ZESZYTY NAUKOWE NR 2 (74) AKADEMII MORSKIEJ W SZCZECINIE. Numerical Wake Assessment of Maneuvering Ship

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1 ISSN Tomas Abramoski ZESZYTY NAUKOWE NR (74) AKADEMII MORSKIEJ W SZCZECINIE EXPLO-SHIP 004 Nmerical Wake Assessment of Maneering Ship Ke ords: nominal ake, maneering The article presents an attempt at nmerical ake determination of a ship moing ith drift. For the calclation of iscos flo a nmerical method based on the soling of RANS eqations has been applied. A blk carrier hll has been chosen for the analsis. The reslts sho comple featres of the flo in the stern area. Distribtions of ake factor are strongl non-niform both in radial and circmferential directions and the non-niformit gets stronger as drift angle increases. Nmercna analia strmienia nadążającego manerjącego statk Słoa klcoe: nominaln strmień nadążając, maneroanie Zapreentoano próbę nmercnej ocen strmienia nadążającego statk porsającego się drfem. Oblicenia opł lepkiego konano metodą opartą na roiąani rónań RANS. Do anali brano kadłb masoca. Oblicenia skają na skomplikoane parametr prepł rejonie rf. Rokład spółcnnikó strmienia nadążającego są silnie niejednorodne tak promienioo, jak i obodoo i niejednorodność ta rasta ra e rostem kąta drf. 1

2 Tomas Abramoski Introdction A lot of attention has been paid recentl to the safet of sea traffic. Maneering simlators are an important part of these stdies. The are presentl a idel accepted tool for the determination of ship maneering featres, hile there are man areas here additional research cold be prposefl. In thisork interest is gien to ake characteristics of a maneering ship. The Flent Inc. soler has been applied for the analsis Present methods for the determination of propeller-hll interaction dring maneering are mainl based on model tests reslts. The athors like Inoe et al. [3] and Kobliński and Zolfaghari [4] present the reslts of simlations ith eperimentall deried thrst and ake factors. Fe attempts hae been made to assess these factors nmericall. Simonsen [8] carried ot calclations for rdder in free stream, rdder behind a propeller and bare hll moing straight ahead ithot drift. Le Th Hang [6] presents an analsis of the propeller-rdder interaction ith lifting srface theor applied to calclations. Yoskaa et al. [9] hae deeloped a method for calclations of forces acting on a ship and hllpropeller interaction coefficients. The method is almost prel theoretical, bt ake factor is obtained eperimentall. El Moctar [1] applies finite olme method to flo calclations of a ship hll. The reslts of hll forces are presented as a fnction of drift angles. 1. Applied nmerical method For the calclation of iscos flo arond a ship ith drift e hae applied nmerical method based on the soling of eqations goerning the case nder consideration, i.e. RANS eqations, haing the folloing form: P F 1 P F P F 3 (1)

3 Nmerical Wake Assessment of Maneering Ship In the aboe eqations,, are components of the mean elocit ector, P is the pressre, is the iscosit,,, are flctation parts of elocit ector, F 1, F, F 3 are olmetric forces. Frthermore, the model mst satisf continit eqation: 0 () For the modeling of the Renolds stresses the RNG k-ε trblence model has been applied. The placement of grid first point as established on the basis of non-dimensional parameter +, describing local Renolds nmber. The + ma be determined according to the theor of flat-plate flo, e.g. Schlichting 7: 017, L 0, 9 R n (3) here: is the distance from the all, L is the bod length. In the considered case all fnctions hae been applied, ith + = 50. Calclations ere carried ot for the Renolds nmber of the model, keeping Frode nmber similarit. The scale factor as λ = 30. The comptational domain, presented in Fig. 1, as designed intentionall for the prpose of elocit direction changing at the inlet bondar. The oter bondar is a srface of reoltion arising from the reoltion of a trapeoid placed at the aterline. otlet rigid srface inlet hll model Fig. 1. The shape of comptational domain Rs. 1. Kstałt diedin nmercnej 3

