energies

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

Krzysztof Kurec * and Janusz Piechna Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24, 00-665 Warsaw, Poland; [email protected] * Correspondence: [email protected]



Received: 23 October 2019; Accepted: 6 December 2019; Published: 10 December 2019


Abstract: This paper discusses the capabilities of side spoilers to improve the aerodynamic properties of a sports car exposed to a non-zero yaw angle flow. In such conditions, the aerodynamic drag and lift both increase with the introduction of a side force and a yawing moment, which contribute to the decrease of the car’s handling properties and force the car to change its driving path. Elements mounted on the side of the car make it possible to obtain an asymmetric aerodynamic load distribution and generate additional forces that can be used to counter these effects. The performance of the side spoilers was analyzed at yaw angles ranging from 0◦ to 15◦ using the results of numerical calculations. It was established that the side spoilers made it possible to generate at low yaw angles aerodynamic forces that exceeded those caused by a crosswind.

Keywords: CFD; automobile aerodynamics; active aerodynamics; side spoilers; crosswind

1. Introduction Analysis of the aerodynamic properties of vehicles is most often performed for a yaw angle equal to zero degrees, which corresponds to an airflow perpendicular to the front of a vehicle. In recent years, more studies have focused on the influence of more complex flow conditions at different yaw angles. Non-zero yaw angle flows play a key role in analyzing issues such as fuel economy, wind sensitivity, and cornering. Investigations of a vehicle subjected to a crosswind have been undertaken with various approaches depending on the investigated scenario. Where experimental methods are concerned, traditional wind tunnel setups make it possible to take measurements under steady-state conditions for different yaw angles, as analyzed in [1]. Unsteady conditions with continuous yawing were studied with the wind tunnel configuration presented in [2], whereas the wind tunnel configuration used in [3,4] makes it possible to study the effects of crosswind gusts. Road tests and tests in facilities equipped with wind generator units are another form of investigation [5]. The use of numerical calculations not only makes it possible to study the effects of real-world wind conditions [6] but also makes it possible to investigate the aerodynamic properties of a vehicle in a steady-state crosswind [7]. The most complex simulations include the influence of a crosswind gust on the movement of a vehicle [8–10], as well as an analysis of the aerodynamic properties of a car during dynamic maneuvers as performed in [11,12]. The need for considering ambient conditions that often involve non-zero yaw angles while performing studies on drag is emphasized in [13]. The yaw that occurs when a vehicle is subjected to a crosswind leads to an increase of the drag and affects fuel economy, and it is very rare that a car is not subjected to these kinds of disturbances. Aerodynamic characteristics of several different cars over a range of yaw angles are presented in [14], where the variation in these characteristics between different vehicles is reported. A rapid increase of the drag coefficient, together with the increase of yaw angle, leads to much higher fuel consumption in comparison with the case when only a zero yaw

Energies 2019, 12, 4697; doi:10.3390/en12244697 www.mdpi.com/journal/energies Energies 2019, 12, 4697 2 of 22 angle is considered. In [15], the flow around a hatchback at a zero and at a four-degree yaw angle was analyzed to make sure that a slight increase of the yaw angle is not followed by a significant increase of the drag. The non-zero yaw angle also plays a very important role in the analysis of the performance of sports cars. In [16], a National Association for Stock Car Auto Racing (NASCAR) race car under various yaw configurations was investigated, and more studies on this car can be found in [17–20]. In [21], flaps on the roof of a NASCAR race car are described. These flaps automatically open when the car is at a yaw angle, which indicates that the car is spinning out of control and, as a result, the flaps are used to reduce lift generated on the car body, by non-zero yaw angle flow conditions, to prevent liftoff. An investigation of a sprint car—a race car that is specially adapted for driving on curves—is presented in [22]. This type of race car features large wings with asymmetrical side plates that improve its performance during cornering. Not only are the actual ambient conditions very important but also the perception of the ambient conditions by the driver and his reactions are very important. In [23], the authors described that short, strong, and sudden bursts of wind gusts cause the biggest course deviations; however, they are directed towards the wind and are the results of steering input, which is too high and delayed. The yawing moment is a key factor influencing vehicle behavior, whereas the side force affects the driver’s perception of wind strength [24]. In [25], the authors investigated by means of experiments and calculations how certain parts of a car can influence its handling while it is driving through a crosswind zone. It was proven that the use of modified aerodynamic parts made it possible to decrease the number of corrective steering maneuvers that had to be undertaken to maintain the desired driving line. The key factors of car body shape in the generation of side forces are listed in [24]; however, it is also noted in [24] that the constraints imposed by designers make it difficult to implement changes in a completed car design that would significantly affect the sensitivity of a vehicle to a crosswind. In [26], devices are proposed that modify the flow around the leeward side of the front bumper of a one-box type car to minimize the yaw moment, namely, a chin spoiler that detaches the flow under the bumper and a side spoiler that promotes separation to the side of the bumper. An internal duct in the front bumper is investigated in [27], which is active only when a crosswind is present and which uses the air collected at the front of the bumper to separate the flow at its side. The most effective device led to a reduction of the yaw moment up to 44%. An asymmetric aerodynamic configuration was used in [28] to investigate vehicle sensitivity to external disturbances and how rear side spoilers can improve the handling of a car by clearly defining where flow separation takes place. The authors of this paper investigated the idea of equipping a car with active aerodynamic devices that, when needed, would make it possible to change a car’s side force and yaw moment coefficients to aid its handling properties. A similar idea was investigated by the designers of the concept car Mitsubishi HSR II. This car was equipped with active aerodynamic devices that made it possible to obtain an asymmetrical aerodynamic setup, which consisted of a canard wing and a rear flap deployed on the side of the car closer to the inner side of a turn [29]. These elements made it possible to generate not only an additional downforce but also a side force that aided cornering. However, the change of the side force coefficient reported in [29] was very small and only reached 0.02 during the experimental investigations, meaning that its contribution to the car’s handling properties was very limited. Such a system is interesting to consider, especially today, when active aerodynamic devices are becoming increasingly widespread, with some examples given in [30]. The aim of this paper is to investigate how the side force and yawing moment of a car can be influenced by the use of side spoilers and whether they are capable of countering the effects of a steady-state crosswind. The side spoilers investigated are intended to work as active aerodynamic elements used only when needed. Due to the steady-state investigations, the phase during which the spoilers were ejected from the car body was omitted. This study focuses on the phenomena that can be Energies 2019, 12, 4697 3 of 22 observed in a steady state by assuming that the side spoilers were activated for at least several seconds to counter the effects of the steady-state crosswind.

2. Materials and Methods The car body geometry used in this study represents the Honda CR-X del Sol, a Targa top sports car. The reason for choosing this particular car was the similarity of its key features to the early prototype versions of the Arrinera Hussarya, a recently developed Polish supercar. The Honda CR-X del Sol was used as a testing platform for the active aerodynamic elements being developed. The authors of this paper previously used the Honda CR-X del Sol car body to test a variety of traditional aerodynamic configurations consisting of a rear wing and a spoiler mounted on the trunk at different inclination angles [31–34].Energies The 2019 previous, 12, x FOR PEER investigations REVIEW focused on the change of the drag and lift3 coe of 21ffi cients and included experimentalThe car resultsbody geometry that wereused in used this study to validate represents CFDthe Honda calculations. CR-X del Sol, a Targa top sports Two locationscar. The of reason the side for choosing spoilers this were particular taken car into was account,the similarity the of parts its key of features the car to bodythe early that could be prototype versions of the Arrinera Hussarya, a recently developed Polish supercar. The Honda CR- used to slide themX del Sol in was are used colored as a testing blue platform in Figure for 1thea, active whereas aerodynamic the red elements lines markbeing developed. their axes The of rotation. It was decidedauthors to focus of this on paper rotational previously elements used the Honda rather CR-X than del Sol sliding car body ones to test because a variety of sliding traditional elements can be more proneaerodynamic to jamming. configurations The reasoning consisting of behind a rear wing choosing and a spoiler the mounted locations on the oftrunk the at sidedifferent spoilers was inclination angles [31–34]. The previous investigations focused on the change of the drag and lift to place themcoefficients at the front and included of the carexperimental body. Theresults main that were principle used to validate of operation CFD calculations. of these spoilers is that, while active, theyTwo induce locations an of increase the side spoilers in pressure were taken in frontinto account, of them the parts and of a the decrease car body inthat pressure could behind them, leadingbe to used the generationto slide them in of are a side colored force. blue Inin Fi addition,gure 1a, whereas the aerodynamic the red lines mark load their on axes the of side spoilers rotation. It was decided to focus on rotational elements rather than sliding ones because sliding and the modifiedelements pressure can be onmore the prone car to body jamming. also The lead reas tooning the behind generation choosing of the the locations yawing of the moment side that can either enhancespoilers its turning was to abilitiesplace them or at prevent the front itof fromthe car turning body. The away main fromprinciple the of drivingoperationline of these while affected by a crosswindspoilers. The is dimensions that, while active, of the they side induce spoilers an increa werese in chosenpressure in to front be as of largethem and as a possible decrease in while taking pressure behind them, leading to the generation of a side force. In addition, the aerodynamic load on into account thatthe side they spoilers have and to fitthe ontomodified the pressure car body. on the The car body spoiler also locatedlead to the at generation the quarter of the glassyawing was shaped to fill the areamoment where that the can quarter either enhance glass isits located,turning abilities whereas or prevent the spoilerit from turning on the away bumper from the was driving shaped to fill as much as possibleline while of affected the area by a on crosswind. the side The part dimensions of the bumper.of the side spoilers There were were chosen no optimization to be as large as techniques possible while taking into account that they have to fit onto the car body. The spoiler located at the used to designquarter these glass spoilers, was shaped and to fill it wasthe area assumed where the thatquarter making glass is lo themcated, whereas as large the asspoiler possible on the would be 2 enough to demonstratebumper was shaped their to potential. fill as much Theas possible area of of the the area quarter on the side glass part of spoiler the bumper. was There equal were to 0.095 m , and the area ofnothe optimization spoiler techniques on the bumper used to design was these equal spoilers, to 0.109 and itm was2. assumed Although that making the final them version as of the large as possible would be enough to demonstrate their potential. The area of the quarter glass spoiler spoiler on thewas bumper equal to turned 0.095 m2 out, and tothe have area of an the area spoiler larger on the bybumper 13% was than equal the to 0.109 quarter m2. Although glass spoiler, the both of these elementsfinal were version tailored of the spoiler to be on of the similar bumper size turned to ou maket to have it easier an area tolarger directly by 13% compare than the quarter their efficiency. The main dimensionsglass spoiler, of both the sideof thes spoilerse elementsare were presented tailored to be in of Appendix similar size Ato. make it easier to directly compare their efficiency. The main dimensions of the side spoilers are presented in Appendix A.

