CFDsimulationofshipturning...

Received：2018 - 05 - 06Supported by: National Natural Science Foundation of China (51809169, 51879159, 51490675, 11432009, 51579145); Chang Ji⁃

ang Scholars Program (T2014099); Shanghai Universities Orientalist Special Professor Post Tracking Program(2013022) ; Shanghai Excellent Academic Leadership Program (17XD1402300) ; Ministry of Industry and Informa⁃tion Technology Numerical Value Pool Innovation Special VIV/VIM Project (2016-23/09)

Author(s): Wang Jianhua, male, born in 1988, Ph.D., assistant researcher. Research interests：the calculation of ship hydrodynam⁃ics and ship maneuvering in waves. E-mail: [email protected] Decheng, male, born in 1967, Ph.D., professor. Research interests：the calculation of ship hydrodynamics,non-grid particle method, ship type optimization, floating fan, fluid-solid coupling and vortex-induced vibration/mo⁃tion. E-mail: [email protected]

*Corresponding author：Wan Decheng

CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019To cite this article：Wang J H, Wan D C. CFD simulation of ship turning motion in waves[J/OL]. Chinese Journal of Ship

Research, 2019, 14(1). http://www.ship-research.com/EN/Y2019/V14/I1/1.DOI：10.19693/j.issn.1673-3185. 01283

CFD simulation of ship turningmotion in waves

Wang Jianhua1，2，3，Wan Decheng*1，2，3

1 State Key Laboratory of Ocean Engineering，Shanghai Jiao Tong University，Shanghai 200240，China2 Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration，Shanghai 200240，China

3 School of Naval Architecture，Ocean and Civil Engineering，Shanghai Jiao Tong University，Shanghai 200240，ChinaAbstract：［Objectives］The ship turning motion can reflect the steerability of the ship during navigation and is closelyrelated to the ship navigation safety.［Methods］ In this paper，the direct numerical simulation of the free turningmotion of the standard ship model ONRT in waves is carried out by using CFD solver naoe-FOAM-SJTU based onoverset grid technology. The dynamic overset grid technology is used to solve the complex motions of the ship，propeller and rudder systems. The simulation of turning motion is carried out at constant propeller rotational speed with35° rudder deflection. Through the global solution of the fully viscous flow field，6 DoF motions of the ship in thewaves and hydrodynamic load changes of the propeller and rudder are given. The parameters of the ship turning motionin waves are presented and compared with the available test results. Wave effects on the free turning motion arediscussed through detailed flow visualizations.［Results］The ship's motion trajectory and the parameters of the turningmotion obtained by numerical prediction are in good agreement with the test values，which fully proves theapplicability and reliability of naoe-FOAM-SJTU solver in the numerical prediction of the ship's free turning motionunder the hull-propeller-rudder interaction of the ship.［Conclusions］Through numerical simulation of the turningmotion，it provides an effectively preliminary assessment for the steerability of the ship.Key words：ship maneuverability； free turning motion；hull-propeller-rudder interaction；naoe-FOAM- SJTUsolver；overset grid methodCLC number: U661.33

0 Introduction

Ship maneuvering motion can reflect the maneu⁃verability, steerability and course keeping ability ofship in the process of navigation. Maneuverability isclosely related to the navigation safety and energyconsumption of ships, and its importance is self-evi⁃dent. At present, the maneuverability evaluation ofships is mainly carried out by typical maneuveringmotion test, among which the numerical simulationof ship free turning maneuvering motion is an impor⁃tant means to evaluate the steerability of ships. The

free turning maneuvering motion of ships generallyrealizes the rotary motion under the action of theturning force and moment provided by the rudderthrough executing the target rudder angle. The typi⁃cal free turning maneuvering motion trajectory andcharacteristic parameters are shown in Fig. 1. Gener⁃ally, in the initial stage of ship design, it is necessaryto evaluate the maneuvering motion characteristics(especially steerability) of the designed ship, so as toguide its operation during navigation and to ensurethe lifecycle safety performance.

