A Practical Hull Form Design of Ferry Using Hybrid Scheme Method and Performing Experiment

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1 Journal of Shppng and Ocean Engneerng 5 (25) -8 do:.7265/ /25.. D DAVID PUBLISHING A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment Suandar Baso, Wardna Suwedy, Rosman, Lukman Bochary and And Ardant Department of Naval Archtecture, Faculty of Engneerng,Hasanuddn Unversty,Makassar 9245, Indonesa Abstract: Predcton of shp performance n prelmnary shp desgn s an mportant consderaton. It could guarantee shp n safe and comfort. However, many desgn works dd not nvolve smultaneously shp performances predctons n prelmnary desgn. Moreover, shp desgners sometmes modfed a shp form to obtan proper desgn wthout shp performance consderaton. Therefore, ths study concerns on predctons of total resstance and added wave resstance of a ferry usng a hybrd partcle-grd method and n ts motons response after modfyng bow and stern parts by conductng experment. Research results show total resstance and added wave resstance have a sgnfcant dfferent, refore, t would be an mportant consderaton n determnng shp powerng n prelmnary shp desgn. The non-dmensonal added wave resstance ncreases n ncreasng wave length from /L pp =.5 to. and t decreases after L/=.. In addton, t tends to decrease caused by ncreasng shp speed. The comparson of averaged heave and ptch ampltudes between basc forms after modfyng bow and stern parts s quet smlar. However, rollng ampltude of modfed form s sgnfcantly hgher comparng wth basc form. We conclude that a shp could be desgn n prelmnary desgn take nto account performances predctons by usng numercal method and expermental work. Keywords: Resstance,added wave resstance,heave moton, ptch moton, rollng moton.. Introducton A proper shp desgn s ownershp expectaton and t could contrbute some benefcal costs. In order to obtan a proper shp desgn, t s teratvely processed that reflects desgn methodology and strategy. However, ths would become dffcult to use approprate desgn tools and possble take longer tme. In 946, CFD (computatonal flud dynamcs)methods began replacng analytc equatons and expermental flud dynamcs n shp desgn. Over past several years, accordng to rapd advances n hardware and several computatonal technques, some researchers concern on developng CFD method take nto account all hydrodynamc behavors to become applcable and practcal tools. In naval archtecture and ocean engneerng feld, developed CFD methods have been done nvolved several computatonal technques [-5] developed The Correspondng author: Suandar Baso, Ph.D., research feld: naval archtecture. E-mal: andar_baso@yahoo.co.d. CFD method to apply to hull form desgn and sterns wth devces of complex forms. However, solutons are suffcent accurate. They stll requre expermental results. Recently, we have developed hybrd scheme whch s Euleran grd wth Lagrangan partcles [6] to combne advantages and to compensate for dsadvantages n both grd-based and partcle based methods. Ths developed method has been appled to many varous cases n naval archtecture and ocean engneerng felds. It was appled to shp propulson performance [7], shp seakeepng performace [8], shp motons wth hydroelastc effects [8], and nvestgaton of resstance reducton by mprovng stern part [9], etc. However, we need more quanttatve assessments n ntegratng desgn for prelmnary desgn step purpose. In addtons, shp hull form under stll water could be optmzed to obtaned proper desgn based on mnmum resstance and good motons by computng smultaneously durng prelmnary shp desgn process.