Quarter glass spoiler Cz Front bumper spoiler Cmz Cmx

Cmy Cx Cy

(a)

(b) (c)

Figure 1. (a) AFigure side 1. view (a) A of side the view Honda of the Honda CR-X CR-X del Sol,del Sol, blue blue color color marksmarks area area of the of theside sidespoilers, spoilers, and and the the red lines are the according rotational axes. Directions of the studied forces and moments are red lines are theincluded, according with the rotational axis placed axes. in the car’s Directions center of ofgravity. the studied(b) Isometric forces view andand (c moments) front view areof included, with the axis placedthe car with in the side car’sspoilers center at a different of gravity. angle of (rotab)tional Isometric (each marked view in and a different (c) front color view to make of it the car with side spoilers atmore a di clear).fferent Forces angle and moments of rotational coefficients: (each Cx (Dra markedg), Cy (Side), in a diCzff (Lift),erent Cmx color (Roll), to Cmy make (Pitch), it more clear). Cmz (Yaw). Forces and moments coefficients: Cx (Drag), Cy (Side), Cz (Lift), Cmx (Roll), Cmy (Pitch), Cmz (Yaw).

Energies 2019, 12, 4697 4 of 22

It was decided to first investigate how the additional side spoilers affect the aerodynamic properties at a 0◦ yaw angle and then to check how a positive yaw angle affects their properties. The side spoilers investigated in this paper were introduced to the windward side of the car, whereas most of the previously studied devices, such as the ones described in the introduction [26,27], were located on the leeward side. The main benefit of using this kind of device on the windward side is that it would be in direct contact with the flow. If it was placed on the leeward side and an unexpected detachment of the flow on the car body took place in front of it, then this element would become completely redundant. Placing these spoilers on the windward side increases the possibility that they will have the desired impact and makes their operation more predictable. The aerodynamic moment coefficients were established according to the car’s center of gravity located 0.51 m above the ground and 1.153 m from the first wheel making the car balance equal to 48.6%/51.4% front/rear for a fully-loaded car, which included the weight of passengers and baggage in the trunk. The placing of the coordinate system in Figure1a represents the position of the center of gravity. The procedure used in calculating the placement of the center of gravity for this particular car is presented in [33]. The first spoiler is located on the quarter glass (front vent glass) and its rotational axis is parallel to the A-pillar, enabling it to generate additional side force and downforce. Placing this element on the quarter glass enables it to move without jamming, whereas in cars lacking a quarter glass, the side mirror would block its movement. The second spoiler is placed between the front wheel and the bumper. In this location, high-performance cars have mounted canards, which increase the downforce on the front axle. The axis of rotation of this element was inclined at 20◦ degrees from the vertical, which, as in the case of the first element, enabled it to generate not only the side force but also the downforce. These forces are generated by the elements themselves after they are rotated, and are due to the change of the pressure distribution on the rest of the car body. It should be noted that, in the case of both of the locations of the described spoilers, these spoilers fit to certain kinds of car body shapes, especially shapes that have quarter glasses and bumper sides with the largest possible area. Looking at Figure1b,c, it can be seen that the spoiler mounted behind the A-pillar can be rotated by any degree within its range of rotation without any risk of hitting a car that might be next to it, whereas in the case of the spoiler mounted on the front bumper it can only be rotated to a certain degree before it starts to protrude sideways. This makes the quarter glass an interesting location for placing a side spoiler; however, a spoiler located on the quarter glass needs to be made from a transparent material to avoid obstructing the driver’s view. Calculations were performed in ANSYS® Fluent, version ANSYS® Academic Associate CFD, Release 16.2. Due to the fact that the calculations were performed at a velocity much smaller than Mach 1, the flow was modeled as incompressible, and the pressure-based solver was used [35]. Second-order upwind spatial discretization schemes were used to solve the moment, turbulent kinetic energy, and specific dissipation rate equations. Pressure equations were solved using a second-order scheme, whereas the gradients were calculated with the least square cell-based method. High order term relaxation was turned on to aid the second-order calculations. In each case, calculations were initialized with the values from the velocity inlet that were different depending on the yaw angle that was being investigated. The calculations were stopped when the residuals converged by at least three orders of magnitude, and at the same time, the values of lift, drag, and side forces reached a constant level. The domain used in calculations can be seen in Figure2a with all the boundary types colored according to the legend placed beneath the figure. A “moving wall motion” was set on the wheels to include the effects of their movement in the calculations. The velocity inlet boundary type was used on the inlet surfaces of the domain, whereas the pressure outlet was used on its exit. Two sides of the domain were declared as inlets and the other two as outlets to make investigations of the different yaw Energies 2019, 12, x FOR PEER REVIEW 5 of 21

Where crosswind conditions are concerned, a more accurate way to represent the flow conditions would be to use a sheared profile. However, it was presented in [7] that the use of a sheared profile gives very similar loads as in the case of a uniform profile in an example of the calculations of a DrivAer model [36] in a crosswind. Energies 2019The, symmetry12, 4697 boundary type was used to model a zero-shear slip flow on the ground to prevent5 of 22 the build-up of a boundary layer. The use of a zero-shear slip flow condition on the ground made it possible to expose the vehicle to the conditions defined on the inlet without being influenced by the angleseffects possible. of the build-up In each of case, the aboundary uniform velocitylayer on profilethe ground, was usedwhich with could a velocitybe different magnitude depending equal on to 40the m/ swidth across of the the whole calculational height domain. of the domain.

(c)

Yaw angle’s direction

(a) (b)

FigureFigure 2. 2.(a )(a The) The computational computational domain, domain, ( b(b)) mesh mesh on on the the symmetry symmetry plane,plane, ((cc)) close-upclose-up onon thethe mesh in thein boundary the boundary layer layer region. region. Type Type of of boundary boundary conditions: conditions: ■ velocity inlet, inlet, ■ pressurepressure outlet, outlet, ■ wall, wall,  symmetry.■ symmetry.

WhereA velocity crosswind magnitude conditions equal areto 40 concerned, m/s was chosen a more for accurate the calculations way to represent as it is within the flow the range conditions of wouldmaximum be to useallowable a sheared speeds profile. that a However, car may attain it was on presented a public road. in [7 ]In that most the countries, use of a shearedthe highway profile givesspeed very limit similar is between loads as 22 in m/s the and case 39 of m/s, a uniform whereas profile there in are an countries, exampleof such the as calculations Germany, ofthat a DrivAer have modelsections [36] of in highways a crosswind. without any speed limits. Such a high speed was chosen for the calculations due to the increase of aerodynamic forces that come together with an increase of speed, which means that The symmetry boundary type was used to model a zero-shear slip flow on the ground to prevent a sudden appearance of a side force or a yawing moment will have a greater impact on the car’s the build-up of a boundary layer. The use of a zero-shear slip flow condition on the ground made it handling than at lower driving speeds. possible to expose the vehicle to the conditions defined on the inlet without being influenced by the The pressure coefficient used in visualizations was defined as: effects of the build-up of the boundary layer on the ground, which could be different depending on the width of the calculational domain. 𝐶 =𝑝𝑝/0.5𝜌𝑉 (1)

