Experimetal ad Numerical Ivestigatio o Parametric Roll of a Large Cotaier hip Chuhui Zhao *,1,, Yoghe Xie 1,, Huamig Wag 1,, Lili Li 1 1 chool of Naval Architecture ad Ocea Egieerig, Zhejiag Ocea Uiversity, Zhousha, Zhejiag 316, Chia Email:137167@qq.com Key Laboratory of Offshore Egieerig Techology of Zhejiag Provice, Zhousha, Zhejiag 316, Chia Abstract Parametric roll may cause serious safety issues of ships, particularly large cotaier ships. The Iteratioal Maritime Orgaizatio (IMO) has bee workig o developig the secod geeratio of the itact stability criteria, parametric roll as a kid of stability failure mode is causig icreasig cocer to academics. This paper focuses o the predictio of the occurrece of parametric roll ad the factors which ifluece it,a series of tests are coducted i a towig tak with varyig speed, wave height, wave frequecy, with ad without wave excitatio. I additio, the tred of the roll respose amplitude of the parametric roll is also discussed. Fially, the oliear 3-D Rakie pael method is used to predict the parametric roll i the head sea for a full-scale ship, the results of which agrees well with the experimetal results. Keywords - Parametric roll; Cotaier ship; Model experimet; Rakie pael I. INTRODUTION A variety of motios happe whe the ship is sailig i waves ad roll is the most dagerous ad commo motio [1-]. Whe parametric roll happes i head ad followig seas, the periodical chage of the GM causes the istataeous variatio of the wet area [7]. Roll agle icreases rapidly i a few periods, which may lead to damage ad great harm to the safety of the ship, its cargo ad crew. everal icidets occurred i the cotaier ship, it s proe to the pheomeo of parametric roll for the slim body ad the complicated hull form of the bow. Today, with the extesive use of cotaier shippig, how to improve the stability performace i waves ad miimize the risk of eterig i parametric roll resoace is causig icreasig cocer to academics. However, i order to icorporate parametric roll i ship desig ad its operatio, a deeper uderstadig of the pheomeo is required. The Iteratioal Maritime Orgaizatio (IMO) is workig o developig the secod geeratio of the itact stability criteria [9], parametric roll, broachig, dead ship, pure loss of stability ad the excessive acceleratio of five kids of stability failure mode as the future stability criterio specify the research object. Recetly, the IMO ad academics ted to use the hydrodyamic theory [16-19] to cosider the secod geeratio of the stability criteria, i order to improve the existig system itact stability criteria ad reassess of the stability rules. I order to be able to develop ad validate a umerical model, havig the access to experimetal data is of high importace. Therefore, it is expected to obtai reliable data o parametric roll hydrodyamic characteristics i the experimetal research program, which ca be compared with that of the umerical models. II. EXPERIMENT A 8TEU cotaier ship i scale 1:8 has bee tested i regular waves at the towig tak (legth width depth=18 7 3.) of Harbi Egieerig Uiversity (see Fig.(1)). The towig tak is equipped with a flap type wave-maker ad a wave height recorder o the other side. esors ad data acquisitio system are istalled o the towig carriage. The data acquisitio system has two heave-poles o it, the distace betwee them is 17.9mm, the bigger oe was located i the ceter of gravity, ad the other oe was i the ster of the model, they ca measure 6-DOF motio ad avoid the yaw pheomeo occur i experimet (see Fig.()). The model was ballasted to correct draft, with the mass uits located to obtai the required distributio for the roll ad pitch radii of gyratio, ad a DOI 1.13/IJT.a.17..1 1.1 IN: 173-8x olie, 173-831 prit
