Wake Structures and Surface Patterns of the Drivaer Notchback Car Model Under Side Wind Conditions

energies

Article Wake Structures and Surface Patterns of the DrivAer Notchback Car Model under Side Wind Conditions

Dirk Wieser *, Christian Navid Nayeri * and Christian Oliver Paschereit Institute of Fluid Dynamics and Technical Acoustics, Technische Universität Berlin, Müller-Breslau-Straße 8, 10623 Berlin, Germany; [email protected] * Correspondence: [email protected] (D.W.); [email protected] (C.N.N.)

Received: 4 December 2019; Accepted: 26 December 2019; Published: 9 January 2020

Abstract: The flow field topology of passenger cars considerably changes under side wind conditions. This changes the surface pressure, aerodynamic force, and drag and performance of a vehicle. In this study, the flow field of a generic passenger vehicle is investigated based on three different side wind angles. The study aimed to identify vortical structures causing changes in the rear pressure distribution. The notchback section of the DrivAer model is evaluated on a scale of 1:4. The wind tunnel tests are conducted in a closed section with a splitter plate at a Reynolds number of 3 million. The side wind angles are 0◦, 5◦, and 10◦. The three-dimensional and time-averaged flow field downstream direction of the model is captured by a stereoscopic particle image velocimetry system performed at several measurement planes. These flow field data are complemented by surface flow visualizations performed on the entire model. The combined approaches provide a comprehensive insight into the flow field at the frontal and side wind inflows. The flow without side wind is almost symmetrical. Longitudinal vortices are evident along the downstream direction of the A-pillar, the C-pillars, the middle part of the rear window, and the base surface. In addition, there is a ring vortex downstream of the vehicle base. The side wind completely changes the flow field. The asymmetric topology is dominated by the windward C-pillar vortex, the leeward A-pillar vortex, and other base vortices. Based on the location of the vortices and the pressure distributions measured in earlier studies, it can be concluded that the vortices identified in the wake are responsible for the local minima of pressure, increasing the vehicle drag.

Keywords: DrivAer; aerodynamics; wind tunnel; vehicle; ﬂow visualization; PIV; wake structures; side wind; crosswind

1. Introduction Road vehicles operate in an environment in which the inflow direction and the magnitude of the velocity vary permanently. The average natural wind speed on the ground is assumed to be between 2 and 5 km/h [1,2]. Moreover, this value is superimposed by wind fluctuations caused by gust, weather, area topology, and road users. Experimental analyses of vehicles equipped with measuring probes on the road have mainly shown that the inflow direction is mostly in the range of 10 [3] and that the ± ◦ turbulence level is in the range of 2 to 10% [4–7]. Guilmineau et al. [8] documented a drag increase of 20% for the Ahmed test body with a ≈ crosswind of 10◦. The drag increase even doubles when the crosswind angle is increased to 15◦. The same correlation is evident for other vehicle geometries, although it is slightly smaller for streamlined vehicle geometries. For the realistic vehicle geometry of the DrivAer model, a drag increase of 10% at a side wind angle of 10 is evident compared to the frontal direction [9,10]. ≈ ◦ In addition to the vehicle drag, the lift force also experiences a significant change in the yawed flow. Side wind leads to higher lift forces and changes the load distribution between the front and the rear

Energies 2020, 13, 320; doi:10.3390/en13020320 www.mdpi.com/journal/energies Energies 2020, xx, 5 2 of 18 axles.Energies This2020 can, 13 have, 320 a negative effect on driving dynamics and vehicle stability [11]. In2 of addition, 18 a change in the vehicle inflow because of crosswind can lead to increased noise emissions and to a changeaxles. in soiling This can in have safety-relevant a negative effect viewing on driving areas, dynamicssuch as water and vehicle soiling stability and water [11]. trickles In addition, [12–15]. aIn change the present in the study,vehicle the inflow notchback because configuration of crosswind can of lead the DrivAer to increased model noise is emissions evaluated. and This to a model waschange developed in soiling at Technische in safety-relevant Universität viewing München areas, such asin water 2011 soiling in cooperation and water trickles with the [12– automotive15]. companiesIn the BMW present AG study, (Munich, the notchback Bavaria, configuration Germany) ofand the Audi DrivAer AG model (Ingolstadt, is evaluated. Bavaria, This model Germany). The geometrywas developed is a design at Technische hybrid Universität of an “Audi München A4TM” and in 2011 a “BMW in cooperation 3 seriesTM with”. The the aim automotive is to develop a realisticcompanies vehicle BMW geometry AG (Munich, that is Bavaria, freely available Germany) to and the Audi research AG (Ingolstadt, community. Bavaria, The model Germany). geometry The geometry is a design hybrid of an “Audi A4TM” and a “BMW 3 seriesTM”. The aim is to develop is available in fastback, notchback, and fullback versions. The underbody is available in a flat and a a realistic vehicle geometry that is freely available to the research community. The model geometry detailed version. Further information on general model design can be found in the literature [9,16]. is available in fastback, notchback, and fullback versions. The underbody is available in a flat and a The effectdetailed of version.crosswinds Further on thisinformation DrivAer on model general has model already design been can investigated be found in the in literature previous [9 studies,16]. by meansThe of effect force of and crosswinds pressure on measurements this DrivAer model [10,17 has,18 already]. The been successive investigated increase in previous in drag studies was attributed by to themeans significant of force change and pressure in pressure measurements distribution [10,17 at,18 the]. The rear successive of the vehicle. increase Significantly in drag was attributed lower surface pressuresto thewere significant measured change particularly in pressure distribution at the rear at window the rear of and the vehicle. the vehicle Significantly base. However, lower surface there are onlypressures a few data were on measured the external particularly flow field at theavailable rear window in order and to the identify vehicle the base. flow However, structures there which are are responsibleonly a few for data this on modified the external behavior. flow field This available deficit in is orderaddressed to identify in this the study. flow structures which are responsible for this modified behavior. This deficit is addressed in this study. The DrivAer model has already been evaluated using various wind tunnel tests at the Technische The DrivAer model has already been evaluated using various wind tunnel tests at the Technische Universität Berlin [10,17,18]. In these studies, the fastback and the notchback versions were investigated Universität Berlin [10,17,18]. In these studies, the fastback and the notchback versions were investigated underunder different different inflow inflow conditions. conditions. For For the the crosswind crosswind investigations, investigations, the the model model was was rotated rotated in the in wind the wind tunneltunnel at the at yaw the yaw angle angleβ relativeβ relative to to the the inflow. inflow. The vehicle vehicle drag dragCDCforD for the the notchback notchback version version increased increased successivelysuccessively from from 0.258 0.258 at at0◦0toto approximately approximately 0.277 0.277 at at1010◦(∆(C∆CD 8%8%) (Figure) (Figure1). The1). DrivAerThe DrivAer model model ◦ ◦ D ≈ ≈ in fastbackin fastback configuration configuration showed showed a a drag drag increase increase of of 10%10% at atβ =β =10◦10(not(not shown shown here). here). ≈≈ ◦ 0.28

0.275

0.27

[-] .