whereA velocity the following magnitude parameters equal toare 40 static m/s pressure was chosen at a point for the (p calculations), reference static as it pressure is within (p theref = range0 Pa), of maximumair density allowable (ρ = 1.225 speeds kg/m3), that and areference car may velocity attain on (Vref a public= 40 m/s). road. In most countries, the highway speed limitThe coefficients is between of 22 mforces/s and and 39 moments m/s, whereas in the there relevant are countries, directions such were as obtained Germany, with that the have sectionsfollowing of highways formulas: without any speed limits. Such a high speed was chosen for the calculations due to the increase of aerodynamic forces that come together with an increase of speed, which means 𝐶,, =𝐹,,/0.5𝜌𝑉𝐴, (2) that a sudden appearance of a side force or a yawing moment will have a greater impact on the car’s handling than at lower driving speeds. 𝐶𝑚,, =𝑀,,/0.5𝜌𝑉𝐴𝑙, (3) The pressure coefficient used in visualizations was defined as: where the following parameters are force (F), moment (M), frontal area (A = 1.660 m2), the length   between the front and the rear axles (l = 2.364 m). In each case,2 the coefficients of forces and moments Cp = p p / 0.5ρV (1) were calculated using the same reference area,− whichre f refers tore the f frontal area of the car body without the side spoilers. where the following parameters are static pressure at a point (p), reference static pressure (p 0 Pa), The way the flow at a non-zero yaw angle was directed was depicted in Figure 2a. The domainref = 3 airwas density discretized (ρ = 1.225 with kg the/m use), and of te referencetrahedral velocityelements, (V andref = a40 mesh m/s). near the car body is presented in FigureThe coe2b. ffiTocients ensure of forcesthat the and mesh moments quality in thewas relevant adequate, directions the tetrahedral were obtained mesh prepared with the followingfor the formulas:   2 Cx,y,z = Fx,y,z/ 0.5ρVre f A , (2)   2 Cmx,y,z = Mx,y,z/ 0.5ρVre f Al , (3) where the following parameters are force (F), moment (M), frontal area (A = 1.660 m2), the length between the front and the rear axles (l = 2.364 m). In each case, the coefficients of forces and moments Energies 2019, 12, 4697 6 of 22 were calculated using the same reference area, which refers to the frontal area of the car body without the side spoilers. The way the flow at a non-zero yaw angle was directed was depicted in Figure2a. The domain was discretized with the use of tetrahedral elements, and a mesh near the car body is presented in Figure2b. To ensure that the mesh quality was adequate, the tetrahedral mesh prepared for the calculations had a maximum skewness lower than 0.95, whereas the average skewness value was lower than 0.33, as suggested in [37]. In Figure2c, a close-up on the mesh in the boundary layer can be seen, where twelve layers of the prism elements were included to accurately predict the flow near the walls. The height of the first element near the wall, in the regions where the flow stayed attached to the walls, was set to match the non-dimensional height of the cell (y+) equal to 30. The steady-state Reynolds-averaged Navier-Stokes (RANS) shear-stress transport (SST) k-ω [38] turbulence model was used, as it was proved by the authors of this paper in [31] and [34] that this model is capable of providing correct results for the particular car body geometry being studied. The mesh independence study is presented in Table1 for calculations performed at a yaw angle equal to 15◦. A non-zero yaw angle was chosen to study not only the drag and the lift coefficients but also the side coefficient, which is very important when the car body is subjected to an asymmetrical aerodynamic load. These calculations were performed to make sure that the aerodynamic coefficients presented later in this paper were independent of the size of the mesh. From the data presented in Table1, it can be concluded that the mesh consisting of 3.269 107 elements is adequate for use in × these studies as the values of the aerodynamic coefficients stay close to the ones obtained with this mesh even when the number of mesh cells is further increased. When the mesh size was increased to 4.395 107 elements, the values of all of the aerodynamic coefficients did not change more than 1.2%. × Table 1. Aerodynamic coefficients obtained with meshes of different sizes.

Number of Cells Drag Coefficient Side Coefficient Lift Coefficient 2.187 107 0.364 0.509 0.056 × 3.269 107 0.383 0.527 0.071 × 4.395 107 0.384 0.533 0.071 ×

3. Results and Discussion

3.1. The Side Spoiler on a Quarter Glass Six different cases were studied, which included the base case without the side spoiler and with the side spoiler inclined at 27.5◦, 55.0◦, 82.5◦, 110.0◦, and 137.5◦ (Figure3). An obvious observation from Figure3 is that the side spoiler increases the frontal area of the car, which indicates that it could be used as an airbrake. In Figure3, it can also be seen that the area of the pressure build-up on the windshield and the spoiler increases together with the increase of the spoiler’s angle of inclination. At first, one might think that the area of pressure build-up as well as the value of the pressure itself should be highest when the spoiler is inclined perpendicular to the free stream, but because of the influence of the car body on the flow field, the most favorable conditions are when the spoiler is inclined perpendicular to the windshield. The highest pressure at the front of the spoiler and the lowest at the back of the spoiler make it possible to generate the greatest possible forces on the side spoiler itself. However, the angle of inclination determines in which direction this force acts and, moreover, it is also very important how the pressure distribution changes on the other parts of the car body. For this reason, the forces and moments generated on the side spoiler and the forces from the whole car body are presented separately in Figure4 (numerical values are included in AppendixB). Energies 2019, 12, x FOR PEER REVIEW 7 of 21

Energies 2019, 12, 4697 7 of 22 Energies 2019, 12, x FOR PEER REVIEW 7 of 21

Figure 3. Contours of pressure coefficient on the front of the car body.

According to Figure 4a, the aerodynamic drag (Cx) generated on the spoiler itself increases together with the increase of its inclination angle and reaches peak values at 82.5° to 110.0°. A similar trend can be observed with the downforce (–Cz, negative lift); however, it decreases more rapidly after reaching its peak value at 82.5°. More complex changes occur with the characteristic of the side force (Cy), positive values of force are generated in the range between 0° to 55.0°, while the force shifts to the opposite direction at higher angles. The principle of operation at lower angles is similar to the one used in [26,27] to detach the flow at the leeward side of the car. This means that in the studied case, a larger overall side force would be obtained with a side spoiler at a high inclination angle on the left side of the car and at a low inclination angle on the right side. FigureFigure 3.3. Contours of of pressure pressure coefficien coefficientt on on the the front front of of the the car car body. body.

According to Figure 4a, the aerodynamic drag (Cx) generated on the spoiler itself increases together with the increase of its inclination angle and reaches peak values at 82.5° to 110.0°. A similar trend can be observed with the downforce (–Cz, negative lift); however, it decreases more rapidly after reaching its peak value at 82.5°. More complex changes occur with the characteristic of the side force (Cy), positive values of force are generated in the range between 0° to 55.0°, while the force shifts to the opposite direction at higher angles. The principle of operation at lower angles is similar to the one used in [26,27] to detach the flow at the leeward side of the car. This means that in the studied case, a larger overall side force would be obtained with a side spoiler at a high inclination angle on the left side of the car and at a low inclination angle on the right side.

FigureFigure 4. (4.a) ( Forcea) Force coe fficoefficientscients on theon spoiler,the spoiler, (b) total (b) total force force coeffi coefficients,cients, (c) moment (c) moment coefficients coefficients on the on spoiler,the spoiler, (d) total (d moment) total moment coefficients. coefficients.

According to Figure4a, the aerodynamic drag (Cx) generated on the spoiler itself increases together with the increase of its inclination angle and reaches peak values at 82.5◦ to 110.0◦. A similar trend can be observed with the downforce (–Cz, negative lift); however, it decreases more rapidly after reaching its peak value at 82.5◦. More complex changes occur with the characteristic of the side force (Cy), positive values of force are generated in the range between 0◦ to 55.0◦, while the force shifts to the opposite direction at higher angles. The principle of operation at lower angles is similar to the one used inFigure [26,27 4.] ( toa) Force detach coefficients the flow on at the the spoiler, leeward (b) sidetotal offorce the coefficients, car. This means(c) moment that coefficients in the studied on case, a largertheoverall spoiler, side (d) total force moment would coefficients. be obtained with a side spoiler at a high inclination angle on the left side of the car and at a low inclination angle on the right side.

Energies 2019, 12, 4697 8 of 22

The characteristics of the total values in Figure4b look very similar to the ones in Figure4a up to the angle equal to 110.0◦, at which point the absolute values of the side force start to decrease, with the values of the downforce staying unchanged. In Figure4c,d, one can see that the yawing moment (Cmz) increases together with the spoiler’s inclination angle and reaches its maximum at angles equal to 82.5◦ and 110.0◦. This shows that at an angle equal to 110.0◦, the side spoiler changes the car’s aerodynamic properties the most. Moreover, the generated side force and the yawing moment could be used to counter the influence of the crosswind, because the crosswind blowing from the side of the car where the spoiler is attached would generate a positive side force and a negative yawing moment. As mentioned earlier, a higher side force could be obtained with the side spoilers active on both sides of the car, but this would occur together with a loss of the yawing moment due to an opposite value of the moment generated by the spoilers on both sides of the car. Values of the pitching moment (Cmy) stay close to a constant level, which means that the balance of the car (the difference of the load on the front and the rear axle) is not subjected to a significant change. The pitching moment presented in Figure4d was normalized to better fit the graph because it is ten orders of magnitude higher than the other two, which is due to the initial balance of the car. In Figure4d, it can also be seen that a rolling moment (Cmx) is created, which means that the downforce increased on the side of the car where the spoiler was mounted. When comparing the total moments and forces with the ones generated only on the spoiler, as presented in Figure4, it should be noted that almost all of the overall value of the yawing and the rolling moments come from the spoiler itself, whereas a higher influence of the car body can be observed in the case of forces. Visualizations in Figure5a,b show how the flow field around the A-pillar is a ffected by the different inclination angles of the side spoiler. One can see that an increase of the inclination angle is followed by an increase in pressure difference on both sides of the spoiler and additional acceleration of the flow on its trailing edge. The only exception is for the lowest studied angle equal to 27.5◦ when the side spoiler generates a side force in the opposite direction than the other cases, which is caused by the overall increase in pressure behind the A-pillar due to the flow separation taking place behind the side spoiler. In Figure5c, one can see the vortices created by the side spoiler, which are similar to the vortex created due to the presence of the A-pillar but stronger, especially for higher angles of inclination due to the increased pressure difference on both sides of the spoiler. Figure6a shows contours of the pressure coe fficient for the base case without the side spoiler. To make the influence of the side spoiler clearer, contours in Figure6b–f were included, which represent the results of subtraction of the pressure coefficient values in the base case and in each of the cases with a spoiler inclined at a corresponding angle. This way of presenting the results indicates which areas of the car body are affected most by the side spoiler. The addition of the side spoiler leads to an increase in pressure on the windshield and the roof, as well as a decrease in pressure on the side due to the vortex except for the highest angle of inclination (Figure6f). An unexpected e ffect that the side spoiler entails is an increase in pressure on the trunk, which is the largest for the inclination equal to 110.0◦ (Figure6e). This can be explained by the fact that the side spoiler on the quarter glass contributes to the increase of the detachment behind the car’s roof on its left side and reduces it on the opposite side, which results in an increase in the area of the stagnation zone and increases pressure on the right side of the trunk (Figure7). Energies 2019, 12, 4697 9 of 22

Energies 2019, 12, x FOR PEER REVIEW 9 of 21 Energies 2019, 12, x FOR PEER REVIEW 9 of 21

No spoiler No spoiler

27.5° 27.5°

55.0° 55.0°

82.5° 82.5°

110.0° 110.0°

137.5° 137.5°

(a) (b) (c) (a) (b) (c) FigureFigure 5. Contours5. Contours of of( (aa)) velocityvelocity (m/s), (m/s), and and (b) ( bpressure) pressure coefficient coefficient on a cross-section on a cross-section through through the A the A pillarpillar.Figure.( (cc) )5. StreamlinesStreamlines Contours of colored colored (a) velocity by by velocityvelocity (m/s), (m/s)and (m (/ bcomings)) pressure coming from fromcoefficient the theside side spoileron a spoiler cross-section mounted mounted on through the on quarter the the quarterA glasspillar. at (differentc) Streamlines inclination colored angles. by velocity (m/s) coming from the side spoiler mounted on the quarter glass at different inclination angles. glass at different inclination angles.