momet of iertia frame was used to measure ad set the pitch radius of gyratio. What s more, the model has bilge keels o it. The mai iformatio of the model is give i table I, while the ship geometry is preseted i Fig.(3). Fig.3 Body Pla of the hip I this study, the vessel is tested i regular waves with headig agle of 18 degree, ad the model speed is desiged accordig to the Froude umber F =,.1,.. r For the wave steepess w, which is the ratio betwee wave height ad wavelegth, is 1/, 1/3, 1/, 1/1. The roll atural period ca be obtaied from Eq. (1). Fig.1 The Towig Tak of Harbi Egieerig Uiversity T J J (1) Dh Here T is the atural period, J is the roll momet of iertia, J is the additioal roll momet of iertia, D is the displacemet, h is the metacetric height without takig the modificatio of the free surface ito 1 cosideratio. I a rough estimate, r xx B ad J is 3 Fig. Two Heave-Poles fixed o the Model of the Cotaiership TABLE I.MAIN INFORMATION OF THE HIP MODEL. Displacemet( ).8kg Breadth(B).m Legth( L ).m pp Draft(T).16m Logitudial ceter of gravity(lcg) 1.7% L pp Vertical positio of the ceter of gravity (VCG).m Pitch gyratio radius( K yy ). L pp m Metacetric height(gm).m Natural roll period( T ).s m about % J Fially, there are ratios betwee the ecouter period Te ad the roll atural period T, sayig T e T, for which the istability occurs more easily. Accordig to the priciple of resoace, T e T =.,.,.,.6. We ca obtai the ecouter frequecy e, the wave period ad the wavelegth form Eq. () V T cos e, e (1 ), T () g g e T is the wave period, is the wave circular frequecy, is the wavelegth, V is the speed, ad is 18 degree. A. Roll dampig The roll dampig is a key desig parameter for the avoidace of parametric roll. Noe of curret tate-of-the-art computatioal programs ca claim to calculate the roll dampig accurately for ay give vessel icludig all roll dampig devices. Assumig the ship do free rollig i still water with a DOI 1.13/IJT.a.17..1 1. IN: 173-8x olie, 173-831 prit
iitial roll agle, eergy dissipatio for water dampig. The roll agle chagig with time is a gradual atteuatio curve, is the amplitude of time, the half a period is, 1 1, the average amplitude of two adjacet samplig poits m ( 1 ), there is a liear relatioship betwee B( ) ad as the same case of ad m. Here, a ad b are the atteuatio coefficiets, A ad B are the dampig coefficiets. η(deg) 1 1 - Φ Φ Φ Φ +1 Dh 3Dh A a, B b (7) Where D is the displacemet of the model, ad h is the metacetric height, is the atural circular frequecy, is the dimesioless atteuatio derived from the least square method. v is the uit momet of iertia dampig coefficiet, ad is the uit square dampig coefficiet of the momet of iertia. 1 3 ( a bm), v a, b (8) T A B v, (9) I I I I The roll atteuatio curves with differet speeds i still water are show i Fig.(), with the results of the roll dampig show i table II. -1 Φ 1 6 8 1 1 m m a b B( ) A B b m B( ) B a m B( ) A Fig. Curve of Extictio (Up) ad the Relatioship betwee Atteuatio ad Dampig (Bottom) Eergy method is used here to obtai the relatioship betwee atteuatio coefficiets ad dampig coefficiet. Reductio of potetial eergy is equal to the dampig momet eergy cosumptio as follows: E Dhd Dh( Dh 1 1 1 W 1 ( A B ) d ) Dhd (3) () W E () 1 ( A Bm ) (6) Dh 3 DOI 1.13/IJT.a.17..1 1.3 IN: 173-8x olie, 173-831 prit
F =.1 1 - -1-1 1 3 6 7 t(s ) F r=. 1 - -1-1 1 1 3 t(s ) F = 1 8 6 - - -6-8 -1 6 8 t(s ) Fig. Roll Atteuatio Curve uder Differet peed i till-water TABLE II. ROLL DAMPING REULT IN DIFFERENT PEEDRoll. Froude umber Fr= Fr=.1 Fr=. The iitial roll agle 9.16 11.6 1. a 1.9E-.3E-.16 b 3.97E-3 3.1E-3 7.8E-3 Liear dampig coefficiet N1. 1..1 The square dampig coefficiet N.E- 3.9E- 9.E- Dimesioless atteuatio of the coefficiet liear dampig.33.7.7 Dimesioless atteuatio of the square dampig.3.3.6 coefficiet Dimesioless atteuatio of the equivalet liear coefficiet.38.6.18 B. Ifluece factors of parametric roll I this part, the aalysis of experimetal results mai take accout of the coditios for the occurrece of parametric roll, the iflueces of speed chage, wave parameters (wave period, wavelegth, wave height), ad the wave excitatio, which is also cosidered i this part. The experimetal results are very meaigful to the umerical simulatios i the future. DOI 1.13/IJT.a.17..1 1. IN: 173-8x olie, 173-831 prit
