Fluid-structure interaction analysis of deformation of sail of 30-foot yacht

Transcription

1 csnak, 2013 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 Fluid-structure interction nlysis of deformtion of sil of 30-foot ycht Ser Bk, Jehoon Yoo nd Chng Yong Song Dept. of Ocen Engineering, Mokpo Ntionl University, Jeollnmdo, Kore ABSTRACT: Most ycht sils re mde of thin fbric, nd they hve cmbered shpe to generte lift force; however, their shpe cn be esily deformed by wind pressure. Deformtion of the sil shpe chnges the flow chrcteristics over the sil, which in turn further deforms the sil shpe. Therefore, fluid-structure interction (FSI) nlysis is pplied for the precise evlution or optimiztion of the sil design. In this study, fluid flow nlyses re performed for the min sil of 30-foot ycht, nd the results re pplied to loding conditions for structurl nlyses. By pplying the supporting forces from the rig, such s the mst nd boom-end outhul, s boundry conditions for structurl nlysis, the deformed sil shpe is identified. Both the flow nlyses nd the structurl nlyses re itertively crried out for the deformed sil shpe. A comprison of the flow chrcteristics nd surfce pressures over the deformed sil shpe with those over the initil shpe shows tht considerble difference exists between the two nd tht FSI nlysis is suitble for ppliction to sil design. KEY WORDS: Ycht; Sil; FSI; Computtionl fluid dynmics (CFD); Structurl nlysis; Cmber deformtion. INTRODUCTION The performnce of siling ycht depends on the blnce between the hydro- nd the erodynmic forces cting on the hull nd the sil. Numerous previous studies hve focused on sil optimiztion, becuse the sil directly ffects the propulsion performnce. Most of these studies minly focused on the bsic geometry of the sil, including the cmber shpe nd sil rrngement, in order to improve the lift, lift-to-drg rtio, effective ngle of ttck, nd interctions between sils. Most of ycht sils re mde of thin fbric, so it cn be esily deformed by wind pressure in vrious forms such s cmber chnging, wrinkling, stretching, shivering nd fluttering. The deformtion of the sil shpe cuses chnges in the forces nd moments cting on the sil, which in turn cuses thrust reductions nd unintended turning forces clled s wether helm. In this light, it is necessry to focus on sil deformtion. Recently, Trimrchi et l. (2009) pplied the finite element method (FEM) to clculte the sil deformtion nd the boundry element method (BEM) to mesure the surrounding flow. Lee et l. (2011) implemented fluid-structure interction (FSI) nlysis using grid deformtion technique to determine the deformtion of the two-dimensionl cross-section of 30-foot ycht sil. As mentioned bove, the fbrics used to mke sils re very thin nd flexible; therefore, even though their initil shpe is quickly restored by n elstic effect, they cn deform considerbly compred to the initil shpe. In this light, it is resonble to clrify their deformtion behvior using nonliner nlysis. Bk et l. (2013) investigted the nonliner behvior of sil by pplying FSI nlysis to the deformtion of simple-shped sil mde of thin fbric. Specificlly, the interction between erodynmics nd finite element nlysis ws studied by one-wy FSI for fbric sil, with the supporting forces generted by the mst, boom, nd rigs pplied s the boundry conditions for structurl nlysis. Corresponding uthor: Jehoon Yoo e-mil: yoojehoon@mokpo.c.kr

