Effect on vortex induced vibrations from radial water jets along a circular cylinder

Transcription

1 Effect on vortex induced vibrations from radial water jets along a circular cylinder K. B. Skaugset and C. M. Larsen Department of Marine Structures Norwegian University of Science and Technology, NTNU, Trondheim, Norway Abstract Most of the latest years' research on vortex induced vibrations (VIV) of circular cylinders in water has been motivated by the offshore industry's need for reliable predictions of the behaviour of deepwater risers and free span pipelines subjected to ocean current. An obvious approach to solve VIV problems is to introduce suppression devices such as helical strakes or fearings. Such devices may influence the vortex shedding process in two ways: 1) 2-dimensional (2-D) effects will influence the local forces on the cross section and damping by altering the separation point as well as creating a general disturbance to the flow. 2) 3-D effects include changes in correlation of the vortex shedding process along the span of the cylinder. It is well known that vortex shedding on a long cylinder will lead to significant vibration amplitudes only if the shedding process along the cylinder is correlated, and that the vibration itself will control this correlation. There is hence a positive feedback from oscillation amplitudes to correlation that under ideal conditions will amplify the oscillation amplitude until a maximum value slightly above one cylinder diameter is reached. The present paper presents a novel approach for VIV suppression based on radial water jets from a prescribed pattern of circular openings in the cylinder wall. This flow will introduce a disturbance that is expected to yield reduced VIV amplitudes. Results will be presented from experiments in a towing tank testing a spring-supported cylinder with a helical pattern of radial water jets. The volume flow rate and reduced velocity have been varied in the tests. Oscillation amplitudes, frequencies, added mass and lift and drag force coefficients are presented and compared to results with a cylinder without any water blowing.

2 156 Fluid Structure Interaction Introduction Vortex-induced vibrations (WV) can cause large amplitude oscillations of many structures of practical interest. Bridges and chimneys as well as oil-canying pipelines and risers are reported to experience VIV. Indeed SPAR buoys, which have a cylindrical shape and large draft, might also experience this problem. A wide range of structures subjected to this phenomenon, and the practical significance related to VIV are discussed in depth by Sarpkaya [l], Griffin & Ramberg [2], Bearman [3], Parkinson [4], and also in text books by Blevins [5], Zdravkowich [6], Naudascher & Rockwell [7] and Sumer & Fredsere [8]. VIV suppression is in many cases needed to reduce fatigue damage rates and prolong operational life of structures subjected to this phenomenon. Blevins [5] divides the suppression options into four categories: 1. Increase damping, 2. Avoid resonance, 3. Streamline cross section and finally; 4. Add a vortex suppression device. In the last category there have been many suggestions over the years. One of the most used by the offshore industry is the helical strakes invented by C. Scruton and D.E. Walshe (Patent 3,076,533m Feb.5, 1963). Perforated shrouds (see Wong [9]), splitter plate (see Sallet [IO]), and other means of VIV suppression have also provided good efficiency. Common disadvantages for suppression devices are handling problems during installation and increased drag forces under non-vibrating conditions. Hence novel concepts for VIV reduction that can solve these problems are needed. As early as 1904 L. Prandtl (see Schlichting [l l]) published his first paper where the flow field around a circular cylinder was modified, and drag force reduced by suction and blowing of water through openings in the cylinder surface. Not only circular cylinders have been subjected to fluid flow modification by suction and blowing. Wood [l21 & [l31 and Bearman [l41 achieved substantial wake modification by the concept of base bleed, steadily injecting fluid fiom the base of a two-dimensional body with a blunt trailing edge. Park & Cimbala [l51 investigated the downstream wake of a twodimensional airfoil in water similar to the ones mentioned above. The aim was to achieve a momentumless wake, and to investigate the downstream evolution of the mean velocity profile and turbulence characteristics. In recent years the interest of VIV suppression and drag force reduction by means of blowing or suction of water has earned an increasing interest. The low Reynolds -number experiments by D.R. Willaims & C.W. Amato [16], used a pulsating jet system in order to decrease the momentum defect of the wake of a cylinder, and thus reduce the drag of the structure. Other low Reynolds -number experiments by Willaims, Mansy, & Amato [l71 showed that the vortex shedding frequency and structure can change by introducing local disturbances generated by an unsteady bleed system. J.C. Lin, 5. Towfighi and D. Rockwell [l81 investigated the wake of a cylinder, containing small jets, in a helical pattern, by particle image velocimetry. They showed that as blowing is applied, the pattern of vorticity undergoes significant distortion.

