Enhancing vehicle performance through the application of airfoils as spoilers with movable trailing edge

Airfoil group

Understanding the aerodynamic characteristics of different airfoil shapes is crucial for the design and performance optimization of aircraft wings. Airfoils are the cross-sectional shapes of wings and are designed to produce lift efficiently while minimizing drag. Table 1 presents a comprehensive comparison of various airfoil groups, detailing their geometric and aerodynamic properties.

Table 1. Airfoil group tables and analyses.

Group A
Name	Thick	Camber	Chord	CD	CL
S1223RTL	13.5	8.3	0.3 m	0.047	1.019
GOE243	14.2	9.2	0.3 m	0.052	1.135
FX73-CL3-152	15.2	8	0.3 m	0.057	0.985
USA32AIRFOIL	14.7	9.3	0.3 m	0.068	1.146

Group B
Name	Thick	Camber	Chord	CD	CL
NREL5801	13.5	3.7	0.3 m	0.027	0.457
EPPIER434	13.3	4.3	0.3 m	0.028	0.531
AH63-IC-127\24	12.7	3.8	0.3 m	0.025	0.47
AH93-K-130\15	13.1	3.5	0.3 m	0.025	0.433

Group C
Name	Thick	Camber	Chord	CD	CL
DoEing737 root	15.4	0.2	0.3 m	0.027	0.024
OAF139	13.7	0	0.3 m	0.024	0
-E474	14.1	0	0.3 m	0.025	0
-EPPIER479	16.6	0	0.3 m	0.028	0

Group D
Name	Thick	Camber	Chord	CD	CL
NACA0012	12	0	0.3 m	0.019	0
-EPPLER EA(6)	12	0	0.3 m	0.019	0
-RAF30	12.6	0	0.3 m	0.021	0
-GOE 409	12.7	0	0.3 m	0.021	0

As shown in Table 1, the NACA0012 airfoil was selected for its symmetrical properties. This design rationale hinges on adopting a spoiler configuration distinguished by symmetrical geometric attributes. Within this framework, the lift force demonstrates asymptotic convergence towards nullity, displaying minimal sensitivity to variations in airspeed. The inherent geometric symmetry of the spoiler facilitates meticulous control over lift force modulation during spoiler articulation, ensuring precision in both lift augmentation and attenuation.

This particular design subtlety assumes significance owing to its contribution to heightened accuracy in lift force management, regardless of the directional adjustments (upward or downward). The deliberately engineered symmetrical spoiler configuration confers stability and predictability to the nuanced control of lift forces, providing a refined and controlled response across diverse aerodynamic conditions. This precision proves integral to optimizing the spoiler’s performance, especially during manoeuvres that demand exacting lift adjustments.

CATIA model

In this section, the shapes provide an illustration of the shape of the spoiler with different angles of trailing edge.

Figure 2. Spoiler model at 0 angle of trailing edge.

Figure 3. Spoiler CATIA model at negative angle of trailing edge.

Figure 4. Spoiler CATIA model at positive angle of trailing edge.

Turbulence model (SST k-ω Model)

The Shear Stress Transport (SST) k- ω turbulence model, introduced by Menter,⁷ is a widely used two-equation eddy-viscosity model known for its versatility in simulating complex flows. This model effectively combines the strengths of the k- ω and k- ε formulations. In the near-wall region, the k- ω formulation is employed, allowing the model to accurately capture boundary layer effects without requiring additional damping functions. In the free-stream region, the model transitions to k- ε behaviour, addressing the sensitivity issues often associated with traditional k- ω models when dealing with free-stream turbulence properties.

One of the key advantages of the SST k-ω model is its robust performance in flows with adverse pressure gradients and separation, making it particularly suitable for simulating the complex airflow patterns around vehicle spoilers. However, the model tends to overpredict turbulence levels in regions with high normal strain, such as stagnation points or areas of strong acceleration. Despite this limitation, the SST k-ω model remains a preferred choice for aerodynamic simulations due to its overall accuracy and reliability.⁸

Figure 5. Turbulence model.

Kinematic Eddy Viscosity:

Where:

a₁: Model constant, typically around 0.31.

S : Strain rate magnitude.

Turbulence Kinetic Energy:

Specific Dissipation Rate:

Where:

k: Represents the energy contained in turbulent eddies.