D 0 265 C 0.26

0.255

0.25 0 2 4 6 8 10 Side wind angle in degree

Figure 1. C for the notchback driver model at varying side wind conditions of 0 β 10 and Figure 1. CD forD the notchback driver model at varying side wind conditions◦ of 0◦SW βSW◦ 10◦ and 6 ≤ ≤ ≤ ≤ at Reat=Re3.2= 3.210610. . × × Figure2 shows the surface pressure distribution CP and the pressure variation p0 in the notchback Figure2 shows the surface pressure distribution CP and the pressure variation p0 in the notchback configuration of the DrivAer model at side wind angles of 0◦, 5◦, and 10◦. The pressure coefficient configuration of the DrivAer model at side wind angles of 0 −, 5 , and− 10 . The pressure coefficient is defined as ◦ − ◦ − ◦ is defined as dp C = (1) P ρ 2 dp C = /2 c∞ ADrivAer (1) P ρ · 2 · /2 c ADrivAer where dp is the pressure difference between quiescent· ∞ · condition and surface pressure, c∞ is the wherefreestreamdp is the velocity, pressure and differenceADrivAer is between the frontal quiescent area of the condition model. It and was found surface that pressure, the pressurec∞ is the recovery at the rear window and on the upper trunk deck gradually decreases with increasing yaw freestream velocity, and ADrivAer is the frontal area of the model. It was found that the pressure angles (marked with 4 in Figure2). Moreover, the local high-pressure area, which is caused by the recovery at the rear window and on the upper trunk deck gradually decreases with increasing yaw C-pillar vortex and depicted by the point 3 , decreases under crosswind conditions compared with the angles (marked with 4 in Figure2). Moreover, the local high-pressure area, which is caused by the one at 0 . In addition, a crosswind sensitive location was identified at the upper edge of the windward C-pillar vortex◦ and depicted by the point 3 , decreases under crosswind conditions compared with the C-pillar ( 1 ). The pressure coefficient C decreased from approximately 0.3 at 0 to 0.6 at 10 ; P − ◦ − − ◦ one atthe0◦ decrease. In addition, was attributed a crosswind to high sensitive velocity. location The pressure was identified at the model at the base upper (vertical edge boot of the area) windward is C-pillar ( 1 ). The pressure coefficient C decreased from approximately 0.3 at 0 to 0.6 at 10 ; responsible for a significant share of CPD. Owing to small differences in pressure− compared◦ − to the − ◦ the decrease was attributed to high velocity. The pressure at the model base (vertical boot area) is responsible for a significant share of CD. Owing to small differences in pressure compared to the rest of the vehicle, the base pressure was illustrated with a separate color bar. The pressure on the Energies 2020, 13, 320 3 of 18

Energies 2020, xx, 5 3 of 18 rest of the vehicle, the base pressure was illustrated with a separate color bar. The pressure on the base surface was almost the same everywhere at an inflow of 0◦. It was found that, with side wind base surface was almost the same everywhere at an inflow of 0◦. It was found that, with side wind atat various various angles, angles, the the pressure pressure decreased significantly at several points on the base ( (66,, 77,, and and 55).).

ItIt was was hypothesized hypothesized that that the the large large increase increase in the drag under crosswind conditions conditions was was due due to to the the aforementionedaforementioned low-pressure low-pressure areas. However, it has not yet been shown which flow flow structures structures are are responsible for these changes. This is the focus of this work. The fluctuations in surface pressure p0 are responsible for these changes. This is the focus of this work. The fluctuations in surface pressure p0 are shownshown on on the the right right side side in in Figure Figure2.. High High fluctuations fluctuations were particularly detected detected in in areas areas where where high high pressurepressure drops drops were were observed. observed.

-1.60 -0.8 2 0 0.08 0.16 p0 CP qq

β =0◦

β = 5 − ◦

2 3 4

6 7 β = 10◦ − -0.6 -0.35 -0.1 CP,base

FigureFigure 2. 2. SurfaceSurface pressure pressure (leftleft)) and and pressure ﬂuctuation (right) at various side side wind wind angles. angles.

2.2. Experimental Experimental Setup Setup TheThe experiments experiments were were conducted conducted in a closed-loop wind tunnel at the Technische Universität Universität BerlinBerlin at at the the Hermann Hermann Föttinger Föttinger Institute (HFI). Figure3 illustratesillustrates the the experimental experimental setup. setup. The The width width andand height height (cross-sectional (cross-sectional area) area) of the wind tunnel test section were 2 and √√22 m,m, respectively. respectively. 1 TheThe inflow inflow velocity, velocity,cc∞∞,, was was approximately approximately 41 m s− and was the same in previous studies studies to to maintain maintain comparability. The freestream turbulence intensity was less than 0.5%. The Reynolds number (Re) Energies 2020, 13, 320 4 of 18 comparability. The freestream turbulence intensity was less than 0.5%. The Reynolds number (Re) was approximately 3 106 based on the overall vehicle length L. For the velocity measurements, × a pitot tube was used, which was installed upstream of the model at the ceiling of the test section, and the air temperature was monitored by means of a thermocouple. The boundary layer effect acting onEnergies the model2020, xx, 5was minimized by a splitter plate that cuts off the boundary layer4 ofof 18 the wind tunnel. This is required because the wind tunnel has no ground simulation system. The model was was approximately 3 106 based on the overall vehicle length L. For the velocity measurements, investigated at yaw angles of× 0◦, 5◦, and 10◦. The inflow Re was always set at 0◦. The zero yaw angle was determineda pitot tube as wasthe angleused, which where was no installed side force upstream occurred. of the model The modelat the ceiling was of mounted the test section, on an external and the air temperature was monitored by means of a thermocouple. The boundary layer effect balance locatedacting on beneath the model the was test minimized section, by which a splitter also plate enabled that cuts the off the yaw boundary movement layer of of the the wind model in the wind tunnel.tunnel. The This mounting is required strut because between the wind the tunnel balance has no and ground the simulation model was system. aerodynamically The model was shielded without physicalinvestigated contact at yaw using anglestwo of 0◦, NACA00255◦, and 10◦. The profiles inflow Re towas minimize always set the at 0 aerodynamic◦. The zero yawforce angle acting on the strut. Awas small determined vertical asthe clearance angle where of approximately no side force occurred.2 mm Thebetween model was the mounted slightly on flattened an external tires and the balance located beneath the test section, which also enabled the yaw movement of the model in the splitter platewind as tunnel. wellThe as between mounting thestrut model between under-floor the balance and and the the model tip was of the aerodynamically NACA profile shielded was required to avoid terminationwithout physical of thecontact force using and two to NACA0025 allow yawing profiles conditions. to minimizethe The aerodynamic blockage ratioforce acting of the on model ϕ in the test sectionthe strut. at A0 smallwas vertical5.4% clearance based of on approximately the frontal2 area mm between of the model the slightlyA of flattened0.135 tires m2. and The the coefficients ◦ ≈ were correctedsplitter by plate adjusting as well as thebetween freestream the model velocity, under-floor e.g., and for the the tip of drag the NACA coefficient. profile was required to avoid termination of the force and to allow yawing conditions. The blockage ratio of the model ϕ in the test section at 0 was 5.4% based on the frontal area of the model A of 0.135 m2. The coefficients ◦ ≈ F were corrected by adjusting the freestream velocity, e.g.,D for the drag coefficient. CD = ρ 2 (2) 2 ((1 + ϕ) c∞) ADrivAer · F·D · CD = (2) ρ ((1 + ϕ) c )2 A The DrivAer model in the notchback2 version· used· ∞ for· DrivAer the wind tunnel measurements had a scale of 1:4 with a totalThe DrivAer length modelL of 1.153 in the mnotchback. The model version had used no for engine the wind compartment tunnel measurements (completely had a scale closed) and a smoothof underbody. 1:4 with a total The length wheelsL of 1.153 were m. designed The model hadstationary. no engine Further compartment information (completely can closed) also and be found in the literaturea smooth [10,17 underbody.]. The wheels were designed stationary. Further information can also be found in the literature [10,17].

