[American Institute of Aeronautics and Astronautics 36th AIAA Fluid Dynamics Conference and Exhibit - San Francisco, California ()] 36th AIAA Fluid Dynamics Conference and Exhibit

American Institute of Aeronautics and Astronautics

1

An Experimental Study of Flow around a Circular Cylinder with and without End Plates in Ground Effect

Takafumi Nishino*, Graham T. Roberts† and Xin Zhang‡ School of Engineering Sciences, University of Southampton, Southampton, SO17 1BJ, United Kingdom

Flow and force characteristics have been experimentally studied for a circular cylinder, with and without end plates, placed near and parallel to a moving ground, over which no boundary layer developed to interfere with the cylinder. Mean drag and lift measurements, surface oil-flow visualisation, and particle image velocimetry (PIV) measurements were carried out at two upper-subcritical Reynolds numbers of 0.4 and 1.0×105 (based on the cylinder diameter d) to investigate the effects of the gap ratio h/d, where h is the gap between the cylinder and the ground. For the cylinder with end plates, the drag rapidly decreased as h/d decreased to less than 0.5, but became constant for h/d of less than 0.35. This distinctive drag behaviour was explained by a global change in the near wake: the Kármán-type vortex shedding was found to be intermittent at h/d = 0.4, and then totally ceased (and instead two nearly parallel shear layers were formed) at h/d = 0.3 and below. Meanwhile, for the cylinder without end plates, no such a critical change in drag was observed as the Kármán-type vortices were not generated in the near wake region for all h/d investigated.

Nomenclature CD = drag coefficient, D/q∞ld CL = lift coefficient, L/q∞ld D = drag force d = cylinder diameter f = frequency h = gap between cylinder and ground L = lift force l = cylinder length q∞ = freestream dynamic pressure, ρU∞

2/2 Re = Reynolds number, ρU∞d/μ St = Strouhal number, fd/U∞ U, V, W = Cartesian (x, y, z) components of velocity U∞ = freestream velocity x, y, z = Cartesian coordinates ye = distance from the bottom edge of end plate to cylinder δB = thickness of the boundary layer on ground μ = viscosity ρ = density ω z = non-dimensional spanwise vorticity, (∂V/∂x – ∂U/∂y) d/U∞

I. Introduction low around a circular cylinder placed near a plane boundary is of fundamental interest as well as of relevance to many engineering applications, and thus has been investigated by a number of authors.1-13 The characteristics of

flow and force acting on the cylinder are governed not only by the Reynolds number Re but also by ‘gap ratio’, i.e., the ratio of the gap between the cylinder and the plane boundary, h, to the cylinder diameter d. However the

* Ph.D. Candidate, Aeronautics and Astronautics, E-mail: [email protected] † Senior Lecturer, Aeronautics and Astronautics, E-mail: [email protected] ‡ Professor, Aeronautics and Astronautics, AIAA Associate Fellow, E-mail: [email protected]

F

36th AIAA Fluid Dynamics Conference and Exhibit5 - 8 June 2006, San Francisco, California

AIAA 2006-3551

Copyright © 2006 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


2

mechanisms of flow and force variations caused by the effect of different h/d, or ‘ground effect’, are still far from being fully understood due to a variety of other influencing factors, such as the state of the boundary layer formed on the plane boundary, the aspect ratio of the cylinder, and the end condition of the cylinder. The main purpose of the present study is to elucidate the mechanisms of the ground effect in more detail by using a moving ground, over which no boundary layer develops, whereas most of the earlier studies were conducted with a fixed wall. A brief review of the earlier studies will be given below and is summarised in Table 1.

One of the earliest studies on the ground effect was carried out by Taneda,1 who visualised the flow behind a circular cylinder towed through stagnant water close to a stationary wall at a very low Reynolds number of 170, and showed that regular ‘Kármán-type’ vortex shedding occurred at h/d = 0.6 whereas only a weak single row of vortices was generated at h/d = 0.1. Later, Roshko et al.2 measured the time-averaged drag and lift coefficients for a cylinder placed near a plane wall in a wind tunnel at an upper-subcritical Reynolds number of 2.0×104 (around which Reynolds number the drag coefficient of a cylinder outside the ground effect shows an almost constant value of about 1.2, see, e.g., Ref. 14), and showed that the drag rapidly decreased and the lift increased as the cylinder came close to the wall (as described later in Figs. 3 and 4, respectively). Bearman and Zdravkovich3 measured the pressure distribution around a cylinder at Re = 4.8×104, and thereby explained the variations of the drag and lift forces caused by different gap ratios. They also measured velocity fluctuations in the wake of the cylinder, and suggested that the critical gap ratio (h/d)c, where the regular vortex shedding ceased, was 0.2 to 0.3. The regular vortex shedding was found to occur at an almost constant Strouhal number St of about 0.2 for all h/d greater than 0.3. Similar measurements of St and (h/d)c were also carried out at higher and lower Reynolds numbers,4-6 as summarised in Table 1. More details of the cessation of the regular vortex shedding were later observed, but only at lower Reynolds numbers, by Zdravkovich7, Price et al.8, and Lin et al.9