2 264 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 In the present study, FSI nlysis of the min sil of 30-foot ycht is crried out. The finite volume method (FVM) is used to clculte the fluid force tht ffects the sil deformtion. In structurl deformtion nlysis by FEM, fixed boundry conditions re pplied to define the supporting force generted by the mst nd boom-end outhul. Nonliner structurl nlyses re itertively crried out until the deformtion is converged. The deformed sil shpe is compred with the initil shpe with regrd to the dynmic pressure on the sil surfce, lift nd drg force, nd loction of center of effort (CE). The effect of the deformed sil on the erodynmic chrcteristics is lso evluted. NUMERICAL ANALYSIS TECHNIQUE FSI method FSI nlysis methods cn be clssified s direct-coupled FSI, one-wy FSI, nd two-wy FSI. Direct-coupled FSI is n nlyticl method in which the flow nd structurl nlyses re simultneously coupled. In one-wy FSI, the result of flow nlysis is pplied to the loding condition of the structurl nlysis in which the interction t the boundry is performed only once nd interctive loding clcultions re not crried out. The two-wy FSI method requires repetitive clcultion s the deformtion of the shpe lrgely depends on the fluid force nd the structurl deformtion ffects the flow gin. This study uses prtil two-wy FSI method, s shown in Fig. 1.The deformtion of the shpe by the fluid force is identified only for the initil geometry but is not clculted itertively. The fluid force is clculted by CFX, commercil CFD code, nd the grid system for CFD clcultion is generted using ICEM-CFD code (ANSYS Inc., 2009). In FSI nlysis, the structurl deformtion is clculted by pplying the fluid forces s the distributed lods for structurl nlysis. CFX clcultes the fluid forces t ech nodl point, nd FEM-bsed LS-DYNA requires the loding force t center of ech elements. Generlly, the integrl method is used to convert the vlues on nodes to n element; however, this pproch is not efficient for model with lrge number of elements. Therefore, the Workbench progrm of ANSYS, which cn be used to perform FSI nlysis by integrting CFX nd LS-DYNA, is used in this study. The sttic structure module in Workbench cn be used for finite element modeling s well s structurl nlysis. This module is used to clculte the structurl deformtion by pplying the pressure vlue, which is clculted using CFX t node, s the distributed lod for the sttic structure module. However, the sttic structurl module cn only be pplied to liner nlysis for smll deformtion. For nonliner nlysis of the lrge deformtion of thin fbric bsed on finite element theory, nonliner FEM code such s LS-DYNA is required. In this study, the pressure lods for structurl nlysis re generted using Workbench, wherein both finite element modeling nd fluid force conversion re crried out. The FSI nlysis of sil deformtion is performed using LS-DYNA. Fig. 1 Procedure of prtil two-wy FSI nlysis. Governing equtions for flow nlysis In this study, turbulent flows round the sil re simulted using CFX by solving the three-dimensionl Nvier Stokes Eq. (2) using the continuity Eq. (1).

3 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~ ( ρ ) ( ρ ) ( ρu ) x i i = 0 Ui Ui P Ui U i + U j = + μ + t xj xi xi xi xi (1) (2) where Ui is the fluctuting velocity of turbulent flow; ρ, the fluid density; μ, the fluid viscosity; nd P, the sttic pressure. Eq. (3) expresses the temporl chnge in the velocity of turbulence U i in terms of the sum of the time-verged velocity U nd fluctution component of the velocity u. i i Ui = Ui+ ui (3) To simplify these complicted expressions, the Nvier Stokes eqution is integrted with time to obtin the time-verged Reynolds-verged Nvier Stokes (RANS) eqution: ( ρ i) ( ρ i) U U P Ui U i + U j = + μ + ρuu i j t xj xi x i xj x i (4) CFX is bsed on FVM, which hs been dopted for the numericl simultion. The governing equtions for viscous flow include the continuity eqution, three momentum equtions, volume frction, nd turbulence equtions. In ddition, the k-ω sher-stress-trnsport (SST) model is dopted, becuse it is designed to give highly ccurte predictions of the onset nd the mount of flow seprtion under dverse pressure grdients by the inclusion of trnsport effects into the formultion of the eddy-viscosity. For the inclusion of the current effect lter on, the k-ω SST model is expected to ccurtely simulte flow seprtion round the sil with reltively low computtionl cost compred to higher-order turbulence models (Menter, 1994). Nonliner structurl nlysis for sil Sil cloth cn be clssified s shell or membrne with lminted composite structure tht shows some distinctive chrcteristics such s nisotropy of multiple lmintions. The sil deformtion cn become geometriclly lrge owing to the thin thickness, elsticity, nd externl forces. Anlysis of the lrge deformtion of n nisotropic membrne requires nonliner FEM. Furthermore, sil shows distinctive structurl behvior, nmely, wrinkling, tht ffects the distribution of tension force on the sil surfce; this my led to chnge in the deformtion chrcteristics of the sil (Heppel, 2002). To more relisticlly describe the sil deformtion behvior, Hughes nd Crnoy (1983), which explins the finite strin nd the thinning behvior, is pplied. The formultion for degenerte shell element is s follows: N ( ξηζ,, ) ( ξηζ,, ) x = N x (5) ( ξηζ,, ) ( 1+ ξ ξ)( 1+ η η)( 1+ ζζ) = (6) 8 ( ξ, η, ζ ) ( ξη, ) ( ξηζ,, ) x = x + X (7) where is n rbitrry point in the element, (ξ, η, ζ ) re the prmetric coordintes, x re the globl nodl coordintes of node, nd N re the element shpe functions evluted t node. The mpping of the bi-unit cube into the shell ele-

