A Study on Tautly-moored Spar Buoys for Offshore Mariculture Cages

Transcription

1 ACTA OCEANOGRAPHICA TAIWANICA VOL.36, NO I, PI' , 3 TABS, 7FIGS., JUNE 1997 Short Note A Study on Tautly-moored Spar Buoys for Offshore Mariculture Cages Nai Kuang Liang', Chi Hsiang Lin! and Churn Chir Liu! (received 1997/5/8, revised 1997/6/25, accepted 1997/6/28 ) ABSTRACT Due to the 200-mile Exclusive Economic Zone (EEZ), the environmental impact of Inland mariculture, such as land subsidence in the western coastal plain of Taiwan and the increasing demand for sea food, open ocean mariculture is one of the major tasks oftaiwan fisheries. However, typhoons invade Taiwan frequently in summer and offshore cages must sustain heavy waves of 10 meters the high. Four tautly-moored spar buoys are employed to hang an offshore cage. According to theoretical analysis and experiment, the net buoyancy and the slenderness ratio of a spar buo y dominate the pitch motion in waves. A spar of cm in diameter and meters in length is suggested. The spar buoy and cage are quite stationary in waves. Further studies are necessary to understand whether the proposed system is suitable for open ocean mariculture or not. (Key words: tautly-moored spar buoy, wave, pitch angle, net buoyancy, slenderness ratio.) INTRODUCTION World fisheries will almost certainly not meet 21st century demands for seafood and other marine bioproducts. The present total of world fish production is about 100 million metric tons, in which, aquaculture amounts to 9.8 million metric tons. An anticipated doubling of the world. population in the coming century, would lead one to anticipate a demand for at least 200 million metric tons of total world fish production within 50 to 70 years (Bardach, 1991). Recently, Norway has become the major salmon export country in the world. However, fish farming has a short history in Norway, but the industry has developed extremely rapidly. At the beginning, the cages were anchored in a sheltered bay and very close to the shore. Due to the generally low water exchange rate, the fish suffered bad water quality. After several years at the same locati on, the production rate decreased and some of the fish farms obviously polluted the enviro nment _._-. I Institute of Oceanography National Taiwan University _.. 69

2 70 A Study on Tautly-moored Spar Buoyfor Offshore Marieulture Cage The cages moved gradually offshore and to the open ocean (Dahle, 1991). offers some specific advantages over inshore mariculture, from both environmental standpoints. Offshore mariculture the production and Fluctuations in water temperature and salinity are more gradual and of lesser amplitude offshore. Water quality and circulation are normally better offshore than those at inshore locations. It follows that the disposal oforganic waste would be improved at an offshore site, thus minimizing local eutrophication and organic enrichment of the benthic sediment and reducing the potential for deleterious environmental impact. Otherwise, offshore mariculture may lower the degree of risk of disease transmission if the culture facility is positioned in an area of relatively low fish density Donaldson, 1991). Due to the 200-mile Exclusive Economic Zone (EEZ), the environmental impact of inland mariculture, such as land subsidence in the western coastal plain of Taiwan, and the increasing demand for sea food, open ocean mariculture is one of the major tasks of Taiwan fishery. Unfortunately, there is hardly any sites of sheltered sea area. Moreover, typhoons invade Taiwan frequently in summer and offshore cages must sustain heavy waves of 10 meters high. Although there are several designs of submerged cages which can survive in a hostile sea condition, these cages are sophisticated but not economical. Hence, it is necessary to develop a native offshore mariculture cage. The principle is that the more stationary the cage is in waves, the better it can resist the waves. A tautly-moored spar buoy may be quite stationary in waves, and then the cage fastened to the spar buoys may also be stationary in waves. THEORETICAL ANALYSIS IN RESPONSE OF TAUTLY-MOORED SPAR BUOYS IN WAVES For simplicity, a theoretical analysis of a tautly-moored spar buoys in waves is based on the following assumptions: (I) The mooring cable is always taut, but the elongation of the cable is neglected. (2) The diameter of the cable is so small that its fluid drag, buoyancy and gravitational forces can be neglected. (3) The hydrodynamic coefficients of spar buoys are independent of particle velocities of waves. (4) The spar buoy is submerged in water and the wind force is neglected. (5) The center ofgravity and the buoyancy center of the spar buoy coincide. (6) The tension ofthe cable is quite high so that the cable and the buoy are considered as a rigid body which takes the anchor as a turning point. The coordinate system is as shown in Fig. I. According to Newton's 2nd law ofmotion, the equations ofmotion for the spar buoy are the following :