In general, ship maneuvering is operated by the

1

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CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019

rear rudder to achieve specific maneuvering motions.Therefore, in order to accurately evaluate the maneu⁃vering motion characteristics of ships, it is necessaryto consider the mutual coupling of hull-propel⁃ler-rudder. At present, the widely applied predictionmethods of ship maneuverability mainly include theship model test method and the CFD-based numeri⁃cal simulation method. The ship model test methodis currently the most widely applied and most reli⁃able method. Especially in recent years, thanks tothe improvement of test devices and methods, the ma⁃neuvering test of self-propelled ship model has be⁃come possible. This method can predict ship maneu⁃verability by conducting specific maneuvering mo⁃tion tests in marine-engineering wave basins or natu⁃ral lakes. However, this method requires a large trialbasin, a precise propeller and rudder control system,and the equipment for measuring the 6 DoF motionsof hull. In addition, in order to truly restore the actu⁃al flow field in ship maneuvering motion, it is neces⁃sary to have a experimental tank similar to the actualenvironment, so the equipment and test cost of theship model test method are high. Moreover, in viewof the limited popularity and applicability of the cur⁃rent flow field measuring devices (like the particleimage velocimetry (PIV)), the detailed flow fieldstructures around the hull, propeller and rudder inthe process of maneuvering are not yet available inthe test, and the variations of ship hydrodynamic per⁃formance in this process cannot be analyzed in detail.

The CFD-based numerical simulation of maneu⁃

vering motion can be divided into the constrainedship model and the free running ship model. The for⁃mer obtains various hydrodynamic derivatives bycombining with the maneuvering motion mathemati⁃cal model on the basis of the constrained ship modelmaneuvering motion of numerical simulation. Andthen it simulates the typical ship maneuverability,which is widely applied in the numerical simulationof ship maneuvering motion. Simonsen et al. [2] usedthe self-developed solver CFDShip-Iowa to numeri⁃cally simulate the static and dynamic Plane MotionMechanism (PMM) test, adopted the CFD calculationand test respectively to measure the obtained hydro⁃dynamic derivatives, and then simulated the rotationmaneuvering and zigzag maneuvers of the KCS shipmodel in still water based on the MMG model. Guoand Zou [3] used the commercial software STAR CCM+to numerically simulate the maneuvering motion ofthe standard ship model ONRT in rotating arm test,static oblique towing test and pure rolling test, ob⁃tained the derivative values of maneuvering hydrody⁃namic by numerical regression, and used the 4 DoFmotion mathematical model (MMG) to simulate theship's 25° free turning and the 20/20 zigzag maneu⁃vering motion. It was found that the predicted motiontrajectory is in good agreement with the test results,which verifies the reliability of the maneuverabilityderivatives obtained by the constrained ship modeltest of CFD simulations. The ship maneuvering pro⁃cess can be described more accurately by construct⁃ing the ship-propeller-rudder integrated coupledmotion solving model and performing the direct nu⁃merical simulation of the maneuvering motion of freerunning model.

At present, with the rapid development ofhigh-performance computers and the gradual im⁃provement of overset grid technology, the direct simu⁃lation on the maneuvering motion of free runningship model has become a reality. Carrica et al. [4]used the self-developed hydrodynamic software CFDShip-Iowa V4 to simulate the free turning (35° rud⁃der angle) and zigzag maneuver (20/20) characteris⁃tics of ships at different speeds (Fr = 0.25, 0.41). Innumerical calculation, Carrica et al. used the dynam⁃ic overset grid technology to deal with thelarge-scale ship maneuvering motion, calculated thecharacteristics under wave conditions, and pointedout that the simplified propeller body force model isthe main reason for the prediction error as the errorbetween the maneuverability parameters of numeri⁃cal prediction and the test values is less than 10% .

