Experimental analysis on the transitional mechanism of the wake structure of the Ahmed Body.
The critical change in drag occurs in the Ahmed Body at 30[degrees] of the slanted base due to the transition in the wake structure. The distinctive feature of this bi-stage phenomenon, which consists of three-dimensional and quasi-axisymmetric separation states, is that the state drastically changes. Because this feature indicates that each state is stable around a critical angle, the transition is believed to be triggered by some instantaneous disturbances. Therefore, in our previous papers, we have paid attention on the unsteady behavior of the wake to determine the trigger that induces the transition. However, the relationship between the spatial transient behavior of the wake structures and the specific frequencies has not been clarified. Then, we tried to control the degree of interaction of the trailing vortices on the downwash by changing the aspect ratio of the slanted base.
In the first half, we studied the effects for typical combinations of the slant angle and aspect ratio and conducted an investigation to clarify the relationship between the geometric condition and the transition in the wake structure. In the second half, we conducted an investigation to clarify whether this instantaneous flow structure was caused by the periodic fluctuation of the downwash and trailing vortices or generated by aperiodic fluctuation, which was not involved in the periodic fluctuation. Finally, based on the above-mentioned investigations of the wake-structure behavior, we propose a hypothesis of the transitional mechanism.
CITATION: Kohri, I., Kobayashi, Y., Kasai, A., Nasu, T. et al., "Experimental Analysis on the Transitional Mechanism of the Wake Structure of the Ahmed Body," SAE Int. J. Passeng. Cars - Mech. Syst. 9(2):2016.
The critical change in drag that occurs in the Ahmed Body (Fig. 1) at 30[degrees] of the slanted base is due to the transition in the wake structure . At slightly below a 30[degrees] slant angle, the coefficient of aerodynamic drag [C.sub.D] shows a high value, whereas this value is low at slightly above 30[degrees]. Ahmed classified the wake structure into two states, namely, three-dimensional separation (TDS) state in the range below 30[degrees] and quasi-axisymmetric separation (QAS) state in the range above 30[degrees]. He explained that the critical change in the drag corresponds to the sudden transition in the flow state from TDS to QAS. He also clarified that a pair of trailing vortices, a downwash, and an upwash appear behind the body in the TDS state, and these significant structures disappear in the QAS state. However, why the transition occurs at a specific angle of the slanted base has not been clarified.
At any rate, the transition concept is based on the fact that the downwash separates at the top of the slanted base and reattaches somewhere on the slanted base below the critical angle, whereas it does not reattach any more beyond the critical angle. With regard to the flow separation/reattachment of the downwash, it occurs at a much smaller slant angle for a two-dimensional flow. Nevertheless, it occurs at 30[degrees] for a three-dimensional flow in the Ahmed Body. This result indicates that the critical angle is strongly dependent on the three-dimensional separated flow. Considering the wake structure explained by Ahmed, the factor that sustains the flow reattachment on the slanted base up to 30[degrees] is believed to be a pair of trailing vortices. The physical mechanism for this phenomenon is considered to be common to that of a delta wing . Therefore, we expect that the critical phenomenon occurs only when some specific conditions are satisfied. The conditions are considered to be the relationship between the magnitude of the lateral vortex, which is generated when the downwash separates at top of the slanted base, and the degree of interaction between the trailing vortices and the downwash. Thus, the reattachment of the downwash should be dominated by the degree of interaction of the trailing vortices with the downwash. From this perspective, the slant angle can be assumed as the parameter that governs the degree of interaction of the trailing vortices. Similarly, the aspect ratio of the slanted base can also be considered as another geometric parameter. Johnson  investigated the effects of the aspect ratio using computational fluid dynamics (CFD), but he did not validate them by experiment. Venning  studied the effects of the aspect ratio in detail at 25[degrees] slant angle and clarified the degree of interaction between the downwash and trailing vortices. Then, in the first half of the present work, we validate these effects for typical combinations of the slant angle and aspect ratio and analyze the interaction between the trailing vortices and downwash.
The distinctive feature of this bi-stage phenomenon, which consists of the TDS and QAS states, is that the state drastically changes at the critical slant angle. Because this feature indicates that each state is stable around the critical slant angle, we estimate that the transition is triggered by some instantaneous disturbances. Therefore, in  and , we paid attention to the unsteady behavior of the wake to determine the trigger that induces the transition.
