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CFD, Potential Flow, and System-Based Simulations of Course Keeping in

Calm Water and Seakeeping in Regular Waves for 5415M

Frederick Stern

a

, Serge Toxopeus

b

, Michel Visonneau

c

, Emmanuel Guilmineau

c

,Woei-Min Lind, and Gregory Grigoropoulos

e

a IIHR - Hydroscience & Engineering, The University of Iowa, Iowa City, IA, 52242, USAb Maritime Research Institute (MARIN), Wageningen / Delft University of Technology, The Netherlands

c ECN - Ecole Centrale de Nantes, Nantes, FrancedScience Application International Corporation (SAIC), Arlington, VA, 22203, USA

eDept. of Naval Architecture and Marine Eng., National Technical University of Athens, Athens, Greece

[email protected]

ABSTRACT

CFD, potential flow and system-based methods are validated for ship course keeping in calm water and

seakeeping in waves. In calm water, a self-propelled free model of 5415M appended with passive, active or nofin stabilizers under either damped or forced roll is simulated using different methods. The forced roll is

induced by either forced rudder motion or forced fin motion. In the presence of waves, the 6DOF motions of

the model appended with active fins are simulated in regular head waves, regular beam waves and quartering

bi-chromatic waves. The predictions for all methods are validated with the extensive data provided by MARIN

for ship motions and forces and moments on the appendages such as rudders, fins and bilge keels. The results

are investigated with consideration to the mathematical model of ship motions and the high fidelity results are

used to explain some of the complex physics. The course keeping and seakeeping of the model, the reduction

rate of the roll motion, the effectiveness of the fin stabilizers as roll reduction device and the interaction of the

roll motion with other motions are also investigated.

1.0 INTRODUCTION

The simulation of ship course keeping and seakeeping has mostly been studied using potential flow (PF) and

system-based (SB) methods and more recently computational fluid dynamics (CFD). In most of the

simulations, however, the degree of freedom was limited to 3DOF or 4DOF and the validation was only

investigated for the ship motions. This was due to both the very high level of complexity of full 6DOF

simulations and few experimental fluid dynamics data (EFD) data available for such simulations to be

validated. In SIMMAN 2008 Workshop [1] extensive EFD free running data was provided for four appendedhull forms including two tankers (KVLCC), a container ship (KCS) and a surface combatant (5415M) to

validate the prediction capabilities of SB, PF, and CFD for maneuvering tests. The workshop was the first of

its kind primarily because most maneuvering simulation methods have yet to be benchmarked for their

prediction capabilities through systematic quantitative validation against EFD for free model. The EFD data,

however, was limited to ship motions in calm water and did not include forces or moments. Extensive

experiments were previously performed at MARIN to generate validation material for 6DOF motions in calmwater and waves and for the forces and moments of the appendages such as bilge keels, rudders and stabilizer

fins, see Toxopeus et al. [2]. The measured data provides a unique opportunity to investigate the prediction

capability of SB, PF and CFD methods for complicated 6DOF motions of the ship, surface controller motions

and forces and moments on the appendages.

The SB methods provide a mathematical framework to study the ship course keeping and seakeeping. The

prediction capability of SB methods are strongly function of the inputs for maneuvering coefficients, the

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degree of freedom of the model and the mathematical model techniques used to include the wave, the rudder

and the propulsion forces. In the past, SB models have been applied extensively to estimate ship maneuvering

capabilities. Loeff and Toxopeus [3] discussed the application of SB prediction tools in concept design and

provide information about the correlation of the predictions with an extensive database of experimental

results. At the SIMMAN Workshop, Toxopeus and Lee [4] used several simulation tools to predict themaneuverability of all test cases. The simulation tools were all of the modular type, i.e. forces and interactions

on each component of the ship were described separately. The coefficients in the model were based on

empirical formulae, such that experimental results were not required to predict the maneuverability of ships. It

was seen that the difference between predictions and the experiments depended strongly on the range of

application of each prediction tool: MPP (originally made for full-block ships) provided good results for the

KVLCCs, FreSim (for naval ships) for the 5415M and SurSim with slender body method (for cruise ships,

ferries, motor yachts) for the KCS. Furukawa et al. [5] studied prediction capability of 3DOF SB model. They

employed the Japanese MMGs (Japanese Mathematical Maneuvering model Group, see Ogawa and Kasai

[6]) model to include rudder and propulsion forces and predicted the turning diameter of KVLCC2 within

20%D accuracy. Kim and Kim [7] investigated the maneuvering performance of KVLCC tankers using a

3DOF SB model established based on MMG concept. Hydrodynamic coefficients were estimated by

analyzing PMM data. Predicted results showed about 5%D error for KVLCC2 turning diameter. To includeroll motion in maneuvering prediction of KCS, Yasukawa and Sano [8] developed 4DOF MMG based SB

model but neglected the hydrodynamic coupling between roll and other modes of motion. The results showed

very good agreement with experiment for the turning trajectory and heel angle but the zigzag overshoot angles

were over predicted. Umeda et al. [9] also employed MMG model and developed a coupled 4DOF SB model

which includes propulsion, rudder and waves forces in following waves with low encounter frequency to

predict the dynamic instability map for ONR Tumblehome. The model showed qualitative agreement but the

predicted roll exceeded 90 for Fr>0.3 while EFD maximum roll angle was 71. Yasukawa [10] designed a

coupled 6DOF SB model for all wave conditions including any heading angles and wave length to predict

motions of a self propelled model with rudder controllers. The MMG model was adopted to include rudder,propulsion and wave forces. A linear time domain strip method was used to calculate wave induced motions.

The total motion was calculated by summation of low frequency motions induced by maneuvering and high

frequency motions induced by waves. The simulations showed only qualitative agreements with EFD and haddifficulties for quantitative prediction in short wave conditions. Ayaz et al. [11] developed a coupled non-

linear 6DOF MMG model with frequency dependent coefficients, incorporating memory effects in randomwaves. The model was validated against free running test data and indicated qualitative agreement.

