An Experimental Study of Wave Runup: Cylinder Fixed in Waves versus Cylinder Surging in Still Water

Transcription

1 International Jornal of Engineering and Technology, Vol. 9, No., April 7 An Experimental Stdy of Rnp: Cylinder Fixed in s verss Cylinder Srging in Still Water Deping Cao, Edmond Lo Yat-Man, Wei Jian, and Zhenha Hang Abstract Many previos stdies have been reported for the wave rnp on fixed cylinders bt few has been done on srging cylinders. Physically, there is conversion of the kinetic energy of water particles into potential energy dring the rnp on a fixed cylinder. Several formlas have been reported to correlate the rnp with the velocity head. Whether this holds for a srging cylinder or not remains nknown. In the present stdy, experiments are condcted to investigate the relationship between rnp on a cylinder and the relative velocity between the cylinder and the water particles arond it. Both rnp on a fixed cylinder de to an incident wave and that on srging cylinders de to the srge motion are stdied. The reslts show that for both cases an increase in velocity head leads to an increase in rnp. Index Terms Fixed cylinder, rnp, srging cylinder, velocity head. I. INTRODUCTION Water wave rnp is the vertical p-rsh of water when an incident wave impinges pon a free srface penetrating body. The offshore indstry is particlarly interested in the accrate prediction of the maximm rnp height for which significant volmes of water can be projected above mean sea level. When an incident wave hits a srface penetrating strctre, the wave ndergoes a violent transformation where some portion of the momentm of incident wave is directed vertically pward. To conserve energy, this momentm flx reslts in a rapid amplification of the waveform at the free-srface-body interface. The wave rnp on the forward vertical legs of both fixed and floating offshore strctres is of particlar interest to platform designers. In harsh ocean environments, the amplification of the incident wave may give rise to pressre implse loads on the nderside of the deck strctre, referred to as a slamming force in the offshore strctre commnity. In the instance of wave rnp, a pressre implse event occrs when a horizontal element, sch as the platform deck or a body sspended from it, is impacted by a discrete volme Manscript received November, 5; revised Janary, 6. This work was spported by the Singapore Maritime Institte (Deepwater Technology R&D Programme). Deping Cao and Wei Jian are with Maritime Institte at Nanyang Technological University, Singapore ( DPCAO@nt.ed.sg, jianwei@nt.ed.sg). Edmond Lo Yat-Man is with School of Civil and Environmental Engineering, Nanyang Technological University, Singapore ( cymlo@nt.ed.sg). Zhenha Hang is with the Department of Ocean and Resorces Engineering, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honoll, Hawaii , USA ( zhenha@hawaii.ed). of water rshing p the weather side of a platform colmn. While not posing a threat to the overall strctral integrity of the platform, wave rnp is generally associated with localized strctral damage. The accrate estimation of wave rnp, and hence the air-gap, is ths extremely important for mitigating the hazards associated with pressre implse events. Sorce TABLE I: FORMULAS USED IN PREVIOUS STUDIES Srging/ fixed Formlas sed R g [] Fixed where R is the wave rnp, η max is the maximm wave crest and the velocity and g is the gravity acceleration, at η max was compted sing McCowan s solitary wave theory [] Fixed N/A [3] Fixed Same as Hallermeier (976) except that at η max was compted sing Dean's fifth-order stream fnction wave theory [4] Fixed Linear theory, Stokes second order, third order theories [5] Fixed R H 7.43 g where H is the incident wave height, was the wave crest velocity obtained from stream-fnction wave theory [6] Fixed R.56H 6.5 g [7] Fixed. Linear diffraction theory;. Kriebel s sperposition theory sing two Forier components; 3. Velocity head method sing linear wave theory for the crest kinematics; 4. Velocity head method sing a high-order wave theory for the crest kinematics; 5. The same method as Niedzwecki and Hston (99) [8] Fixed [9] Fixed [] Fixed max R, max g where max is the maximm water particle velocity at η max, which is calclated sing second order Stokes theory % R, %,% m g where η max,% is the crest level of the % highest wave, % is the horizontal particle velocity in the top of the crest for the same wave; m was a fnction of peak wave steepness; stream fnction theory was sed to calclate η max, % and % % max R, %,% m R, max m g g m was a fnction of peak wave steepness; stream fnction theory was sed to calclate η max, η %, max and % Many previos stdies []-[] have been reported on wave rnp on fixed colmns. Most of these stdies frther DOI:.7763/IJET.7.V