Sims-Williams  measured the unsteady behavior of the vortices to identify some distinctive characteristics of their motion. Few years later, he showed the transient behavior of the detailed wake structure very close to the slanted base . During the same period, Vino  also measured a detailed transient vortex structure near the surface at 25[degrees] and estimated it at the critical angle. In a previous paper, we showed the existence of individual frequencies corresponding to several typical wake structures and clarified the dependence of the slant angle on their specific frequencies by hot-wire measurement. However, the correlation between the spatial transient behavior of the wake structures and the specific frequencies has not been well known yet. Then, in the second half of the current study, we conducted an investigation to clarify whether this instantaneous flow structure is due to the periodic fluctuation in the downwash and trailing vortices or is generated by the aperiodic and irregular fluctuation that is not involved in the periodic fluctuation.
EXPERIMENTAL FEATURES AND CONDITIONS
A series of experiments was conducted in a small wind tunnel at Tokyo City University (TCU), as shown in Fig. 2. The size of the nozzle was 366 mm x 366 mm, and the test section was 1800 mm (L) x 900 mm (W) x 900 mm (H). The distance from the nozzle to the center of the model was 450 mm. The maximum wind speed was 25 m/s, and the turbulence was approximately 0.5% at the inlet nozzle. Aerodynamic force balance was installed under the ground wall of the wind tunnel. The ground plate was 30 mm from the ground wall.
The Re number was approximately 7.31 x [10.sup.4], which corresponds to a wind speed of 12.0 m/s, where the reference length is the square root of the frontal area ([square root of (term)]A), [u.sub.[infinity]] is the freestream velocity, and v is the kinematic viscosity of air.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
The above condition was the regular condition throughout this series of experiments. In the present work, the Re number effects were neglected in investigating this problem, as discussed in a previous paper .
Measurement of the aerodynamic forces was conducted using a three-component balance. Particle image velocimetry (PIV) measurements were performed using a Flow Master PIV system (LaVision). Irradiation was conducted using YFL, 33 mL/pulse with 1-kHz laser (Omicron-Laserage Laserprodukte GmbH), and photographs were taken using HSS-8 with 1024 x 1024 pixel, 1000-fps camera (LaVision GmbH). Fig. 3 shows the measurement systems used in this study.
INTERACTION BETWEEN THE TRAILING VORTICES AND DOWNWASH
As mentioned in the Introduction, the downwash reattachment to the slanted base is dominated by the degree of interaction of the trailing vortices in the downwash. Accordingly, the slant angle can be assumed as the parameter that determines the degree of interaction of the trailing vortices. Similarly, the aspect ratio of the slanted base can also be considered as another geometric parameter. Then, we focus on the aspect ratio of the slanted base, instead of slant angle [theta]. Here, aspect ratio [lambda] is defined as the ratio of width W of the slanted base to its original length [L.sub.s].
[lambda] = [W/[[L.sub.s]]] (2)
In this section, the relationship between these geometric conditions and the transition of the wake structure are discussed.
Preceding Review by CFD Regarding the Aspect Ratio Effects
Johnson  systematically discussed the effects of the aspect ratio on the flow state using CFD simulation. He proposed the classification of the wake structure of the Ahmed Body into three states. They are as follows: attached low-drag (ALD) state at slant angle from 0[degrees] to 20[degrees] where downwash flow separation rarely occurs on the slanted base, high-drag (HD) state from 20[degrees] to 30[degrees] where the downwash separates from the top of the slanted base and reattaches at the middle, and separated low-drag (SLD) state where reattachment does not occur above 30[degrees]. In fact, the ALD state corresponds to a part of the TDS state where the slant angle is below 20[degrees], and the HD state corresponds to a part of the TDS state for slant angle between 20[degrees] and 30[degrees]. The SLD state is an alternate name of the QAS state.
