Numerical Investigations of Open-water Performance of Contra-Rotating Propellers

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1 Poceedings of the Twenty-seventh (2017) Intenational Ocean and Pola Engineeing Confeence San Fancisco, CA, USA, June 25-30, 2017 Copyight 2017 by the Intenational Society of Offshoe and Pola Enginees (ISOPE) ISBN ; ISSN Numeical Investigations of Open-wate Pefomance of Conta-Rotating Popelles Dongya He 1, Decheng Wan 1*, Xinguo Yu 2 1 Collaboative Innovation Cente fo Advanced Ship and Deep-Sea Exploation, State Key Laboatoy of Ocean Engineeing, School of Naval Achitectue, Ocean and Civil Engineeing, Shanghai Jiao Tong Univesity, Shanghai, China 2 China Ship Development and Design Cente, Shanghai Banch, China * Coesponding autho ABSTRACT In this pape, the open-wate pefomance of conta-otating popelles (CRPs) has been investigated using CFD method with sliding mesh model dealing with the elative otation of CRPs. Results show that CRPs exhibits appaent peiodical unsteady thust and toque. Afte FFT (Fast Fouie Tansfom) of those foces coefficients, esults show that they ae composed of amplitudes of 8 times, 16 times and 24 times shaft fequency. Time-aveages of pedicted unsteady thust and toque agee well with thei expeimental countepats. On the othe hand, CRPs wake flow field has been analyzed in detail to pove that CRPs is supeio in efficiency and stability to single popelle since majoity of otational enegy poduced by font popelle can be almost fully ecoveed. KEY WORDS: CRPs; open-wate pefomance; enegy saving device; CFD; sliding mesh method. INTRODUCTION Right now, the majoity of ships opeating in the wold ae poweed by diesel engine, with taditional shaft popelle as thei main populsion type. This type is poo in efficiency, vibation quality and easy to cause popelle cavitation. Evey yea, cabon emission in ship opeation accounts a big popotion than othe industies. On the othe hand, in ode to educe costs in opeation, caies such as containe ship become bigge and faste, thus popelle needs bigge diamete and become moe and moe heavie. On the othe hand, such conventional single scew populsion mode has technically eached its limits due to engine powe, popelle loading and weight, hull vibation, maneuveability, etc.(kim et al., 2002), theefoe it s essential to seek fo moe advanced popelling system. In this cicumstance, IMO put fowad thee indexes, namely EEDI (Enegy Efficiency Design Index), EEOI (Enegy Efficiency Opeational Index), SEEMP (Ship Enegy Efficiency Management Plan) to pomote geen ship development. A lot of opeating ships in China ae going to be banned fo mismatching those standads. Theefoe, eseaches have designed many types of enegy-saving devices to impove popelle populsion efficiency. Thee ae thee main easons that will degade populsion efficiency which ae nonunifom inflow at popelle disk, votex esistance at hub and blade tip and otational wake flow behind popelle. Wake equalizing duct, popelle boss cap fin and CRPs ae the common enegy saving devicts. they can impove efficiency fom 2% to 8%. CRPs has two conventional popelles which otate coaxially in evese diection. The ea popelle can geatly ecove votex kinetic enegy left by font popelle, futhemoe, CRPs can weaken unbalanced moment, thus it has been extensively applied to popel topedo which needs high standad of couse keeping stability. Since 1970 s, many eseaches in the wold have investigated steady and unsteady open-wate pefomance of CRPs. Some of them in David W Taylo Naval Ship R&D Cente (1976) tested two sets of CRPs, thei model and expeimental data have been used by many CFD eseaches. Yang (1992) developed the steady and unsteady lifting suface models which ae based on potential flow theoy. Since the late 1990 s, CFD method has been inceasingly used in maine hydodynamics owing to the apid impovement in compute capabilities and numeical method. Because CFD method is based on actual fluid contol functions (Navie-Stokes equations) which take the viscosity and otation into account, thus it can coectly model nonlinea wake defomation and flow sepaation due to heavy loading. Up to now, MRF (Multiple Refeence Fame) method, oveset mesh method, and sliding mesh method ae the thee main techniques dealing with popelle otation. MRF method can only be used to pedict steady foces, in othe wods, dynamic flow field cannot be obtained. Though this method has high efficiency, its pecision is not so good as oveset mesh method and sliding mesh method. Oveset mesh method has been extensively applied to handle poblems that have multiple moving objects with many degees of feedom. Diffeent gids will exchange thei infomation though an intepolating code named SUGGAR++(Noack et al., 2009)on the ovelapping aea of sliding mesh. At sacifice of elatively lage of computing esouces, this method will guaantee high accuacy. Shen, et al (2012) caied out KCS self-populsion and maneuveing by CFD solve naoe-foam- SJTU with oveset mesh technique, pedicted esults agee well with thei expeimental data. Compaing with MRF and oveset mesh method, sliding mesh method keeps equal pecision as oveset mesh method, but its computing efficiency is geatly impoved since this method only needs intepolation between ovelapping aea of otational egion and static egion. Wu (2016) compaed accuacy and computing 1085

