EFFECTS OF WATER-DEPTH ON HYDRODYNAMIC FORCE OF ARTIFICIAL REEF

372Available online at www.sciencedirect.com* ScienceDirecttIHD}Joumal of HydrodynamicsSB2Ser.B, 2007,19(3):372-377sdlj.chinajournal.net.cnEFFECTS OF WATER-DEPTH ON HYDRODYNAMIC FORCE OFARTIFICIAL REEF*MIAO Zhen-qingCollege of Environmental Science and Engineering, Ocean University of China, Qingdao 266003, ChinaSchool of Naval Architecture and Civil Engineering, Zhejiang Ocean University, Zhoushan 316004,China,E-mail: mzq @ zjou.edu.cnXIE Yong-heSchool of Naval Architecture and Civil Engineering, Zhejiang Ocean University, Zhoushan 316004, China(Received October 29, 2006; Revised November 29, 2006)ABSTRACT: The effects of water. depth on the hydrodynamicand implemented to study shollow water effects onforce of the artifcial reef were studied by simulating regularfloating ocean structures. Stability and mixingand irregular waves. The computational results show that thecharacter for buoyant jets in quiescent shallow waterwater-depth has a substantial effect on hydrodynamic force. Thewas studied by Zeng". Fang et al. 4 developed ahydrodynamic force increases with the decrease of water depthnumerical model of the two-dimensional fullyin shallow. Especially, in the ultra-shallow water these loadsnonlinear shallow water equations for the wave run-upincrease very evidently with the decrease of water-depth. Theon a beach, Wang et al. 5I presented an unstructuredlong-term values of hydrodynamic force increase with thefinite-volume numerical algorithm for solving thedecrease of the ratio of water-depth to reef height, and are abouttwo-dimensional shallow water equations based on10% larger than those of deep water when the ratio oftriangular or arbitrary quadrilateral meshes, Shenl4)water-depth to reef height is 4.0. However water-depth hardlydiscussed the well-posedness of the initial valueaffects the long term values of hydrodynamic force when theproblem for the linear shallow-water equations on anratio of water depth to reef height is larger than 6.0.equatorial beta-plane based on the theory ofKEY WORDS: arificial reef, water _depth, hydrodynamice forcestratification, Pan'l transformed and solved 2-Dshallow water equations by using the finite volumemethod with unstructured mesh in order to establish a1. INTRODUCTIONwell-balanced scheme, Chen et al. 6 presented theThe atificial reefs are becoming the importantsolution of 2-D shallow water equations by genuinelyfacilities for fishery in recent years. Most artificialmultidimensional semi-discrete central scheme, andreefs in China are operated in shallow water. TheLai et al." studied a new efficient characteristic-basedsmall ratio of water-depth to reef height makes thenumerical model for 3-D shallow water.hydrodynamic characteristics quite different fromAlthough a large number of variousthose of artificial reefs operated in deep water. Sincehydrodynamic formulations have been published,artificial reef design is based mainly on the magnitudethese works have been mainly concerned with theof the allowable bydrodynamic force, it is ofdeep water sea state. Only a few papers studied thesignificance to study hydrodynamic force of artificialeffects of various water-depth on floating oceanreefs in shallow water.structure dynamic response. He and Zhousl discussedHydrodynamic force of floating ocean structure atthe trends of the hydrodynamic force responses of ainfinite water-depth can be determined theoretically orship with water-depth variation. In a recent work,experimentally. Various theories have been developed中国煤化工* Project supported by the Natural Science Foundation of Zhjiang PBiograpby: MIAO Zhen-qing (1959>).Male, Ph. D, ProfessorYHCNMHG373Jelena and Jorgen!I studied the effect of water- depthwhere a is the wave-height, L is wave-length, T ison, the hydrodynamic force acting on a ship. Yu etwave-period, H is water-depth,D is reef-height.al!10] calculated the bending moment of a very largeThe bydrodynamic force is made up of the dragFPSO in the ultra-shallow by using the 3-D potentialforce and added mass force, the calculation formulatheory, Xie and Li studied the hydroelasticis written asresponses of a very large FPSO in variouswater-depth with 3-D hydroelastic theory.However, how