The systematic calculations by Johnson revealed that the state directly changed from ALD to SLD at a slant angle of 20[degrees] when [lambda] was above 1.80, whereas it gradually changed from ALD to HD from 20[degrees] to 30[degrees] and steeply changed to SLD at 30[degrees] when [lambda] was below 1.75, which is the original value of the Ahmed Body. Then, a specific value of [lambda] between 1.75 and 1.80 divided the state above 20[degrees] of the slant angle. This transition of state clearly reflects the characteristics of [C.sub.L], whose value steeply decreases with the increase in the slant angle around 20[degrees]. In contrast, the wake structure changed from ALD to HD above 20[degrees] of the slant angle and rapidly changed to SLD at 20[degrees] when the aspect ratio was below 1.75, which is the original value of the Ahmed Body. Because the state gradually changed from ALD to HD, [C.sub.D] and [C.sub.L] also gradually changed. These characteristics are believed to be caused by the fact that the separated region near the top of the slanted base gradually expands toward the bottom of the slanted base with the increase in the slant angle. According to Johnson's calculation, the transition from HD to SLD is gradual with the increase in the slant angle above 30[degrees] for [lambda] below 1.75. When [lambda] was 1.30, [C.sub.D] and [C.sub.L] displayed middle values between HD and SLD. Therefore, the critical phenomenon at a slant angle of 30[degrees] is believed to be related to some specific values of [lambda].
Systematic Experimental Study on the Aspect Ratio Effects
We attempted to validate the Johnson's predictions. Three conditions, namely, [lambda] = 1.29, [lambda] = 1.77 and [lambda] = 2.26, were adopted for the validation. The variation in the slant angle is listed in Table 1 and shown in Fig. 6. Because the Re number in our experiments was different from that in the Johnson's calculation, the friction drag indicated a different value from the Johnson's result. However, as presented in our previous paper , the friction effects could be ignored when the change characteristics are studied because the change characteristics of an aerodynamic force due to a slanted-base surface are mainly determined by the change in the pressure distribution on the slanted base. Accordingly, the characteristics of the aerodynamic force at any angle were evaluated using the difference from the aerodynamic force at 0[degrees].
Fig. 7 shows that at [lambda] =1.29, [C.sub.D] indicated an HD state at 27.5[degrees] slant angle and an SLD (QAS) state at 32.5[degrees]. Unfortunately, we could not obtain the data at 30[degrees], but it was clear that transition occurred between 27.5[degrees] and 32.5[degrees]. Therefore, the tendency of the transition was evidently different from the Johnson's result. Similarly, at [lambda] = 2.25, the tendency was different. According to our experiments, [C.sub.D] indicated an HD state at 27.5[degrees] (although the absolute value was not very large) and an SLD state at 32.5[degrees]. This trend was completely different from the Johnson's result, i.e., [C.sub.D] represented an SLD state at 27.5[degrees], and an HD state never occurred between 20[degrees] and 30[degrees]. On the other hand, at [lambda] = 1.77, which corresponds to the original dimension of the Ahmed Body, the transition phenomenon across a slant angle of 30[degrees] was clearly evident in both studies.
Figs. 7 and 8 show that the calculated values indicate good agreement with our experimental values at [lambda] = 1.77, but the calculated and experimental values indicate different trends at [lambda] away from 1.77 regardless whether the value is larger or smaller than 1.77. This reason might be because accurately capturing the reattachment on the slanted base is not possible owing to the lack of grid resolution.
Venning  focused on a model whose slant angle was 25[degrees] and researched the relationship between the aspect ratio and trailing vortex structure in detail by PIV measurement. He found that the trailing vortex structure drastically changed above [lambda] = 1.9 and validated the Johnson's calculation. Clearly, when [lambda] became smaller than 1.75, the development of the circulation of the trailing vortex ([GAMMA]) showed a distinctive trend, as shown in Fig. 9. Here, [xi] is defined as the ratio of the distance from the rear end of the model (x) to the length of the slanted base ([L.sub.s]).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
The magnitude of [GAMMA] increased with the increase in [lambda] up to 1.75. Furthermore, when [lambda] became 1.93, [GAMMA] remarkably decreased, whereas [GAMMA] almost did not change with the increase in [lambda] above 2.10.