3 Fluid Structure Interaction 157 N.A. Brown and V.G. Grinius [l91 demonstrated a tremendous decrease in vortex-induced lift force for reduced velocity U~5.86 using a pair of slot-nozzles with tangential directed mouths located 180" apart. A.C. Fernandes eta1 [20] found that by using a 90" duct with nozzles, blowing in the longitudinal direction driven by the pressure difference on the low and high-pressure side of the cylinder, a 30% reduction in oscillation amplitude was achieved. When using more than one duct firther reduction in amplitude was found. In the present investigation we intend to reduce the oscillation amplitudes by modifying the flow (2-D effect), and also reduce the correlation build-up along the cylinder (3D-effect), by introducing steady radial water jets along the cylinder. The openings are found in a helical pattern along the circumference and cylinder axis. Basic concept Vortex shedding from a f ~ed circular cylinder is in general a local phenomenon with a correlation length along the cylinder of the order of one to four cylinder diameters depending on the ~e~nolds number. However if the vortex shedding and hence the local hydrodynamic forces becomes correlated along the span of the cylinder, the local forces act in phase with each other resulting in a considerable total force resultant in the crossflow direction. The lock-in phenomenon means that the cylinder motions will control the vortex shedding process. The oscillation fiequency will appear as a compromise between the vortex shedding fiequency for the fixed cylinder and the eigenfiequency for the cylinder in still water. The fiequency will change for varying flow velocity within the lock-in regime, but the oscillation will still take place at the eigenfrequency since added mass will vary and thereby tune the eigenfrequency. A good overview of different experimental and numerical findings for these oscillations with respect to amplitude and frequency is found in A. Khalak & C.H.K. Williamson [2 l]. The purpose of the present investigation is to demonstrate the effect on VIV from radial water jets from the cylinder surface. It is expected that the jet flow will have an Influence on the 2-D vortex shedding process, but also that the arrangement of the jets along the cylinder will give rise to a 3-D effect that will reduce the correlation length. Attempts will be made to break down the VIV oscillation amplitude reduction into 2-D and 3-D effects as previously mentioned. However, the tests reported herein is the first part of a lager program where other jet arrangements will be investigated. Experimental set-up The experiments were conducted in the smallest towing tank at NTNU's facility in Trondheim, Norway. Dimensions of the towing tank are (L,xB,xD,) 25x2.5x1.2 meter. A schematic view of the experimental set-up is shown in Fig. l.

4 158 Fluid Structure Interaction Spring, k, j I + B Flow meter I Electric pump Rails / 4 Cylinder displacement, X The apparatus supports a circular cylinder with a diameter, D, of 10cm. The cylinder ;s horizontiily oriented in thk water. In order to eliminate end-effects, endplates of diameter 0.5m (5 D) are fitted at each end of the cylinder. The cylinder is connected to a freely supported tubular aluminum bar frame, which allows crossflow motion of the cylinder only. A vertical spring supports the framework connected to the submerged cylinder. The spring provides restoring forces in the dynamical system as well as providing the cylinder with the optimal mid-water static position in the towing tank. At the support of both ends of the cylinder (point A in Fig.l), force sensors are installed to measure horizontal and vertical force components. Vertical accelerations are measured at the top of the frame above the cylinder (marked B in Fig.1) one measurement at each side of the fiame, right above the cylinder support. At the same locations, two force rings connected to springs provide position and restoring force measurement. The cylinder used for this investigation is drawn in Fig. 2. The cylinder is perforated with mm diameter holes in a helical pattern, with pitch equal to 4.5. Each cross-section has three openings oriented 120" apart and spaced 25mm (Dl4) apart. Table 1 : Specification of the experimental apparatus