3 Te/T=. w=1/3 1 Te/T=. w=1/ 1-1 - - -3 1 3 6-1 1 3 6 1 Te/T=. w=1/ 1 Te/T=. w=1/3 1 - -1 - -1 - -1 1 1 3 1 3 6 Fig.6 Fr=.1, No Wave Excitatio, the Wave Legth-to-hip Ratio L is.78. Te/T=. w=1/ 1 1 Fig.8 Fr=, Wave Excitatio, the Wavelegth to -hip Ratio L is.7. 1 1 Te/T=. w=1/ - -1 - -1-1 -1-1 3 1 3 6 Te/T=. w=1/3 1 1 Te/T=. w=1/3 1 () - - -1-1 -1 1 3-1 1 3 6 7 Fig.7 Fr=., No Wave Excitatio, the Wave Legth-to-hip Ratio L is 1.. Fig.9 Fr=.1, Wave Excitatio, the Wavelegth -to-hip Ratio L is.91. DOI 1.13/IJT.a.17..1 1. IN: 173-8x olie, 173-831 prit
3 Te/T=. w=1/ 1 1 Te/T=. w=1/ 1-1 - - -3-1 - - -1 1 3 6 7 8-1 -1 1 3 6 7 Te/T=. w=1/ 3 Te/T=. w=1/3 3 1 1-1 -1 - -3 - - - -1 1 3 6 7 Fig.1 Fr=.1, No Wave Excitatio, the Wave Legth-to-hip Ratio L is.91. -3 1 3 6 Fig.11 Fr=., Wave Excitatio, the Wavelegth -to-hip Ratio L is.89. Whe the ratio betwee ecouter period ad the roll atural period T e T is., parametric roll occurs easily (see Fig.(6) ad Fig.(7)). As the wave height icreases, the time of the pheomeo gets shorter, ad the roll amplitude icreases rapidly. Uder the same wave coditio, there is o parametric roll at zero speed, eve though add wave excitatio to the model, roll motio fially decay. Whe the ratio betwee ecouter period ad the roll atural period is ot., it eeds a log time for the pheomeo to start. The, whe addig a wave excitatio, the parametric roll occurs. The iitial agle is preseted i the Figures which have a wave excitatio (see Fig.(8), Fig.(9) ad Fig.(11)). DOI 1.13/IJT.a.17..1 1.6 IN: 173-8x olie, 173-831 prit
TABLE III. ROLL EXCITATION INFLUENCE IN EXPERIMENT. Fr Te/T L w Roll excitatio Parametric roll(yes/no).1..91 1/ Yes.1..91 1/ NO.1..91 1/3 NO.1..66 1/3 Yes.1..66 1/ Yes.1..66 1/ NO.1.6.68 1/ Yes.1.6.68 1/3 NO...89 1/ NO...89 1/3 Yes...89 1/ Yes.. 1.1 1/ NO.. 1.1 1/3 NO.. 1.1 1/ Yes..38 1/ NO..7 1/ NO Fig.1 erious Parametric Roll Pheomeo i Experimets The ifluece of wave excitatio ca be see i table III, the roll agle time history for each test i waves is examied ad placed ito oe of two categories: parametric roll; o parametric roll, after the iitial wave excitatio the roll motio decayed. The wave excitatio is made by usig a bamboo pole press the side of the model leadig a small roll agle (see the right of Fig.(1)). 1 1 - -1 w=1/ w=1/3-1 - 8 1 16 Fig.13 Fr=.1,Te/T=. DOI 1.13/IJT.a.17..1 1.7 IN: 173-8x olie, 173-831 prit
w=1/ w=1/3 the ed. 1 1 18 16 1 PP curve Curve fittig 1 1 8-6 -1-1 - 1 3 1 1 3 3 Fig.1 Fr=.,Te/T=. F=.1 F=. 1 PP curve Curve fittig 1 1-1 3 3 - -3 1 1 3 3 16 1 1 1 PP curve Curve fittig Fig.1 w =1/3, Te/T=. 8 6 1 Excitatio No excitatio 1 8 6-1 3 1 PP curve Curve fittig 6 8 1 1 1 1 Fig.16 Fial Roll Agle Ifluece of the Wave Excitatio Fig.(13) ad Fig.(1) show the iflueces of wave steepess. With the same speed, roll agle icreases with the icreasig of the wave height. It s cocered that the icrease of the wave height ca icrease the probability of occurrece of the parametric roll i a certai rage util reachig the threshold. Fig.(1) shows whe the wave steepess is idetical, low speed may lead to serious parametric roll more easily. However, i complicated sea coditio, wave excitatio is a importat issue for the parametric roll motio. Whatever, whether the wave excitatio will affect the result of the fial roll agle? It ca be observed from Fig.(16) that the roll agle coicidece i 6 Fig.17 Cubic Fit with the Peak Poit Curve As we have kow, whe the ship ecouter with parametric roll, the roll agle icrease quickly i a short time, but the tred of roll agle has ever bee discussed before. Pickig the peak poit of roll curve from Fig.(6) ad Fig.(7), a cubic polyomial fit has a good agreemet with the peak poit curve (see Fig. (17)). DOI 1.13/IJT.a.17..1 1.8 IN: 173-8x olie, 173-831 prit