Actually, this trend indicates the existence of the critical aspect ratio similar to the critical slant angle. This trend also appeared in our results. As mentioned earlier, such drastic change in the phenomenon similar to the Venning's result was not observed, but [C.sub.L] clearly decreased with the increase in the slant angle above 22.5[degrees] at [lambda] = 2.25, whereas it increased at [lambda] = 1.75. Therefore, we have proven that some critical phenomenon occurred even in our experiment. Unfortunately, the interval of the slant angle variation was too large to resolve the drastic change in the phenomenon. From the experimental results of [C.sub.D] and [C.sub.L], we understand that the critical slant angle depends on the aspect ratio because the critical angle increased with the decrease in the aspect ratio.
Slant Angle-Aspect Ratio ([theta]-[lambda]) Performance
The critical phenomenon of the Ahmed Body is well known to be dominated by the flow reattachment of the downwash on the slanted base. In the first investigations presented in this section, we clarified that the slant angle and aspect ratio of the slanted base are the primary parameters that dominate the reattachment performance. Second, transition in the state of the wake structure occurs at the critical slant angle when the aspect ratio is fixed and occurs at the critical aspect ratio when the slant angle is fixed at a significant value. Third, we also clarified that the critical slant angle depends on the aspect ratio of the slanted base. Finally, we confirmed that these trends correspond to the trend of the degree of interaction between the trailing vortex and the downwash. Therefore, to intuitively understand the overall performance, we try to represent them as a characteristic surface by considering the combination of the slant angle and the aspect ratio ([theta]-[lambda]).
Fig. 10 shows the characteristic surface of the [theta]-[lambda] performance, which was interpolated from the combination of the slant angle and the aspect ratio by Johnson's calculation. Here, because the [C.sub.D] values by Johnson's calculation are inconsistent with the values obtained by Ahmed's experiment, we are limited to qualitative discussion. However, the most important point in this result is the fact that the critical change in the flow structure occurs with respect to not only the slant angle but also the aspect ratio. Fig. 11 shows a conceptual schematic of the characteristic surface drawn from our experimental results, which were interpolated and extrapolated by considering the results obtained by Johnson and Venning to fill the missing data. The primary differences between Figs. 10 and 11 are the critical aspect ratio and the change characteristics around the critical region. Clarification of the detailed characteristics will be expected in future research. At any rate, both figures clearly show the tendency with respect to the combination of the slant angle and aspect ratio.
Now, the issue that remains is to provide a suitable explanation of the physical and fluid-dynamic reasons that determine the values of the critical slant angle and the critical aspect ratio.
UNSTEADY CHARACTERISTICS OF THE WAKE STRUCTURE
Previous Works Regarding Unsteady Behavior of the Wake
From the flow visualization test by Takeda and Kohri  in a symmetric plane of a body at a 27.5[degrees] slant angle (Fig. 12), we observed that the lateral vortices generated at the top of the slanted base randomly advected along the surface or passed far from the surface, although the probability of the former was higher. The body indicated high drag values when the vortices continuously advected along the slanted base and a low drag when they continuously passed far from the surface. At 27.5[degrees], even if the vortices were detached from the surface, they soon returned to reattach on the surface; thus, the TDS state was sustained. However, at 30[degrees], because they did not always return to reattach, once a large separation occurred, the flow state transitioned to the QAD state. Unfortunately, such transition phenomenon was captured only by flow visualization, and measuring the transitional flow field by PIV measurement was difficult. Therefore, we aim to explain its fluid-dynamic mechanism.
Venning  measured the fluctuation and direction of the flow at the bottom edge of the slant base to evaluate the unsteadiness of the separation/reattachment phenomena (Fig. 13). Then, using these data, he calculated the probability of the attachment onto the slanted base of the downwash by considering the fact that the vorticity was directly shed downstream as lateral vorticity when the flow was separated at a trailing edge. As a result, at [theta] = 25[degrees] and [lambda] = 1.75, the reattachment probability at the center of the slanted base was approximately 50%. However, at [lambda] = 1.90, it decreased to 15%. Furthermore, when [lambda] became 2.25, reattachment did not occur at the central position at the bottom edge. The reattachment probability was 20% at the position one-third of the width.