2 International Jornal of Engineering and Technology, Vol. 9, No., April 7 developed eqations by empirical fits to experimental data involving both the velocity head and incident wave height, as smmarized in Table I. Floating offshore strctres are generally not completely fixed and how the motion of the strctre inflences the wave rnp has seldom been reported. Intitively, one may envisage that the wave rnp shold be correlated with the relative velocity when srging motion is involved. In the present stdy, two different scenarios are stdied. One is wave rnp on a fixed cylinder and the other is rnp on a cylinder srging in still water in a sinsoidal way. Reslts are analyzed and compared to stdy the relationship between the rnp and the relative velocity head. A. Experimental Setp II. EXPERIMENTAL SETUP The experiments were condcted in a wave flme at the Hydralics Modelling Laboratory, Nanyang Technological University. The flme has dimensions of 44.5 m long,.55 m wide and.5 m deep, as sketched in Fig.. Wg 5 Wg 6 Motion control CameraWg ~4 Rler for wave rnp 44.5 Dewesoft 8 Wg Wg Actator direction Wg 3 Wg 4 maker Rler Wg 5 Wg 6 gage LabVIEW Artificial wave absorber Incident waves are generated by a two dimensional wave generator that is controlled by a DHI active wave absorption control system at the pstream end of the flme while an artificial wave absorber is installed at the downstream. A platform driven in srge by an actator is located at a distance of 7 m from the wave generator. A cylinder model (see Fig. c for the sketch of the model) with diameter = cm and length = 36 cm is attached to the platform. A total of 6 HR Wallingford resistance type wave gages are installed, two at.8 and 3. m in front of the cylinder respectively, to measre the incident waves and for monted arond the cylinder model to characterize the wave elevation (see Fig. b for detailed locations of the gages). A high speed camera (DS-CAM-3) is sed to captre the wave rnp via images of a measrement tape gled onto the front face of the cylinder. The camera records at a frame rate of 6 f/s reslting in the accracy of video pictres being p to.5 mm. An Ultralab sensor (ULS 4D) is sed to record the srge motion of the actator-driven platform and cylinder with a resoltion of mm achieved. A Dewesoft data acqisition system is sed to: () synchronize the camera and the wave gages and () collect the wave elevation and wave rnp data. LabVIEW programing is sed to prescribe a sinsoidal signal for the actator srge. B. Experimental Conditions Two different scenarios are experimentally tested. One is to stdy the rnp of reglar waves on a fixed cylinder with wave conditions shown in Table II (specifically F-F6). The other is to investigate the rnp on a srging cylinder de to the srge motion at the same freqencies as F-F6 (see Table II, S-S6 for the amplitde of srge motion). The water depth is kept constant at d =.7 m. Note that in order to have a direct comparison between rnp on fixed cylinder in wave and cylinder srging in still water for the same freqency, the srge amplitdes are set to be the vales in Table II so that the velocity of the srge motion is close to that of maximm water particle velocity calclated sing linear theory for the corresponding case of fixed cylinder in wave. TABLE II: EXPERIMENTAL CONDITIONS FOR FIXED (F-F6) AND SURGING (S-S6) CYLINDERS Test No. amplitde, A w or Amplitde of srge motion, A s F.6.9 F.49. F F4.9.8 F5.35 F S.33.9 S.5. S S S5.9 S6 4.4 period, T w (s) or Period of srge motion, T s (s) (c) Fig.. Schematic drawing of wave flme setp; detailed locations of wave gages (Wg); (c) cylinder model. (Note nits for are m, and for and (c), mm). C. Data Analysis Since all the freqencies sed in the stdy is less than Hz (see Table II), in order to eliminate higher freqency 5

3 International Jornal of Engineering and Technology, Vol. 9, No., April 7 components, a low pass filter with a ct-off freqency of 5 Hz is sed to filter all the original recorded signals while retaining some harmonics. For fixed cylinder in waves, Fast Forier Transform (FFT) is applied to a time window of wave periods for the most stable waves for all 6 wave gages in order to obtain the fndamental amplitde and freqency. Goda and Szki s method [] is sed to do wave separation for signals from wave gages 5 and 6 to obtain the incident wave amplitde. For the cylinder srging in still water, the fndamental amplitde and freqency of the motion are similarly obtained via FFT on the most stable section of the recorded trajectory signals. The srge velocity of the cylinder is then calclated from the measred srge displacement. In all tests, the corresponding sections of the videos recorded by the high speed camera are digitized to obtain the rnp on the cylinders. III. RESULTS AND DISCUSSION A sample of the time series of srface elevations of wave gages 5 and 6 for Test F is shown in Fig. a. The most stable sections of ten cycles (9 s, the section in the dotted frame) of wave signals are chosen for FFT (the reslt is shown in Fig. b) and then wave separation is condcted to obtain the incident wave amplitde sing Goda and Szki s method []. The corresponding video recorded dring this time section is digitized to obtain the wave rnp. The digitized rnp on the fixed cylinder