(a) (b) (c) (a) (b) (c)

(d) (e) (f) (d) (e) (f) Figure 6. (a) Contours of pressure coefficient on the car body for the base case. Contours of pressure FigurecoefficientFigure 6. (a )6. Contours difference(a) Contours ofdue pressureof to pressure the introducti coe coefficientfficienton of on onthe thethe side car spoiler body body inclinedfor for the the base at base (b case.) 27.5°, case. Contours (c Contours) 55.0°, of (d pressure) 82.5°, of pressure (ecoefficient) 110.0°, and difference (f) 137.5°. due to the introduction of the side spoiler inclined at (b) 27.5°, (c) 55.0°, (d) 82.5°, coefficient difference due to the introduction of the side spoiler inclined at (b) 27.5◦,(c) 55.0◦,(d) 82.5◦, (e) 110.0°, and (f) 137.5°. (e) 110.0◦, and (f) 137.5◦.

EnergiesEnergies2019 2019, 12, 12, 4697, x FOR PEER REVIEW 10 of10 21 of 22 Energies 2019, 12, x FOR PEER REVIEW 10 of 21

Figure 7. Contours of pressure coefficient on the car body and iso-surfaces of total pressure equal zero Figure 7. Contours of pressure coefficient on the car body and iso-surfaces of total pressure equal zero Figurefor the 7.spoiler Contours at the of quarter pressure glass coefficient at 110.0°. on the car body and iso-surfaces of total pressure equal zero forfor the the spoiler spoiler at at the the quarter quarter glass glass at at 110.0 110.0°.◦. 3.2.3.2. The The Side Side Spoiler Spoiler onon aa FrontFront BumperBumper 3.2. The Side Spoiler on a Front Bumper In the case of the side spoiler located at the front bumper, as before, six different cases were In the case of the side spoiler located at the front bumper, as before, six different cases were studied, studied,In the with case the of side the spoiler side spoiler inclined located from 25° at upthe to front 125°, bumper, as depicted as inbefore, Figure six 8. Fromdifferent Figure cases 8, itwere with the side spoiler inclined from 25◦ up to 125◦, as depicted in Figure8. From Figure8, it should be studied,should be with noted the that side the spoiler maximum inclin safetyed from limit 25° is reached up to 125°, when as the depicted spoiler’s in inclination Figure 8. angleFrom reaches Figure 8, it noted that the maximum safety limit is reached when the spoiler’s inclination angle reaches 50◦. Above should50°. Above be noted 50°, thethat side the spoilermaximum might safety interfere limit wiis reachedth other whenobjects the on spoiler’s the road. inclination Higher angles angle were reaches 50◦, the side spoiler might interfere with other objects on the road. Higher angles were studied to gain 50°.studied Above to gain 50°, knowledgethe side spoiler on how might effective interfere a side wi spoilerth other in objectsthis location on the might road. be. Higher In comparison angles were knowledge on how effective a side spoiler in this location might be. In comparison with the previous studiedwith the to previous gain knowledge case, the side on howspoiler effective at the bump a sideer spoiler does not in increasethis location the car might body’s be. frontal In comparison area, case, the side spoiler at the bumper does not increase the car body’s frontal area, assuming that its withassuming the previous that its inclination case, the sideangle spoiler is less atthan the 50°. bump Withiner does this rangenot increase of angles, the the car side body’s spoiler frontal stays area, inclination angle is less than 50◦. Within this range of angles, the side spoiler stays hidden within the assuminghidden within that theits inclinationcar’s silhouette. angle is less than 50°. Within this range of angles, the side spoiler stays car’s silhouette. hidden within the car’s silhouette.

FigureFigure 8.8. Contours of of pressure pressure coefficien coefficientt on on the the front front of ofthe the car car body. body.

LookingLooking atat thethe contourscontours in Figure 88,, itit cancan be seen that that the the biggest biggest differences di fferences in inpressure pressure Figure 8. Contours of pressure coefficient on the front of the car body. distributiondistribution occur occur in in thethe directdirect vicinityvicinity of the spoile spoiler.r. Due Due to to the the fact fact that that the the spoiler spoiler is located is located in the in the area affected by the build-up of pressure taking place at the front of the bumper, the inside of the area aLookingffected by at the the build-up contours of in pressure Figure taking8, it can place be seen at the that front the of biggest the bumper, differences the inside in pressure of the spoiler is subjected to high pressure even when the spoiler is inclined at a low angle. The pressure spoilerdistribution is subjected occur in to the high direct pressure vicinity even of whenthe spoile the spoilerr. Due to is the inclined fact that at a the low spoiler angle. is The located pressure in the distribution on the outer side of the spoiler is subjected to bigger changes due to the fact that at lower distributionarea affected on by the the outer build-up side of of the pressure spoiler istaking subjected place to at bigger the front changes of the due bumper, to the fact the that inside at lower of the angles, it faces the flow, whereas at higher angles, it is in the wake created by the side spoiler. angles,spoiler it is faces subjected the flow, to high whereas pressure at higher even angles, when itth ise inspoiler the wake is inclined created at by a thelow sideangle. spoiler. The pressure AsAs in in the the case case of of the the spoilerspoiler locatedlocated on the the quar quarterter glass, glass, the the downforce downforce and and drag drag that that the the side side distributionspoiler generates on the both outer increase side of with the the spoiler inclination is subjec angleted (Figureto bigger 9a), changes with the due exception to the factof the that lowest at lower spoiler generates both increase with the inclination angle (Figure9a), with the exception of the lowest angles,angle equal it faces to 25°, the whichflow, whereasdoes not affectat higher the drag.angles The, it maximumis in the wake side createdforce that by the the spoiler side spoiler. generates angle equal to 25 , which does not affect the drag. The maximum side force that the spoiler generates occursAs between in the case◦ 50° ofand the 75°; spoiler however, located the ontotal the va quarlue ofter the glass, side the force downforce generated and on dragthe whole that thecar side occurs between 50 and 75 ; however, the total value of the side force generated on the whole car body spoilerbody (Figure generates 9b) ◦ isboth significantly increase◦ withhigher the at inclination 75°, when it angle reaches (Figure its maximum. 9a), with Thethe exceptionyaw moment of the is the lowest (Figure9b) is significantly higher at 75 , when it reaches its maximum. The yaw moment is the highest anglehighest equal at 75° to and25°, 100°which (Figure does no9d).t affectThe◦ rolling the drag. moment The maximumincreases when side forcethe spoiler that the is movedspoiler above generates atoccurs25°, 75◦ and between 100its maximum◦ (Figure 50° and9d). value 75°; The ishowever, rolling similar moment to the the total case increases va oflue the whenof side the thespoiler side spoiler force located isgenerated moved on the above quarteron the 25 ◦wholeglass;, and itscar maximumbodyhowever, (Figure valueit is 9b)lower is is similar significantly by approximately to the higher case ofone at the third75°, side wh across spoileren it the reaches located whole its studied on maximum. the quarterangle Therange. glass; yaw The however,moment pitching is it the is lowerhighestmoment by approximatelyat stays 75° andat a 100°constant one (Figure third level. 9d). across When The the studyingrolling whole moment studiedthe graphs increases angle in range.Figure when The9, it the pitchingcan spoiler be concluded moment is moved staysthat above at a25°,constant and its level. maximum When studyingvalue is thesimilar graphs to the in Figurecase of9 ,the it can side be spoiler concluded located that on there the isquarter no need glass; to however, it is lower by approximately one third across the whole studied angle range. The pitching moment stays at a constant level. When studying the graphs in Figure 9, it can be concluded that

Energies 2019, 12, x FOR PEER REVIEW 11 of 21

there is no need to increase the inclination angle of the side spoiler located at the front bumper above 75°, because it does not lead to a significant improvement in efficiency. Energies 2019Also, 12 interesting, 4697 is that the value of the yawing moment at angles equal to 25°, 50°, and11 of75° 22 is higher on the spoiler itself (Figure 9c) than the total value generated on the whole car body (Figure 9d). This suggests that there is a potential to improve the efficiency of this element by eliminating its increase the inclination angle of the side spoiler located at the front bumper above 75◦, because it does notnegative lead to ainfluence significant arising improvement from its interaction in efficiency. with the car body.

FigureFigure 9. (9.a) ( Forcea) Force coe fficoefficientscients on theon spoiler,the spoiler, (b) total (b) total force force coeffi coefficients,cients, (c) moment (c) moment coefficients coefficients on the on spoiler,the spoiler, (d) total (d moment) total moment coefficients. coefficients.