Fig.1 Free turning maneuvering motion trajectoryand main parameters of ship［1］

Tactical diameter

Transfer 90° changeof heading

180° changeof heading

Turning radius

Path of midship pointAdvan

ce

Drift angle

DistanceRudder execution

Approach course

Distan

ce

2


However, this model ignores the factors such as theresistance to hull motion caused by propeller rotationunder real conditions and the influence of lateralforce. Mofidi and Carrica [5] used the same solver, butconsidered the propeller rotating under real condi⁃tions, and performed the numerical simulation on atypical 10/10 zigzag maneuver and a modified 15/1zigzag maneuver. And then they analyzed the de⁃tailed flow field during the self-propelled maneuver⁃ing motion, as the hull motion and maneuverabilityparameters of the numerical prediction are in goodagreement with the test results. Broglia et al. [6] andDubbioso et al. [7] respectively carried out the numeri⁃cal simulation on the free turning test of twin-screwship in the case of single rudder and twin rudders(among which the rudder and hull motions are pro⁃cessed by dynamic overset grid), compared the ob⁃tained hull motion trajectories with test results, andthen compared the free turning motion trajectoriesand the time history curves such as rotation decelera⁃tion, drift angle and rolling in the case of single rud⁃der and twin rudders. Moreover, they analyzed therudder force and the lateral force variation of hulland appendage during the whole process of turningmotion, and pointed out that the rudder will stronglyinterfere with the load on the propeller in the case oftwin propellers. Based on the open source CFD com⁃puting platform OpenFOAM, Shen et al. [8] developedthe ship hydrodynamic solver naoe-FOAM-SJTUsolver [9-11], introduced and extended the overset gridmodule to the simulation calculation of ship self-pro⁃pelled[12] and maneuvering motions [13-15] under thehull-propeller-rudder interaction, and validated thefeasibility of using unstructured grids to directly car⁃ry out the numerical simulation on the maneuveringmotion of ships with propellers and rudders.

In summary, although the CFD method combinedwith the overset grid technology has been widely ap⁃plied to the direct numerical simulation of ship ma⁃neuvering motion, most of the research is directed tothe maneuvering motion under still water conditions,while the ships sailing at sea are often in waves.Therefore, it is necessary to carry out the accurateprediction of the maneuvering motion under waveconditions, so as to provide more accurate data sup⁃port for ship design. In this paper, thenaoe-FOAM-SJTU solver of CFD , which combineswith overset grid technology, is used to directly simu⁃late free turning motion in waves for a twin-screwship with rotating propellers and turning rudders.Through the numerical calculation of the detailed

flow field around ship, propeller and rudder, the in⁃fluence of the hydrodynamic variation of the ships,the ship-propeller-rudder interference and wavesduring the free turning process on ship steerability isanalyzed.1 Numerical calculation methods

1.1 Governing equations of fluidcalculations

The governing equation of the flow field in thecomputational domain in this paper is the steady orunsteady two-phase incompressible RANS equationas follows:

Ñ ×U = 0 （1）¶¶ρUt

+ Ñ ×(ρUU ) = -Ñpd - g × xÑρ +

Ñ ×(μeffÑU ) + (ÑU ) × Ñμeff + fσ （2）where Ñ is the divergence; U is the velocity field;pd = p - ρg × x , is to the dynamic pressure, and itsvalue is equal to the total pressure value minus thestill water pressure; ρ is the density of liquid or gas;x is the space coordinate; t is time; g is the gravityacceleration vector; μeff = ρ(ν + ν t) , is the effectivedynamic viscosity, among which ν indicates the ki⁃nematic viscosity and v t indicates the eddy viscosi⁃ty; fσ is the surface tension term.

The turbulence model adopts SST k -ω [16], and itcombines the advantages of the standard k -ω andk - ε models, which can ensure the accuracy and re⁃liability of the solution at the wall and far flow fields.The free surface solution adopts the Volume of Fluid(VOF) method with an artificially compressible term [17],and the two-phase VOF transportation equation isdefined as follows:

¶¶αt+ Ñ ×(Uα) + Ñ ×[U r (1 - α)α] = 0 （3）

where U r is the velocity field used to compress theinterface; α is the volume fraction of two-phase flu⁃id, which represents the percentage of the volume oc⁃cupied by the liquid portion, and ranges from 0 to 1(with 0 representing gas and 1 representing water;and the figure between 0 and 1 representing the posi⁃tion of free surface). Therefore, the two-phase flowcan be normalized into a uniform fluid domain by thevolume fraction α .