3 Nai Kuang Liang, Chi Hsiang Lin and Churn Chir Liu 7 1 z h (d e p t h) T l Anch o r bloc k Fig. 1 Schematic graph ofa tautly-moored spar buoy in waves 5 Surge mx ='L F Xl (1) j ~ 1 5 heave mi = 'LFZj (2) j~ 1 5 pitch!b='lmj... (3) j ~ l

4 72 A Study on Tautly-moored Spar Buoy for Offshore Mariculture Cage in which m is the mass ofthe buoy, F the force, M the moment and 1 the moment ofinertial and equal to in which 1 0 : length of mooring line L : length ofbuoy The forces and moments are the following : (I) Buoyant forces and moments(j= I) F =0 x l (4) r: = P"Vg (5) M = - F (I +~)sin B ) z ) 0 2 (6) in which V is the volume ofbuoy and B the pitch angle. (2) Gravity(j =2) F X2 =0 (7) (8) (9) in which Wa is the weight of the spar buoy. (3) Viscous forces and moment(j=3) Following Morison equation and Huang (1990), the viscous forces and moment are as follows : F X3 = J, rr'-i PwCdx D (U - X) " 1 U - X" 1dz r.2 (10) (II)

5 Nai Kuang Liang, Chi Hsiang Lin and Churn Chlr Liu 73 M 3 = f,lpwcd<d(u - X) IU - XI(h + z) sec 6t1zcosg fa 2 +F z3(l o+ ~) sing (12) in which U is the water particle velocity in X direction, W the water particle velocity in Z direction, D the diameter of the spar buoy, A I the projected area of the spar buoy in Z direction and fa ' r c are the integral limits ofthe spar buoy in Z direction Cd< is the drag force coefficient in surge and C dz the drag force coefficient in heave. And, (4) Added mass forces and moment 0=4) Following the Morison equation and Huang(1990), the added mass forces and moment are as follows: (13) (14) (15) in which W = 1 f 'Wdz L f a Cax is the added mass coefficient in surge and Caz the added mass coefficient in heave. (5) Tensiontj-S) The tension force of the mooring line exerts at the lower end of the spar buoy, as the following : F x 5 =- Tx F z5 =-Tz (16) (17) (18)

6 74 A Study on Tautly-moored Spar Buoyfor Offshore Mariculture Cage Substituting equations(4)-( 18) into Equations( I)-(3), one gets the following equations: Surg e... (19) Heave 3 _ [m + p w ( Cax + 1)17]2 = LJ~J +Pw ( C,,: + l)vw - ~ J= 1... (20) Pitch»-».«: +l)17x(/ o+ L) coso=±m J + f 'pw(c ax +l)a'u(h+ z)dz 2 J= 1 r, (21) + F: 4 ( /o + ~) sine' From field experimental experience, if the length and the buo yancy of the spar buo y are enough, the pitching angle is kept very small. Then the hydro- dynamic forces in z-direction and the influence by pitch on the hydrodynamic forces in x-direction may be neglected. Further, (U- X)IU- X! is simplified to be (U - X)IU!' which is then linearized. Then eq. (21) becomes in which AB +BB +CO= Dcosat + E sin at (22) A=(;: +Ca< + I) Jr~2 L[~2 + /o(!o + L)] B = Cdx DHg {[(lo + L) 2sinh k(lo + L) - 2(10 + L) cosh k(lo + L) 2JrCY cosh k(lo + L) k +~ sinh k(lo + L)] - [/5sinh kl o - 2/ 0 cosh kl o + ~ sinh kl o]} k k k C= ( I -~) JrD 2 Lg(/ o + L)2 Pw 4 2 Cdx DH 2g k (21 + L) 1 D=. 0 {L(2/0+ L)+ - [(lo+ L ) sinh2k (lo+ L) - /osinh2klo] 6JrsInh k(lo+l) k 1-2k 2 [cosh2k(lo + L) - cosh2klo]} «; + I)JrD 2 Hg.. E = - ( ) [sinh k(!o + L) - SInhklo] coshk L