2 efficiency of those thee method applied to numeical pediction of open-wate pefomance of single popelle. Based on sliding mesh method, Zhou (2014) investigated unsteady flow aound wind tubines with diffeent blades numbes. Wang, et at (2012) studied two sets of CRPs open-wate pefomance developed by David W Taylo Naval Ship R&D Cente using CFD method, numeical pedicted esults agee well with thei expeimental countepats, futhemoe, he investigated CRPs peiodical unsteady thust and toque in detail. Consideing accuacy and computing efficiency, sliding mesh method was adopted to settle CRPs otation in this pape. In ode to make it easy to illustate CRPs supeioity to single popelle, CRPs font popelle called single popelle has also been simulated independently. NUMERICAL METHOD In this pape, single phase flow solve, pimpledymfoam, has been used, its capability of solving unsteady poblem could help to simulate CRPs unsteady flow field well. The Reynolds Aveaged Navie- Stokes(RANS) functions with tubulence model k ω SST which was put fowad by Mente (2003) have been veified by many scholas to be efficient to simulate popelle flow field. A second-ode TVD limited linea scheme was used to discetize the convection tems in RANS functions while the diffusion tems wee discetized by a second-ode cental diffeence scheme. Pimple algoithm was used to solve coupling poblem of pessue and velocity. Time step was equal to 1.157e-04 second so the popelle could otate about 1 degee. Govening Equations Fo the incompessible viscous fluid flow, the continuity equation and RANS equations ae expessed as follows: u i 0 xi p 1 ui uj ( u ) ( ) ( ) ( ' ' i + uu i j uu i j) t x j x j Re xj xj xi xj (1) (2) Fig. 1 shows diagam of the ovelapping aea of sliding meshes. In ode to keep flux tansmitting and flow field infomation exchanging easonable, intepolation manne is based on weight coefficient meaning how much contibution one cell on one side of sliding sufaces makes to the othe side. Fo example, blue mesh and ed mesh ae assumed to be the main suface and slave suface espectively. The weight one cell owes fom main suface to the cell in slave suface in the ovelapping cell is the atio how much ovelapping aea the cell in main suface accounts. COMPUTATIONAL OVERVIEWS Geometic Model and Case One of test models of CRPs developed by David W Taylo Naval Ship R&D Cente has been chosen as the object of study. The font popelle is named DTMB3686 and the ea named DTMB3687. Table 1. Paametes of CRPs Paametes DTMB3686 DTMB3687 Diamete/mm Blade numbe 4 4 (P/D) Aea atio Rotating diection Left Wight Section NACA66mod/a0.8 NACA66mod/a0.8 Modeling of CRPs is based on popelle pojection theoy(wang, et al., 2007), as Fig. 2 shows. The two dimensional coodinates of blade sections can be tansfomed into global thee dimensional coodinates by Eqs. 3~10. Whee ui ae aveages of velocity components in thee diections; j (1, 2, 3) means diffeent diection; Re is Reynolds numbe; uu ' ' i j ae Reynolds stess. Sliding Mesh Method Supposing that the open-wate calculation of single popelle is going to be simulated, the computation domain will be divided into two pats. One of them suounds and otates with popelle, the othe is the esidual domain and keeps static. Both domains will exchange infomation in the ovelapping meshes. Gid numbes on both sufaces ae not stictly equied to be consistent, but flux must be equal, o numeical computing pocess will become diveging. Fig. 1 Diagam of sliding mesh Fig. 2 Diagam of popelle poject theoy xup C( )( s 0.5)sin ϕ( ) ( f ( s) + t( s) )cosϕ( ) + x( ) (3) cosϕ( ) sinϕ( ) θup( ) C( )( s 0.5) + ( f ( s) + t( s) ) + θ ( ) (4) yup( ) cosθ up() (5) zup( ) sinθ up( ) (6) xdown( ) C( ) ( s 0.5)sin ϕ( ) ( f ( s) t( s) )cosϕ( ) + x( ) (7) cosϕ( ) sinϕ( ) θdown( ) C( )( s 0.5) + ( f ( s) t( s) ) + θ ( ) (8) ydown( ) cosθ down() (9) zdown( ) sinθ down( ) (10) 1086