The above RANS equations (Eq. (1)-Eq. (2)),VOF transportation equation (Eq. (3)) and turbu⁃lence equation are all discretized by finite volumemethod. The built-in discretization schemes inOpenFOAM is used to discretize the equations. The

Wang J H, et al. CFD simulation of ship turning motion in waves 3


CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019temporal term adopts the implicit Euler scheme, theconvection term takes the second-order TVDscheme, the dissipation term takes the central differ⁃ence scheme, and the convection term in the VOFequation takes the Van Leer scheme. In the solutionof fluid governing equations, the velocity and pres⁃sure decoupling adopts the PISO algorithm [18].1.2 Control module of free running ship

Ship maneuver generally has a large-amplitudeship motion. The traditional deforming grids will de⁃grade the quality of grids when simulating large-am⁃plitude motion of objects, which will affect the accu⁃racy. However, the overset grid technology allowsmultiple independent grids to generate uncon⁃strained relative displacements, and can ensure thatthe grids do not deform during the calculation pro⁃cess, thus ensuring the quality of the grids during thecalculation process. Therefore, it is very suitable forthe numerical solution of maneuvering motion prob⁃lems of ships with rotating propellers and turningrudders. The motion model in ship-propeller-ruddermulti-level objects discrete by dynamic overset gridtechnology is shown in Fig. 2. According to differenthull motion modes, propeller and rudder can rotatearound the rotating axis according to the specifiedcontrol parameters (such as propeller speed and max⁃imum rudder angle). The hull can rotate 6 DoF mo⁃tions under the conditions of propeller, rudder mo⁃tion and hull forces.

Based on the overset grid method and themulti-level object motion module, the maneuveringmotion control of the free running ship can be conve⁃niently realized, namely that, the numerical simula⁃tion of specific ship maneuvering motion can be real⁃ized by controlling the rudder angle. The governingequation of the rudder angle of free turning maneu⁃vering motion of the full rudder to starboard at 35° isas follows:

δ(t) =ìíî

ï

ï

max(0 kt) δ 3535max(35 - k(t - tp) 0) t tp

（4）where δ(t) is the rudder angle; k is rudder rate; tpis the time when the rudder is returned, thus endingthe rotation motion, namely that, when the rudder isreturned to its initial zero angle. At the initial mo⁃ment, the rudder is executed according to the rudderrate k until it is full, and then the rudder angle ismaintained to complete the turning maneuvering mo⁃tion. And the rudder is turned back to finish the rota⁃tion motion according to the simulation demands.1.3 Wave generation method with relax-

ation zone

The direct difference between the relaxation zonewave generation method and the velocity inlet bound⁃ary wave generation method is that the former not on⁃ly needs boundary wave generation, but also needs totransform the flow field in a specific area. The specif⁃ic implementation method is to ensure that there isno wave reflection at the outer boundary by using therelaxation zone, and also to ensure that the wave re⁃flection inside the calculation domain does not inter⁃fere with the wave generation boundary, which is al⁃so a feature that the boundary wave generation meth⁃od does not have. In this paper, waves2Foam [19], anopen source wave generation toolbox, is adopted togenerate wave environment in the moving computa⁃tional domain. As shown in Fig. 3, the circular wavegeneration zone is used for wave generation in theprocess of turning maneuvering motion, and wavegeneration and wave absorption can both be realizedin the circular zone by the relaxation method. Thewave generation zone can follow the computationaldomain to move in the calculation, thus ensuring thatthe waves can propagate throughout the entire com⁃putational domain during the 360° rotation motion ofthe ships. In Fig. 3, L is the length of ship.

