Proceedings of OMAE25 24 th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 25) June 2-6, 25, Halkidiki, Greece OMAE25-672 EXPERIMENTAL INVESTIGATION OF FLOW-INDUCED VIBRATIONS INTERFERENCE BETWEEN TWO CIRCULAR CYLINDERS IN TANDEM ARRANGEMENTS Gustavo R. S. Ássi Peter W. Bearman Imperial College - London Aeronautics Dept., United Kingdon Julio R. Meneghini Bruno S. Carmo University of São Paulo Dept. of Mechanical Engineering José A. P. Aranha Enrique Casaprima Petrobras CENPES, Rio de Janeiro,. ABSTRACT This paper presents experimental results concerning flow-induced oscillations of rigid-circular cylinders in tandem. Preliminary results are presented: new measurements on the dynamic response oscillations of an isolated cylinder and flow interference of two cylinders in tandem are shown. The oscillations are due to vortexinduced vibrations (VIV) Models are mounted on an elastic base fitted with flexor blades and instrumented with strain gages. The base is fixed on the test section of a water channel facility. The flexor blades possess a low damping characteristic [ζ.8 and less] and they are free to oscillate only in the cross-flow direction. The Reynolds number of the experiments is from 3, to 3, and reduced velocities, based on natural frequency in still water, range up to 2. The interference phenomenon on flow-induced vibrations can be investigated by conducting experiments in two ways: first, the upstream cylinder is maintained fixed and the downstream one is mounted on the elastic base; subsequently, an investigation will be carried out letting both cylinders oscillate transversally. The results for an isolated cylinder are in accordance with other measurements in the literature for m* 2 and m* 8. For the tandem arrangement (m* 2), the trailing cylinder oscillation presents what previous researchers have termed interference galloping behaviour for a centreto-centre gap spacing ranging from 3 D to 5 6D. These initial results validate the experimental set up and lead the way for future work; including tandem, staggered and side-by-side arrangements with the two cylinders free to move. Keywords: vortex-induced vibration; flow interference; bluff body flow; experimental analysis. INTRODUCTION Flow interference among groups of cylinders has been the subject of many studies in the past. The interference is responsible for several changes in the characteristics of fluid loads when more than one body is placed in a fluid stream. Investigations of the flow around pairs of cylinders can provide a better understanding of the vortex dynamics, pressure distribution and fluid forces, in cases involving more complex arrangements. This paper presents an experimental study of the flow interference between a pair of rigid cylinders, in tandem configurations, with the rear cylinder elastically mounted and free to oscillate transversely to the flow. In addition, it presents new measurements for an isolated rigid cylinder. In all cases the cylinders are allowed to oscillate only in the transverse direction. The main practical application of this investigation is to have a better understanding of the flow interference around a bundle of risers which link the seabed to the offshore platforms used for oil exploration. Most of s floating platforms are installed along the continental shelf of the Atlantic Ocean where water depths over m are common. New discoveries in the ian continental shelf are pushing the need for oil production beyond 2m depths. In such conditions, a better understanding of the dynamic responses causing vibration of risers is essential. Dynamic response of an isolated cylinder has been carefully studied through the past years. Detailed Copyright 25 by ASME
information and accurate data are found in many reviews: Bearman (984); Blevins (99); Khalak & Williamson (996, 999) among others. The phenomenon has also been intensely analysed by numerical methods, as seen in Meneghini & Bearman (995), for instance. Nowadays, new studies are focusing on understanding vortexsuppressor methods, as presented by Bearman & Brankovic (24) and Owen et al. (2). Zdravkovich (977, 987) has also reviewed the problem of flow interference when two cylinders are placed in side-by-side, tandem and staggered arrangements in a steady current. Quoting his words, he observed that when more than one bluff body is placed in a fluid flow, the resulting forces and vortex shedding pattern may be completely different from those found on a single body at the same Reynolds number. A variety of flow patterns, characterized by the behaviour of the wake region, may be discerned as the centre-to-centre spacing between two circular cylinders (gap S) is varied. Some results about flow interference between a pair of cylinders in tandem can be found in the investigations by Bokaian & Geoola (984); King & Johns (996); Brika & Laneville (997, 999) and Hover & Triantafyllou (2). All these papers present experimental results of a trailing rigid cylinder oscillating in the wake of an upstream one. According to Bokaian & Geoola (984), in the case of a fixed leading cylinder, both vortex-resonance and wake galloping instability phenomena are relevant and can occur separately or combined, depending on the separation distance. Brika & Laneville (999) concluded that vortex-resonance occurs alone for S/D>3. For high Reynolds numbers, galloping predominates for S/D<7, while vortex-induced vibrations are recovered for large S/D. S and data processing for future investigations. In addition, they introduce the base results for comparisons with induced oscillations of a trailing rigid cylinder in a tandem arrangement. A brief description of the apparatus and some remarks regarding future investigations complements the material. EXPERIMENTAL SET-UP Tests were conducted at the Hydrodynamics Laboratory of Imperial College, London. The circulating water channel facility had a ( 6 x 7 x 8 )m test section and could operate at good quality and well controlled flows up to 6m/s. Rigid cylinder models were made of aluminium tubes with diameter D=32mm and wet-length L=56mm under the water level. Cylinders were vertically clamped by their upper end at the bottom block of elastic supports (firmly fixed on the channel structure) and terminated at their lower end with a 2 mm gap on to the test section floor. The open section channel facility was equipped with glass walls and a glass floor offering a complete view of the models. For tandem arrangements (no bundle inclination for all cases, staggered angle β=º) the gap between the cylinder centres varied through four different discrete displacements: G/D= (3.; 4 ; 5 ; 5 6). Figure 2 presents a schematic cross view of the apparatus mounted on the channel structure. U D Figure. Configuration for the tandem arrangement. According to Zdravkovich, three possible regimes are found with two circular cylinders in tandem. The first is observed when S/D< 2~ 8 (depending on the Reynolds number). In this case, the downstream cylinder is within the recirculating flow from the upstream cylinder, producing only one wake due to the separating shear layers from the upstream cylinder. In the second regime, observed for 2~ 8<S/D<3 4~3 8, a recirculation bubble is formed between the cylinders and there is reattachment of the shear layers emanating from the first cylinder to the wall of the second one. The wake is formed behind the downstream body due to separation occurring on its surface. Finally, in the third regime, for gaps S/D>4, vortex shedding begins from both cylinders. This paper presents new measurements of vortexinduced vibration on a single cylinder. The experiments are carried out in order to validate the experimental set up Figure 2. Cylinder and elastic base mounted on the channel test section structure. Both cylinders were independently mounted under an individual elastic base free to oscillate transversely to the flow direction, i.e., only in the cross-flow direction. For each flexible base system, the transverse degree of freedom could be locked, so every model could or could not be free to move in cross-flow oscillations, resulting in different tandem oscillating configurations. Both elastic systems were built with two parallel rigid aluminium blocks, coupled by a pair of thin spring-steel blade flexors. These not only acting as the cylinder support, but also providing the restoration system response. This flexion-based arrangement was confirmed as a low-damping elastic system. In order to measure cylinder displacements, four strain gages were built in each pair of 2 Copyright 25 by ASME
blades close to the highest bending region of the face. A complete bridge was built up providing a cylinder displacement linear signal to be acquired. A set of three base systems were available for isolated cylinder experiments, while another two systems were prepared for tandem arrangement tests. The different bases providing different mass ratios. Mass ratio and spring stiffness were the structural parameters that were varied. Table lists the oscillation parameters obtained for all those configurations. Decay tests in water were employed to obtain the natural oscillation frequency (f N ), while the structural damping parameter (ζ) were obtained from decay test performed in air. Mass ratio (m*) is defined as 2 m* = 4M ρπd L (where M represents the total mass considered in oscillations and ρ is the water density). The added mass is not considered in the mass ratio definition. Figure 3 details the elastic base and its spring blades. (cross-flow direction is identified by y axis) and Figure 4 shows the experimental apparatus installed in the channel test