7 Nai Kuang Liang, Chi Hsiang Lin and Churn Chir Liu 75 H is wave height, (J" is wave frequency and k is wave number. Eq.(22) is a second ord er ordinary differential equation. The solution consists of homogeneous and parti cular ones. The former is a transient solution and vanishes when time elapses. Therefore, only a particular solution is left, i.e. (23) F F (24) fj = tan " [ CJ Au- - B a (25) in which 4 spar buoy models have been selected. The parameters are shown in Tablel. The water depth is set to be 60cm and the wave period 1sec. Following eq.(24), the relationship between ()max and non-dimensional wave height kh is shown in Fig.2. One can find that the net buo yancy is the major fact or. ()max decreases as the net buoyancy increases. Otherwise slenderness LID also has influence. The net buoyancy of model D is about halfofmodel E. However, ()max ofmodel E is a little smaller than that ofmodel D. The reason is that the slenderness ofmodel E is 8 and that of model D is If the net buoyancy is kept constant the relationship between ()max and LID for constant wave period but different wave height is shown in Fig.3. One can observe that ()maxdecreases as the slenderness LID increases. This tendency is more obvious for larger wave heights. (26) Table 1 Parameters of the spar buo y models Model type length diameter volume weight average density net buoyancy (ern) (cm) (cubic ern) (gm) (gm/cubic em) (gm) A D E H

8 76 A Study on Tautly-moored Spar Buoyfor Offshore Mariculture Cage 8.00 T=1.0 see ;h=60 em A buoy 6 00! 0 buoy OJ 01 ~ '" 01 ~ 4.00 s: u"c, 2.00.r:..~ ~ ~ ~ I E buoy,i ~ H b "OY 0.00 I I kh Fig. 2 The relationship between B max and non-dimensional wave height kh H=4.0cm I '" 0, ~~ "0 '" J?: H=3.0cm ~ L B 0:: '001 : 2.00 l H=2.0cm.1,J : r I- I I I Length/Diameter Fig. 3 The relationship between B max and the slenderness LID FIELD EXPERIMENT In order to compare the theoretical results further, a field test was carried out at a coastal site near Keelung. The spar buoy, which is 300 ern in length and 20cm in diameter, is made of a stainless steel frame and several buoyant cylinders. On top of the spar buo y, a cylindrical case is

9 Nai Kuang Liang, Chi Hsiang Lin and Churn Chir Liu 77 fixed, in which a Dual-axis Inclinometer (SSY0090) and a recorder are installed. The inclinometer can measure the inclinations in the two horizontal axes i.e, ()x and ()y. The principal inclination angle () can be calculated by the following equation: At the bottom of the buoy, there is a room, in which 5 iron discs(5.5 kg each) can be put as a ballast weight. A schema of the model is shown as in Fig. 4. A wave-rider was employed to measure the wave. The experiment was executed by a fishing boat, two divers and two assistants. The field experiment lasted about 2 hours and the wave record are shown in Table 2. Two spar buoys were tested and a 5mx3m fishing net was hung on the buoys in some cases. The results are summarized in the following 6 cases as shown in Table 3. f 0.5 I B~ 81 kg. : inclinometer kg. r ~ spa r fra me :/i 2 5? / buoyant cylinder II. J kg kg. V; [7: ' '/ 1, cylinder case ' 2S: i r on d i sc I~ s hackl e T \ I- c hain j-' I 0 hook swivel 1 1 wi r e kg kgw ) t kg kg. o 13 k~ kg. 1.2 kg shackl e h o o k sh'; c kle chain kg. o 15 kg. O. 06 kg kg. w ~ 50 5 kg. Fig. 4 Schema of spar buoy

