Investigation on Hull Hydrodynamics with Different Draughts for 470 Class Yacht

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1 Proceedngs Investgaton on Hull Hydrodynamcs wth Dfferent Draughts for 470 Class Yacht Yong Ma 1, *, Shje Ln 1,2, Yangyng He 1, Xaoshan Le 1,2 and Song Zhang 1,2 1 School of Sports Engneerng and Informaton Technology, Key Laboratory of Sports Engneerng of General Admnstraton of Sport of Chna, Wuhan Sports Unversty, Wuhan , Chna; shjeln900819@foxmal.com (S.L.); yangynghe0915@foxmal.com (Y.H.); lexaoshan1010@126.com (X.L.); songzhang0830@foxmal.com (S.Z.) 2 Graduate School of Wuhan Sports Unversty, Wuhan , Chna * Correspondence: small_ma@163.com; Tel.: Presented at the 12th Conference of the Internatonal Sports Engneerng Assocaton, Brsbane, Queensland, Australa, March Publshed: 22 February 2018 Abstract: Class 470 yacht attracts more and more attenton at the World Champonshps. The hull hydrodynamcs s mportant for wnnng the games. Hull draughts nfluence shp maneuverablty, seakeepng, rapdty and stablty. Numercal smulaton by solvng RANS equatons s used to hull hydrodynamcs wth dfferent draughts for the 470 Class yacht. Turbulence model s (SST) k-ω. The results show that wave resstance, vscous pressure resstance, frcton resstance wth the Froude number s dfferent when the hull draught s dfferent. Accordng to the results about hull hydrodynamcs wth dfferent draughts and the aerodynamcs of the sal wng, the resstance performance of the hull s good when the hull draft for 470 Class yacht s wthn a relatvely reasonable zone. Ths study on resstance performance of the hull provdes a theoretcal reference for coaches to talent selecton of salng athletes, weght dstrbuton of athletes, estmate the salng route and maneuverablty of the salng boat. Keywords: CFD; yacht; hull; draughts; Froude number; wave resstance 1. Introducton The salng of class 470 s a double boat racng project whch follows the certan rules of the game wthn a certan zone of water racng. The class 470 yacht s gettng more and more attenton n the world champonshps and the Olympc Games. The key to wnnng the game s to master salng characterstcs, select the optmal route and optmze the selecton of athletes [1]. The depth of the hull draft has serous nfluence on maneuverablty of the salng, wave resstance of the salng, rapdty of the salng, stablty of the salng and dstrbuton of trm stress on the hull [2]. The depth of the hull draft has a sgnfcance of compettve strategy to the selecton and collocaton of athletes weght. Wth the mpressve promoton of the speed and capacty of computers, the contnuous mprovement of the numercal computaton method, the accuracy of makng a predcton about the hull hydrodynamc performance of the salng shp whch s based on the numercal computaton method s hgher and hgher [3 5]. Paroln et al. (2005) [1] made a research on the Amerca s cup salng shp of dfferent states by solvng the Reynolds-averaged Naver-Stokes (RANS) equatons and the result of ths research made a contrbuton for the ttle of alngh n the Amerca s cup. Mylonas et al. (2012) [6] made a research on the hydrodynamc performance of the Amerca s cup salng shp, whch showed that smulated result of the large eddy smulaton (LES) method and the detached eddy smulaton method s smaller than the test results, whch can more accurately smulate Proceedngs 2018, 2, 307; do: /proceedngs