Whee x( ) is ake downwad, θ ( ) is heeling angle, ϕ ( ) is angle of pitch, C ( ) chod length, s is dimensionless location of hydofoil points along chod, f ( s) is cambe, t ( s) is maximum thickness

4 shows. Thee ae five cases in this pape. Thust and toque of CRPs wee computed when inlet coefficient, J, is at 0.7, 0.8, 0.9, 1.

Thee ae about 4.5 million cells in global mesh. As Fig. 7 shows, mesh has been efined aound aea of CRPs in ode to captue cucial flow field infomation.. Fig. 6 Global mesh Fig. 3 CRPs model Fig.

5D to 5D in x diection with diamete of 3 times font popelle. Thee ae two sets of sliding sufaces suounding font and ea popelles espectively. Fig.

Non-slipping wall condition is applied to popelle and stem sufaces. Fist, some coefficients need to be defined that will help to analyze the open-wate pefomance of CRPs.

3 Whee x( ) is ake downwad, θ ( ) is heeling angle, ϕ ( ) is angle of pitch, C ( ) chod length, s is dimensionless location of hydofoil points along chod, f ( s) is cambe, t ( s) is maximum thickness of hydofoil. Afte lofting of diffeent blade sections, the final CRPs model was built as what Fig. 3 shows. In ode to analyze CRPs supeioity, single popelle, DTMB3686, has also been calculated, as Fig. 4 shows. Thee ae five cases in this pape. Thust and toque of CRPs wee computed when inlet coefficient, J, is at 0.7, 0.8, 0.9, 1.0, 1.1. Font and ea popelle otated at the evolution ate of 12 in evese diection. Mesh Configuation Fig. 6 shows global mesh ceated by softwae, ICEM, who is adept at ceation of O-block mesh. Thee ae about 4.5 million cells in global mesh. As Fig. 7 shows, mesh has been efined aound aea of CRPs in ode to captue cucial flow field infomation.. Fig. 6 Global mesh Fig. 3 CRPs model Fig. 7 Local mesh NUMERICAL RESULTS AND ANALYSES Numeical Results Fig. 4 Single popelle model Computational Domain and Bounday Conditions As Fig. 5 shows, the lage domain extends fom -3.5D to 5D in x diection with diamete of 3 times font popelle. Thee ae two sets of sliding sufaces suounding font and ea popelles espectively. Fig. 5 Global computational domain At the inlet, U is inflow velocity while pessue gadient is zeo. At the outlet, pessue is zeo while velocity gadient is zeo. Bounday condition of outecylinde is symmety. Non-slipping wall condition is applied to popelle and stem sufaces. Fist, some coefficients need to be defined that will help to analyze the open-wate pefomance of CRPs. They ae defined as follow: V J ndf (11) TF KTF 2 4 (12) Q F KQF 2 5 (13) TA KTA 2 4 (14) Q A KQA 2 5 (15) KT KTF + KTA (16) K Q KQF + KQA (17) JK T η 2π K Q (18) Whee subscipt F means font popelle and subscipt A means ea popelle. K T and K Q ae hydodynamic coefficients of CRPs. Fig. 8 shows evident unsteady foces of CRPs when J is 1. As we can see, thee ae eight small peiods afte font o ea popelle otates 360 degees, that s because both popelles have fou blades. What s moe, the amplitudes of foce coefficients vaiation suffeed by font popelle ae lage than ea popelle while time-aveages of unsteady foces ae in evese. Afte FFT of those foces coefficients, Fig. 9 shows that they ae mainly composed of amplitudes of 8 times, 16 times, and 24 times shaft fequency with thei amplitudes deceasing as 1087

