On interference between two circular cylinders at supercritical Reynolds number

JOURNAL OF

Journal of Wind Engineering ~ 1 / ~ and Industrial Aerodynamics 62 (1996) 175-190 ELSEVIER

On interference between two circular cylinders at supercritical Reynolds number

Zhifu Gu State Key Laboratory for Turbulence Research, Department of Mechanics and Engineering Science,

Peking University, Beijing 100871, China

Received 2 April 1996; revised 27 May 1996; accepted 29 May 1996

Abstract

The results of investigation of interference between two identical parallel circular cylinders carried out in a uniform smooth flow at supercritical Reynolds number (4.5 x 105), by means of pressure distribution measurement in wind-tunnel testing, are presented and discussed. The results show that the characteristics of interference are completely different with those at subcritical Reynolds number due to the difference of wake structure behind cylinders. The flow around two cylinders in tandem arrangement, which is somewhat like the case of subcritical Reynolds number, may be classified into two distinct regimes and four patterns of pressure distribution. On the other hand, two distinct regimes and three types of pressure patterns may be identified in side-by-side arrangement. The abrupt changes in pressure distributions on both cylinders were observed in the special case of two cylinders in staggered arrangement. In general, the significant effect of interference between two circular cylinders at supercritical Reynolds number is restricted to be within a rather small spacing ratio (N/d = 1.7), except for two cylinders in tandem arrangement and its vicinity.

I. Introd~action

In marly cases of engineering practices, objects often appear in the form of groups, e.g. groups of buildings, chimneys, stacks, chemical reaction-towers, supports of off-shore platform, etc. Due to mutual interference, the aerodynamic characteristics, such as pressure distributions and vortex-shedding patterns, for each member of a group are completely different from isolated ones.

A circular cylinder is a typical bluff body and is one of the structural components mostly employed. Numerous investigations have been made of the flow past two circular cylinders, which is the simplest case of a group, in the last two decades. Extensive reviews were given by Zdravkovich [1] and Ohya et al. [2]. At subcritical Reynolds number, many interesting and unexpected phenomena were found, such as the biased bistable flow which occurred at specific ratios between the two circular cylinders :in side-by-side arrangement and the fluid forces have a discontinuity for the

0167-6105/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S01 67-6 105(96)00056-6

176 Z Gu/J. Wind Eng. Ind. Aerodyn. 62 (1996) 175-190

two cylinders in tandem and staggered arrangements at certain spacing ratios. More detailed investigations of discontinuities of pressure distributions on two circular cylinders in staggered arrangement were recently given by Gu and Sun [3,4].

Nevertheless, most problems in wind engineering practices are associated with high Reynolds number, as well as with high turbulence intensity. It is well known that the Reynolds number plays an important role in the aerodynamics forces on flow past a circular cylinder, thus, it is expected that it should have great influence on the interference effect between two circular cylinders. However, for supercritical and transcritical Reynolds number flows, available data are very few and this is specially important for circular cylinders in tandem or staggered arrangement as indicated in [2]. Okajima [5] studied two tandem circular cylinders at Reynolds numbers from 0.8 x 105 to 4.0 x 105 by means of measuring forces and using the surface oil-flow technique for flow visualization. He noted that in the subcritical flow regime, there occurred distinct step-like jumps of drag coefficients at critical gap ratio of 3.8, and in the supercritical flow regime the positions of laminar bubbles and flow separation hardly changed with gap ratios. The latter means that the drag coefficients of two tandem cylinders remain nearly constant regardless of the gap ratio. He also studied two side-by-side circular cylinders at Reynolds number from 0.25 x 105 to 4.5 x 105 [6]. Pressure distributions, lift and drag coefficients and Strouhal numbers were measured. The relationships among the formations of separation bubbles, the aspect of wakes, and the lift and drag coefficients were examined. No biased flow like that at subcritical Reynolds number was observed in the supercritical case. Some results of fluctuating pressure on two circular cylinders at high Reynolds number, including the supercritical regime were reported by Sun et al. [7], which suggest that the interference effects are weaker than those in the subcritical range. Results of the interference of two circular cylinders in high-turbulence flow at supercritical Reynolds number were presented by Gu et al. [8], which show that the overall effect of flow interference may not be as large as first thought except for the case of very small gap ratios.