Although the fundamental effects of h/d have been successfully observed by the above authors, the mechanisms of those striking changes, especially in drag coefficient, are still unclear. Zdravkovich10 observed that the rapid decrease in drag occurred as the gap was reduced to less than the thickness of the boundary layer δB on the fixed wall, and concluded that the variation of the drag coefficient was dominated by h/δB rather than by the conventional gap ratio h/d. However, Hiwada et al.11 reported, for the case of δB/d = 0.23, that the decrease in drag started around h/d = 0.5, where the cylinder was still outside the thin wall boundary layer, suggesting that the drag reduction could be caused not only by the direct interference of the wall boundary layer. A further investigation was conducted for a wider range of δB/d by Lei et al.,12 but the relation between δB and the gap at which the decrease in drag occurred was not clear in their measurements. They noted that the scatter of their results for h/δB < 1 might be attributed to the unstable nature of the artificial wall boundary layers used in their study. More recently, Zdravkovich13 reported the drag behaviour for a cylinder placed near a moving floor running at the same speed as the freestream (i.e., there was practically no boundary layer formed on the floor) for a higher Reynolds number of 2.5×105, which lies within the critical flow regime rather than the subcritical flow regime.14 In contrast to all the above studies, the decrease in drag due to the decrease in h/d did not occur. It was not clear, however, whether this was attributed to the non-existence of the wall boundary layer or the higher Reynolds number, or any other influencing factors.

Among a number of the other influencing factors, the end condition of a cylinder might be one of the most significant since the aspect ratio of a cylinder cannot be large enough in practical experiments, especially at high Reynolds numbers, to ensure the quasi-two-dimensionality of flow around it. A closed end condition, where a cylinder spans a closed test section of a wind or water tunnel, was used in most of the earlier studies (noted as ‘CE’

Table 1. Summary of earlier studies on flow around a circular cylinder placed near a plane boundary.

Authors Re h/d δB/d l/d Key measurements Taneda1 (1965) 170 0.1 – 0.6 (towed cylinder) n.a. WFV Roshko et al.2 (1975) 2.0×104 0 – 6.0 0.5 n.a. CD, CL Bearman and Zdravkovich3 (1978) 2.5×104 – 4.8×104 0 – 3.5 0.8 32 (CE) Cp, St, SFV Buresti and Lanciotti4 (1979) 8.5×104 – 3.0×105 0 – 2.5 0.1 6.6 (CE) St Angrilli et al.5 (1982) 2860 – 7640 0.5 – 6.0 < 0.25 9.0 (OW) St Grass et al.6 (1984) 2000 – 4000 0 – 2.0 0.28 – 6.0 20 (CE) St, WFV Zdravkovich7 (1985) 3550 0.1 – 1.6 (towed cylinder) 11.8 (OW) WFV Zdravkovich10 (1985) 4.8×104 – 3.0×105 0 – 2.0 0.52 – 0.97 13.5, 25 (EP) CD, CL Hiwada et al.11 (1986) 2.0×104 0 – 4.0 0.23 – 2.82 20 (CE) CD, CL, St, SFV, WFVLei et al.12 (1999) 1.4×104 0 – 3.0 0.14 – 2.89 26 (EP) CD, CL, Cp, St Price et al.8 (2002) 1200 – 4960 0 – 2.0 0.45 16.25 (CE) St, WFV, PIV Zdravkovich13 (2003) 2.5×105 0.02 – 0.5 (moving ground) 21 CD, CL Lin et al.9 (2005) 780 0 – 4.0 (towed), 0.86 – 1.41 33.1 (FE) St, WFV, PIV Present study 4.0×104 – 1.0×105 0.05 – 2.0 (moving ground) 8.33 (EP, FE) CD, CL, SFV, PIV

(CE: closed end, EP: end plate, FE: free end, OW: open water channel, SFV: surface flow visualisation, WFV: wake flow visualisation)


3

in Table 1), but in that case the so-called ‘horseshoe-vortex’15,16 formed around the closed end might change the wake pattern of the cylinder significantly. Zdravkovich10 and Lei et al.12 attached end plates to both ends of a finite-span cylinder with the aim to minimise the end-effect; the effectiveness of such plates has been confirmed for a cylinder in a freestream.17-19 However the influence on the physics of the ground effect, that is, how the use of end plates affects the flow and force characteristics of a cylinder in ground effect, has not been examined explicitly.