Unlike SB models, the PF methods employ strip theory, lifting line/surface or panel methods to compute

directly the forces and moments used to predict 6DOF ship motions. However, empirical corrections to

account for viscous effects are required. Yen et al. [12] used Large Amplitude Motion Program (LAMP) panel

method code to study the maneuvering capability of 6DOF 5415M model. The hull and rudder maneuvering

forces were implemented using a systems-based approach and the propeller was included using open-water

curves. The results showed better agreement with EFD for turning than zigzag maneuvering. The heel and

drift angle and speed loss were also well predicted for turning. Similar predictions with similar comparison

errors were made with the simulation code Fredyn, see Toxopeus and Lee [4]. Chen and Zhu [13] used timedomain Rankine panel method for predicting motions of a ship only restrained in surge in oblique waves.

Linear free surface boundary condition and mean wetted surface were adopted, while the numerical damping

method was used for the radiation conditions. The artificial spring model was used to control the numerical

drifting in sway and yaw motions. The empirical method was employed for roll damping due to viscous

effects. The motions for Flokstra container in oblique waves were compared and validated against

experimental data. The results showed good agreement for heave and pitch but not for roll as it depends on the

roll damping of viscous effect. Other motions were not validated since they were not recorded by the model

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test. Song et al. [14] employed a 3D Rankine panel method to investigate the 6DOF motion response and

structure loads on a containership. The numerical code was based on the weakly nonlinear method including

nonlinear FroudeKrylov and restoring forces. The empirical value was used for viscous damping due to roll

motion. An artificial spring model was employed for surge, sway and yaw motions to restrict the divergence

of numerical solutions. The comparisons showed some difference at low frequency region for horizontalmotions, i.e. surge, sway and yaw while heave, roll, and pitch showed acceptable agreement. At low

frequencies, the spring model had a significant effect on motion responses and better treatments were required

to control non-restoring motions such as surge, sway, and yaw. An extensive benchmark study of state-of-the-

art seakeeping prediction tools was presented by Bunnik et al. [15]. In this study, 11 different codes (9 PF

codes and 2 CFD codes, of which one was ISIS-CFD) were used to calculate motions of ships in a seaway.

Generally, it was found that good PF codes produce good results. When the motions are moderate and in the

absence of large viscous effects, the benefit of using CFD instead of the best PF methods was found to be

small.

CFD has the advantage of predicting course keeping and seakeeping without using a mathematical model or

empirical values for viscous effect, but it is considerably more expensive than SB or PF approaches. Huang et

al. [16] demonstrated full 6DOF simulations capability in irregular waves, including the effects of air, with asteered rudder using body force propeller model. Muscari et al. [17] studied 3DOF turning circle maneuver of

the KVLCC2 in no free surface environment using RANS with the rudders and propellers. Jacquin et al. [18]

performed 6DOF turning maneuver simulation of series 60 hull form with steered rudder and body force

propeller model using RANS code ICARE. The 6DOF motions of a KVLCC1 tanker with moving rudder and

rotating propeller in a free surface flow were simulated by Carrica and Stern [19]. The rudder geometry was

approximated by a spade rudder to simplify the geometry. The 6DOF motions were validated against

experiment but the turning diameter was under predicted. Carrica et al. [20] performed model and full scale

simulations of turning and zigzag maneuver for 5415M hull form including rudder and body force propellers.

Sadat-Hosseini et al. [21] studied full 6DOF simulations of surf-riding, periodic motion and broaching in

regular waves for a ONR Tumblehome model with steered rudder using body force propeller model. The

results were validated against experimental data and compared with 4DOF SB model solutions. Also, 2DOF

captive simulations were carried out to evaluate the coefficients for the SB model. Such an approach was alsofollowed by Toxopeus [22]: RANS calculations were used to derived coefficients for an SB model and the

results of consecutive maneuvering simulations were compared with model experiments, demonstrating a

large improvement compared to the simulations with the original coefficients derived from empirical

formulae. The same ONR Tumblehome used in [21] but with rotating propellers are employed by Carrica et

al. [23] to improve the predicted motions. All the recent simulations [20,21,23] provide prediction capability

for 6DOF motions while detailed validation for forces and moments of appendages are not studied. The forces

of bilge keels are studied by Miller et al. [24] for 1DOF forced roll motion with large amplitude for ONR

Tumblehome for a range of forward speeds using CFDShip-Iowa. It was shown that CFDShip-Iowa was able

to distinguish between the eddy-making and bilge keel contributions of the total roll moment which are

difficult to accurately predict using potential flow simulation tools. Bassler et al. [25] expanded 1DOF

simulation in [24] to 2D and 3D using CFDShip-Iowa. They also studied the bilge keel forces in beam waves.

Dai and Miller [26] investigated inflow conditions to the propellers from the bilge keels and forces on thebilge keel in steady turn using CFDShip-Iowa for DTMB 5617 model. Dai and Miller [27] investigated the

forces on propellers and rudders as well as bilge keels. It was shown that the propeller side force needs to be

taken into account when comparing hull and appendages generated side forces in the simulations. The

qualitative comparisons for the rudders forces showed large discrepancies and it was indicated that the

primary cause of discrepancies was due to poor predictions of velocity inflow at the rudder plane.

The objective of this paper is to perform and validate CFD, PF, and SB simulations for extensive experiments

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performed at MARIN in calm water and waves for 5415M as part of international collaboration under

auspices NATO AVT-161. The experiments were previously performed as part of THALES Project -the

cooperative research program initiated between the Royal Netherlands Navy, the Italian Navy and the Danish

Navy. The CFD, PF, and SB results are investigated with consideration to the mathematical model of ship

motions similar to the analysis performed for parametric rolling and broaching by Sadat-Hosseini et al.[21,28]. Also, the detailed validation study is performed for forces and moments on the appendages including

rudders, fins and bilge keels and the high fidelity results are used to explain some of the complex physics.

