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

Airfoil group

Understanding the aerodynamic characteristics of various airfoil shapes is essential for the design and performance optimization of aircraft wings and vehicle spoilers. Airfoils, the cross-sectional profiles of wings or spoilers, are designed to generate lift efficiently while minimizing drag. Table 1 provides a detailed comparison of different airfoil groups, highlighting their geometric parameters and aerodynamic coefficients.

Table 1. Airfoil group classification with geometric and aerodynamic data.

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

Based on these comparisons, the NACA0012 airfoil was chosen due to its well-documented symmetrical geometry and widespread acceptance in spoiler design applications. Its symmetrical profile ensures the lift force approaches zero at neutral angles of attack and exhibits minimal sensitivity to changes in airflow velocity, which is advantageous for spoilers that require precise lift control during both upward and downward deflections.

The geometric symmetry of the NACA0012 enables accurate and predictable modulation of lift force as the spoiler’s trailing edge angle changes. This stability and repeatability in aerodynamic response are critical for optimizing spoiler performance, especially during dynamic vehicle maneuvers demanding precise lift adjustments.

CATIA model

The spoiler shapes were modeled using CATIA software to visualize the effects of varying trailing edge angles on the spoiler profile:

Figure 2. Spoiler model with trailing edge at 0° (neutral position).

Figure 3. Spoiler model with trailing edge deflected negatively (downward angle).

Figure 4. Spoiler model with trailing edge deflected positively (upward angle).

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 behavior, 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 simplified Tesla-inspired car model was designed using CATIA software, as shown in Figure 6.

Figure 6. Car model designed in CATIA.

Car model with spoiler

The spoiler design utilizes the NACA0012 airfoil profile, with dimensions of 120 cm length by 45 cm width. The spoiler features multiple trailing edge angles (AOTE) to investigate aerodynamic variations.

Figure 7. Car model equipped with adjustable trailing edge.

Simulation Workflow

The ANSYS simulation process follows a structured sequence to ensure accurate results. Key steps include pre-processing, mesh generation, boundary condition setup, and turbulence model selection. The overall workflow within ANSYS Workbench is summarized in Figure 8.

Figure 8. Simulation process workflow in ANSYS Workbench.

Pre-processing :

During pre-processing, the CATIA 3D car model is imported into ANSYS Geometry. A computational domain (“enclosure”) simulating the wind tunnel is created around the car. The enclosure dimensions are summarized in Table 2, and its 3D visualization is shown in Figure 9.

Figure 9. Computational domain enclosing the car model.

Meshing:

The computational domain was discretized using a polyhedral mesh generated with ANSYS meshing tools. Local mesh refinement was applied around the entire vehicle surface, including the spoiler, to accurately capture flow gradients and aerodynamic phenomena across all critical regions.

The mesh employed a curvature-based size function with high smoothing and a medium relevance center to balance accuracy and computational efficiency. Key mesh parameters include:

This mesh resolution ensures detailed representation of complex flow behavior around the vehicle. The meshed model is illustrated in Figure 10.

Figure 10. Meshed computational domain around the car model.

Boundary conditions:

Realistic airflow conditions were defined via boundary conditions as listed in Table 3. The inlet boundary is a velocity inlet with specified speeds of 120, 180, 250, 300, and 350 km/h, and a turbulence intensity of 5%.

The outlet is set as a pressure outlet at atmospheric conditions. The car and spoiler surfaces apply no-slip wall conditions, while symmetry boundary conditions reduce computational requirements by simulating half the domain.

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

Streamline and Pressure Contour Analysis:

Following preprocessing and mesh generation, CFD simulations were executed using ANSYS Fluent to analyze the aerodynamic effects of varying Angles of the Trailing Edge (AOTE) on the vehicle’s performance. This section presents the results in the form of streamline plots and pressure contours, which offer critical insights into airflow behavior and the resulting aerodynamic forces.

Figure 11 shows the baseline pressure distribution around the car model without a spoiler. The majority of pressure is concentrated on the front bumper, with minor accumulation near the windshield region. This distribution reflects typical drag behavior experienced by streamlined bluff bodies at high speeds.

The addition of a spoiler with 0° AOTE ( Figure 12) leads to a significant pressure buildup on the spoiler’s leading edge, contributing to increased downforce. Although a symmetrical airfoil like NACA0012 is expected to generate zero lift at 0° angle, the streamline analysis in ( Figure 15) reveals that airflow interacts with the spoiler at a slight angle due to vehicle-induced flow curvature. This results in an effective increase in downforce, contrary to theoretical expectations for neutral configurations.

At negative AOTE settings ( Figure 14), the trailing edge deflects downward, causing the airflow to be redirected upward. This produces a counter-lifting effect that slightly reduces overall downforce. In contrast, at positive AOTE ( Figure 13), airflow is deflected more aggressively downward at the trailing edge, leading to high pressure concentration and a substantial increase in downforce. This configuration enhances rear-end grip and aerodynamic stability, particularly at higher velocities.

These variations in flow behavior demonstrate the dynamic aerodynamic response enabled by adjusting the spoiler’s trailing edge. By modifying the AOTE, the vehicle can fine-tune lift and downforce characteristics in real time, which is particularly beneficial for improving handling and performance under changing driving conditions.

Figure 11. Pressure contour of the base car model without a spoiler.

Figure 12. Pressure contour for the car with a spoiler at 0° AOTE.

Figure 13. Pressure contour for spoiler at positive AOTE.

Figure 14. Pressure contour for spoiler at negative AOTE.

Figure 15. Streamlines for car with spoiler at 0° AOTE.

In summary, the streamline and pressure contour analysis emphasize the aerodynamic effectiveness of a movable trailing edge spoiler. Adjustments in the spoiler’s geometry can significantly influence airflow patterns and pressure distribution, resulting in measurable improvements in downforce and vehicle stability.

Lift force variation with AOTE

The relationship between AOTE and lift force across multiple vehicle speeds is shown in Figure 16 and Table 4. Results indicate that increasing AOTE (up to 30°) consistently enhances negative lift (downforce), particularly at high speeds. For instance, at 350 km/h, downforce increases from –5015 N (no spoiler) to –8043 N at 30° AOTE.

Figure 16. Variation of lift force with different AOTE across speed range.

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 maneuvers 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. Real-world Tesla Model S (2015) front bumper with drag-reducing features.

Figure 19. Pressure contour showing airflow interaction with the simplified bumper design.

Drag Force

The simulated drag coefficient was 0.256, representing a 6% deviation from Tesla’s reported value of 0.24⁹.This discrepancy can be attributed to two primary factors:

Figure 20. The difference between spoiler with and without a holder.

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 determining aerodynamic 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 (i.e., feet or holders),^10,11 can affect its aerodynamic performance. This study investigates this phenomenon by analyzing lift force data obtained from spoilers with and without stands. Comparing the results highlights notable differences in aerodynamic behavior 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 20 indicates a clear difference between the results obtained for the spoiler with or without a holder (stand, feet, etc.). This variation highlights the aerodynamic influence of the holder’s design, shape, and placement. 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.

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.