# Aerodynamic Study of the Wake Effects on a Formula 1 Car

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geometry

#### 2.2. Solver

#### 2.3. Domain and Mesh

#### 2.4. Boundary Conditions

- Inlet velocity set at 50 m/s, as it corresponds to a value which can be easily replicated in a wind tunnel (for experimental validation purposes).
- Pressure outlet set at Atmospheric pressure.
- Symmetry plane.
- Ground velocity set at 50 m/s.
- Slip condition on the side wall and the top of the fluid domain.
- Angular velocity and rotational axis of the wheels (MRF).

#### 2.5. Simulation Performance

## 3. Results and Discussion

#### 3.1. Free Stream Condition

#### 3.2. Under Wake flows

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

FVM | Finite Volume Method |

GAMG | Geometric Algebraic Multi Grid |

GCI | Grid Convergence Index |

FIA | Federation Internationale de l’Automobile |

CAD | Computer Aided Design |

RAM | Random Access Memory |

L | Vehicle length [m] |

$\varphi $ | Reference parameter [${\mathrm{m}}^{2}$] |

l | Turbulent length scale [m] |

I | Turbulent intensity [%] |

Re | Reynolds Number |

Cp | Pressure coefficient |

$\rho $ | Fluid density [kg/${\mathrm{m}}^{3}$] |

${U}_{\infty}$ | Fluid velocity [m/s] |

g | Gravitational acceleration [m/${\mathrm{s}}^{2}$] |

$\mu $ | Dynamic viscosity [kg/m·s] |

S | Reference Surface [${\mathrm{m}}^{2}$] |

${C}_{L}$ | Lift coefficient |

${C}_{D}$ | Drag coefficient |

E | Aerodynamic Efficiency |

FB | Front Balance |

## References

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**Figure 1.**Ferrari SF70H, a 2017 spec. car. Extracted from Reddit [9].

**Figure 10.**Several axial vorticity contours: (

**A**) YZ plane at 0.65 m in the X direction, (

**B**) YZ plane at 3.65 m in the X direction, (

**C**) YZ plane at 2.60 m in the X direction, and (

**D**) XY plane at 0 m in the Z direction.

**Figure 12.**Comparison between values of S${C}_{L}$ under wake flows and under free stream conditions.

**Figure 13.**Comparison between values of S${C}_{D}$ under wake flows and under free stream conditions.

**Figure 14.**Comparison between values of efficiency under wake flows and under free stream conditions.

**Figure 15.**Comparison between values of front balance under wake flows and under free stream conditions.

**Figure 17.**Pressure coefficient distribution on the front wing of the second car at a distance of 0.25 L, 0.5 L, 1 L, and 2 L as compared to the free stream case.

**Figure 18.**Streamlines of the velocity. Front wing of the second car at a distance of 0.25 L, 0.5 L, 1 L, and 2 L as compared to the free stream case.

**Figure 19.**Pressure coefficient distribution on the rear wing of the second car at a distance of 0.25 L, 0.5 L, 1 L, and 2 L as compared to the free stream case.

**Figure 20.**Streamlines of the velocity. Rear wing of the second car at a distance of 0.25 L, 0.5 L, 1 L, and 2 L as compared to the free stream case.

**Figure 21.**Pressure coefficient distribution on the diffuser of the second car at a distance of 0.25 L, 0.5 L, 1 L, and 2 L as compared to the free stream case.

**Figure 22.**Streamlines of the velocity. Diffuser of the second car at a distance of 0.25 L, 0.5 L, 1 L, and 2 L as compared to the free stream case.

**Figure 24.**Velocity contours on a top plane at a distance of (

**A**) 0.25 L, (

**B**) 0.5 L, (

**C**) 1 L, and (

**D**) 2 L.

**Figure 25.**Streamlines of the velocity at a distance of (

**A**) 0.25 L, (

**B**) 0.5 L, (

**C**) 1 L, and (

**D**) 2 L.

Mesh Parameters | $\mathit{\varphi}$ = S·${\mathit{C}}_{\mathit{L}}$ |
---|---|

Number of elements N1, N2, N3 | 18055055, 13793013, 10634551 |

Refinement ratio ${r}_{21}$ | 1.309 |

Refinement ratio ${r}_{32}$ | 1.297 |

Finest result ${\varphi}_{1}$ | −3.43 |

Intermediate result ${\varphi}_{2}$ | −3.40 |

Coarsest result ${\varphi}_{3}$ | −3.28 |

Order of convergence p | 4.37 |

Error $GC{I}_{fine}$ | 1.1% |

Error $GC{I}_{coarse}$ | 3.7% |

Variable | Value |
---|---|

Free stream velocity ${U}_{\infty}$ | 50 m/s |

Fluid density ($\rho $) | 1.225 kg/${\mathrm{m}}^{3}$ |

Turbulent Intensity (I) [22] | 0.15% |

Turbulent length scale (l) | 3.475 m |

Reynolds Number (Re) | $12\times {10}^{6}$ |

S${\mathit{C}}_{\mathit{L}}$ (${\mathbf{m}}^{\mathbf{2}}$) | S${\mathit{C}}_{\mathit{D}}$ (${\mathbf{m}}^{\mathbf{2}}$) | |${\mathit{C}}_{\mathit{L}}$/${\mathit{C}}_{\mathit{D}}$| | FB (%) | |
---|---|---|---|---|