In order to elucidate the complicated physics of the ground effect in more detail, it is important to consider all the possible influencing factors involved, and to make it clear which factors are to be focused on and which to be restricted or eliminated. At the same time, a more intensive investigation into the characteristics of the flow field itself, e.g., vortical structures in the near wake of the cylinder, should be indispensable. In the present study, the time-averaged drag and lift forces were measured for a cylinder near a moving ground, similar to the measurements by Zdravkovich13 reviewed above but within the upper-subcritical flow regime. The purpose of using the moving ground is to eliminate the influence of the wall boundary layer, which is probably one of the most crucial but confusing factors for the ground effect. Meanwhile, the influences of the end condition of the cylinder were investigated in detail by using and not using a pair of end plates, the position of which relative to the cylinder was adjustable. The effects of other influencing factors, such as the levels of freestream turbulence and flow-induced vibration of the cylinder, were minimised as far as reasonably possible to simplify the problem. In addition to the time-averaged force measurements, oil flow visualisation on the cylinder surface and particle image velocimetry (PIV) measurements of the near wake of the cylinder were also conducted to show the instantaneous and statistical characteristics of the flow field. The results give new insights into the physics of the ground effect, and could serve as a database for both experimental and computational studies on the ground effect in the future.

II. Experimental Details

A. Wind Tunnel, Cylinder and End Plates The force measurements, surface flow visualisation and PIV measurements were performed in the 2.1 × 1.5 m

wind tunnel at the University of Southampton. The tunnel is of conventional closed circuit design, and the working section of 2.1 m wide × 1.5 m high × 4.4 m long is equipped with a large moving belt rig (1.5 m wide × 3.2 m long) and also with a three-component overhead balance to measure time-averaged forces. The moving floor works in conjunction with a boundary layer suction system, which ensures uniform airflow in the near-floor region. The freestream turbulence level is less than 0.3%. A further description of the wind tunnel facilities has been given by Burgin et al.20

Figure 1 describes a standard layout of the circular cylinder model and the end plates. The cylinder was placed above the moving floor with the axis lying parallel to the floor and normal to the freestream. The cylinder model used in the present study is 6 cm in diameter and 50 cm in length: the aspect ratio l/d = 8.33. The model is made of aluminium alloy, and the surface is smooth; the relative roughness K/d, where K is the estimated height of excrescences, is less than 0.01%. Aluminium end plates 3 mm thick (or Perspex end plates 6.5 mm thick in the case of PIV measurements) were attached to both ends of the cylinder. The size of the end plates, given in Fig. 1, basically follows recommendations by Stansby,17 who optimised the distance from the leading edge of the plates to a cylinder placed in a freestream. An additional factor to be considered here, however, is the gap between the end plates and the moving floor since the plates are not allowed to contact the moving floor. In this study, the distance from the bottom edge of the plates to the cylinder, denoted by ye in Fig. 1, was set at three different levels of 0, 0.2d

Figure 2. Model installation in the wind tunnel.

8d

3.5d 4.5d

yed

h

4d

U�

End plate

Cylinder

Moving floor

y

x

Figure 1. A standard layout of the cylinder model.


4

and 0.4d to examine the effect of the end plate position. The experiments were also performed for the cylinder without the end plates to show the influence of the end plates themselves on the physics of the ground effect; i.e., four different end conditions in total were investigated in this study.

Figure 2 shows a photograph of the cylinder model and end plates installed in the wind tunnel. The model was mounted on two steel struts, which were connected to the overhead balance of the wind tunnel. Two thin steel wires crossed between the struts to minimise the vibration of the model. The total blockage of the test section caused by the cylinder model, end plates and struts was less than 3%, and hence no corrections concerning the blockage effect were made for the experimental results.

B. Experimental Procedure The time-averaged drag and lift forces acting on the cylinder were measured through the following processes.

First, the forces acting on the ‘total’ package, consisting of the cylinder model, end plates, struts and wires, were measured for each experimental condition (Reynolds numbers of 0.4 and 1.0×105, gap ratio h/d of 0.05 to 2.0, and the four end conditions). Second, the forces acting on the 'tare' package, consisting only of the end plates, struts and wires, were measured for each condition. The drag and lift coefficients for the cylinder, CD and CL, were then calculated from the two sets of measurements, taking into account the changes in air density due to the slight variations of the freestream temperature and pressure during the tests.

For the surface flow visualisation, the cylinder model was painted matt black to obtain clear images of the flow pattern. A mixture of liquid paraffin and fine powder ‘Invisible Blue T70’ was applied to the model surface, and then the tunnel was run for about 30 minutes to evaporate the paraffin, making the flow pattern visible and to be photographed. The tests were carried out for different gap ratio h/d and cylinder end conditions, but only for the higher Reynolds number of 1.0×105.

The PIV measurements were performed using a Dantec FlowMap 2D-PIV system (PIV2100). A double-pulse Nd:YAG laser (120 mJ/pulse) was located approximately 1.5 m (25d) downstream of the centre of the cylinder to create a laser sheet of about 1 mm thick, illuminating the mid-span, x-y plane behind the cylinder. Smoke particles of about 1 μm in size were used as tracer particles to be illuminated. The illuminated particle images were captured using a Dantec HiSense CCD camera (1280×1024 pixels, 8 bits/pixel), which was synchronised with the laser so as to implement the so-called ‘double-frame/single-exposure’ recording.21 The time delay between the two laser pulses was set at 50 μs, and 400 pairs of images were continuously recorded for each experimental condition with a sampling rate of 2 Hz. Each pair of images was analysed using the cross-correlation technique with an interrogation area of 32×32 pixels with 50% overlapping in both horizontal and vertical directions. The resulting vectors were validated by the correlation-peak-height, velocity-range, and moving-average validations.22 The rejected vectors were replaced with interpolated values from the surrounding valid vectors, to which no filtering was applied. The measurements were carried out only for Re = 0.4×105.