AlsoIn Figure interesting 10a, isa detachment that the value of the of the flow yawing from th momente car body at angles can be equal observed to 25 at◦, angles 50◦, and above 75◦ is75°, higherwhereas on the at spoilerlower angles, itself (Figure the flow9c) accelerates than the total on value the outer generated side of on the the spoiler whole and car remains body (Figure attached9d). to Thisthe suggests car body, that which there is isconsistent a potential with to the improve streamli thenes e ffidepictedciency ofin thisFigure element 10c, where by eliminating it is shown its that negativethe vortices influence created arising on fromthe side its interactionspoiler inclined with theup carto 50° body. stay attached to the side of the car. The highestIn Figure drop 10 ina, pressure a detachment on the of outer the flowside of from the thespoi carlerbody is observed can be at observed inclination at angles angles above equal 75to◦ 50°, whereasand 75° at (Figure lower angles, 10b) due the to flow the accelerates acceleration on of the the outer flow side in that of the region. spoiler When and remainsa complete attached separation to thetakes car body, place, which the pressure is consistent increases with thebut streamlinesis still lower depicted than without in Figure the 10sidec, where spoiler. it is shown that the vorticesThe created most on significant the side spoiler differences inclined in upthe to pressure 50◦ stay attacheddistribution to the (Figure side of 11) the occur car. The in highestthe direct dropproximity in pressure of the on spoiler, the outer which side ofcan the be spoilerobserved is observed as the pressure at inclination increases angles in front equal of toit 50and◦ and decreases 75◦ (Figurebehind 10 b)it. dueThis toarea the increases acceleration in size of the above flow the in incl thatination region. angle When equal a complete to 75° and separation is the greatest takes place, at 125° the(Figure pressure 11f) increases when it but stretches is still lowerup to thanthe A-pillar. without It the can side be spoiler. clearly seen that this area is much more confined in comparison with Figure 7 representing the change of pressure distribution for the case of the spoiler located at the quarter glass. It should be noted that at the angles of inclinations equal to 25° and 50° (Figure 11a,b), the pressure increases exactly between the side spoiler and the front wheel. This occurs because the inclination angle is too small to detach the flow, which leads to a pressure build-up in that region. This effect lowers the efficiency on the side spoiler and decreases the side force, as well as the yawing moment, which can be seen in Figure 9b as the absolute value of the side force decreases at an angle equal to 50°. Even more important is that the increase in pressure on the

Energies 2019, 12, x FOR PEER REVIEW 12 of 21 car body in front of the spoiler has the same effect and occurs on an even larger area. For this reason, the yawing moment generated on the whole car body is lower than the yawing moment generated on the side spoiler itself (Figure 9c,d). To solve this problem, the side spoiler could be either moved Energiesto the 2019front, 12 or, 4697 its rotation axis could be switched from the trailing edge of the spoiler plate12 to of its 22 leading edge to ensure that the activation of the spoiler decreases pressure on the side of the car body.

No spoiler

25°

50°

75°

100°

125°

(a) (b) (c)

Figure 10.10. Contours of ( a)) velocity (m/s) (m/s) and ( b) pressure coecoefficientfficient on a cross-section through the bumper. ((cc)) StreamlinesStreamlines colored colored by by velocity velocity (m /s)(m/s) coming coming from from the side the spoiler side spoiler mounted mounted on the bumperon the bumperat different at different inclination inclination angles. angles.

The most significant differences in the pressure distribution (Figure 11) occur in the direct proximity of the spoiler, which can be observed as the pressure increases in front of it and decreases behind it. This area increases in size above the inclination angle equal to 75◦ and is the greatest at 125◦ (Figure 11f) when it stretches up to the A-pillar. It can be clearly seen that this area is much more confined in comparison with Figure7 representing the change of pressure distribution for the case of the spoiler located at the quarter(a) glass. It should be noted that( atb) the angles of inclinations equal(c) to 25◦ and 50◦ (Figure 11a,b), the pressure increases exactly between the side spoiler and the front wheel. This occurs because the inclination angle is too small to detach the flow, which leads to a pressure build-up in that region. This effect lowers the efficiency on the side spoiler and decreases the side force, as well as the yawing moment, which can be seen in Figure9b as the absolute value of the side force decreases at an angle equal to 50◦. Even more important is that the increase in pressure on the car body in front of the spoiler has the same effect and occurs on an even larger area. For this reason, the yawing moment generated on the whole car body is lower than the yawing moment generated on the side spoiler itself Energies 2019, 12, x FOR PEER REVIEW 12 of 21

car body in front of the spoiler has the same effect and occurs on an even larger area. For this reason, the yawing moment generated on the whole car body is lower than the yawing moment generated on the side spoiler itself (Figure 9c,d). To solve this problem, the side spoiler could be either moved to the front or its rotation axis could be switched from the trailing edge of the spoiler plate to its leading edge to ensure that the activation of the spoiler decreases pressure on the side of the car body.

No spoiler

25°

50°

75°

100°

125°

Energies 2019, 12, 4697 13 of 22

(a) (b) (c)

(FigureFigure9c,d). To10. solveContours this of problem, (a) velocity the (m/s) side and spoiler (b) pressure could coefficient be either movedon a cross-section to the front through or its the rotation axis couldbumper. be switched (c) Streamlines from thecolored trailing by velocity edge of (m/s) the spoilercoming platefrom tothe its side leading spoiler edge mounted to ensure on the that the activationbumper of the at different spoiler decreasesinclination angles. pressure on the side of the car body.

Energies 2019, 12, x FOR PEER REVIEW 13 of 21 (a) (b) (c) Energies 2019, 12, x FOR PEER REVIEW 13 of 21

(d) (e) (f) (d) (e) (f) FigureFigure 11. 11(.a ()a Contours) Contours of of pressure pressure coecoefficientfficient on the car car body body for for the the base base case. case. Contours Contours of ofpressure pressure

coecoefficientFigurefficient 11 di. (differenceffa)erence Contours due due of toto pressure thethe introduc introduction coefficienttion of ofon the thethe side car side spoilerbody spoiler for inclined the inclined base at case.(b at) 25°, ( bContours) 25(c)◦ 50°,,(c ) of( 50d pressure) ◦75°,,(d ()e 75) ◦, (e)100°,coefficient 100◦ and, and ( fdifference ()f 125°.) 125 ◦. due to the introduction of the side spoiler inclined at (b) 25°, (c) 50°, (d) 75°, (e) 100°, and (f) 125°. 3.3.3.3. Cases Cases Chosen Chosen for for Di Differentfferent Yaw Yaw Conditions Conditions 3.3. Cases Chosen for Different Yaw Conditions ThreeThree car car body body geometries geometries werewere chosenchosen for comparison across across different different yaw yaw angles, angles, a model a model withwith two Threetwo additional additional car body side sidegeometries spoilers spoilers were (Figure(Figure chosen 1212a),a), for theth ecomparison base case case model modelacross (Figure (Figuredifferent 12b), 12 yawb), and andangles, a model a model a model with with thethewith spoiler spoiler two removedadditional removed on onside the the spoilers trunktrunk (Figure(Figure(Figure 12c).1212a),c). Thisth Thise baseset set of case of cases cases model makes makes (Figure it possible it possible12b), toand compare to a comparemodel how withhow a a typicaltypicalthe spoiler aerodynamicaerodynamic removed onenhancement, the trunk (Figure such such as 12c). as a arear rearThis spoiler spoilerset of casesplaced placed makes on on a acar’sit car’spossible trunk, trunk, to can compare can improve improve how the a the aerodynamicaerodynamictypical aerodynamic properties properties enhancement, of of a a car car in in comparisoncomparison such as a rear with spoiler an unconventional unconventional placed on a method,car’s method, trunk, such such can as as theimprove the addition addition the ofof sideaerodynamic side spoilers. spoilers. properties The The angle angle of of of a inclinationcarinclination in comparison of the si side withde spoilers spoilers an unconventional was was kept kept the the method, same same across acrosssuch all as all studiedthe studied addition yaw yaw angles,of side spoilers.the side spoilerThe angle at theof inclination quarter glass of the was si deinclined spoilers at was110°, kept and the the same side acrossspoiler all at studiedthe bumper yaw angles, the side spoiler at the quarter glass was inclined at 110◦, and the side spoiler at the bumper was wasangles, inclined the side at 50°. spoiler In the at casethe quarter of the spoiler glass wasat the in quarterclined at glass, 110°, it and is possible the side that spoiler adjusting at the itsbumper angle inclined at 50◦. In the case of the spoiler at the quarter glass, it is possible that adjusting its angle of of inclination would be beneficial, and the angle should be decreased with an increase of the yaw inclinationwas inclined would at 50°. be beneficial,In the case andof the the spoiler angle at should the quarter be decreased glass, it is with possible an increase that adjusting of the yawits angle angle. angle.of inclination In the wouldcase of be the beneficial, side spoiler and thelocated angle on should the quarterbe decreased glass, withthe anmost increase efficient of thevariant yaw In the case of the side spoiler located on the quarter glass, the most efficient variant investigated at investigatedangle. In the at casea zero of yaw the angle side wasspoiler selected located (inclination on the anglequarter equal glass, to 110°),the most and inefficient the case variant of the a zero yaw angle was selected (inclination angle equal to 110 ), and in the case of the spoiler located at spoilerinvestigated located at ata zerothe front yaw bumper,angle was the selected highest (inclination inclination angle◦ equaldeemed to acceptable110°), and inwas the equal case toof 50°the the front bumper, the highest inclination angle deemed acceptable was equal to 50 as this meant that asspoiler this meant located that at thethe frontside spoilerbumper, did the no highestt significantly inclination protrude angle outsidedeemed the acceptable car body.◦ was equal to 50° the side spoiler did not significantly protrude outside the car body. as this meant that the side spoiler did not significantly protrude outside the car body.