CFD computations are performed using the CFDShip-Iowa code [29], a finite difference code employing a

single-phase level set method and a blended k-/k-turbulence model, and ISIS-CFD code [30,31,32] which

is a finite volume code using VOF method and k- turbulence model. PF simulations are performed by

employing Fredyn which is a non-linear strip theory based potential flow code supplemented by empirical

models for viscous forces [4] and SWAN [33,34] and LAMP [12,35-39] which are potential flow panel codes.

The SB roll decay and forced roll predictions are carried out by using both SurSim and FreSim codes [4]

developed by MARIN.

2.0 EFD METHOD

2.1 Ship Model

Free running experiments in calm water and waves were conducted for 5415M. The 5415M model is a geosim

of the DTMB 5415 ship model, but with different appendages. Main particulars and body plan are shown in

Table 1 and Fig. 1, respectively. The model was manufactured of wood and appended with skeg, twin split

bilge keels, roll stabilizer fins, twin rudders and rudder seats slanted outwards, shafts and struts, and counter-

rotating propellers. The rudder was of the spade type. The lateral area of the rudders was 215.4m2 i.e.

21.8% of the lateral area of the vessel, LppT. The propellers were fixed pitch type with direction of rotation

inward over top. The stabilizer fins were of the non retractable low aspect ratio type. The scale ratio of the

model was 35.48.

2.2 Test Setup

All experiments were carried out in the MARIN seakeeping and maneuvering basin which measures

170m40m5 m. The water depth to ship draft ratio was 29 in all tests indicating deep water condition. The

tests were performed with the ship model free running and the propeller rate of revolutions adjusted to the

self-propulsion point of the model for the envisaged speed. During the test, the wave elevation, ship motions,

ship accelerations, rudder and fin angles and propellers revolutions were measured. Also, propeller torque and

thrust and loads on bilge keels, rudders and fins were recorded. The wave elevations were measured in front

of the vessel and beside the vessel at mid-ship using resistance type wave probes and used to represent the

wave elevation at center of gravity. The ship motions were recorded through optical tracking system. The ship

accelerations were measured at three locations on the model using accelerometer. Several Potentio-meters

were employed to measure rudder and fin angles. Strain gauge transducers were used to measure loads on the

propellers, rudders, and fins. For loads on bilge keels, one component force transducers were utilized. More

details of test setup can be found in [2].

The coordinate system is ship-fixed located at centre of gravity, with x pointing toward the bow, y to portside

and z upward, as shown in Fig. 2. Thus the forces and moments are positive for X-force forwards, Y-force to

portside, Z-force upward, K-moment pushing starboard into the water, M-moment pushing the bow into the

water and N-moment pushing the bow to portside. The ship positions (x,y) were measured in an Earth-fixed

coordinate system with x pointing North and y pointing West. The roll () is positive for starboard down, the




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pitch () is positive for bow down and the yaw angle () is positive for bow turned to portside. The rudder

angle () is positive for trailing edge to portside and the stabilizer fin angles (F)are positive for nose down

position.

2.3 Test Conditions

In calm water, a self-propelled free model appended with passive, active, or no fin stabilizers under either

damped or forced roll is tested and the course keeping of the model is investigated. Also, the reduction rate of

the roll motion, the effectiveness of the fin stabilizers as roll reduction device, the interaction of the roll

motion with other motions and forces or moments on all appendages are investigated. In the presence of

waves, the course keeping of the ship as well as the ship responses (RAOs) are measured. Also, different wave

types such as regular waves and bi-chromatic waves are considered. The conditions for different tests in calm

water and waves are summarized in Table 2 and 3, respectively.

Herein, some of the cases are selected based on careful studies of the test results for validation of

computations. Three roll decay test at Fr=0.248 are considered: initial roll deg with passive fins,

deg with no fins, and deg with active fins. Also, three forced roll test conditions will be

studied: passive fins with forced rudder, active fins with forced rudder, forced fins with passive rudder. In

presence of waves, two test conditions in regular beam and head waves with active fins and once case in

quartering bi-chromatic waves with active fins are considered.

In roll decay test, the initial roll angle is applied by pushing the side of the model into the water. In forced roll,

the roll motion is applied by moving the rudders or fins in a sinusoidal motion. The frequency of rudders or

fins oscillation is 0.55Hz in full scale. The amplitude of oscillation is 15 deg for rudders and 25 deg for fins.

For active fins cases, the fins are controlled with autopilot controller in which D=5 sec in full scale.

Also, the rudders are controlled by an autopilot controller, with but the controller

settings were not recorded during the test. After the tests the coefficients , , andwere determined for

each test individually by least-square fitting.

3.0 CFD METHOD

3.1 CFDShip-Iowa 4.5

CFDShip-Iowa [29] is designed for ship applications using either absolute or relative inertial non-orthogonal

curvilinear coordinate system for arbitrary moving but non-deforming control volumes. Turbulence models

include blended k-/k-based isotropic and anisotropic RANS and DES approaches with either integration to

the wall or wall functions. The free surface is modeled using a single-phase level set method. The domain is

discretized using multiblock/overset structured grids. The overset connectivity is obtained using the code

Suggar. Convection terms are approximated with finite differences second-order upwind for RANS or fourth-

order upwind biased for DES. The second-order centered scheme is used for the viscous terms. The temporal

terms are discretized using a second-order backwards Euler scheme. Incompressibility is enforced by a strong

pressure/velocity coupling, achieved using either PISO or projection algorithms. The 6DOF capabilities areimplemented using Euler angles and enabled with a hierarchy of bodies. The rigid body equations are solved

in the ship system while the fluid flow equations are solved in an earth-fixed inertial reference system such

that the forces and moments are projected appropriately to perform the integration of the rigid body equations

of motion.