4 Tomas Abramoski For tpes of bondar conditions ere placed at oter srfaces of comptational domain: 1. Free srface as replaced ith a rigid bondar and is treated as a plane of smmetr, for hich conditions of ero normal elocit and ero gradient of other components mst be satisfied. This assmption ma be legitimate taking into accont that Frode nmber is relatiel lo (F n = 0.16).. The bondar condition on the hll is a no-slip condition ith ero relatie speed enforced. 3. At the inlet bondar condition all flo parameters mst be specified: components of free stream elocit ector, kinetic energ of trblence and its dissipation rate. 4. The otlet condition as set sch that longitdinal gradients of elocit and pressre are eqal to ero: (,,, p) 0 (4) The arrangement of bondar conditions is presented in Fig. 1. The flo as compted for drift angles aring from 0 to 35, ith the 5 step.. Model parameters and nmerical grid topolog The hll of a blk carrier has been chosen for the analsis. The intention as to obtain relatiel comple flo pattern in the stern area of a shape haing a high block coefficient. Parameters of the ship hll together ith flo nmbers characteristics are presented in Table 1. The sketch of bod lines is gien in Fig.. Parameters of ship and model Parametr statk i model Table 1 Length, L 185 m m Breadth, B 5.3 m m Draght, T m m Speed, V m/s Frode nmber, Fn Renolds nmber, Rn

5 Nmerical Wake Assessment of Maneering Ship We hae applied Tribon Initial Design [5] sstem for the modeling of hll srface and the Gambit sstem for grid generation. The hbrid grid ith tetrahedral elements placed in the most part of domain and prisms near the hll hae been applied. The grid is presented in Fig. 3 (ie from the bottom and stern part). Total nmber of elements as Fig.. Blk carrier bod lines Rs.. Kstałt kadłba analioanego masoca Fig. 3. Vie of the nmerical grid in the stern area Rs. 3. Siatka nmercna rejonie rf. Widok od stron dna 5

6 Tomas Abramoski 3. The reslts The reslts sho comple featres of the flo in the stern area. Streamlines are presented in Fig. 4 and 5 in the ie from the stern. Formations of strong ortices are present, een for the straight ahead corse. Distribtions of nominal ake factor W N are calclated according to Talor method: W N V V AX 1 (5) X In the aboe eqation V AX is the aial component of the elocit in the scre plane and V X is the aial component of ship s speed. Wake is strongl non-niform both in radial and circmferential directions and the non-niformit is stronger as drift angle increases. The flo straightening effect of the hll cases strong non-niformit of the ake, hich becomes isible in regions here backflo occrs. Mean ales of ake factor, presented in Fig. 6, ere calclated on the basis of its radial distribtion: WN (r) 360 WN()d (6) In the aboe eqation r is assmed to be the radis of scre and is circmferential position. Hence, the mean ale of ake factor as determined as: 0 r 1 1 W N rwn ( r) dr (7) 0,48 r 0, Unfortnatel, e did not hae an eperimental reslts of ake and streamlines for a reliable erification process. We hae attempted to assess the reslts for straight ahead corse, related to iscos part of the total resistance. According to Frode s hpothesis the hll resistance can be diided beteen its iscos and residal parts: here: C T is the total resistance coefficient, C R is the residal resistance coefficient, C V is iscos resistance coefficient. C T = C R +C V (8) 6

7 Nmerical Wake Assessment of Maneering Ship The iscos coefficient is a fnction of Renolds nmber and the shape of a ship. It can be epressed as: C V = (1+k 0) C F0 (9) here: k 0 is the form factor, C F0 is the frictional resistance coefficient. The frictional resistance coefficient and the form factor k 0 can be estimated b means of the ITTC friction line. The nmerical algorithm calclates hdrodnamic forces b integration of normal pressre stresses and the frictional shear stresses oer the hll srface. Hence, the total resistance coefficient can be epressed as a sm: here: C p is the resistance coefficient from the pressre, C f is the frictional resistance coefficient. C = C p + C f (10) Neglecting the free srface effect implies that residal coefficient C R in (8) can be assmed to be eqal to ero. The pressre coefficient C p epresses the form resistance of the hll, and it is possible to se it for the calclation of the form factor k 0 and C f can be compared ith the ITTC formla. Hence the epression (8) can be ritten as: C T = k 0C F0 + C F0 (11) B comparison of (10) ith (11) the k 0 can ritten as: C p k0 (1) C f The reslts of calclations presented aboe are shon in Table. Compted ales of resistance coefficients and ITTC ales Oblicone artości spółcnnikó opor porónane artościami skanmi godnie aleceniami ITTC Table CF Cp C 1+ k0 Calclations ITTC