(a) (b) (c) (a) (b) (c) Figure 12. The car body geometries chosen for studies at non-zero yaw angles. (a) Combined case, (b) FigurebaseFigure case, 12. 12The. (Thec) clear car car body bodycase. geometriesgeometries chosen chosen for for studies studies at atnon-zero non-zero yaw yaw angles. angles. (a) Combined (a) Combined case, ( case,b) (b)base base case, case, (c ()c clear) clear case. case. The aerodynamic properties for each case at a zero yaw angle are presented in Table 2. One can seeThe thatThe aerodynamic the aerodynamic base case properties model properties in forcomparison for each each case case with at at a zeroathe zero clean yaw yaw anglecase angle model are are presented presented has an increased in in Table Table2 .downforce 2. One One can can see thatduesee the thatto base the the casereduction base model case ofmodel in the comparison lift in comparisonforce on with the thewith rear clean theaxle clean case by half. modelcase Whenmodel has anboth has increased anof increasedthe side downforce spoilers downforce dueare to themounteddue reduction to the onto reduction of thethe liftcar forceofbody, the on thelift the effectsforce rear on axleof thethe by rearasymme half. axle Whentrical by half. both loads When of can the be sideboth observed, spoilersof the sidesuch are mountedspoilers as the side are onto theforce,mounted car body, the ontorolling the the eff ectsmoment, car ofbody, the and the asymmetrical theffectse yawing of theloads moment. asymme can betricalIn observed,comparison loads can such withbe observed, as the the base side such force,case, as the thethe drag rollingside coefficientforce, the rollingincreases moment, by 48%, and which the meansyawing that moment. these devicesIn comparison could be with used the as base efficient case, airbrakes, the drag moment, and the yawing moment. In comparison with the base case, the drag coefficient increases especiallycoefficient asincreases this value by 48%,would which be even means higher that if thes thesee devices devices could were be mounted used as onefficient both sides.airbrakes, The by 48%, which means that these devices could be used as efficient airbrakes, especially as this value downforceespecially asis alsothis increased,value would approximately be even higher twice if as these much devices as due towere the mountedaddition ofon the both spoiler sides. on Thethe would be even higher if these devices were mounted on both sides. The downforce is also increased, trunkdownforce and, atis alsothe sameincreased, time, approximatelythe balance of twicethe car as was much kept as duealmost to the the addition same with of the the spoiler value onof the pitchingtrunk and, moment at the chansameging time, only the by balance 7%. of the car was kept almost the same with the value of the pitching moment changing only by 7%. Table 2. Breakdown of the aerodynamic loads generated on the car body and the side spoiler mounted onTable the 2.front Breakdown bumper ofand the the aerodynamic quarter glass—at loads generateda zero yaw on angle. the car body and the side spoiler mounted on the front bumper and the quarter glass—at a zero yaw angle. Drag Coefficient Side Coefficient Lift Coefficient Lift Distribution Moment Coefficients Case. DragSpoile Coefficientr Total Spoile Side Coefficientr Total Spoile Lift Coeffir Totalcient Lift Front Distribution Rear Moment Cmx Cmy Coefficients Cmz Case. Clean Spoile– r 0.339Total Spoile– r –Total0.001 Spoile– r Total0.147 – Front0.125 Rea0.272r 0.000 Cmx –Cmy0.273 0.000Cmz CleanBase –– 0.3330.339 –– –0.0020.001 –– 0.0020.147 ––0.1410.125 0.1430.272 0.000 0.000 ––0.2140.273 0.0010.000 Base – 0.333 – 0.002 – 0.002 –0.141 0.143 0.000 –0.214 0.001

Energies 2019, 12, 4697 14 of 22 approximately twice as much as due to the addition of the spoiler on the trunk and, at the same time, the balance of the car was kept almost the same with the value of the pitching moment changing only by 7%.

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

Drag Side Lift Lift Moment Coefficients Case. Coefficient Coefficient Coefficient Distribution Spoiler Total Spoiler Total Spoiler Total Front Rear Cmx Cmy Cmz

Clean – 0.339 – –0.001 – 0.147 –0.125 0.272 0.000 –0.273 0.000 Base – 0.333 – 0.002 – 0.002 –0.141 0.143 0.000 –0.214 0.001 Energies 2019, 12, x FOR PEER REVIEW 14 of 21 Fr. bumper 0.012 0.368 –0.081 –0.028 –0.025 –0.074 –0.185 0.111 0.016 –0.226 0.053 Fr.Qtr. bumper glass 0.012 0.048 0.3680.451 ––0.0660.081 ––0.1200.028 –0.042–0.025 ––0.1960.074 –0.188–0.185 –0.008 0.111 0.035 0.016 – –0.1850.226 0.053 0.033 Combined 0.061 0.492 –0.152 –0.285 –0.069 –0.301 –0.278 –0.023 0.040 –0.230 0.074 Qtr. glass 0.048 0.451 –0.066 –0.120 –0.042 –0.196 –0.188 –0.008 0.035 –0.185 0.033 Combined 0.061 0.492 –0.152 –0.285 –0.069 –0.301 –0.278 –0.023 0.040 –0.230 0.074 The interaction between the two side spoilers should also be considered. They are located at differentThe heights, interaction so therebetween is no the risk two that side one spoilers will be should in the aerodynamicalso be considered. wake They of the are other; located however, at datadifferent in Table heights,2 suggests so there that is no an risk interaction that one betweenwill be in thesethe aerodynamic two spoilers wake is taking of the place.other; however, When both ofdata these in spoilersTable 2 suggests are mounted that an together interaction in the between combined these case,two spoilers the aerodynamic is taking place. forces When on the both spoilers of themselvesthese spoilers are almostare mounted equal totogether the sum in ofthe forces combin thated they case, generate the aerodynamic when they forces are mounted on the spoilers separately. Thisthemselves also applies are whenalmost the equal total to values the sum generated of forces on that the wholethey generate car body when are considered they are mounted for the drag andseparately. for the liftThis force. also applies However, when in the the total case values of the generated total side on force, the whole it is almost car body twice are considered as high when for the drag and for the lift force. However, in the case of the total side force, it is almost twice as high the two spoilers are combined together in comparison with the cases when they are used separately. when the two spoilers are combined together in comparison with the cases when they are used The interaction between these two spoilers is depicted in Figure 13. One can see that, when both side separately. The interaction between these two spoilers is depicted in Figure 13. One can see that, spoilers are present, more of the flow is sucked upwards, towards the wake behind the spoiler on when both side spoilers are present, more of the flow is sucked upwards, towards the wake behind the quarter glass, which leads to a decrease in pressure on the side of the car. However, pressure is the spoiler on the quarter glass, which leads to a decrease in pressure on the side of the car. However, decreasedpressure inis frontdecreased as well in asfront behind as well the centeras behind of gravity, the center which of gravity, according which to Table according2, leads to to Tablea decrease 2, ofleads the yawing to a decrease moment of the for yawing the combined moment for case the by combined approximately case by 14%approximately in comparison 14% in with comparison the yawing momentwith the generated yawing moment when thegenerated side spoilers when the were side mounted spoilers separately.were mounted separately.

(a) (b) (c)

FigureFigure 13. 13Contours. Contours of of pressure pressure coe fficoefficientcient on theon carthe body car body together together with thewith grey the colored grey colored 3D streamlines 3D startedstreamlines from started the front from of the the fr caront body,of the car for body, the (a for) front the (a bumper) front bumper case, ( bcase,) quarter (b) quarter glass glass case, case, and (c) combinedand (c) combined case. case.

ToTo conclude, conclude, thethe sideside spoilersspoilers mounted together together work work well, well, and and it would it would appear appear that that there there is is roomroom to to increase increase their their eefficiencyfficiency even more if if th thee interactions interactions between between them them are are taken taken into into account. account.

3.4.3.4. Results Results at at DiDifferentfferent YawYaw AnglesAngles TheThe investigations investigations of the car body geometries geometries presented presented in inFigure Figure 12 12were were performed performed for foryaw yaw angles between 0° and 15°. The characteristics of the aerodynamic forces and moments obtained are angles between 0◦ and 15◦. The characteristics of the aerodynamic forces and moments obtained are presentedpresented in in Figure Figure 14 14,, inin whichwhich the results results can can be be compared compared for for the the base base case case (car (car body body with with a spoiler a spoiler onon the the trunk), trunk), for for the the combined combined case case (includes (includes two two side side spoilers), spoilers), andand forfor thethe cleanclean casecase whichwhich doesdoes not not have any aerodynamic devices. have any aerodynamic devices. The configurations with and without the rear spoiler have similar characteristics. As pointed out in the previous section, the biggest difference between them is the increase of downforce due to the addition of the rear spoiler, which also results in a decrease of the pitching moment because of a smaller difference of the loads on the front and rear axles. According to data presented in [39], where the influence of rear spoilers was studied, the attachment of a rear spoiler was followed by a reduction of the lift force and the yawing moment as well as an increase of the side force and the rolling moment. These findings are consistent with the results of numerical calculations for the car body geometry with and without the rear spoiler, as presented in Figure 14. To include more than just CFD results in the data presented in Figure 14, a formula proposed in [24] was used that makes it possible to calculate the side force derivative for a three-box car body type:

𝐶𝑠 =2.07𝐻 /𝐴0.75 + 0.25𝐻/𝐻 +0.03𝐿/𝐻𝐻/𝐻 (4)

Energies 2019, 12, x FOR PEER REVIEW 15 of 21

where vehicle dimensions such as height (H), boot height (Hte), frontal area (A), and length (L) are considered. Taking into account all of those dimensions makes it possible to predict the side force more accurately; however, as identified in [24], vehicle height has the most dominant influence on the side force. The side force derivative in Equation (4) represents the change of side force coefficient with the yaw angle. It was concluded in [24] that the yaw moment could not be predicted with a similar formula due to its high sensitivity to the distribution of the side force load. The case without the rear spoiler was chosen for comparison with the results from the analytical calculations and the

Energiesones obtained2019, 12, 4697 with the use of CFD, and, in Figure 14b, one can see that the formula matches the15 ofCFD 22 results very closely throughout the studied yaw angle range.