P: Production of k, usually due to velocity gradients.

β^∗: Model constant, controls the dissipation rate of k to ω.

ω: Specific dissipation rate.

v: Kinematic viscosity.

σ: Model constant, controls the turbulent diffusion of k.

v _t: Turbulent viscosity.

Closure Coefficients and Auxiliary Relations:

Car model

A simple Tesla model was drawn on CATIA software, which is shown in Figure 6.

Figure 6. Car model.

Car model with spoiler

The design of the spoiler type is NACA0012, 120*45 cm with different AOTE.

Figure 7. Car model with spoiler.

Process procedure

The ANSYS simulation process involves several sequential steps to ensure accurate and reliable results. These steps include pre-processing, meshing, setting up boundary conditions, and selecting the appropriate turbulence model. Each stage is critical for achieving a realistic representation of the aerodynamic behaviour of the vehicle. The sequence of processes in the ANSYS Workbench is illustrated in Figure 8.

Figure 8. Sequence of processes in ANSYS.

Pre-processing :

The first step in the simulation process is pre-processing, where the car model is prepared for analysis. The 3D model of the car, designed in CATIA, is imported into ANSYS Geometry. A computational domain, or enclosure, is then created around the car to simulate a wind tunnel environment. The dimensions of the enclosure are provided in Table 2, and the enclosure is visualized in Figure 9.

Figure 9. Enclosure.

Meshing:

The next step is meshing, where the computational domain is divided into a grid of small elements. Proper meshing is essential for accurate results, as an improperly meshed model can lead to incorrect solutions. Special attention is given to refining the mesh around the car and spoiler, where the interaction between air molecules and the vehicle is most significant. The meshed model is shown in Figure 10.

Figure 10. Car model after meshing process.

Boundary conditions:

After meshing, the boundary conditions are defined to simulate real-world airflow conditions. The inlet is set as a velocity inlet with speeds ranging from 120 km/h to 350 km/h, while the outlet is defined as a pressure outlet. No-slip boundary conditions are applied to the car and spoiler surfaces, and symmetry conditions are used to reduce computational cost. The details of the boundary conditions are provided in Table 3.

Turbulence model:

The final step in the setup process is selecting the turbulence model. The Shear Stress Transport (SST) k- ω model is chosen for its ability to accurately capture the complex airflow patterns around the vehicle, particularly in regions with adverse pressure gradients and flow separation.

Result analysis and discussion

After finishing the fourth pre-process step, the model was ready to do the final step, which is the solution to get the results.

Streamline and pressure contour for car model and spoiler with difference AOTE:

The following figure illustrates the airflow streamlines and pressure contour around a car model equipped with a spoiler at various angles of trailing edge (AOTE). As the AOTE changes, the behaviour of the airflow around the car and spoiler also changes, influencing the aerodynamic forces such as lift, drag, and downforce. These streamlines help visualize how different AOTE settings impact the car’s performance and stability.

The illustrations provide a captivating exploration of the aerodynamic complexities surrounding a car’s wings. Initially, in the absence of a moving wing Figure 11, the car experiences a distribution of air pressure, mainly concentrated on the front bumper with slight effects on the windshield near the wipers. With the introduction of a rear wing with a trailing edge equal to zero degrees, as shown in Figure 12, we notice that a clear concentration of pressure appears in the front part of the spoiler, which affects the increase in downforce. This unexpected observation challenges the traditional assumptions of this type of airfoil, where no lift or pressure force is generated when the angle is zero. Figure 13 reveals the reason for this, as it reveals that the dynamic air flow interacts with the front part of the spoiler at an angle instead of colliding with the spoiler horizontally, which leads to an increase in downforce.

Figure 11. Pressure contour for car model.

Figure 12. Pressure contour for car model and spoiler at 0 AOTE.

Figure 13. Streamline for car model and spoiler at 0 AOTE.

And in Figure 15, a higher trailing edge angle results in a noticeable concentration of pressure on the trailing edge of the wing, resulting in a significant increase in downforce and a consequent enhancement of the vehicle’s aerodynamic stability. Figure 14. Here, the downward motion of the trailing edge angle redirects airflow down the trailing edge of the wing, generating lift forces. This aerodynamic phenomenon introduces a counterforce that reduces the overall downforce.

Figure 14. Pressure contour for car model and spoiler at negative AOTE.