4 266 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 ment is seprted into two prts, where x denotes position vector to point on the reference surfce of the shell nd X is position vector bsed t point x on the reference surfce tht defines the fiber direction through tht point. In the context of kinemtics, the sme prmetric representtions used to describe the geometry of the shell element, reference surfce, nd fiber vector interpoltion re used to interpolte the shell element displcement, n iso-prmetric representtion. Agin, the displcements re seprted into the reference surfce displcements nd rottions ssocited with the fiber direction. ( ξ, η, ζ ) ( ξη, ) ( ξηζ,, ) u = u + U (8) ( ξη, ) ( ξη, ) u = N u (9) ( ξ, ηζ, ) ( ξη, ) ( ζ) U = N U (10) ( ζ) ( ζ) ˆ U = z U (11) where uis the displcement of generic point; u, the displcement of point on the reference surfce; nd U, the fiber displcement rottions. The motion of the fibers cn be interpreted s either displcements or rottions. For shell element with four nodes, the known quntities will be the displcements of the reference surfce u obtined from the trnsltionl equtions of motion nd some rottionl quntities t ech node obtined from the rottionl equtions of motion. To complete the kinemtics, reltion between the nodl rottions nd fiber displcements U is needed. At ech node, unique locl Crtesin coordinte system is constructed for use s reference frme for the rottion increments (Hllquist et l., 1985; Hughes nd Liu, 1981; Hughes nd Liu, 1981b). FLOW ANALYSIS FOR A SAIL In this study, numericl nlysis is crried out on the min sil of 30-foot sloop ycht, the KORDY30 (Yoo et l., 2005). The cmber shpe of the sil is expressed by zero-thickness wing section with the NACA = 0.8 men-line (Abbott nd Doenhoff, 1949), which is known to be similr to modern sil. Lee et l. (2006), Yoo nd Kim (2006), Kim et l. (2011), nd Kim et l. (2012) hve previously crried out numericl nd experimentl studies for this sil system. The initil shpe of the min sil is defined s shown in Fig. 2 nd Tble 1. Anlysis conditions nd ssumptions CFD nlyses for the min sil re crried out under the following ssumptions nd conditions: (1) Both the mst nd the boom re considered s rigid structures tht re not deformed. (2) The incident ngle of pprent wind is 20 with speed of 20 knots, nd the corresponding Reynolds number is (3) The governing equtions for viscous flow re RANS, nd the solutions re obtined using FVM. (4) For turbulent flow nlysis, n SST turbulent model bsed on k-ω nd the wll function method is employed. (5) 2,140,815 unstructured grids re used for CFD nlysis. Both the windwrd nd the leewrd sides of the sil surfce use 32,457 grids. Tble 1 Geometricl prmeters of the min sil. Loction from foot Foot 25% 50% 75% Top Height (mm) 0 3,000 6,000 9,000 11,900 Chord Length (mm) 4,000 3,000 2,000 1, Bseline Angle (deg.) Cmber Rtio (%) P = 11.9 m, E = 4.0 m, re of min sil A M = m 2, P : height of min sil, E : length of mil sil foot.

5 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~ Fig. 2 Schemtic view of the min sil geometry. Grid genertion The grid system for the CFD clcultion is generted by using the ICEM-CFD code, nd the C-type grid topology is used, which is tht pprent wind flow with ngle of ttck t sil fixed. Fig. 3 shows the grid system used for this clcultion; it consists of 2,140,815 unstructured grids nd 32,457 grids on both the windwrd nd the leewrd sides of the sil surfce. The size of the grid round the sil is kept smll to relize ccurte clcultions, s shown in Fig. 4. All forces nd flow simultions re computed t Reynolds number of ; this corresponds to wind speed of 20 knots nd min sil with reference length of 4.0 m t 25 C; furthermore, the distnce of the first djcent grid from the sil surfce is djusted to y+ = 100. Fig. 3 Grids nd topology for fluid nlysis. Fig. 4 Grids on sil surfce.