is almost constant for the cycles analyzed as the incident wave is qite stable. ten cycles (9 s, the section in the dotted frame) of displacement signals are chosen for FFT (the reslt is shown in Fig. 3b). The corresponding video recorded dring this time section is digitized to obtain the wave rnp. It shold be noted that althogh efforts have been made to rigidly fix the frame holding the actator on the flme wall, the actator motion still indced high freqency components, as cold be seen in the FFT of the actal actator displacement (Fig. 3b). Althogh the amplitdes of sch high freqency components are small (<% that of the fndamental freqency component), they cold lead to similar high freqency components in the radiated wave and rnp on the colmn. Displacement Raw signal of actator displacement Filtered signal of actator displacement Time (s) Srface elevation Amplitde Wg 5 Wg Time (s) Freqency (Hz) Fig. Time series and FFT reslt of srface elevations of Wg 5 for Test F. A sample of the time series of actator displacement for Test S is shown in Fig. 3a. Again the most stable sections of Amplitde Freqency (Hz) Fig. 3 Time series and FFT reslt of the actator displacement signal for Test S. To remove the effects of high freqency components, the signals of Wg 4, the velocity calclated based on the actal displacement signal and the rnp profile, are filtered sing a low pass filter (elliptic nd order with ctoff freqency = 6). Fig. 4 shows sample filtered signals of Test S. The correlation between wave rnp and srging velocity is then analyzed sing these filtered signals. As seen in Fig. 4, there are two peaks in the rnp for each cycle of srge. There is also a minor phase difference between the velocity and rnp. These two peaks are close to the trogh and peak of actator velocity which cold be physically explained as follows. Firstly when the actator velocity reaches a positive maximm vale, the relative velocity between the cylinder and water particles srronding it is similarly at a maximm, ths generating the first peak in the rnp thogh with a possible phase difference. The second peak corresponds to when the 6

4 International Jornal of Engineering and Technology, Vol. 9, No., April 7 actator velocity reaches a negative maximm. Here the water particles behind the cylinder follow the cylinder velocity and ths its velocity will also increase negatively. After the cylinder velocity reaches its negative maximm vale, it starts to decrease. De to inertia, the water particles in front of the cylinder contine to rn towards the cylinder, leading to the second rnp peak, with another phase difference. Fig. 4 shows that the troghs of the rnp occrs when the radiated wave srface (Wg 4) in front of the cylinder is in the trogh while the srging velocity is zero, so that the relative velocity between the cylinder and water particles in front of it are zero. Both figres show that the similar root mean sqare errors (rmse), ths based on the physical analysis, eqation in Fig. 5b is chosen. It shows that rnp on cylinder increases linearly with the increasing velocity head as the velocity of wave water particle or srge motion increases. Althogh these two scenarios involve different physical mechanisms, the reslting rnps are linearly correlated with the relative velocity between the cylinder and water particles arond it. The linear fitted eqation in Fig. 5 is R () g It is apparent that Eq. () is similar with those listed in Table I, althogh the coefficient of the velocity head is different. The above findings cold have potential applications for the investigation of wave rnp on a cylinder srging nder incident waves, which is a combination of the two scenarios investigated in the crrent stdy. For sch cases, the velocity shold be the combined velocity of both srging cylinder and moving particles. Fig. 4. Time series of wave rnp, srface elevation of wave gages 4 and filtered velocity for Test S. Based on the physical process presented above, the experimental data is analyzed sing water particle velocities as listed in Table III. Linear wave theory is sed to calclate the maximm horizontal water particle velocity at the wave amplitde. Rnp, R Fixed cylinder in waves Cylinder srging in still water Fitted eqation, R-=5.333 /g-.499, rmse =.68 TABLE III: EXTRACTED EXPERIMENTAL DATA FOR F-F6 TEST Test No. η /g R- η F F F F F F Note: R = rnp on cylinder; η = A w. The water particle velocities at the crest is calclated based on linear wave theory. For cylinder srging in still water, the initial elevation η is cm (radiated wave only); is calclated to be based on the srge trajectory. For tests S-S6, the velocity head /g is calclated to be.36,.88,.57,.44,.43 and.97 cm, respectively; rnp (R- η) is calclated to be.8,.5,.3,.,.5 and.4 cm, respectively. Figs. 5 and show the plots of (R-η) against velocity head /g. The difference is that the eqation in Fig. 5b is fitted with constraint that it mst cross the origin while that in Fig. 5a hasn t sch constraint. The constraint means that when velocity head is