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3.1.1 Computational Domain and Grids

In order to achieve a large size computational domain with reasonable number of grid points, a cylinder shape

computational domain was used for cases in calm water. The radius of domain is 4.5 times larger than ship

length and the domain extends from z=-1L to z=0.25L in vertical direction. For cases in waves, the domain is

in box shape extending from -0.5


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method. The solver is based on the finite volume method to build the spatial discretization of the transport

equations. The unstructured discretization is face-based, which means that cells with an arbitrary number of

arbitrarily shaped faces are accepted. A detailed description of the solver is given in [30,31]. The velocity

field is obtained from the momentum conservation equations and the pressure field is extracted from the mass

conservation constraint, or continuity equation, transformed into a pressure equation. In the case of turbulentflows, transport equations for the variables in the turbulence model are added to the discretization. Free-

surface flow is simulated with a multi-phase flow approach: the water surface is captured with a conservation

equation for the volume fraction of water, discretized with specific compressive discretization schemes

discussed in [30]. The method features sophisticated turbulence models: apart from the classical two-equation

k-w and k-e models, the anisotropic two-equation Explicit Algebraic Stress Model (EASM), as well as

Reynolds Stress Transport Models are available [31,32]. The technique included for the 6 degree of freedom

simulation of ship motion is described by Leroyer and Visonneau [40]. Time-integration of Newtons laws for

the ship motion is combined with analytical weighted or elastic analogy grid deformation to adapt the fluid

mesh to the moving ship. Furthermore, the code has the possibility to model more than two phases. For

brevity, these options are not further described here.

3.2.1 Computational Domain and GridsThe computational domain extends from -1.5L < x < 3.5L, -1.5L < y < 1.5L and -1.25L < z < 0.375L. The

ship axis is located along x-axis with the bow located at x=0.5L and the stern at x=-0.5L. The free-surface at

rest lies at z=0. The unstructured hexahedral grid is generated with HEXPRESS. All appendages are taken

into account except the propellers which are modeled as a body force field applied at the position of

propellers. A local zone of refinement is created near the hull, to ensure small grid spacing. This grid is

composed of 5.9 million cells with about 300,000 cells located on the hull. Figure 3b illustrates the local mesh

distribution close to the bow and the stern.

3.2.2 Case Setup

The roll decay tests with no fins or passive fins are investigated. Firstly, an initial simulation with a ship free

to move in trim and sinkage with no roll angle is carried out. For this simulation, the actuator disk theory is

applied. Then, the initial roll angle is applied. The flow around the ship is computed by imposing the surge

motion while all other modes of motion are free. Moreover, the rudder action due to the autopilot is ignored in

these computations.

4.0 PF METHOD

4.1 FREDYN

Fredyn is developed by the Cooperative Research Navies (CRNAV) group. Its fundamentals are discussed in

De Kat and Paulling [41]. The version considered in this paper is Fredyn version 10.3. Fredyn is a program

dedicated to simulate the motions of high-speed semi-displacement ships in severe conditions. All six degrees

of freedom are computed in the time domain, where the motions can be large, up to the point of capsize. It is

also capable of computing the ingress of water through openings in the hull and superstructure. The programis intended to be used in the initial design stage when model test data are not available.

The mathematical model consists of a non-linear strip theory approach, where linear (wave radiation and

diffraction) and non-linear (Froude-Krylov, including buoyancy) potential flow forces are combined with

viscous forces (propeller, bilge keel, rudder and fin forces, hull lift and drag, roll damping, wind loads and

etc). These viscous force contributions are of a nonlinear nature and based on (semi)empirical models. The

program can handle regular waves or irregular waves, including directional spreading. Wind can also be taken





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into account.

Several options exist to model the viscous forces on the hull during maneuvers. In the present work, the

viscous forces are based on the default Fredyn model. Alternatively, the modeling from FreSim, see section

5.1, can be used or user-defined coefficients can be provided. The roll damping is based on an adapted methodfor fast displacement ships (FDS). The Fast Displacement Ship method was obtained from analyzing

systematic model tests on fast displacement type vessels (frigates). Possible other options for the roll damping

are the Ikeda-Himeno-Tanaka method, obtained from model tests on non-frigate type ships at low to moderate

speeds and the option in which coefficients can be defined by the user.

Fredyn has been validated against model tests with frigates and containerships. For frigate-type hull forms, in

particular, both excitation forces and motion response in waves have been considered in detail, including

conditions leading to capsize. Examination of the various assumptions embedded in Fredyn shows that in

general the program should be valid for any type of a relatively slender mono-hull operating at a Froude

number below 0.5. All force contribution formulations are independent of ship type, except for part of the

maneuvering forces.

A recent application of Fredyn for the 5415M hull form in calm water and waves can be found in Carette andVan Walree [42] and Quadvlieg et al. [43]. Validation of amongst others roll damping predictions or motions

in waves with Fredyn can be found in Boonstra et al. [44] and Levadou and Gaillarde [45]. The maneuvering

prediction capability of Fredyn was validated by Toxopeus and Lee [4].

4.1.1 Case Setup

The hull form (sectional data) and the particulars of the propeller, bilge keels, rudders and stabilizer fins as

described in Section 2.1 were used as input to the program. The bare hull resistance curve was based on an

estimation using a modified version of the Holtrop and Mennen method [46]. This method also provides

estimates of the propeller wake fraction and thrust deduction fraction. The propeller thrust curve was obtained

from open water tests with the model propeller. Other than the use of the propeller open water tests and

estimation of the resistance curve, wake fraction and thrust deduction fraction, all coefficients were based onthe default values calculated by Fredyn. No additional tuning of the empirical coefficients based on model testdata was conducted. The rudder seats were modeled as additional fixed rudders.

During the cases with the rudders steered by autopilot, the coefficients determined from least-square fitting of

the rudder angle signal during the experiments were used, see section 2.3. However, for simplification of the

setup, the sway gain coefficient was ignored. This means that deviations in the y position between the

simulations and experiments can occur.

