fluids

Article Aerodynamic and Structural Design of a 2022 Front Assembly

Xabier Castro and Zeeshan A. Rana * Centre for Computational Engineering Sciences, School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43 0AL, UK; Xabier.Castro-Villanueva@cranfield.ac.uk * Correspondence: zeeshan.rana@cranfield.ac.uk

 Received: 30 October 2020; Accepted: 7 December 2020; Published: 9 December 2020 

Abstract: The aerodynamic loads generated in a wing are critical in its structural design. When multi-element with wingtip devices are selected, it is essential to identify and to quantify their structural behaviour to avoid undesirable deformations which degrade the aerodynamic performance. This research investigates these questions using numerical methods (Computational Fluid Dynamics and Finite Elements Analysis), employing exhaustive validation methods to ensure the accuracy of the results and to assess their uncertainty. Firstly, a thorough investigation of four baseline configurations is carried out, employing Reynolds Averaged Navier–Stokes equations and the k-ω SST (Shear Stress Transport) turbulence model to analyse and quantify the most important aerodynamic and structural parameters. Several structural configurations are analysed, including different materials (metal alloys and two designed fibre-reinforced composites). A 2022 front wing is designed based on a bidimensional three-element wing adapted to the 2022 FIA and its structural components are selected based on a sensitivity analysis of the previous results. The outcome is a high-rigidity-weight wing which satisfies the technical regulations and lies under the maximum deformation established before the analysis. Additionally, the superposition principle is proven to be an excellent method to carry out high-performance structural designs.

Keywords: ; structural design; Formula One; wing; structural deformation

1. Introduction Aerodynamics has been considered in the design of Formula One cars since the beginning of the competition in the early 1950s. However, its role was secondary and aerodynamic considerations were focused on reducing the amount of generated in the car. The apparition of wings in Formula One cars took place in 1968, when introduced front and rear wings in the to achieve aerodynamic [1–3], which highlighted the importance of the aerodynamic design of a racing car in its performance. The downforce can increase the tyre’s maximum lateral and tangential forces [1,4], resulting in an increment in the car’s cornering speed and an improvement in car’s acceleration and braking performance. Additionally, the most important influence of the reduction in drag is the increment in the car’s maximum speed. Every external component of a is exposed to a thorough aerodynamic design prior to its implementation. Nonetheless, most of these components have other goals, and therefore their aerodynamic design is only based on reducing the amount of generated drag. Almost all generated downforce in the car is provided by three main aerodynamic devices: front wing, rear wing and diffuser-floor [1,5]. They are designed exclusively according to aerodynamic considerations, and thus cannot be designed separately. If aerodynamic effects are employed to increase the performance of the car, an optimal downforce balance between front and rear wheels is crucial to equilibrating the normal force applied in both tyres [4]. The pressure centre, when placed in the rear part of the car, ensures that

Fluids 2020, 5, 237; doi:10.3390/fluids5040237 www.mdpi.com/journal/fluids Fluids 2020, 5, 237 2 of 23 the front wheels have less maximum lateral force and the car understeers. On the other hand, if the pressure centre is placed in the front part of the car, the rear wheels have less maximum lateral force, and therefore the car oversteers. Focused on the front wing, this aerodynamic device is the frontmost component of an open-wheeled racing car. It consists of a negative attack angle wing with additional devices, such as flaps, flaps Gurney or endplates. Two major features have a critical influence in its design: the proximity of the tarmac (ground effect) and the tyres [1]. It possesses several targets: to generate a downforce (25–30% of the overall car’s downforce [3,5]) in the front part of the car with high aerodynamic efficiency, to reduce the drag generated in the front wheels and to canalise the airflow to the rearmost components. Hence, racing car front wings possess a very high lift-to-drag ratio [6]. The high magnitude of the aerodynamic forces generated in the wings makes the structural design critical. In a Formula One front wing, the aerodynamic loads are considerably smaller than in a commercial aircraft because the maximum speed and wing aspect ratio are remarkably lower. The main objective of the structural design of a front wing is the reduction in structural weight. In an extremely competitive motorsports sector, the correct parametrisation of the limit between lightweight and structural reliability is essential. Furthermore, FIA Formula One regulations establish that all the aerodynamic devices of the car, including the front wing, rear front and bodywork, among other external components, need to be immobile according to the car’s reference plane [7]. Thereby, the front wing of a Formula One car possesses extremely high rigidity, thus minimising its deformation, which has a negative influence in the aerodynamic performance of the car [8]. The topology of a Formula One front wing has changed along the years, from the first design in the late 1960s until the sophisticated designs of the 2010s. The first front wing introduced in the Lotus 49 was a simple rectangular one-element wing with flap vertical endplates [3]. In the 1970s, the main developments in the front wings were the introduction of flaps Gurney and top-view elliptical shape [3]. Multi-element wings were introduced in 1984 by McLaren [3], but three-element wings were not designed until 2004. Due to the enormous ground effect employed in the 1980s, the distance between the front wing and the tarmac was extremely short. In a dynamic situation, the flow behind the wing usually was blocked, generating an important fluctuation in the downforce. This undesired effect, called porpoising [9], obligated the FIA to restrict the minimum distance between the wing and the ground for safety reasons after Imola 1994. In 1990, Tyrrell raised the front bodywork to increase the aerodynamic performance under the car and to reduce the wing–body interaction [3]. Due to the increase in aerodynamic performance, in 2001 the FIA increased the minimum distance between wing and tarmac again, from 40 to 100 mm [2], and teams started to design front wings with a positive dihedral angle. The use of slats has not been common in Formula One cars, with the Ferrari F2005 being the most well-known car employing this leading edge aerodynamic device. Since the 2010s, strict regulations did not allow for new innovative concepts, but the introduction of computational fluid dynamics (CFD) methods has allowed teams to develop extraordinary high-performance, multi-element front wings. For the year 2022, a new aerodynamic concept has been established in Formula One cars, provoking the beginning of a new era in the competition. To improve the spectacle [10], the championship promotors and teams created new technical regulations [7] focused on increasing the aerodynamic performance of the cars located in the wake of the previous cars, boosting overtake possibilities. The outcomes are wings with lower aerodynamic performance, but whose design remains one of the most important stages in the design of the car. The extremely high competitiveness provokes secrecy regarding the aerodynamic performance of the cars, and hence there is not a high amount of public research information. However, several authors performed aerodynamic investigations applied to Formula One cars: Petrone et al. [11], Gorostidi et al. [12], Arrondeau et al. [13] and Syazrul [14] optimised and analysed the aerodynamic behaviour of a F1 front wing. Heyder-Bruckner [15] and van den Berg [16] analysed the aerodynamic interaction between the front wing and wheels. Azmi et al. [17] analysed the airflow characteristics of a rear wing and Bhatnagar [18] optimised the aerodynamic relationship between the front and rear wings. Fluids 2020, 5, 237 3 of 23

Castro [4] performed an aerodynamic optimisation of the whole car. Ahlfeld et al. [19] quantified the uncertainty of CFD methods for Formula One aerodynamic devices. Regarding the structural analysis of front wings, the teams usually perform fluid–structure interactions (FSI), where the fluid and the solid are coupled into a single problem and the set of partial differential equations (PDE) describing fluid and solid motion has to be satisfied simultaneously [20]. Due to the computational restrictions, fluid–structure interactions have commonly been analysed through aeroelastic wind tunnels [21] instead of solved with numerical methods [22]. Hence, the amount of public research is extremely limited, highlighting the analysis of FSI in racing car spoilers performed by Landvogt [8]. The research is split into two blocks. Firstly, a thorough investigation is performed, including the analysis of the most important aerodynamic and structural parameters, among a detailed selection and analysis of the most suitable materials. Moreover, two composites are created based on the mechanical properties of reinforcement and matrix, packing and volume of constituents. Lastly, a 2022 front wing is designed through the application of the most relevant aerodynamic features and its structural components are made based on a sensitivity analysis. After the analysis, several conclusions are extracted and a thorough validation is performed to ensure the accuracy of the results and to quantify its uncertainty.

2. Methodology

2.1. Front Wing Design The front wing design is one of the most complex and time-consuming tasks in the whole design of the Formula One car. It needs to achieve all the aerodynamic and structural targets and to satisfy the technical regulations. The designed front wing satisfies the articles of the 2022 FIA Formula One regulations presented in Table1.

Table 1. 2022 FIA Formula One Technical Regulations [7].

Parameter Articles Front Bodywork Art. 3.6.1, Art. 3.9.9 and Art. 3.11.5 Front Wing Airfoils Art. 3.9.1 Front Wing Endplates Art. 3.9.2 and Art. 3.9.5 Front Wing Tip Art. 3.9.3 Front Wing Diveplane Art. 3.9.4 Front Wing Assembly Art. 3.9.6 Materials Art. 15.3.1, Art. 15.3.2, Art. 15.3.3 and Art. 15.3.4 Art. 2.9.1, Art. 2.9.2, Art. 2.9.3, Art. 2.9.4, Art. 2.11.1, Coordinate Systems, Reference Surfaces and Art. 2.11.2, Art. 2.11.3, Art. 3.4.1, Art 3.4.2, Art 3.4.3, Reference Volumes Art. 12.1.4, Art. A.9, Art. A.12, Art. A.21, Art A.22, Art. A23, Art. A24, Art. A25 and Art. A26.

2.1.1. Design of Front Wing Baseline Configurations Four baseline configurations (Figure1) are designed to analyse the influence of flaps and endplates in the aerodynamic and structural performance of the wing. They are based on the optimised bidimensional (2D) three-element configuration achieved by Gorostidi et al. [12] through the analysis of several high-efficiency airfoils and multiple degrees of freedom (chord, attack angles, overlapping between elements, among other minor considerations). The four configurations are extruded 900mm in the spanwise direction, which is the maximum length allowed by the 2022 FIA Formula One regulations to the front wings. Additionally, the baseline configurations are employed to carry out the analysis of the front wing structural components because of the complex shape of the 2022 wing (composed of 21 different 2D sections). After the structural and sensitivity analysis, the selected wing components are implemented in the designed 2022 Formula One front wing. The main features of this bidimensional configuration are provided in Table2. Fluids 2020, 5, x 4 of 23

Table 2. Features of bidimensional three-element F1 front wing achieved by Gorostidi et al. [11].

Feature Symbol Value Units Airfoil S1210 - -

Chord of Main Element 𝑐 250 mm

Chord of Primary Flap 𝑐 125 mm

Chord of Secondary Flap 𝑐 62.5 mm

Attack Angle of Main Element 𝛼 3 °

Attack Angle of Primary Flap 𝛼 6 °

Attack Angle of Secondary Flap 𝛼 9 °

Gap between elements 1 and 2 𝑔 19.43 mm

Gap between elements 2 and 3 𝑔 16.27 mm

Overlap between elements 1 and 2 𝑜 29.87 %

Overlap between elements 2 and 3 𝑜 35.46 %

Distance to the Reference Plane ℎ 75 mm Distance to the Floor ℎ 160 mm

The simple one-element configuration (a) provides reference values for further simulations. The second configuration (b) possess endplates which increase the pressure differential over the top and bottom surfaces of the wing, decreasing the induced drag and vortices [23]. The third configuration (c) is designed to analyse the influence of the aspect ratio in the flap structural behaviour and the influence of flaps on the overall wing performance. In the last configuration (d) (three-element wing withFluids endplates),2020, 5, 237 the wingtip devices create a new mechanical ligature between elements, 4and of 23 therefore the structural behaviour of this configuration is similar to Formula One front wings.