6 268 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 Numericl clcultion method In this study, the commercil softwre ANSYS-CFX, which is bsed on FVM, is dopted for the numericl simultion. The governing equtions for viscous flow include the continuity eqution nd RANS eqution. The computtionl conditions re n pprent wind speed of 20 knots nd stedy stte, s shown in Tble 2. The k-ω SST model is dopted for the boundry conditions in the numericl clcultion. The SST model ws designed to provide highly ccurte predictions of the mount of flow seprtion under dverse pressure grdients rther thn k-ε. Therefore, it is used for this clcultion becuse it is importnt to predict the seprtion generted in the sil. Tble 2 Computtionl conditions & method. Governing eqution Discretiztion of momentum trnsport eqution Turbulence model Wll function Advection term Diffusion term Incompressible RANS eqn. Element-bsed finite volume method k-ω sher stress trnsport (SST) Automtic ner-wll tretment High resolution scheme Centrl difference scheme Density kg/m 3 Reynolds number Apprent wind velocity 10.3 m/s (20 kts) Results of CFD clcultions on initil sil shpe The flow chrcteristics re reviewed vi the pressure distribution nd limiting stremlines on the min sil surfce. Fig. 5 shows the limiting stremlines nd the distribution of the dynmic pressure coefficient on the sil surfce, wherein flow seprtion is found round the sil leech in the leewrd side. The flow seprtion cn lso be detected by representing the field stremlines round the sil on the section of 25% sil height. The pressure vlues obtined on the initil sil surfce re pplied to the loding conditions for structurl nlysis. Fig. 5 Pressure distribution nd limiting stremlines on the initil sil.

7 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~ Fig. 6 Stremlines round the initil sil on the section of 25% sil height. Fig. 7 Stremlines round the initil sil on the three-dimensionl section of 25% sil height. STRUCTURAL ANALYSIS OF A SAIL Anlysis conditions nd ssumptions The structurl nlyses of sil re crried out bsed on the following ssumptions: (1) Kevlr 49 fbric (E. I. DuPont de Nemours nd Co., Inc.) is used to pproximte the mteril properties of ctul sil fbric, nd their vlues re shown in Tble 3. (2) 7,824 finite elements re used for the structurl nlysis, nd the pressure of the sil s clculted in the flow nlysis is considered s the loding condition. (3) All trnsltionl motions re constrined to describe the boundry conditions on the fixed support by the mst nd boomend outhul, s shown in Fig. 8. (4) The ctul sil is fixed by the mst on the sil luff edges, nd the sil foot, which is the end of the edge (sil clew) is supported by the tension force owing to the boom-end outhul. Tble 3 Mteril properties of Kevlr 49 fbric. Density kg/m 3 Elstic modulus 124 GP Poisson rtio 0.36 Thickness 0.34 mm

8 270 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 Fig. 8 Boundry conditions for structurl nlysis. Results of structurl nlysis LS-DYNA is generl-purpose nonliner explicit finite element code for nlyzing the lrge deformtion sttic nd dynmic response of structures. The min solution methodology is bsed on explicit time integrtion, nmely, constnt loding long the deformed sil surfce. Therefore, lrge structurl deformtion is required to verify the tidl convergent process, s shown in Fig. 10. Fig. 9 shows the deformtion of sil subjected to dynmic lods, nmely, dynmic pressures cused by flow. The mximum sil deformtion is 0.16 m in the cse tht the dynmic pressure chnges linerly over time. The figure lso shows tht n unsupported edge represents reltively lrge deformtion nd the vrition of deformtion becomes uniform with time. Fig. 9 Displcement contours of the sil deformtion ccording to time. Fig. 10 History of the sil deformtion t node with mximum displcement.

9 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~ The deformtion of node locted on the 25% section of the height of the sil is selected to review the convergence of this deformtion. Fig. 10 shows the time history of the displcement t node with mximum deformtion; it is found tht the difference in displcement is below m fter ~10 s, nd therefore, the convergence of the clcultion of the structurl deformtion cn be confirmed. The re of the deformed sil is compred with the re of the initil sil to verify tht the shpe of the cmber vries with the stretching of the sil fbric itself. Tble 4 shows tht the re of the deformed sil incresed by 0.001%. It is found tht the vrition of the sil re is negligibly smll nd the stretching of the fbric under wind pressure is not the min reson for cmber chnge. Tble 4 Comprison of surfce res of the initil nd the deformed sils. Initil Deformed Difference Sil Are (m 2 ) (0.001%) Fig. 11 shows the sectionl cmbers t ech height of the sil. Cmbers ner the sil luff re found to be deformed deeper t lower sections, nd the mximum drft moves to the leech t higher sections, which is lso clled sil twisting. At 25% of the height, the sil cmber ner the leech is closed to the windwrd side, which my be expected owing to the pressure chnge on the leewrd side of the sil. Fig. 11 Comprison of cmber lines of the initil nd the deformed sils. FLOW ANALYSIS FOR DEFORMED SAIL To identify the vrition of the erodynmic performnce of the deformed sil, the CFD clcultion is performed under the sme nlysis conditions s those for the initil sil. The flow chrcteristics, surfce pressure distribution, lift-drg forces, nd the chnge in CE re reviewed for the initil nd the deformed sils. Flow over the deformed sil The distribution of the dynmic pressure nd the limiting stremlines on the sil surfce re reviewed for the initil nd the deformed sils. Fig. 12 shows tht the rnge of positive pressure ner the luff is expnded on the windwrd side, which is why the cmbers ner the sil luff re deformed deeper t lower sections, s shown in Fig. 11. Fig. 14 shows tht the eddy section resulting from the flow seprtion generted round the leewrd side of the sil leech is incresed compred to tht in the initil sil, which cn lso be observed from the field stremlines in Figs. 6 nd 14. Consi-