Hull grid

ORudderOPropeller

X

Background grid Propeller grid

Y

Z

O

Fig.2 Diagram of motions in ship-propeller-rudder system

Fig.3 Diagram of wave generation zone

Wave generation zone

Ship1.0L

1.5L

4


2 Geometry model and test condi-tions

The ship model calculated in this paper adopts theONRT ship model with full-appendage, twin propel⁃lers and twin rudders, which is widely applied forCFD verification, and is listed as the benchmarkship model at the Tokyo2015 CFD workshop andSIMMAN 2021 workshop. For this ship model, thereis a wealth of maneuvering test data to verify the reli⁃ability of the current numerical prediction methods.The geometry model of the hull is shown in Fig. 4.The main dimensions of the hull are shown in Table 1.

In numerical calculation, the overset grid methodis used to directly divide the grids of hull, propellerand rudder. The overset grid arrangement is shownin Fig. 5. The computational domain is divided intosix parts, namely the background grid, the gridaround the hull, two sets of propeller grids and twosets of rudder grids. The completed grids are shownin Fig. 6, and the total number of computationalgrids is 7.11 million.

This paper performs the direct simulation of theturning motion of the ship in waves at 35° rudder an⁃

gle. The initial speed of the ship is 1.11 m/s, corre⁃sponding to Fr = 0.2. The rotation speed of the pro⁃peller in the numerical calculation is set to the mod⁃el self-propulsion point corresponding to this speed,which is 529.14 r/min[13]. The incident waves are setaccording to the test of IIHR [20]. The wavelength λ ofthe incident waves is equal to the ship length LWL ,and the wave steepness H/λ is 0.02.3 Analysis of numerical results of

ship free turning in waves

The numerical simulation of free turning maneu⁃vering motion in waves starts from the final stableself-propulsion numerical calculation, and then be⁃gins to release the 6 DoF motions of the ship. In ac⁃cordance with the test, the rudder is steered whenthe peak of the incident waves reaches the bow, andthe rudder is controlled according to the free turningmaneuvering motion. All numerical calculations arecarried out in the high performance computing clus⁃ter of the Computational Marine Hydrodynamics Lab(CMHL) of Shanghai Jiao Tong University. And 40processes are adopted for parallel calculation, andthe calculation time step is Dt =0.000 5 s, corre⁃sponding to the propeller rotation of 1.5° for eachtime step. It takes a total of 1 206 h to complete thefree turning maneuvering motion in waves, corre⁃sponding to 155 000 time steps.

Fig. 7 shows the motion trajectory obtained fromthe free turning of the ship in waves and its compari⁃son with the test results [17]. As can be seen from thefigure, the current numerical results are in goodagreement with test results, but the turning diameterof numerical prediction is larger than that of the testresults. This is mainly due to the modification of thegeometric model of the rudder in order to ensureenough interpolation grids between overset grids innumerical calculation, which reduces the effectiverudder area and thus reduces the rudder efficiency.In addition, it can be seen from the figure that theturning trajectory shows significant fluctuations

Fig.4 Geometry model of ONR Tumblehome ship

Main parametersWaterline length/m

Ship width/mDraft/m

Displacement/kgDiameter of propeller/m

Inclination angle of propellershaft/（°）

Rotation direction of propellerRudder speed/（（°）·s-1）

Model size3.1470.3840.11272.6

0.106 65

Internal rotation35.0

Actual size154.018.785.494

8.507×106—

—

Internal rotation—

Table 1 Main particulars of ONR Tumblehome ship model

Fig.5 Overset grid arrangement

Hull grid

Background grid

Propeller grid

Rudder grid

Fig.6 Local grid distribution around twin propellers and rudders

Hull grid

Rudder gridPropeller grid

Overset grid distribution XZ

Y



CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019when the ship's heading angle changes by 90° and270°. Fig. 8 shows the corresponding local magnifica⁃tion comparison chart. In the corresponding two timeinstants, the ship's motion trajectory produces signifi⁃cant fluctuations, and both the test and CFD predic⁃tion results show this phenomenon. The fluctuationamplitude obtained by numerical calculation is obvi⁃ously smaller than the fluctuation value in the test,which also shows that the ship's turning ability inCFD simulation is slightly worse than that in the test,and also explains the reason why the ship's turningcircle predicted by numerical method in Fig. 7 islarger.