8 Tomas Abramoski Fig. 4. Streamlines on the hll srface. Drift angle β = 0. The ie from the stern Rs. 4. Linie prąd na poierchni kadłba idok od stron rf. Kąt drf β = 0 Fig. 5. Streamlines on the hll srface. Drift angle β = 35. The ie from the stern Rs. 5. Linie prąd na poierchni kadłba idok od stron rf. Kąt drf β = 35 8

9 Nmerical Wake Assessment of Maneering Ship 0,7 W N 0,6 0,5 0,4 0,3 0, 0,1 0, Fig. 6. The nominal ake factor plotted s. drift angle Rs. 6. Nominaln spółcnnik strmienia nadążającego fnkcji kąta drf Drift angle β = 0 Drift angle β = 35 Fig. 7. Transerse elocities in propeller plane; VY [m/s] Rs. 7. Prędkości poprecne płascźnie kręg śrboego; VY [m/s] 1,00 0,90 0,80 0,70 0,60 W N 0,50 0,40 r=0,7 R r=0,6r r=0,5r 0,30 0,0 0,10 0, F 9

10 Tomas Abramoski Fig. 8. Circmferential distribtion of ake factor. Drift angle β = 0 Rs. 8. Obodo rokład strmienia nadążającego. Kąt drf β = 0 1,0 1,00 0,80 WN 0,60 0,40 r=0,7r r=0,6r r=0,5r 0,0 0, F Fig. 9. Circmferential distribtion of ake factor. Drift angle β = 35 Rs. 9. Obodo rokład strmienia nadążającego. Kąt drf β = 35 Drift angle β = 0 Drift angle β = 35 Fig. 10. Wakes distribtions in propeller plane Rs. 10. Rokład strmienia nadążającego płascźnie kręg śrboego Conclsions The case of ship moing ith drift cases complicated flo patterns in the stern region. Carring ot sch calclations reqires the application of most adanced nmerical techniqes, taking into consideration real hdrodnamics effects. The RANS iscos method has been applied and the reslts are at least 30

11 Nmerical Wake Assessment of Maneering Ship qalitatie for mean and integral ales. Inaccracies ma come from an imperfection of the applied trblence model and from the errors of nmerical method. The reslts obtained for streamlines are especiall interesting and comple orte formations can be obsered. The assmption neglecting free srface effects seems to be legitimate in the considered range of the Frode nmber and for the prpose of research, i.e. the inestigation of ake. If the analsis aimed atthe calclation of hll forces, more accracold be adisable. The reslts of flo calclation can be applied in the algorithm for the determination of scre propeller forces in maneering conditions. Literatre 1. El Moctar O.M., Nmerical comptations of flo forces in ship maneering, Ship Technolog Research, Vol. 48, Flent INC.: Flent 5 User s Gide, Inoe S., Hirano M., Kijima K., Takashina J., A Practical Calclation Method of Ship Maneering Motion, Int. Ship. Progress, ol. 8, Kobliński L., Zolfaghari G., Prediction of maneering characteristics in ship design, 1th Int. Conf. on Hdrodnamics in Ship Design, Sklarska Poręba, September Kockms Compter Sstems Ltd., Tribon Init. Design User Gide, Le Th Hang, Calclation of the inflence of propeller operation on the hdrodnamic characteristics of the rdder, Polish Maritime Research, no (8), ol. 8, Schlichting H., Bondar Laer Theor, McGra-Hill, Ne York, Simonsen C.D., Rdder, Propeller and Hll Interaction b RANS, PhD thesis, T.U. of Denmark, Yaskaa H., Yoshimra Y., Nakatake K., Hdrodnamic Forces on a Ship ith Constant Rdder Angle, Int. Conf. On Marine Simlation and Ship Maneerabilit, Rotterdam Recenenci prof. dr hab. inż. Tades Selangieic dr inż. Zbignie Soda Wpłnęło do redakcji ltm 004 r. 31

12 Tomas Abramoski Adres Atora dr inż. Tomas Abramoski Politechnika Scecińska, Wdiał Techniki Morskiej 3