# Influence of Side Spoilers on the Aerodynamic Properties of a Sports Car

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}, and the area of the spoiler on the bumper was equal to 0.109 m

^{2}. Although the final version of the spoiler on the bumper turned out to have an area larger by 13% than the quarter glass spoiler, both of these elements were tailored to be of similar size to make it easier to directly compare their efficiency. The main dimensions of the side spoilers are presented in Appendix A.

^{®}Fluent, version ANSYS

^{®}Academic Associate CFD, Release 16.2. Due to the fact that the calculations were performed at a velocity much smaller than Mach 1, the flow was modeled as incompressible, and the pressure-based solver was used [35]. Second-order upwind spatial discretization schemes were used to solve the moment, turbulent kinetic energy, and specific dissipation rate equations. Pressure equations were solved using a second-order scheme, whereas the gradients were calculated with the least square cell-based method. High order term relaxation was turned on to aid the second-order calculations. In each case, calculations were initialized with the values from the velocity inlet that were different depending on the yaw angle that was being investigated. The calculations were stopped when the residuals converged by at least three orders of magnitude, and at the same time, the values of lift, drag, and side forces reached a constant level.

_{ref}= 0 Pa), air density (ρ = 1.225 kg/m

^{3}), and reference velocity (V

_{ref}= 40 m/s).

^{2}), the length between the front and the rear axles (l = 2.364 m). In each case, the coefficients of forces and moments were calculated using the same reference area, which refers to the frontal area of the car body without the side spoilers.

^{7}elements is adequate for use in these studies as the values of the aerodynamic coefficients stay close to the ones obtained with this mesh even when the number of mesh cells is further increased. When the mesh size was increased to 4.395 × 10

^{7}elements, the values of all of the aerodynamic coefficients did not change more than 1.2%.

## 3. Results and Discussion

#### 3.1. The Side Spoiler on a Quarter Glass

#### 3.2. The Side Spoiler on a Front Bumper

#### 3.3. Cases Chosen for Different Yaw Conditions

#### 3.4. Results at Different Yaw Angles

_{te}), frontal area (A), and length (L) are considered. Taking into account all of those dimensions makes it possible to predict the side force more accurately; however, as identified in [24], vehicle height has the most dominant influence on the side force. The side force derivative in Equation (4) represents the change of side force coefficient with the yaw angle. It was concluded in [24] that the yaw moment could not be predicted with a similar formula due to its high sensitivity to the distribution of the side force load. The case without the rear spoiler was chosen for comparison with the results from the analytical calculations and the ones obtained with the use of CFD, and, in Figure 14b, one can see that the formula matches the CFD results very closely throughout the studied yaw angle range.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

NASCAR | National Association for Stock Car Auto Racing |

RANS | Reynolds-Averaged Navier Stokes |

SST | Shear Stress Transport |

## Appendix A. The Main Dimensions of the Spoilers and the Car Body

## Appendix B. Tables with the Values Used in Each Graph

**Table A1.**Breakdown of the aerodynamic loads generated on the car body and the side spoiler mounted on the quarter glass and inclined at different angles, presented on graphs in Figure 4.

Angle [°] | Cx | Cy | Cz | Cmx | Cmy | Cmz | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Spoiler | Total | Spoiler | Total | Spoiler | Total | Spoiler | Total | Spoiler | Total | Spoiler | Total | |

0.0 | – | 0.333 | – | 0.002 | – | 0.002 | 0.000 | 0.000 | 0.000 | –0.214 | 0.000 | 0.001 |

27.5 | 0.011 | 0.370 | 0.014 | 0.058 | –0.025 | –0.088 | 0.005 | 0.009 | –0.001 | –0.239 | 0.002 | 0.007 |

55.0 | 0.038 | 0.410 | 0.004 | 0.007 | –0.063 | –0.160 | 0.019 | 0.025 | –0.002 | –0.241 | 0.011 | 0.025 |

82.5 | 0.051 | 0.440 | –0.032 | –0.063 | –0.066 | –0.218 | 0.027 | 0.037 | 0.000 | –0.232 | 0.021 | 0.024 |

110.0 | 0.048 | 0.448 | –0.066 | –0.121 | –0.042 | –0.198 | 0.027 | 0.036 | 0.004 | –0.186 | 0.025 | 0.034 |

137.5 | 0.037 | 0.433 | –0.097 | –0.072 | –0.007 | –0.200 | 0.024 | 0.033 | 0.007 | –0.224 | 0.028 | 0.027 |

**Table A2.**Breakdown of the aerodynamic loads generated on the car body and the side spoiler mounted on the front bumper and inclined at different angles, presented on graphs in Figure 9.