C. Uncertainties in Measurements The random uncertainties, or precision errors, were estimated for the measurements of the time-averaged drag

and lift coefficients, CD and CL, following the theory of uncertainties analysis by Moffat.23 At the worst case under the condition of Re = 0.4×105, the uncertainties in CD and CL were estimated to be ±0.016 and ±0.011, respectively, with 95% confidence. Those for Re = 1.0×105 were ±0.008 and ±0.003, respectively. For the gap ratio h/d, an accuracy of ±0.002 was kept for the smallest h/d of 0.05, and ±0.01 was ensured for the other cases. A further description of the uncertainties has been given in Ref. 24.

III. Results and Discussion

A. Drag and Lift Coefficients The variations of the time-averaged drag coefficient of the cylinder are shown in Fig. 3 for the four different end

conditions investigated. The results of some of the earlier studies reviewed above are also shown in this figure for the purpose of comparison. For the present results, indicated by the symbols, only those for Re = 1.0×105 are shown here since there were no substantial differences between the two Reynolds numbers tested. As is obvious from the figure, the rapid decrease in CD did occur, despite no boundary layer on the moving floor, as h/d decreased to less than about 0.5 for all three cases where the end plates were used (ye/d = 0, 0.2, and 0.4). This agrees with, and more clearly supports, the observation by Hiwada et al.11 that the drag reduction is caused not only by the direct interference of the wall boundary layer but also by the proximity of the plane boundary itself. The drag reduction, however, suddenly stopped around h/d = 0.35 and then CD remained almost constant at slightly less than 1 as the cylinder came close to the wall in this study; such a distinctive drag behaviour has not been observed in the earlier


5

studies by Hiwada et al.11 and any other authors who used a fixed wall boundary. As will be shown later, the critical change in CD around h/d = 0.35 most likely coincides with a global change in the near wake, i.e., the cessation of Kármán-type (alternating) vortex shedding behind the cylinder.

The effects of the different end conditions will be discussed here in more detail. As concerns the effects of the position of the end plates, there is a clear difference between the results for ye/d = 0 and 0.2, but little difference between ye/d = 0.2 and 0.4, at large gap ratios of h/d > 0.6. At the largest gap ratio of h/d = 2, the drag coefficient for ye/d = 0.4 was 1.3, which is comparable to that for an isolated, long circular cylinder in a freestream in the upper-subcritical flow regime.14 Meanwhile, the drag behaviour observed for the cylinder without the end plates was

Figure 4. Time-averaged lift coefficient vs. gap ratio for different end conditions.

Figure 3. Time-averaged drag coefficient vs. gap ratio for different end conditions.


6

totally different from that for the cylinder with end plates; the drag gradually decreased, with no critical change, as the gap increased. At h/d = 2, the drag coefficient for the cylinder without the end plates was found to be 0.85, which is consistent with that for an isolated, short circular cylinder of similar aspect ratio reported by Zdravkovich et al.25 Interestingly, the end conditions had no substantial influence on the drag at small gap ratios of h/d < 0.35, where CD showed an almost constant value of 0.95 for the cylinder with the end plates at ye/d = 0 and 0.2, and also for the cylinder without the end plates.

The variations of the average lift coefficient of the cylinder at Re = 1.0×105 are presented in Fig. 4 for the four different end conditions. Similar but a little more scattered variations of CL were observed at the lower Reynolds number of Re = 0.4×105, details of which are not provided here. Instead the results for a fixed ground by Roshko et al.3 are shown in the same figure for the purpose of comparison. It can be seen from this figure that the end conditions have only small effects on the lift behaviour of the cylinder; CL rapidly increases as h/d decreases to less than about 0.5.

B. Surface Flow Pattern Figures 5 and 6 show the oil flow patterns on the upper (open-side) and bottom (gap-side) surfaces of the

cylinder for six different model configurations (four cases for the cylinder with the end plates at ye/d = 0 and the other two for the cylinder without end plates), respectively. Note that only half part of the cylinder is shown here since the pattern appeared to be symmetric in the spanwise direction for all cases tested. The flow direction is from downside to upside in Fig. 5, and is from upside to downside in Fig. 6.

With end plates (ye/d = 0) No end plates

(a) (e)

(b)

(c)

(d) (f)

Figure 5. Oil flow patterns on the upper surface of the cylinder with the end plates (a, b, c, d) and without the end plates (e, f) for h/d = 1.0 (a, e), 0.4 (b), 0.3(c), and 0.2 (d, f), Re = 1.0×105.