to study the hydrodynamic forceF=c;号pAu2 +CnpvC(3)responses of a fixed ocean structure under wave andflow is an important project. The main objective ofthis work is to find out the trends of the hydrodynamicwhere, CJ is the drag coefficient, Cm the addedorce with water-depth variation by theoreticalmass coefficient, ρ the sea water desity, A thepredictions. The effects of various water-depth on theincident area of the artificial reef, and V the solidhydrodynamic force acting on an artificial reef arevolume of the artificial reef. Equation (3) can bestudied by the hydrodynamic theory.results showthathegiven ashydrodynamic force increases with the decrease ofwater-depth in shallow water. Especially, in theF= F(inθ+a)2 -Fm cosθ(4) .ultra-shallow water these loads increase veryevidently with the decrease of water- depth. In addition,wherethe results of long-term prediction indicate that thehydrodynamic force increase very rapidly with thedecrease of water- depth when the ratio of water-depthto height is less than 4.0. But water-depth hardlyF=Gjp4u_'a=",affects the long term prediction values ofhydrodynamic force when the ratio of water-depth toheight is larger than 6.0.p_. = 2rmC.Vpu.T2. THEORETICAL PREDICTION METHOD2.2 Long -term predictionBecause the artificial reefs are operated inThe fixed ocean structure is assumed to be adifferent sea conditions, the hydrodynamic forcesteady linear system and the short- term sea state istheory of finite water-depth must be employed toa stationary random process of ergodicity. Let Asolve the hydrodynamic force responses of thebe wave-direction angle, Sg(@) be the spectralatificial reef in this work.2.1 Hydronamic force theorydensity function of wave energy, R be theWhen wave and. current jointly act on thearbitrary mechanic quantity. The response spectralartificial reef, Wu et al.12 derived the hydrodynamic density function takes the following formforce equationu=uo +u =uo+um sinβ(1)Sq(@,B)=| Hn:(@,B)| S;(@)(5)where, um is the wave amplitude, β thewhere Hk:(@,B)= 2 R,p,(,B) is the transferwave- direction angle, and Uo the flow velocity,function of vibration mode R,, m is the totaland the expressions for um and β are defined asnumberofsuperimposedrigidbodymotion, p,(o,B) is the r-th principal coordinateun=na cosh(2xD1L)(2a)amplitude of structure.Based on the assumption that the short-termT sinh(2πH1L)distribution of the response satisfies the Rayleighdistributinn the. sionificant amnlitude of response2rx_ 2ntcan中国煤化工θ=二(2b)ITHCNMHG.R/3(pr-c.vvvyj(6a)374reef operated in shallow water. The artificial reefparticulars are listed in Table 1. The calculationσ°(β)= Se(w,B)do(6b)model of the artificial reef is shown in Figure 1. Thecalculation case of the artificial reef is shown inTable 2.Since the long-term distribution can bconsidered as the sum of short-term distributions,then Chen et al. 的described it by the curve ofTable 2 Calculation casestranscendentalaccumulative frequencies. TheRegular wave Iregular wavetranscendental accumulative frequency function ofthe hydrodynamic force for short-term sea state iswritten asWater -depth(m)0-40 .0-40X、XF,(X)=1-.exp(-,f)dS =exp(- -2σ2'Wave-frequency(rad/s)0-6(7)For the probability of bydrodynamic force, WWave direction angle(° ) 0.30.60.90， 0.30.60,90,120,150,180 120,150,180larger than X in the circle of Q-' hydrodynamicforce is written asWave spectrumDouble parametersPM spectrumQ(W 2X)= 222p(Hyp),T)p(B,)=exp(-2o)(8)where X may be regarded as the long-termdistribution 0hydrodynamic force whoseprobability level is equal to Q，p(H(y3),Tz)the sea state encounter probability of structure inservice life, p(Bk ) the probability of occurrenceof wave-direction.Fig. 1 The calculaion modelTable 1 The principal particulars of the artificial reef3.2 Computational resultsParticularsModelThe computational results are obtained for theartificial reef in shallow water by the hydrodynamicHeight(D )(m)2.00theory. And the trends in the hydrodynamic forceresponses to the water-depth variation are1.00Radius( R )(m)illustrated.In the Figs.2-5, the non-dimensional operatorsRadius of longitude component (r )(m)0.05for the hydrodynamic force is defined asFx100f=- = nDP , where 5。is wave amplitude, 5。Radius of ltitude component (r2 )(m)pgDR5。