2 2 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment Therefore, n ths study, developed method has been extended ts usefulness n prelmnary desgn step combned wth conductng experment. 2. Computatonal Method In ths secton, numercal method, whch combnes Euleran scheme and Lagrangan partcles by couplng SPH (Smood Partcle Hydrodynamcs) method and CIP(Cubc-Interpolated Pseudo Partcle) method wth partcle, are descrbed concsely. Frst, CIP method wth partcles s ntroduced as a numercal scheme that combnes accuracy of Lagragan front trackng. Thereafter, SPH method s employed to calculate deformaton, stran, stresss of elastc body, and 3D moton. constructed by usng a Kernel functon n SPH method. 2.2 Governng Equatons for Flud Phase The governng equatons for flud phase consst of Naver-Stokes equaton and equaton of contnuty, I-phase densty functon I ( ) and ts advecton equaton. The equatons are expressed as follows: mass conservaton equaton, ncompressblee I 2. Arrangement of Grds and Partcles The developed Euleran scheme wth Lagrangan partcles has been llustrated as shown n. Ths scheme uses a staggered grd system and has two types of Lagrange partcles,.e. SPH partcles todescrbe sold and freee surface partcles to capture free surface accurately. Densty functon I defned on a grd node s corrected by usng densty functon P on free surface partcles wthn referenced area wth radus h. A smooth approxmaton of a densty functon can be where, u s velocty, μ coeffcent of flud vscosty, ρ flud densty, P pressure, F fs flud-structure nteracton, g acceleraton due to garvty, τ j SGS stress term, and I densty functon. To reduce model parameters, SGSS (Subgrd-Scale)stress term s solved by usng dynamc SGS model proposed by Germano.Moree detals are provded by Mutsuda and Yasuda []. 2.3 Advecton Step and Non-advecton Step The governng equatons are solved by usng splttng method whch s sutable for solvng a mult-phase flow wthout smearng a densty acrosss nterface between ar and water. The advecton step s calculated by CIP method proposed by Takewak and Yabe []. Then, type-m scheme of CIP method s employed by usng thrd-order accuracy n tme and space. On or hand, non-advecton step s solved by usng second-order fnte dfferencee method. Illustraton of proposed model ( I ndcates densty functon; Lagrangan partcles are located on Euleran grd). 2.4 Governng Equatons for Sold Phase The governng equatons for sold phase are

3 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment 3 contnuty and momentum equatons as follows: D u D t x Du Dt x j g j F fs (4) (5) j where, S s densty, u velocty, P - kk /3 poston vector of vector j components, stress tensor of sold phase, and F fs flud structure nteracton term. The stress j tensor s n Eq.(5) s gven by: j j j s - P S (6) j where, S s devatorc stress tensor, pressure solved by Posson seq. (9) as mentoned below. Our numercal model consders a large deformaton of an elastoplastc body. The sold body changes at every calculaton step by usng followng equaton: j ep j {d S } [ D ]{d } (7) ep where, D s elastoplastc matrx, d j tme ncrement of stran, and ds j tme ncrement of devatorc stress. To solve rotaton of sold phase durng a deformaton, Jaumann dervatve s used to ensure materal frame ndfference wth respect to rotaton as follow: j ds j j jk kj 2 S k k S dt 3 j (8) where, s stran rate tensor and spn tensor. The pressure wth specfed jump condtons s solved by Posson s equaton gven by: n P u (9) t where, denotes a physcal value after advecton step. The pressure for sold phase can be obtaned by ths equaton and be appled n solvng a sold deformaton. The flud structure nteracton F fs s solved by acceleraton obtaned from pressure on SPH partcles nterpolated usng pressure on grds solved by Posson s Eq. (2). In model, flud structure nteracton F fs n Eqs.(2) and (5) can be gven by followng equaton: P( rb ) Ffs( ra ) - mb aw( ra rb, h) () ( r ) ( r ) a b To keep computatonal effcency and stablty, tme ncrement n sold phase s approxmately / to /5 of that n flud phase. 2.5 Shp Motons A shp moton s solved by usng nformaton obtaned from SPH partcles because a shp hull conssts of SPH partcles capturng moton and deformaton of a shp. Therefore, 3D moton of a shp hull s represented by descrbng translaton and rotaton of center of gravty of a shp hull by usng followng equatons: 2 x t F b sk, sk, 2 m t I T F fs t () (2) (3) where, I s rotatonal angle, angular velocty, T torque, I nerta moment, and F fs flud structure nteracton. In addton, center of gravty of a shp hull can be obtaned by solvng nerta moment of SPH partcles, and ths s calculated by usng Baraff ory [2]. Therefore, coordnates of velocty of each SPH partcle n every tme step can be tracked by usng rotaton matrx and amount of angle rotaton of center of gravty. The quaternon s also used nstead of rotaton matrx R(t) n 3D to avod Gmbal lock phenomenon. 3. Expermental Method The motons test s performed n water tank whch belongs to Naval Archtecture Department, Hasanuddn Unversty. The purposes are to measure heave, ptch, and roll ampltudes n zero speed. The ferry model was made of wood and t s