U�

Cylinder

x

z

Upper surface

h/d = 1.0

h/d = 0.4

h/d = 0.3

h/d = 0.2


7

As is obvious from the orderly oil-flow patterns in the upstream region, the airflow is laminar and almost two

dimensional, for all cases, before the separation. The separation line on the upper surface is straight when the end plates are used [Figs. 5(a) to (d)], and is slightly curved near the ends when the plates not used [Figs. 5(e) and (f)]. A similar pattern of this slightly-curved separation near the free end has been reported for a circular cylinder placed normal to a ground (i.e., having one free end) by Okamoto and Yagita,26 and also in a free stream (i.e., having two free ends) by Zdravkovich et al.25 On the bottom surface, however, the separation line becomes straight, even when the end plates are not used, as the gap decreases [Figs. 6(e) and (f)]. It can also be seen that the angular position of the separation moves upstream on the upper side and downstream on the bottom side as the cylinder comes close to the ground; this qualitatively agrees with an observation reported by Bearman and Zdravkovich3 for a fixed ground. Figure 7 summarises the separation angle θsep [the angle from the front (x/d = –0.5, y/d = 0) to the separation point estimated from the oil flow patterns at the mid-span of the cylinder] for all gap ratios investigated.

Although the flow in the separated region is basically time-dependent and thus cannot be exactly captured by the present oil flow tests, an interesting trend can be observed in the oil patterns behind the separation lines on both upper and bottom surfaces. That is, a dominant pattern in the spanwise direction appears when the end plates are not used [Figs. 5(e), (f) and 6(e), (f)], suggesting the existence of a quasi-steady (non-periodic) flow in that region, and a similar pattern can be recognised on the plate-equipped cylinder but only with smaller gap ratios of h/d ≤ 0.3 [Figs. 5(c), (d) and 6(c), (d)]. Meanwhile, no such a clear dominant pattern can be seen on the plate-equipped cylinder with larger gap ratios of h/d ≥ 0.4 [Figs. 5(a), (b) and 6(a), (b)]. As will be described in the next section, for the plate-equipped cylinder, there is in fact a significant change in the near wake flow pattern between the two gap ratios of 0.3 and 0.4, and this explains the critical drag behaviour shown in Fig. 3.

With end plates (ye/d = 0) No end plates

(a) (e)

(b)

(c)

(d) (f)

Figure 6. Oil flow patterns on the bottom surface of the cylinder with the end plates (a, b, c, d) and without the end plates (e, f) for h/d = 1.0 (a, e), 0.4 (b), 0.3(c), and 0.2 (d, f), Re = 1.0×105.

U�

Cylinderx

z

Bottom surface

h/d = 1.0

h/d = 0.4

h/d = 0.3

h/d = 0.2


8

C. Near Wake Structure 1. Cylinder with End Plates

Figure 8 shows the time-averaged, mid-span (z/d = 0) flow field data, obtained from 400 samples of PIV data for each case, behind the cylinder with end plates at ye/d = 0. The time-averaged velocity vectors, streamwise velocity contours, and spanwise vorticity contours are depicted in Figs. 8(a-d), (e-h), and (i-l), respectively, for four different h/d of 0.6 (a, e, i), 0.4 (b, f, j), 0.3 (c, g, k), and 0.2 (d, h, l). Note that the data in the vicinity of the cylinder and ground surfaces have been discarded as they were disturbed by the reflection of light from the surfaces. It can be seen from the figures that the recirculation region behind the cylinder is significantly elongated as the gap ratio h/d is reduced from 0.6 to 0.3, but no substantial difference can be seen between h/d = 0.3 and 0.2. This apparently corresponds to the drag behaviour described in Fig. 3: the longer the recirculation region, the lower the drag on the cylinder. It is also observed that the two separated shear layers are deflected slightly upward as the cylinder comes close to the ground. The strength of the two shear layers, however, is about the same even at the smallest h/d of 0.2 as practically no boundary layer develops on the moving ground to interfere with the shear layers separated from the bottom side of the cylinder.

More details of the mechanisms of the ground effect can be explained with instantaneous flow field data behind the cylinder. Figures 9(a) and (b) show typical instantaneous velocity fields for h/d = 0.6 and 0.2, respectively, and the corresponding instantaneous vorticity contours are plotted in Figs. 10(a) and (b), respectively. For h/d = 0.6, large-scale Kármán-type (asymmetric, alternating) vortices are formed just behind the cylinder, which is a common wake flow pattern for an isolated circular cylinder in the upper-subcritical flow regime (Re = 0.2 to 2.0×105).14 As suggested by Bearman and Trueman,27 this type of vortices continuously draws in fluid from the base region during their growth, and this entrainment process sustains low base pressure and therefore high drag force acting on the cylinder. For h/d = 0.2, however, such large-scale vortices are not generated and instead the so-called ‘dead-fluid’ zone is created behind the cylinder, bounded by two nearly parallel shear layers each producing only small-scale vortices (due to the shear layer instability) in the near wake region. Hence the cessation of the Kármán-type vortex shedding and the continuous existence of the dead-fluid zone, which was also the case for h/d = 0.3, should be the main reason for the low drag forces observed at the smaller gap ratios of h/d < 0.35.