10 272 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 dering the flow seprtion on the leewrd side recovers the surfce suction pressure, which is why the cmber line ner the leech moves to the windwrd side, s shown in the 25% section in Fig. 11. Fig. 12 Pressure distribution nd limiting stremlines on the initil nd the deformed sils (windwrd side). Fig. 13 Pressure distribution nd limiting stremlines on the initil nd the deformed sils (leewrd side). Fig. 14 Stremlines round the deformed sil on the two-dimensionl section of 25% sil height. Fig. 15 Stremlines round the deformed sil on the three-dimensionl section of 25% sil height.

11 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~ Surfce pressure nd forces Figs show the dynmic pressure distributions on the sil surfce for sections of 5%, 25%, 50%, nd 75% sil heights. Fig. 16, for section of 5% sil height, shows tht the negtive pressure on the suction side of the deformed sil ner its foot is incresed compred to the initil pressure in the rnge of x/c = nd reltively decresed in the rnge of x/c > 0.55, wherein the cmber lines re lso crossed s shown in Fig. 11. nd Fig. 19 shows tht the difference between the positive nd the negtive pressures is remrkbly reduced for section of 75% sil height. The effective ngle of ttck t the leech of the upper sil is considered to be reduced by the sil twist becuse of which the leech of the upper sil retrets. Eventully, the differentil between the positive pressure on the windwrd side nd the negtive pressure on the leewrd side is considered to reduce the lift force owing to the sil twist, s shown in Fig. 11. Fig. 16 Comprison of pressure distributions on the section of 5% sil height. Fig. 18 Comprison of pressure distributions on the section of 50% sil height. Fig. 17 Comprison of pressure distributions on the section of 25% sil height. Fig. 19 Comprison of pressure distributions on the section of 75% sil height. The coefficients of the lift nd drg forces re compred to study the chnges in the erodynmic performnce of the sil before nd fter deformtion. In the deformed sil, it is ssumed tht the lift force will increse becuse the cmber of the lower sil, which hs reltively lrge re, deepens. However, the clculted results show tht the drg force increse by ~4.9% nd

12 274 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~276 the lift force decreses by ~0.2%, nd therefore, the lift-drg rtio indicting the sil performnce decreses by ~4.9%. The results in this study conflict with those of Lee et l. (2011), who studied two-dimensionl sil by FSI nlysis nd showed tht the lift force increses with the chnge in cmber. This is becuse unlike the two-dimensionl sil section, the three-dimensionl sil genertes prtil stll by the seprtion flow on the leewrd side of the lower sil, nd the effective ngle of ttck is reduced by leech sgging on the upper sil. Therefore, the increse in the lift force decreses overll when compred with the increse in the lift force by the deepening cmber. Tble 5 Lift nd drg coefficients of the initil nd the deformed sils. Initil Deformed Difference C L % C D % C / C % L D Loction of CE When the sil is deformed, the CE loction moves nd the ycht loses blnce with the center of the lterl resistnce, the underwter hydrodynmic force, which results in some forces cting on the ycht. In prticulr, these forces cuse n unintended turning force clled s wether helm or thrust deduction. This study exmined the chnge in CE loction due to sil deformtion. As shown in Fig. 20 nd Tble 6, the CE loctions of the initil nd the deformed sils re compred bsed on the results of n empiricl method (Lrsson nd Elisson, 2000) in which the centroid of the lterl projected surfce is considered s the CE. The CE moves slightly stern nd downwrd, wheres the CEs vry slightly for the initil shpe nd the deformed sil. The results of CE movement cn be interpreted by both lrger lift force on the lower prt of the sil nd the retret of the cmber center. Tble 6 Comprison of the CE loctions. Initil Deformed Difference Centroid Longitudinl (stern) Verticl (downwrd) CE loction bsed on min sil tg, unit: mm Fig. 20 Comprison of CE loctions.