(a) (b)

(c) (d)

FigureFigure 1. 1. BaselineBaseline configurations: configurations: (a ()a one-element) one-element without without endplates; endplates; (b (b) one-element) one-element with with endplates; endplates; (c(c) )three-element three-element without without endplates; endplates; ( (dd)) three-element three-element with with endplates. endplates.

2.1.2. DesignTable of 2. Features2022 Formula of bidimensional One Front three-element Wing F1 front wing achieved by Gorostidi et al. [11]. The 2022 front wing is anFeature adaptation of a three-element Symbol bidimensional Value configuration Units performed by Gorostidi et al. [12] accordingAirfoil to the FIA 2022 Formula S1210 One regulations - [7]. The - volume assigned for the front wing elementsChord (main of Main element Element and flaps) is derivedc1 from250 Art. A21 is mm split into 21 sections. The configuration of airfoilsChord in of each Primary section Flap is performedc2 through the125 maximisation mm of the generated Chord of Secondary Flap c 62.5 mm downforce. Thereby, it is important to select the main influence3 parameters: wing area, attack angle Attack Angle of Main Element α1 3 ◦ Attack Angle of Primary Flap α2 6 ◦ Attack Angle of Secondary Flap α3 9 ◦ Gap between elements 1 and 2 g12 19.43 mm Gap between elements 2 and 3 g23 16.27 mm Overlap between elements 1 and 2 o12 29.87 % Overlap between elements 2 and 3 o23 35.46 % Distance to the Reference Plane hRP 75 mm Distance to the Floor h 160 mm

The simple one-element configuration (a) provides reference values for further simulations. The second configuration (b) possess endplates which increase the pressure differential over the top and bottom surfaces of the wing, decreasing the induced drag and vortices [23]. The third configuration (c) is designed to analyse the influence of the aspect ratio in the flap structural behaviour and the influence of flaps on the overall wing performance. In the last configuration (d) (three-element wing with endplates), the wingtip devices create a new mechanical ligature between elements, and therefore the structural behaviour of this configuration is similar to Formula One front wings.

2.1.2. Design of 2022 Formula One Front Wing The 2022 front wing is an adaptation of a three-element bidimensional configuration performed by Gorostidi et al. [12] according to the FIA 2022 Formula One regulations [7]. The volume assigned for the front wing elements (main element and flaps) is derived from Art. A21 is split into 21 sections. The configuration of airfoils in each section is performed through the maximisation of the generated downforce. Thereby, it is important to select the main influence parameters: wing area, attack angle and gap and overlap between elements. The first parameter to modify is the top-view area, which has a proportional influence on the downforce without modifying the two-dimensional optimal configuration. Thereby, the total chord of each section is scaled to match the maximum chord allowed by the front wing reference volume. The second parameter to adapt is the attack angle. Due to the interest in Fluids 2020, 5, x 5 of 23

and gap and overlap between elements. The first parameter to modify is the top-view area, which Fluidshas a2020 proportional, 5, 237 influence on the downforce without modifying the two-dimensional optimal5 of 23 configuration. Thereby, the total chord of each section is scaled to match the maximum chord allowed by the front wing reference volume. The second parameter to adapt is the attack angle. Due to the increasing the downforce, it is a parameter to maximise. However, this is only interesting in the interest in increasing the downforce, it is a parameter to maximise. However, this is only interesting sections where the trailing edge position is limited by the length of the reference volume, otherwise the in the sections where the trailing edge position is limited by the length of the reference volume, top-view area is decreased. Overall, 18 sections are limited by the length, and therefore their angle is otherwise the top-view area is decreased. Overall, 18 sections are limited by the length, and therefore increased to achieve the maximum total attack angle allowed by the maximum volume allowed by Art. their angle is increased to achieve the maximum total attack angle allowed by the maximum volume A21. On its behalf, the sections limited by height are modified thought the gap and overlap between allowed by Art. A21. On its behalf, the sections limited by height are modified thought the gap and elements to match the maximum length allowed by the regulations in each section. overlap between elements to match the maximum length allowed by the regulations in each section. Furthermore, more components are added to the wing geometry. In the first place, the endplates Furthermore, more components are added to the wing geometry. In the first place, the endplates are designed through a 90 circular path from the main element satisfying Art. 3.9.2, Art. 3.9.5 and Art. are designed through a 90°◦ circular path from the main element satisfying Art. 3.9.2, Art. 3.9.5 and A23. Secondly, a diveplane is added in the endplate external surface following the indications and Art. A23. Secondly, a diveplane is added in the endplate external surface following the indications restrictions explained in Art. 3.9.4, Art. A22 and Art. A25. Lastly, a nose satisfying front bodywork and restrictions explained in Art. 3.9.4, Art. A22 and Art. A25. Lastly, a nose satisfying front articles (Art. 3.6.1, Art. 3.9.9, Art. 3.11.5, Art. A9 and Art. A11) is designed to analyse the fluid bodywork articles (Art. 3.6.1, Art. 3.9.9, Art. 3.11.5, Art. A9 and Art. A11) is designed to analyse the interaction with the wing, but its shape does not fulfil any aerodynamic requirement fluid interaction with the wing, but its shape does not fulfil any aerodynamic requirement The 2022 front wing is shown in Figure2, where it is attached to a 2018 Formula One car, The 2022 front wing is shown in Figure 2, where it is attached to a 2018 Formula One car, fully fully designed by the author [4]. This is the basis of the upcoming analysis, where the authors will designed by the author [4]. This is the basis of the upcoming analysis, where the authors will analyse analyse the impact of the designed front wing in the aerodynamic performance of the overall Formula the impact of the designed front wing in the aerodynamic performance of the overall Formula One One car. car.

Figure 2. 2022 front wing attached to a 2018 Formula One car (the whole design is performed and Figure 2. 2022 front wing attached to a 2018 Formula One car (the whole design is performed and developed by the authors). developed by the authors).

2.1.3.2.1.3. Design of Structural ComponentsComponents AlthoughAlthough thethe currentcurrent frontfront wingswings possesspossess a sandwich composite structure with a fibre-reinforced fibre-reinforced skinskin andand aa polymericpolymeric interiorinterior withwith innerinner ribs,ribs, thisthis researchresearch employsemploys aa mostmost conventionalconventional structure, basedbased onon ribs,ribs, spars spars and and skin, skin, similar similar to to commercial commercial aircraft aircraft [24 ].[24]. The The internal internal structure structure of the of wingthe wing was submittedwas submitted to a thorough to a thorough investigation investigation to analyse to anal the influenceyse the influence of each component of each component in the final in structural the final behaviour,structural thebehaviour, nature of the their nature main of stresses their andmain strains stresses and and the strains influence and of thethe mostinfluence important of the design most parameters.important design Firstly, parameters. a baseline Firstly, configuration a baseline was conf designediguration to was obtain designed a first to approach obtain a first of the approach wing’s structuralof the wing’s behaviour. structural This behaviour. configuration This isconfiguration based on qualitative is based engineeringon qualitative design engineering and it consisted design and of fiveit consisted ribs, five of spars five ribs, and afive skin. spars Once and the a skin. baseline Once configuration the baseline isconfiguration established, is several established, designs several were madedesigns to were analyse made their to performance.analyse their Someperformance. of these Some designs of arethese shown designs in Figureare shown3. in Figure 3. TheThe first first components components to to design design are are the the spars, spars, which which are arethe longitudinal the longitudinal beams beams of the of wing. the wing.Their Theirmain mainfunction function is to avoid is to avoid the vertical the vertical deformation deformation of the of wing the wingand to and absorb to absorb the loads the loads coming coming from fromthe skin. the skin.They They are exposed are exposed to shear to shear stress, stress, and, and, for for this this case, case, the the shear shear modulus modulus became became a criticalcritical factor.factor. TheThe designeddesigned sparsspars consistconsist ofof aa normal extrusionextrusion along the span width direction, whosewhose sectionsection isis basedbased onon anan II beam,beam, whichwhich provedproved toto bebe thethe bestbest choicechoice inin termsterms ofof stistiffness–weightffness–weight ratio.ratio. TheThe initialinitial number of spars is set in five (four normal I-section beams and one beam in the trailing edge of Fluids 2020, 5, x 6 of 23 number of spars is set in five (four normal I-section beams and one beam in the trailing edge of 10mm width whose section matches the airfoil geometry), whose position is mainly placed in the frontmost part of the wing for two main reasons: pressure distribution is higher near the leading edge and the airfoil S12010 has a much thinner section after the maximum thickness position. However, due to the structural behaviour of the wing, the trailing edge achieves the highest deformation in the wing, and this is the reason why the last spar becomes a critical component in the structure. Another important parameter of the spars is their size. Due to the aforementioned complex cambered airfoil selected, the size of each spar must be adjusted to the environment. Hence, the most suitable approach to parametrise the size of the spars is to set it according to the rib vertical length in each position. Lastly, the spar shape is analysed according to three parameters of freedom: root width, head width and head length (all of them measured as a percentage of the root length). Overall, a total of 324 spar configurations are analysed. The second components to design are the ribs. They are the transversal element of the wing, whose shape is an airfoil, and they support stiffness to the wing. The ribs are exposed to normal stresses of compression. These stresses can be achieved in the pressure coefficient in each rib, where the maximum load is present in the front part. Besides, the ribs near the tip suffer less load due to the loss of aerodynamic efficiency in the wing. The rib analysis is performed in three degrees of freedom: Fluidsnumber2020 ,of5, 237ribs in the structure, thickness and circular holes. The last parameter is essential to6of the 23 reduction in structural weight because the centre of the ribs is a region with lower stresses. These holes were also decided to be circular because they better absorb the stresses than sharped 10mm width whose section matches the airfoil geometry), whose position is mainly placed in the geometries, such as triangles or squares. Overall, a total of 80 configurations of ribs were investigated. frontmost part of the wing for two main reasons: pressure distribution is higher near the leading edge It is very important to notice that each rib has a different volume for each spar set and skin thickness. and the airfoil S12010 has a much thinner section after the maximum thickness position. However, Lastly, the skin is the external component of the wing. It is exposed to high flexion loads which due to the structural behaviour of the wing, the trailing edge achieves the highest deformation in depend on the number of ribs and spars of the wing. The skin of an aircraft wing needs to be resistant the wing, and this is the reason why the last spar becomes a critical component in the structure. to corrosion because the coatings increase the structural weight. On the contrary, Formula One wings Another important parameter of the spars is their size. Due to the aforementioned complex cambered have a short life expectancy and, therefore, corrosion is not a problem. The skin was created airfoil selected, the size of each spar must be adjusted to the environment. Hence, the most suitable throughout an internal extrusion of the wing surface and it is designed with five different thickness. approach to parametrise the size of the spars is to set it according to the rib vertical length in each Even if the thickness of the skin is very small, its volume is the highest of all components, and thereby, position. Lastly, the spar shape is analysed according to three parameters of freedom: root width, it will have enormous importance in the structural design. Additionally, it is important to remark head width and head length (all of them measured as a percentage of the root length). Overall, a total that a bigger thickness provokes a reduction in the section of the rib and spar, which is properly of 324 spar configurations are analysed. treated in the structural design.

