Investigation on Rudder Hydrodynamics for 470 Class Yacht

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1 Proceedngs Investgaton on Rudder Hydrodynamcs for 470 Class Yacht She Ln 1,, Yong Ma, *, Wetao Zheng, Song Zhang 1,, Xaoshan Le 1, and Yangyng He 1, 1 Graduate School of Wuhan Sports Unversty, Wuhan , Chna; (S.L.); (S.Z.); (X.L.); (Y.H.) School of Sports Engneerng and Informaton Technology, Health Promoton and Key Laboratory of Sports Engneerng of General Admnstraton of Sport of Chna, Wuhan Sports Unversty, Wuhan , Chna; * Correspondence: Tel.: Presented at the 1th Conference of the Internatonal Sports Engneerng Assocaton, Brsbane, Queensland, Australa, 6 9 March 018. Publshed: February 018 Abstract: The rudder s an mportant appendage and used to adust the course and balance the lateral dsplacement n the salng regatta. RANSE (Reynolds-averaged Naver-Stokes Equatons) was used to smulate the vscous flow feld of the hull for 470 Class yacht based on CFD (Computatonal Flud Dynamcs). It s found that the stall angle was 30 degrees when the dsplacement s 80 kg and the boat speed s m/s to 8 m/s. If the speed ncreases, the wake flow of the hull wll nfluence the vald area of the rudder and span-chord rato and the stall angle wll be 35 degrees at the speed of 10 m/s. The lft-drag rato wll ncrease when the rudder angle s from 10 degrees to 5 degrees. The results would provde a theoretcal reference for athletes to manpulate the salboat. Keywords: 470 Class yacht; rudder; stall angle; numercal smulaton; hydrodynamcs 1. Introducton Class 470 yacht s one of the most mportant events at the Olympc Games, and salng competton s course n the complex sea condton of certan sea areas. Each game s subected to multple rounds of up wnd, down wnd and crosswnd processes [1]. Excellent athletes have tactcs when bng and tackng. The rudder plays an mportant role n adustng courses and balancng the hull n a competton. Research on rudder hydrodynamcs wth dfferent controllng methods would reveal the performance of the rudder equpment, promote coaches and athletes understandng of the equpment performance, whch can make the adustment of salng equpment n the competton more reasonable, make a better control of the hull, help athletes keep headng, choose a better route to complete the race, and reduce resstance durng the salng process. The scentfc manpulaton of salng s a guarantee of wnnng. Wth the mprovement of computer performance and numercal method, researches on the yacht proect based on the CFD had become popular. Paroln et al. (005) [] made a research on the Amerca s cup salng shp of dfferent states by solvng the Reynolds-averaged Naver-Stokes equatons, and the result of ths research made a contrbuton for the wnner of Alngh Team n the Amerca s cup. Mylonas et al. (01) [3] made a research on the hydrodynamc performance of the Amerca s cup salng shp, whch showed that smulated result of the Large Eddy Smulaton method and the Detached Eddy Smulaton method s smaller than the test results, t can more accurately smulate the near wall flow by usng the LES model. Vola et al. (014) [4] conducted a test of the optmal locaton of athletes on Aura 1:4 model n the towng tank. Gulo et al. (016) [5] used CFD Proceedngs 018,, 308; do: /proceedngs

2 Proceedngs 018,, 308 of 6 method to capture the hydrodynamc performance of a naval supply vessel wth a sngle rudder and a par of rudders. It was found that twn rudder can mprove stablty of the hull. Chna n recent years has wtnessed many researches n ths doman, Ma Yong et al. (007) [6,7] worked on wndsurfng and salng for the flud performance. Zheng Qnzhen et al. (015) [8] based on the total staton measured the 470 Class yacht and Laser yacht shape. Ln She et al. [9] used CFD to study the varaton law of hull resstance under dfferent ptch angle of Laser hull, and obtaned the best aspect angle of hull. Zhang Zhyong (016) [10] used CFD to study hydrodynamc performance of the dfferent centerboard angle of the 470 Class yacht, analysed the law of the centerboard acton and combned the salng competton. Summary foregn researchers manly focus on the Amerca s Cup keel-type galleon research, whle Chnese researchers gradually carred out the applcaton of ndvdual salng from 1980s of last century. There s stll room for research n 470 Class yacht rudder. In order to nvestgate the hydrodynamc performance of 470 Class yacht rudder. Ths research method based on CFD for vscous flow of 470 Class yacht rudder assembly smulaton s carred out through the analyss of hydrodynamc parameters, a clear effect of hull and rudder hydrodynamc performance, provded the bass for rudder maneuverng and the strategy am to explore around the standard n salng the actual game n the process, to provde theoretcal and scentfc gudance for coaches and athletes. Forthemore, the result preferred rudder manpulaton and hull performance.. Methods of Analyss.1. Numercal Model and Condtons Class 470 yacht s a two-person racng boat wth excellent drgbltes. The weght of the hull s 118 kg, and the weght of the two athletes ranges from110 kg to 180 kg. The tunnage s assumed to be 80 kg n ths study. The numercal model s the hull-rudder assembly, modelng n CAD and ANSYS The related parameters are shown n Table 1. Table 1. Parameters of Class 470 yacht. Hull (L) Beam (B) Span-Rudder (h) Chord-Length (b) Wetted Area-Rudder ( A R ) 4.7 m 1.89 m m 0.5 m m Ths paper smulated hull-rudder assembly of Class 470 yacht n dfferent rudder angles and wth dfferent speeds and the data accordng to the actual research of the natonal salng team. The veloctes of yacht are m/s, 4 m/s,6 m/s,8 m/s,10 m/s and the rudder angle range s from 0 to 40 degrees, and each nterval s 5 degrees... Research Methods..1. Governng Equatons Assumng that the flow feld around the salboat s ncompressble, ths study adopted RANS equatons and contnuty equatons as governng equatons. In Cartesan coordnates, the contnuty equaton and the momentum equaton can be expressed asfollows: Contnuty equaton: Momentum conservaton equaton: u 0, (1) x ' ' ( uu ) 1 p u u u u vt B, () x x x x x x