Measurement of Unsteady Interaction between the Downwash and Trailing Vortex
We measured the unsteady flow in the symmetric and horizontal planes at the middle of the height of the vertical base at a slant angle of 27.5[degrees] using the PIV system. The photographs in Fig. 14 show the side views at one-fifth interval of the peak fluctuation period of a downwash of 65 Hz (St [approximately equal to] 0.51) arranged in chronological order. These representative frequencies were obtained from our previous study . On the other hand, the photographs of the plane views at one-fifth interval of the peak fluctuation period of a trailing vortex of 11.6 Hz (St [approximately equal to] 0.10) were also arranged in chronological order. Here, the Strouhal number St is defined by the following formula:
St = [[f * [square root of (term)]A]/[[u.sub.[infinity]]]] (4)
where [u.sub.[infinity]] is the free-stream velocity and f is the frequency of the fluctuation.
In the symmetric plane, the lateral vortex induced at the top of the slanted base was entrained along the slanted base and was detached from the lower edge of the slanted base. At the instant when the vortex was detached from the lower edge, the stationary vortex structure behind the vertical base collapsed, and a separate region was then formed for a moment in a wide space up to the rear of the vertical base from the top of the slanted base. However, because a small separation vortex was soon generated again at the top of the slanted base, the TDS state was sustained. In particular, by referring to the behavior of the vortex at the bottom of the slanted base, large velocity fluctuation was observed at the instant when the vortex was detached, and it corresponded to the results measured by Venning at the same position. Therefore, we realized that the aperiodical fluctuation in the reattachment position corresponded to the instantaneous phenomenon of shedding of a large-scale vortex generated by the coalescence of the separated vortex entrained along the slanted base and the stationary vortex behind the vertical base. Thereafter, this large-scale vortex was entrained downstream.
On the other hand, in the horizontal plane, by referring to the contour of the absolute value of the flow velocity, we can clearly observe the separation into three regions, namely, the mainstream region at the outer side of the body, the trailing vortex region, and the downwash region. We found that the outer side of the trailing vortex did not significantly fluctuate. In contrast, the inner side of the trailing vortex remarkably moved. We found that the central position between the left and right inner edges swung. Simultaneously, we realized that the distance between the left and right inner edges also periodically varied.
Analysis of the Trailing Vortex and Downwash Behavior
To quantitatively analyze the behavior of the trailing vortex, its location is identified by the following procedure. Specifically, as shown in Fig. 15, the absolute value of the flow velocity is extracted along the y-direction at the assigned position in the x-direction, and the flow velocity is read in the order from the outside region of the body toward the symmetric plane. Then, the position where the flow velocity becomes 60% of the mainstream velocity for the first time is defined as the position of the outer surface of the trailing vortex. The position where it is found for the second time in the same manner is defined as the position of the inner surface. Although the "60% of the mainstream velocity" is not always based on the exact physical background, it is tentatively regarded as the representative position of the outer surface of the trailing vortex because it substantially corresponds to the outer surface position of the trailing vortex measured in the cross section behind the body.
Fig. 16 shows the results obtained by measuring the time-series variation of the deviation from the mean value of the representative position. The graphs show that the position at the outer edge of the trailing vortex does not very significantly fluctuate, and the inner edge remarkably fluctuates. The distinctive point here is that the position of the inner edge indicates sometimes an extremely large displacement value toward the outer direction of the body width from the mean position, whereas such trend does not appear toward the inner direction with the exception of the noise component.
Fig. 17 shows the time-series deviation of the center position between both inner sides of the trailing vortices, and Fig. 18 shows its power spectrum. This result clearly indicates the existence of a peak at around St [approximately equal to] 0.1, which is the representative frequency of the swinging of the trailing vortex mentioned above. Fig. 19 shows the calculated result of the time-series variation of the width between both inner sides of the trailing vortices, and Fig. 20 shows its power spectrum. A peak of the frequency appears at around St [approximately equal to] 0.51, which is the representative frequency of the downwash mentioned earlier.
Accordingly, we realize that the periodic change in the wake structure is due to the representative fluctuation of both the trailing vortex and the downwash. We confirm that both trailing vortices concurrently swing mainly to the lateral direction at a frequency of St [approximately equal to] 0.1, and the width between the inner sides of the trailing vortices alternately fluctuates at a frequency of St [approximately equal to] 0.51.