In Fredyn, the RPM of the propellers needs to be specified. In the present work, the RPM from the

experiments was used as input. Due to a different balance of resistance and propeller thrust, this may result in

a different speed during the simulation.

4.2 SWAN

SWAN2 2002 [34] is a 3D time-domain, panel code developed at MIT. The general formulation is described

by Sclavounos [33] while the specific time-domain solution was presented in detail by Kring et al. [47]. The

software implements a fully 3D approach based on the distribution of Rankine sources over the wetted and the

free surface. The linear free-surface condition is satisfied, while it has the capability of taking into account the

non-linear Froude-Krylov and hydrostatic forces. This option however, was not activated in the calculation




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presented herein.


A sensitivity analysis was conducted in order to define suitable extent of the free surface grid in the

longitudinal and lateral direction, as well as the respective number of panels fitted on the wetted surface of thevessel in both directions.

The number of desired hull sheet nodes in a direction parallel to the X-axis is 30. The respective number of

nodes on a direction perpendicular to X-axis is 8. The respective number of panels is N-1. Furthermore, the

panel mesh extends on the free surface 0.5 L upstream, 1.5 L downstream and 1.0 L in sides. A total of 2300

panels are fitted on the hull form and the free surface.

4.2.2 Case Setup

A time step of 0.05 sec has been used in the calculations. The simulated time history was 300 sec. The code

can handle only passive fins providing also the variation of the angle of attack. The rudders are also handled

as fins. Furthermore, in the use of SWAN2 an iterative procedure was added to converge to the actualdynamic draft and trim of the vessel at each speed. That pair of draft and trim was subsequently used in the

unsteady calculations. In general, the linearity assumption and the fact that viscous roll damping is not taken

into account reduces the reliability of the predictions in very high dynamic responses.

4.3 LAMP

In LAMPs 3-D time-domain dynamic simulation, the wave-body hydrodynamic forces are calculated using a

potential flow panel method to solve the wave-body interaction problem in the time domain; forces due to

viscous flow effects and other external forces such as hull lift, propulsors, rudders, etc. are modeled using

other computation methods or with empirical or semi-empirical formulas. Calm water maneuvering is a

special application of the general methodology, with no incident wave but retaining the wave-body

interactions related to forward speed and ship motions. For a ship maneuvering in waves, either body linear or

nonlinear hydrodynamic problems can be solved. The body nonlinear approach, which considers the effects ofthe ships vertical motion relative to the calm water or incident wave, is almost always used for the hydrostatic

and Froude-Krylov wave forces. Details of the mathematical formulation, numerical implementation, and

application of LAMP for nonlinear seakeeping or maneuvering problems can be found in [12,35-39] amongother publications.


A sensitivity study was carried out to determine the computation domain and grid size. To get stable and

converged results, 1388 hydrodynamic body panels were used on the submerged portion of the whole ship

surface including the skeg and 2208 panels were used on the whole free surface. The free surface domain

extents from one ship length upstream and one ship length downstream in the longitudinal direction, and

extents one and a half ship lengths to the starboard and to the port side of the ship centerline.

4.3.2 Case Setup

The procedure to derive LAMPs maneuvering forces coefficients was developed and validated through

participation in the SIMMAN 2008 Workshop. This procedure was described in Yen et al. [8]. The PMM tests

were done at MARIN using an appended model with the propeller rotating at the model self-propulsion point.

The measured forces on the rudder and propeller during various forced maneuvering motions were used to

derive the rudder and propeller coefficients. LAMPs hull lift model and higher-order damping coefficients





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were adjusted to fit the measured forces and moments from the PMM test. The bilge keels, rudder, and

stabilizing fins were modeled as low-aspect ratio lifting surfaces which are sized and positioned based on the

MARINs seakeeping test report. Skeg was modeled using a lifting surface.

The 6DOF time domain runs were carried out for each of the test cases. In these calculations, the LAMPsimulations were done at model scale and then scaled to full scale for the final results. The LAMP

maneuvering model was tuned to match the calm water experimental data for resistance, linear and nonlinear

coefficients for surge and sway forces and yaw moment due to maneuvering motions, rudder lift and drag

coefficients, velocity increment on rudder inflow due to propeller wash, wake fraction and thrust deduction,

and open-water propeller thrust curve. However, the propeller RPM was set to match the initial speed in calm

water for each the experiment only and was held to constant for the whole simulation. LAMP implements a

slightly different autopilot algorithm than the one used in the experiment. For small course errors, LAMPs

algorithm behaves almost exactly like the one for the experiment, where values of P,D, andAare identical to

the experimental configuration, but the rudder bias (0)is not included.

5.0 SB METHOD

5.1 SurSim and FreSim

SurSim and FreSim are basically the same programs, but with different implementations of the hull forces and

rudder/fin forces. All other aspects are modeled using shared libraries. SurSim is dedicated to the simulation

of the maneuverability of mainly twin-screw ferries, cruise ships and motor yachts, while FreSim is used for

high-speed semi-displacement ships. Both codes model the motions of the ship in four degrees of freedom.

SurSim and FreSim do not contain wave modeling and therefore cannot be applied to study the course keeping

of ships in waves. The programs are of the modular type, i.e. forces on each component of the ship are

modeled separately. The rationale behind the modular models is that this approach will provide the easiest

means to incorporate physical background or more complex methods into the modeling of the forces on the

ship. Another advantage is that this approach enables a somewhat easier comparison of the coefficients across

different mathematical models. Both models utilize cross flow drag coefficients (see e.g. Hooft [48]) to model

non-linear effects in the forces and moments on the ship. The linear maneuvering coefficients are estimatedusing the slender body method described by Toxopeus [49]. Alternatively, the hydrodynamic coefficients canbe given by the user. In Toxopeus [22], an example of this approach is given using coefficients calculated

with RANS computations. More information about SurSim and FreSim and their validation can be found in

Toxopeus and Lee [4]. For maneuvering predictions, FreSim is mostly applicable to slender naval ships, while

SurSim is mostly applicable to ships of moderate L/B ratio and moderate block coefficients.