Interestingly, at an ‘intermediate’ gap ratio of 0.4, the Kármán-type vortex shedding was found to be intermittent in the near wake region. Two typical instantaneous velocity fields for this gap ratio are shown in Fig. 11, and the corresponding instantaneous vorticity contours are plotted in Fig. 12. As can be seen from these figures, at a certain moment when the large-scale vortices are formed behind the cylinder [Figs. 11(a) and 12(a)] the near wake structure looks similar to that for the larger gap ratio [Figs. 9(a) and 10(a)], whereas at another moment when the shedding temporarily ceases [Figs. 11(b) and 12(b)] the wake structure becomes similar to that for the smaller gap ratio [Figs. 9(b) and 10(b)]. Although the time evolution of the wake structure was not able to be captured in this study due to the low sampling rate of the PIV recording, both types of instantaneous wake patterns were frequently observed throughout the measurements at this gap ratio. It should therefore be reasonable to suggest that the intermittency of

Figure 7. Time-averaged separation angle (estimated from surface oil-flow patterns) vs. gap ratio for the cylinder with the end plates (ye/d = 0) and without the end plates, Re = 1.0×105.


9

Figure 8. Time-averaged flow fields behind the cylinder equipped with the end plates (ye/d = 0): velocity vectors (a, b, c, d), contours of non-dimensional streamwise velocity (e, f, g, h), and contours of non-dimensional spanwise vorticity (i, j, k, l), for h/d = 0.6 (a, e, i), 0.4 (b, f, j), 0.3 (c, g, k), and 0.2 (d, h, l), Re = 0.4×105. Solid and dashed contour lines indicate positive and negative values, respectively.

(a) (e) (i)

(b) (f) (j)

(c) (g) (k)

(d) (h) (l)


10

Figure 9. Typical instantaneous velocity fields behind the plate-equipped cylinder (ye/d = 0) for two different gap ratios: (a) h/d = 0.6, and (b) h/d = 0.2, Re = 0.4×105.

Figure 10. Typical instantaneous non-dimensional spanwise vorticity contours behind the plate-equipped cylinder (ye/d = 0) for two different gap ratios: (a) h/d = 0.6, and (b) h/d = 0.2, Re = 0.4×105. Solid and dashed contour lines indicate positive and negative vorticity, respectively.

(a) (b)

(a) (b)


11

Figure 11. Two typical instantaneous velocity fields behind the plate-equipped cylinder (ye/d = 0) for h/d = 0.4, Re = 0.4×105, demonstrating the intermittency of the Kármán-type vortex shedding at this ‘intermediate’ gap ratio.

Figure 12. Two typical instantaneous non-dimensional spanwise vorticity contours behind the plate-equipped cylinder (ye/d = 0) for h/d = 0.4, Re = 0.4×105. Solid and dashed contour lines indicate positive and negative vorticity, respectively.

(a) (b)

(a) (b)


12

the Kármán-type vortex shedding in the near wake region results in the medium level of the time-averaged drag forces observed at the intermediate gap ratios of 0.35 < h/d < 0.5.

2. Cylinder without End Plates

Figure 13 shows the time-averaged, mid-span (z/d = 0) flow field data for the cylinder without end plates. The time-averaged velocity vectors, streamwise velocity contours, and spanwise vorticity contours are described in Figs. 13(a, b), (c, d), and (e, f), respectively, for two different h/d of 0.6 (a, c, e) and 0.2 (b, d, f). As is obvious from the figures, the recirculation region behind the cylinder without end plates is elongated even at the larger gap ratio of 0.6. In other words, the effects of h/d for the cylinder without end plates are moderate compared with those for the cylinder with end plates. This is consistent with the results for the time-averaged drag coefficients (Fig. 3) and also for the surface oil flow patterns behind the separation lines (Figs. 5 and 6), on which the effects of h/d for the cylinder without end plates were very small. In fact the instantaneous, mid-span flow fields for the two cases (h/d = 0.6 and 0.2, without end plates) were found to be quite similar to those for the plate-equipped cylinder with the lower h/d of 0.2 [Fig. 9(b)], i.e., two nearly parallel shear layers were regularly observed in the near wake region. In this connection, Zdravkovich et al.25 reported for an isolated short circular cylinder (2 ≤ l/d ≤ 8) that the vortex shedding frequency was different from that for a long circular cylinder, suggesting the existence of a different vortex shedding mode from the Kármán-type vortex shedding. Also Okamoto and Sunabashiri28 reported for a short circular cylinder placed normal to a ground (i.e., having one free end) that the vortex shedding pattern was changed from the antisymmetric Kármán-type to a symmetric ‘arch-type’ (but the vortex formation region was not elongated) when l/d was reduced to less than 4 to 7. It might be said that the present results show the combined effect of small h/d and l/d, both of which tend to discourage the formation of the Kármán-type vortices.

Figure 14 shows a comparison of the time-averaged streamwise velocity profiles between the cylinders with and without end plates, for (a) h/d = 0.6 and (b) h/d = 0.2. Note that the profiles at x/d = 1.0, 1.5, 2.0, and 2.5 at the mid-span of the cylinder are plotted in the figures. It can be seen from the figures that the effects of the end plates are

Figure 13. Time-averaged flow fields behind the cylinder without the end plates: velocity vectors (a, b), contours of non-dimensional streamwise velocity (c, d), and contours of non-dimensional spanwise vorticity (e, f), for h/d = 0.6 (a, c, e), and 0.2 (b, d, f), Re = 0.4×105. Solid and dashed contour lines indicate positive and negative values, respectively.