(a) (b)

(c) (d)

Figure 3. Examples of wing structural designs: ( a) wing structure with high-density ribs;ribs; ((b)) ribsribs withwith implementedimplemented circularcircular holes;holes; ((cc)) wingwing structurestructure withwith high-densityhigh-density spars;spars; ((dd)) ribsribs withwith highhigh thickness.thickness.

The second components to design are the ribs. They are the transversal element of the wing, whose shape is an airfoil, and they support stiffness to the wing. The ribs are exposed to normal stresses of compression. These stresses can be achieved in the pressure coefficient in each rib, where the maximum load is present in the front part. Besides, the ribs near the tip suffer less load due to the loss of aerodynamic efficiency in the wing. The rib analysis is performed in three degrees of freedom: number of ribs in the structure, thickness and circular holes. The last parameter is essential to the reduction in structural weight because the centre of the ribs is a region with lower stresses. These holes were also decided to be circular because they better absorb the stresses than sharped geometries, such as triangles or squares. Overall, a total of 80 configurations of ribs were investigated. It is very important to notice that each rib has a different volume for each spar set and skin thickness. Lastly, the skin is the external component of the wing. It is exposed to high flexion loads which depend on the number of ribs and spars of the wing. The skin of an aircraft wing needs to be resistant to corrosion because the coatings increase the structural weight. On the contrary, Formula One wings have a short life expectancy and, therefore, corrosion is not a problem. The skin was created throughout an internal extrusion of the wing surface and it is designed with five different thickness. Even if the thickness of the skin is very small, its volume is the highest of all components, and thereby, it will have enormous importance in the structural design. Additionally, it is important to remark that a bigger thickness provokes a reduction in the section of the rib and spar, which is properly treated in the structural design. Fluids 2020, 5, 237 7 of 23

2.1.4. Selection of Front Wing Materials The selection of the materials is a critical stage in the structural design of a wing. Formula One cars, always immersed in the research and development of new technologies, have improved and changing their materials over the years. They started with metallic structures at the beginning of the Formula One competition in the 1950s, but nowadays they are mostly built of composites [25]. According to the most important physical (density) and mechanical properties (rigidity, yield strength, tensile strength and toughness), three metal alloys are selected and two fibre-reinforced wovens are designed to be implemented in the designed front wings. Thermal and electrical properties, as well as other physical (melting temperature) and mechanical properties (hardness and machinability), are discarded in the material selection process due to their lack of importance in Formula One wing designs. The metals employed in the wing structure were selected by comparing the mechanical properties of 41 preselected metal alloys (8 steels, 4 cast irons, 9 aluminium alloys, 6 titanium alloys, 8 copper alloys and 6 magnesium alloys) based on several material databases [26–30]. After this analysis, three metal alloys were selected for their implementation in the structural components of the front wing: titanium alloy R54810, which possesses the highest specific Young’s modulus of all preselected alloys (27.46 GPa cm3/g) and a medium-density (4.37 kg/cm3), magnesium alloy AZ31B, which have a · very low density (1.77 kg/cm3) and excellent specific modulus (25.42 GPa cm3/g) and aluminium alloy · 2024 T3, which possesses intermediate properties (specific modulus of 26.29 GPa cm3/g and density of · 2.81 kg/cm3). The fibre-reinforced composites were designed in several steps. Firstly, 50 ceramic fibres (8 glass fibres, 30 carbon fibres, 8 para-oriented aramid fibres and 4 meta-oriented aramid fibres) and 10 polymeric matrices were investigated (4 thermosetting polymers and 6 thermoplastics) were preselected through several material databases [26,31–36]. Secondly, the best two fibres were selected. The first reinforcement choice was carbon fibre: two of them, HS40 and UHMS, possess the highest elasticity modulus (441 GPa) and the same density (1.81 kg/cm3), but HS40 was selected due to its higher tensile strength (4400 MPa vs. 3450 MPa). The second choice was the aramid fibre with the highest mechanical properties: Kevlar K149, which possesses an elasticity modulus of 147 GPa and a very low density (1.47 kg/cm3). Thirdly, assuming that the selected fibres have enough ultimate strength to avoid the composite breaking, the matrices were only selected according to Young’s modulus and the specific Young’s modulus: the first choice was the epoxy polymer, with a Young’s modulus of 6 GPa and a specific Young’s modulus of 4.29 GPa cm3/g and the second selection was the · thermoplastic Polyetherketone (PEK), which possesses a Young’s modulus of 4.6 GPa and a specific Young’s modulus of 3.49 GPa cm3/g. Lastly, after all considerations and mathematical relationships · needed, four composites were created with the two selected fibres (carbon and aramid) and the two selected matrices (Epoxy and PEK) with a 78.5% of fibre volume. The orthotropic mechanical properties and density of the designed composites are provided in Table3.

Table 3. Orthotropic mechanical properties and density of the designed composites.

Property HS40-Epoxy HS40-PEK K149-Epoxy K149-PEK Density ρ 1.73 1.71 1.46 1.44 Longitudinal Young’s Modulus E1 354.0 353.7 118.8 118.5 Transversal Young’s Modulus E2 28.5 22.1 25.8 20.4

2.2. Fluid Conditions Sea-level fluid conditions were assumed in concordance with the International Standard Atmosphere. Regarding the flow conditions, the velocity of the flow was considered as a one-dimensional streamwise velocity whose magnitude is a typical maximum speed of a Formula Fluids 2020,, 5,, 237x 8 of 23

Table 4. Summary of fluid and flow conditions. One car, where the aerodynamic forces are maximum in the wing. A summary of the fluid and flow conditions is provided in TableFlow4. Condition Symbol Value Units Fluid Density 𝜌 1.225 kg/m Table 4. Summary of fluid and flow conditions. Fluid Temperature 𝑇 288.15 K Flow Condition Symbol Value Units Atmospheric Pressure 𝑝 101325 Pa Fluid Density ρ 1.225 kg/m3 FluidDynamic Temperature Viscosity T𝜇 1.8288.15 × 10−5 Pa · K s Aospheric Pressure p 101325 Pa Streamwise Air Velocity 𝑢 105 m/s Dynamic Viscosity µ 1.8 10 5 Pa s × − · StreamwiseSpanwise Air Air Velocity Velocity u𝑣 1050 m/s m/ s Spanwise Air Velocity v 0 m/s

2.3. Mesh Design 2.3. Mesh Design The fluid-dynamic simulations of this research are performed with a hybrid mesh (Figure 4), The fluid-dynamic simulations of this research are performed with a hybrid mesh (Figure4), which is suitable because offers the highest accuracy–cost ratio. It is composed of a structured which is suitable because offers the highest accuracy–cost ratio. It is composed of a structured boundary boundary layer of 30 elements and unstructured methods in the other regions of the domain. On its layer of 30 elements and unstructured methods in the other regions of the domain. On its behalf, behalf, the mesh of the inner structure of the front wing is carried out with structured methods the mesh of the inner structure of the front wing is carried out with structured methods (hexahedrons). (hexahedrons).

Figure 4. MeshMesh of of the the 2022 2022 Formula Formula One front wing assembly.

The fluidfluid domain selection is one of the most challengingchallenging decisions due to the presence of the road under the car. Even Even if if several several sizes sizes are are used used by by different different authors authors with with ac accuratecurate results, results, something is clear: the the most most suitable suitable topology topology is a cubical domain. Ashton Ashton et et al. al. [37] [37] employed employed a cubical domain of 8 H height, 14 H wide, 13 H upstream, 19 H downstreamdownstream and 14 H cross-stream in the analysis of Reynolds-averaged Navier–Stokes (RANS)(RANS) and detacheddetached eddy simulation (DES) methods for realistic automotive models, models, where where H H is is the the height height of of the the car. car. Heft Heft et etal. al.[38] [38 used] used the the length length of the of thecar carto set to setthe theupstream upstream (2 L) (2 and L) andthe downstream the downstream (7 L) (7 sizes L) sizes of the of domain. the domain. Arrondeau Arrondeau et al. et[13] al. used [13] useda fluid a fluiddomain domain based basedon the onheight the heightin their in study their of study a 2021 of F1 a 2021front F1wing. front They wing. set They5 H height, set 5 H3 H height, upstream 3 H upstreamand 10 H downstream. and 10 H downstream. They used Theythe same used height the same as Ashton height asand Ashton a cross-stream and a cross-stream length of (11 length W). In of (11the W).most In conservative the most conservative domain, Simmonds domain, Simmonds et al. [39] employed et al. [39] employed10 L height, 10 20 L height,L wide, 20 12 L L wide, upstream 12 L upstreamand 15 L downstream. and 15 L downstream. Furthermore, Furthermore, it is important it is important to remark to remark that Ashton that Ashton et al. [37], et al. Heft [37], Heft[38] and [38] andSimmonds Simmonds [39] [did39] didnot notemploy employ symmetrical symmetrical boundary boundary conditions conditions in inthe the central central plane plane of of the the car, car, implying additionaladditional computational computational cost. cost. In the In analysis the ofanalysis the results of achievedthe results by theachieved abovementioned by the authors,abovementioned the selected authors, fluid domainthe selected demonstrates fluid doma thein dimensions demonstrates employed the dimensions by Simmonds employed et al. [ 39by], butSimmonds using the et al. chord [39], as but a relativeusing the measurement chord as a re method.lative measurement The number method. of nodes The in number the airfoil of nodes needs toin bethe enough airfoil needs to accurately to be enough represent to accurately the original represent geometry the andoriginal to be geometry considered and grid-independent; to be considered followinggrid-independent; the experience following of the the authors experience with similarof the airfoils,authors 250with nodes similar were airfoils, selected. 250 The nodes density were of selected. The density of nodes is maximum in the leading edge, with a minimum tangential grid Fluids 2020, 5, 237 9 of 23 nodes is maximum in the leading edge, with a minimum tangential grid spacing of 0.002, and it is minimum in the maximum thickness location, with a maximum tangential grid spacing of 0.006. Regarding the boundary layer treatment, ε-based and ω-based models present y+ insensitive wall treatment options through the wall function approach [40]. Using the wall functions, the normal spacing is considered optimal when y+ 30 (if it is lower, the accuracy of the wall shear stress and the ≈ heat transfer can be seriously degraded) [41]. Thereby, a preliminary y+ = 30 and posterior analysis of computed y+ are performed to ensure the correct caption of the boundary layer. The second boundary layer meshing requirement is to ensure its full meshing: the theoretical thickness of the boundary layer is calculated [42] and the number of elements is set as 30 according to Castro [42]. Hence, through mathematical relationships between the abovementioned three parameters (minimum normal grid spacing, maximum thickness and number of elements), the growth rate was set as 1.1. Once all the mesh parameters are obtained, the boundary layer is generated with triangular prisms through a normal extrusion from the wall.