4 4 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment sutable wth dmensonss of water tank. The body lnes plan of shp s shown n 2. Then, man dmensons of actual shp and model are presented n Table. The expermental set up was determned and desgned. The shp model s kept on constant and free poston wth stll water draft. The man dmensons of water tank are provded n Table 2. The water tank s equpped wth wave maker. Here, wave perode T s set to,2ms. The crcle of regular wave s stable greater than 6,ms. Therefore, expermental data s collected from 6,ms to 7,ms. The experment desgn and motons measurement are shown schematcally n Valdatons 4 showss comparson results of resstance of hghh speed ferry n calm water between computaton and experment. From fgure, tendency of resstance shows same. Then, ths shows overalll results of computaton are n good agreement wth expermental results. Fgs. 5 and 6 show comparson of fshng boat motons between numercal and expermental results. Ct*.8.7 experment computaton Table Lpp (m) B (m) H (m) T (m) V (knot) Shp body lnes plan. Man dmensons of actual shpand model. Actual shp Model Fn= V/ gl 4 Comparson of resstance between computaton and experment..5 Computaton Experment Z a / w.5 Table 2 The dmensons of water tank. Length (m) 8 Wdth (m) Heght (m) Depth (m) Heave transfer functon of shp / (H w *2/) Computaton Experment Experment desgn. 6 Ptch transfer functon of shp.

5 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment 5 Based on transfer functon of heave and ptch, motons were yelded maxmum value when =. Therefore, numercal results show n good agreement wth expermental results. Bow part Stern part 5. Results and Dscussons 5. Resstance and Added Wave Resstance Usng Numercal Method The computatonal condtons were set where grd sze s normalzed by length between perpendculars (L pp ).25-.5L pp and radus of free surface partcle s.25-.5l pp. Then, radus of SPH partcle s.25l pp. In model, ferry s represented by a large number of SPH partcles traced by partcle based method as shown n 7. For wave condtons, ncdent regular wave heght s set toh w /L pp =.. The wave length s ranged from /L pp =.5 to 2.. In addtons, speed s set n maxmum Fn=.29. Shp resstance and added wave resstance have been normalzed. Non-dmensonal resstance s defned by water densty, speed V, and wetted surface area S. 8 shows total resstance of ferry. The total resstance conssts of both frctonal resstance and pressure resstance. The frctonal resstance s calculated usng densty functon consderng a water lne and coeffcent of resstance for flat plate turbulent boundary layer based on Schoenherr formula. The tendency of total resstance from Fr=.2 to.7 decreasesand n ncreases untl ncreases untl Fn =.29. Ths resstance tendency s same wth our prevous results [7] where t had been valdated wth expermental result. 9 shows non-dmensonal added wave resstance n wave heght H w /L pp =. and Fr=.29. The nondmensonal added wave resstance R/(g(H w /2) 2 B 2 /L) s normalzed by wave heght H w, shp length L and shp wdth B. Usng ths method, added wave resstance s obtaned from computaton resultsbetween resstancen calm waterand that n 7 The ferry model represented by a number of SPH partcle. R* Fr 8 The total resstance of ferry. Added Wave Resstance ( R/g(H w /2) 2 B 2 /L) L/ 9 The added wave resstance of ferryn H w /L pp =.. regular wave. The non-dmensonal addedwave resstance decrease n ncreasng shp speed. The non-dmensonal added wave resstance ncreases n ncreasng wave length /L pp =.5 to. n Fr=.29 and t n decreases after /L pp =.. In addton, our method was appled also to that ferry wth waveheght H w /L pp =.8, where, ths means extreme condton. The added wave resstance s hgher than wave heght H w /L pp =..