Figure 15. Pressure contour for car model and spoiler at positive AOTE.

In summary, the figures underscore the essential function of spoilers in aerodynamic control. Through visual examination, it becomes evident how alterations in spoiler angles can profoundly influence airflow patterns, leading to enhanced performance and manoeuvrability. This emphasizes the significance of carefully adjusting spoiler configurations to optimize vehicle dynamics and efficiency.

Lift force chart and table

The relationship between speed, angle of trailing edge (AOTE), and the resulting lift force is illustrated in Figure 16 and Table 4. The data points represent measurements taken at specific speeds with corresponding AOTE values, demonstrating how these factors influence the lift force generated. The results highlight the significant impact of AOTE adjustments on vehicle aerodynamics, particularly at higher speeds.

Figure 16. Down force with different AOTE.

The presented Figure 17 delineates the influence of controlled downforce manipulation on vehicle dynamics, specifically focusing on lift and downforce. In the baseline scenario, the vehicle exhibits a progressive increase in downforce with rising velocity, reflecting its inherent design characteristics.

Figure 17. Down force at (-30, 0, 30) AOTE.

Upon the introduction of a spoiler mechanism and subsequent adjustments to its configuration, a discernible alteration in lift and downforce profiles is observed. This controlled manipulation of aerodynamic forces enables a targeted optimization strategy aimed at augmenting both stability and efficiency metrics.

Lowering the spoiler configuration results in a reduction of downforce, thereby mitigating lift and enhancing overall aerodynamic efficiency. This reduction translates into diminished aerodynamic drag, consequently improving the vehicle’s efficiency profile. Conversely, elevating the spoiler configuration yields an amplification of downforce, concurrently bolstering vehicle stability, particularly during high-speed manoeuvres where lateral stability is critical.

Notably, the depiction of lift and downforce values as negative underscores their respective orientations. This negative representation signifies their downward and upward forces, respectively. Thus, even amid downforce reduction, stability remains preserved, mitigating potential risks associated with compromised stability, such as lateral instability or loss of traction.

In summary, the chart elucidates the efficacy of controlled downforce manipulation in optimizing vehicle dynamics. Through strategic adjustments to spoiler configuration, this study presents a scientifically grounded approach to concurrently enhancing stability and efficiency without compromising safety or performance criteria in vehicular engineering.

Figure 18. Boundary layer.

Figure 19. Boundary layer.

Drag Force

The simulation results yielded a drag force coefficient of 0.256 for the car, which represents a 6% deviation from Tesla’s officially reported coefficient of 0.24.⁹ This discrepancy can be attributed to two primary factors:

Figure 20. Tesla S model 2015 front bumper design.

Figure 21. Pressure contour.

To address this discrepancy, future simulations should focus on improving mesh resolution and incorporating detailed design elements, such as the front bumper perforations. These adjustments would enable the simulation results to more accurately reflect the aerodynamic performance reported by Tesla. The drag coefficients for various spoiler configurations are presented in Table 5.

The simulations were conducted in compliance with Tesla’s testing guidelines, which specify a test speed of 70 mph for determiningaerodynamic coefficients. This ensures that the simulation conditions are consistent with real-world testing protocols, providing a reliable basis for comparison.

Spoiler with and without holder effect

The placement of a rear spoiler on a vehicle, whether with or without stands (feet),^10,11 can affect its aerodynamic performance. This study investigates this phenomenon by analysing lift force data obtained from spoilers with and without stands. Comparing the results highlights notable differences in aerodynamic behaviour based on stand placement. This underscores the importance of stand configuration in rear spoiler design and its implications for optimizing vehicle aerodynamics.

The graph in Figure 22 indicates a clear difference between the results obtained for the spoiler with or without a holder (stand, feet, etc.). This variance underscores the significant influence of the holder’s design, shape, and positioning on aerodynamics. It emphasizes the importance of carefully considering these factors in holder design to optimize aerodynamic performance and ensure effective integration with the vehicle’s overall aerodynamic profile.

Figure 22. The difference between spoiler with and without holder.

Note

Some of the simulated data has been attached to a public database that you can view.¹²

Ethics and consent

Ethical approval and consent were not required for this study, as it did not involve human participants, animal subjects, or sensitive data. The research focused solely on computational simulations and analysis of aerodynamic performance using publicly available data and software tools.