2.4. Numerical Framework The fluid dynamic analyses were carried out in ANSYS® Fluent (v2019), which employs the finite volume method to solve the partial differential equations governing the fluid dynamic problem. Additionally, decoupled structural analysis were carried out with ANSYS® Mechanical (v2019), a finite element analysis solver (FEA). Regarding the turbulence models, in the same way as the majority of the engineering simulations, the equations employed in the solver are Reynolds Averaged Navier–Stokes (RANS) equations. These simulations present a lower computational cost than Large Eddy Simulations (LES), which are employed mainly in research fields. All the simulations were carried out with the k-ω SST turbulence model. It is widely used for engineering applications and motorsport aerodynamic designs, being the most important turbulence model in the Formula One fluid dynamic simulation, where an optimal balance between accuracy and time is needed [13]. The fluid dynamic simulations were performed in a coupled incompressible solver based on the SIMPLE algorithm. The iterative scheme significantly affects the computational cost and cost per iteration. Therefore, the coupled pressure-velocity method was set because it has some advantages, such as robustness and efficient single-phase implementation [41]. The coupled scheme is suitable for steady flows. The recommended gradient discretisations are the Least Squares Cell-Based or the Green-Gauss Node Based options. The accuracy between them is similar, but the Least Squares Cell-Based is less expensive to compute [43]. The discretisation of the density, momentum, turbulent viscosity and energy was performed through second-order methods. The boundary conditions of a Formula One front wing are an important challenge to achieve high accuracy in the fluid dynamic simulations. In a common CFD simulation, the superposition principle is applied. However, it is only valid when the object moving through the air is not near walls. In a Formula One car, the floor is near the wing, and it is very important to make some adjustments to the wall-modelling and boundary conditions. In order to employ the optimal boundary conditions, the experience of some authors provides important advice. Arrondeau et al. [13] split the ground into two parts in their study of a 2021 Formula One front wing: before the wing, a stationary wall with slip condition was applied and after that, the floor was modelled as a moving wall with a no-slip condition. In the other parts of the domain, they employed a one-directional streamwise velocity for the inlet, outflow for the outlet, with symmetry conditions in the side and upper walls. In the optimisation of a 2020 Formula One front wing, Gorostidi et al. [12] divided the floor into three sections: prior and after the wing, a stationary slip-wall was selected, and under the wing, a no-slip moving wall was set. Besides this, the inlet was a one-directional velocity, the outlet was modelled as pressure-outlet, symmetry was employed in the plane Y = 0, and a slip-wall was set in the opposite sidewall. A different approach to the ground was employed by van den Berg [16] in his analysis of the interaction of a Formula One front wing with the wheels. In this Fluids 2020, 5, 237 10 of 23 case, all the floor was modelled as a no-slip moving wall. The simulations of the current research were carried out using pressure outlet as outlet, and the side and top planes were modelled with symmetry conditions. The same boundary conditions as van den Berg were used by Heyder-Bruckner [15] in a similar analysis, and the results were compared with the experimental data obtained in a wind tunnel. Simmonds et al. [39] used the same asphalt, inlet and outlet boundary conditions, but they employed slip-walls to the top, and side surfaces (as mentioned, they did not use symmetry conditions in the centre of the car). The boundary conditions employed are summarised in Table5: a streamwise velocity of 105 m /s is employed in the inlet of all the simulations and a zero-pressure gradient is selected in the outlet. Symmetry boundary conditions are employed along the plane Y = 0, whose target is to reduce the mesh size by half, and hence to drop the computational cost of the simulations. The asphalt, top and side walls are modelled using the simulations performed by van den Berg [16] and Heyder-Bruckner [15] as a reference, because they were compared with wind tunnel experimental data, achieving high accuracy.

Table 5. Summary of boundary conditions employed in the simulations.

Surface Boundary Condition Value Units Description Velocity-inlet (105, 0, 0) m/s Inlet Turbulence Intensity 0.3 % Normal to boundary 7 Turbulent Viscosity Ratio 10− - Outlet Pressure-outlet ( p ) (0, 0, 0) Pa/m Allows for recirculation ∇ Asphalt No-slip moving wall (105, 0, 0) m/s Enforces relative movement Left-Wall Symmetry - - Saves computational time Top-Wall Symmetry - - Verified with experimental data Right-Wall Symmetry - - Verified with experimental data Wing No-slip stationary wall (0, 0, 0) m/s Allows boundary layer build-up

3. Results

3.1. Validation and Verification When an analysis is performed through computational fluid dynamic and finite element analysis methods, is crucial to ensure the accuracy of the results and to quantify its uncertainty. Hence, an enormous amount of the available time was destined to select the optimal methodology and to establish several validation methods. The most important applied validation methods are the grid convergence analysis, the verification of convergence throughout the aerodynamic coefficients and residuals and the analysis of the boundary layer’s quality. Furthermore, other validation methods were applied, such as the analysis of the pressure between the CFD solver and the FEA solver. The first validation method is the grid convergence index (GCI) [44,45] developed by Roache [46]. This method applies Richardson extrapolation to determine the order of convergence of the grids and the asymptotic solution of the representative magnitudes. Two additional meshes of the one-element baseline configuration are created to analyse the mesh convergence analysis, whose relative refinement ratio is 2. The GCI is performed through a MatLab® (R2020) file developed by the author [47]. Table6 provides a summary of the most important parameters of the grid convergence study, including the refinement ratio, the order of convergence, the asymptotic solution and the Grid Convergence Index of the two aerodynamic coefficients.

Table 6. Results of grid convergence analysis.

p Parameter r p fh=0 GCI12 GCI23 GCI12/r GCI23

CL 2 1.5850 0.0655 2.9297 0.9615 1.0156 CD 2 1.8074 1.1868 0.2956 0.0843 1.0017 Fluids 2020, 5, 237 11 of 23

Fluids 2020, 5, x 11 of 23 Additionally, Figure5 provides the relationship between the aerodynamic coe fficients and their asymptoticinfluenced limitby the according number toof the elements mesh size. of the As grid can be than observed, the lift the coefficient drag coe ffibecausecient is its more magnitude influenced is byremarkably the number lower of elements (aerodynamic of the grid efficiency than the of lift 18.12). coefficient However, because in its grids magnitude with ismore remarkably than 5 lower× 106 (aerodynamic efficiency of 18.12). However, in grids with more than 5 106 elements, the error between elements, the error between the lift and drag coefficients and their grid-independent× values is smaller thethan lift 1% and (0.067% drag coe andffi cients0.763%, and respectively). their grid-independent After this number values isof smaller elements, than the 1% dependence (0.067% and between 0.763%, respectively).results and mesh After size this can number be considered of elements, neglectable. the dependence Therefore, between this mesh results size is and selected mesh to size represent can be consideredthe front wing. neglectable. More Therefore,elements would this mesh immensely size is selected increase to represent the computational the front wing. cost More without elements any wouldrelevant immensely accuracy improvement. increase the computational cost without any relevant accuracy improvement.

Lift Coefficient Drag Coefficient 100 99 98 97 % 96 95 94 93 92 0.0E+0 1.0E+6 2.0E+6 3.0E+6 4.0E+6 5.0E+6 6.0E+6 Grid Elements

Figure 5. Approximation of the aerodynamic coecoeffifficients according toto thethe gridgrid size.size.

The second validation method consistsconsists of ensuring the optimal convergence of the solution, achieving resultsresults independent independent of theof iterationsthe iterations of the solver.of the Assolver. mentioned, As mentioned, fluid dynamic fluid simulations dynamic needsimulations an optimal need balance an optimal between balance accuracy between and computational accuracy and cost. computational In the process, cost. geometries, In the process, meshes, numericalgeometries, schemes meshes, andnumerical turbulence schemes models and turbulence need to be models adapted need to the to be necessities adapted to of the the necessities problems andof the the problems computational and the performance computational available. performance All these available. efforts canAll bethese disrupted efforts can if engineers be disrupted do not if properlyengineers analyse do not theproperly solution analyse convergence the solution and run convergence simulations and with run thousands simulations of useless with thousands iterations inof high-performanceuseless iterations in computing high-performance (HPC) facilities. computing To avoid (HPC) that, facilities. the convergence To avoid that, in preliminary the convergence and final in simulationspreliminary wasand thoroughly final simulations analysed was throughout thoroughly aerodynamic analysed forcesthroughout and residuals. aerodynamic The convergence forces and ofresiduals. results wasThe analysed convergence through of theresults residuals was andanal theysed value through of aerodynamic the residuals coeffi cientsand the according value toof theaerodynamic iterations. coefficients The most important according target to the in theiteratio convergencens. The most of the important equations target is to achieve in the aerodynamicconvergence forcesof the independentequations is to of achieve the iterations aerodynamic of the solver. forces Thisindependent parameter of allowsthe iterations for verifying of the thesolver. physical This convergenceparameter allows in the for simulation: verifying the if aerodynamic physical converge forcesnce are in independent the simulation: of the if iterations,aerodynamic it means forces that are theindependent surface pressure of the fielditerations, is invariant, it means and that hence, the the surface velocity pressure field is field invariant is invariant, as well. and If aerodynamic hence, the forcesvelocity achieve field is an invariant equilibrium as well. state If aerodynamic in the solution, forces it means achieve that an allequilibrium the computational state in the domain solution, is converged.it means that Satisfactorily, all the computational a very good domain and fast is convergence converged. wasSatisfactorily, achieved duea very to the good high-quality and fast geometriesconvergence and was meshes. achieved due to the high-quality geometries and meshes. The last validation method consistsconsists of analysing if the boundary layer of the airfoils was solved accurately. The computed yy++ ofof every every simulation simulation wa wass obtained obtained and and compared compared with the the desired desired value, value, ensuring that the computed yy++ does not exceed 30 at any point on the wing surface.

3.2. Aerodynamic and Structural Analysis of Baseline Wings The firstfirst set ofof resultsresults providesprovides thethe mostmost importantimportant aerodynamicaerodynamic and structural findingsfindings of the investigations performedperformed on on the the four four three-dimensional three-dimensional baseline baseline front front wings wings designed designed in Section in Section 2.1.1. The2.1.1. target The target is to analyse is to analyse the main the main aerodynamic aerodynami andc structural and structural behaviour behaviour of a three-element of a three-element wing wing with endplateswith endplates in comparison in comparison with with a one-element a one-element wing wi withoutng without endplates endplates with with a similar a similar airfoil, airfoil, chord chord and attackand attack angle. angle.