traverse system

wind tunnel ceiling Pitot-tube

∆xPIVsystem = 0.62 (x/L)

thermocouple

L=1153.3 1410

camera 1+2 splitter plate z overall 33 PIV (stationary laser light sheets ground) 348.2 348.2 x NACA 0025 proﬁles ∆x = 20 ∆x = 50 (last two)

wind tunnel ﬂoor mounting strut external balance and turn table β = 0 , 5 , 10 1250 ◦ ◦ ◦ 5000

Figure 3. Setup of the wind tunnel: Units are in millimeters. Figure 3. Setup of the wind tunnel: Units are in millimeters. The flow field downstream direction of the DrivAer model was captured using stereo particle The flowimage field velocimetry downstream (PIV). The direction measurement of the planes DrivAer were oriented model perpendicular was captured to the using inflow stereo at a particle image velocimetrydistance of 20 (PIV). mm from The each measurement other (last two planes planes50 mm were), resulting oriented in an perpendicular overall measurement to area the of inflow at a approximately 0.26 x/L 0.87. The coordinate system is located in the centre between the vehicle distance of 20 mm from each≤ other≤ (last two planes 50 mm), resulting in an overall measurement area of axles. Each investigated side wind configuration at βSW = 0◦, 5◦, and 10◦ was captured by 33 PIV approximately 0.26 x/L 0.87. The coordinate system is− located− in the centre between the vehicle planes. Cameras≤ and laser≤ systems were mounted on an external traversing system, so that the whole axles. Each investigated side wind configuration at β = 0 , 5 , and 10 was captured by 33 PIV SW ◦ − ◦ − ◦ planes. Cameras and laser systems were mounted on an external traversing system, so that the whole measurement system could be moved. Thus, all measuring planes were captured directly one after the other and only one calibration plane was required for all measurements. The optical access for the Energies 2020, 13, 320 5 of 18 cameras was enabled by two large windows on both sides of the test section. The view angles between the laser light sheet and the cameras were approximately 35 . The 14-bit CCD cameras featured ± ◦ a resolution of 2048 2048 pixels. The dual cavity Nd:YAG was located on the wind tunnel ceiling × and emitted light through a window toward the wake of the vehicle. The thickness of the laser light sheet in the measured region was approximately 2 mm. The wave length of the laser light was 532 nm, with a maximum energy per laser pulse of 170 mJ. The time resolution of the PIV system was 5 Hz, and the pulse delay between the double pulses of the laser was 15 µs. Each measured PIV plane was recorded with 1000 pairs of double images to ensure the statistical convergence of the mean values. The air in the tunnel was seeded with silicon oil droplets (DEHS) of approximately 1 µs diameter. The evaluation process of the PIV plane included enhanced filters to improve the validity of the results, e.g., background subtractions, signal-to-noise ratio filters, and correlation coefficient filters. The grid refinement has an initial size of 112 112 pixels and a final size of 96 96 pixels. The cross-correlation × 1× window overlap is 50%. The physical resolution is about 8 px mm− . A previously applied disparity correction eliminated minor mismatches between camera viewing areas. The software used was PIVview (Version 3.60, PIVTEC GmbH, Göttingen, Germany). The PIV measurements were complemented using oil visualization experiments. These experiments were performed in an earlier measurement campaign, where Re was 3.2 106 × and thus slightly higher than that in the PIV measurements. This difference was assumed to be insignificant because of the independence of the Reynolds number on Re 3 106, as shown by ≥ × Strangfeld et al. [17]. A mixture of white oil-based paint and petroleum was applied to the surface as thinly as possible using paint rollers to reduce large liquid accumulations. This reduced oil pooling, trickles, and droplets ensured the rapid drying of the mixture during the tests. The underbody and tires were not considered in these tests. The effect of gravity on the oil mixture was insignificant as the same surface trace patterns were seen at low Reynolds number. The flow visualizations were carried OP out analogously based on the PIV measurements at three side wind angles, βSW of 0◦, 5◦, and 10◦. The superscript OP denotes the oil paint experiments. Please note that the crosswind in the PIV and the oil paint measurements were sideways reversed. The dried surface traces were photographed in the front, back, and both side views using a digital camera. These captured images were then further processed with in-house trace software. In the first step, a large amount of oil trace directions (friction lines) were detected in the image. In the second step, an entire flow field was computed using a linear interpolation approach. A large number of supporting points were essential to ensure a valid and representative flow pattern all over the model. With these digitized trace patterns, deviations in the flow pattern between the examined crosswind cases were detected and visualized.

3. Results The results of the experiments in this study are thematically structured in two parts. First, the oil flow visualizations regarding the flow directions of 0◦, 5◦, and 10◦ are presented. The respective external flow fields captured using PIV are shown afterward. In this study, the inflow without crosswind is referred to as the baseline case.

3.1. Surface Traces without Crosswind OP Figure4 illustrates the surface traces on the DrivAer model at βSW of 0◦ in the front, rear, and side views. Only one side of the model is shown here as both sides look the same. The main ﬂow characteristics of the oil traces are emphasized by superimposed limiting streamlines obtained from the in-house trace software. EnergiesEnergies2020, xx2020, 5, 13, 320 6 of 18 6 of 18

a) b)

S1 F W F 4 F3 1 F2 S2 B1 B2

C F5 F5

G F6 B F6

c) P M D

Figure 4. Surface traces at β = 0◦ in the frontal view (a), rear view (b), and side view (c). Figure 4. Surface traces at β = 0◦ in the frontal view (a), rear view (b), and side view (c). The surface traces on the model front are side-symmetrical and characterized by two stagnation Thepoints. surface One is traces located on the the lower model windshield front are and side-symmetrical another is on the lower and grille. characterized Both are indicated by by two stagnation W and G, respectively. However, it is not possible to depict the exact locations, as almost no oil traces points.are One visible is located within the on areas. the lower A closer windshield examination and of the another front fascia is on reveals the lower further grille. stagnation Both lines are indicated by W andlocatedG, respectively. on the side and However, center grills, it is as not shown possible by the todashed depict lines theB and exactC, respectively. locations, as However, almost no oil traces are visiblethese can within be attributed the areas. to the A closed closer grill examination design of the model of the that front prevents fascia any reveals flow. further stagnation lines located onFigure the side4b shows and the center oil traces grills, on the as back shown of the by model. the dashed Distinct oil lines patternsB and canC be, respectively. seen in the However, upper part of the rear window and on the upper trunk deck. A closer examination shows that this these can be attributed to the closed grill design of the model that prevents any flow. asymmetrical structure consists of two counter rotating vortex structures that are located directly next Figureto each4 other.b shows The focus the oil points traces are indicated on the back with F of1 and theF2 model.. Both upstream Distinct and oil downstream patterns can of the be seen in the uppercentral part of structure the rear are orthogonal window saddle and on points the that upper formed trunk (see S deck.1 and S A2, respectively). closer examination The existence shows that this asymmetricalof an asymmetric structure flow consists pattern on of reartwo windows counter (often rotating referred vortex to as structures backlight) of that a notchback are located has directly next been repeatedly documented in several studies [19,20]. Nevertheless, the basic driving mechanism to each other. The focus points are indicated with F and F . Both upstream and downstream of the is not yet fully understood. Sims et al. [20] showed that1 this asymmetric2 flow topology is always centralformed structure for certain are orthogonal geometric vehicle saddle rear-end points designs. that Furthermore,formed (see oilS1 mixtureand S pooling2, respectively). is visible on The existence of an asymmetricthe outer sides offlow the rear pattern window on (see rear points windowsF3 and F (often4). The mixture referred dried to inas circular backlight) paths reflects of a notchback has been repeatedlythe direction ofdocumented the rotation of in the several C-pillarstudies vortices. Furthermore,[19,20]. Nevertheless, on both sides the of the basic rear window driving mechanism and the trunk deck, the characteristic patterns of the C-pillar vortices were visible, with the oil pattern is not yet fully understood. Sims et al. [20] showed that this asymmetric flow topology is always lines pointing outwards. In addition, the bifurcation lines B1 and B2 were visible on both sides. formed forThe certain development geometric of C-pillar vehicle vortices rear-end depends designs. considerably Furthermore, on the rear geometry oil mixture of the pooling vehicle. is visible on the outerBasic sides studies of can the be rear found window in Ahmed (see et al. points [21]. NoF3 oiland tracesF4 are). The visible mixture on the vertical dried trunk in circular surface paths reflects the directionbecause of of the the flow rotation separation of along the C-pillar the downstream vortices. direction Furthermore, of the vehicle on and both the resulting sides of low the air rear window and thespeed. trunk However, deck, the two characteristic focus points are visiblepatterns on each of the side. C-pillar The patterns vortices around were the visible,focus point withF5 is the oil pattern lines pointing outwards. In addition, the bifurcation lines B1 and B2 were visible on both sides. The development of C-pillar vortices depends considerably on the rear geometry of the vehicle. Basic studies can be found in Ahmed et al. [21]. No oil traces are visible on the vertical trunk surface because of the flow separation along the downstream direction of the vehicle and the resulting low air speed. However, two focus points are visible on each side. The patterns around the focus point F5 is caused by the inclined surface of the bumper and, around the focus point F6, is induced by the flow in the lower trunk corner, which is often seen on vehicles and bluff bodies [22,23]. Ekman et al. [24] simulated the entire setup of the DrivAer, including the wind tunnel from this study. They showed that there are noticeable differences among the underlying turbulence models of the simulation. In an effective agreement, the vehicle drag between experiment and simulation were found for the SBES Energies 2020, 13, 320 7 of 18