section. Table. Oscillation parameters for all the various bases. Base identification m* f N (Hz) ζ (m* ζ) Single (low mass) 96 56 8 8 Single (median mass) 92 98 7 3 Single (high mass) 8 6 7 2 6 Pair: Downstream 92 98 7 3 RESULTS The dynamic responses of the models are described in terms of reduced amplitude versus reduced velocity. Some classical literature results are shown for comparison. Amplitude peaks were calculated employing the Hilbert transform, as described in Khalak & Williamson (999). Reynolds number (calculated for a single cylinder with diameter D and current velocity U ranges from Re=3 and Re=3 in all experiment cases. The reduced velocity Vr = U ( f N D) range extended to a maximum value of 2, hence covering the occurrence of several possible phenomena. Single cylinder The responses for an isolated cylinder, with three different mass and damping parameters, are shown in Figure 5, Figure 6, and Figure 7. These three figures compare the present data to significant literature results for the three different conditions mentioned before: low mass, median mass and high mass. They are employed as a baseline for comparisons with the tandem arrangement cases. This following series presents the dynamic response of a single cylinder, free to oscillate in the cross-flow direction, mounted on a low damping elastic system. In Figure 5, the non-dimensional amplitude of oscillation is presented versus the reduced velocity for m*. The current speed was increased in order to obtain this curve. Our maximum amplitude is slightly below D and it occurs at a reduced velocity V 6. Results compare r relatively well with Brankovic (24), in which the reduced velocity range was extended up to 4. Figure 3. Detail of the elastic base at a flexing instant. W.L. represents the water line level and δ the horizontal displacement of the cylinder centre. m* = 2 Brankovic (24) m* =.96 Present work 2 4 6 8 2 4 Figure 4. Picture of an instrumented base and isolated cylinder mounted on the channel test section. The strain gages are positioned on the inside face of the blades. Figure 5. Variation of the reduced amplitude versus reduced velocity for an isolated cylinder with the low mass ratio parameter. Present work:, m*= 96, (m* ζ)= 3; Brankovic (24), m*= 82, (m* ζ). 3 Copyright 25 by ASME
m* = 2.4 Khalak-Williamson (999) m* = 3. Hover-Triantafyllou (2) m* =.9 Present work sustained up to Vr =2.. The peak amplitude in the present investigation is around.9d. Finally, in Figure 7, the results for m* 8 are shown and compared to those by Khalak and Williamson (999), and Fujarra (22). The oscillation starts at about Vr = 3.5 and the peak amplitude observed in the present results is around D. 2 4 6 8 2 4 Figure 6. Variation of the reduced amplitude versus reduced velocity for an isolated cylinder with the median mass ratio parameter. Present work:, m* 2, (m* ζ)= 3; Khalak and Williamson (999), m* 2, (m* ζ)= 4; Hover and Triantafyllou (2), m* 3. m* =.3 Khalak-Williamson (999) m* =. Fujarra (22) m* = 8. Present work Tandem arrangement Figure 8 presents the dynamic results for flow interaction of a trailing rigid cylinder oscillating in the wake of a fixed leading one. The rear model is only free to move in the cross-flow direction. For this case m* 2, and m* ζ= 3. The results are compared with those obtained by Hover and Triantafyllou (2) with a cylinder with a slightly higher mass parameter. The distance S/D is measured centre to centre. The results shown in Figure 8 are for four gaps: S/D = 3., 4., 5. and 5.6. For each gap the response is entirely expressed by a single curve without an upper and lower branch typical of an oscillating single cylinder. This continuous increase in the response with increasing reduced velocity is typically found in galloping like oscillations. To verify this galloping behaviour, higher reduced velocities tests are planned. The oscillation starts at about Vr = 2.5 and grows continuously..6.4.2 2 4 6 8 2 4 Figure 7. Variation of the reduced amplitude versus reduced velocity for an isolated cylinder with the highest mass ratio parameter. Present work:, m* 8, (m* ζ)= 6; Khalak and Williamson (999), m*, (m* ζ)= 7; Fujarra (22), m*, (m* ζ)= 3. For this low mass parameter case, one can notice that oscillation starts at about Vr = 2.5 and is sustained up to very high reduced velocity. Such behaviour is expected for very low mass parameter experiments and has already been observed by other investigations. For the low mass parameter model in the present experiment, the maximum reduced velocity tested could not be increased beyond Vr = 7 due to the low stiffness of the flexor blades. Figure 6 shows the response for m* 2. In this case, we compare our results with those by Khalak and Williamson (999), and Hover and Triantafyllou (2). Although the experimental apparatus used were based on different concepts, the mass and damping parameters are very similar and the observed responses are in close agreement. The oscillations start at about Vr = 3. and are S/D=4.75 Hover-Triantafyllou (2): m*=3. S/D=3. Present work: m*=.9 4. 