# Feasibility Study of a Fan-Driven Device Generating Downforce for Road Cars

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, which was 3/4 of the total surface viewed from above) and later exhausted behind the vehicle. A 45 horsepower auxiliary engine mounted behind the rear wheels powered two rear fans pumping 9650 cubic feet of air per minute (4.55 m

^{3}/s) at 6000 RPM. With the Chevrolet engine off, rumor has it, they could even push the car forward at 25 to 40 miles per hour (40–65 km/h). In theory, the Chaparral 2J could generate up to 11,000 N of downforce. Considering the area of 4.5 m

^{2}, this allows us to estimate the pressure under the car to be −2400 Pa. When the fans were turned on, the vehicle settled 5 cm on the suspension. With full fuel, the 2J could take corners at speeds that generate lateral accelerations of 1.25 to 1.5 g. The car had an incredible grip from zero traffic speed, allowing it to take corners at tremendous speed, and providing excellent acceleration and braking abilities. During qualifying, passing times were up to two seconds shorter than the competition. However, the car never won a race, often due to fan drive failures. Reliability proved to be an issue.

## 2. Materials and Methods

#### 2.1. The Basic Theory of Periferial Jet

_{1}and P

_{2}. These areas are separated by an air curtain of height H and are supplied from the source of air at pressure P

_{0}through a nozzle of width b, where the nozzle is inclined at an angle α to the ground. Internal velocity v

_{1}and external velocity v

_{2}are present due to the different outlet pressures.

_{p}and pressures p

_{1}and p

_{2}, one can calculate required pressure p

_{0}

_{p}was calculated using inviscid and incompressible fluid flow, mixing theory, and compressible fluid flow (Mach number equal 0.51, 0.75 and 0.94).

_{2}− p

_{1}that can be sustained at a given pressure p

_{0}, with a known ratio of curtain height to width H/b and the angle α of the initial curtain nozzle axis position. For a constant nozzle angle α, the pressure coefficient’s C

_{p}value decreases with an increasing height to width ratio H/b.

#### 2.2. CFD Methodology

_{i}represents the i-th component of velocity at a point x

_{i}in space, ρ is the fluid density, f

_{i}is the body force (e.g., gravity), p represents the static pressure, μ is the dynamic viscosity, δ

_{ij}is the Kronecker delta, bars denote mean values, and apostrophes represent instantaneous values. Because of the Reynolds stress tensor $-\rho \overline{{{v}^{\prime}}_{i}{{v}^{\prime}}_{j}}$, the closure problem arises, and additional equations are needed. They are supplemented by turbulence models, which can be roughly categorized in two basic groups: models that solve transport equations for Reynolds stress tensor components, and models that follow the Boussinesq hypothesis and introduce turbulent viscosity. The turbulence model selected for this work belongs to the latter group. It is assumed, that the Reynolds stress tensor is proportional to the mean strain rate tensor:

_{t}is the turbulent viscosity. The shortcoming of turbulence models based on turbulent viscosity is that they fail to predict strongly rotating flows, strongly decelerated flows, or curvature effects. Nevertheless, they were validated in car aerodynamic analyses with satisfying results [27]. For this study, a realizable k-ε turbulence model [28] was used.

_{K}in the transport equation of turbulent kinetic energy k.

_{lim}was a constant equal to 10.

## 3. Results and Discussion

#### 3.1. CFD Analyses of a Two-Dimensional Stationary Air Curtain

#### 3.1.1. Curtain Height Considerations

_{p}curve shown in Figure 2, after a certain height the downforce curve starts to flatten, and the curtain can be moved further away with a relatively small loss. Above the height of 50 mm, the downforce decrease is approximately 2 N of downforce per 1 mm of height. Smaller sensitivity to changes in height also means that disturbances in the form of uneven ground surface would be less harmful.

_{p}value of about 0.3 can be expected.

#### 3.1.2. Curtain-Only Variant of FDDG

^{2}.