caused by the inclined surface of the bumper and, around the focus point F6, is induced by the flow in the lower trunk corner, which is often seen on vehicles and bluff bodies [22,23]. Ekman et al. [24] simulated the entire setup of the DrivAer, including the wind tunnel from this study. They showed that there are noticeable differences among the underlying turbulence models of the simulation. In an effective agreement, the vehicle drag between experiment and simulation were found for the SBES model. The best results to reproduce the oil traces were also obtained by the SBES model. The surface pressure correlation varied with turbulence model and vehicle regions considered. Figure4c illustrates the oil traces on the vehicle side. As both sides look the same, only one side is shown. Two small recirculation areas are present along the downstream direction of the front and rear wheels around the focus points FF and FR. The influence of the A-pillar vortex on the oil traces is visible on the upper part of the side window. The traces in this area are significantly directed upward, provoking a separation line directly below the A-pillar edge, as shown by line P. A stagnation point and an attachment line are also present on the mirror cover (not shown here). At the upstream part of the side mirror exists a further detachment line M, which is provoked by high static pressure. Below the mirror, there are distinctive flow redirections, which indicate high local pressure gradients around the side mirror. The interference of the side mirror trailing edge with the side window and the side door up to the B-pillar is clearly visible in the D area by the diverging traces.

3.2. Surface Traces with Crosswind OP Figures5 and6 show photos of the dried oil traces for βSW of 5◦ and 10◦ in the front-, sides-, and rear views, respectively. Similarly, as shown in Figure4, characteristic oil traces from the in-house trace software are superimposed into the photos to emphasize the main flow qualities. Moreover, a superimposed, colored map on the sides of the model shows the changes in flow direction between the crosswind case and the baseline case. Red areas indicate more upward directed oil traces compared with the baseline case. Blue areas represent the opposite course. The color map was only used for the model sides because the changes are subtle and difficult to see. The flow pattern at the front end was no longer side-symmetric under crosswind conditions. The stagnation points at the lower windshield and the grill shifted considerably to the windward side. The oil traces on the leeward side of the front end indicated that a significant portion of the flow passes across the engine hood and the A-pillar toward the model side into the leeward region. The contrary OP behavior was seen on the windward side of the front end. Particularly at βSW of 10◦, there was almost no flow around the A-pillar and the engine hood side area towards the vehicle side. The changed flow around the front section has a significant impact on the flow at the sides, as shown later. Studies have shown that the side wind significantly changes the flow around the A-pillars and, thus, the development of the A-pillar vortex [25,26]. At the top right of the figures, the traces are visible on the rear side of the model. The large asymmetric flow pattern composed of the focus points F1 and F2 on the rear window were clearly shifted leeward and reduced in spatial dimensions compared to the baseline case. The C-pillar vortex on the windward side and the focus point F3 were still present at side wind conditions. The characteristic oil pattern on the rear window and boot deck caused by the C-pillar vortex extended further toward the center of the vehicle, as can be seen by the bifurcation line B1. This was concordant with the pressure measurements shown in Figure2, where the local maximum pressure caused by this vortex also gradually shifted leeward. A completely opposite effect OP was observed for the C-pillar on the leeward side. While at βSW of 5◦, a small focus point F4 was visible, at 10◦, it disappeared completely because of the reduced flow around the C-pillar. In addition, the flow structure consisting of F1 and F2 in this area could also have an influence. Energies 2020, 13, 320 8 of 18 Energies 2020, xx, 5 8 of 18

βSW =5◦ a) βSW =5◦ b)

F3 F1 F2 F4

B1 windward leeward F8 leeward

F6 F7

c) βSW =5◦

∆◦ +15 ≤

15 ≤−

windward

d) βSW =5◦

∆◦ +15 ≤

15 leeward ≤−

Figure 5. Surface traces at side wind condition of 5 :(a) front view, (b) rear view, (c) leeward side, Figure 5. Surface traces at side wind condition of 5◦:(a) front view, (b) rear view, (c) leeward side, andand ( (dd)) windward windward side. side. The color indicates the changes in the oil trace trace directions directions in in relation relation to to the the baselinebaseline case. Energies 2020, 13, 320 9 of 18 Energies 2020, xx, 5 9 of 18

βSW =10◦ a) βSW =10◦ b)

F3 F 1 F2

B1 leeward F8 leeward windward F7 F6

c) βSW =10◦

∆◦ +15 ≤

15 ≤−

windward

d) βSW =10◦

∆◦ +15 ≤

15 leeward ≤−

FigureFigure 6. 6.SurfaceSurface traces traces at at side side wind wind condition condition of of1010◦◦:(:(aa)) front front view, view, (b (b)) rear rear view, view, (c ()c) leeward leeward side, side, andand ( (dd)) windward windward side. side. The The color color indicates indicates the the changes changes in in the the oil oil trace trace directions directions in in relation relation to to the the baselinebaseline case. case.