5 Fluid Structure Interaction 159 Cylinder volume I VWI m' Natural frequency in still water, I Hz zero jet velocity Effective dry mass Effective wet mass Mass ratio Specific gravity Surface holelcvlinder diam. ratio mdrv 46.9 mwet 68.5 dry mass1 ~ D ~ ~ L2.343 C dry massldispl. water Kg Kg - [-1 [-l r-1 with water outflow though openings indicated by arrows b) Longitudinal view, with the spanwise pattern of holes indicated, and the term pitch defined. Results in the following are presented by use of the dimensionless parameters reduced velocity, U,, (Eq.l), and dimensionless frequency;, (Eq.2). When U denotes the ambient flow, and D is the cylinder diameter, definitions are as follows: wherefo is the eigenfrequency of the cylinder in still water, fox D f=r where fosc is the actual oscillation frequency. The cylinder is tested for a variety of towing velocities ranging fiom reduced velocity Ur=3 to U71 l. The corresponding range of Reynolds number is about Rez When blowing is applied, three outflow velocities are tested, v1.01 mis, V,=1.47 mls and V,=2.79mls. This implies that the velocity ratio V,/U is 1.74<V,/U<18.03.

6 160 Fluid Structure Interaction Results Fig. 3 shows oscillation amplitude normalized by cylinder diameter as a function of dimensionless frequency, when no blowing is applied. In the same figure a curve fiom Vikestad [22] is also shown. The maximum oscillation amplitudes from the present study are somewhat smaller than those from Vikestad's experiments. These two investigations are different with respect to mass ratio (2.343 for the present study and for Vikestad's experiments). However this will not influence the results when using the dimensionless frequency as parameter. Hence increased damping due to the arrangement for providing water to the cylinder (flexible water hoses and two under-water protection caps) must cause the difference seen in Fig. 3. Figure 3: Dimensionless frequency, f A=lgC.~~~ (-1 Dimensionless oscillation amplitude versus dimensionless frequency.

7 A 0.7 Fluid Structure Interaction V =O.O mls. Pure IV * Vj=l.47 m/s + V.279 mls Figure 4: Reduced velocity, Ur [-] Dimensionless oscillation amplitude versus reduced velocity. It is also seen that for low dimensionless frequency, the oscillation amplitude, A, is close to zero in the present study, while Vikestad's results reach a somewhat constant level of A/D=OS. Fig. 4 shows the oscillation amplitude versus reduced velocity ibr different jet flow rates. The curve with no blowing, denoted "Vj =0.0 mls, Pure VIV", is shown for comparison. Note that this curve is the same as shown in Fig. 3, but now presented as function of the reduced velocity. The general trend within the lock-in region is that as V, increases, the oscillation amplitude decreases. The reduction is most evident at reduced velocity about Ur=6 which corresponds to the peak of the "pure VIV" amplitude plot. For the weakest blowing, the response peak occurs for a slightly lower reduced velocity than for a smooth cylinder. In fact at Ur about 4.5, the response is larger than for the smooth cylinder. For the high and moderate blowing rates however, the increase in oscillation amplitude occurs for higher reduced velocity than for the "pure VW'-case. This is expected, and takes place most likely because the ambient flow senses a larger structure than the actual cylinder diameter due to the upstream jet flow. For reduced velocity above the lock-in region, blowing seems to increase the amplitude rather than decrease it. This will be subjected to further study by the authors. However the authors believe that the level of response when blowing is applied also will experience a drop-off for large values of reduced velocity. The potential of the method in terms of VIV suppression is seen comparing the "pure V1V"-curve and the maximum V,-curve. If blowing is applied for

