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