SeveralSeveral oil oil traces, traces, which which were were caused caused by by secondary secondary flows flows and and were were previously previously not not present present at at 00◦◦,, were were visible visible on on the the vehicle vehicle base. base. In In the the lower lower part part at at the the center center of of the the base, base, a a large large structure structure was was visiblevisible at at55◦◦andand1010◦◦,, which which is is indicated indicated with withFF77.. On On the the leeward leeward side side of of the the base base surface, surface, another another vorticalvortical structure structure was was visible visible around around the the focus focus point pointFF88.. Exact Exact localization localization of of both both positions positions of of the the focusfocus points points was was impossible impossible as as only only a a few few discrete discrete traces traces were were present present at at the the center center of of the the structures. structures. AtAt the the lower lower corner corner on on the the windward windward side, side, the the focus focus point pointFF6,6, which which represented represented the the only only remaining remaining OPOP = structurestructure compared compared to toββSWSW= 00◦◦,, was was present present (Figure (Figure44).). OPOP FiguresFigures55 andand66cc show show the the oil oil traces traces on on the the windward windward side side of of the the model model at at ββSWSW==5◦5◦andand OPOP ββSWSW ==1010◦◦,, respectively. respectively. In In the the lower lower midsection midsection of of the the side side doors, doors, there there were were only only minimal minimal effects effects of of thethe crosswind. crosswind. The The flow flow directions directions of of the the oil oil traces traces were were almost almost identical identical at at00◦,◦,55◦,◦ and, and1010◦.◦. However, However, onon the the engine engine hood, hood, the the roof roof rail, rail, and and the the trunk, trunk, significant significant changes changes were were visible, visible, especially especially at at1010◦.◦. TheThe red red areas areas reveal reveal a a distinct distinct upwind upwind compared compared to to00◦◦.. Moreover, Moreover, the the wake wake of of the the side side mirror mirror was was displaceddisplaced upward upward and and lay lay now now completely completely on on the the vehicle vehicle side side window. window. A A blue blue area area is is visible visible below below the A-pillar. Already, according to the front view, the flow around the windward A-pillar reduced with Energies 2020, 13, 320 10 of 18 the A-pillar. Already, according to the front view, the flow around the windward A-pillar reduced with the side wind, which led to a reduced intensity of the A-pillar vortex. Consequently, the shear stresses on the oil mixture through the A-pillar vortex were also reduced, causing the oil mixture to be less clearly transported upward. Finally, the flow separations downstream of the wheels around the focus points FF and FR were no longer present. Figures5 and6d illustrate the oil traces on the leeward side of the model at 5◦ and 10◦, respectively. The trace pattern on the leeward side differed completely from those on the windward side. A significant influence of the crosswind was especially visible in the front area through the red area, which reveals oil traces directed upwards compared to 0◦. The reason for this cannot be disclosed here, as no data of the external flow field were available. The literature shows that a longitudinal vortex can occur on the leeward side of the engine hood in crosswind, e.g., on the Willy model [8]. This longitudinal vortex can be responsible for the upward shear stresses. A further red area was visible below the A-pillar because of the intensified vortex, as the flow around the A-pillar was considerably more pronounced at side wind conditions. The increase in the intensity of the A-pillar vortex in the DrivAer model at crosswind conditions was also reported in the results of other studies [25]. The impact of this intensified A-pillar vortex on the wake will be discussed later in the PIV results. The oil traces further downstream on the rear area of the model side on the fender showed a downward direction (blue area). The reason for this cannot be clarified as no information on the flow field data existed in this area either. However, it is evident that the flow topology on the vehicle side prevents the flow around the C-pillar and, thus, the development of the C-pillar vortex.

3.3. Wake Flow Field without Side Wind Figure7a–f shows the flow field without the crosswind downstream direction of the model. In the top four images, selected longitudinal vortices are shown by isosurfaces of dimensionless vorticity ω~ , which is determined by Ω~ L ω~ = · (3) c~∞ where Ω is the vorticity. Figure7a,c visualizes the vortices along the downstream direction of the rear window. The two longitudinal vortices of the C-pillars look qualitatively similar for ω = 3.5. Both isosurfaces extend | x| to the end of the captured measurement region and thus confirm the robustness of the vortices. In the middle part of the rear window, there are two counter rotating vortex structures, with the vortex on the left side much more pronounced than that on the other side. However, both intensities are considerably lower than those of the C-pillar vortices. The flow structures identified by PIV shows excellent accordance with the surface traces of the oil paint in Figure4. Both the locations of the oil mixture pooling around the focus points F1 to F4 and the courses of the attachment lines at the rear window and at the boot deck can be attributed to these flow structures. Qualitative overviews of the courses of the vortex cores both in the top view and in the side view are shown separately later. Figure7b,d shows the downstream vorticity ωx of the vehicle base. At the center of the base, there are two large-scale counter-rotating vortices. Although their vorticity is very high, their existences remained undiscovered in the flow visualization, which suggests that they do not exist directly at the base surface. Two further vortices are visible at each side of the vehicle base. The intensity of the base vortex is slightly less than that of the upper vortex, which is induced by the geometric shape of the bumper. The isosurfaces of the vortices are similar on both sides and differ only in the respective direction of the rotation. The comparison with Figure4 shows that these side vortices are accountable for F5 and F6. Energies 2020, 13, 320 11 of 18 Energies 2020, xx, 5 11 of 18

a) β = 0◦ b) β = 0◦

c) β = 0◦ d) β = 0◦

β = 0 β = 0 e) ◦ f) ◦

u = 0 m/s λ2 = 100,000

FigureFigure 7. 7.VorticalVortical structures structures along along the the downstream downstream direction of of the the rear rear window window and and the the vehicle vehicle base base surface without side wind: (a–d) streamwise vortices, (e) λ2-criterion, and (f) recirculation area. surface without side wind: (a–d) streamwise vortices, (e) λ2-criterion, and (f) recirculation area.

The downstream vortex criterion λ2 of the model is shown in Figure7e. This criterion is applicable The downstream vortex criterion λ2 of the model is shown in Figure7e. This criterion is applicable to identify vortex structures in a three-dimensional and complex flow field. λ2 is defined as the second to identify vortex structures in a three-dimensional and complex flow field. λ2 is defined as the second eigenvalue of the equation S2 + Ω2 = 0, where S = 0.5 J + JT and Ω = 0.5 J JT . The exponent eigenvalue of the equation S2 + Ω2 = 0, where S = 0.5· J + JT and Ω = 0.5· J− JT . The exponent T denotes the transpose operation, and J is defined as the· gradient velocity tensor· −~c. As can be seen, T denotes the transpose operation, and J is defined as the gradient velocity tensor 5 ~c. As can be seen, there is a so-called downstream ring vortex on the base. It only gets bifurcated at5 the low corners, there is a so-called downstream ring vortex on the base. It only gets bifurcated at the low corners, which is probably caused by the rear wheels’ wake. The small enlargements at the upper part of which is probably caused by the rear wheels’ wake. The small enlargements at the upper part of the ring vortex reflect the impact of the C-pillar vortices. Thus, the effect of the C-pillar vortices is the ring vortex reflect the impact of the C-pillar vortices. Thus, the effect of the C-pillar vortices is less significant in this area. The examination of the vorticities, ωy and ωz, in this area shows that the ω ω lessvorticity significant level inis approximately this area. The examinationfive times as high of the as vorticities, that of the C-pillary and vorticesz, in this (not area shown shows here). that the vorticityFigure level7f is illustrates approximately the contour five timesof zero as downstream high as that velocity of the C-pillaru = 0m/ vorticess of the (not model. shown The contourhere). is shapedFigure7 slightlyf illustrates asymmetrical, the contour which of zero may downstream be caused velocity by a largeu = number0 m/s of of the vortices model. in The that contour area. isThe shaped maximum slightly extension asymmetrical,x/L in the which plane may of symmetry be caused is by approximately a large number 0.15. of In vortices an earlier in study that area. by The maximum extension x/L in the plane of symmetry is approximately 0.15. In an earlier study by Wieser et al. [10], where the laser light sheet was parallel to the x–z plane and at y = 0 mm, a maximum Energies 2020, xx, 5 12 of 18 Energies 2020, 13, 320 12 of 18

Wieser et al. [10], where the laser light sheet was parallel to the x–z plane and at y=0 mm, a maximum lengthlength of ofx/Lx/L==0.1480.148waswas determined. determined. Thus, Thus, there there is is an an excellent agreement between between the the two two studies, studies, althoughalthough the the setup setup of of the the measurement measurement was was different. different.