In the present paper, a systematic pressure distribution of two identical circular cylinders of various arrangements including in tandem, side-by-side and staggered arrangement with different spacing ratios in uniform smooth flow at supercritical Reynolds number (Re -- 4.5 x 105) are presented and discussed. More attention has been paid on the classification of pressure patterns, as well as the mechanism of interference in nature.

2. Experimental apparatus and data reduction

The experiment was conducted in a closed-return low-speed wind tunnel located at Peking University. The tunnel has an open circular test section of 2.25 m in diameter and 3.65 m long. Maximum speed was 50 m/s with turbulent intensity about 0.2%.

The circular cylinders tested were seamless steel tubes with machine-finished surface. The cylinders were of identical size (diameter of 157 mm and 1 m long). The relevant aspect ratio was equal to 6.4 and the wind tunnel blockage was 8% of the cross section area of the test section. Pressure taps were installed every ten degrees

Z. Gu/J. Wind Eng. Ind. Aerodyn. 62 (1996) 175-190 177

b-- d --~

,f-L C

Fig. 1. Schematic diagram showing the arrangement of the two parallel cylinders and the definition of force coefficien ts.

circumfl~rentially around the cylinders at the mid-span. The cylinders, with circular end plates of 1.5 m diameter on both ends, were mounted horizontally in two adjustable guide-ways. The cylinders with two guide-ways made adjustment of gap ratio relatively easy and could be rotated for different directions of wind angle. The system was fixed on two columns which were rigidly attached to the ground floor.

The raeasurement system of the surface pressure consisted of pressure transducers (PDCR.-23d), a set of Scanivalve (SGM-48), two amplifiers (6M72), an A/D converter and a personal computer (IBM PC/XT). Two individual transducers were used for each cylinder such that the pressure signals at the same position (i.e., same azimuth angle 0, see Fig. 1) of both cylinders being tested were recorded simultaneously. A typical experiment took about 60 s to complete the data-logging of all pressure taps for both cylinders. Only time-averaged pressures were measured in the present test. The staggered configuration of the two cylinders is shown in Fig. 1 together with the sign corLventions of the fluid-force coefficients. Various values of spacing ratio N/d combine, d with various values of stagger angle fl give all possible arrangements of the two cylJ[nders. The pressure coefficient Cp(O) is defined as Cp(O)= [p(0)- p~]/ 0.5pV~, where 0 is the azimuth angle measured from the wind direction, positive clockwise. The pressure, density and velocity of oncoming flow are denoted by p~, p and V~, respectively. The Reynolds number Re depends on the diameter of the cylinder, d. In most cases, a Reynolds number of 4.52 x 105 was applied. No correction for blockage effect was made to the pressure data presented in this paper. It was felt that the blockage effect was small, especially in the open test section in recent experiments, compared to the large flow interference that were measured.

Drag and lift coefficients, denoted by CD and CL respectively, are defined conven- tionally and were obtained by integrating the pressure distributions around the mid-span circumference of the cylinder.

3. Resuh:s and discussion

3.1. Single cylinder

Pressure distributions around a single cylinder were measured first and used for comparison and discussion of the interference effect. The time-mean-pressure


distributions on a single cylinder with three typical Reynolds numbers, which correspond to subcritical, critical and supercritical Reynolds number regions, are shown in Fig. 2. At Re = 2.2 x 105, it shows a result of typical laminar separation flow. The separate points are at about 0 = + 80 ° and the values of base pressure Cpb are equal to -- 1, but it drops a little bit at the right backside of cylinder. Compared with those at the critical Reynolds number (Re = 3.9 x 105), the flow around one side of the cylinder transfers to the turbulent separation. The local minimum pressure C p m i n

reaches the value of - 3 . 0 and then raises with a small "step-like" curve, which indicates that the laminar separation "bubble" existed. While on the other side of the cylinder, the laminar separation flow is maintained with rather high base pressure Cpb of --0.5. At Re = 4.5 x 105, a typical supercritical flow pattern is present. The separation points shift backward at 0 = + 120 ° and the base pressure further reduces to - 0.2. Steady Cp distributions result [9]. The values of drag coefficients, CD, with various Reynolds numbers, are shown in Fig. 3, which coincide with the classical results published in the literature previously. A hot wire probe was placed in the near wake behind the cylinder. The signal of flow velocity was sampled and analyzed. No dominant peaks were found in the power spectra of the flow velocity. This suggests that the strong organized shedding disappears and a relatively stable wake structure, a cavity enclosed by the shear layers, is formed behind the cylinder. More detailed experiments and discussions on vortex shedding from a circular cylinder were reported by Farell [9] and Bearman [10].

