## Abstract

The effects of short automatic moving deflectors (AMD) on the aerodynamic characteristics of Ahmed body are considered in this study. AMDs, known as biomimetic control devices, were added to the leading edge of the slanted surface. Its position was automatically adjusted in a separation flow. The aerodynamic drag, the pressure, and the skin-friction distribution on the slanted surface were measured for the model with three deflectors with lengths of 9%, 18%, and 30% of the slant. Particle image velocimetry was also utilized to assess the flow on the vertical symmetric plane. The Reynolds number based on the height of the model is between 1.44 × 105 and 2.80 × 105. The results showed that at a low Reynolds number, a short deflector increases the drag of the model. The effectiveness of the deflector in reducing the drag arises at a high velocity, where a maximum drag reduction of 11% was observed. The deflectors also reduced the lift coefficient by as much as 89%. Global luminescent oil-film skin-friction measurements showed that in the low drag state, the structure of the longitudinal vortexes and the separation bubble disappear on the surface. A complex flow structure is classified for the baseline model and the model with deflectors. The relationship between the surface flow, pressure distribution, and flow on the symmetric vertical plane is discussed in detail.

## 1 Introduction

Reducing fuel consumption and increasing the performance capabilities of vehicles are important tasks for mechanical engineering. To reduce the fuel consumption of moving vehicles while also improving the efficiency of their engines, reducing the aerodynamic drag has attracted attention recently. The aerodynamic drag is estimated to contribute up to 46% of the total fuel consumption for cars on highways [1]. High fuel consumption also causes the problem of greater pollution given the large amount of carbon dioxide emitted into the environment.s

To understand the aerodynamic phenomena of moving vehicles and to propose a control technique, the Ahmed body is a standard model [2,3]. This model has the shape of a truck with a rectangular cross section and a slanted surface at the rear part. The flow behavior of the rear surface changes with the slant angle and is strongly three-dimensional. At a slant angle below 12.5 deg, the flow becomes attached to the surface and the drag of the model decreases steadily with the slant angle. At angles above 12.5 deg and up to 25 deg, a separation bubble is generated in the middle of the slanted surface and two counter-rotation longitudinal vortexes (C-pillar vortexes) develop on two edges of the surface. Formalization of the separation bubble and the C-pillar vortexes results in a low-pressure region on the slanted surface, which contributes to a remarkably large amount of drag. At slant angles above 25 deg, the C-pillar vortexes can break down, with the drag suddenly being reduced. Numerous studies, therefore, focused on a critical angle of 25 deg [49]. It was also shown that drag generated by a separation bubble on the slant accounts for around 34% of the total drag, the pressure drag due to longitudinal vortexes accounts for approximately 12% and the wake drag causes 44% [10]. Attempts have been made to eliminate the separation bubble on the surface, resulting in a reduction of the total drag from 5 to 15% [1113].

To reduce the drag of the Ahmed body, both active and passive control devices were investigated in previous studies [3]. Active control devices delay the development of the separation bubble by generating an additional flow around the rear surface [1416]. The passive technique controls the flow on the slanted surface by means of a straightforward modification of the geometry around the slanted surface. Consequently, the structures of the separation bubble and the longitudinal vortexes on the slant are modified. In most cases, this reduces the pressure drag acting on the slant as well as the overall drag of the model. Passive control devices include vortex generators [17], a rounded edge [10], rear linking tunnels [18], deflectors [12,13,1922], and a cavity at the base [23]. Beaudoin and Aider [19], who studied the effect of deflectors on the drag reduction of the Ahmed body, showed that by adding deflectors at different positions on the rear part, the separation flow can be eliminated on the slant. In the highest case, the drag of the model reduces up to 25% by attaching the deflectors at both the slant and base surfaces. When the length of deflectors is short, Fourrie et al. [12], who attached deflectors on the leading edge of the slant, showed that the surface flow and drag reduction are sensitive to deflection angles. In their study, the drag increases first with deflector angles. Then, the flow becomes fully separated at a deflection angle of around 5 deg with a reduction drag of 9%. Hanfeng et al. [13], who investigated the effect of deflection length on the drag reduction with a fixed deflection angle of 0 deg, indicated that the structure of the separation bubble and longitudinal vortexes depends on the length of the deflector. In the case when this structure breaks down, the drag reduces up to 8%, which is similar to the observation by Fourrie et al. [12]. Up to the present, the effect of short deflectors on reducing drag has attracted high attention, where the level of drag reduction depends on its length, position, and flow conditions. Additionally, although both active and passive methods work well for reducing drag, they have some limitations. For example, the active methods are required additional energy sources, which is a problem for generating and installing on vehicles. On the other hand, passive devices work efficiently in limited cases of upstream flow conditions.