is 4.6 m in the present work.Figure 2 shows the changes of transfer3. ANALYSIS OF THE RESULTSfun |中国煤化工- force acting on theartind flow with the3.1 Calculation model and calculation casesdeHCNMH Gre 3 indicates theThe object studied in the article is an artificialchanges of transfer functions of the wave force with375the decrease of water-depth. Figure 4 plots theshallow water. But the wave-frequency hardlyfigures of transfer functions of the hydrodynamicaffcts the amplitudes of the hydrodynamic forceforce with wave-direction angle variation. Figure 5when the wave-direction angle is 0° or 180°.gives the changes of transfer functions of thehydrodynamic forceagainst wave-frequencyvariation.4F12TIDFig.4 Transfer functions of hydrodynamic force at variouswave-dirction angle十HID2-3+ H/D=7“4040 50 100 150 200b/Fig.5 Transfer functions of hydrodynamic force at variousFig.2 Transfer functions of hydrodynamic force at variouswave-frequencywater-depthThe amplitudes of the hydrodynamic forceincrease with the decrease of water-depth fordifferent wave -direction angle in shallow water, butthe peak values appear when the wave-direction is90°. In addition, in the ultra-shallow water thehydrodynamic force increase very evidently withthe decrease of water-depth, the values ofhydrodynamic force is 3 times larger when 5=182 16than those of deep water. The change trends that theamplitudes of the wave force increases with thedecrease of water-depth show a good agreementwith the hydrodynamic force.士3.3 Results of long term predictionFang et al.14.5 carried out long-termprediction of the hydrodynamic force of theartificial reef according to the scatter diagram of thenorthwest Pacific Ocean area.Figure 6 shows the long-term prediction curvesof the hydrodynamic force acting on the artificialreef under wave and flow with the decrease ofFig.3 Transfer functions of wave force at various water depthwate中国煤化工re 7 shows thelongthe wave forceactinCNMH G the decrease ofincrease with the decrease of wave-frequency in376water-depth.hydrodynamic force increase remarkably with thedecrease of water-depth in the ultra-shallow water.The change trends that the amplitudes of the waveforce increase with the decrease of water-depth16pshow a good agreement with the hydrodynamicforce.It appears from Figs.6-7 that the long-term nvalues of the hydrodynamic force acting on theartificial reef are about 10% larger than those indeep water. However, water depth hardly affectsthe long term prediction values of hydrodynamic0482 16TIDforce of the artificial reef when P =6. The changeD6°[trends that the amplitudes of the wave forceincrease with the decrease of water-depth have agood agreement with the hydrodynamic force.-84.CONCLUSIONSThe hydrodynamic force of the artificial reefincreases with the decrease of water-depth inT/Dshallow. Especially, in the ultra- shallow waterhydrodynamic force increases very evidently withFig.6 The long term change trends of hydrodynamic forcethe decrease of water-depth.with water-depth variationThe long-term values of the hydrodynamicforce on the artificial reef increase with the decreaseof the ratio of water-depth to reef height. In theultra-shallow water the increase is very evident withthe decrease of water-depth. The long-term valuesof the hydrodynamic force of the artificial reef areabout 10% larger than those in deep water. Butwater-depth hardly affects the long term prediction-25481216values of hydrodynamic force of the artificial reefwhen the ratio of water-depth to reef height is largerthan 6.0.Therefore it is crucial to take account into theeffects of water-depth on the hydrodynamic force ofthe artificial reef in the structure design of theartificial reef in shallow water.“2REFERENCES°[1] ZENG Yu-hong. Stability and mixing character forbuoyant jets in quiescent shallow water[J]. Journal ofFig.7 The long-term change trends of wave _force withHydrodynamics, Ser, B, 2005, 17(6): 776.water -depth variation[2FANG Ke-zhao, ZOU Zhi-li,WANG Yan. An explicithigh resolution scheme for nonlinear shallow waterequations[J]. The Ocean Engineering, 2005,19(3):349-364 (in Chinese).The computational results show that the[3] WANG Zhi-li,GENG Yan-fen, JIN Sheng. 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