III. THE VALIDATION OF NUMERICAL METHOD AND EXPERIMENTAL FOR THE FULL-CALE HIP A. Numerical ivestigatio of the oliear model i regular waves Based o the 3-D liear potetial flow theory, the defiite coditios of velocity potetial of the disturbace flow field aroud the ship with forward speed are established. Artificial umerical beach is itroduced to absorb disturbace waves, keepig them from reflectig back. The radiatio potetial ad the disturbace are solved by 3-D Rakie pael method. Takig the cosideratio of oliear factors due to the istataeous positio variatio of the body surface, the oliear ship motio equatio is established ad solved i time domai. The followig oliear effects are icluded with the oliear optio: Itegratio of Froude-Krylov ad hydrostatic pressure over exact wetted surface. Quadratic terms i Beroulli equatio are icluded. Exact treatmet of rotatio agles i iertia ad gravity terms. Quadratic roll dampig. A velocity potetialt ca be used to describe the water velocity based o the basic assumptios that the sea water is icompressible, iviscid ad the fluid motio is irrotatioal. Laplace equatio ca be derived: ga I e ga e kz kz si( kx t ) cos( kx t ) Fig.18 Hydrodyamics Mesh Model for the Cotaier hip 3 1 (1) T (1) Dyamic boudary coditio is: g, z (11) t Kiematic boudary coditio is:, z (1) t z where is the total disturbace free surface elevatio. The surface of the object B should satisfy the impeetrable coditio: V I (13) where is the outer ormal of, V is the velocity. The iitial coditios are: B, t, t (1) The icidece wave potetial ad wave height are defied as: -1 - -3 6 8 1 t (s ) Fig.19 Fr=.1,Te/T=. w =1/3 Here, A is the wave amplitude ad is the phase agle. The equatio of the motio is dv m F dt d d( r V ) I m M dt dt (16) where m is the mass of the ship, F ad M are the force ad momet of the ceter of gravity. I is the momet of iertia matrix of the ship. The force (momet) o the hull is: F Noliear T oliear RE oliear FK Liear HD F F F (17) oliear F where RE, F oliear FK, F liear HD are the restorig DOI 1.13/IJT.a.17..1 1.9 IN: 173-8x olie, 173-831 prit
force(momet), Froude-Krylov force (momet) ad the hydrodyamic force (momet). 3 3D-R Exp 3 1 1 1-1 - -3 3 3 1 1 6 8 1 t (s) Fig. Fr=.1,Te/T=. w =1/ Fig. Fr=.,Te/T=. w =1/ From Fig.(19) to Fig.() are the umerical results of the cotaier ship i head seas, ad experimet ad umerical results are preseted i Fig.(3) ad Fig.(),which show that the umerical results ad the experimetal results agree well. - -1-1 3 1-1 - 6 8 1 t (s) Fig.1 Fr=.,Te/T=. w =1/ -3 1 3 6 7 8 1 1 1 8 6 Fig. Fr=.,Te/T=. w =1/3 3D-R Exp IV. CONCLUION I this paper, experimetal ad umerical results of the pheomeo of parametric roll resoace i a towig tak for a 8TEU cotaier ship i regular waves, have bee preseted. The data of the experimet have a crucial effect o promotig the developmet of the umerical simulatio. Roll dampig is obtaied by fittig the extictio curve, which is a accurate way i studies. By aalyzig the effects that ifluece the parametric roll, it is cocluded that the icrease of wave height ca result i a icrease of the roll agle util reachig the threshold. Improvig the speed appropriately ca reduce the parametric roll momet. Wave excitatio is a importat issue to the parametric roll motio, but it will ot affect the fial roll agle. I additio, the tred of the roll agle is oted that a cubic polyomial fit has a good agreemet with the roll peak poit curve. The 3-D Rakie pael method for the regular wave i head seas has a high agreemet with the experimet. Cosiderig the oliear factors, the method ca predict the roll agle durig the desig phase ad has further evidece of its referece value. CONFLICT OF INTERET The authors cofirm that this article cotet has o coflicts of iterest. 