One promising technique by which to reduce the drag of a blunt base is to apply a biomimetic device of the type that automatically adjusts under wind flow conditions. This control method mimics the secondary feathers of birds at high angles of attack, where a large separation flow occurs. In detail, the feathers pop up automatically, responding to a reverse flow at high angles of attack, such as when landing. Consequently, they reduce the separation on the surface and allow birds to reserve energy and fly smoothly [6,24]. When the separation flow does not occur, the device stays on the surface, resulting in a similar level of drag. The device control is referred to as a self-adaptive movable flap [25] or an automatic moving deflector (AMD) [6], representing a mix of active and passive control techniques. Generally, AMD mechanisms to control the flow are investigated by adding the mechanism to a square model [25], to a wing by numerical methods and during flight tests [26,27], and to an Ahmed body with a slant angle of 25 deg [6]. It was shown for the wing that the deflector will automatically lift at high angles of attack, resulting in an increasing pressure on the surface. Consequently, the lift of the wing and the stall angle of attack increase. Unlike a fixed deflector, which can create a separation flow on its surface under high-speed conditions, the AMD is always inside the regions of attached or wake flows. Otherwise, the flow pushes up the deflector at a lower elevation. That is the strongest advantage of the AMD in comparison to fixed methods and other active control techniques.

In an attempt to understand the mechanisms and effects of deflectors and how they reduce the drag of automobiles, Kim et al. [6] attached a thin AMD to the leading edge of the slanted surface of an Ahmed body using thin cellophane tape. The deflector could rotate freely around the leading edge at Reynolds number between 1.9 × 105 and 3.4 × 105 during a wind tunnel test. The length of each deflector changed at lengths of the slanted surface of 0.65–1.00. By conducting different experimental techniques, Kim et al. [6] showed that such a device allows a redistribution of the pressure on the slanted surface. Additionally, the longitudinal vortex and separation bubble completely disappear for the model with deflectors. The maximum drag reduction by the AMD becomes as high as 19%. However, a long deflector is complicated to use in real vehicles due to design problems and safety problems. A short deflector is a more effective, alternative device. Nonetheless, the flow on the slant is highly sensitive to the angle of the deflector when its length is short [12]. In our reviews, the mechanisms and effectiveness of short AMDs in reducing drag were not investigated for automobile models.

In this study, we applied the concept of the AMD as presented in Kim et al. [6] to investigate its effect on the aerodynamic drag of an Ahmed body with a slant angle of 25 deg at Reynolds numbers between 1.44 × 105 and 2.80 × 105. In contrast to earlier work, short deflectors with lengths from 9% to 30% of the slant were selected for the investigation. The main purpose of this study is to answer the question about the effectiveness of short AMDs on drag reduction of the model and to determine the connections to the flow on a slanted surface and the pressure distribution of the model. For these purposes, force and pressure measurements are conducted. Additionally, we apply a global skin-friction measurement technique to ascertain the effects of deflectors on the detailed flow structures on the slant. Particle image velocimetry (PIV) is also utilized on the symmetric plane to analyze the wake flow. The results indicate that the short AMD is an effective device to increase the aerodynamic performance of the model with a maximum drag reduction of 11%. The reduction of the drag is connected to the shift of the slant to a fully separated state. The effects of short deflectors on the drag, the flow on the slant, the pressure distribution, and the wake are classified in this study. The concept of a short AMD, presented for the first time, can be applied to reduce the drag of road vehicles.

## 2 Experimental Setup

### 2.1 The Model and Deflectors Design.

We use a 70% scaled Ahmed body with a standard slant angle of 25 deg in this study. The dimensions of the model are a length of 731 mm, a width of 272 mm, and a height of 202 mm. The length of the slant surface S is 155 mm. The model is supported by four legs with a diameter of 21 mm and a length of 35 mm at the bottom. The main body of the model is made of aluminum. The nose and rear parts were created using a high-resolution three-dimensional printer and are connected to the main body by bolts. The other parameters of the model are shown in Fig. 1. For the experiments, two rear parts were designed, one for skin-friction measurements and the other for pressure measurements. The model was painted white to reduce the roughness and to increase the illumination of the luminescent oil used during the skin-friction measurement process. Additionally, the painted layer also helps to smooth the connections between the main body and the other parts.

Fig. 1
Fig. 1
Close modal

The selected shape, length, and weight of the AMDs critically affect the drag reduction strategy. As shown by Kim et al. [6], a long deflector is helpful to break down the C-pillar vortex and the separation bubble on the surface. However, the selection of a long, high-density deflector presents a problem when attempting to lift and maintain the position of the deflector during the experimental processes. Additionally, dynamic vibration can occur in some cases, which increases the turbulent intensity and drag of the model. Because a short deflector may increase the drag of the model by increasing the length of the separation bubble [12], such a deflector is likely to be insufficient to reduce the drag. Generally, the lift angle of a deflector and the drag reduction levels differ considerably when the deflection length changes.