2 Proceedngs 2018, 2, of 6 the near wall flow by usng the LES model. Vola et al. (2014) [2] conducted a test of the optmal locaton of athletes from the stern on the shp model of 1:4 by the draggng pool at Chna n recent years. At present, Chnese research projects about salng manly concentrate n the study of aerodynamc performance of sal wng [7], the study about the hull hydrodynamc performance of the salng hull has just started. Ths research conducted a study on the hull hydrodynamc performance of the class 470 yacht of dfferent depths of the hull draft based on computatonal flud dynamcs (CFD) methods, whch provdes a bass for salng athletes manpulatng the salng boat, the collocaton of athletes weght and selectng athletes and sports equpment. 2. Methods of Analyss 2.1. Numercal Model and Condtons The numercal model computed was the Olympc Class 470 yacht, whch amed to nvestgate the flow feld around the hull. The prncpal dmenson of the hull length s 4.7 m and the wdth s 1.68 m. The numercal model s obtaned by surveyng the competton yacht and drawng n CAD & ANSYS. Ths experment was modelled wth CFD usng a hexahedral grd bult wth ANSYS ICEM CFD (verson 15.0) and solved wth ANSYS Fluent (verson 15.0) [8]. The total hexahedral grd element number s more than 4 mllon. The grd around hull and free surface specal encrypton and the grd allowed 80 < y + < 200 on the hull sde, where the boundary layer s attached. Investgaton on hull hydrodynamcs wth sx dfferent draughts were performed when dsplacement s 230 kg, 240 kg, 250 kg, 260 kg, 270 kg, 280 kg for 470 Class yacht respectvely. The transent ncompressble RANS equatons for Newtonan fluds were solved wth a pressure based solver and a fnte volume approach s one of the man methods to calculate the lqud-phase flow. The control equaton based on contnuty equaton and RANS n ths study. The flow feld around the 470 Class yacht s ncompressble lqud. Contnuty equaton and momentum equaton n the Cartesan coordnate system s defne as follows: Contnuty equaton: u = 0 (1) x Momentum conservaton equaton: = + + B ' ' ( uu j) 1 p u uj ( uu j) + vt xj ρ x x j xj x xj (2) ' where u s average speed and u s fluctuaton velocty ( = 1,2,3), ρ s the flud densty, t s tme, v t s the knetc vscosty of the flud, B s body force and ' ' uu s turbulent nfluence Boundary Condtons The related boundary condtons are the key to smulate the flow feld around the 470 Class yacht accurately. In ths research, the type of nlet s the velocty-nlet that selected average speed of the Yacht (V = 6 m/s, Kn), the type of outlet s the pressure-outlet that converges rapdly, the hull wall type s the wall that shear condton s no slp [9] Soluton Setup The VOF method unte developed double model method to do nvestgaton on hull hydrodynamcs wth dfferent draughts for the 470 Class yacht. Turbulence was modelled wth the SST K-ω turbulence model. A SIMPLEC scheme was used to couple velocty and pressure. Second order accuracy dscretzaton algorthms were used n the transent nvestgaton because thrd order accuracy algorthms showed dffculty convergng. j

3 Proceedngs 2018, 2, of 6 3. Numercal Results and Analyss 3.1. Draught Resstance Coeffcents Changng wth the Froude Number ( ) Froude number s one of the mportant coeffcents of smlarty crteron when smulated wth the free surface lqud flow. The smulaton model of 1:1 real Olympc Class 470 yacht. and draft depth can be reference to the relatonshp between volume dsplacement defntons: Fr = 6 ( g ) s the dsplacement of dfferent drafts. Wth draft depth ncreases, reduces gradually. Whle s greater than 1 n the total 6 condtons wth dsplacement range from 230 kg to 280 kg and nerta force plays the leadng role. From Fgure 1, drag coeffcent ( ) and are the nonlnear relatonshp. At a constant speed, wth the decreases, namely the draft depth ncreases, hull resstance coeffcent frst decreases slghtly, then gradually ncreases and decreases at last. The mnmum resstance coeffcent occurs at = 2.43 and the maxmum resstance coeffcent happens at = When equpment s selected n the actual competton, from 230 kg to 280 kg. 240 kg dsplacement s the preference selecton from ths study. From the relatonshp between and, we can conclude that the smulaton calculaton results have a sgnfcance reference on choosng athletes and sports equpment. (3) 3.2. Resstance Analyss Fgure 1. Draught resstance coeffcents changng wth the Froude number. Hull resstance s the man factors nfluencng the salng shp speed, the hull sde force and are almost zero when shp sals on the postve drecton. The total resstance conssts of frctonal resstance, vscous pressure resstance and wave resstance. By consderng the free surface wave resstance combnng the developed double model method wthout wave resstance, rough estmate of the wave-makng resstance are extracted, as shown n Table 1. The 470 salng n nearly 12 knots, namely V = 6 m/s, wave resstance n total resstance components accounted for about 46%, vscous pressure resstance s slghtly small, but they should not be gnored. As shown n Fgure 2, wth the ncrease of the draft, decreases, pressure drag gradually becomes bgger, vscous pressure resstance has lttle change, wave resstance gradually