#### 3.1.3. Curtain with Depressurizing Fan

#### 3.2. CFD Analyses of a Three-Dimensional Moving Air Curtain

#### 3.2.1. Discussion of Various FDDG Variants

**,**in order to increase the height of the curtain while maintaining the same downforce, either the nozzle discharge width can be increased at the same nozzle supply pressure, or the discharge velocity can be increased at the same nozzle width. In both cases, this involves an increase in the flow rate through the nozzle and an increase in the energy consumed by the fan supplying the nozzle.

#### 3.2.2. Taking Advantage of the Stagnation Pressure

#### 3.3. CFD Analyses of the FDDG in a Sports Car

#### 3.3.1. Analysis of FDDG Performance

^{3}and velocity equal to inlet air velocity. A low-pressure region in the area surrounded by air curtains can be seen, which contributes to high downforce at low vehicle speeds. However, for the case without an FDDG, downforce is generated with increasing velocity due to the action of the underbody, diffuser, and spoiler. In the case with the FDDG, the diffuser is hidden in the wake of air curtain components and is not used effectively. Moreover, a massive stagnation region upstream of the FDDG can be observed. This is the main reason for decreased downforce at high speeds.

#### 3.3.2. Further Optimization Directions

#### 3.4. Dynamic Model of a Car with FDDG

#### 3.4.1. Acceleration

- a—acceleration in m/s
^{2} - μ—friction coefficient (0.8)
- g—gravitational acceleration in m/s
^{2} - F
_{z}—downforce in N - F
_{d}—drag force in N - m—car mass (1300 kg)
- v—car velocity in m/s
- P—power in W
- P
_{limit}—engine power (588,000 W)

#### 3.4.2. Cornering

#### 3.4.3. Braking

## 4. Conclusions

- The presented solution is the first approximation showing the potential construction possibilities and advantages of the FDDG with air curtains.
- In the tested application of a sports car, the device provided additional downforce, 2600 N at zero velocity: to 1000 N at 40 m/s, using 17 kW of power supplying idealized fans. Koenigsegg Agera R, according to the official data [32], generates 3000 N total downforce at 250 km/h (69.5 m/s).
- Most importantly, the area of effective use of artificially generated aerodynamic downforce can be very wide. In the last subsections of the article, scenarios of fan-enhanced acceleration and braking were studied. The acceleration time to achieve 100 km/h was reduced from 3.6 s to 3.0 s. In the case of braking from 216 km/h to a halt, the braking distance was reduced by 11 m.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Velocity values on pathlines passing through a fan with a constant pressure increment of 1000 Pa for different curtain heights (from the left: 10 mm, 20 mm, 30 mm, 40 mm, 50 mm) and nozzle width of 10 mm.

**Figure 5.**Variation of generated downforce with constant fan pressure in function of the curtain height.

**Figure 8.**Downforce generated by curtain fan and required power as a function of the curtain fan compression.

**Figure 10.**Velocity and pressure contours for the FDDG with air curtain and depressurizing fan, with curtain fan Δp = 3000 Pa and pressure at the outlet to depressurizing fan p = −1000 Pa.

**Figure 11.**The downforce generated by FDDG and the required power with air curtains and depressurizing fan running as a function of the depressurizing fan compression. The air curtain fan was operating at constant Δp = 3000 Pa.

**Figure 12.**Geometry of the shell object of FDDG used for 3D CFD simulation of the moving object: (

**a**) bottom view; (

**b**) angled view from bottom.

**Figure 13.**Velocity vectors at curtain nozzles, seen from the bottom, on a half part of the shell object traveling at speed of 40 m/s.

**Figure 14.**Comparison of the aerodynamic downforce achieved using only the air curtain fans and additionally supported by the depressurizing fan.

**Figure 15.**Conditions needed to change curtain height from 50 mm to 75 mm for the same aerodynamic downforce generated.