In this study, we use deflectors with a shape of a rectangular plate, as shown in Fig. 2. The deflectors were designed with hard strawboard with a density of 0.22 kgm2 and a thickness of 2 mm. The width of the deflector equals the width of the model, while its length is changed from 0.09S to 0.30S to comprehend the effect of the length on the flow structure and aerodynamic performance of the model. Note that the above range of the deflector is reliable for actual vehicles. Additionally, as shown later in this study, this range suitably covers the flow phenomena associated with a short deflector. These types of deflectors are connected to the leading edge by thin cellophane tape, similar to a previous method by Kim et al. [6]. The model with the deflector in the wind tunnel is shown in Fig. 2(b). The density of the deflector is also much lower than in the design by Kim et al. [6], allowing it to pop up easily during the experimental process. Additionally, given the thinness of the deflector, the flow structure when the deflector is attached to the slant remains similar to the case without a control device. Note that a fixed deflector with a length of 0.09S was mainly applied in previous studies by Fourrie et al. [12] and Hanfeng et al. [13]. Consequently, the relevant results can be validated and compared.

Fig. 2
Fig. 2
Close modal

### 2.2 The Working Principle of the Deflector.

The deflector is attached to the leading edge by light tape and can pop up automatically in windy conditions. The lift angle is determined by the balance between the moments generated by the weight of the deflector and the aerodynamic force. The aerodynamic force is determined by the differential pressure at the upper and lower surfaces of the deflector. However, given the thinness of the deflector, measuring the pressure at the upper surface of the deflector by means of pressure taps is impossible. Generally, the aerodynamic force is proportional to the second-order velocity magnitude. Consequently, the force increases quickly with the velocity of the flow. When the velocity is sufficiently high, it can be considered that the deflector pops up at a position that does not have a separation flow on its surface. In this case, the deflector reduces the drag of the model.

Various factors can affect the lift-up angle of the deflector, including the aerodynamic effect, the weight of the deflector, and other technical issues such as the moment generated by the connection tape and the friction around the connections. Consequently, there is a critical velocity required for the deflector to pop up. Above this velocity, the effects of the technical issues can be considered to be minor. Kim et al. [6] when applying deflectors with a mass density of 0.92 kg/m2 showed that the deflector lifts at a velocity above 12 m/s, resulting in a drag reduction. By reducing the density of the deflector and using the principle proposed by Kim et al. [6], it is expected that the minimum velocity that automatically lifts the deflector in this study would be approximately 6 m/s. In the initial tests of the model with a deflector length of 9% and velocity exceeding 14 m/s, it was found that the deflector lifts at an angle of around 2.2 deg above the horizontal axis, close to the angle with the minimum drag, as shown by Fourrie et al. [12]. Consequently, the main work of this study is focused on the velocity of 20 m/s. It is expected that for other deflector models with lengths from 9% to 30%, that velocity is sufficient for lifting the deflector and the technical problem can be neglected. The details effect of velocity on the drag of the model with deflectors will be discussed in Sec. 3.

### 2.3 Force and Pressure Measurements.

Force measurements are conducted to ascertain the effects of deflectors on the drag and lift of the model. The forces are measured by a force balance (model LMC-61447, Nissho Electric Works, Japan) capable of measuring three components of the force as well as three-moment components. The force balance has measurement ranges of ±50 N for the drag and ±200 N for the lift. The model is connected to the force balance by an H-shaped plate at the bottom position. Among these connections, the four legs of the model are linked to the upper part of the H-shaped plate, while the center of the plate is connected to the balance system. The measurement data from the force balance are transferred to a computer through a dynamic strain amplifier. The maximum errors of the force measurements by the system are ±0.031 N for the drag and ±0.124 N for the lift.

There are 105 pressure taps on the slant and 47 taps on the base for the pressure measurements. To obtain high resolutions of the pressure fields, all of the taps are located on the left side of the slant and base surfaces. A large number of pressure taps were installed, especially on the side edge and the reattachment region on the slant surface. Each pressure tap has an inside diameter of 0.86 mm. They are connected to the pressure sensors using silicon tubes 30 mm long with identical inner diameters.

To measure the pressure on the slant surface, three pressure scanners (model MPS4264-Scanivalve) were used. Each pressure sensor has 64 measurement ports. The pressure sensors have a measuring range of ±2.0 kPa with an accuracy of ±3 Pa. All pressure sensors are located inside the model and are connected to the computer through an Ethernet port.