However, we can hardly explain that the transition phenomenon is caused by such periodic fluctuation because if it is caused by the periodic fluctuation, the probability of occurrence of the transition is believed to become higher, and the transition will take place at a much lower slant angle. Therefore, we are interested in the phenomenon where the position of the inner edge sometimes indicates an extremely large displacement toward the outer side only, which aperiodically occurs. The concrete procedure is described as follows:
First, with respect to the position data at the left inner edge, we created new data (Fig. 21) by removing the original data (Fig. 16) whose displacement is less than 15 mm. Because the aperiodic displacement, which indicates a displacement beyond 15 mm, is noticeable, this value is adopted, although this threshold is certainly not based on a strong physical background. Second, because the displacement of the left inner edge has a negative value, it is converted to a positive value and then converted again to binary data, as shown in Fig. 22, (Data-1). Third, with regard to the frequency band other than that around 65 Hz corresponding to St [approximately equal to] 0.51, which is the representative frequency of the downwash, the original data of the width between both inner sides of the trailing vortices are attenuated using a band-pass filter (Fig. 23). Then, these data are converted into binary data. Furthermore, these negative values are extracted and are converted to positive values, as shown in Fig. 24 (Data-2). Finally, the product of Data-1 and Data-2 is calculated to evaluate the coincidence of the fluctuation of the trailing vortex and the downwash, as shown in Fig. 25.
This process aims to extract the representative fluctuation component of the downwash from the fluctuation in the width between both inner edges and to extract only the outward displacement. Then, we can obtain the matching probability for the aperiodic fluctuation of the inner edge and the periodic fluctuation of the downwash. Here, matching probability [phi] is defined by the following formula:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
where [summation][S.sub.[alpha]] denotes the area of the pulse in Data-2 and [summation][S.sub.[alpha]] * [S.sub.[beta]] denotes that in Data-3 (Fig. 25). As a result, [phi] is calculated as 49%. Here, the probability of occurrence of the significant increase in the width calculated by Data-2 is 48%. This means that the probability of occurrence of the increase in the width and the large displacement is almost the same. Therefore, it is evident that the large outward displacement of the trailing vortex occurs independently of the periodic fluctuation of the width due to the movement of the downwash. The reason of this, if the large displacement occurs in conjunction with the periodic fluctuation of the width, the matching probability [phi] must become close to 100% or 0% when it occurs concurrently or alternately respectively.
Finally, a new parameter of probability [psi] where the aperiodic fluctuation itself in this inner edge of the trailing vortex occurs is presented. Here, [psi] is defined to evaluate the probability of occurrence of each magnitude range of the aperiodic fluctuation. Clearly, the absolute value of the fluctuation is a stratified at 5-mm interval, and probability [psi] is evaluated by the contribution of each interval. From the result shown in Fig. 26, at a slant angle of 27.5[degrees], we can understand that a displacement of more than 15 mm has an approximately 10% chance to occur. In addition, considering the result that [psi] indicates a 1% at 12.5[degrees], we can expect that [psi] will increase with the increase in the slant angle. By considering this trend, we expect that this will also continue up to the critical slant angle.
Fig.27 shows conceptual schematics of periodic and aperiodic phenomenon drawn based on the results of above investigation. The figure-(a) represents the periodic fluctuation of vortex structures. Along the stream lines of upwash and downwash, lateral vortices pass periodically. At the same time, trailing vortices swing to the lateral direction periodically. This schematic is drawn according to Fig.14, which is a result of the PIV test where vortex structures fluctuate periodically. The figure-(b) represents the aperiodic generation and convection of a large vortex lump. The first figure shows the generation phase of a large scale separation which occurs irregularly and aperiodically. This schematic is drawn according to Fig.12, which is a result of the flow visualization test at a moment of the transition. After the growth of the separation region, it detaches from the base of the boy as a large vortex lump. The second figure shows convection phase of the large vortex lump. This schematic is drawn according to the analysis of the fluctuation of the width between both inner edges of the trailing vortices.
Hypothesis of the Transition Mechanism
By consolidating the investigated results in this work, the transition phenomenon mechanism of the wake structure of the Ahmed Body would be explained by the following hypothesis.