Angle [°] | Cx | Cy | Cz | Cmx | Cmy | Cmz | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Spoiler | Total | Spoiler | Total | Spoiler | Total | Spoiler | Total | Spoiler | Total | Spoiler | Total | |

0 | – | 0.333 | – | 0.002 | – | 0.002 | 0.000 | 0.000 | 0.000 | –0.214 | 0.000 | 0.001 |

25.0 | –0.007 | 0.346 | –0.046 | –0.061 | –0.008 | –0.084 | 0.000 | 0.000 | –0.006 | –0.247 | 0.032 | 0.020 |

50.0 | 0.012 | 0.368 | –0.081 | –0.030 | –0.025 | –0.065 | 0.004 | 0.016 | –0.020 | –0.230 | 0.067 | 0.053 |

75.0 | 0.045 | 0.403 | –0.084 | –0.135 | –0.044 | –0.179 | 0.011 | 0.021 | –0.037 | –0.284 | 0.081 | 0.074 |

100.0 | 0.065 | 0.404 | –0.039 | –0.109 | –0.046 | –0.166 | 0.016 | 0.023 | –0.039 | –0.282 | 0.055 | 0.077 |

125.0 | 0.075 | 0.415 | –0.003 | –0.103 | –0.050 | –0.193 | 0.020 | 0.029 | –0.042 | –0.281 | 0.033 | 0.059 |

**Table A3.**Aerodynamic loads generated on the car body with different aerodynamic configurations, presented on graphs in Figure 14.

Combined case | Base case | ||||||||||||

Yaw [°] | Cx | Cy | Cz | Cmx | Cmy | Cmz | Yaw [°] | Cx | Cy | Cz | Cmx | Cmy | Cmz |

0 | 0.492 | –0.285 | –0.301 | 0.040 | –0.230 | 0.074 | 0 | 0.333 | 0.002 | 0.002 | 0.000 | –0.214 | 0.001 |

5 | 0.480 | 0.064 | –0.096 | 0.033 | –0.195 | 0.052 | 5 | 0.377 | 0.218 | –0.072 | 0.003 | –0.202 | –0.019 |

10 | 0.454 | 0.246 | –0.037 | 0.044 | –0.178 | –0.011 | 10 | 0.379 | 0.371 | –0.012 | 0.024 | –0.189 | –0.059 |

15 | 0.414 | 0.430 | 0.063 | 0.051 | –0.172 | –0.066 | 15 | 0.383 | 0.527 | 0.071 | 0.041 | –0.168 | –0.100 |

Clean case (CFD) | Clean case (analytical) | ||||||||||||

Yaw [°] | Cx | Cy | Cz | Cmx | Cmy | Cmz | Yaw [°] | Cx | Cy | Cz | Cmx | Cmy | Cmz |

0 | 0.339 | –0.001 | 0.147 | 0.000 | –0.273 | 0.000 | 0 | – | 0.000 | – | – | – | – |

5 | 0.356 | 0.150 | 0.096 | 0.008 | –0.277 | –0.040 | 5 | – | 0.161 | – | – | – | – |

10 | 0.394 | 0.331 | 0.147 | 0.035 | –0.264 | –0.064 | 10 | – | 0.323 | – | – | – | – |

15 | 0.366 | 0.467 | 0.218 | 0.042 | –0.261 | –0.113 | 15 | – | 0.484 | – | – | – | – |

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**Figure 1.**(

**a**) A side view of the Honda CR-X del Sol, blue color marks area of the side spoilers, and the red lines are the according rotational axes. Directions of the studied forces and moments are included, with the axis placed in the car’s center of gravity. (

**b**) Isometric view and (

**c**) front view of the car with side spoilers at a different angle of rotational (each marked in a different color to make it more clear). Forces and moments coefficients: Cx (Drag), Cy (Side), Cz (Lift), Cmx (Roll), Cmy (Pitch), Cmz (Yaw).

**Figure 2.**(

**a**) The computational domain, (

**b**) mesh on the symmetry plane, (

**c**) close-up on the mesh in the boundary layer region. Type of boundary conditions: ■ velocity inlet, ■ pressure outlet, ■ wall, ■ symmetry.

**Figure 4.**(

**a**) Force coefficients on the spoiler, (

**b**) total force coefficients, (

**c**) moment coefficients on the spoiler, (

**d**) total moment coefficients.

**Figure 5.**Contours of (

**a**) velocity (m/s), and (

**b**) pressure coefficient on a cross-section through the A pillar. (

**c**) Streamlines colored by velocity (m/s) coming from the side spoiler mounted on the quarter glass at different inclination angles.