8 162 Fluid Structure Interaction Figure 5: RMS Lift coefficient versus reduced velocity. Figure 6: RMS Drag coefficient versus reduced velocity. reduced velocities below Ur=8 and switched off above this value, a system with good suppression characteristics is achieved. Fig. 5 shows RMS lift coefficient versus reduced velocity. A dramatic reduction in lift coefficient is experienced as blowing is applied. Also here we can see that the weakest blowing rate shifts the response peak in negative direction on the reduced velocity scale. Further, for reduced velocities above the lock-in region, blowing increases the lift coefficient. However the increase is not of a significant magnitude compared to the oscillation amplitude increase. The RMS drag coefficient plotted in Fig. 6 shows that for low reduced velocities the drag forces in general increases somewhat as blowing is applied. However for the region of main interest, blowing reduces the drag on the cylinder. An interesting feature of the drag coefficient curve is that increased blowing weakens the increase in drag due to blowing at large reduced velocities. This means that the change in drag force is not controlled by the oscillation amplitude only, but by the blowing flow rate as such. Another intriguing result from the drag coefficient curve is that the curves for the moderate and largest blowing are almost linear with respect to reduced velocity. Note that the RMS drag coefficient for the case with no blowing fits well with the empirical curve from Vandiver [23]. Fig. 7 shows the added mass coeff~cient calculated from the oscillation frequency and dry mass. The normalized oscillation frequency curve is seen in Fig. 8. The trend in these curves is consistent with previously published results from pure VIV tests, e.g. Vikestad [22]. Oscillation frequency increases with increasing reduced velocity, which is consistent with the reported added mass reduction. For the largest blowing ratio and low ambient velocity, the natural frequency is found to be higher than expected, and hence the added mass coefficient lower than expected. This is most likely due to the decrease in accuracy of the frequency determination for the oscillation when the amplitude signal is close to zero.

9 Fluid Structure Interaction I 1 a Reduced ".bly ur [.l Figure 7: Added mass coefficient versus reduced velocity. Figure 8: Oscillation frequency normalized by the natural frequency of the apparatus reduced velocity. In general increased blowing tends to reduce the added mass variation. For the cylinder with no blowing, the added mass becomes negative at reduced velocity about 9. When blowing is applied, added mass stays positive for all the towing velocities investigated. I V.2.79 mis, polynomial fit Amplitude, AID [-l Figure 9: Damping coefficient versus oscillation amplitude in decay tests. Based on the lift-coefficient curves from Gopalkrishnan [24], a first attempt to break down the relative contributions to the reduction of oscillation amplitude by use of energy considerations. The method relates the increased damping seen in Fig. 9 to an equivalent lift coefficient, and uses the curves from Gopalkrishnan [24] to link this to a modified oscillation amplitude. Comparing this with the actual oscillation amplitude when blowing gives a rough estimate of how

10 164 Fluid Structure Interaction important increased damping is compared to the 3-D effects seen in the experiments. When doing this, and considering the maximum blowing velocity in the lock-in region, the increased damping accounts for about 5-6% of the decrease in amplitude of the system. Hence about 94-95% of the reduction in oscillation amplitude is due to other effects such as reduction of correlation length. Conclusion The results presented in this paper clearly show that steady blowing of water at discrete locations along a cylinder can provide effective suppression of vortexinduced vibrations. Increased damping, due to the water exiting from the cylinder, causes a reduction in the oscillation amplitude. However, the main portions of the reduction are other 2-D and 3-D effects. Among the most important effects is the 3-D effect of the reduction of the correlation length. The authors believe that the main contribution to the VIV suppression is that the blowing of water disturbs the hydrodynamic load build-up of lock-in. Blowing effectively cuts the communication of the vortex shedding along the span of the cylinder. The correlation length of the vortex shedding is reduced. The oscillation amplitude is proven to reduce from about 0.9 to below 0.1 in the lock-in region when blowing of magnitude Vjz2.79 mls is applied. Both drag and lift coefficients experience dramatic reductions when blowing is applied in the lock-in region. When also taking the reduction in oscillation amplitude into account, this has proven to be a promising method of VN suppression. The potential of the method is seen comparing the "pure VWcurve and the maximum Vj-curve in Fig. 4. If blowing is applied for reduced velocities below Ur=8 and switched off above this value, a system with good suppression characteristics is achieved. Further research is needed in order to identify and map all the 2-D and 3-D effects embedded in the present results. At present the authors are working disclosing more of the physical effects of this method. Special emphasis will be put on investigating a larger number of jet patterns as well as towing at higher velocities. Acknowledgements We would like to thank Anders Jahres Fond as well as The Norwegian Research Council for providing funding for the experiments. Further we would like to thank The Norwegian Research Council for sponsoring the Dr.ing scholarship of the first author though the Strategic University Program on Marine Cybernetics. References [l] Sarpkaya, T., Vortex-induced oscillations. Journal of Applies Mechanics, 46, pp , 1979.