The force and pressure measurements were conducted simultaneously at a closed-loop open test section at Hiroshima University, Japan (Hiroshima University Wind Tunnel). The cross-test section of the wind tunnel is 2 m × 2 m. The velocity of the wind tunnel is from 5 to 25 m/s with a turbulent intensity rate of less than 1% at the velocity of 15 m/s. The model is supported by a smooth ground plate, which is 0.5 m above the working section with a dimension of 4.0 m × 2.0 m in length × width. Initial measurements indicate that the velocity distribution is uniform around the center of the plate. Consequently, the model is located 0.5 m from the top and center of the plate. The experimental setup for force and pressure measurements is shown in Fig. 3.

Fig. 3
Fig. 3
Close modal

Each measurement is conducted for 180 s to ensure steady aerodynamic characteristics. The frequencies of the force measurements and pressure measurements are 1000 Hz and 500 Hz, respectively. The drag and lift coefficients are calculated based on the frontal area of the model.

### 2.4 Particle Image Velocimetry Measurements.

Particle image velocimetry is used to assess the effect of the deflector on the flow behavior on the symmetric plane. The experimental setup for the PIV measurements is shown in Fig. 4. The flow was seeded by a smoke generator (model 8304; KANOMAX Japan Inc.) with an average particle from 0.3 to 1 μm. The volume of generated air containing the smoke particles is between 15-80 l/min. Laser light generated by a laser source (Vlite-200, Beamtech) was guided by a beam delivery arm and irradiated from above the model to illuminate the smoke particles on the symmetric plane. The thickness of the laser sheet is around 1 mm in the region of interest and the time between the generation of two laser sheets is 100 μs. A CMOS camera k8-USB (Kato Koken) equipped with a Nikkor lens (50 mm) is positioned on the side to record the movement of the particles. The aperture of the lens is set to f = 2.8 and the speed of the CMOS camera is fixed at 30 frames per second. The resolution of the camera is 2048 × 2592 pixels, providing an image resolution of around 9.4 pixels/mm. The field of view is a rectangular region beginning close to the leading edge with a dimension of 218 × 276 mm2.

Fig. 4
Fig. 4
Close modal

The experiments for the PIV measurements were conducted at the Hiroshima University Wind Tunnel in Hiroshima, Japan, using flow conditions identical to those of the force and pressure measurements. For data processing, a cross-correlation algorithm with an interrogation window of 8 × 8 pixels was used to obtain highly accurate results near the surface. A modified function of the open-source software matlabpivlab was adopted to recover the velocity fields. For the details about the algorithm, readers can refer to Thielicke and Stamhuis [28]. A total of 2000 image pairs were used for average velocity fields. The initial test indicated that the current setup and number of image pairs are sufficient for averaged velocity fields.

### 2.5 Global Skin-Friction Measurement.

Global luminescent oil film (GLOF) skin-friction measurements are taken to obtain the skin-friction fields on the surface. This is a semiquantitative technique for skin-friction measurement. The technique is based on solving the thin oil-film equation by a global optical flow algorithm. A description of the algorithm is presented by Tran et al. [29]. Applications of these techniques in research on the surface flows of an Ahmed body are available in Tran et al. [30,31]. The errors of the skin-friction measurement arise due to various parameters, such as the gradient intensity of the images, the pressure gradient, gravity acting on the oil, and the initial parameters of the numerical programs. An evaluation of the measurement errors is presented in earlier work by Liu et al. [32] and Thibault et al. [33]. It is expected that the measurement errors of the skin friction will be less than 12% of the measurement values [30].

The experimental setup for the skin-friction measurements is similar to that used in conventional oil surface flow visualization techniques, as shown in Fig. 5. Here, a luminescent oil film consisting of a mixture of silicon oil 10 CST and a fluorescent dye, DFS-K175, is used to measure the skin-friction fields. The mass ratio of the oil and pigment is 99.5:0.5. It should be noted that the viscosity of the oil is much lower than those in previous studies [3436]. Consequently, the movement of the oil is much easier and the low-skin-friction region can be visualized. The oil is coated onto the surface by a spray gun before the wind-tunnel test. The luminescent oil film is illuminated by a blue LED (IL-105/6X Illuminator) with a wavelength of 462 nm. The reflected intensity of the oil is then recorded by a high-speed camera hung from the top surface of the wind tunnel during the experimental process. A laser line was used to adjust the position of the camera. The angle of the camera was also changed so that the camera plane is parallel to the slant of the model. When the thickness of oil is relatively thin, it can be considered to be linearly proportional to the intensity. Consequently, the thin-oil-film equation can be transferred to an equation that takes into account the relationship between the relative skin-friction vectors and the gradient intensity of the image. A variational method was then applied to solve the thin-oil-film equation to determine the skin-friction fields. For details about the measurement technique and process used to select the parameters for the skin-friction measurements, readers can refer to Tran et al. [29,30].