**Figure 6.**(

**a**) Contours of pressure coefficient on the car body for the base case. Contours of pressure coefficient difference due to the introduction of the side spoiler inclined at (

**b**) 27.5°, (

**c**) 55.0°, (

**d**) 82.5°, (

**e**) 110.0°, and (

**f**) 137.5°.

**Figure 7.**Contours of pressure coefficient on the car body and iso-surfaces of total pressure equal zero for the spoiler at the quarter glass at 110.0°.

**Figure 9.**(

**a**) Force coefficients on the spoiler, (

**b**) total force coefficients, (

**c**) moment coefficients on the spoiler, (

**d**) total moment coefficients.

**Figure 10.**Contours of (

**a**) velocity (m/s) and (

**b**) pressure coefficient on a cross-section through the bumper. (

**c**) Streamlines colored by velocity (m/s) coming from the side spoiler mounted on the bumper at different inclination angles.

**Figure 11.**(

**a**) Contours of pressure coefficient on the car body for the base case. Contours of pressure coefficient difference due to the introduction of the side spoiler inclined at (

**b**) 25°, (

**c**) 50°, (

**d**) 75°, (

**e**) 100°, and (

**f**) 125°.

**Figure 12.**The car body geometries chosen for studies at non-zero yaw angles. (

**a**) Combined case, (

**b**) base case, (

**c**) clear case.

**Figure 13.**Contours of pressure coefficient on the car body together with the grey colored 3D streamlines started from the front of the car body, for the (

**a**) front bumper case, (

**b**) quarter glass case, and (

**c**) combined case.

**Figure 14.**Characteristics for force and moment coefficients for a range of yaw angles. The characteristics are: (

**a**) drag force coefficient, (

**b**) side force coefficient, (

**c**) lift force coefficient, (

**d**) rolling moment coefficient, (

**e**) pitching moment coefficient, and (

**f**) yawing moment coefficient.

**Figure 15.**Contours of pressure coefficient on the car body and iso-surfaces of total pressure equal zero for consecutive yaw angles for the (

**a**) combined case, (

**b**) base case, and (

**c**) clear case.

Number of Cells | Drag Coefficient | Side Coefficient | Lift Coefficient |
---|---|---|---|

2.187 × 10^{7} | 0.364 | 0.509 | 0.056 |

3.269 × 10^{7} | 0.383 | 0.527 | 0.071 |

4.395 × 10^{7} | 0.384 | 0.533 | 0.071 |

**Table 2.**Breakdown of the aerodynamic loads generated on the car body and the side spoiler mounted on the front bumper and the quarter glass—at a zero yaw angle.

Case. | Drag Coefficient | Side Coefficient | Lift Coefficient | Lift Distribution | Moment Coefficients | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Spoiler | Total | Spoiler | Total | Spoiler | Total | Front | Rear | Cmx | Cmy | Cmz | |

Clean | – | 0.339 | – | –0.001 | – | 0.147 | –0.125 | 0.272 | 0.000 | –0.273 | 0.000 |

Base | – | 0.333 | – | 0.002 | – | 0.002 | –0.141 | 0.143 | 0.000 | –0.214 | 0.001 |

Fr. bumper | 0.012 | 0.368 | –0.081 | –0.028 | –0.025 | –0.074 | –0.185 | 0.111 | 0.016 | –0.226 | 0.053 |

Qtr. glass | 0.048 | 0.451 | –0.066 | –0.120 | –0.042 | –0.196 | –0.188 | –0.008 | 0.035 | –0.185 | 0.033 |

Combined | 0.061 | 0.492 | –0.152 | –0.285 | –0.069 | –0.301 | –0.278 | –0.023 | 0.040 | –0.230 | 0.074 |

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## Share and Cite

**MDPI and ACS Style**

Kurec, K.; Piechna, J.
Influence of Side Spoilers on the Aerodynamic Properties of a Sports Car. *Energies* **2019**, *12*, 4697.
https://doi.org/10.3390/en12244697

**AMA Style**

Kurec K, Piechna J.
Influence of Side Spoilers on the Aerodynamic Properties of a Sports Car. *Energies*. 2019; 12(24):4697.
https://doi.org/10.3390/en12244697

**Chicago/Turabian Style**

Kurec, Krzysztof, and Janusz Piechna.
2019. "Influence of Side Spoilers on the Aerodynamic Properties of a Sports Car" *Energies* 12, no. 24: 4697.
https://doi.org/10.3390/en12244697