(a) (c) (e)

(b) (d) (f)


13

significant for h/d = 0.6 since the Kármán-type vortex shedding occurs if the plates are used at this gap ratio, whereas the effects are small for h/d = 0.2 as the vortex shedding does not occur regardless of the cylinder end conditions. Of interest is that the profiles for the cylinder without the end plates at h/d = 0.6 look similar to those observed at h/d = 0.2 rather than to those observed at the same gap ratio of 0.6 but with the end plates. Considering the gradual change in CD presented in Fig. 3, it is reasonably expected that the cylinder without the end plates would experience no critical change in the near wake structure, i.e., the Kármán-type vortex shedding would not occur, as h/d is further increased to at least 2.0. Further investigations are needed, however, to fully understand the ground effect for a circular cylinder without end plates, where the combined effects of h/d and l/d would be the key issue to be investigated.

IV. Conclusions The characteristics of flow around a circular cylinder in ground effect were experimentally investigated at two

upper-subcritical Reynolds numbers of 0.4 and 1.0×105. Specifically, the results of the time-averaged drag and lift measurements, surface oil-flow visualisation and PIV measurements were presented in this paper. The experiments were carried out using a moving ground running at the same speed as the freestream to eliminate the notoriously confusing effects of the boundary layer formed on the ground, and thereby to elucidate the essential mechanisms of the ground effect. The influences of the end condition of the cylinder were also examined by using and not using a pair of end plates.

For the cylinder with end plates, distinctive effects of the gap ratio h/d were observed on the near wake structure and also on the time-averaged drag coefficient CD, despite no boundary layer on the moving ground to interfere with the cylinder. The characteristics of flow might be classified into three regimes: large-gap (h/d > 0.5), intermediate-gap (0.35 < h/d < 0.5), and small-gap (h/d < 0.35) regimes. In the large-gap regime, large-scale, Kármán-type vortices were generated just behind the cylinder, resulting in higher values of CD around 1.3. In contrast, in the small-gap regime, the large-scale vortex shedding totally ceased and instead a dead-fluid zone was created, bounded by two nearly parallel shear layers each producing only small-scale vortices in the near wake region. No substantial effect of h/d was observed in this regime: CD was almost constant at a lower value of about 0.95. In the inter-mediate-gap regime, the Kármán-type vortex shedding was found to be intermittent (i.e., typical instantaneous wake patterns of both the large- and small-gap regimes were intermittently observed), and CD rapidly decreased as h/d decreased from 0.5 to 0.35.

As for the cylinder without end plates, no such significant effects of h/d were observed either on the near wake structure or on the value of CD. The Kármán-type vortices were not generated behind the cylinder, and the time-averaged wake profiles at the mid-span of the cylinder were found to be very similar to those for the plate-equipped cylinder in the small-gap regime. Further investigations are needed, however, to fully understand the overall picture of the ground effect for a cylinder without end plates as the effects of the aspect ratio of the cylinder should be of great importance in that case.

Figure 14. Time-averaged streamwise velocity profiles for (a) h/d = 0.6, and (b) h/d = 0.2, Re = 0.4×105. The circles (○) show the results for the cylinder with the end plates (ye/d = 0), and the cross marks (×) indicate the results for the cylinder without the end plates.

(a) (b)


14

Acknowledgement The work reported in this paper was supported in part by a research scholarship from the School of Engineering

Sciences, University of Southampton, United Kingdom.

References 1Taneda, S., “Experimental Investigation of Vortex Streets,” Journal of the Physical Society of Japan, Vol. 20, 1965, pp.

1714-1721. 2Roshko, A., Steinolfson, A., and Chattoorgoon, V., “Flow Forces on a Cylinder near a Wall or near Another Cylinder,”

Proceedings of the Second U.S. national Conference on Wind Engineering Research, Fort Collins, 1975, Paper IV-15. 3Bearman, P. W., and Zdravkovich, M. M., “Flow around a Circular Cylinder near a Plane Boundary,” Journal of Fluid

Mechanics, Vol. 89, 1978, pp. 33-47. 4Buresti, G., and Lanciotti, A., “Vortex Shedding from Smooth and Roughened Cylinders in Cross-Flow near a Plane

Surface,” Aeronautical Quarterly, Vol. 30, 1979, pp. 305-321. 5Angrilli, F., Bergamaschi, S., and Cossalter, V., “Investigation of Wall Induced Modifications to Vortex Shedding from a

Circular Cylinder,” Transactions of the ASME: Journal of Fluids Engineering, Vol. 104, 1982, pp. 518-522. 6Grass, A. J., Raven, P. W. J., Stuart, R. J., and Bray, J. A., “Influence of Boundary Layer Velocity Gradients and Bed

Proximity on Vortex Shedding from Free Spanning Pipelines,” Transactions of the ASME: Journal of Energy Resources Technology, Vol. 106, 1984, pp. 70-78.