Fluids 2020, 5, 237 12 of 23 Fluids 2020, 5, x 12 of 23

3.2.1. Influence of Flaps and Endplates in the Aerodynamic Performance of the Wings 3.2.1. Influence of Flaps and Endplates in the Aerodynamic Performance of the Wings The aerodynamic objective of the front wing is to achieve maximum negative lift in the front part The aerodynamic objective of the front wing is to achieve maximum negative lift in the front of the car, to canalise the airstream to the floor, diffuser and other parts of the car, and to reduce the part of the car, to canalise the airstream to the floor, and other parts of the car, and to reduce drag generated in the front wheels. However, to analyse the two last benefits it is necessary to perform the drag generated in the front wheels. However, to analyse the two last benefits it is necessary to fluid dynamic simulations of the front wing attached to the other parts of the car, something out of the perform fluid dynamic simulations of the front wing attached to the other parts of the car, something scope of this research. Hence, the aerodynamic goal is to optimise aerodynamic forces and to analyse out of the scope of this research. Hence, the aerodynamic goal is to optimise aerodynamic forces and the pressure distribution in the wing walls to properly design their internal structure. to analyse the pressure distribution in the wing walls to properly design their internal structure. Aerodynamic forces are generated by the difference in pressure between the upper and lower Aerodynamic forces are generated by the difference in pressure between the upper and lower surfaces of the wing. Figure6 provides the pressure distribution in the lower surface of the wing, surfaces of the wing. Figure 6 provides the pressure distribution in the lower surface of the wing, which possesses negative manometric pressures. The most striking feature is that the negative pressure which possesses negative manometric pressures. The most striking feature is that the negative peak is located near the front bodywork, far away from wingtip effects (circulation of air with different pressure peak is located near the front bodywork, far away from wingtip effects (circulation of air pressures from the upper surface to the lower surface). Additionally, the peak increases with the with different pressures from the upper surface to the lower surface). Additionally, the peak increases introduction of endplates and flaps. with the introduction of endplates and flaps.

FigureFigure 6. DistributionDistribution of ofpressure pressure in the in lower the lower surface surface of (a) one-element of (a) one-element without without endplates; endplates; (b) one- (elementb) one-element with endplates; with endplates; (c) three-element (c) three-element without without endplates; endplates; (d) three-element (d) three-element with endplates. with endplates.

FigureFigure7 7 provides provides the the pressure pressure distribution distribution inin the the surfaces surfaces of of the the first first element element of of the the wing wing at at sectionssections 0.050.05 andand 0.950.95 ss (measured(measured inin percentagepercentage ofof spanspan width).width). InIn allall thethe configurations,configurations, nearnear thethe frontfront bodyworkbodywork (0.05(0.05 s)s) thethe wingwing hashas anan aerodynamicaerodynamic performanceperformance moremore similarsimilar toto aa commoncommon 2D2D airfoilairfoil atat highhigh attackattack angleangle (minimum(minimum pressurepressure locatedlocated inin thethe frontfront partpart ofof thethe suctionsuction sideside withwith aa suddensudden incrementincrement inin pressurepressure duedue toto thethe boundaryboundary layerlayer separation).separation). TheThe incrementincrement inin thethe variationvariation inin pressurespressures isis highhigh withwith thethe introductionintroduction ofof endplatesendplates andand veryvery high with the introduction of flaps. flaps. Additionally,Additionally, the the three-element three-element configurations configurations possess possess a reduction a reduction in performance in performance in the upperin the surface upper nearsurface the near trailing the edge,trailing area edge, highly area influenced highly influenc by theed overlapping by the overlapping of the flap. of the Near flap. the Near wingtip the wingtip (0.95 s), each(0.95 configurations), each configuration has a diff haserent a different aerodynamic aerody behaviour:namic behaviour: configurations configur withations endplates with endplates possess apossess suction a peaksuction near peak the near trailing the edgetrailing due edge to the due air to circulation the air circulation between between surfaces surfaces and multi-element and multi- configurationselement configurations are affected are byaffected the flap by in the the flap upper in the surface upper near surface thetrailing near the edge. trailing edge. The aerodynamic performance of the baseline configurations is assessed through its aerodynamic coefficients (Figure 8). The introduction of endplates in the one-element configuration derives from an increment in the lift coefficient of 12.39% (1.186 vs. 1.333) and decrease in the drag coefficient of 12.28% (0.065 vs. 0.057), provoking an increase in aerodynamic efficiency of 28.70% Fluids 2020, 5, x 13 of 23

(23.45 vs. 18.22). The introduction of flaps generated an increment of a 37.69% (1.633 vs. 1.186) in the downforce coefficient (measured in the configurations without endplates). However, the increment in drag was higher (124.61%), which derived from an aerodynamic efficiency loss of 38.47% (11.21 vs. 23.45). Additionally, it is important to remark that the introduction of flaps increases the top-view area Fluidsof the2020 front, 5, 237wing by 29.53% (0.62885 vs. 0.48546 m2), and thereby the increment in aerodynamic 13forces of 23 Fluidsbetween 2020 ,single-element 5, x and multi-element configurations is still higher. 13 of 23

-3.5 -3.5 (23.45 vs. 18.22). The introduction1-Element of flaps generated an increment of a 37.69% (1.6331-Element vs. 1.186) in the 1-Element + Endplates 1-Element + Endplates downforce-3 coefficient (measured in the configurations without-3 endplates). However, the increment 3-Elements 3-Elements in drag was higher (124.61%), which3-Elements derived + Endplates from an aerodynamic efficiency loss 3-Elementsof 38.47% + Endplates (11.21 vs. -2.5 23.45). -2.5 ) ) P P Additionally,-2 it is important to remark that the introduction-2 of flaps increases the top-view area of the front wing by 29.53% (0.62885 vs. 0.48546 m2), and thereby the increment in aerodynamic forces -1.5 -1.5 between single-element and multi-element configurations is still higher. -1 -1 -3.5 -3.5 -0.5 1-Element -0.5 1-Element 1-Element + Endplates 1-Element + Endplates -3 0 0.2 0.4 0.6 0.8 1 -3 0 0.2 0.4 0.6 0.8 1 Pressure Coefficient (C Pressure Coefficient (C 3-Elements 3-Elements 0 0 3-Elements + Endplates 3-Elements + Endplates -2.5 -2.5 ) ) 0.5 0.5 P P -2 -2 1 1 X-Position (%c) X-Position (%c) -1.5 -1.5 (a) (b) -1 -1 Figure 7. Pressure distribution in baseline configurationsconfigurations at sections: (a) 0.05 s; (b) 0.95 s. -0.5 -0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Pressure Coefficient (C Pressure Coefficient (C The0 aerodynamic2 performance of the baseline configurations0 0.16 is assessed through its aerodynamic coefficients (Figure8). The introductionOne-Element of endplates in the one-element configurationOne-Element derives from 1.8 Without an increment0.5 in the lift coefficient of 12.39% (1.186 vs. 1.333)0.5 0.14 and decrease in the dragWithout coefficient of 1.6 Endplates Endplates 12.28%1 (0.065 vs. 0.057), provoking an increase in aerodynamic1 0.12 efficiency of 28.70% (23.45 vs. 18.22). 1.4 One-Element One-Element The introduction ofX-Position flaps generated (%c) an increment of a 37.69% (1.633X-Position vs. 1.186) (%c) in the downforce With Endplates 0.1 With Endplates coefficient1.2 (measured in(a the) configurations without endplates). However,( theb) increment in drag was 1 0.08 higherCL (124.61%), which derived from an aerodynamicC eDfficiency loss of 38.47% (11.21 vs. 23.45). Figure 7. Pressure distributionThree-Elements in baseline configurations at sections: (a) 0.05 s; (b) 0.95Three-Elements s. 0.8 Without 0.06 Without 0.6 Endplates Endplates 2 0.160.04 One-Element One-Element 0.4 Three-Elements Three-Elements 1.8 Without 0.14 Without 0.2 With Endplates 0.02 With Endplates 1.6 Endplates Endplates 0 0.120 1.4 One-Element One-Element 1.2 (a) With Endplates 0.1 (b) With Endplates 1 0.08 CL Figure 8. (a) Lift coefficients;C (bD) Drag coefficients. Three-Elements Three-Elements 0.8 Without 0.06 Without Several0.6 conclusions can be extractedEndplates from the aerodynamic investigation: the endplatesEndplates increase 0.04 the overall0.4 aerodynamic performanceThree-Elements of the wing, increasing the downforce and decreasingThree-Elements the drag of the front0.2 wing. Hence, there are noWith contraindicati Endplates ons of 0.02the use of endplates. Meanwhile,With Endplates the flaps are an effective0 way to extremely increase the generated downforce,0 but its introduction generates an increase in the drag of higher magnitude, decreasing the aerodynamic efficiency. Nonetheless, the flaps proved to be a better(a) tool to increase the downforce generated in the (wingb) than the attack angle increment, which derives fromFigure the 8. still-higher ((aa)) Lift Lift coefficients; coe ffigrowthcients; ( ofb)) dragDrag Drag andcoefficients. coeffi acients. possible wing stall, an extremely undesired phenomenon. SeveralAdditionally, conclusions it is important can be extracted to remark from that the the ae introductionrodynamic ofinvestigation: flaps increases the the endplates top-view increase area of the overall front wing aerodynamic by 29.53% performance (0.62885 vs. of 0.48546 the wing, m2), in andcreasing thereby the the downforce increment and in decreasing aerodynamic the forces drag ofbetween the front single-element wing. Hence, and there multi-element are no contraindicati configurationsons of the is still use higher. of endplates. Meanwhile, the flaps are anSeveral effective conclusions way to extremely can be extracted increase fromthe generated the aerodynamic downforce, investigation: but its introduction the endplates generates increase an increasethe overall in aerodynamicthe drag of higher performance magnitude, of the decreasing wing, increasing the aerodynamic the downforce efficiency. and decreasing Nonetheless, the drag the flapsof the proved front wing. to be Hence,a better there tool to are increase no contraindications the downforce of generated the use of in endplates. the wing than Meanwhile, the attack the angle flaps increment,are an effective which way derives to extremely from the increasestill-higher the growth generated of drag downforce, and a possible but its wing introduction stall, an extremely generates undesiredan increase phenomenon. in the drag of higher magnitude, decreasing the aerodynamic efficiency. Nonetheless,

Fluids 2020, 5, 237 14 of 23 the flaps proved to be a better tool to increase the downforce generated in the wing than the attack angle increment, which derives from the still-higher growth of drag and a possible wing stall, an extremely undesired phenomenon.