Fig. 5
Fig. 5
Close modal

Experiments for the skin-friction measurements were conducted on the boundary layer wind tunnel at Kyushu University, a closed-circuit wind tunnel with a test section 15 m long, 3.6 m wide, and 2.0 high. The maximum velocity of the wind tunnel is around 30 m/s. The turbulent intensity of the wind tunnel is less than 1%.

In this study, experiments are conducted at velocities from 10 m/s to 20 m/s, providing a based-height Reynolds number that ranges from 1.44 × 105 to 2.80 × 105. The main work utilized a value of ReH = 2.80 × 105 to understand the effects of AMDs on the flow around the rear part of the model under high-velocity conditions. The Reynolds number in this study is close to those in previous studies by Kim et al. [6] and by Fourrie et al. [12].

## 3 Results and Discussion

### 3.1 Aerodynamic Drag of the Model With Deflectors.

Drag and lift coefficients of the baseline model are first presented with relevant studies by Fourrie et al. [12] and Kim et al. [6] for validation. As shown in Table 1, the drag coefficient of this study is close to previous results with a maximum difference of around 5.8%. However, the lift coefficient shows a large difference from that by Fourrie et al. [12] at around 24%. The reason is due to the difference in the model size and experimental setup, which affects pressure distribution at the lower surface of the model.

Table 1

Comparison of drag and lift of the current and previous studies

StudiesReynolds number ReH (× 105)Drag coefficient CDDrag coefficient CLDifferent CD to this study (%)
Fourrie et al. [12]3.100.3260.3863.8
Kim et al. [6]1.900.3323.1
Kim et al. [6]2.900.3254.8
This study2.800.3420.311
StudiesReynolds number ReH (× 105)Drag coefficient CDDrag coefficient CLDifferent CD to this study (%)
Fourrie et al. [12]3.100.3260.3863.8
Kim et al. [6]1.900.3323.1
Kim et al. [6]2.900.3254.8
This study2.800.3420.311

Figure 6 shows the drag and lift coefficients of the Ahmed body with and without a deflector. The aerodynamic coefficients at l/S =0 represent the values of the baseline case. As the deflector is added to the slant, we observe a different drag trend for low and high Reynolds numbers, corresponding to the low and high freestream velocities of the wind tunnel. In detail, when the velocity of the flow is low at 10 m/s, the aerodynamic force due to the different pressures at the lower and upper surfaces of the deflector is not strong enough to lift the deflector to reduce the drag. The effect of the weight on the position of the deflectors is considerable when the deflector lengths are 9% and 18%. At the deflector length of 9%, the measurement results show that the drag increases by approximately 8% in comparison to the baseline case. However, when the freestream velocity is high at 20 m/s, the total drag of the Ahmed body decreases quickly for all deflectors tested (Fig. 6(a)). The maximum drag reduction is observed at around 11% when the deflection length is 30%. At the deflection length of 9%, the drag is reduced by around 9%, similar to the observation by Fourrie et al. [12] for the same length, when the angle of deflectors is 5 deg above the horizontal axis. This can be explained by the modified flow fields on the slant for the model with deflectors, as shown in Figs. 7 and 15. The drag reductions caused by the short deflectors tested in this study are weaker than those observed by Kim et al. [6], where long AMDs were tested. They obtained a drag reduction of 19% with the deflection length l/S =1.0. It is expected that the level of drag reduction increases with the length of the deflector. The application of deflectors has a positive effect on reducing the lift of the model at high Reynolds number ReH = 2.80 × 105 (Fig. 6(b)). The lift reduces by around 89% when the deflectors are added and the level of lift reduction is similar for three deflector configurations.

Fig. 6
Fig. 6
Close modal
Fig. 7
Fig. 7
Close modal

### 3.2 Skin-Friction Topology of the Baseline Model.

First, the flow topology around the baseline model is presented to confirm the measurement method used to extract the flow fields. Here, we concentrate on the Reynolds number of ReH = 2.80 × 105, where the AMD effectively reduces the drag. Figure 8 shows the last oil-film images, the skin-friction topology, and the skin-friction magnitude on the slant. The x′ is determined by the axis associated with the slant surface as shown in Fig. 1. The skin-friction magnitude is normalized by the maximum skin-friction value on the slant. The separation positions, at which points the oil accumulates, can be observed clearly from the oil-film image. The skin-friction structure for the reference model shows a large separation bubble in the middle and longitudinal vortexes on two side edges of the slant. The reattachment position of the separation bubble can be predicted from the oil-film image. However, the attachment positions due to longitudinal vortexes are not clearly shown in these images. The streamlines of the skin friction obtained by the global skin-friction measurement technique are highly consistent with the last oil film image. The structure of the flow on the slant is similar to those in previous observations by Krajnovic and Davidson [37,38] who applied the large eddy simulation method and by Tran et al. [30], who used experimental methods for skin-friction measurement. The formation of large recirculation regions and longitudinal vortexes is the main reason for the high drag of the model. The advantage of the global skin-friction measurement technique is that it allows the extraction of the semiquantitative skin-friction magnitude, as clearly shown in Fig. 8(c). Note that in a comparison with the traditional oil-flow visualization technique, much more information, such as the separation, attachment lines, node, focus, and saddle points, can be extracted from GLOF measurements.