13 Int. J. Nvl Archit. Ocen Eng. (2013) 5:263~ CONCLUSION In this study, sil deformtion under wind pressure is identified by pplying the fluid force clculted by CFD to nonliner finite element nlysis. CFD nlysis is crried out itertively on the deformed sil shpe, nd the shpes of the initil nd the deformed sils re reviewed to determine the erodynmic chrcteristics. In structurl deformtion nlysis by FEM, fixed boundry conditions re pplied to define the supported force by the mst nd outhul, nd nonliner structurl nlyses re itertively crried out for the deformed sil shpe, which is compred to the shpe one in terms of the chrcteristics of the sil shpe. First, the re of the deformed sil is compred with tht of the initil sil to identify the vrition cuse in the cmber shpe by the stretching of the sil fbric itself. The vrition of the sil re is found to be negligibly smll, nd the stretching of the fbric under wind pressure is not the min reson for cmber chnge becuse the re of the deformed sil is incresed by 0.001% compred to the initil sil. Second, the sectionl cmber shpe of the deformed sil for ech height of the sil is compred with the initil shpe. The cmbers ner the sil luff re deformed deeper t lower sections, nd the mximum drft moves to the leech t higher sections, which is clled s sil twisting. Owing to these chnges in the sil cmber, the rnge of positive pressure ner the luff nd the eddy section resulting from the flow seprtion is expnded compred to the initil rnge, the drg coefficient increses by ~4.9%, nd the lift coefficient decreses by ~0.2%. These results conflict with those obtined for two-dimensionl sil by FSI nlysis. This is becuse the three-dimensionl sil genertes prtil stll by the seprtion flow on the leewrd side of the lower sil, unlike the two-dimensionl sil section, nd the effective ngle of ttck is reduced by leech sgging on the upper sil; therefore, the increse in lift force decreses overll. Furthermore, the CE loction moves slightly stern nd downwrd becuse of both lrger lift force on the lower prt of the sil nd the retret of the cmber center. As result, the deformtion nlysis of the three-dimensionl sil geometry using FSI indictes tht the sil shows complicted flow phenomen such s chnge in the effective ngle of ttck nd stlling cused by flow seprtion owing to the deformtion of the cmber shpe nd sil twisting. A comprison of the flow chrcteristics nd the lift nd drg forces of the deformed sil shpe with those of the initil one shows tht considerble difference exists between the two nd tht FSI nlysis is suitble for ppliction to sil design. ACKNOWLEDGMENT This reserch ws supported by Bsic Science Reserch Progrms through the Ntionl Reserch Foundtion of Kore (NRF) funded by the Ministry of Eduction (Grnt No nd 2012R1A1A ). It ws finncilly supported by the Ministry of Knowledge Economy (MKE) through project for fostering the convergence of industry nd cdemi, NT- IS Grnt No REFERENCES Abbott, I.H. nd Doenhoff, A.E.V., Theory of wing sections. Dover Publictions, New York. ANSYS Inc., ANSYS ICEM CFD 12.0 User Mnul. ANSYS Inc. Bk, S., Yoo, J. nd Song, C., Fluid-structure interction nlysis on the deformtion of simplified ycht sils. Journl of the Society of Nvl Architects of Kore, 50(1), pp Hllquist, J., Benson, D. nd Goudreu, G., Implementtion of modified Hughes-Liu shell into fully vectorized explicit finite element code. Proceedings of the Interntionl Symposium on Finite Element Methods for Nonliner Problems. University of Trondheim, Trondheim, Norwy. Heppel, P., Accurcy in sil simultion: Wrinkling nd growing fst sils. Proceedings of the High Performnce Ycht Design Conference. Aucklnd, New Zelnd. Hughes, T. nd Crnoy, E., Nonliner finite element shell formultion ccounting for lrge membrne strins. Computer Methods in Applied Mechnics nd Engineering, 39(1), pp Hughes, T. nd Liu, W., Nonliner finite element nlysis of shells: Prt I. three-dimensionl shells. Computer Methods in Applied Mechnics nd Engineering, 26(3), pp

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