3.4.3.4. Wake Wake Flow Flow Field Field with with Side Side Wind Wind

FigureFigure8 8illustrates illustrates the the external external flow flow field field at at a a side side wind wind condition condition of of βSW ofof 55◦.. The The arrow arrow sign sign SW −− ◦ inin the the figures figures indicates indicates the the direction direction of of the the freestream. freestream. Please Please note that the the crosswind crosswind direction direction of of the the PIVPIV measurement measurement and and that that of of the the flow flow visualization visualization are are the inverse of each other other because because of of different different OP windwind tunnel tunnel experiments: experiments:ββSW== ββOPSW.. SW −− SW

β = 5 β = 5 a) SW − ◦ b) SW − ◦

βSW = 5◦ βSW = 5◦ c) − d) −

u = 0 m/s λ2 = 150,000

Figure 8. Vortical structures at side wind direction of 5◦:(a,b) streamwise vortices, (c) λ2-criterion, Figure 8. Vortical structures at side wind direction of −5◦:(a,b) streamwise vortices, (c) λ2-criterion, and ( ) recirculation area. − and (d)d recirculation area.

Figure8a visualizes ωx of the windward downstream C-pillar vortex of the rear window. It can be Figure8a visualizes ωx of the windward downstream C-pillar vortex of the rear window. It can be seen that the vortex level rises significantly with crosswind. The size of the isosurface with ωx = +6 is seen that the vortex level rises significantly with crosswind. The size of the isosurface with ωx = +6 is considerably larger than it was seen at β = 0◦ at ωx = +3.5. The C-pillar vortex extends across the considerably larger than it was seen at β = 0◦ at ωx = +3.5. The C-pillar vortex extends across the entire top side of the vehicle. The increase in the vortex was already observed in the flow visualization entire top side of the vehicle. The increase in the vortex was already observed in the flow visualization as the characteristic footprint in the oil traces was also significantly increased. The comparison with the as the characteristic footprint in the oil traces was also significantly increased. The comparison with the pressure distribution in Figure2 proves that the locations of the pressure minima and maxima coincide pressure distribution in Figure2 proves that the locations of the pressure minima and maxima coincide with the course of the C-pillar vortex, as marked in the points 1 , 2 , and 3 . The vortices in the middle with the course of the C-pillar vortex, as marked in the points 1 , 2 , and 3 . The vortices in the middle of the rear window, emanating from the focus points F1 and F 2, appeared to be insignificant and were of the rear window, emanating from the focus points F1 and F2, appeared to be insignificant and were almost invisible in the PIV; therefore, they are not shown here. ωx of the leeward C-pillar vortex will almost invisible in the PIV; therefore, they are not shown here. ωx of the leeward C-pillar vortex will be addressed later. The flow visualization revealed the existence of three focus points (F6, F7, and F8). be addressed later. The flow visualization revealed the existence of three focus points ( , , and ). The corresponding flow structures were identified in the PIV (Figure8 b)). The highestF6 intensitiesF7 F8 The corresponding flow structures were identified in the PIV (Figure8b). The highest intensities of of ωx were caused by the vortices of the focus points F7 and F8. However, the PIV showed that both ωvorticesx were caused were more by the centrally vortices located of the than focus the pointstraces inF7 theand oilF paint8. However, suggested. the The PIV vortex showed at the that lower both vortices were more centrally located than the traces in the oil paint suggested. The vortex at the lower windward corner, which was responsible for the focus point F6, was much less intense with ωx = +2. In addition to the vortices already mentioned, two more vortices were found in the PIV, which were Energies 2020, xx, 5 13 of 18 Energies 2020, 13, 320 13 of 18

windward corner, which was responsible for the focus point F6, was much less intense with ωx = +2. not indicated in the flow visualization. One emerged from the underbody (ω = 3), and the other In addition to the vortices already mentioned, two more vortices were found inx the− PIV, which were wasnot on indicated the lower in lee the side flow of visualization. the base surface One ( emergedωx = 2). from The theλ2 underbodyvortex criterion (ω = is shown3), and in the Figure other8c. − x − Thewas level on the of the lowerλ2 isosurface lee side ofthe had base to be surface increased (ω from= 2 100,000). The λ atvortexβSW = criterion0◦ to 150,000 is shown at in5◦ Figureto display8c. x − 2 theThe isosurface level of the completely.λ2 isosurface It can had be to seen be increased that the fromformerly 100,000 existing at βSW ring= 0 vortex◦ to 150,000 characteristic at 5◦ to display decays intothe several isosurface fragments completely. and becomes It can be clearly seen that asymmetrical. the formerly The existing reason ring for vortex this was characteristic high differences decays in speedinto several at the vehicle fragments base and (not becomes shownhere). clearly The asymmetrical. contour of Thezero reason downstream for this velocity was highu differences= 0 m/s of in the modelspeed base at the is visualizedvehicle base in (not Figure shown8d. Moreover, here). The this contour isosurface of zero was downstream characterized velocity by anu=0 asymmetrical m/s of the deformationmodel base iswith visualized the largest in Figure extension8d. Moreover, on the windward this isosurface side. was The characterized deformation by can an be asymmetrical attributed to thedeformation high local velocity with the differences largest extension and the on multiple the windward vortices side. shown The in deformation Figure8a–e. can be attributed to theThe high increase local velocity of βSW differencesfrom 5 and◦ to the10 multiple◦ causes vortices further shown changes in Figure in the8a–e. flow field. To illustrate The increase of β from− 5 to− 10 causes further changes in the flow field. To illustrate the specific differences,SW Figure9 −shows◦ − all results◦ at 10◦ with the same limits as at 5◦. It was the specific differences, Figure9 shows all results at −10 with the same limits as at −5 . It was found that all identified vortices at βSW of 5◦ also existed− ◦ at 10◦, even though the− sizes◦ of the found that all identified vortices at β of −5 also existed at −10 , even though the sizes of the vortex isosurfaces slightly changed. ThisSW is− especially◦ visible in− the◦ windward C-pillar vortex and vortex isosurfaces slightly changed. This is especially visible in the windward C-pillar vortex and the two base vortices (Figure9a,b). Figure9c shows λ2 in the downstream region of the model base area.the twoMoreover, base vortices in this (Figure contour,9a,b). a clearly Figure increased9c shows asymmetryλ2 in the downstream and a larger region extension of the in model the driving base area. Moreover, in this contour, a clearly increased asymmetry and a larger extension in the driving direction was more apparent than it was seen at βSW = 5◦. Furthermore, the contribution of the direction was more apparent than it was seen at β = −5 . Furthermore, the contribution of the intensified C-pillar vortex was now also clearly visibleSW based− ◦ on this criterion. The enclosed area of intensified C-pillar vortex was now1 also clearly visible based on this criterion. The enclosed area of the recirculation area of u = 0 ms− shrank significantly under high crosswind conditions (Figure9d). the recirculation area of u = 0 m s 1 shrank significantly under high crosswind conditions (Figure9d). For a clear illustration of the isocontours− shown here and the recirculation area for all investigated For a clear illustration of the isocontours shown here and the recirculation area for all investigated inflow directions, a qualitative representation of top and side views is given at later stage. inflow directions, a qualitative representation of top and side views is given at later stage.