3 3 Fig.3 Fr=.1,Te/T=. w =1/3 ACKNOWLEDGMENT This work was supported by Zhejiag Provicial Natural ciece Foudatio of Chia uder Grat DOI 1.13/IJT.a.17..1 1.1 IN: 173-8x olie, 173-831 prit
No.LY1E93, No.LY16E9, No. LQ1F3 7, No. LZ1E91, ad the Natioal Natural ciece Foudatio of Chia (17678),ciece Research Program of ciece Techology Departmet of Zhejiag Provice (1C313), ciece Research Program of Zhousha (1C13). umerical aalysis of parametric roll, Ocea Egieerig. Volume 67, Pages 1-1, 1 July 13. [19] Qua u, Jiaju Che, Xiaoxue Li, Hogliag Pa. Parametric tudy of Edge Crack of ilico teel trip i Cold Rollig based o a hear Modified GTN Damage Model, Procedia Materials ciece. Volume 3, Pages 163-1637, 1. REFERENCE [1] Nayfeh. A.H. et al. Noliear couplig of pitch ad roll modes i ship motios, Jour. Hydro. No.(1973). [] N.E. achez ad Nayfeh. A.H. Noliear rollig motios of ships i logitudial waves, Iteratioal shipbuildig progress. 37(11): 7~7, 199. [3] Yoshiho Ikeda, Abdul Muif, Toru Katayama ad Fujiwara. Large parametric rollig of a large passeger ship i beam seas ad role of bilge keel i its restrait, Proceedig of 8th Iteratioal hip tability Workshop-Istabul Techical Uiversity, Iatabul, Turkey 6-7 October. [] Jiabo Hua ad Wei-Hui Wag. Roll motio of a RORO-HIP i irregular followig waves, Joual of Marie ciece ad Techology, Vol.9,No.1, pp.38-(1). []. Ribeiro e ilva, T.A. atos ad C. Guedes oares. Parametrically excited roll i regular ad irregular head seas, It. hipbuild.progr..o.1, pp.9-6,. [6] Gabriele Bulia, Alberto Fracescutto ad Claudio Lugi. O the oliear modelig og parametric rollig i regular ad irregular waves, It. hipbuild. Progr.,1,o./3, pp. 173-3,. [7] Gabriele Bulia, Noliear parametric rollig i regular waves-a geeral procedure for the aalytical approximatio of the GZ curve ad its use i time domai simulatio, Ocea Egieerig 3, 39-33,. [8] Ciha Emre Uzuoglu, Numerical ad Experimetal tudy of Parametric Rollig of a Cotaier hip i Waves, Uiversidade Técica de Lisboa.Thesis for obtaiig the degree of Master. July 11. [9] Fial Report ad Recommedatios to the 6th ITTC. The pecialist Committee o tability i Waves. Proceedigs of 6th ITTC-Volume II. [1] Frace,W.L.,Levadou,M.,Treakle,T.W.et al. A ivestigatio of head-sea parametric rollig ad its ifluece o cotaier lashig systems., Marie techology. (1):1-19, 3. [11] Japa. Developmet of ew geeratio itact stability criteria. LF /INF.. 3 October 9. [1] Japa ad the Uited tates. Developmet of ew geeratio itact stability criteria, LF 3/3/8. 19 November 1. [13] Japa. Developmet of secod geeratio itact stability criteria. LF/INF.1. 11 November 11. [1] wede. ample calculatios o the Level Vulerability criteria for parametric roll. LF 3/INF.8. November 1. [1] Naoya Umeda, Hirotada Hashimoto, Izumi Tsukamoto. Estimatio of Parametric Roll i Radom eaways, Parametric Resoace i Dyamical ystems. pp -9. 16 November 11. [16] Marilea Greco, Claudio Lugi, Odd Magus Faltise. Ca the water o deck ifluece the parametric roll of a FPO? A umerical ad experimetal ivestigatio, "Europea Joural of Mechaics - B/Fluids, Volume 7,Pages 188-1, eptember October 1, [17]. Ribeiro e ilva, C. Guedes oares. Predictio of parametric rollig i waves with a time domai o-liear strip theory model, Ocea egieerig. Volume 7, Pages 3 69, 1 November 13. [18] Dog-Mi Park, Yog-hwa Kim, Kag-Hyu og. esitivity i DOI 1.13/IJT.a.17..1 1.11 IN: 173-8x olie, 173-831 prit