the drag force it produces, we have to flag each and individual components manually. For example, right tire, left tire, front wing, etc. as shown in Figure 3.a, and 3.b. Boundary Fences were created where two components were connected, either by Fence By selected edges or Fence Between two vertices. The reason to create fences is to flag components more accurately and speed up the process due to the complexity of the geometry. With the angle method, Converge would not be able to get accurate fencing around the component.
FIGURE 3.A Top view geometry shown with boundary colors
FIGURE 3.B Boundary flags
Virtual Wind Tunnel
Once the geometry was cleaned up and individual components were flagged, the virtual wind tunnel was created. The standard virtual wind tunnel has the front length of 5*base length and 10*base length in the back or even 50 to capture the wake region and return the flow to atmospheric pressure.
FIGURE 4.A Virtual wind tunnel length calculation
FIGURE 4.B Virtual wind tunnel with flagged walls
Simulation Case Setup
Two race simulation was simulation as follow:
Race-1
- 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
Race-2
- Racing track conditions - Straights
- Average lap speed - 75kmph
For Race-1, the average angle of the FSAE car was calculated to be 49.5 degrees, as shown in Figure 5. Apart from the different speed, both races are set up exactly the same.
FIGURE 5 Calculation for an average degree for Race-1
Application: General flow
Materials: Air as a predefined mixture (all other the parameters were the default)
Simulation Parameters: Fully hydrodynamic compressible Transient simulation with 5.2 seconds and 4.0 seconds end time for Race 1 and Race 2 respectively. Time step was 1E-06 for both cases.
Boundary: Inlet with 12.5 m/s and 20.75 m/s velocity for Race-1 and Race-2 respectively. The outlet was defined with atmospheric pressure. The front, top, and backside from the side view were symmetry walls, and the bottom of the wind tunnel was defined as the wall. All other boundary was configured with wall type boundary.
Regions and Initialization: Was defined with the specific speed as with inlet.
Turbulence modeling: k-omega SST model was chosen since it known to capture flow over the external body due to its automatic wall function.
Base grid: dx=0.057, dy=0.25, dz=0.057 was chosen along with fixed embedding with a scale of 6 on FSAE car to achieve desired plus value. Due to computational resources, simulation result was provided since the number of cells is very large that it would take a very long time to complete this simulation.
Output/Post Processing: Yplus variable was selected and the time interval was calculated to 0.016s.
Results and Discussion
Race 1
Figure R1.D.+X Drag magnitude for Race 1 shown from +X direction
Figure R1.D.-X
Figure R1.D.-Z
Figure R1.D Maximum drag region shown for Race 1
All the above figures, i.e. R.1.D, shows the drag over the FSAE at 49.5-degree turn. Drag force (also known as air resistance) is a type of force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. In general, one of the main objective while designing a race car is to minimize drag forces since it lowers the car performance and top speed. It also makes the car less efficient. The aerodynamic drag coefficient is a measure of the effectiveness of a body in reducing drag force, which given by following:
`C_d = (2*F_d)/(rho*u^2*A)`
where:
`C_d` is the drag coefficient
`F_d` is the drag force
`rho` is the density of the fluid
`u` is the flow speed
`A` is the frontal area of the object
As seen from the figures, the underbody component generates the largest amount of drag when the car is at an angle. The component of the car is designed to minimize drag, thus, aerodynamically designed to increase the performance of the car. Figure R1.L.+X Lift magnitude for Race 1 shown from +X direction
Figure R1.L.-X
Figure R1.L.+Z
Figure R1.L.-Z
All the above figures, i.e. R.1.L, shows the lift over the FSAE car for 49.5 degrees. Lift Force is a force acting perpendicular to the flow direction and it is the primary force that makes planes take-off and F1 cars to take turns at a faster speed. As drag coefficient defines how aerodynamic an object is in reducing the drag force, lift coefficient relates to how much lift the object can generate and defined as follows:
`C_l = (2*F_l)/(rho*u^2*A)`
where:
`C_d` is the drag coefficient
`F_l` is the drag force
`rho` is the density of the fluid
`u` is the flow speed
`A` is the frontal area of the object
When the lift is negative (pushing downwards), it is called the downforce. As seen from the above figures, the underbody is generating very large downforce to keep the car on the ground and provide grip to tires. This allows tires to contact with the road much better and take a turn at a higher speed due to higher friction. The principle reason behind why underbody is generating such a large downforce is because of the ground effect. Ground effect is an effect due to manipulating the airflow in order to create additional downforce resulting from the venturi effect. Venturi effect is when the fluid flows through a constricted area relative to the inlet and outlet.
Figure R.1.P Pressure on suspension shown for Race 1
Figure R.1.T Temperature on suspension showed for Race 1
Figure R.1.P shows the pressure on the suspensions of the car. Due to the angle of the car (49.5 degree) and the flow direction, the front-right suspension experiences the highest pressure out of all. A linear relationship between pressure and temperature exits, thus, temperature increase aswell as shown in Figure R.1.T.
Race 2
Figure R2.D.+X Drag magnitude for Race 2 shown from +X direction
Figure R2.D.-X
Figure R2.D.+Z
Figure R2.D.-Z
Figure R2.D Maximum drag region shown for Race 2
Above figures show the drag on a straight track. As expected, the overall drag force is increased due to rear vacuum. As seen in Figure R2.D.-X, the back of the car experience highest drag force. This is due to the fact that at such a high speed, it leaves a void shape in the air. The air rushes around from the side and top to fill the gap as quickly as possible. However, the effect gets larger at increasing speed. A way to improvise the redesign the back end of the car which converges smoothly which fills the rear vacuum smoothly.
Figure R2.L.+X Lift magnitude for Race 2 shown from +X direction
Figure R2.L.-X
Figure R2.L.+Z
Figure R2.L.-Z
Figure R2.L.Wing
As seen from the figures, the underbody creates the largest downforce along with the rear wing due to the venturi effect. It is the design of underbody of the car which acts as an inverted airfoil, creating downforce the car higher speed. Due to health and safety concern, modern-day race regulation has limited on the design of underbody.
Figure R.2.a Velocity contour for Race 2
Figure R.2.b Vorticity contour for Race 2
Figure 6 Drag Plot for Race 1
Figure 7 Downforce Plot for Race 1
Figure 8 Drag Plot for Race 2
Figure 9 Downforce Plot for Race 2
Suggestions for improving the design
After analyzing the data and the result, it was observed that tires generated a portion of overall drag. To reduce drag on tire, wheels can be covered to make it more aerodynamic. Due to regulation, full covering might not be allowed, but if partial bodywork is permitted, placing a converging fairing behind the wheels provides maximum benefit.
Front wing did not generate much downforce than needed, thus, the front wing should be redesign to increase the overall downforce on the car.
It was found the end of the body had the larger drag due to rear vacuum. This can be solved by extending the tail of the car and narrowing it to allow air molecules to converge back into the vacuum smoothly along the body. Such type of design is found in modern F1 cars and Le Mans race cars.