In SurSim and FreSim rudders and fins are modeled as lifting surfaces, treating fins as "rudders" without

propeller in front. The forces and moments generated by the lifting surfaces are all added in the output files

and therefore the forces generated by the rudders cannot be separated by the forces generated by the fins. In

this paper, based on the type of test, it was decided to attribute the full loads generated by all lifting surfaces

as rudder loads, or as fin loads. In some cases in which both the rudders and the fins generate large forces,

deviations from the loads found during the experiments or in the results from other methods can be expected.Furthermore, bilge keel forces are included in the hull forces and cannot be analyzed separately.

For the setup of the cases (roll decay and forced oscillation) identical input parameters were used for SurSim,

FreSim and Fredyn, except for the setting of the propeller RPM. In SurSim and FreSim, the RPM was

determined by the program while in Fredyn the RPM value was taken from the measurements. See section


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4.1.1 for more details of the setup.

6.0 COMPARISON CFD, PF, AND SB METHODS

The results for all prediction methods are transformed into EFD coordinate system described in Section 2.2and then compared against EFD. The comparisons include the 6DOF ship motions ( , the

ship speed (uG), the rudder and fin angles ( , the wave elevation at center of gravity (Wave) and the loadson the bilge keels (Fbk), rudders (Fr) and fins (Ff). The propeller loads for all the simulations are based on the

body force propeller model and are compared against the reported EFD thrust (T) and rpm (n). For each case,

the EFD outputs are discussed first. Then the prediction models are compared with EFD focusing first on

CFDShip-Iowa which covers the test cases more extensively. The discussions start from the 6DOF ship

motions and rudder and fin angles and then focus on the loads on the appendages. All the results and

measured EFD data are reported in full scale.

6.1 Data Analysis Method

For roll decay cases, the roll damping coefficients are derived based on Himeno Method [50] to study the

effects of the stabilizer fins. In this method, it is assumed that the roll motion can be described by thefollowing 1DOF equation:

|| (1)

Here is moment of inertia around x axis,is added inertia, and are linear, quadratic and cubic

damping coefficients, is ship mass and GMis metacenteric height.

By plotting roll decrement (is roll value at peaks) versus mean roll

and fitting the extinction curve in form of

through the data points, the

damping coefficients can be estimated by:

(2)

(3)

(4)

Herein is natural roll period.

6.2 Roll Decay in Calm Water

6.2.1 Roll Decay with No Fins

For no fins condition, the EFD model is released at about 12 deg roll angle which reaches to 5 deg roll angle

in one cycle and reduces to less than a deg in four cycles, as shown in Fig. 4. The damped roll periods Td at

first and last cycles, where the mean roll angle is at its maximum and minimum respectively, are about 11.1

sec i.e. close to hydrostatic natural roll period (Th= 11.5 sec). Thus, the restoring moment of this hull is linear

function of roll angle. During the test, the ship is bow up with the average of 0.28 deg trim while the initial

trim of the ship is about 0.45 deg probably induced by putting the ship at desired initial roll angle. The trim

shows some oscillations at Tdwith amplitude of 0.05 deg for large roll angle conditions. The amplitude of



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oscillations reduces at small roll angle but it is hard to evaluate and compare it with hydrostatic heave/pitch

period Tzh=Th= 5.7 sec (see Irvine et al. [51]) as it includes noticeable noises. The sinkage indicates

oscillations at period of 6.2 sec close to hydrostatic heave period Tzh. The mean value of sinkage is about -

0.07 m during the test. The heading of the ship changes slightly between 0.2 to -0.5 deg during the test and

oscillates at damped roll period. In fact, from positive to negative roll angle, the induced yaw moment changesthe sign causing oscillations at Tdon yaw motion. The target heading seems to be around -0.13 deg such that

the rudders turn to starboard with the average value of 5 deg to induce enough negative yaw moment to turn

the ship to the desired heading. The oscillations on heading cause oscillations at Td on side motion.

Throughout the test the model moves 1m toward starboard after the ship travels 3.5L. The ship speed is fairly

constant during the test and corresponds to Fr=0.231 rather than the desired Fr=0.248. The propeller RPS is

106.3 rpm making the average of 500 kN thrust induced by each propeller. The forces on the rudders show a

mean value of 50 kN for resistance induced by rudders. The side force induced by rudders is about 240 kN for

max rudder angle and it oscillates at damped roll period. The bilge keels side force and roll moment show

damped harmonic oscillations at Tdwith peaks at max roll rate as the lift forces induced by bilge keels are

dependent on roll rate not roll motion. The max side force is about 50 kN producing 500 kNm roll moment.

The results for different types of simulation are plotted on Fig. 4 as well. CFDShip-Iowa predicts very wellthe roll motion period but damping is under predicted such that the roll peaks are over predicted by 15%D.

The results show same period (Td=11.2 sec) at large and small roll angle confirming linear behavior for

restoring moment. The pitch motion increases from initial value (which is same as EFD) to 0.53 deg by

releasing the model and then drops to average value of 0.25 deg compared with 0.28 deg in experiment. The

oscillation of pitch at large roll angle is at damped roll period similar to experiment but at small roll angle is at

2Td. The source of this harmonic should be investigated in future. CFD predicts the effect of roll on heave

motion very well but the mean value (sinkage) is over predicted. The predicted yaw motion shows oscillations

similar to experiment induced by roll motion. The CFD model reaches to -0.13 deg heading since that was

used as target heading for PID controller. To steer the ship at the desired heading, the controller turns hard the

rudder toward starboard with about 7 deg right after releasing the roll and keeps the rudder at about 4 deg for

the rest of the simulation. The ship speed throughout the simulation is fairly constant U=8.65 m/s and very

close to EFD value (E=-2%D). The CFD propeller RPS is found from self propulsion test and it is 1.4%Dhigher than the averaged EFD rps. The CFD thrust for both propellers are the same and close to the EFD data.