3.2. Two circular cylinders in tandem arrangement (fl = 0 °)

For/3 = 0 °, where two cylinders are in tandem, the downstream cylinder (cylinder B) is submerged in the wake of the upstream one (cylinder A). The interference will be

0 Re=2.2xl0

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o,-ii -0.5 t ....................

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Fig. 2. Pressure distributions of a single cylinder at three typical Reynolds numbers .


L~

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Fig. 3. Drag coefficients of a single cylinder for various Reynolds numbers.

greatly effected by the wake behavior of the upstream cylinder. The interference between two tandem cylinders should be very different due to the different features of the wake structure between subcritical and supercritical Reynolds number. Two effects in different regimes with cylinder B being either located in or out of the wake cavity of upstream cylinder may be classified.

Selected typical pressure distributions with different spacing ratios (N/d --- 1.1, 1.2, 1.7, 2.2, 2.8 and 3.0) of two cylinders in tandem are shown in Fig. 4.

For the first regime, a downstream cylinder is located in the wake cavity of the upstream one, three patterns of pressure distributions on the downstream cylinder may be fllrther subdivided: (a) When the spacing ratio is very small (N/d = 1.1), two cylinders behave as a single lengthened body. The downstream cylinder is wrapped in the shear layers separated from the upstream cylinder and there is almost no fluid flow in the gap. Pressures on a wide area in the front part of the downstream cylinder with an approximate value of zero is the characteristic of this pattern. (b) When the spacing ratios are between 1.2 and 1.7, the separated shear layers from the upstream cylinder act directly on the front part of downstream cylinder; thus, pressure patterns with two peaks of positive pressure result. The values of pressure between two peaks are equal to the values of back pressure, Cpb, of the upstream cylinder. (c) When the spacing ratio increases further from 2.0 to 2.5, the downstream cylinder is now located at the rear of the wake cavity, the pressure pattern with fiat distribution on the front part of downstream cylinder appears again; nevertheless, its area is contracted a great deal compared with those of pattern (a).

The second regime begins when the spacing ratio is equal to or greater than 2.8. Shear layers separated from the upstream cylinder are no longer acting directly on the downstream cylinder. In other words, the downstream cylinder is affected only by the

180 Z. Gu/J . Wind Eng. Ind. Aerodyn. 62 (1996) 175 -190

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z Gu/.Z WindEng. Ind. Aerodyn. 62 (1996) 175-190 181

wake effect. The main effects of this regime, corresponding to the downstream cylinder, may be described by the greatly reduced time-averaged velocity and significant high turbulence intensity in oncoming flow. These effects are reduced monotonically as the spacing gets larger. The pressure pattern on the downstream cylinder, if it is normalized by the front actual dynamic pressure head of cylinder B, would be very similar to those obtained in the case of high-turbulence flow. This pressure pattern is denoted as pattern (d).

On the other hand, the effect of the downstream cylinder on the upstream cylinder is relatively smaller. No evident boundary between two different regimes can be found. However, when the first two pressure types (pattern (a) and (b)) prevailed, the pressure distribut:ions, the same as those on the downstream cylinder, are asymmetrical. There are pronounced differences in the values of Cpmin and Cpb between the two sides. In the second regime of only the wake effect, the symmetry of pressure distributions on both sides of the cylinders is quite good. In the meantime, the characteristics of the effect are evident zLnd regular, i.e., both values of Cpmjn and Cpb reduce monotonically from a large spacing ratio up to N/d = 1.7.

In view of the sudden changes in pressure distributions, the critical spacing no longer exists at supercritical Reynolds number. However, the term "transition spacing" was used to express the boundary of these two different regimes, the value of which would be between 2.5 and 2.8. It also can be referred to as the length of wake cavity behind a circular cylinder or its equivalent in supercritical flow.

Except for the characteristics of drag forces of two tandem cylinders which remain nearly constant regardless of the different spacing, another significant difference with the case of subcritical Reynolds number is that the values of the drag force on the upstream cylinder are always lower than that of downstream cylinders. As a result the base pressure Cpb of the upstream cylinder is reduced due to the blockage effect of the downstream cylinder.

A schematic classification of the flow regimes in tandem arrangement at supercritical Reynolds number, which is something like those shown by Zdravkovich [11] at subcritic~.l Reynolds number, is shown in Fig. 5.