Drag force coefficient Rolling moment coefficient Coefficient value value Coefficient Coefficient value value Coefficient

Yawing angle [°] Yawing angle [°] (a) (d) Side force coefficient Pitching moment coefficient Coefficient value value Coefficient Coefficient value value Coefficient

Yawing angle [°] Yawing angle [°] (b) (e) Lift force coefficient Yawing moment coefficient Coefficient value value Coefficient Coefficient value value Coefficient

Yawing angle [°] Yawing angle [°] (c) (f) Combined case Base case Clean case (CFD) -- Clean case (analytical)

FigureFigure 14. 14Characteristics. Characteristics for forcefor andforce moment and moment coefficients coefficients for a range for of yawa range angles. of The yaw characteristics angles. The are:characteristics (a) drag force are: coe (affi) dragcient, force (b) side coefficient, force coe (ffib)cient, side force (c) lift coefficient, force coeffi (cient,c) lift (forced) rolling coefficient, moment (d) coerollingfficient, moment (e) pitching coefficient, moment (e) pitching coefficient, moment and (f )coefficient, yawing moment and (f) coe yawingfficient. moment coefficient.

TheThe configurations key findings of with our andpaper without refer to the the rear result spoilers of the have flow similar around characteristics. a car body equipped As pointed with outside in spoilers. the previous One can section, see, from the biggestthe results diff oference the side between force (Figure them is 14b) the for increase the combined of downforce case where due to the addition of the rear spoiler, which also results in a decrease of the pitching moment because of a smaller difference of the loads on the front and rear axles. According to data presented in [39], where the influence of rear spoilers was studied, the attachment of a rear spoiler was followed by a reduction of the lift force and the yawing moment as well as an increase of the side force and the rolling moment. These findings are consistent with the results of numerical calculations for the car body geometry with and without the rear spoiler, as presented in Figure 14. Energies 2019, 12, 4697 16 of 22

To include more than just CFD results in the data presented in Figure 14, a formula proposed in [24] was used that makes it possible to calculate the side force derivative for a three-box car body type:

 2  2  Csψ = 2.07 H /A 0.75 + 0.25(Hte/H) + 0.03(L/H)(Hte/H) (4) where vehicle dimensions such as height (H), boot height (Hte), frontal area (A), and length (L) are considered. Taking into account all of those dimensions makes it possible to predict the side force more accurately; however, as identified in [24], vehicle height has the most dominant influence on the side force. The side force derivative in Equation (4) represents the change of side force coefficient with the yaw angle. It was concluded in [24] that the yaw moment could not be predicted with a similar formula due to its high sensitivity to the distribution of the side force load. The case without the rear spoiler was chosen for comparison with the results from the analytical calculations and the ones obtained with the use of CFD, and, in Figure 14b, one can see that the formula matches the CFD results very closely throughout the studied yaw angle range. The key findings of our paper refer to the results of the flow around a car body equipped with side spoilers. One can see, from the results of the side force (Figure 14b) for the combined case where the two side spoilers were mounted, that the side spoilers make it possible to generate a side force that counters the side force generated by the crosswind up to the yaw angle equal to 4◦ and, more importantly, a yawing moment, which negates the effects of the crosswind up to an angle equal to 9◦ (Figure 14f). In Figure 14, when considering the influence of the side spoilers, one can see that most of the aerodynamic characteristics are shifted by a constant value. The most notable exception is the lift force coefficient characteristic (Figure 14c), which shows that the side spoilers used are significantly less effective at increasing the total value of the car’s downforce at non-zero yaw angles. In addition to this, the drag characteristics (Figure 14a) for all three cases converge together as the yaw angle increases. This occurs due to the fact that, at a zero yaw angle, the side spoilers generated additional drag because of the increase of the frontal area that they created. With the increase of the yaw angle and the constant angle at which the side spoilers are inclined, the side spoilers create less and less drag, and, for this reason, the drag generated by the car body starts to dominate the total values of the drag. This also applies to the rolling moment characteristics (Figure 14d), which converge together due to the decrease of the downforce that each side spoiler generates at the increased yaw angle. The characteristic of the change in the car’s balance is not modified by the side spoilers in comparison with the other cases (Figure 14e), which is positive because the driver would not suddenly become confused by it. This would be especially important when driving on a curve where a sudden change in the car’s balance might cause it to oversteer or understeer. Apart from the forces directly counteracting the crosswind, another positive effect is a slight increase of the downforce across the whole studied yaw angle range; however, as noted earlier, the side spoilers were much less effective in generating additional downforce at non-zero yaw angles. Contours of pressure coefficient on the car body for each of the three studied cases are presented in Figure 15. This figure also includes iso-surfaces of total pressure equal to zero, which give information on how the 3D features corresponding to the flow losses are affected by the non-zero yaw angle flow. As mentioned before, the side spoilers are located on the windward side of the car (they can be seen at the bottom of the car body in Figure 15). The pressure distribution on the windshield and the shape of the iso-surfaces in the passenger’s cabin wake in Figure 15 at a zero yaw angle flow for a car with side spoilers (the combined case) look similar as for the car without side spoilers but at non-zero yaw angles. The vortex created on the side spoiler at the quarter glass becomes weaker at higher yaw angles because the direction of the flow becomes aligned to it. For this reason, consideration should be given to modify its inclination angle to the optimal one at a given yaw angle, which should improve its efficiency across the range of non-zero yaw angles. The side spoiler on the quarter glass contributes to the increase of the detachment behind the car’s roof on its left side and reduces it on its right side, which results in an increase in pressure on the leeward side of the trunk, but only at a zero yaw angle. Where the pressure distribution on the side of the car is concerned, the introduction of the side spoiler Energies 2019, 12, x FOR PEER REVIEW 16 of 21

the two side spoilers were mounted, that the side spoilers make it possible to generate a side force that counters the side force generated by the crosswind up to the yaw angle equal to 4° and, more importantly, a yawing moment, which negates the effects of the crosswind up to an angle equal to 9° (Figure 14f). In Figure 14, when considering the influence of the side spoilers, one can see that most of the aerodynamic characteristics are shifted by a constant value. The most notable exception is the lift force coefficient characteristic (Figure 14c), which shows that the side spoilers used are significantly less effective at increasing the total value of the car’s downforce at non-zero yaw angles. In addition to this, the drag characteristics (Figure 14a) for all three cases converge together as the yaw angle increases. This occurs due to the fact that, at a zero yaw angle, the side spoilers generated additional drag because of the increase of the frontal area that they created. With the increase of the yaw angle and the constant angle at which the side spoilers are inclined, the side spoilers create less and less drag, and, for this reason, the drag generated by the car body starts to dominate the total values of Energies 2019, 12, 4697 17 of 22 the drag. This also applies to the rolling moment characteristics (Figure 14d), which converge together due to the decrease of the downforce that each side spoiler generates at the increased yaw onangle. the quarter glass decreases the pressure the most in direct proximity of the side spoiler, which appliesThe across characteristic the whole of studied the change yaw anglein the range. car’s ba However,lance is not in themodified case of by the the spoiler side spoilers mounted inon comparison with the other cases (Figure 14e), which is positive because the driver would not the bumper at angles equal to 10◦ and 15◦, one can see that the pressure in the region of the front suddenly become confused by it. This would be especially important when driving on a curve where tire is higher. When comparing the base case and the clean case where there is no spoiler on the a sudden change in the car’s balance might cause it to oversteer or understeer. Apart from the forces trunk, the most noticeable change is the decrease in pressure on the trunk, which results in a decreased directly counteracting the crosswind, another positive effect is a slight increase of the downforce downforce on the rear axle. This also leads to a decrease in pressure on the windward side of the trunk across the whole studied yaw angle range; however, as noted earlier, the side spoilers were much when the car is subjected to non-zero yaw angle flows. less effective in generating additional downforce at non-zero yaw angles.

0°

5°

10°

15° (a) (b) (c)

FigureFigure 15. 15Contours. Contours of of pressure pressure coe coefficientfficient on on the the car car body body and and iso-surfaces iso-surfaces of of total total pressure pressure equal equal zero forzero consecutive for consecutive yaw angles yaw angles for the for (a )the combined (a) combined case, case, (b) base (b) base case, case, and and (c) clear (c) clear case. case.

TheContours increase of ofpressure drag from coefficient using on the the presented car body for side each spoilers of the couldthree studied be perceived cases are as presented a negative consequence,in Figure 15. which This means figure that also this includes kind of iso-surfaces mechanism of should total bepressure treated equal as an to emergency zero, which device give and usedinformation only for short on how periods the 3D of timefeatures (several corresponding seconds), otherwiseto the flow fuel losses consumption are affected would by the be non-zero increased. However,yaw angle if these flow. elementsAs mentioned were usedbefore, symmetrically the side spoile onrs bothare located sides ofon the the car, windward then they side could of the be car used as(they an airbrake can be which seen at would the bottom not shift ofthe the balance car body of thein Figure car so much15). The to thepressure rear as distribution when a rear on wing the is used in braking mode [34], making it a good airbrake during cornering. Moreover, the rolling moment and side force generated by the side spoilers are other properties that could be used when a car is driving on a curve; therefore, the use of these elements could improve driving safety. The generated rolling moment would increase the downforce on the car’s wheels on the inward side of the curve, whereas the side force would decrease the centrifugal force that a cornering car is subjected to. In order to efficiently use the presented side spoilers during a gust of wind or cornering, their operation should be fully automatic. This would make them especially suitable for fully autonomous vehicles. Apart from a steering mechanism that would enable a quick adjustment of the inclination angle of the side spoilers, such a device would also need to rely on a set of sensors that would deliver information about the kind of force or moment that needs to be generated on the car body to improve driving stability. The ability to detect the need to perform a rapid maneuver or to detect a gust of wind that is about to hit the car would also increase its capabilities, because the autonomous system could either decide to activate some of the active aerodynamic elements beforehand or put them on standby to ensure that they can be activated as soon as possible. Energies 2019, 12, 4697 18 of 22