Direct integration of the forces and moments in the ship coordinates system was performed for bare hull and

appendages including rudders, twin bilge keels and propellers. Figure 4 shows some selected loads on the

bilge keels (Xbk,Ybk,Kbk,Nbk), rudders (Xr,Yr,Kr,Nr) and fins (Xf,Yf,Kf,Nf). The other components of loads on

appendages, the bare hull forces, the propeller forces and total forces are not shown here and reported in [52].

The surge forces (resistance) of both rudders are 77 kN while bilge keels induce 22kN surge force. The

contribution of the rudders and bilge keels to the total resistance is approximately 12.5%, a considerable

number. The bare hull resistance is about 600 kN, 77% of the total resistance. Thus the resistance for other

appendages is not negligible as well, about 10% of the total resistance. The total side force is mainly induced

by rudders and hydrostatic side force acting on the hull. The rudder induced side force shows a very good

agreement with EFD. The propeller induced side force is zero due to axisymmetric body force propeller model

and port-starboard symmetric condition of the ship hull. The bilge keels side force is very small compared torudders side force and it is over predicted by CFDShip-Iowa. For heave force and roll moment, the hydrostatic

force/moment of the bare hull is dominant. The induced roll moment by rudders and bilge keels counteract

partially the hydrostatic roll moment induced by bare hull. The predicted bilge keel roll moment is in phase

with EFD showing maximum value for max roll rate. However, the amplitude is over predicted. The pitch

moment shows bow up pitch moment induced by the bare hull, bilge keels and propellers. This moment is

counteracted by the moment induced by rudders. The total yaw moment of rudders and the bare hull are at the


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same order and much larger than the contribution of the other appendages. Comparing roll motion and bare

hull yaw moment shows that rolling to starboard causes positive yaw moment acting on the hull which pushes

the ship to turn to portside.

Comparing all the predicted motions with EFD data shows that most methods predict relatively the roll decaytime history well. For damped roll period, LAMP and CFDShip-Iowa show the best agreement while FreSim

and SWAN2 over predict the period by 11%D. For roll damping, ISIS-CFD and SWAN2 under predict the

roll damping such that the roll peaks are over predicted significantly. For pitch motion, all the methods except

CFDShip-Iowa strongly under estimate the pitch mean value. Also, the oscillations on pitch motion at large

roll angle are under predicted by all methods except CFDShip-Iowa showing that the coupling between roll

and pitch is not predicted well for most methods. Most of the simulations show oscillations at 2T don pitch

motion while EFD shows harmonics at Td. The heave time history shows ISIS-CFD and SWAN2 under

predict the mean value. The yaw motion time history is not predicted well by most of the methods but the

trend and the harmonics is well predicted. The ISIS-CFD prediction shows large deviation from target headingsince the rudders are not activated to control the heading. Also rudders are passive for SWAN2 simulations.

The rudder angle for all predictions except CFDShip-Iowa shows the initial rudder angle is ignored. The ship

velocity for all methods agrees with EFD data but ISIS-CFD and Fredyn show significant over prediction. InFredyn, the applied RPM apparently does not correspond to the required approach speed. Comparing propeller

loads explains under prediction of resistance by all PF and SB methods as thrust is noticeably under estimated.The loads on rudders show that CFD simulations over predict the rudder resistance force. The side force of

rudders is predicted quite well for all methods. The rudders side force for all predictions show oscillations at

Tdwith same amplitude of EFD data. The loads on bilge keels are under estimated by PF significantly while

CFD methods predict the roll moment induced by bilge keels relatively well. This is due to capability of eddymaking forces prediction in CFD simulations.

6.2.2 Roll Decay with Passive Fins

The results for roll decay with passive fins are shown in Fig. 5. The ship is released at -10 deg roll angle

which is reduced 60% in one cycle due to large roll damping. The damped roll period is about 11.3 sec for

both large and small roll angles explaining linear restoring moment similar to previous case. The pitch timehistory shows the model is released at 0.18 deg bow down condition and oscillates at T h= 5.7 sec for onecycle until reaches to dynamic trim value of 0.1 deg during the test. Heave motion shows similar trend. The

model is pushed down into water during the roll initial condition setup such that the sinkage is about -0.36 m

at t=0 and then fluctuates at hydrostatic heave period until the ship stays at -0.26 m. The yaw motion shows

the ship slightly turns to starboard and portside in each roll cycle but stays fairy well at 0.17 deg of heading.

Such a heading causes the ship moves toward portside about 0.4 m after sailing 3.2L. The ship speed is fairly

constant during the test and it is about 9.5 m/s corresponding to Fr=0.254 close to the desired Fr=0.248. The

propellers rotate at 115.5 rpm to provide the required thrust. The propeller thrust oscillates at damped roll

period with the average of 600kN.The forces on rudders show significant noises on the resistance force. The

average resistance force varies throughout the test but at small rudder angle reaches to about 95 kN. The

rudder side force is correlated with rudder angle. For maximum rudder motion to portside/starboard the side

force is at max negative/positive peak which is about 200kN. The forces on fins show that the resistanceinduced by fins is about 16 kN in average. The side forces of the fins are correlated with fins angle. Thus, it

oscillates at Tdwith maximum value of 60 kN for max fins angle. The bilge keel side force and roll moment

shows that the bilge keels produce forces in phase with roll rate. The side force/roll moment is negative

(acting toward portside) when the ship rolls from portside to starboard to damp the roll motion.