3.3. Two circular cylinders in side-by-side arrangement (fl = 90 °)

It is nol:ed that if the wake region of a single circular cylinder is much narrower than in the case of subcritical Reynolds number, it is expected that the effective region of interference of two circular cylinders in side-by-side arrangement should be contracted in the supercritical case. The detailed information about the flow past two cylinders in side-by-side arrangement at various gap ratios, such as formation of laminar separation bubbles on both or only one side of individual cylinder combined with the :results of pressure distributions were reported and discussed by Okajima et al. [6]. There is good agreement between the present results and those presented in [6]. Pressure patterns together with their classifications are presented and discussed in greater detail here.

Fig. 6 shows selected cases of pressure distributions on both cylinders (N/d = 1.1, 1.2, 1.5, 1.7, 2.0 and 3.5) in side-by-side arrangement.

182 Z. Gu/J. Wind Eng. Ind. Aerodyn. 62 (1996) 175-190

(a) ~ N/d=l. I

(b) ~ ~ _ ~ N/d =1.2-1-7

(e) ~ N/d=2.0-2.5

a b c d

1 2 .1 3 4 N/d /

I: wake cavity interfere~eel II: wake offect

Fig. 5. Classification of flow regimes of two cylinders in tandem at supercritical Reynolds number (Re = 4.52 x 105).

Two different effect regimes, one for shear layers interaction and the other for wake influence or effects of the neighborhood, may be classified. Three different pressure patterns on cylinders which correspond with these two regimes are presented and discussed as follows.

As for the regime of interaction of shear layers, two pressure patterns may be subdivided. (a) For very small gap ratio (1.1-1.2), some strange pressure distributions on both cylinders result due to the asymmetric gap flow. It is reasonable that the positive area on the windward side of both cylinders becomes significantly wide and the stagnation points, 0m, move towards inner-sides more than 20 °. However, the minimum pressures Cpmin and base pressure Cvb of the two cylinders are significantly different. The pressure on certain areas at the backside of cylinder B increases even up to nearly zero. This phenomenon, something like the Coanda effect, also had been observed in other experiments of two circular cylinders at the same spacing at subcritical Reynolds number (Re = 2.2 x 105). It presents a striking contrast with that of cylinder A, its base pressure Cpb remains at the value of -- 0.5. A similar phenomenon also may be found in [6] (Re = 4.5 x 105, N/d = 1.25). Some repeated tests were made to confirm the result and no biased flow was found, although two different types of pressure distributions did occur at N/d = 1.2 and fl = 86 °, which will be presented later. It is noticed that the surface roughness of cylinder A differs slightly from those of cylinder B, the latter is more rough. It could have influence on the results. Anyway, it should be noted that the asymmetric wake was produced when the cylinders were sufficiently close regardless of being either in tandem or in side-by-side arrangement. (b) At N/d = 1.5, the symmetry of pressure distributions on the two cylinders about the axis of the central line between cylinders is quite good. The maximum pressure

Z Gu/J. WindEng. Ind. Aerodyn. 62 (1996) 175-190 183

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points 0 m move to 0 = _+ 15 °, respectively. Pressure patterns of turbulent separations are present on both sides of the cylinder. Values of minimum pressure Cpmin are significantly decreased on the inner sides whereas they are greatly increased and reach values of - 3 . 5 on the outer sides. This suggests that the gap flow is somewhat blocked, whereas the flow around the outer sides of cylinders is accelerated. As reported by Okajima et al. [6], separation bubbles are formed only on the outer sides of the two cylinders. The separation points on the outer sides further shift leeward up to 135 ° . Thus the great lift forces, which pull cylinders away, result. It may be expressed that the wake cavity is formed behind each cylinder, but they are squeezed close to each other. Nevertheless, the shear layers, acting as the boundary of wake cavity, do not interact with each other significantly. Thus, symmetric pressure distributions with respect to the central line about the two cylinders result.

The second regime begins as the spacing increases further, say N/d-- 1.7, the pressure distributions (denoted as pattern (c)) on both cylinders, in general, are similar to those of the single one. It means that only the effect of neighbourhood or wake influence exists. The effect of neighborhood is characterized by the shift 0m and increasing values of Cpmin and Cpb. These effects are relatively smaller. Values of Cpmin on both sides of the cylinders are almost the same and larger than those of the single cylinder (e.g. Cpmln ---- -- 3 at N/d = 1.7). This suggests that the flow both in the gap and around the outer sides of the two cylinders is accelerated for two circular cylinders in side-by-side arrangement at certain spacing.