10 78 A Study on Tautly-moored Spar Buoy for Offsho re Mariculture Cage Table 2 Wave da ta (Keelung 1994/12/22) Time Hmax Tmax HI/10 TI/IO H I/3 TI /3 Hmean Tmean 11: : : : : : : Table 3 Field experiment data No. H 1/3 Hmax T V3 number of Distance between centers of net ()max (m) (m) (sec) iron disc gravity & buoyancy (em) I no no yes yes no no 9 From the 6 cases, it was found that the ballast weight does not have significant influences on th e pitch angle of a tautly-moored spar buoy. But the fishing net may reduce the angle. As menti oned in the theoretical analysis, the main factor is the net buoyancy. As the ballast weight is releas ed and the distance between the centers of gravity and bu oyanc y are de creased, however the net buoyancy of spa r buoy increases. The scale length of model is 1:4. i.e. a 2 meter wave height in the mod el becom es 8 meters. A spar buoy of 3 ton buoyan cy force may have pitch ang le of 10 degrees in a wave of 9 m wave heigh t. The calculation of the 3 ton buoyan cy for ce is based on the following assumptions: ( I) T he buoy's ce nter of gravity coincides with that of bu oyancy if 3 ballast wei ghts are release d. (2) The net buoyancy force of the model buoy is tim ed by 64, which is the cubic of the mod el sca le lengt h 4.

11 Nai Kuang Liang, Chi Hsiang Lin and Churn Chir Liu 79 A TENTATIVE DESIGN OF AN OFFSHORE FISH FARM According to theoretical analysis and field experiments, a spar buoy of40-60 em in diameter and cm in length is suggested. A concrete block of 3-5 ton s is used as an anchor, which can be reused. The deployment of the blocks is rather hard work. A proposed array of blocks is shown in Fig.5. The arrangement ofthe spar buoy and cage is shown in Fig.6. The water depth is about meters. The small buoys are to support the weight ofthe cage and the spar buoys are to take the burden of drag force due to the current. One cage is fastened to four spar buoys and each spar buoy is tied with upper and lower ropes to the cage. Becau se the tautly-moored spar buoy is almost stationary in waves, the cage is also quite stable. This may be favorable for mariculture : s par m. b uoy 0 0 Fig. 5 A proposed array ofblocks spar buoy v anchor b l ock Fig. 6 The arrangement ofspar buoy and cage

12 so A Study on Tautly-moored Spar Buoy/or Offshore Mariculture Cage The current usually flows along the coastline. The drag force by current is as follows: Then it is better to employ rectangular cages. in which J~ drag force in newtons C, drag coefficient p w the sea -water density V current speed in m/s A projected area of a body to the approaching current velocity The drag coefficient of a cylinder is about depending on the Reynolds number. The drag coefficients of netting material have been presented by Milne (1967). He demonstrated that marine fouling increases the coefficients significantly. clean, unfouled nets are as follows: For a knotted net c, = 1+ J77(d/l) + 9J7(d/I)2 and for a knotless net Cd = (d/I) + JI2(djIr in which d diameter ofthe net material in inches I length ofone bar ofthe mesh in inches The definition of d and I is shown in Fig.7 shown as follows: knotted net diameter of net material d length of one bar 1 current speed V dimension ofnet pen diameter of spar buoy length of spar buoy drag coefficient C, 0.06" The formulae for the coefficient of drag on OA" 0.5 m/s length 12m, width 8m, height 8m OAm 10m 1.3 The drag force ofone spar buoy JJ x 1000 x lox 0.4 x 0.5 x 0.5 / 2 = 650(N. T.) ~ 66Jkg The projected area of one smaller side ofthe net pen ( )2! OA 2 = = x 8 x 0.28 = (square meters) An example to check the drag of current is