Fig. 8
Fig. 8
Close modal

### 3.3 Surface Flow of the Model With Deflectors.

The pressure drag acting on the slant occupies around 40% of the total drag of the model [13]. Consequently, the surface flow on the slant is important for understanding the drag behavior. In this section, the skin friction on the slant surface is analyzed with different deflectors. Since painting the oil inside the region between the deflector and the slant surface is impossible, only skin-friction fields on the region without deflectors were measured. Additionally, these measurements focused solely on the high-velocity case, where a positive effect of the AMDs was observed. Note that the uniformity of the initial oil film layer is important to obtain highly accurate results. However, the results of skin friction are not affected by ignoring the oil layer painted on deflectors.

Figure 9 shows the average skin-friction topology on the surface obtained from the global skin-friction measurement method. Clearly, compared to the baseline case, the flow topology on the slant completely changes. Around the middle of the slanted surface, a separation line is evident, while near the trailing edge, a D-shaped attachment line is observed for the models with deflection lengths of 9% and 18%. Additionally, the D-shaped attachment region moves slightly upward and the separation line moves downstream with an increase in the deflection length, which leads to a reduction of the reversed flow region on the slant. The flow near the trailing edge of the model with deflectors is similar to the flow on the upper surface of a cubic model, as found in a previous study that used near-wall particle image velocimetry [39]. At the deflection length of 30%, the flow becomes mostly attached to the slant, except near the side edges. This can be explained by the movements downstream of the separation line and upstream of the D-shaped attachment line with an increase in the deflector length. A mixed structure of the two lines results in an attached line around the center (Fig. 9(c)). The PIV results, shown in Fig. 10, demonstrate that the flow on the slant is fully separated around the leading edge. It is expected that the flow on the slant is strongly affected by the wake behind the model. Consequently, a complex structure with the D-shaped attachment is generated on the slant. A fully separated flow was also observed by Fourrie et al. [12] for an Ahmed body with a fixed deflector of 9% under similar Reynolds number conditions. However, Fourrie et al. [12] used the traditional oil flow visualization technique, and D-shaped attachment lines as well as a reversed flow region were not found in their study. It should be noted that some nonsymmetric flow pattern occurs near two side edges for the short deflector of 9%. This arises due to the imperfect connection of the deflector to the leading edge of the short and light deflector.

Fig. 9
Fig. 9
Close modal
Fig. 10
Fig. 10
Close modal

For details of skin-friction characteristics, Fig. 7 shows the relative mean skin friction along the centerline of the slant. Here, skin-friction values are normalized according to the maximum value on the attachment region. From the skin-friction results, separation and reattachment positions can be observed. In detail, the separation and attachment positions are determined by the skin-friction values crossing the horizontal axis and becoming negative and positive, respectively. For the baseline case, it was observed that the length of the separation bubble is approximately 0.6S. Inside the separation bubble, large skin-friction values arise. The skin-friction magnitude increases near the trailing edge of the slant and shows a similar pattern for all models tested.

### 3.4 Flow on the Symmetric Plane.

For detailed flow fields around the slant surface and to confirm the results obtained by the skin-friction measurement method, PIV measurements were conducted on the symmetric plane. Figure 10 shows the results of streamlines and the streamwise velocity fields on the symmetric plane. For the baseline case, the flow strongly converges on the slant, which indicates the existence of a separation bubble. Behind the base, two large focus points are formed, corresponding to the wake of the model. The large focus F1 is located at around x/H =0.2, which is close to the base.

As the deflector is added, the wake region expands remarkably and both focus F1 and F2 move downstream. Additionally, the upper focus F1 moves up in a vertical direction, as shown in Fig. 11. Similar wake structures were obtained for the three deflector models. As the deflector is added to the model, the upper and lower shear layers are shed separately, resulting in a large wake region. The structure of the wake is similar to the case of the Ahmed body with slant angles of 30 deg and 35 deg as reported by Tunay et al. [40]. The role of the deflector is to shift the flow above the slant surface to the fully separated condition earlier, which increases the pressure on the slant. Generally, the wake of vehicles is three dimensions and sufficiently complicated [8,41]. Consequently, other measurements should be conducted to classify the topology in three-dimensional flow.