**Figure 16.**Comparison of operation parameters in the case with active curtain and curtain deactivated.

**Figure 18.**Variation of aerodynamic downforce values produced by a shell object moving at different speeds with the chamber front curtain fed by a supporting fan or circulation fan.

**Figure 19.**The geometry of the analyzed car: (

**a**) Without the FDDG, different views; (

**b**) With the FDDG marked in magenta, cross-section view.

**Figure 20.**Size of the computational domain with length L = 4.6 m height H = 1.1 m and width W = 1.1 m.

**Figure 22.**Grid convergence test in the undercarriage area: (

**a**) Cross-section view, refinement in the proximity of curtains can be seen; (

**b**) Ground view from the bottom; (

**c**) Zoom at the front nozzle, various mesh sizes; (

**d**) Velocity contours at the front nozzle for various mesh sizes.

**Figure 23.**Aerodynamic forces for the baseline case and the case with FDDG for various inlet speeds: (

**a**) Downforce; (

**b**) Drag force.

**Figure 25.**Pressure coefficient for inlet speed of 40 m/s, bottom, and symmetry views. (

**Top**): without FDDG; (

**bottom**): with the FDDG.

**Figure 26.**Pressure coefficient at the bottom surface for the case with fans turned on for various inlet speeds.

**Figure 27.**Pressure coefficient for the inlet speed of 20 m/s. On the (

**left**), circulation fans generating air curtains were deactivated; on the (

**right**)—they were active.

**Figure 28.**Velocity distribution and pathlines at front nozzles of FDDG for various inlet velocities.

**Figure 29.**Pathlines released from the fan surfaces for inlet velocity of 20 m/s. (

**a**) Angled view from bottom; (

**b**) Bottom view.

**Figure 30.**Velocity distribution at front nozzles of the fan-generating device for inlet speed of 40 m/s. (

**a**) Air curtain fan active; (

**b**) Support fan active.

**Figure 32.**Pressure coefficient for inlet speed of 10 m/s, the case with the FDDG on the left and without FDDG on the right: (

**a**) The upper side of the spoiler; (

**b**) The lower side of the spoiler.

**Figure 33.**Pathlines released from nozzles for various inlet velocities. The border between pathlines released from the front and side curtains was marked with a dashed line.

**Figure 34.**Comparison of car performance equipped with FDDG and without it in acceleration from a full stop: (

**a**) Acceleration; (

**b**) Velocity.

**Figure 36.**Comparison of car performance equipped with FDDG and without it in braking from a set speed of 216 km/h: (

**a**) Deceleration; (

**b**) Braking distance.

**Figure 37.**Differences of braking distance in function of speed of braking commencement, with and without FDDG.

Parameter | Coarse Mesh | Medium Mesh | Fine Mesh |
---|---|---|---|

Cell count | 7 mln | 8 mln | 9 mln |

Force in the forward direction in N | 87 (+3.1%) | 86 (+1.7%) | 84 |

Downforce in N | 2541 (−3.3%) | 2624 (−0.2%) | 2629 |

Volumetric flow rate through all fans in m^{3}/s | 5.81 (+1.9%) | 5.79 (+1.5%) | 5.70 |

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**MDPI and ACS Style**

Szudarek, M.; Piechna, A.; Piechna, J.
Feasibility Study of a Fan-Driven Device Generating Downforce for Road Cars. *Energies* **2022**, *15*, 5549.
https://doi.org/10.3390/en15155549

**AMA Style**

Szudarek M, Piechna A, Piechna J.
Feasibility Study of a Fan-Driven Device Generating Downforce for Road Cars. *Energies*. 2022; 15(15):5549.
https://doi.org/10.3390/en15155549

**Chicago/Turabian Style**

Szudarek, Maciej, Adam Piechna, and Janusz Piechna.
2022. "Feasibility Study of a Fan-Driven Device Generating Downforce for Road Cars" *Energies* 15, no. 15: 5549.
https://doi.org/10.3390/en15155549