β = 10 β = 10 a) SW − ◦ b) SW − ◦

β = 10◦ β = 10◦ c) SW − d) SW −

u = 0 m/s λ2 = 150,000

Figure 9. Vortical structures at side wind direction of 10◦:(a,b) streamwise vortices, (c) λ2-criterion, Figure 9. Vortical structures at side wind direction of −10◦:(a,b) streamwise vortices, (c) λ2-criterion, and (d) recirculation area. − and (d) recirculation area. The development of the A-pillar and C-pillar vortices on the leeward side in crosswind has not The development of the A-pillar and C-pillar vortices on the leeward side in crosswind has not yet been discussed. Figure 10 shows both vortices for 5 and 10 . The inflow direction of 0 yet been discussed. Figure 10 shows both vortices for −5◦ and − 10◦ . The inflow direction of ◦0 − ◦ − ◦ ◦ is not shown here as the A-pillar vortex was not observed in the PIV and the C-pillar vortex was already shown. The traces in the flow visualization already indicated that the A-pillar vortex seems Energies 2020, xx, 5 14 of 18 Energies 2020, 13, 320 14 of 18

is not shown here as the A-pillar vortex was not observed in the PIV and the C-pillar vortex was to bealready successively shown. The stronger traces and in the that flow the visualization C-pillar vortex already is weaker indicated under that the the A-pillar increasing vortex crosswind seems conditions.to be successively Both were stronger confirmed and by that the the flow C-pillar field measurements. vortex is weaker Figure under 10 thea shows increasing that,at crosswind side wind conditions. Both were confirmed by the flow field measurements. Figure 10a shows that, at side wind of βSW = 5◦, the A-pillar and C-pillar vortices were directly located next to each other. The vorticity of βSW −= 5◦, the A-pillar and C-pillar vortices were directly located next to each other. The vorticity level, ωx, of the− C-pillar vortex decreased significantly by approximately 80% to 0.7 compared to that level, ωx, of the C-pillar vortex decreased significantly by approximately 80% to −0.7 compared to that at βSW = 0◦ with 3.5. In contrast, the vorticity of the A-pillar vortex was about− three times higher at β = 0 with− 3.5. In contrast, the vorticity of the A-pillar vortex was about three times higher than thatSW of the◦ C-pillar− vortex, although it originated from further upstream. than that of the C-pillar vortex, although it originated from further upstream.

β = 5 β = 10 a) SW − ◦ b) SW − ◦

A-pillar vortex A-pillar vortex

Figure 10. A-pillar and C-pillar vortices at the leeward side of the model at a side wind of 5◦ Figure 10. A-pillar and C-pillar vortices at the leeward side of the model at a side wind of (a−) 5◦ and 10 . − and (b)− 10◦ . − ◦ A further increase from β to 10◦ has fundamentally changed the flow topology. The vorticity A further increase from β SWto −10 has fundamentally changed the flow topology. The vorticity of the A-pillar vortex in FigureSW 10b− shows◦ that its intensity approximately doubled while the C-pillar of the A-pillar vortex in Figure 10b shows that its intensity approximately doubled while the C-pillar vortex was no longer detectable. The A-pillar vortex dominated the entire upper area of the flow vortexfield was on the no leeward longer detectable. side of the model. The A-pillar This observation vortex dominated perfectly thecomplemented entire upper the area results of the of the flow fieldflow on visualization. the leeward side The traces of the showed model. an This increased observation A-pillar perfectly vortex and complemented a suppressed flow the results around of the the flow visualization. The traces showed an increased A-pillar vortex and a suppressed flow around the C-pillar. In addition, the focus point F4 of the C-pillar vortex was absent. Below the A-pillar vortex, C-pillar.there was In addition, a new longitudinal the focus vortex. point F It4 isof assumed the C-pillar here vortex that this was was absent. induced Below by the the A-pillar A-pillar vortex vortex, as therea secondary was a new flow longitudinal structure. vortex. It is assumed here that this was induced by the A-pillar vortex as a secondary flow structure. Figures 11 and 12 show qualitativelywindward the courses of the vorticeswindward and the wake for all investigated inflows for the top and side views,1 respectively. The length of the vortex core traces is derived from 1 the isosurfaces shown above and their vorticity intensities. For a better representation, the upper and1 β = 0 β = 5 β = 10◦ lowerSW parts◦ of the flow field are shownSW − separately.◦ The aforementionedSW − figures clearly show that the asymmetry of the flowu = field0m/s increases2 significantly under crosswind conditions and that the vortex propagation is clearly influenced. In addition, it can be seen that the quantity of vortex structures 2 3 changes noticeably. While some vortices become weaker and disappear, new vortices are formed3 at y Centerline α other locations. Table1 lists the directionsxy of the vortexC-pillar courses vortices visible in the upper region of Figure 11. z x leeward leeward Centerline This is only done for this region because the courses are mainly straight. The downstreamA-pillar vortex vortices of the base surface are more curved, short, and diffusely scattered, which makes it difficult to determine 1 their directions. The length x/L of2 the recirculation area confirms the1 comparability and validity of the 3 2 results of this study compared with1 the earlier studies having the3 same model setup. u = 0m/s

z αxz y x leewardleeward

Figure 11. Centerlines of the vortex cores and the size of the recirculation area in the upper part of the model at changing side wind directions. Energies 2020, xx, 5 14 of 18

is not shown here as the A-pillar vortex was not observed in the PIV and the C-pillar vortex was already shown. The traces in the flow visualization already indicated that the A-pillar vortex seems to be successively stronger and that the C-pillar vortex is weaker under the increasing crosswind conditions. Both were confirmed by the flow field measurements. Figure 10a shows that, at side wind of β = 5 , the A-pillar and C-pillar vortices were directly located next to each other. The vorticity SW − ◦ level, ω , of the C-pillar vortex decreased significantly by approximately 80% to 0.7 compared to that x − at β = 0 with 3.5. In contrast, the vorticity of the A-pillar vortex was about three times higher SW ◦ − than that of the C-pillar vortex, although it originated from further upstream.

β = 5 β = 10 a) SW − ◦ b) SW − ◦

A-pillar vortex A-pillar vortex

Figure 10. A-pillar and C-pillar vortices at the leeward side of the model at a side wind of 5 − ◦ and 10 . − ◦ A further increase from β to 10 has fundamentally changed the flow topology. The vorticity SW − ◦ of the A-pillar vortex in Figure 10b shows that its intensity approximately doubled while the C-pillar vortex was no longer detectable. The A-pillar vortex dominated the entire upper area of the flow field on the leeward side of the model. This observation perfectly complemented the results of the flow visualization. The traces showed an increased A-pillar vortex and a suppressed flow around the C-pillar. In addition, the focus point F4 of the C-pillar vortex was absent. Below the A-pillar vortex, Energiesthere2020 was, 13 a, new 320 longitudinal vortex. It is assumed here that this was induced by the A-pillar vortex15 as of 18 a secondary flow structure.

windward windward

1 1 1 β = 0 β = 5 β = 10◦ SW ◦ SW − ◦ SW −

u = 0m/s 2

2 3 3 y Centerline α xy C-pillar vortices z x leeward leeward Centerline A-pillar vortex

1 2 1 3 2 1 3 u = 0m/s

z αxz y x leewardleeward

Figure 11. Centerlines of the vortex cores and the size of the recirculation area in the upper part of the EnergiesFigure2020 11., xxCenterlines, 5 of the vortex cores and the size of the recirculation area in the upper part of15 the of 18 model at changing side wind directions. model at changing side wind directions.