The characteristic parameters of the ship's turningcircle predicted by numerical method and the com⁃parison with the test results [20] are shown in Table 2.

In the simulation process, in order to ensure the re⁃

liability of the comparison, the time scale is adjustedso that the CFD simulation and the physical test canperform rudder operation at the same time. It can beseen from the comparison results in the table that theerrors of all the characteristic parameters and test re⁃sults are within 10%, and the current numerical cal⁃culation can predict the maneuvering motion charac⁃teristics of the free turning ship in waves with higherprecision.

Fig. 9 shows the time history curves of ship mo⁃tions for turning circle maneuvering in waves. It canbe seen that the ship's heaving, pitching and rollingmotions present more obvious wave-frequency oscil⁃lation characteristics (Fig. 9(a), Fig. 9(b) and Fig. 9(c)).In addition, since the wave angles encountered bythe ship during the turning maneuvering motion alsochange at any time, there are also low-frequencyfluctuations caused by turning maneuvering motionunder high-frequency motion. During the entire turn⁃ing maneuvering motion, the maximum pitching am⁃plitude can reach up to 2.5° , and the amplitude ofrolling motion is from -4.4° to 8° . Furthermore, itcan be seen from the time history curves of the roll⁃ing motion (Fig. 9(c)) that the amplitude of rollingmotion caused by waves is larger than that caused byinitial steering. However, the motions of the threeplanes, namely the surging, swaying and yawing mo⁃tions, show less wave-frequency motion characteris⁃tics. Small fluctuations can be seen from the yaw mo⁃tion (Fig. 9(d)), which may also result in the localfluctuations in the plane motion trajectory shown inFig. 8.

Fig.7 Comparison of turning circle trajectory-15 -10 5 0

X/m

15

10

5

0

-5

Y/m

Simulation valueTest value

-13 -12 -11X/m

-3 -2 -1X/m

7

6

5

4

3

Y/m

Fig.8 Local comparison of trajectory

Simulation valueTest value

Main parametersLongitudinal distance/mHorizontal distance/mSteering time at 90°/sTactical diameter/m

Steering time at 180°/sTurning diameter/m

CFD results6.917 14.106 3

12.282 210.183 824.589 410.280 7

Test results6.997 83.879 7

11.570 09.621 3

22.410 09.646 4

Error/%-1.155.846.155.859.726.57

Table 2 Comparison of main parameters of turningcircle trajectory

（c）Rolling motion

0.040.02

0-0.02-0.04

Heavi

ng/m

0 10 20 30 40 50 60Time/s

0 10 20 30 40 50 60Time/s

0 10 20 30 40 50 60Time/s

20

-2Pitch

ing/（°）

86420-2-4Rolli

ng/（°）

（a）Heaving motion

（b）Pitching motion

6


Fig. 10 shows the changing curves of ship speedand yawing rate for free turning circle maneuver inwaves. It can be seen that in the course of ship turn⁃ing maneuvering motion, the ship's turning speedwill decrease obviously, and the maximum decelera⁃tion can be up to 40% . The initial deceleration iscaused by the rudder turning, and will be maintainedwithin an average deceleration of 30% after enteringthe turning maneuvering motion. For the yawing rate,the initial significant rate change is due to the influ⁃ence of the rudder, while the later fluctuation iscaused by the wave direction that brings changes tothe ship, and the maximum yawing rate can reach12.2 (°)/s.

Fig. 11 shows the changing curves in propellerthrust and torque for turning circle maneuver inwaves. It can be seen that the thrust and torque ofthe propeller exhibit obvious wave-frequency vibra⁃tion characteristics, which are mainly caused by thechange of the propeller inflow in the process of shipmotion, thus resulting in the fluctuation of propul⁃sion performance. The higher frequency oscillationcan be seen from the local magnification diagram,which is caused by the real rotating propeller bladespassing through flow field.