6 6 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment The numercal method was n appled to resstance of ferry after modfcaton ts hull under stll water. Bow and stern parts weree only consdered to be modfed smultaneously. Fgs. and are show an example bow and stern part modfcaton. The bow-stern modfcatons are lmted by longtudnal centre buoyancy LCB n range -3% to +3% of amdshp to avod trm condtons. Ths means also that ferry volume s kept constant eventhought t s after modfcaton. The modfcaton of bow and stern sectons was done by tral and error where movement of buoyancy pont n range -3% to +3% whch has been explaned prevously. Therefore, modfcaton forms were resulted sevenforms; M, M2, M3, M4, M5, M6 and M7, respectvely. 2 shows resstance reducton each modfed form. Based on 2, M form has hgher resstance reducton around 5.7% compared wth or modfcatons. The dsplacement of LCB pont s about -2.9% from amdshp. Ths means that modfcaton n bow part could reduce sgnfcantly resstance compared wth n stern part. Based on research result, ths s ndcated that modfcaton M can reduced more generaton of wave makng resstance through bow of M comparng wth ors and t also has slghtly better and fnest bow. The numercal method can be used n prelmnary desgn stage to predct shp resstancee and added wave resstance. In order to optmze shp hull form under stll water based on resstance and added wave resstance durng ntal desgn process, t could be useful as well. 5.2 Predcton on Shp Motons by Conductng Experment The seakeepng performance of a shp n prelmnary desgn process s sometmes neglected. It s an mportant consderaton to obtan proper desgn. Nowadays, re are some numercal methods avalable that could be used. To make more detal nterpretaton concernng on shp seakeepng per for mance and n develope our numercal method, we need more expermental results. Therefore, n secton 5.2 motons of ferry whch has hgher resstance (a). Bow secton enlargement y x (b). Stern secton y x Bow and stern sectonss area of ferry. Body lnes form amdshp to bow part both basc and modfcaton forms. 6 Resstance reducton (%) M M2 M3 M4 M5 M6 M7 Modfcaton Form 2 The resstance reducton of each modfed form.

7 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment 7 Heave ampltude (mm) Ptch ampltude (degree) Roll ampltude (degree) 5 6, 62, 64, 66, 68, 7, 5 2 Basc Modf 6, 62, 64, 66, 68, 7, Wave Perode (ms) 3 Tme hstory of heave, ptch, and roll ampltudes both basc andd modfcaton forms. reducton M are n predcted by conductng experment n order to nterpret shp seakeepng for prelmnary desgn purpose. The speed model was setto zero. The heave, ptch, and roll are consdered and ors are fxed. The ferry man dmensons have smlar wth prevous computatonal work. The or expermental parameters have been stated prevously nto expermental set-up sub-secton. In nterpretng motons, heave and ptch motons have been normalzed. Non-dmensonal heave s defned by H v /H w and n ptch and roll are defned by /(H w K), where,h v andare heave and ptch motons ampltude, respectvely, H w ncdent wave heght and K wave number. 3 shows tme hstores of heave, ptch, and roll ampltudes. Based on that fgure, average non-dmensonal heave ampltudes of basc form and modfcaton form are.44 and.4, respectvely. Moreover, averaged non-dmensonal ptch ampltudes of basc form and modfcaton form are.93 and.97, respectvely. They are seen closer both basc form and modfcaton form. However, average non-dmensonal roll ampltudes of basc form and modfcaton form are suffcent dfferent.5 and.38, respectvely. The heave moton for both forms s less than H v /H w =.. Also ptch moton for both form s/(h w K)=.. These means that shp forms have a good geometry even wave length /L s greater than 2.. However, roll moton s greater than /(H w K)=.. Ths moton s concern pont for that wave condton. 6. Conclusons The present study, hybrd Euleran scheme wth Lagrangan partcle method can be appled practcally to predct shp resstance and added wave resstance n prelmnary desgn stage. Moreover, t s useful also to optmze shp hull form under stll water based on resstance and added wave resstance. Based on modfcaton work, optmum resstance reducton of modfed form under stll water could be acheved approxmately 5.7%. The modfcaton n bow part could reduce sgnfcantly resstance compared wth n stern part. In addtons, heave, ptch, and roll motons have been predcted as well by conductng experment. The modfed form affects approxmately 9% on ncreasng quet small heave, ptch, and roll moton. Therefore, numercal method nvolved smultaneously wth expermental work s proper way n prelmnary desgn stage. Acknowledgments Ths research was funded by LP2M Hasanuddn Unversty wth contract No. 687/UN4-42/PL.9/24. The authors are sncerely grateful to Prof. Sudrman as Head of LP2M Hasanuddn Unversty. The author would lke to