3.2.2. Influence of Flaps and Endplates in the Structural Performance of the Wings The structural analysis of the four baseline configurations is performed through FEA methods. All the configurations possess a structure based on five ribs, five spars and a skin. Additionally, the structural components of the flaps of the three-element configurations are designed with a scale factor proportional to the chord length. The material employed in the structural components is aluminium alloy 2024 T3, the most extended material for aircraft wings [48]. The deformation of the wing follows a linear distribution from the nose ligature to the wingtip. The deformation possesses higher gradient in the trailing edge than in the leading edge. Therefore, the deformation of the configurations is analysed in the upper part of the trailing edge (Figure9). The one-element configuration without endplates (Figure9a) presents a maximum deformation of 4.28 mm. With the introduction of endplates (Figure9b), this deformation is increased by 28.73% (5.51 mm) but followed the same distribution. The three-element configuration without endplates (Figure9c) experiences an important increment of 44.85% in the maximum deformation of the main element due to the increase in aerodynamic forces in the wing. However, the most critical feature of the configuration is the maximum deformation in the secondary flap (110.25 mm). This element, although present in smaller loads in its surface, suffers the effects of the components scaling without a reduction in spanwise size (increasing the aspect ratio). This configuration is unacceptable because the secondary flap crashes with the primary flap (distance between elements of 16.27 mm and overlapping of 35.46%). Finally, the introduction of endplates in the multi-element configuration (Figure9d) provokes a di fferent structural behaviour. Firstly, it is noticeable than the deformation of all elements along the spanwise direction is not proportional, and hence the position of the maximum relative distance between elements is located at y = 0.55 m. Secondly, the maximum deformation of the second flap (7.68 mm) is located at y = 0.743 m, and in the main element and primary flap, it is located in the wingtip (6.84 and 7.14 mm, respectively). Lastly, the deformation in the endplate ligature is different for each element (6.84, 7.14 and 7.27 mm) because the endplate is undergoing an internal deformation along the Z-direction. This deformation comes from the high normal loads (traction) provoked by the difference in deformations of the wing elements in the configuration without endplates (Figure9c). Hence, the introduction of endplates in a multi-element configuration generates a new mechanical ligature between the wing elements, and hence the behaviour of the wings is analogous to a bi-embedded beam with some differences: Firstly, the endplate is a ligature between the elements but its position is not fixed, and secondly, the low thickness of the endplate derives from internal deformations. Therefore, the maximum deformation of the elements is not necessarily in the wingtip, and also its deformation in the wingtip is not certainly the same.

3.3. Structural Analysis of Front Wing Components The structural investigation consists of analysing the structural behaviour of the internal wing components: spars, ribs and skin. The degrees of freedom of the structural design are the number of ribs (A = 3, B = 5, C = 9 and D = 17), rib thickness (A = 2.5 mm, B = 5 mm, C = 10 mm and D = 20 mm), the circular holes implemented in the ribs (A = without holes, B = 20%, C = 40%, D = 60% and E = 80%), the number of spars (A = 4, B = 5 and C = 8), spar size (A = 20%, B = 40%, C = 60% and D = 80%), spar root width (A = 5%, B = 10% and C = 20%), spar head length (A = 10%, B = 50% and C = 100%), spar head width (A = 5%, B = 10% and C = 20%) and skin thickness (A = 0.5 mm, B = 1 mm, C = 1.5 mm, D = 2 mm and E = 2.5 mm). A total of 129,600 combinations were achieved from the investigation of the structural components to the posterior sensitivity analysis. Fluids 2020, 5, x 14 of 23

3.2.2. Influence of Flaps and Endplates in the Structural Performance of the Wings The structural analysis of the four baseline configurations is performed through FEA methods. All the configurations possess a structure based on five ribs, five spars and a skin. Additionally, the structural components of the flaps of the three-element configurations are designed with a scale factor proportional to the chord length. The material employed in the structural components is aluminium alloy 2024 T3, the most extended material for aircraft wings [48]. The deformation of the wing follows a linear distribution from the nose ligature to the wingtip. The deformation possesses higher gradient in the trailing edge than in the leading edge. Therefore, the deformation of the configurations is analysed in the upper part of the trailing edge (Figure 9). The one-element configuration without endplates (Figure 9a) presents a maximum deformation of 4.28 mm. With the introduction of endplates (Figure 9b), this deformation is increased by 28.73% (5.51 mm) but followed the same distribution. The three-element configuration without endplates (Figure 9c) experiences an important increment of 44.85% in the maximum deformation of the main element due to the increase in aerodynamic forces in the wing. However, the most critical feature of the configuration is the maximum deformation in the secondary flap (110.25 mm). This element, although present in smaller loads in its surface, suffers the effects of the components scaling without a reduction in spanwise size (increasing the aspect ratio). This configuration is unacceptable because the secondary flap crashes with the primary flap (distance between elements of 16.27 mm and overlapping of 35.46%). Finally, the introduction of endplates in the multi-element configuration (Figure 9d) provokes a different structural behaviour. Firstly, it is noticeable than the deformation of all elements along the spanwise direction is not proportional, and hence the position of the maximum relative distance between elements is located at y = 0.55 m. Secondly, the maximum deformation of the second flap (7.68 mm) is located at y = 0.743 m, and in the main element and primary flap, it is located in the wingtip (6.84 and 7.14 mm, respectively). Lastly, the deformation in the endplate ligature is different for each element (6.84, 7.14 and 7.27 mm) because the endplate is undergoing an internal deformation along the Z-direction. This deformation comes from the high normal loads (traction) provoked by the difference in deformations of the wing elements in the configuration without endplates (Figure 9c). Hence, the introduction of endplates in a multi-element configuration generates a new mechanical ligature between the wing elements, and hence the behaviour of the wings is analogous to a bi- embedded beam with some differences: Firstly, the endplate is a ligature between the elements but its position is not fixed, and secondly, the low thickness of the endplate derives from internal deformations.Fluids 2020, 5, 237 Therefore, the maximum deformation of the elements is not necessarily in the wingtip,15 of 23 and also its deformation in the wingtip is not certainly the same.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0E+0 0E+0

-1E-3 -1E-3 -2E-3 -2E-3

-3E-3 -3E-3 -4E-3 -4E-3

Z-Deformation (m) -5E-3 -5E-3

Fluids 2020, 5, x Z-Deformation (m) 15 of 23 -6E-3 -6E-3 Y-Position (m) Y-Position (m) Figure 9. Z-Position of the trailing edge along with spanwise direction in (a) one-element without (a) (b) endplates;0 0.1 (b 0.2) one-element 0.3 0.4 0.5 with 0.6 endplates; 0.7 0.8 ( 0.9c) three-element0 0.1without 0.2 endplates; 0.3 0.4 0.5(d) three-element 0.6 0.7 0.8 0.9 0E+0with endplates. 0E+0 -2E-2 -1E-2

-4E-2 3.3. Structural Analysis of Front Wing Components -2E-2 -6E-2 -3E-2 -8E-2The structural investigation consists of analysing the structural behaviour of the internal wing Z-Position (m) components:Z-Position (m) -1E-1 spars, ribs and skin. The degrees of freedom-4E-2 of the structural design are the number of Main Element Primary Flap Secondary Flap ribs (A-1E-1 = 3, B = 5, C = 9 and D = 17), rib thickness (A = 2.5-5E-2 mm, B = 5 mm, C = 10 mm and D = 20 mm), Y-Position (m) Y-Position (m) the circular holes implemented in the ribs (A = without holes, B = 20%, C = 40%, D = 60% and E = (c) (d) 80%), the number of spars (A = 4, B = 5 and C = 8), spar size (A = 20%, B = 40%, C = 60% and D = 80%), spar Figureroot width 9. Z-Position (A = 5%, of B the = 10% trailing and edge C = along20%), with spar spanwise head length direction (A = in10%, (a) one-elementB = 50% and without C = 100%), spar endplates;head width (b )(A one-element = 5%, B = with10% endplates;and C = 20%) (c) three-element and skin thickness without (A endplates; = 0.5 mm, (d) B three-element = 1 mm, C = 1.5 mm,with D = 2 endplates. mm and E = 2.5 mm). A total of 129,600 combinations were achieved from the investigation of the structural components to the posterior sensitivity analysis. FigureFigure 1010 providesprovides thethe variationvariation inin maximummaximum deformationdeformation andand structuralstructural weightweight inin thethe aforementionedaforementioned degrees of freedom.freedom. The parameters with more influenceinfluence in thethe deformationdeformation andand weightweight ofof thethe wingwing areare thethe skinskin thickness,thickness, ribrib thicknessthickness andand thethe numbernumber ofof ribs.ribs. On the opposite side, thethe widthwidth ofof thethe sparspar sectionsection and the circular holesholes implemented in the skin possess a low influence. influence. InIn termsterms ofof deformation–weightdeformation–weight ratio, the circularcircular holesholes oofferffer aa perfectperfect balancebalance becausebecause theythey reducereduce thethe weightweight withoutwithout anan increaseincrease inin deformation.deformation. All the data obtained were used as an inputinput ofof thethe structuralstructural sensitivitysensitivity analysisanalysis (Section(Section 3.53.5).).

140 Number of Ribs 80 Number of Ribs Rib Thickness Rib Thickness Circular Holes Size Circular Holes Size 120 Skin Thickness 70 Skin Thickness Number of Spars Number of Spars Spar Size Spar Size 100 Spar Root Width 60 Spar Root Width Spar Head Length Spar Head Length Spar Head Width Spar Head Width 80 50 % % 60 40

40 30

20 20

0 10

-20 0 ABCDEABCDE

(a) (b)

FigureFigure 10. 10. IncrementIncrement in weight in weight (a) and (a) reduction and reduction in deformation in deformation (b) according (b) according to the structural to the structuralconfiguration. configuration.

3.4. Analysis of Materials The three selected alloys (Titanium R54810, aluminium 2024 T3 and magnesium AZ31B), the carbon-reinforced composite (HS40-Epoxy) and the aramid-reinforced composite (Kevlar K149- Epoxy) were implemented in the structural components to analyse their performance. Both composite wovens were placed properly in each component to achieve the best efficacy. Additionally, due to the complex shape of the spars (I-section), the carbon-reinforced composite (HS40-Epoxy) and the aramid-reinforced composite (Kevlar K149-Epoxy) were discarded instead of implemented. The analysis of materials is decoupled for each structural component. Table 7 gives the weight and maximum deformation of the wing according to the component material. Due to the orthotropic properties of the fibre-reinforced composites, the most rigid material depends on the structural composites: the wing with ribs made of titanium R54810 possessed the Fluids 2020, 5, 237 16 of 23

3.4. Analysis of Materials The three selected alloys (Titanium R54810, aluminium 2024 T3 and magnesium AZ31B), the carbon-reinforced composite (HS40-Epoxy) and the aramid-reinforced composite (Kevlar K149-Epoxy) were implemented in the structural components to analyse their performance. Both composite wovens were placed properly in each component to achieve the best efficacy. Additionally, due to the complex shape of the spars (I-section), the carbon-reinforced composite (HS40-Epoxy) and the aramid-reinforced composite (Kevlar K149-Epoxy) were discarded instead of implemented. The analysis of materials is decoupled for each structural component. Table7 gives the weight and maximum deformation of the wing according to the component material. Due to the orthotropic properties of the fibre-reinforced composites, the most rigid material depends on the structural composites: the wing with ribs made of titanium R54810 possessed the minimum deformation (4.25 mm) and the wing with skin made of a carbon–epoxy composite achieved the minimum deformation (2.33 mm). The data obtained were the input of the structural sensitivity analysis.

Table 7. Weight and maximum deformation of the wing according to the materials employed.

Ribs Spars Skin Material Max. Def. Weight Max. Def. Weight Max. Def. Weight (mm) (kg) (mm) (kg) (mm) (kg) Aluminium 4.28 7.707 4.28 7.707 4.28 7.707 Titanium 4.25 8.421 4.03 8.413 2.74 10.585 Magnesium 4.32 7.234 4.47 7.248 6.51 5.778 Carbon–Epoxy 4.29 7.228 - - 2.33 5.738 Aramid–Epoxy 4.31 7.095 - - 4.05 5.234

Additionally, the mechanical investigation proved that skin is exposed to the highest normal loads, mainly in its mechanical ligature with the front bodywork. Furthermore, it is exposed to high-flexion stresses which directly depend on the number of ribs and spars and the skin thickness. Therefore, this is the component with the highest fluctuation according to the analysed configuration. The ribs, the component whose main target is to transmit loads from the skin to the spars, is the structural element most exposed to normal stresses of compression. Lastly, due to the overall structural behaviour of the 2022 front wing, similar to a bi-embedded beam, the spars are the component most exposed to shear stresses.