Fig. 12 shows the time history curves of hydrody⁃namic load acting on rudder during rudder execu⁃tion. It can be seen that before the rudder execution,the resistance acting on the rudders on both sides isbasically the same, and the lateral forces are symmet⁃rical. However, after the rudder execution, the rud⁃

Fig.9 Time history curves of ship motions for turning circlemaneuvering in waves

240160

800

-80-160-2400 10 20 30 40 50 60

Time/s

Yawing

/（°）

0 10 20 30 40 50 60Time/s

0 10 20 30 40 50 60Time/s

0-2-4-6-8-10-12-14

Surgin

g/m

121086420-2

Swayin

g/m

（d）Yawing motion

（e）Surging motion

（f）Swaying motion

（b）Yawing rate change

（a）Speed change

Fig.10 Time history curves of ship speed and yawing rate forturning circle maneuver in waves

0 10 20 30 40 50 60Time/s

1.21.11.00.90.80.70.60.5

U/（m

·s-1 ）

0 10 20 30 40 50 60Time/s

0-2-4-6-8-10-12Yawing

rate/（（

°）·s-1 ）

Fig.11 Time history curves of propulsion coefficients forturning circle maneuver in waves

0 10 20 30 40 50 60

0 10 20 30 40 50 60Time/s

28.4 28.6 28.8 29.0 29.2 29.4

5.04.54.03.5

PortStarboard10

50

-5-10

Thrust

/N0.05

0

-0.05

-0.10

Torque

/（N·m

）

（a）Thrust change

（b）Torque change

（a）Rudder resistance

（b）Lateral forceFig.12 Time history curves of rudder forces

during rudder execution

4.0 4.5 5.0 5.5 6.0 6.5 7.0Time/s

PortStarboard

4.0 4.5 5.0 5.5 6.0 6.5 7.0Time/s

PortStarboard

43210

-1

Rudde

rresist

ance/N

20

-2-4-6

Latera

lforce

/N

Rudde

rexecu

tion

Maxru

dderan

gle

Rudde

rexecu

tion

Maxru

dderan

gle

PortStarboard



CHINESE JOURNAL OF SHIP RESEARCH，VOL.14，NO.1，FEB 2019der resistance is significantly increased, and the lat⁃eral forces become the same direction forces, whichproduce larger lateral resultant forces. Furthermore,the lateral resultant forces also cause the ship to pro⁃duce turning maneuvering motion.

Fig. 13 shows the changes of vortical field aroundtwin propellers and rudders during rudder execution.It can be seen that at the initial stage, when the rud⁃der angle is 0° , the distribution of vorticity aroundtwin propellers and rudders is basically symmetrical.However, with the increase in rudder angle, the rud⁃ders will cause obvious interference to the front pro⁃pellers. As the rudders rotate to the larboard, theport rudder will interfere with the hub vorticity of thepropellers, while the starboard rudder will affect thetip vorticity of the starboard propeller. This also ex⁃

plains the difference between the hydrodynamic forc⁃es of propellers and rudders on both sides in Fig. 11and Fig. 12. There is a significant flow separationaround the rudders, but the currently used RANSmethod cannot accurately capture the separatingflow in this case, so it will cause errors in the calcula⁃tion of the rudder force, which is one of the reasonsfor the turning circle in the current calculation to be⁃come larger.

Fig. 14 indicates the changes in the free surfacewaveforms at four typical moments for turning circlemaneuvering in waves, corresponding to the mo⁃ments of heading angles at 0°, 120°, 240° and 360°.It can be seen that the wave environment around theship is basically symmetrical when there is no steer⁃ing, but when the heading angle reaches 360° , thedifference between the wave patterns on both sidesdue to the turning can be seen at the bow and thestern. However, from the free surface at the 120° and240° heading angles, it can be seen that there is asignificant height difference between the wave surfac⁃es on both sides, which also leads to uneven pressuredistribution on both sides of the hull. Fig. 14(d) alsoshows that the bow will be lifted out of the water,which proves that the ship will produce large-scale6 DoF motions under this wave condition.