When the combination of the slant angle and aspect ratio is closer to a critical condition, the mean reattachment position of the downwash extends closer to the lower end of the slanted base. In this case, a slightly large variation in the downwash dominates the probability of whether or not to reattach. For example, if the scale of the lateral vortex entrained by the downwash becomes greater than the mean value, the downwash can no longer be reattached to the slanted base. As a result, the lateral vortex coalesces with the stationary bubble that exists behind the vertical base; thus, a large-scale separation vortex is generated. We should note here that this phenomenon aperiodically occurs. Furthermore, the large-scale separation vortex is entrained downstream, and it pushes both trailing vortices toward the outer side. Because the large-scale separation vortex is oriented by the lateral vortex, which is transported by the downwash, we considered this to be natural in which the extrusion phenomenon is synchronized by the representative frequency of the downwash downstream.
In conclusion, we consider that the coalescence of the downwash with the stationary bubble could be a trigger of the transition under the critical condition of the combination of the slant angle and aspect ratio as shown in Fig. 28.
In the first half of this work, we have studied the effects of the typical combinations of the slant angle and the aspect ratio and have conducted an investigation to clarify the relationship between the geometric condition and the transition in the wake structure. In the second half, we have analyzed the instantaneous flow structure of the wake to determine the essential phenomenon that dominates the transition. Finally, a hypothesis of the mechanism of the transition has been proposed. The concrete results and information are summarized as follows:
We have clarified that the transitional characteristics of the wake structure of the Ahmed Body is dominated by the combination of the slant angle and aspect ratio. We experimentally confirmed that the transition phenomenon occurs by changing the aspect ratio relative to the slant angle. Then, we elaborated the description by introducing the [theta]-[lambda]-characteristic surface to represent this trend. Based on the characteristic surface, we understood that the Ahmed Body possesses the property of [C.sub.D] and [C.sub.L] that extremely increases in the region for a particular combination of [theta] and [lambda]. Because the results of this study are limited to the basic characteristics, performing further systematic experiments is necessary to elucidate the detailed characteristics.
In the next phase, unsteady fluctuation of the wake was measured using a dynamic PIV system. As a result, we found that in case of a slant angle close to the critical angle, an instant occurred when the downwash, which was separated at the upper end of the slanted base, did not reattach to the slanted base. We found that at this instant when the lateral vortex transported by the downwash reached the rear-end position of the slanted base, the lateral vortex coalesced with the stationary bubble in the body backward, and a large separation vortex was then generated. As a result, this large separation vortex was expected to become a trigger of the transition.
In addition, we revealed the unsteady behavior of the trailing vortex, which was focused in our previous papers. We confirmed that the trailing vortices on both sides concurrently fluctuated in the lateral direction with frequency St [approximately equal to] 0.1. Simultaneously, the width between the trailing vortices was aperiodically increased by the fluctuation of the trailing vortex.
Unfortunately, in this experimental analysis, the proposal of a hypothesis of the transitional mechanism suffers from a limitation, i.e., carrying out experiments to verify this hypothesis is difficult. In other words, grasping the three-dimensional total picture of the transient phenomena is difficult, although we were able to partially elucidate some of the symptoms. Therefore, to confirm this hypothesis, numerical analysis using CFD is considered to be inevitable in the next study phase.
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Thermo and Fluid Dynamics Laboratory
Department of Mechanical Systems Engineering
Tokyo City University
1-28-1, Tamazutsumi, Setagaya-ku, Tokyo, 158-8557, Japan
A - front area of the body
[C.sub.D] - coefficient of drag
[C.sub.L] - coefficient of lift
[L.sub.s] - length of slated base
Re - Reynolds number
St - Strouhal number
x - distance from the vertical base
W - width of slated base
[lambda] - aspect ratio of the slanted base
[theta] - slant angle of the upper rear base
[phi] - matching probability
[psi] - ratio of frequency to number of data
[xi] - ratio of the distance from the back end of the model (x) to the length of the slanted base ([L.sub.s])
Itsuhei Kohri, Yuji Kobayashi, Akira Kasai, and Takayoshi Nasu
Tokyo City University
Daichi Katoh and Yoshimitsu Hashizume
Suzuki Motor Corp.
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|Author:||Kohri, Itsuhei; Kobayashi, Yuji; Kasai, Akira; Nasu, Takayoshi; Katoh, Daichi; Hashizume, Yoshimitsu|
|Publication:||SAE International Journal of Passenger Cars - Mechanical Systems|
|Date:||Jun 1, 2016|
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