3 Proceedngs 018,, of 6 Where tme, u s average velocty and v t s the knetc vscosty of the flud,... Boundary Condtons ' u s fluctuaton velocty ( = 1,, 3), s the flud densty, t s B s body force and u u s turbulent nfluence. The computatonal doman and boundary condtons as shown n Fgure 1, the boundary condtons were velocty-nlet, the drecton was the negatve X drecton; pressure-outlet, whch s easy for teraton converges; left and rght boundares were symmetry planes; the bottom boundary was slp wall named movng wall; rudder wall was no slp wall. ' ' Fgure 1. Computatonal Doman and Boundary Condtons of Numercal model (The green plane s the free surface)...3. Mesh Generaton The rudder grds were meshed n ICEM CFD 15.0, and the computatonal doman of the hullrudder assembly was a hybrd grd. The hull-rudder assembly area was unstructured grd. As a result, t mproves the computatonal effcency of the numercal smulaton. Among them, the frst mesh sze and the gradent parameter were set up to capture the boundary layer n unstructured grds, so that the boundary layer satsfed the dstance of the frst neghbor grd, the frst mesh dstance y + = 60~100, and the total grd amount was about 5 mllon...4. Coordnate System and Dmensonless Expresson of Hydrodynamc Force The hull-rudder assembly XY secton coordnate system can be ndcated by Fgure. The bow was along the X postve drecton, and the Z drecton was the water depth drecton. The flow drecton was negatve X. The dstance between the center of the rudder and the center of gravty of the hull was.5 m. Fgure. Coordnate System of Shp-Rudder Assembly on XY Cross Secton. In ths paper, the hydrodynamc performance of rudder was manly studed. The dmensonless expressons of lft coffcent, drag coeffcent and moment coeffcent were as follows: Lft Coeffcent of Rudder:

4 Proceedngs 018,, of 6 Drag Coeffcent of Rudder: Moment Coeffcent of Rudder: C L Cl, 1 U AR C m d D, 1 U AR M, 1 U AR xe where L s lft force of rudder, D s the drag force of rudder, M s moment of turnng hull. (3) (4) (5) 3. Numercal Results and Analyss Ths paper used Reynolds-averaged Naver-Stokes Equatons to smulate the vscous flow feld of 470 Class yacht by ANSYS Consderng the mpact of free lqud used VOF method, ths paper made Turbulence modelled wth SST k- turbulence model. And the numercal smulaton of ths model was analysed through frst-order upwnd dfference scheme and QUICK scheme Results and Analyss of Rudder Lft Force Transform the rudder lft force nto dmensonless coeffcent, as shown n Fgure 3a, the relatonshp between lft coeffcent and rudder angle. The results shown that when the speed was at the range from m/s to 8 m/s, when rudder angle ranged from 0 degree to 30 degrees, the lft coeffcent ncreased, and 35 degrees to 40 degrees, the lft coeffcent decreased. It s found that the stall angle was 30 degrees. Wth the ncrease of speed, the stall angle was 35 degrees at the speed of 10 m/s. Fgure 3b shown the relatonshp between lft force and rudder angle. Numercal smulaton results shown that the faster the salboats, the greater dsparty the change-over plug of lft force wll have, whch has practcal applcaton n the actual competton for rudder control. (a) (b) Fgure 3. The relatonshp between the lft force and rudder angle. (a) Lft coeffcent; (b) Lft value. Fgure 4 shown the appearance of free surface when salboat was at a speed of 10 m/s, dfferent rudder angles at 5 degrees, 30 degrees, 35 degrees and 40 degrees, lower water level was found near the rudder, so a hgh speed of 10 m/s, the stern wake mpact would cause effectve areas of the rudder reduce, and the correspondng aspect rato decreased, the stall angle of rudder ncreased. As a result, the lft force of rudder came to maxmum at the rudder angle of 35 degrees. It can be found that the presence of the hull affected the stall angle of the rudder and t was related to the speed.