Similar to the case of two cylinders in tandem, the value of "transition spacing", which identifies the regimes of shear layers interaction and effect of neighbourhood, is between N/d = 1.5 and 1.7. In the first regime, the gap flow is skewed or blocked. It is in striking constrast with the second regime, where the flow in the gap is accelerated. Schematic classifications of flow regimes are shown in Fig. 7.

shear layers interaction wake influence or effect of neighborhood

N/d=l. 1~1.2 N/d=l.5 N/d>l.7

(a) asymmelric wake 0a) squeezed wake cavity (c) effect of neighborhood

Fig. 7. Classification of flow regimes on two cylinders in side-by-side arrangement at supercritical Reynolds number (Re = 4.52 x 105).

Z. GulJ. Wind Eng. Ind. Aerodyn. 62 (1996) 175-190 185

3.4. Two circular cylinders in staggered arrangement (0 ° < fl < 90 °)

Based on the results of two cylinders in tandem and in side-by-side arrangements discussed above, it is expected that for two circular cylinders in staggered arrangement for small[ spacing, e.g. NId = 1.2, interference of wake cavities or shear layers or their combination are significant, whereas for larger spacing, e.g. Nld = 1.7, only interference of wake cavities at small angle of stagger and the effect of neighbourhood, which is relatively weaker compared with the former one, need to be considered.

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Fig. 8. The pressure distributions C v as a function of 0 for different fl's, on cylinders A (upstream) and B (downstream) for Re = 4.52 x 10 s, N/d = 1.2 and N/d = 1.7.


Measurements of pressure distributions on two cylinders at seven different spacing ratios (N/d = 1.2, 1.5, 1.7, 2.0, 2.2, 3.0 and 3.5) in staggered arrangement were carried out during the experiments. As typical cases, results of pressure distributions as a function of O, for only two spacing ratios, i.e., N/d = 1.2 and 1.7 are presented and discussed here. Fig. 8 shows the pressure distribution with various angles of staggering on two cylinders at N/d = 1.2. For cylinder B at fl = 5 °, Cp as a function of 0 has only one peak at 0m - 30 °. The Cv values on the inner side (0 ° < fl < - 60 °) are uniformly constant, whereas the pressure pattern on the outer side keeps the turbulent separation with the minimum pressure Cpmln = - 2.0. When the angle of stagger fl increases, the area of suction on the inner side of cylinder B increases and 0m moves back to its original stagnation point gradually. Finally, 0m moves back to the original stagnation point when fl = 45 °. 0m continues to move inside up to 25 ° for two cylinders in side-by-side arrangement. On the other hand, the interference on the inner-side of cylinder A is also increased remarkably. No abrupt changes or discontinuity of pressure distributions on cylinder B, as those at subcritical Reynolds number [1, 4], were observed in the region of small angle of attack (say, fl = 10° -15° ) .

When 3 = 86°, to the author's great surprise, two completely different pressure distributions on both cylinders were obtained (see Fig. 9). Both sudden changes in drag and lift forces on cylinders result (see Fig. 10). Some runs were repeated to confirm the results. However, it is not observed for other slightly larger spacing ratios, e.g. N/d = 1.5. The mechanism of occurrence of this special switching process is not clear yet.

When the spacing ratio increases to N/d = 1.7 (Fig. 8), the effects on cylinder B are reduced greatly compared with those at N/d = 1.2. The significant changes in pressure distributions can be found only at fl < 45 °. On the other hand, only small effects on cylinder A can be found except for the values of Cvml, and Cpb. The values of Cvml, on both sides of a cylinder increase from - 1.8 (at fl = 0 °) to - 2.9 (fl = 90°); meanwhile,

1

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Z Gu/J. WindEng. Ind. Aerodyn. 62 (1996) 175-190 187

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Re=4.5xlO s ¢yI.B

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0 30 60 90 #

Fig. 10. Drag and lift force coefficients Co and C L o n both cylinders of different N/d varied with the angle of staggering/L

Cpb increases from almost zero to - 0.45. Or, moves slightly towards the inner side when fl > 30 °.

Fig. 10 shows the drag and lift force coefficients CD and CL on both cylinders varied with the angle of stagger fl with different gap ratios, which were obtained by means of integration of the circumferential pressure on both cylinders. It is evident that the significant effect of interference is only restricted to small spacing, i.e., N/d = 1.2 and 1.5, especially the great changes in lift forces on both cylinders. For larger spacing, the regular ,effect becomes clear when fl is larger than 20 °. The effects of drag force coefficients on cylinder A are most pronounced in these four cases.