3.5. Sensitivity Analysis of Wing Structure The geometrical design and materials of the structural components of the Formula One 2022 front wing are selected through a sensitivity analysis. The objective is to design the lightest structure whose maximum deformation is lower than 2 mm in the most deformed position. The degrees of freedom are the number of ribs, rib thickness, the circular holes implemented in the ribs, the number of spars, spar size, spar root width, spar head length, spar head width, skin thickness, spar material, ribs material and skin material. The sensitivity analysis performed in each wing element is decoupled, and therefore a total of 29.16 million combinations are possible. The selection of the most suitable wing structural components can be summarised in three steps. The first step consists of setting the most rigid combination of each degree of freedom. Thereby, it is possible to obtain the least deformed structure inside the structural and material combinations analysed. This value is equal to 1.61 mm in the main element, 1.68 mm in the primary flap and 1.80 mm in the secondary flap. Once a preliminary structure satisfying the deformation limitation established in the objectives (2 mm) is obtained, the reduction in weight is carried. The second step consists of obtaining the weight-deformation variation gradient, shown in Table8. These values are achieved through several applied mathematics relationships between sequential Fluids 2020, 5, 237 17 of 23 configurations in each degree of freedom of the data obtained (Figure 10). Hence, the values provided represent the sensitivity of the wing in terms of deformation and weight when a lighter combination is implemented. As can be observed, the best measure to implement in the structure is the introduction of circular holes in the structure, which reduces the structural weight without an increase in deformation. Other good measures are the introduction of lighter materials in the ribs and the reduction in rib thickness. On the contrary, the reduction in the skin thickness, spars size and the introduction of lighter materials in the skin are the worst measures to reduce structural weight.

Table 8. Weight-deformation variation gradient of the entire wing according to the sequential combination in each degree of freedom.

Parameter i1 i2 i2 i3 i3 i4 i4 i5 → → → → ∂W/∂def ∂W/∂def ∂W/∂def ∂W/∂def Number of ribs 2.1736 1.6456 0.9305 - Rib thickness 3.3456 3.3726 1.9640 - Rib circles ∞ ∞ ∞ ∞ Number of spars 1.2502 1.1961 - - Spars size 0.5920 0.8885 0.5606 - Spar root width 2.8754 2.4763 - - Spar head length 1.0638 0.9743 - - Spar head width 2.2526 1.0046 - - Skin thickness 0.6954 0.6062 0.7233 0.3456 Spars material 1.3632 1.3423 - - Ribs material 10.9533 66.1858 18.1257 - Skin Material 0.1195 1.6456 0.9305 -

Once the gradient table is made, the methodology of the sensitivity analysis consists of selecting the combinations with the highest gradient until the maximum established deformation value is reached. Two main restrictions are applied to ensure the viability and robustness of the model. Firstly, the sensitivity analysis is performed sequentially. Secondly, if the highest gradient variation provokes a higher maximum deformation than the applied restriction, it is discarded and the next highest gradient is implemented. The features of the selected mechanical components of the main element and flaps are presented in Table9, including the expected deformation.

Table 9. Features of the structural elements of each wing, including deformation.

Parameter Main Element Primary Flap Secondary Flap Number of ribs 17 17 17 Rib thickness mm 5 5 20 Rib circles % 80 80 80 Number of spars 8 8 8 Spars size mm 80 80 80 Spar root width % 10 20 20 Spar head length % 100 100 100 Spar head width % 10 20 5 Skin thickness mm 2.5 2.5 2.5 Spars material Titanium R54810 Titanium R54810 Titanium R54810 Aramid Aramid Aramid Ribs material K149-Epoxy K149-Epoxy K149-Epoxy Carbon Carbon Carbon Skin material HS40-Epoxy HS40-Epoxy HS40-Epoxy Expected mm 1.98 1.98 1.97 Deformation Fluids 2020, 5, 237 18 of 23

3.6. Formula One 2022 Front Wing Finally, the aerodynamic and structural parametrical studies of the designed 2022 front wing (Section 2.1.2) are carried out. The aerodynamic performance of the 2022 wing is evaluated through the distribution of pressures in the wing and the aerodynamic coefficients. Comparing them with the baseline three-element configuration with endplates, it is possible to understand and assess how 2022 technical rules influence the front wing performance. The structural analysis is carried out with the structural components selected in Section 3.5 and shown in Figure 11. Fluids 2020, 5, x 18 of 23

Figure 11. Selected structural components of the Formula One 2022 front wing. Figure 11. Selected structural components of the Formula One 2022 front wing.

FigureDue to 12 the provides geometric the complexity distribution of of the pressure front wing, in the each lower element and upper was designed surfaces inof detail:the front each wing rib elements.possesses The a particular pressure shape, field, and,which consequently, possesses al thel the relative aerodynamic measures phenomena and dimensions explained used in to Section design 3.2.1,the spars presents and some circular interesting holes are features different. to Inanalyse. order Firstly, to achieve the maximumlow-pressure structural region performance,in the lower surfaceeach spar of andthe main hole waselement designed has a specificallybigger magnit to matchude and the its position adverse assigned gradient and along their the dimensions spanwise directionwere set is based slower. on theThe ribreason thickness behind of this each performa position.nce Hence, is the increment each one ofof thechord 51 and aramid-epoxy attack angle ribs, in the21 titaniumcentral sections spars and of 306the circularwing. Therefore, holes possesses the 2022 unique wing dimensions. does not present the minimum pressure near theFigure front 12 bodywork provides the(it is distribution located at 0.47 of pressures). Besides, in thethe lowervolume and assigned upper for surfaces the front of thewing front in thewing Article elements. A21 of The the pressure2022 FIA field,Formula which One possesses regulations all possesses the aerodynamic a negative phenomena dihedral angle explained from iny =Section 0.125 m 3.2.1 to y, presents= 0.900 m some of φ interesting = 2.586°. Hence, features the to airfoils analyse. loca Firstly,ted near the the low-pressure airfoil possess region a smaller in the distancelower surface to the of asphalt, the main rising element the ground has a bigger effect. magnitude Lastly, the and rear its part adverse of the gradient upper surface along the of the spanwise main elementdirection near is slower. the wingtips The reason possesses behind negative this performance manometric is the pressure. increment This of is chord the consequence and attack angle of the in maximisationthe central sections of the area of the allowed wing. by Therefore, the regulation the 2022s and wing the endplate does not design. present However, the minimum although pressure this isnear an undesired the frontbodywork effect, the maximisation (it is locatedat of0.47 the area s). Besides, allows very the volumehigh negative assigned pressures for the in front the leading wing in edgethe Article of the A21wing of near the 2022the wingtip. FIA Formula Besides, One the regulations benefits of possesses the area maximisation a negative dihedral near the angle wingtip from possess a higher magnitude than the negative effects of the excessive overlapping. y = 0.125 m to y = 0.900 m of ϕ = 2.586◦. Hence, the airfoils located near the airfoil possess a smaller distance to the asphalt, rising the ground effect. Lastly, the rear part of the upper surface of the main element near the wingtips possesses negative manometric pressure. This is the consequence of the maximisation of the area allowed by the regulations and the endplate design. However, although this is an undesired effect, the maximisation of the area allows very high negative pressures in the leading edge of the wing near the wingtip. Besides, the benefits of the area maximisation near the wingtip possess a higher magnitude than the negative effects of the excessive overlapping.

(a) (b)

Figure 12. Pressure field in lower (a) and upper (b) surfaces of the Formula One 2022 front wing. Fluids 2020, 5, x 18 of 23

Figure 11. Selected structural components of the Formula One 2022 front wing.

Figure 12 provides the distribution of pressure in the lower and upper surfaces of the front wing elements. The pressure field, which possesses all the aerodynamic phenomena explained in Section 3.2.1, presents some interesting features to analyse. Firstly, the low-pressure region in the lower surface of the main element has a bigger magnitude and its adverse gradient along the spanwise direction is slower. The reason behind this performance is the increment of chord and attack angle in the central sections of the wing. Therefore, the 2022 wing does not present the minimum pressure near the front bodywork (it is located at 0.47 s). Besides, the volume assigned for the front wing in the Article A21 of the 2022 FIA Formula One regulations possesses a negative dihedral angle from y = 0.125 m to y = 0.900 m of φ = 2.586°. Hence, the airfoils located near the airfoil possess a smaller distance to the asphalt, rising the . Lastly, the rear part of the upper surface of the main element near the wingtips possesses negative manometric pressure. This is the consequence of the maximisation of the area allowed by the regulations and the endplate design. However, although this is an undesired effect, the maximisation of the area allows very high negative pressures in the leading Fluids 2020, 5, 237 19 of 23 edge of the wing near the wingtip. Besides, the benefits of the area maximisation near the wingtip possess a higher magnitude than the negative effects of the excessive overlapping.

(a) (b)

Fluids 2020Figure, 5, x 12. Pressure field in lower (a) and upper (b) surfaces of the Formula One 2022 front wing. 19 of 23 Figure 12. Pressure field in lower (a) and upper (b) surfaces of the Formula One 2022 front wing. Figure 13 gives the pressure distribution of the 2022 front wing in the sections 0.05 and 0.95 s. Figure 13 gives the pressure distribution of the 2022 front wing in the sections 0.05 and 0.95 s. Focused in the airfoils located near the front bodywork, the minimum pressure in the lower surface Focused in the airfoils located near the front bodywork, the minimum pressure in the lower surface is is achieved near the leading edge (0.0617c), where it achieves a peak of −27,100 Pa. After this position, achieved near the leading edge (0.0617c), where it achieves a peak of 27,100 Pa. After this position, the lower surface experiences a pressure increment of constant gradient− until the trailing edge, where the lower surface experiences a pressure increment of constant gradient until the trailing edge, where it it reaches a value of −6711.3 Pa. Its behaviour is slightly different from the baseline three-element reaches a value of 6711.3 Pa. Its behaviour is slightly different from the baseline three-element configuration with −endplates, where the peak in minimum pressure is located in a more convex configuration with endplates, where the peak in minimum pressure is located in a more convex surface, but with a noticeably slower peak (−22,602.3 Pa). However, the upper surface of the main surface, but with a noticeably slower peak ( 22,602.3 Pa). However, the upper surface of the main element and the flaps possess similar aerodynamic− features. The airfoils near the wingtip presents element and the flaps possess similar aerodynamic features. The airfoils near the wingtip presents the the worst aerodynamic performance for three reasons: they possess a low attack angle (α = 13.02°) worst aerodynamic performance for three reasons: they possess a low attack angle (α = 13.02 ) and and chord (c = 554.29 mm), they are influenced by the negative effects of the wingtip, and◦ the chord (c = 554.29 mm), they are influenced by the negative effects of the wingtip, and the overlapping overlapping between elements reaches a critical value. Hence, its minimum pressure is highly between elements reaches a critical value. Hence, its minimum pressure is highly affected and the affected and the upper surface of the main element reaches negative manometric pressures after 50% upper surface of the main element reaches negative manometric pressures after 50% of the chord. of the chord.