5 Proceedngs 018,, of 6 (a) (b) (c) (d) Fgure 4. The free surface appearance of shp-rudder assembly. (a d) ndcate rudder angles of 5 degrees, 30 degrees, 35 degrees and 40 degrees wth speed of 10 m/s. 3.. Results and Analyss of Moment of Turnng Hull The steerng of the hull s manly based on rudder angle, resultng n the asymmetry of the water on both sdes of the rudder. The core was the rudder s moment of turnng hull. Fgure 5a shown the relatonshp between moment of turnng hull coeffcent and rudder angle wth dfferent speeds. It could be seen that the turnng moment s consstent to the trend of lft force. Wth a speed of 10 m/s and a deflecton angle of 35 degrees, the turnng moment reached maxmum. (a) (b) Fgure 5. (a) s the relatonshp between moment of turnng hull and rudder angle; (b) s the relatonshp between rudder s lft-drag rato and angle Results and Analyss of Rudder s Lft-Drag Rato Fgure 5b shown the lft-drag rato of the rudder wth the change of the rudder angle. The lftdrag rato s an ndex parameter that reflects the hull rapdty. It was found that the lft-drag rato was somewhat dfferent at dfferent speeds. When the speed was m/s and 6 m/s, the maxmum of

6 Proceedngs 018,, of 6 the lft-drag rato shown at the rudder angle of 15 degrees; When the speed was 4 m/s, the maxmum of the lft-drag rato shown at the rudder angle of 0 degrees. It s found that the lft-drag rato of the rudder ncreased wth the ncrease of speed, and the rudder angle decreased conversely. In a word, the rudder angle of the hgh lft-drag rato came at 10 degrees to 5 degrees. 4. Conclusons Ths paper used the CFD to smulated hull-rudder assembly of Class 470 yacht wth dfferent rudder angles and dfferent speeds. The hydrodynamc performance through knetc parameters and flow phenomenon was analysed and the stall angle of hull-rudder was at 30 to 35 degrees. In the seres under the condton of hgh lft-drag rato of rudder angle ranged from 10 to 5 degrees. After the free surface was analysed, a concluson could be drawn that the hull had some effects on the rudder s stall angle, and wth the ncreased of speed, the effectve area of rudder the stern wake shock leaded to lower, and when the correspondng aspect rato decreases, the rudder stall angle ncreased. These knds of studes would provde theoretcal gudance to coaches, and help athletes get a breakthrough n tranng and matches. Acknowledgments: Ths study was partally supported by Natonal Natural Scence Foundaton of Chna (Grant No , ), the Fok Yng-Tong Educaton Foundaton for Young Teachers n the Hgher Educaton Insttutons of Chna (Grant No ), Hube Natural Scence Funds for Dstngushed Young Scholar (Grant No. 013CFA038), Outstandng Youth Scence and Technology Innovaton Team Foundaton of the Colleges and Unverstes of Hube Provnce (Grant No. T0130), the East Lake Scholars Sponsorshp Program of Wuhan Sports Unversty and Hube Domnant Characterstc Dscplne Group. Conflcts of Interest: The authors declare no conflct of nterest. References 1. Zheng, W.; L, Q.; Ma, Y.; Sh, Q. Event characterstcs and laws of wnnng for salng and wndsurfng. J. Wuhan Inst. Phys. Educ. 008, 6, Paroln, N.; Quarteron, A. Mathematcal Models and Numercal Smulatons for the Amerca s Cup. Comput. Methods Appl. Mech. Eng. 005, 194, Mylonas, D.; Sayer, P. The hydrodynamc flow around a yacht keel based on LES and DES. Ocean Eng. 01, 46, Vola, I.M.; Enlander, J.; Adamson, H. Trm effect on the resstance of salng plannng hulls. Ocean Eng. 014, 88, Dubboso, G.; Durante, D.; D Masco, A.; Brogla, R. Turnng ablty analyss of a fully appended twn screw vessel by CFD. Part II: Sngle vs. twn rudder confguraton. Ocean Eng. 016, 117, Ma, Y.; Zheng, W.T. Evaluaton of Hydrodynamc Performance of the Salboard. In Proceedngs of the 007 Internatonal Conference on Intellgent Pervasve Computer, Jeu Island, Korea, October 007; pp Ma, Y.; Tang, Y.H.; West, N.; Zhang, Z.Y.; Ln, S.J.; Zheng, Q.Z. Numercal Investgaton on Trmmng of a Sngle Sal n a Regatta. Sports Eng. 016, 19, Zheng, Q.Z.; Ma, Y.; Zhang, Z.Y.; Ln, S.J.; Tang, J.T.; Lu, L. Expermental Research of Salng Hull Shape Measurement n Olympc Games. J. Sports Adult Educ. 015, 31, Ln, S.J.; Ma, Y.; Zheng, Z.Y.; Zheng, Q.Z.; Tang, J.T. Investgaton on hull Hydrodynamcs wth dfferent trm angles for Laser Radal Class Yacht. J. Wuhan Inst. Phys. Educ. 016, 50, Zhang, Z.Y. Investgaton on Centerboard Hydrodynamcs for 470 Class Yacht. Master s Thess, Wuhan Sports Unversty, Wuhan, Chna, by the authors; Lcensee MDPI, Basel, Swtzerland. Ths artcle s an open access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton (CC BY) lcense (

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