4 exponential function, this phenomenon illustates stong inteaction between font and ea popelles. Fig. 10~12 eflect open-wate pefomance of font popelle, ea popelle and CRPs espectively. Numeical esults agee well with thei expeimental countepats. Fig. 10 shows eos of K T ae aound 5% while eos of K Q ae aound 1%. Fig. 11 tells that pedicted K T is lowe than expeimental data about 1.893% while pedicted K Q is elatively lage than expeimental data about 8%. That s because the ea popelle woks in the complex wake flow of font popelle. Moe accuate simulation may equie moe efined mesh and advanced tubulence model. Fig. 12 shows aveages of foces coefficient of CRPs. Eos of K T and K Q ae aound 2% and 4.5% espectively. Fig. 11 Open-wate pefomance cuves of ea popelle Fig. 8 Time histoy of hydodynamic coefficients of CRPs Fig. 12 Open-wate pefomance cuves of CRPs Table 2 shows that pedicted foces of single popelle ae lage than font popelle when J is 1. Since the suction effect of the ea popelle on the font popelle, effective inflow velocity has inceased to a cetain extent. On the othe hand, the efficiency of CRPs is 2.2% highe than single popelle. It is woth mentioning that, besides the distance of popelles discs, the atios of blade numbe and otating speed also have lage effect on efficiency of CRPs. Fig. 9 Fast fouie tansfom of thust and toque coefficients Table 2. Compaison between single popelle and CRPs Items KT 10KQ Efficiency Single popelle Font popelle Rea popelle CRPs Votical Stuctue Fig. 13 shows obvious diffeences of votical stuctue between CRPs and single popelle. The votical stuctue is coloed by Ux/U0 whee U0 is inflow velocity. As we can see, the velocity in x diection has geatly been impoved by the ea popelle. Pessue Distibution Fig. 10 Open-wate pefomance cuves of font popelle Fig. 14 shows high pessue is mainly distibuted aound 0.7 whee is adius of popelle. Leading edge on pessue side encountes peak value of positive pessue. Peak value in single popelle is highe than font popelle. Fig. 15 shows peak value of negative pessue is distibuted aound leading edge of suction side. Peak value of single popelle is 720pa highe than font popelle, theefoe single popelle is easie to cause cavitating. 1088

vaiation aound the blade tips which will induce stong tip votex. Fig.

Meanwhile the lowe magnitude of tangential and adial velocity with highe axial velocity will impove hydodynamic pefomance of udde. Fig. 13 Votical stuctue at J0.9 Fig.

17 Distibution of adial velocity at diffeent axial location Velocity Distibution Fig. 16~17 ae the velocity components distibution at diffeent axial location.

16 suggests how Ux is acceleated. Fig. 16 (a) says Ux will be acceleated dastically on the suction side of blade suface induced by the ciculation effect of hydofoil.

5 vaiation aound the blade tips which will induce stong tip votex. Fig. 19 shows that, compaed with single popelle, CRPs magnitude of Ut in the wake field has been educed dastically, that s why CRPs could achieve highe efficiency than single popelle. Meanwhile the lowe magnitude of tangential and adial velocity with highe axial velocity will impove hydodynamic pefomance of udde. Fig. 13 Votical stuctue at J0.9 Fig. 16 Distibution of axial velocity at diffeent axial location Fig. 14 Pessue distibution on pessue side Fig. 15 Pessue distibution on suction side Fig. 17 Distibution of adial velocity at diffeent axial location Velocity Distibution Fig. 16~17 ae the velocity components distibution at diffeent axial location. Ux, U and Ut ae velocities in axial diection, adial diection and tangential diection espectively. U is defined to be positive outwad, Ut is positive anticlockwise. Fig. 16 suggests how Ux is acceleated. Fig. 16 (a) says Ux will be acceleated dastically on the suction side of blade suface induced by the ciculation effect of hydofoil. Afte acceleation by ea popelle, the maximal magnitude of Ux is distibuted aound 0.7. Thee ae moe inteesting phenomena in Fig. 17. Fig. 17 (a) suggests that the highe U is centeed in blade tips whee thee is a elative small aea of negative velocity on the pessue side and a lage aea of positive velocity on the suction side, Violent change of velocity will induce a stong tip votex. Fig. 17 (c) suggests that the ea popelle will induce opposite U compaed with the font popelle, so magnitude of U in wake field of CRPs has been geatly educed. Fig. 18 shows that thee ae small aeas of velocity Fig. 18 Distibution of tangential velocity at diffeent axial location 1089