5. 5.6 2 4 6 8 2 4 6 Figure 8. Variation of the reduced amplitude versus reduced velocity for the trailing cylinder of a pair in tandem arrangement. Present work:, m* 2, (m* ζ)= 3; Hover and Triantafyllou (2),, m* 3. The peak amplitude in our experiment is about.4d, which is 5% higher than the maximum amplitude observed for the isolated cylinder case. This peak occurred for the maximum reduced velocity that could be reached by the water channel, i.e. Vr = 2. This peak amplitude of the downstream cylinder is observed for a gap S/D=3. It is interesting to note that this increase in amplitude is not observed in interference experiments carried out in air at a higher mass ratio, as reported by Brika and Laneville (999). Although they observed a 4 Copyright 25 by ASME
continuous response curve, the amplitude reached a maximum similar to the case of an isolated cylinder. As one can see in Figure 8, the response of the downstream cylinder at = 2 decreases slowly with increasing value of the gap spacing. For S/D =5.6, the largest gap spacing tested, the influence of the upstream cylinder is still pronounced. CONCLUSION The results for an isolated cylinder were found to be in accordance with other reported measurements for m*, m* 2 and m* 8. Consequently, the results are satisfactory to validate the experimental set up. The decay tests performed in air verified the low damping behaviour of the base. For the tandem configuration (m* 2), one can notice a predominance of the galloping phenomenon for the gap range 3 <S/D<5 6, since the amplitude curve does not show a peak response, and increases continuously with increasing reduced velocity. Higher reduced velocity experiments are planned to be carried out to confirm such behaviour. The peak amplitude observed for the downstream cylinder was about 5% higher than the one observed for the isolated cylinder case. The experiments shown in this paper are still preliminary and are part of an ongoing research project. Future investigations will include tandem, staggered and side by side arrangements with the two cylinders free to move. ACKNOWLEDGMENTS The authors gratefully acknowledge the support by FINEP/CTPetro, FAPESP, and Petrobras, providing a research grant for this investigation. The first author is also grateful to FAPESP for his MSc research grant. Especial thanks are due to Masa Brankovic, from Imperial College, London (where the experiments were conducted), for her valuable help. The comments and suggestions made by Dr. A. Fujarra and Prof. Celso P. Pesce were greatly appreciated. REFERENCES BEARMAN, P.W. (984) Vortex shedding from oscillating bluff bodies; Annu. Rev. Fluid Mech.; 6, 95 222. BEARMAN, P.W., BRANKOVIC, M. (24) Experimental studies of passive control of vortex-induced vibration; Europ. J. Mech. B: Fluids, 23, 9-5. BLEVINS, R.D. (99) Flow-induced Vibrations; New York: Van Nostrand Reinhold. BOKAIAN, A., GEOOLA, F. (984) Wake-Induced Galloping of Two Interfering Circular Cylinders; J. Fluid Mech.; 46, 383-45. BRANKOVIC, M. (24) Vortex-Induced Vibration Attenuation of Circular Cylinders with Low Mass and Damping; PhD Thesis, Imperial College University of London, 9 pages. BRIKA, D., Laneville, A. (997) Wake Interference Between Two Circular Cylinders; J. Wind Eng. & Ind. Aerod.; 72, 6-7. BRIKA, D., Laneville, A. (999) The flow interaction between a stationary cylinder and a downstream flexible cantilever; J. Fluids Structures; 3, 579-66. FUJARRA, A.L.C (22) Estudos experimentais e analíticos das vibrações induzidas pela emissão de vórtices em cilindros flexíveis e rígidos; PhD Thesis, Univ. of São Paulo,. HOVER, F.S., TRIANTAFYLLOU, M.S. (2) Galloping response of a cylinder with upstream wake interference; J. Fluids Structures; 5, 53-52. KHALAK, A., WILLIAMSON, C.H.K. (996) Dynamics of a hydroelastic structure with very low mass and damping. J. Fluids Structures;, 973-982. KHALAK, A., WILLIAMSON, C.H.K. (999) Motions, Forces and mode transitions in vortex-induced vibrations at low massdamping; J Fluids Structures; 3, 83-85. MENEGHINI, J.R., BEARMAN, P.W. (995) Numerical simulations of a high amplitude oscillatory flow about a circular cylinder; J. Fluids Structures; 9, 435-455. OWEN, J.C., BEARMAN, P.W., SZEWCZYK, A.A. (2) Passive Control of VIV with Drag Reduction; J. Fluids Structures; 5, 597 65. ZDRAVKOVICH, M.M. (977) Review of flow interference between two cylinders in various arrangements; ASME J. Fluids Eng.; 99, 68-633. ZDRAVKOVICH, M.M. (987) The effects of interference between circular cylinders in cross flow; J. Fluids Structures;, 239-26. 5 Copyright 25 by ASME