zero, (R-η) =. It is noted (R- crest) is sed to focs on the trend of rnp and velocity head. For the fixed cylinder in wave, the rnp is eqal to the crest if water particle velocity head is neglected. In contrast, for the cylinder srging wave, the rnp is eqal to zero if srge velocity is zero Rnp, R Velocity head, /g Fixed cylinder in waves Cylinder srging in still water Fitted eqation, R-=4.795 /g, rmse = Velocity head, /g Fig. 5. Plot of rnp against velocity head: Fitted eqation withot constraint; Fitted eqation with constraint that the fitted line mst cross the origin. IV. CONCLUSIONS Experiments were condcted to investigate the relationship between wave rnp on a cylinder and the relative velocity between the cylinder and water particles arond it. Both the rnp on a fixed cylinder in wave conditions and the rnp on a srging cylinder in still water 7

5 International Jornal of Engineering and Technology, Vol. 9, No., April 7 were stdied. The reslts show that the rnp is linearly increasing with increasing velocity head and can be fitted sing the same linear relationship. ACKNOWLEDGMENT Spport for the research from Singapore Maritime Institte Deepwater Technology (DWT) R&D Programme is grateflly acknowledged. Dr. Hai G and Mr. Zhiping Cheng from American Brea of Shipping (Singapore Innovation and Research Center), Dr. Xiaobo Chen and Dr. Binbin Li from Brea Veritas (Singapore) and Dr. Chin Lee Lim from Sembcorp Marine Technology (Singapore), are acknowledged for valable discssions at or project meetings. REFERENCES [] R. J. Hallermeier, Nonlinear flow of wave crests past a thin pile, Jornal of Waterway, Harbors & Coastal Engineering Division, vol., no. 4, pp , Nov [] C. J. Galvin and R. J. Hallermeier, rnp on vertical cylinders, Coastal Engineering Proceedings, vol., no. 3, pp. -4, 97. [3] J. P. Haney and J. B. Herbich, flow arond thin piles and pile grops, Jornal of Hydralic Research, vol., no., pp. -4, 98. [4] D. L. Kriebel, Nonlinear wave interaction with a vertical circlar cylinder. Part II: rn-p, Ocean Engineering, vol. 9, no., pp , Jan. 99. [5] J. M. Niedzwecki and A. Dggal, rnp and forces on cylinders in reglar and random waves, Jornal of Waterway, Port, Coastal, and Ocean Engineering, vol. 8, no. 6, pp , Nov. 99. [6] J. M. Niedzwecki and J. R. Hston, interaction with tension leg platforms, Ocean Engineering, vol. 9, no., pp. -37, Jan. 99. [7] A. Martin, W. Easson, and T. Brce, Rnp on colmns in steep, deep water reglar waves, Jornal of Waterway, Port, Coastal, and Ocean Engineering, vol. 7, no., pp. 6-3,. [8] L. De Vos, P. Frigaard, and J. De Rock, rnp on cylindrical and cone shaped fondations for offshore wind trbines, Coastal Engineering, vol. 54, no., pp. 7-9, Jan. 7. [9] T. Lykke Andersen, P. Frigaard, M. L. Damsgaard, and L. De Vos, rn-p on slender piles in design conditions Model tests and design rles for offshore wind, Coastal Engineering, vol. 58, no. 4, pp. 8-89, Apr.. [] J. Ramirez, P. Frigaard, T. L. Andersen, and L. De Vos, Large scale model test investigation on wave rn-p in irreglar waves at slender piles, Coastal Engineering, vol. 7, pp , Feb. 3. [] Y. Goda and T. Szki, Estimation of incident and reflected waves in random wave. Experiments, in Proc. 5th Conference on Coastal Engineering, Honoll, Hawaii, USA, 976. Engineering. Deping Cao was born in Anhi province, China in 983. He was conferred the doctor s degree in hydralics from School of Civil and Environmental Engineering, Nanyang Technological University in 5. He is now a post-doctoral research fellow in Maritime Institte at Nanyang Technological University. Dr. Cao is a reviewer of Jornal of Hydralic Edmond Lo Yat-Man received his doctor s degree in civil engineering (hydrodynamics) from Massachsetts Institte of Technology in 985. He is an associate professor in School of Civil and Environmental Engineering, Nanyang Technological University. Prof. Lo joined NTU in 996 where he was the head of the Division of Environmental and Water Resorces Engineering (5-8) and the chair of the School of Civil and Environmental Engineering (8-). He is also crrently the depty director of NTU s Institte of Catastrophe Risk Management and the dep. director of the Maritime Institte@NTU. Wei Jian is a research fellow at Maritime Institte at Nanyang Technological University, Singapore. She received her bachelor of engineering degree from University of Canterbry, New Zealand in 8 and Ph.D in engineering from University of Cambridge, UK in 3. Dr. Jian s crrent research interest incldes comptational flid dynamics application in offshore strctres. Zhenha Hang obtained his doctor s degree in environmental flid mechanics from Massachsetts Institte of Technology in 4. He is an associate professor in Ocean and Resorces Engineering Department, School of Ocean and Earth Science and Technology, University of Hawaii. Prof. Hang is a member of American Geophysical Union (AGU), Member of International Association for Hydro-Environment Engineering (IAHR), Member of American Coast and Edcation Society (CERF). 8