-4.5 -4.5 Main Element Main Element First Flap First Flap -3.5 -3.5 Second Flap Second Flap ) ) P P

-2.5 -2.5

-1.5 -1.5

-0.5 -0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Pressure Coefficient (C Pressure Coefficient (C

0.5 0.5

1.5 1.5 X Coordinate (%c) X Coordinate (%c)

(a) (b)

Figure 13. Pressure distribution in th thee three elements of the 2022 F1 front wing at sections: ( (aa)) 0.05 0.05 s; s; (b) 0.95 s.

The most important parameter to analyse is the Z-direction deformation (Figures 14 and 15). Due to the complex shape of the wing, the deformation does not follow an exactly linear path. The maximum relative deformation between components is 0.31 mm at Y = 0.453 m. This low number ensures the negligible variation in aerodynamic performance under big loads because the elements possess an extremely small variation according to the optimised gap and overlapping between elements. The maximum deformation of the main element, primary flap and the secondary flap is 2.26, 2.19 and 2.24 mm, respectively. Comparing these deformations with the expected deformations (Table 9), the difference is 14.14%, 10.66% and 13.70%. These differences are mainly originated by the particular features of the 2022 high-performance front wing. Additionally, using the gradient method it is possible to know the best way to reduce the deformation or to reduce the structural weight in each element, depending on the engineering purposes. In this development, a target of maximum deformation in the wing of 2 mm was established, but there is not a general requirement. Moreover, the velocity employed in the analysis was the historical maximum velocity achieved by a Formula One car, and hence the designed structure satisfies the established target in most of the tracks. Due to all these reasons, there is not any advantage of modifying and generating a new structural design. Fluids 2020, 5, 237 20 of 23

The most important parameter to analyse is the Z-direction deformation (Figures 14 and 15). Due to the complex shape of the wing, the deformation does not follow an exactly linear path. The maximum relative deformation between components is 0.31 mm at Y = 0.453 m. This low number ensures the negligible variation in aerodynamic performance under big loads because the elements possess an extremely small variation according to the optimised gap and overlapping between elements. The maximum deformation of the main element, primary flap and the secondary flap is 2.26, 2.19 and 2.24 mm, respectively. Comparing these deformations with the expected deformations (Table9), the difference is 14.14%, 10.66% and 13.70%. These differences are mainly originated by the particular features of the 2022 high-performance front wing. Additionally, using the gradient method it is possible to know the best way to reduce the deformation or to reduce the structural weight in each element, depending on the engineering purposes. In this development, a target of maximum deformation in the wing of 2 mm was established, but there is not a general requirement. Moreover, the velocity employed in the analysis was the historical maximum velocity achieved by a Formula One car, and hence the designed structure satisfies the established target in most of the tracks. Due to all these reasons, there is notFluids any 2020 advantage, 5, x of modifying and generating a new structural design. 20 of 23

Fluids 2020, 5, x 20 of 23 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0E+00 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0E+00 Main Element -5.0E-04 MainFirst Element Flap -5.0E-04 FirstSecond Flap Flap -1.0E-03 Second Flap -1.0E-03 -1.5E-03 -1.5E-03 Deformation (m)

-2.0E-03Deformation (m) -2.0E-03

-2.5E-03 -2.5E-03 Y Position (m) Y Position (m)

Figure 14. Z-deformation in the trailing edge of the Formula One 2022 front wing. FigureFigure 14. 14.Z-deformation Z-deformation in in the the trailing trailing edgeedge ofof the Formula One One 2022 2022 front front wing. wing.

FigureFigure 15. 15. Z-deformation Z-deformation measured measured inin metersmeters ofof the Formula One One 2022 2022 front front wing. wing.

4. Conclusions 4. Conclusions ThisThis research research provides provides interestinginteresting interesting observationsobservationsobservations regardingregarding the the aerodynamic aerodynamicaerodynamic and and structural structuralstructural performanceperformance of ofmulti-element multi-element multi-element wings wings wings with with wingtip wingtip wingtip devicesdevices devices that that can can bebe be usefuluseful useful to to readers toreaders readers fascinated fascinated fascinated by by byFormulaFormula One One One aerodynamic aerodynamic aerodynamic devices devices devices and and and readers readers readers intereintere interestedstedsted in building in building theirtheir their own own own wing wing wing who who who want want want to to have a starting point to analyse the structural behaviour of the wing, such as Formula Student tohave have a starting a starting point point to toanalyse analyse the the structural structural behaviour behaviour of of the the wing, wing, such such as Formula StudentStudent engineers. Besides, the research brings knowledge about the influence of the 2022 FIA Formula One engineers. Besides, the research brings knowledg knowledgee about the influenceinfluence of the 2022 FIA Formula One regulations on the wing performance. regulations onon thethe wingwing performance.performance. Several conclusions about multi-element structural designs can be achieved. Firstly, the Several conclusions conclusions about aboutmulti-element multi-element structural designs structural can be designsachieved. Firstly, can the be achieved.deformationFirstly, of the a wing deformation is extremelyof a wingaffected is extremely by the aspect affected ratio, by and the aspecttherefore, ratio, in anda three-element therefore, in a deformationwing, the ofsecondary a wing isflap extremely suffers aaffected bigger bydeform the aspectation, whichratio, andneeds therefore, to be compensated in a three-element with wing,structural the secondary components flap or materialssuffers a of bigger higher deformrigidity.ation, In this which research, needs the second to be flapcompensated possesses four with structuraltimes more components aspect ratio or materials than the of main higher element rigidity. (7.2 In vs. this 1.8) research, which thederives second from flap a possessesvariation fourin timesmaximum more aspectdeformation ratio 17.81than timesthe main (110.25 element vs. 6.19 mm)(7.2 vs.when 1.8) they which possess derives the same from components a variation and in maximummaterials. deformation Secondly, the 17.81 endplates times (110.25 create vs.a mechan 6.19 mm)ical when ligature they between possess the the elements same components of the wing, and materials.changing Secondly, their mechanical the endplates behaviour create from a mechan an embeddedical ligature beam between to a bi-embedded the elements beam. of the When wing, changingwingtip their devices mechanical are employed, behaviour the wing from element an embeddedof lower aspect beam ratio to (1.8) a bi-embedded experiences an beam. increasing When wingtiplight deformation devices are employed,(from 6.19 to the 6.84 wing mm), element and the of el loementwer aspectwith a higherratio (1.8) aspect experiences ratio (7.2) anexperiences increasing lighta remarkable deformation decreasing (from 6.19 deformation to 6.84 mm), (from and 110.25 the el toement 7.68 mm)with Additionally, a higher aspect this ratio mechanical (7.2) experiences ligature a remarkableis mobile, and decreasing consequently deformation the position (from of 110.25 the maximum to 7.68 mm) deformation Additionally, of the thiswings mechanical is located ligaturein the is mobile,secondary and flap consequently at 0.743 s andthe positionnot in the of centrethe maximum of the wingspan deformation width. of theRegarding wings isthe located structural in the secondarycomponents, flap theat 0.743best ways and to reducenot in weightthe centre in a ofwing the is wingspan to introduce width. circular Regarding holes in thethe centrestructural of components,the ribs, because the best this way does to not reduce affect weight the deformatio in a wingn. Besides,is to introduce the skin circular thickness holes in a wingin the made centre of of thespars, ribs, becauseribs and thisskin doespossesses not affect a high the influence deformatio on then. deformationBesides, the (12.52skin thickness mm when in skin a wing thickness made is of spars,0.5 mm,ribs andand skin3.56 mmpossesses when skina high thickness influence is 2.5 on mm)the deformation and the weight (12.52 (4.013 mm kg when when skin skin thickness thickness is is 0.5 mm, and 8.958 kg when skin thickness is 2.5 mm) of the wing. Lastly, it is possible to apply the 0.5 mm, and 3.56 mm when skin thickness is 2.5 mm) and the weight (4.013 kg when skin thickness is 0.5 mm, and 8.958 kg when skin thickness is 2.5 mm) of the wing. Lastly, it is possible to apply the Fluids 2020, 5, 237 21 of 23 three-element wing, the secondary flap suffers a bigger deformation, which needs to be compensated with structural components or materials of higher rigidity. In this research, the second flap possesses four times more aspect ratio than the main element (7.2 vs. 1.8) which derives from a variation in maximum deformation 17.81 times (110.25 vs. 6.19 mm) when they possess the same components and materials. Secondly, the endplates create a mechanical ligature between the elements of the wing, changing their mechanical behaviour from an embedded beam to a bi-embedded beam. When wingtip devices are employed, the wing element of lower aspect ratio (1.8) experiences an increasing light deformation (from 6.19 to 6.84 mm), and the element with a higher aspect ratio (7.2) experiences a remarkable decreasing deformation (from 110.25 to 7.68 mm) Additionally, this mechanical ligature is mobile, and consequently the position of the maximum deformation of the wings is located in the secondary flap at 0.743 s and not in the centre of the wingspan width. Regarding the structural components, the best way to reduce weight in a wing is to introduce circular holes in the centre of the ribs, because this does not affect the deformation. Besides, the skin thickness in a wing made of spars, ribs and skin possesses a high influence on the deformation (12.52 mm when skin thickness is 0.5 mm, and 3.56 mm when skin thickness is 2.5 mm) and the weight (4.013 kg when skin thickness is 0.5 mm, and 8.958 kg when skin thickness is 2.5 mm) of the wing. Lastly, it is possible to apply the superposition principle in a structural design, allowing the analysis of millions of configurations with accurate results. The 2022 Formula One regulations have a big influence on the aerodynamic and structural performance of the front wing. Firstly, they provoke a bad aerodynamic performance near the wingtip due to the new endplates and their influence on the bidimensional configuration of the wing near the endplate. Secondly, the designed 2022 front wing presents a minimum pressure at 0.47s due to the volume assigned in the Article A21 of the 2022 FIA Formula One regulations: the wing possesses a negative dihedral angle from y = 0.125 m to y = 0.900 m of ϕ=2.586º, increasing the ground effect and, additionally, the central sections have a higher chord and attack angle. Lastly, the flaps of the 2022 F1 undergo deformations and stresses of remarkably lower magnitude than embedded flaps (2020 front wing style), something observed in the baseline configurations.

Author Contributions: Z.A.R. and X.C. performed investigations into the concept. X.C. performed numerical analysis and mesh generation. X.C. obtained the results and performed analysis and visualisations. Z.A.R. provided supervision and guidance to the whole research, including analysis of data and post-processing. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: All the simulations are performed using Cranfield High-Performance Computing Cranfield HPC) facility. We acknowledge the support received from Mick Knaggs from Cranfield HPC during the simulation process. Conflicts of Interest: The authors declare no conflict of interest.

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