Fig. 11
Fig. 11
Close modal

Interestingly, a counterclockwise vortex occurs near the trailing edge on the slanted surface for the model with deflectors. The vortex becomes larger when the length of the deflector increases. The existence of the counterclockwise vortex confirms the existence and development of a D-shaped attachment line, which was observed from the skin-friction pattern on the slanted surface, as shown in Fig. 9. The stability of the counterclockwise vortex also contributes to the focus F1 moving up, as shown in Fig. 11. Note that the PIV measurement results can show flows above the slant, while skin-friction measurements indicate flows close to the surface. Both the PIV and global skin-friction measurement results suggest that a thin vortex is most likely generated close to the surface for the deflector length of 30%. Consequently, an attached flow around the centerline is observed when using the skin-friction method, while the PIV results indicate a reversed flow on the slant. A counterclockwise vortex is observed clearly for the model with the 30% deflector length according to the PIV measurements. However, it is expected that the vortex moves upward and hence the D-shaped attachment line does not appear clearly in the skin-friction measurements.

### 3.5 Pressure Distributions on Slant and Base Surfaces.

Figure 12 shows the pressure distribution on the slanted surface for the baseline case and the models with deflectors. Here, the black dots show the locations of pressure taps on the surfaces. The errors of the pressure coefficient are ΔCp = 0.0112. For the baseline case, significant pressure drops around the leading edge of the slant due to the existence of the separation bubble were observed. The pressure recovery gradually increases along the central region of the model. Additionally, because a longitudinal vortex is formed on the side edge, a low-pressure region is generated at that location. At the base surface, the pressure distribution is nearly uniform. The pattern of the pressure distributions on the slant is in good agreement with those in previous results by Kim et al. [6] and Joseph et al. [42].

Fig. 12
Fig. 12
Close modal

When the AMD is added, the separation bubble and longitudinal vortexes break down and the pressure distribution becomes nearly uniform on the slant. Generally, the low-pressure regions around the leading and on the side edges disappear. The high pressure on the slant results in a decrease in the pressure drag acting on the surface and lift of the model. Although a counterclockwise vortex occurs above the slant surface, its effect on the pressure distribution on the surface is minor. In detail, only a slight increase in the pressure near the upper edges of the base surface (z/H >0.5) for the models with deflectors is observed in comparison to that of the baseline case. Similar to the baseline case, the pressure distribution on the base surface is almost uniform for the cases with deflectors. From the results of the pressure measurements, it is confirmed that the main effect of the reducing drag stems from the flow on the slant surface. Interestingly, although the flow phenomenon on the slant for short deflectors in this study is quite different from those of long deflectors shown by Kim et al. [6], a similar effect on drag is obtained in both studies.

Figure 13 shows the pressure distribution on the centerline for the baseline model and the models with deflectors. Here, h is the height of the vertical base surface. The level of pressure on the slant is similar to that in the model with three deflectors. The base pressure at the centerline remains nearly constant for both the baseline case and models with a deflector. Because the low-pressure region around the leading edge disappears for the models with deflectors, the drag of these models decreases considerably.

Fig. 13
Fig. 13
Close modal

### 3.6 Angle of the Deflector in Wind-Tunnel Test.

For the 25 deg Ahmed body, a low-pressure region is formed near the shoulder due to the reversed flow fields. The reversed flow region and low pressure in this case lead to the lifting of the deflector under windy conditions. The working principle of the AMD was presented by Kim et al. [6] for deflection lengths from 0.65S to 0.90S. The lift angle of the deflector is determined to be where the moment by its weight is balanced with the moment generated by the aerodynamic force from the difference in the pressure at the lower and upper surfaces. The selection of a deflector with a low mass density is very important to realize a drag reduction, particularly for short deflectors, where the drag of the model strongly depends on the deflection angle [12]. In this study, we use a camera on the side to measure the angle of the deflector during the skin-friction measurement process. Figure 14 shows the position of the AMDs during the wind tunnel test. Their average angles of the deflectors on the horizontal axis are summarized in Table 2 for the case with high velocity at ReH = 2.8 × 105. The determination of the deflection angle θ is shown in Fig. 2(a).

Fig. 14
Fig. 14
Close modal
Table 2

Lifting angle of different deflector models

l/S (%)91830
$θ(deg)$2.2–1.1–1.3
l/S (%)91830
$θ(deg)$2.2–1.1–1.3

At l/S =9%, the average lift angle is around 2.2 deg, which is close to the angle of a fixed deflector with the lowest drag, as shown by Fourrie et al. [9] at Reynolds numbers between ReH = 3.1 × 105 and ReH = 7.7 × 105. For the deflectors with lengths of 18% and 30%, the deflection angle is slightly below the horizontal axis. The advantage of such an AMD is that under a flow, it lifts to an angle with much lower drag. This is sufficiently helpful for the initial design. Previously, Kim et al. [6] showed a lifting angle of around –8 deg for deflectors with lengths ranging from l/S = 65% to l/S = 100%. It is expected that the lifting angle of the AMD decreases with an increase in its length. Additionally, it should be noted that relative to those of long deflectors, the lifting angles of short deflectors are much higher. Interestingly, although the deflection angles differ for the different models, a similar pressure level is obtained on the slant, as shown in Fig. 12.