4. Conclusions A new location for a side spoiler was presented, with the side spoiler mounted on the quarter glass, which proved to be very efficient. Its operation was studied when it was the only additional element attached to the car body and when it was accompanied by another side spoiler mounted on the side of a fender, which is a more common location for attaching aerodynamic devices. The studied side spoilers were located on the windward side, whereas in other investigations, most of the focus was on the modifications of the leeward side of a vehicle. It was proven that side spoilers could significantly change the side force and the yawing moment coefficients over a wide range of yaw angles. Using these kinds of elements could enhance car safety during a steady-state crosswind. The studied aerodynamic elements generated additional drag, which means that they can only be used for short periods of time to decrease a car’s sensitivity to a crosswind and therefore increase driving safety. Unfortunately, they cannot be used to improve fuel economy, which is affected by the increase in yaw angle. However, on the other hand, they provide an interesting alternative for the rear wing as an airbrake as well as a device that improves the downforce of a vehicle without shifting the balance of the car towards the rear axle. Another potential application is when it is necessary to perform a rapid turning maneuver, and the possibility of generating a yaw moment might prove to be beneficial for its successful completion. Different car body types should be studied to investigate their influence on the operation of the side spoilers and the interaction between each of the used side spoilers to improve their efficiency depending on the desired force or moment that they are expected to generate. Such a study should be undertaken because this paper presented that side spoilers can significantly influence the flow downstream, even in locations that are not directly behind the side spoilers. With a larger result dataset available, a best practice guide for designing side spoilers could be prepared to aid car designers. This should also lead to establishing the most efficient shapes of side spoilers mounted at each location, and also whether the same shape could be used for different kinds of car bodies or if it should be tailored depending on a given car body shape. The use of active side spoilers could lead to benefits when combined with autonomous vehicles. A driver’s reflexes would be too slow for efficient use, and manual operation would pose an additional distraction. An especially important factor is that a change in the design of future vehicles could facilitate the inclusion of these kinds of aerodynamic elements. Despite all the advantages, there are many challenges that need to be overcome to implement such devices. The algorithm used for controlling the steering mechanism of the side spoilers when the car is subjected to a crosswind would have to take into account the current yaw angle that the crosswind creates and align the side spoilers accordingly. It should also be investigated whether the value of force and moment coefficients that are influenced by side spoilers differ depending on the speed. Future investigations on this matter should include unsteady calculations that would take into account the dynamic phenomena that take place when the side spoilers are activated and while they are being ejected from the car body. The most complete analysis of the efficiency of this mechanism would involve performing simulations combining aerodynamics and vehicle motion.

Author Contributions: Conceptualization, K.K. and J.P.; methodology, K.K. and J.P.; software, K.K.; validation, K.K.; formal Analysis, K.K. and J.P.; investigation, K.K. and J.P.; resources, K.K. and J.P.; data curation, K.K.; writing—original draft preparation, K.K.; writing—review and editing, J.P.; visualization, K.K.; supervision, J.P.; project administration, J.P.; funding acquisition, J.P. Funding: This project was funded by the National Centre for Research and Development (Narodowe Centrum Bada´ni Rozwoju), grant number PBS3/B6/34/2015, “The active system of car body oscillation damping”. Conflicts of Interest: The authors declare no conflict of interest. The sponsors had no role in the design, execution, interpretation, or writing of the study. Energies 2019, 12, x FOR PEER REVIEW 18 of 21

the balance of the car towards the rear axle. Another potential application is when it is necessary to perform a rapid turning maneuver, and the possibility of generating a yaw moment might prove to be beneficial for its successful completion. Different car body types should be studied to investigate their influence on the operation of the side spoilers and the interaction between each of the used side spoilers to improve their efficiency depending on the desired force or moment that they are expected to generate. Such a study should be undertaken because this paper presented that side spoilers can significantly influence the flow downstream, even in locations that are not directly behind the side spoilers. With a larger result dataset available, a best practice guide for designing side spoilers could be prepared to aid car designers. This should also lead to establishing the most efficient shapes of side spoilers mounted at each location, and also whether the same shape could be used for different kinds of car bodies or if it should be tailored depending on a given car body shape. Despite all the advantages, there are many challenges that need to be overcome to implement such devices. The algorithm used for controlling the steering mechanism of the side spoilers when the car is subjected to a crosswind would have to take into account the current yaw angle that the crosswind creates and align the side spoilers accordingly. It should also be investigated whether the value of force and moment coefficients that are influenced by side spoilers differ depending on the speed. Future investigations on this matter should include unsteady calculations that would take into account the dynamic phenomena that take place when the side spoilers are activated and while they are being ejected from the car body. The most complete analysis of the efficiency of this mechanism Energieswould2019, involve12, 4697 performing simulations combining aerodynamics and vehicle motion. 19 of 22

Abbreviations: The following abbreviations are used in this manuscript:

AbbreviationsAuthor Contributions: Conceptualization, K.K. and J.P.; methodology, K.K. and J.P.; software, K.K.; validation, The followingK.K.; formal abbreviations Analysis, K.K. are and used J.P.; in in thisvestigation, manuscript: K.K. and J.P.; resources, K.K. and J.P.; data curation, K.K.; writing—original draft preparation, K.K.; writing—review and editing, J.P.; visualization, K.K.; supervision, J.P.; CFDproject administration, Computational J.P.; funding Fluid acquisition, Dynamics J.P. NASCARFunding: This project National was Associationfunded by the for National Stock CarCentre Auto for RacingResearch and Development (Narodowe Centrum RANSBadań i Rozwoju), Reynolds-Averaged grant number PBS3/B6/34/2015, Navier Stokes “The active system of car body oscillation damping”. SST Shear Stress Transport Conflicts of Interest: The authors declare no conflict of interest. The sponsors had no role in the design, execution, interpretation, or writing of the study. Appendix A. The Main Dimensions of the Spoilers and the Car Body Appendix A: The main dimensions of the spoilers and the car body: 4 m

0.352 m 1.247 m m 1.247 0.268 m m 0.268 2.364 m

0.339 m

FigureFigure A1.1. CarCar body body and and spoilers spoilers (marked (marked in blue) in blue)dimensions. dimensions. .

Appendix B. Tables with the Values Used in Each Graph

Appendix B: Tables with the values used in each graph: Table A1. Breakdown of the aerodynamic loads generated on the car body and the side spoiler mounted Table B1. Breakdown of the aerodynamic loads generated on the car body and the side spoiler on the quarter glass and inclined at different angles, presented on graphs in Figure4. mounted on the quarter glass and inclined at different angles, presented on graphs in Figure 4. Angle Cx Cy Cz Cmx Cmy Cmz

[◦] Spoiler Total Spoiler Total Spoiler Total Spoiler Total Spoiler Total Spoiler Total 0.0 – 0.333 – 0.002 – 0.002 0.000 0.000 0.000 –0.214 0.000 0.001 27.5 0.011 0.370 0.014 0.058 –0.025 –0.088 0.005 0.009 –0.001 –0.239 0.002 0.007 55.0 0.038 0.410 0.004 0.007 –0.063 –0.160 0.019 0.025 –0.002 –0.241 0.011 0.025 82.5 0.051 0.440 –0.032 –0.063 –0.066 –0.218 0.027 0.037 0.000 –0.232 0.021 0.024 110.0 0.048 0.448 –0.066 –0.121 –0.042 –0.198 0.027 0.036 0.004 –0.186 0.025 0.034 137.5 0.037 0.433 –0.097 –0.072 –0.007 –0.200 0.024 0.033 0.007 –0.224 0.028 0.027

Table A2. Breakdown of the aerodynamic loads generated on the car body and the side spoiler mounted on the front bumper and inclined at different angles, presented on graphs in Figure9.

Angle Cx Cy Cz Cmx Cmy Cmz [◦] Spoiler Total Spoiler Total Spoiler Total Spoiler Total Spoiler Total Spoiler Total 0 – 0.333 – 0.002 – 0.002 0.000 0.000 0.000 –0.214 0.000 0.001 25.0 –0.007 0.346 –0.046 –0.061 –0.008 –0.084 0.000 0.000 –0.006 –0.247 0.032 0.020 50.0 0.012 0.368 –0.081 –0.030 –0.025 –0.065 0.004 0.016 –0.020 –0.230 0.067 0.053 75.0 0.045 0.403 –0.084 –0.135 –0.044 –0.179 0.011 0.021 –0.037 –0.284 0.081 0.074 100.0 0.065 0.404 –0.039 –0.109 –0.046 –0.166 0.016 0.023 –0.039 –0.282 0.055 0.077 125.0 0.075 0.415 –0.003 –0.103 –0.050 –0.193 0.020 0.029 –0.042 –0.281 0.033 0.059 Energies 2019, 12, 4697 20 of 22

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

Combined case Base case Yaw Yaw Cx Cy Cz Cmx Cmy Cmz Cx Cy Cz Cmx Cmy Cmz [◦] [◦] 0 0.492 –0.285 –0.301 0.040 –0.230 0.074 0 0.333 0.002 0.002 0.000 –0.214 0.001 5 0.480 0.064 –0.096 0.033 –0.195 0.052 5 0.377 0.218 –0.072 0.003 –0.202 –0.019 10 0.454 0.246 –0.037 0.044 –0.178 –0.011 10 0.379 0.371 –0.012 0.024 –0.189 –0.059 15 0.414 0.430 0.063 0.051 –0.172 –0.066 15 0.383 0.527 0.071 0.041 –0.168 –0.100 Clean case (CFD) Clean case (analytical) Yaw Yaw Cx Cy Cz Cmx Cmy Cmz Cx Cy Cz Cmx Cmy Cmz [◦] [◦] 0 0.339 –0.001 0.147 0.000 –0.273 0.000 0 – 0.000 –––– 5 0.356 0.150 0.096 0.008 –0.277 –0.040 5 – 0.161 –––– 10 0.394 0.331 0.147 0.035 –0.264 –0.064 10 – 0.323 –––– 15 0.366 0.467 0.218 0.042 –0.261 –0.113 15 – 0.484 ––––

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