windward windward 9 11 10 11 4 8 10 4

5 βSW = 0◦ 5 βSW = 5◦ βSW = 10◦ u = 0m/s − − 5 4

7 6 6 6 y αxy z x leeward leeward

u = 0m/s 5 5 4 8 4 4 7 9 5 11 11 6 6 6 z αxz 10 10 y x leewardleeward

Figure 12. Centerlines of the vortex cores and the size of the recirculation area in the lower part of the Figure 12. Centerlines of the vortex cores and the size of the recirculation area in the lower part of the modelmodel at changing at changing side side wind wind directions. directions. Table 1. Courses of selected vortical structures and wake length values depending on the Figures 11 and 12 show qualitatively the courses of the vortices and the wake for all investigated inflowinflows direction. for the top and side views, respectively. The length of the vortex core traces is derived from the isosurfaces shown above and their vorticity intensities. For a better representation, the upper and βSW = 0◦ βSW = 5◦ βSW = 10◦ lower parts of the flow field are shown separately. The aforementioned− figures− clearly show that the asymmetry of the flow field increasesαxy, 1 significantly= 4◦ αxy under, 1 = crosswind10◦ αxy conditions, 1 = 12◦ and that the vortex − − − propagation is clearly influenced.α Inxy, addition,2 = 7◦ it canαxy be, 2 seen= 3◦ that the quantity of vortex structures top view − changes noticeably. While some vortices become weakerαxy, 3 = and3 disappear,◦ αxy, 3 new= vortices8◦ are formed at xmax − xmax − xmax − other locations. Table1 lists the directionsu=0m/s of0.15 the vortexu=0 coursesm/s 0.17 visible inu=0 them/s upper0.14 region of Figure 11. L ≈ L ≈ L ≈ This is only done for this region because the courses are mainly straight. The downstream vortices of αxz, 1 = 10◦ αxz, 1 = 7◦ αxz, 1 = 0◦ the base surface are more curved, short, and diffusely scattered, which makes it difficult to determine side view αxz, 2 = 9◦ αxz, 2 = 20◦ their directions. The length x/L of the recirculation area confirms the comparability− and validity of the αxz, 3 = 17◦ αxz, 3 = 15◦ results of this study compared with the− earlier studies having the same model setup.

Finally,Table the 1. inﬂuenceCourses of of selected the vortices, vortical structures which were and wake extracted length invalues earlier depending studies on [ the10] and were illustratedinﬂow in Figure direction.2, on the surface pressure is examined. It can be now seen that local pressure phenomena are directly related to the vortices, their locations of origin, or their directions of βSW = 0◦ βSW = 5◦ βSW = 10◦ propagation. The C-pillar vortex led to a high pressure− drop (see− 2 ). Conversely, the C-pillar αxy, 1 = 4◦ αxy, 1 = 10◦ αxy, 1 = 12◦ − − − αxy, 2 = 7◦ αxy, 2 = 3◦ top view − αxy, 3 = 3◦ αxy, 3 = 8◦ xmax − xmax − xmax − u=0m/s 0.15 u=0m/s 0.17 u=0m/s 0.14 L ≈ L ≈ L ≈ αxz, 1 = 10◦ αxz, 1 = 7◦ αxz, 1 = 0◦

side view αxz, 2 = 9◦ αxz, 2 = 20◦ − αxz, 3 = 17◦ αxz, 3 = 15◦ −

Finally, the inﬂuence of the vortices, which were extracted in earlier studies [10] and were illustrated in Figure2, on the surface pressure is examined. It can be now seen that local pressure phenomena are directly related to the vortices, their locations of origin, or their directions of propagation. The C-pillar vortex led to a high pressure drop (see 2 ). Conversely, the C-pillar

vortex on the trunk deck causes an increase in the local pressure because of the induced velocity (see 3 ). The same applies to the base surface. The lowest pressure values were obtained where strong

Energies 2020, 13, 320 16 of 18 vortex on the trunk deck causes an increase in the local pressure because of the induced velocity (see 3 ). The same applies to the base surface. The lowest pressure values were obtained where strong vortex structures existed, especially under crosswind conditions. The low pressure points 5 , 6 , and 7 can be attributed to the vortices around the focus points F , F , and F , respectively. 8 6 7 4. Conclusions In this study, the external flow field of a passenger car was investigated at various inflow conditions. The aim was to identify vortical structures under frontal inflow and their changes under crosswind conditions. The investigated inflow conditions were set at angles of 0◦, 5◦, and 10◦. The wind tunnel test was conducted on the notchback version of the DrivAer model on a scale of 1:4. This study is based on two separate experiments. The external downstream flow field of the model was measured using stereo PIV at several measuring planes. These measurements were supplemented by flow visualization studies carried out on the entire model surface. The flow field was completely symmetrical for the inflow direction at 0◦. Only on the rear window, there was a large asymmetrical flow structure comprising two interacting counter-rotating vortices. At the model front, there were two stagnation points. One was on the lower windshield, and the other was on the lower grille. Longitudinal vortices were formed at the A- and C-pillars. The vehicle base surface did not show any traces except on the sides where two focus points were seen. However, the PIV showed that there was also a vortex pair at the center of the vertical trunk surface, which was not discovered in the oil traces. In addition, an almost closed ring vortex was identified along the downstream direction of the vehicle base edges using the λ2-vortex criterion. The presence of crosswind fundamentally changed the flow topology around the vehicle. All sides of the vehicle were now asymmetrical. The stagnation points at the model front were clearly shifted to the windward side. The changed flow around the A-pillars caused the A-pillar vortex on the windward side to be weakened and on the leeward side to be more pronounced. The opposite flow was observed at the rear end of the model, where all flow structures were shifted leeward. The intensified flow around the windward side of the C-pillar strengthened the C-pillar vortex. At the same time, the leeward C-pillar vortex became gradually weaker and disappeared completely at 10◦ crosswind. The PIV results at 10◦ revealed that the A-pillar and C-pillar vortices dominated the upper downstream flow field of the vehicle. Significant changes were also observed in the downstream direction of the vehicle base. Some vortex structures were no longer present under the crosswind conditions, while new vortices were formed in other places. This study further analyzed the DrivAer model based on earlier studies. The measurements of the surface pressure showed that the pressure distribution changes significantly under crosswind conditions. This also changed the vehicle drag by 10% at 10 crosswind. It is now evident that the changes in the ≈ ◦ pressure were caused by the flow structures as the locations of the vortices identified in this study coincided with the positions of the local pressure phenomena.

Author Contributions: D.W.: Planning, experimental work, analysis, interpretation, and presentation of the results. C.N.N.: Review and assessment of the results; C.O.P.: Review and assessment of the results. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

Abbreviations CCD Charge-coupled device HFI Hermann–Föttinger Institut NACA National Advisory Committee for Aeronautics PIV Particle Image Velocimetry OP Oil paint/ﬂow visualization Energies 2020, 13, 320 17 of 18

SBES Stress-Blended Eddy Simulation SW Side wind Greek Letters αxy Projected angle on the x–y plane αxz Projected angle on the x–z plane OP βSW Side wind angle for oil paint experiment βSW Side wind angle for PIV experiment ∆ Difference λ2 Vortex criterion ρ Density of air ϕ Blockage ratio in the test section Ω~ Vorticity ω~ Nondimensional vorticity c~∞ Freestream velocity Latin Letters A Frontal area of the model CD Drag coefﬁcient CP Pressure coefﬁcient L Total length of the model p Static pressure q Dynamic pressure Re Reynolds number u, v, w Cartesian components of vector~c x, y, z Axis of coordinates B Bifurcation line F Focus point

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