Another problem when using AMD is its dynamic behavior. Generally, the deflector is inside a large wake region and in this position, it can vibrate during the experimental process. In most cases, such vibration results in an increase in drag. This effect is significantly large for the square model, where the wake is dominated by the Karman vortex [25]. Kim et al. [6] observed a large flutter for a deflector at a high Reynolds number of Re = 3.8 × 105 and with l/S >81%. Interestingly, the vibration of the deflector is sufficiently weak in this study. This stems from the fact that the deflector is far from the rear wake region and the turbulent intensity of the flow above the slant is low. Additionally, the stiffness of the deflector is sufficient to prevent it from fluttering during the wind tunnel test. However, for a detailed understanding of the dynamic behavior, further measurements should be conducted. Note that the length of AMDs from 0.09S to 0.30S was used in this study for reliability application. Additionally, those ranges of deflector length can cover the phenomenon of short deflectors. It is expected that the flow phenomenon around the rear and pressure distributions should be similar for longer deflectors.

## 4 Conclusions

The effect of short AMDs with different lengths from 9% to 30% of the slant length on the flow around the slant and aerodynamic forces of the Ahmed body was investigated experimentally. It was found that the deflectors lift automatically during flow and allow a reduction of aerodynamic drag at high Reynolds numbers. The main contributions of this study are as follows.

Automatic moving deflectors are highly effective devices for reducing drag at high velocities with a maximum drag reduction of 11% and lift reduction of 89% for the model with a length of 30% of the slant. The level amount of drag reduction increases and the lifting angle decreases with an increase in the deflection length. The lifting angles of short deflectors are much higher than those of long deflectors, as shown by Kim et al. [6].

The global skin-friction measurement shows that the decrease in the drag is related to the breakdown of the separation bubble and longitudinal vortex, which leads to fully separated on the slant. The pressure distribution on the slant and base surface is almost uniform when the flow is fully separated. The pressure on the base is similar for both cases with and without deflectors. Near the trailing edge, a D-shaped attachment line is formed for the model with deflectors and expands with increasing deflection length. The upper focus positions of the wake move upward and far from the base when the deflector is added.

Finally, although a deflector is not an effective device at low velocities, this study confirms that short AMDs are a promising technique applicable to actual vehicles to reduce drag and increase their stability. This study also provides good reference data for numerical simulations, which can be used to analyze the pressure distribution around the deflector and the corresponding dynamic behavior.

## Funding Data

• JSPS KAKEN (Grant No. JP 21F21347).

• Collaborative Research Program of the Research Institute for Applied Mechanics, Kyushu University.

### Appendix: Flow on the Surface and Pressure Distributions at Low-Velocity Flows

Previously, Kim et al. [6] presented that the AMDs have a positive effect on the drag reduction of the model in the range of Reynolds number between 1.9 × 105 and 3.4 × 105. The length of deflectors is from 0.65S to 1.00S in the previous study, which is longer than the length of the recirculation. However, when the length of deflectors is short and the freestream velocity is low, the deflector may increase drag of the model. We analyze the aerodynamic characteristics of a case with the 9% deflector at Reynolds number ReH = 1.44 × 105 to understand the reason for the high aerodynamic drag. For that purpose, the surface skin-friction fields and pressure measurements are conducted in the same experimental setups, which were presented in Sec. 2 of this study. In the initial test, the lifting-up angle of the deflector corresponding to this flow condition was –1.8 deg to the horizontal axis.

Figure 15 represents skin-friction streamline and pressure distributions on the slant surface of the model with the 9% deflector at ReH = 1.44 × 105. Interestingly, when the length of deflectors is short and the angle of the deflector is low, the application of deflectors causes an expansion of the separation bubble on the slant. The maximum length of the separation bubble is around 0.7S. On the two side edges, the longitudinal vortexes are observed. Consequently, the low-pressure region on the surface is expanded and the drag of the model increases.

Fig. 15
Fig. 15
Close modal

The results of skin friction and pressure distributions on the slant surface confirm that the short AMD does not always have positive effects on reducing drag. The deflector helps to reduce drag at high-speed conditions, where the moment due to aerodynamic force is sufficient to balance with the moment generated by the weight of the model, and other technical problems can be considered low.

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