11 Fluid Structure Interaction Griffin, O.M. & Ranberg, S.E., Some recent studies of vortex shedding with application to marine tubular$ and risers. ASME Journal of Energy resources Technology, 104, pp. 2-13, Bearman, P.W., Vortex shedding fiom oscillating bluff bodies. Annual review of Fluid Mechanics, 16, pp , Parkinson, G., Phenomena and modelling of flow-induced vibrations of bluff bodies. Progress in Aerospace Sciences, 26, pp , Blevins, R.D., Flow-induced Vibrations, Van Nostrand reinhold: NewYork, Zdravkovich, M.M., Flow around circular cylinders, Vol. 1 : Fundamentals, Oxford University Press: London, Naudascher, E & Rockwell, D., Flow-Induces Vibrations: An Engineering Guide. Balkema: Rotterdam, Sumer, B.M. & Fredsse J., Hydrodynamics around Cylindrical Structures. World Scientific: Singapore, Wong H.Y., An aerodynamic means of suppressing vortex-excited oscillation. Proc. Inst. Civ. Engrs., 63 (2), pp , Sallet, D.W., A method of stabilizing cylinders in fluid flow, Journal of Hydronautics, 4, pp.40-45, Schlichting, G., Boundary Layer Theory. 7ed., McGraw-Hill Book Company: New York, Wood, C.J., The effect of base bleed on a periodic wake. Journal of Royal Aeronautical Society, 68, pp , Wood, C.J., Visualisation of an incompressible wake behind a base bleed. Journal of Fluid Mechanics, 29, pp , Bearman, P.W., The effect of base bleed on the flow behind a twodimensional model of a blunt trailing edge. Aeronautical Quarterly, 18, pp , Park,W., & Cimbala, J.M., The effect of jet injection geometry on twodimensional momentumless wakes. Journal of Fluid Mechanics, 258, pp , Willaims, D.R., & Amato, C.W., Unsteady pulsing of cylinder wakes (chapter 7). Frontiers in Experimental Fluid Mechanics, ed. Gad-el-Hak, M., Lecture Notes in Engineering, 46, pp Springer Verlag: New York, Willaims, D.R., Mansy, H., & Amato, C.W., The response of asymmetry properties of a cylinder wake subjected to localized surface excitation. Journal of Fluid Mechanics, 234, pp , Lin, J.C., Towfighi, J., & Rockwell, D., Near-wake for a circular cylinder: Control by steady and unsteady surface injection, Journal of Fluids and Structures, 9, pp , Brown, N.A., & Grinius, V.G., Active Suppression of Vortex Induced Vibration and Drag for Marine Drilling Risers, Proc. of ETCE/OMAE2000 Joint Conference, OFT-2 1, New Orleans, Fernandes, A.C, Esperanca, P.T.T., Sphaier, S.H. & Silva R.M.C., VIV migration: Why not porosity. Proc. of ETCE/OME2000 Joint Conference, OFT-4 150, New Orleans, l65

12 166 Fluid Structure Interaction [21] Khalak,A. & Williamson, C.H.K., Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping. Journal of Fluids and Strucrures, 11, pp , [22] Vikestad,K., Multi-frequency response of a cylinder subjected to vortex shedding and support motions, Dr.ing thesis, Department of Marine Structures, NTNU, Trondheim, [23] Vandiver, J.K., Drag coefficients of long flexible cylinders. Proc. Of the 1 s '~ Annual Offshore Technology Conference, Houston, TX, pp OTC Paper No.4490, [24] Gopalkrishnan, R., Vortex-induced forces on Oscillating Bluff Cylinders. S.Dc. thesis, Department of Ocean Engineering, MIT, Boston, 1993.