13 Nai Kuang Liang, Chi Hsiang Lin and Churn Chir Liu 81 The projected area ofthe net pen A x 2 = (square meter) The drag coefficient Cd x (0.06 / 0.4) x (0.06 /0.4)2 == The drag force ofthe net pen x l 000 x x 0.5 x 0.5 / 2 == 5268(N.1'.) == 527 kg 527kg is distributed in the two spar buoys. d Fig. 7 Diameter ofthe net material and length ofone bar of the mesh DISCUSSION AND CONCLUSION Although in the theoretical analysis there are assumptions that are not realistic, i.e. that the spar buoy and the mooring line are like a rigid body, the conclusion that the buoyancy and slenderness ratio(l/d) of the spar buoy dominate the pitch motion in waves is supported by the field experiment. A practical design of an offshore mariculture farm is to install 2 rows of tautly-moored spar buoys along coast. The distance between them is about 20 meters. 4 spar buoys can serve for one cage. Because each intermediate spar buoy serves for two cages, each cage requires a little more than 2 spar buoys in average. The dimension is suggested to be 40 em in diameter and cm in length. The design wave height Hm is 9m and current speed is 1 knot. If the waves and currents are bigger, the dimension of the spar buoy must be enlarged. The spar buoy and cage are quite stationary in waves. Whether this system is suitable for open ocean mariculture in Taiwan or not, further field experiments are needed.

14 82 A Study on Tautly-moored Spar Buoyfor Offshore Mariculture Cage ACKNOWLEDGEMENT This paper is part ofthe research projects sponsored by the National Science Council, Rep. of China (NSC E-002A-001, NSC E-002A-00 1). REFERENCES Bardach, J. (1991) Open ocean mariculture(biological aspects), Proceedings, Workshop or; engineering research needs for off-shore mariculture systems, Honolulu, Hawaii, September 26-28,1991, pp Dahle, L A. (1991) Exposed fish farming: biological and technical design criteria and possibilities, Proceedings, Workshop on engineering research needs for off-shore mariculture system, Honolulu, Hawaii, September 26-28, 1991, pp Donaldson, E. M. (1991) Application ofbiotechnology to biological problems, associated with off-shore mariculture, Proceedings, Workshop on engineering research needs for off-shore mariculture system, Honolulu, Hawaii, September 26-28, 1991, pp Huang, M. C (1990) Numerical model for ocean buoy-tether-anchor system, Proc. National Science Council, ROC, Pt. A, 14(6), pp Milne, P. H. (1967) Interim report of water forces on fish netting, Department of Civil Engineering, University ofstrathclyde, Glasgow, Scotland.

15 台灣海洋學刊 第 3 6 期第 l 號, 頁,3 求, 7 圈, 中華民國 8 6 年 6 月 簡錄 繫箱網拉緊式圓柱浮體的研究 梁乃匡 1 林吉祥 1 "J 純琪 1 (rece ived 1997/5/8, revised 1997/6/25, accepted 1997/6/28) 摘要 由於 2 00 涅經濟專屬區的出現 陸上養殖造成的環境衝擊及海產食品需求 的增加, 外海養殖將成為台灣漁業的一項重要工作 由於颱風經常在台灣出現, 外海箱網必須能承受 1 0 米浪高的巨浪 本文採用拉緊式圓柱型荐 體作為繫箱網的樁柱, 根撮理論與實驗得知, 淨浮力與細長比是主宰拉緊式圓柱型浮體在波浪中作縱傾大小的因素 建議採用直徑 公分長 米的圓管作浮體, 沿海岸安裝兩排拉緊式圓柱浮體, 4 支持 : 體可掛一具箱網 本文建議的外海箱網在渡浪中幾乎不動, 是否適合本地, 尚需進一步試驗 關鍵詞 ; 拉緊式圓柱浮體 波浪 縱傾角度 淨浮力 細長比 l 國立台灣大學海洋研究所台北台灣中華民國 83