Reference Data | −3.59 | 1.23 | 2.92 | 44.80 |

Simulation Results | −3.43 | 1.15 | 2.98 | 41.23 |

Error (%) | 4.45 | 6.50 | 2.15 | 7.97 |

Elements | Downforce Contribution (%) | Drag Contribution (%) |
---|---|---|

Bargeboards and vanes | −1.71 | +2.97 |

Bodywork | +21.10 | +10.7 |

Front suspension | +2.36 | +2.88 |

Front Tires | +2.94 | +10.30 |

Front Wing | −22.84 | +12.69 |

Rear suspension | −0.40 | +3.93 |

Rear tires | +1.42 | +20.06 |

Rear wing | −35.46 | +20.38 |

Underbody | −61.09 | +15.05 |

Others | −6.65 | +1 |

**Table 5.**Percentage of change of the aerodynamic coefficients of the second car as regards the first car.

Distance | S${\mathit{C}}_{\mathit{L}}$ (${\mathbf{m}}^{\mathbf{2}}$) | S${\mathit{C}}_{\mathit{D}}$ (${\mathbf{m}}^{\mathbf{2}}$) | |${\mathit{C}}_{\mathit{L}}$/${\mathit{C}}_{\mathit{D}}$| | FB |
---|---|---|---|---|

0.25 L | −62% | −40% | −37% | +28.5% |

0.5 L | −54.1% | −30.7% | −34% | +35.8% |

1 L | −42.3% | −21% | −27% | +40.7% |

2 L | −23.5% | −14.2% | −11% | +26.1% |

Distance | Power Required (kW) | Energy Required (kJ) |
---|---|---|

0.25 L | 33.44 | 668.8 |

0.5 L | 40.39 | 807.84 |

1 L | 50.77 | 1015.52 |

2 L | 67.32 | 1346.4 |

Free stream | 88 | 1760 |

**Table 7.**Percentage of change of the aerodynamic coefficients in the front wing of the second car as regards the first car.

Distance Front Wing | S${\mathit{C}}_{\mathit{L}}$ (${\mathbf{m}}^{\mathbf{2}}$) | S${\mathit{C}}_{\mathit{D}}$ (${\mathbf{m}}^{\mathbf{2}}$) |
---|---|---|

0.25 L | −38% | −36.1% |

0.5 L | −29% | −19.3% |

1 L | −10.7% | −1.1% |

2 L | −3.6% | +3% |

**Table 8.**Percentage of change of the aerodynamic coefficients in the rear wing of the second car as regards the first car.

Distance Rear Wing | S${\mathit{C}}_{\mathit{L}}$ (${\mathbf{m}}^{\mathbf{2}}$) | S${\mathit{C}}_{\mathit{D}}$ (${\mathbf{m}}^{\mathbf{2}}$) |
---|---|---|

0.25 L | −57.9% | −53.3% |

0.5 L | −54.8% | −50.6% |

1 L | −52% | −48% |

2 L | −40.3% | −36.2% |

**Table 9.**Percentage of change of the aerodynamic coefficients in the diffuser of the second car as regards the first car.

Distance Diffuser | S${\mathit{C}}_{\mathit{L}}$ (${\mathbf{m}}^{\mathbf{2}}$) | S${\mathit{C}}_{\mathit{D}}$ (${\mathbf{m}}^{\mathbf{2}}$) |
---|---|---|

0.25 L | −70.2% | −57.2% |

0.5 L | −62.8% | −48.7% |

1 L | −46.1% | −29% |

2 L | −25.3% | −16.9% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Guerrero, A.; Castilla, R.
Aerodynamic Study of the Wake Effects on a Formula 1 Car. *Energies* **2020**, *13*, 5183.
https://doi.org/10.3390/en13195183

**AMA Style**

Guerrero A, Castilla R.
Aerodynamic Study of the Wake Effects on a Formula 1 Car. *Energies*. 2020; 13(19):5183.
https://doi.org/10.3390/en13195183

**Chicago/Turabian Style**

Guerrero, Alex, and Robert Castilla.
2020. "Aerodynamic Study of the Wake Effects on a Formula 1 Car" *Energies* 13, no. 19: 5183.
https://doi.org/10.3390/en13195183