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,
9,
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 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,
18,
19,
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 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,
32,
33,
34]. The previous investigations focused on the change of the drag and lift coefficients and included experimental results that were used to validate CFD calculations.
Two locations of the side spoilers were taken into account, the parts of the car body that could be used to slide them in are colored blue in
Figure 1a, whereas the red lines mark their axes of rotation. It was decided to focus on rotational elements rather than sliding ones because sliding elements can be more prone to jamming. The reasoning behind choosing the locations of the side spoilers was to place them at the front of the car body. The main principle of operation of these spoilers is that, while active, they induce an increase in pressure in front of them and a decrease in pressure behind them, leading to the generation of a side force. In addition, the aerodynamic load on the side spoilers and the modified pressure on the car body also lead to the generation of the yawing moment that can either enhance its turning abilities or prevent it from turning away from the driving line while affected by a crosswind. The dimensions of the side spoilers were chosen to be as large as possible while taking into account that they have to fit onto the car body. The spoiler located at the quarter glass was shaped to fill the area where the quarter glass is located, whereas the spoiler on the bumper was shaped to fill as much as possible of the area on the side part of the bumper. There were no optimization techniques used to design these spoilers, and it was assumed that making them as large as possible would be enough to demonstrate their potential. The area of the quarter glass spoiler was equal to 0.095 m
2, and the area of the spoiler on the bumper was equal to 0.109 m
2. Although the final version of the spoiler on the bumper turned out to have an area larger by 13% than the quarter glass spoiler, both of these elements were tailored to be of similar size to make it easier to directly compare their efficiency. The main dimensions of the side spoilers are presented in
Appendix A.
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
Figure 1a 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
Figure 1b,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
Figure 2a 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 angles possible. In each case, a uniform velocity profile was used with a velocity magnitude equal to 40 m/s across the whole height of the domain.
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.
The symmetry boundary type was used to model a zero-shear slip flow on the ground to prevent 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 effects of the build-up of the boundary layer on the ground, which could be different depending on the width of the calculational domain.
A velocity magnitude equal to 40 m/s was chosen for the calculations as it is within the range of maximum allowable speeds that a car may attain on a public road. In most countries, the highway speed limit is between 22 m/s and 39 m/s, whereas there are countries, such as Germany, that have sections of highways 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 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.
The pressure coefficient used in visualizations was defined as:
where the following parameters are static pressure at a point (
p), reference static pressure (
pref = 0 Pa), air density (
ρ = 1.225 kg/m
3), and reference velocity (
Vref = 40 m/s).
The coefficients of forces and moments in the relevant directions were obtained with the following formulas:
where the following parameters are force (
F), moment (
M), frontal area (
A = 1.660 m
2), the length between the front and the rear axles (
l = 2.364 m). In each case, the coefficients of forces and moments were calculated using the same reference area, which refers to the frontal area of the car body without the side spoilers.
The way the flow at a non-zero yaw angle was directed was depicted in
Figure 2a. The domain was discretized with the use of tetrahedral elements, and a mesh near the car body is presented in
Figure 2b. 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
Figure 2c, 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
Table 1 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
Table 1, it can be concluded that the mesh consisting of 3.269 × 10
7 elements is adequate for use in these studies as the values of the aerodynamic coefficients stay close to the ones obtained with this mesh even when the number of mesh cells is further increased. When the mesh size was increased to 4.395 × 10
7 elements, the values of all of the aerodynamic coefficients did not change more than 1.2%.
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.