Fig.13 Snapshots of vortical field around twin propellers andrudders during rudder execution

（a） θ = 0°

（b） θ = 11.7°

（c） θ = 23.3°

（d） θ = 35°

（a）0° heading change

（b）120° heading change

（c）240° heading change

8


4 Conclusions

In this paper, the CFD solver naoe-FOAM-SJTUthat combines the overset grid technology is appliedto perform the direct simulation for the ship free turn⁃ing maneuvering motion in waves with hull-propel⁃ler-rudder interaction. The characteristic parameters(such as the longitudinal distance, transverse dis⁃tance, tactical diameter and turning diameter) pre⁃dicted by numerical value for turning circle maneu⁃vering in waves are in good agreement with the testresults, and the errors are less than 10%, which veri⁃fy the applicability and reliability of the current solv⁃er to the prediction of ship free turning maneuveringmotion in waves under the hull-propeller-rudder in⁃teraction. In addition, according to the calculation re⁃sults, the ship's heaving, pitching and rolling mo⁃tions show obvious wave-frequency motion response,while the wave-frequency vibration characteristicsof the three plane motions of surging, swaying andyawing are not obvious. The maximum ship stall canbe up to 40% when the ship performs free turning inwaves. At the same time, the changes in propulsionperformance and rudder force during the entire ma⁃neuvering motion process are given. And the reasonsfor the hydrodynamic changes under the turning ma⁃neuvering motion in waves are analyzed through de⁃tailed flow field information, such as the change offree surface and the change of vorticity field aroundtwin propellers and rudders at different times.

Because the current numerical simulation uses thetime-averaged RANS method to solve the flow field,it obtains the poor accuracy when capturing the largeseparation flow around the propellers and rudders,which also leads to some errors in the current numer⁃ical prediction. Therefore, the future work will main⁃ly focus on solving this problem based on the moreaccurate simulation method for separation vortex, soas to give more precise flow field simulation and ob⁃tain more accurate numerical prediction results.

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（d） 360° heading changeFig. 14 Snapshots of wave elevation around ship hull for

turning circle maneuvering in waves



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CFD数值模拟船舶在波浪中的回转操纵运动

王建华 1，2，3，万德成*1，2，3

1 上海交通大学海洋工程国家重点实验室，上海 2002402 高新船舶与深海开发装备协同创新中心，上海 2002403 上海交通大学船舶海洋与建筑工程学院，上海 200240

摘要：［目的目的］船舶回转操纵运动能够反映出船舶的回转特性，与船舶的航行安全密切相关。［方法方法］为此，采

用基于重叠网格技术的 CFD求解器 naoe-FOAM-SJTU，对标准船模 ONRT在波浪中自由回转操纵运动进行直接数值模拟。运用动态重叠网格技术求解船、桨、舵系统复杂运动，计算中，螺旋桨转速对应于静水中的船模自航

点进行 35°转舵，实现自由回转船舶操纵运动。通过全粘性流场的整体求解，给出波浪中自由回转操纵运动中船舶六自由度运动、螺旋桨和舵的水动力载荷变化，以及波浪中船舶的回转圈特征参数，并与同试验结果进行

对比。通过数值计算得到精细的流场信息，分析波浪对船舶自由回转操纵运动的影响。［结果结果］数值预报得到的

船舶运动轨迹、回转圈参数与试验值吻合较好，证明 naoe-FOAM-SJTU 求解器对于波浪中船—桨—舵相互作用下的船舶自由回转操纵运动数值预报的适用性和可靠性。［结论结论］船舶回转操纵运动的数值模拟，可为回转性能

的评估提供有效的前期评估手段。

关键词：船舶操纵性；自由回转；船—桨—舵相互作用；naoe-FOAM-SJTU求解器；重叠网格方法

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