8 8 A Practcal Hull Form Desgn of Ferry Usng Hybrd Scheme Method and Performng Experment extend my acknowledgments to Prof. Hdem Mutsuda who has always been sncere and helpful n makng understandng and supportng me, and to all authors for r help n completng research report and ths paper. References [] Zhu, M., Yoshda O., and Myata, H Verfcaton of VscousFlow-Feld Smulaton for Practcal Hull Forms by a Fnte Volume Method. InProceedngsof 6th Int Conf on Numercal Shp Hydrodynamcs, [2] Stern, F., Paterson, E.G., and Tahara, Y CFDSHIP-IOWA: Computatonal Flud Dynamcs Method for Surface-Shp Boundary Layers, Wakes, and Wave Felds.Issue 38 of IIHR report, Iowa Insttute of Hydraulc Research, College of Engneerng, Unversty of Iowa. [3] Sato, Y., Myata, H., and Sato, T CFD Smulaton of 3-Dmensonal Moton of a Shp n Waves: Applcaton to an Advancng Shp n Regular Headng Waves. J Mar Sc Technology 4: 8-6. [4] Hu, C., Faltnsen, O.M., and Kashwag, M D Numercal Smulaton of Freely Movng Floatng Bodyby CIPMethod. InProceedngsof 5th Int Offshore and Polar Eng Conf(ISOPE), 4: [5] Nshgak, M., Sato, K., and Ishkawa, S. 27. Shp Desgn Technology wth CFD-Improvement of Propulsve Performance. Mtsubsh Heavy Industres, Ltd. Techncal Revew, Vol. 44 No. 3 (Sep. 27). [6] Mutsuda, H., and Do, Y. 29. Numercal Smulaton of Dynamc Response of Structure Caused by Wave Impact Pressure Usng an Euleran Scheme wth Lagrangan Partcles. In Proceedngs of 28th Internatonal Conference on Ocean, Offshore and Arctc Engneerng, [7] Baso, S., Mutsuda, H., Kurhara, T., Kurokawa, T., Do, Y., and Sh, J. 2. An Euleran Scheme wth Lagrangan Partcles for Evaluaton of Seakeepng Performance of a Shp n Nonlnear Wave. Internatonal Journal of Offshore and Polar Engneerng2(2): 3-. [8] Baso, S., Mutsuda, H., Kawakam, K., Hashhra, K., and Do, Y. 2. Numercal Study on Nonlnear Hydroelastc and Hydrodynamc Effects on Floatng Body Usng Euleran Scheme wth Lagragan Partcles. In Proceedng of 2st Internatonal Socety Offshore and Polar Engneers Conference, 6-7. [9] Mutsuda, H., Ishda, A., Baso, S., and Do, Y. 23. Numercal Investgaton of Resstance Reducton of Fshng Boat by Improvng Stern Part. Advanced Shppng and Ocean Engneerng 2(3): [] Mutsuda, H., and Yasuda, T. 2. Numercal Smulaton of Turbulent Ar-Water Mxng Layer Wthn Surf-Zone. In Proceedngs of 27th Int Conf on Coastal Eng, [] Takewak, H., and Yabe, T Cubc-Interpolated Pseudo Partcle (CIP) Method Applcaton to Nonlnear or Mult-dmensonal Problems. Journal of Computatonal Physcs7: [2] Barraf, D An Introducton to Physcally Based Modelng: Rgd Body SmulatonI Unconstraned Rgd Body Dynamcs. SIGGRAPH 97 course note, D3.

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