4 Proceedngs 2018, 2, of 6 ncreases. Along wth, hull wet area s gradually ncreasng, besdes, hull frctonal resstance has a lttle change n cause of the ncreased wave, but tends to ncrease. In general, along wth the draft depth ncreases, the number decreases, wave resstance and pressure drag gradually ncrease, frctonal resstance slghtly ncreases and vscous pressure resstance shows lttle change. The above analyss on workng condtons of 6 knds of the 470 Class yacht can conclude that to some extent draft had sgnfcant effect on the change of wave, as s shown n Fgures 3 and 4. So, the coaches and athletes should put great attenton to the materal weght factors. At the same tme, t can offer some scence and techncal gudance for wnnng the game for the salboat dsplacement can be adjust wthn the game rules. Table 1. Numercal results of the Olympc Class 470 yacht. The Project of the Olympc Class 470 Yacht Numercal Results Dfferent draughts (m) Hull dsplacement (kg) Froude number (Fr) Pressure drag coeffcents ( ) Frctonal resstance coeffcents ( ) Vscous pressure resstance coeffcents ( ) Wave resstance coeffcents ( ) / 42.7% 45.8% 45% 46.6% 46.4% 49.7% Fgure 2. Resstance Coeffcents changng wth the Froude number. a b Fgure 3. Numercal wave results of the free surface wth dsplacement of the hull (a) 230 kg and (b) 270 kg.

5 Proceedngs 2018, 2, of 6 a b c d e f Fgure 4. Numercal wave results of the Olympc Class 470 yacht wth dfferent hull dsplacements (a) 230 kg, (b) 240 kg, (c) 250 kg, (d) 260 kg, (e) 270 kg and (f) 280 kg. 4. Conclusons Ths paper stmulated the hydrodynamc performance of a Class 470 yacht n dfferent draughts by the SST K-ω turbulence model, the VOF method untes the developed double model method. Ths experment was modelled wth CFD usng a hexahedral grd bult wth ANSYS ICEM CFD and solved wth ANSYS Fluent. The smulaton results of dfferent hull draughts show that dfferent draughts play a major role on the performance of yacht salng. The draught of the hull can affect the component of wave resstance n the total resstance sgnfcantly, and brng just a lttle nfluence on the components of frcton resstance and vscous pressure resstance. In the analyss of the relatonshp between and, we found that the lowest resstance coeffcent appears when = 2.43, and hghest when = As for the gudance for select athletes, the establshed scentfc results ndcate that the athletes combnaton wth 240 kg dsplacement can be a good choose n a match. Ths study found a relatvely reasonable droughts zone exsts n the class 470 yacht. Studyng propertes of draughts resstance of the class 470 hull can offer theoretcal reference for coaches to select athletes, scentfcally match weghts of athletes n a match, for route strategy adjustment and athletes to have a quanttatve control of the yacht.

6 Proceedngs 2018, 2, of 6 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. 2013CFA038), Outstandng Youth Scence and Technology Innovaton Team Foundaton of the Colleges and Unverstes of Hube Provnce (Grant No. T201320), 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. Paroln, N.; Quarteron, A. Mathematcal Models and Numercal Smulatons for the Amerca s Cup. Comput. Meth. Appl. Mech. Eng. 2005, 194, Vola, I.M.; Enlander, J.; Adamson, H. Trm Effect on the Resstance of Salng Plannng Hulls. Ocean Eng. 2014, 88, Akmoto, H.; Myata, H. Fnte-volume Smulaton Method to Predct the Performance of a Salng boat. J. Mar. Sc. Technol. 2002, 7, Böhm, C.; Graf, K. Advancements n Free Surface RANSE Smulatons for Salng Yacht Applcatons. Ocean Eng. 2014, 90, Campbell, I.; Owen, M.; Provncal, G. Dagger-board Evaluaton for an IMOCA 60 Yacht. Ocean Eng. 2014, 90, Mylonas, D.; Sayer, P. The Hydrodynamc Flow around a Yacht Keel Based on LES and DES. Ocean Eng. 2012, 46, 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. 2016, 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. 2015, 31, Huetz, L.; Gullerm, P.E. Database Buldng and Statstcal Methods to Predct Salng Yacht Hydrodynamcs. Ocean Eng. 2014, 90, 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 (