7Zdravkovich, M. M., “Observation of Vortex Shedding behind a Towed Circular Cylinder near a Wall,” Flow Visualization III: Proceedings of the Third International Symposium on Flow Visualization, edited by W. J. Yang, Hemisphere, Washington DC, 1985, pp. 423-427.

8Price, S. J., Sumner, D., Smith, J. G., Leong, K., and Paidoussis, M. P., “Flow Visualization around a Circular Cylinder near to a Plane Wall,” Journal of Fluids and Structures, Vol. 16, 2002, pp. 175-191.

9Lin, C., Lin, W-J., and Lin, S-S., “Flow Characteristics around a Circular Cylinder near a Plane Boundary,” Proceedings of the Sixteenth International Symposium on Transport Phenomena (ISTP-16), Prague, Czech Republic, 2005, (CD-ROM).

10Zdravkovich, M. M., “Forces on a Circular Cylinder near a Plane Wall,” Applied Ocean Research, Vol. 7, 1985, pp. 197-201.

11Hiwada, M., Mabuchi, I., Kumada, M., and Iwakoshi, H., “Effect of the Turbulent Boundary Layer Thickness on the Flow Characteristics around a Circular Cylinder near a Plane Surface,” (in Japanese), Transactions of the Japan Society of Mechanical Engineers B, Vol. 52, 1986, pp. 2566-2574.

12Lei, C., Cheng, L., and Kavanagh, K., “Re-Examination of the Effect of a Plane Boundary on Force and Vortex Shedding of a Circular Cylinder,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 80, 1999, pp. 263-286.

13Zdravkovich, M. M., Flow around Circular Cylinders: Vol 2: Applications, Oxford University Press, Oxford, UK, 2003, pp. 880, 881.

14Zdravkovich, M. M., Flow around Circular Cylinders: Vol 1: Fundamentals, Oxford University Press, Oxford, UK, 1997, Chapter 1.

15Baker, C. J., “The Laminar Horseshoe Vortex,” Journal of Fluid Mechanics, Vol. 95, 1979, pp. 347-367. 16Baker, C. J., “The Turbulent Horseshoe Vortex,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 6, 1980,

pp. 9-23. 17Stansby, P. K., “The Effects of End Plates on the Base Pressure Coefficient of a Circular Cylinder,” Aeronautical Journal,

Vol. 78, 1974, pp. 36, 37. 18Fox, T. A., and West, G. S., “On the Use of End Plates with Circular Cylinders,” Experiments in Fluids, Vol. 9, 1990, pp.

237-239. 19Szepessy, S., and Bearman, P. W., “Aspect Ratio and End Plate Effects on Vortex Shedding from a Circular Cylinder,”

Journal of Fluid Mechanics, Vol. 234, 1992, pp. 191-217. 20Burgin, K., Adey, P. C., and Beatham, J. P., “Wind Tunnel Tests on Road Vehicle Models Using a Moving Belt Simulation

of Ground Effect,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 22, 1986, pp. 227-236. 21Raffel, M., Willert, C., and Kompenhans, J., Particle Image Velocimetry: A Practical Guide, Springer-Verlag, Berlin,

Germany, 1998. 22Jensen, K.D., “Flow Measurements”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 26,

2004, pp. 400-419. 23Moffat, R. J., “Contributions to the Theory of Single-Sample Uncertainty Analysis,” Transactions of the ASME: Journal of

Fluids Engineering, Vol. 104, 1982, pp. 250-260. 24Nishino, T., “Experimental Study of Drag and Lift Forces Acting on a Circular Cylinder in Ground Effect,” Technical

Report AFM05-TN01, School of Engineering Sciences, University of Southampton, UK, Aug. 2005. 25Zdravkovich, M. M., Brand, V. P., Mathew, G., and Weston, A., “Flow Past Short Circular Cylinders with Two Free Ends,”

Journal of Fluid Mechanics, Vol. 203, 1989, pp. 557-575. 26Okamoto, T., and Yagita, M., “The Experimental Investigation on the Flow Past a Circular Cylinder of Finite Length

Placed Normal to the Plane Surface in a Uniform Stream,” Bulletin of the Japan Society of Mechanical Engineers, Vol. 16, 1973, pp. 805-814.


15

27Bearman, P. W., and Trueman, D. M., “An Investigation of the Flow around Rectangular Cylinders,” Aeronautical Quarterly, Vol. 23, 1972, pp. 229-237.

28Okamoto, S., and Sunabashiri, Y., “Vortex Shedding from a Circular Cylinder of Finite Length Placed on a Ground Plane,” Transactions of the ASME: Journal of Fluids Engineering, Vol. 114, 1992, pp. 512-521.

Documents

[American Institute of Aeronautics and Astronautics 36th AIAA Fluid Dynamics Conference and Exhibit - San Francisco, California ()] 36th AIAA Fluid Dynamics Conference and Exhibit