In order to provide more information of interference, the drag and lift forces acting on both cylinders in the form of surface drawing are given in Fig. 11. For convenience, two parameters T/d and L/d are used to show the relative position of the two cylinders instead of N/d and fl (T/d = N/dsinfl, L/d = N/dcosfl). In general, the significant effects are limited to the rather small spacing ratios except in tandem arrangement and


Cy~, A Dra@ Cyl, B One@

c , , . a [_~,~

t-,

Fig. 11. Surface drawing of drag and lift forces acting on cylinders for Re = 4.52 x 105.

its vicinity. Due to the effect of cylinder B, the base pressure of cylinder A is remarkably reduced. Thus, in most regions the drag forces on cylinder A are reduced, especially in tandem arrangement and its vicinity. However, in the region of small spacing ratio for staggered and side-by-side arrangement, the base pressures of cylinder A are increased a great deal because of the effect of blockage caused by interference of shear layers. As for cylinder B, the drag forces are greatly reduced within the area of stagger angle fl less than 45 ° and increased when fl is larger than 45 °. On these occasions, the result is due to both contributions: base pressure increase and positive pressure area extension on the upstream surface of cylinder B. It is in sharp contrast with the case of subcritical Reynolds number [3], in which the drag forces on cylinder B are always reduced. On the other hand, a repulsive force results due to accelerated flow around the outside of cylinder A. The same does happen on cylinder B in the area of fl larger than 45 °. When fl is less than 45 ° or so, attractive forces result (positive lift force on cylinder A and negative force on cylinder B) due to the effect of


blockage and the asymmetric gap flow, caused by the dominant effect of wake interference.

4. Conclusions

The results of interference of two identical cylinders in various arrangements at supercritical Reynolds number (Re -- 4.52 x 105) by means of wind-tunnel testing, are presented and discussed. More attention has been paid to the classification of flow regimes as well as the pressure patterns. The following conclusions were obtained.

In tandem arrangement, the drag forces on the downstream cylinder are greater than those on the upstream cylinder. The influence of spacing is reduced greatly compared to the subcritical case. In general, two different regimes, wake cavity interference and wake effect, and four pressure patterns on the downstream cylinder may be: classified. The values of transition spacing, which is referred to as the boundary of two regimes or the length of wake cavity behind the cylinder, may be between 2.5 and 2.8.

For two circular cylinders in side-by-side arrangement, two different regimes, shear layers interaction and effect of neighborhood or wake influence, and three types of pressure distributions also may be identified. The value of transition spacing, which indicates gap flow is skewed and blocked or accelerated, is between 1.5 and 1.7. No biased flow can be found like those at subcritical Reynolds number, although at very small gap ratio the pressure on the two cylinders does show some special features of asymmetry.

As for two circular cylinders in the staggered arrangement, the sudden changes in pressure.' or the discontinuity on downstream cylinder at small angle of stagger no longer existed. Nevertheless, in the case of N/d = 1.2 and fl = 86 °, special sudden changes in pressure distributions on both cylinders were observed. Both the effect of wake and interference of shear layers should be considered in the case of small spacing. The attractive or repulsive force results depend on which kind of effect is dominant due to the relative position of the two cylinders.

In general, due to the different characteristics of flow around the circular cylinder at supercritical Reynolds number compared with those at the subcritical one, such as the wake narrowing, no strong regular shedding and formation of relative stable wake structure, the effects of interference between two circular cylinders of various arrangements are completely different. The interference area is greatly reduced and the effect ofinterfi~rence may be ignored in most arrangements when spacing ratios are equal to or larger than N/d = 1.7, except for two cylinders in tandem arrangement and their vicinity.

Acknowledgements

The work described in this paper was supported by the National Natural Science Foundation of China. The author is very grateful to Professor T.F. Sun and Professor

190 z. Gu/J. Wind Eng. Ind. Aerodyn. 62 (1996) 175-190

R.S. Lin for their valuable advice and to other colleagues of Peking Univers i ty for their help dur ing the wind- tunne l testing. Special thanks to Professor Bruce R. Whi te for his great help dur ing the author ' s stay in U C Davis while prepar ing the paper.

References

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On interference between two circular cylinders at supercritical Reynolds number