Fig. 19 Compaison of tangential velocity distibution CONCLUSIONS Based on sliding mesh method, the open-wate pefomances of CRPs and single popelle have been investigated in detail.

6 Fig. 19 Compaison of tangential velocity distibution CONCLUSIONS Based on sliding mesh method, the open-wate pefomances of CRPs and single popelle have been investigated in detail. Time histoies of KT and KQ exhibit obvious peiodical unsteady featue with eight small peiods afte font o ea popelle otates 360 degees, Meanwhile, time-aveages of KT and KQ agee well with thei expeimental countepats, meaning that geomety models and numeical method used in this pape ae eliable and cedible. Afte compaison of calculated esults of CRPs and single popelle, efficiency of CRPs is 2.2% highe than single popelle with the specific design paametes in this pape. What s moe, votical stuctue of CRPs is quite diffeent fom single popelle, otational enegy left by font popelle has been fully ecoveed by ea popelle as expected. OpenFOAM with application to KCS self-populsion and maneuveing, Ocean Eng, 108, Wang G, Dong S (2007). Theoy and application of popelle fo ship, Habin Eng Univ Pess. Wang Z, Xiong Y and Qi W (2012). Numeical pediction of openwate pefomance of conta-otating popelles, J Huazhong Univ of Sci & Tech, 40(11), Wu J, Yin C, and Wan, D (2016). Numeical pediction of open-wate pefomance of popelle based on thee methods, Chin J Hydodyn, 31(2), Yang C, Tamashima M and Wang G (1991). Pediction of the steady pefomance of conta-otating popelles by lifting suface theoy, Tansactions of the West-Japan Society of Naval Achitects, 82, Yang C, Tamashima M and Wang G (1992). Pediction of the unsteady pefomance of conta-otating popelles by lifting suface theoy, Tansactions of the West-Japan Society of Naval Achitects, 83, Zhou H, Wan DC (2014). Numeical simulation of the unsteady flow aound wind tubines with diffeent blades numbes, J Hydodyn Se A, 29(4): Futue wok will focus on the open-wate pefomance of the so-called hybid CRP podded populsion system. The atios of blade numbe, otating speed and distance between font and ea popelles may geatly affect efficiency of such hybid system. Theefoe, it s necessay and meaningful to have a systematic investigation of those paametes effect on the hybid system. ACKNOWLEDGEMENTS This wok is suppoted by the National Natual Science Foundation of China ( , , , ), Chang Jiang Scholas Pogam (T ), Shanghai Excellent Academic Leades Pogam (17XD ), Shanghai Key Laboatoy of Maine Engineeing (K ), Pogam fo Pofesso of Special Appointment (Easten Schola) at Shanghai Institutions of Highe Leaning ( ), Innovative Special Poject of Numeical Tank of Ministy of Industy and Infomation Technology of China( /09) and Lloyd's Registe Foundation fo doctoal student, to which the authos ae most gateful. REFERENCES Kim, S, Choi S (2002). Model tests on populsion systems fo ulta lage containe vessel, Poc 12 th Int Offshoe and Pola Eng Conf, Kitakyushu, ISOPE, (4) Mente, F, Kuntz M, and Langty R (2003). Ten yeas of industial expeience with the SST tubulence model, Tubulence, Heat and Mass Tansfe, (4) Mille, M (1976). Expeimental detemination of unsteady foces on conta-otating popelles in unifom flow, Technical Repot No. AD-A032337, David W Taylo Naval Ship R&D Cente. Noack, RW, Boge, DA, Kunz, RF, and Caica, PM (2009). Sugga++: An impoved geneal oveset gid assembly capability, Poc 47th AIAA Aeosp Sci Exhib, Shen, Z, Wan, DC and Caica, PM (2015). Dynamic oveset gids in 1090

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