The CFDShip-Iowa predictions are shown in Fig. 5. The roll decay damped period is predicted very well and



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is the same for both small and large roll angle confirming linear restoring moment behavior. However, the

amplitude is a bit smaller than EFD introducing slightly larger damping prediction. The pitch time history

shows similar trend to EFD as the ship is released at 0.15 deg bow down condition and oscillates around 0.1

deg for small roll angle. For heave motion, the ship is pushed into water at t=0 and then released such that the

ship starts oscillating at heave natural/hydrostatic frequency Tzh= 5.7 sec for about 10 sec like EFD. Theamplitude of oscillations is predicted very well. It should be noted that the heave damping is significant as it

was expected such that the amplitude of oscillations drops 80% after only one cycle. The heave motion

converges to -0.22 m compared with -0.26 m in experiment. After releasing the ship at zero heading, the ship

turns toward starboard for 0.14 deg and then portside for 0.54 deg in first roll cycle. The variation of heading

is over predicted by CFD probably because the yaw damping is under predicted due to the simplicity of the

body force propeller model. However, the ship sails at average heading of 0.17 deg to portside similar to EFD

as that was set as target heading in PID controller on rudders. Comparing CFD and EFD rudders show rudder

angle amplitude is over predicted but mean value is the same as EFD similar to the prediction for yaw motion

as the rudder angle is correlated with heading. As shown in surge and sway motion, the heading of 0.17 deg in

average moves the ship toward West for 1.36 m after 40 sec when ship has traveled 2.5L toward North.

During the simulation, the ship speed is nearly constant corresponding to Fr=0.246. The body force propeller

model predicts 115.2 RPM for propellers very close to EFD value of 115.5 rpm. However, the thrust on thepropellers are under estimated by 17%D. The forces and moments are integrated on bare hull, rudders, fins

and bilge keels to evaluate their contribution on total forces and moments. Figure 5 shows some selected loads

on the bilge keels (Xbk,Ybk,Kbk,Nbk), rudders (Xr,Yr,Kr,Nr) and fins (Xf,Yf,Kf,Nf). The other components of

loads on appendages, the bare hull forces, the propeller forces and total forces are not shown here and reported

in [52]. The rudder surge force produces maximum resistance at maximum rudder angle with about 110 kN

which drops to 90kN for small rudder angles, close to EFD value. The bilge keels produce 24kN resistance in

average. The passive fins produce only 18 kN resistance which is negligible compared with other appendages

as measured in EFD. The propeller thrust in ship coordinate system produces 920 kN surge force which is

nearly the same as the total resistance of the ship including all appendages. The rudders, bilge keels and fins

have remarkable role in the resistance as they contribute to 24% of the total resistance. The maximum total

side force is 400 kN (half of the resistance) which occurs at maximum drift angle of 1 deg. The share of

rudders is comparable with the hull side force and agrees well with EFD. The bilge keels and fins have sameorder side forces which are over predicted. Note that that the propeller side force is zero as the y-component

of the twin propellers' thrust are the same but acting on the opposite sides with zero net. For heave force androll moment, the hydrostatic hull force is dominant while the role of appendages is not noticeable. The pitch

moment induced by rudders is half of the magnitude of that for hull and attempts to put the ship at bow down

position. The passive fins also provide pitch moment assisting bow down condition but the magnitude is only

2% compared to that of rudders. The combined bilge keels and propellers induce 35% rudders' pitch moment

but in the opposite direction, helping the ship for bow up condition. The yaw moments induced by the rudders

and the hull are dominant and both are maximum at maximum roll angle. The hull yaw moment is negative

for negative roll angles explaining tendency to turn the ship to starboard by rolling to portside. The rudders

yaw moment reacts against the hull yaw moment to steer the ship. It is interesting that the bilge keels assist the

turning of the hull with negative yaw moment for negative roll angles even though their yaw moment is very

small compared to that for the hull. The passive fins and propellers apply negligible yaw moment on the ship.

The predictions for different methods are also shown in Fig. 5. The roll motion time history shows all methods

except FreSim and SWAN2 predict the roll period fairly well. The damped period prediction errors are 10.5

and 8%D for FreSim and SWAN2, respectively. The roll amplitude is significantly over predicted by

SWAN2, ISIS-CFD and SurSim. The pitch motion time history indicates that most of the methods show large

errors in prediction of the dynamic trim. Also, the SWAN2 prediction shows very large amplitude oscillations

on pitch motion compared to other methods and EFD. Note that the heave and pitch motion is not predicted by


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the SB methods. Both CFD methods and LAMP show good prediction for heave motion while Fredyn under

predicts significantly the mean value (dynamic sinkage). For heading, ISIS-CFD shows fairly large errors

because the rudders are not used to control the heading and rudders angle are zero during the simulation. Also

SWAN2 ignores the rudder actions. The rudder angle time history shows similar trend as EFD rudder angle

but with different mean value as the rudders are not located at initial angle provided by EFD data. The errorfor ISIS-CFD heading prediction induces large prediction error for side motion as well while the surge motion

is predicted well by all methods as the ship velocity is close to EFD value. The loads on the propellers are

under predicted for all methods especially for PF and SB methods partially due to simplicity of body force

propeller model and partly because they used bare hull resistance curve to estimate the propeller RPM. The

resistance force induced by rudders are predicted nearly zero for all methods except CFD methods which

agree fairly well with EFD data. The side force on rudders are predicted very well by CFD and SB methods

and under predicted by PF methods. The resistance induced by fins are estimated fairly well by CFDShip-

Iowa but under predicted for other methods. The side forces induced by fins are over predicted by PF and

CFD methods. The forces on bilge keels are over predicted by CFD methods and strongly under predicted by

PF methods. Note that there is no force for passive fins (it is included in the rudder forces) or bilge keels

(included in the hull forces) in SB methods such that those forces are shown as zero.

6.2.3 Roll Decay with Active Fins

As shown in Fig. 6, the ship is released from 18 deg roll to portside. Thanks to the active fins the damping is

significantly large such that the roll is reduced to 2 deg after one cycle and reaches to less than a deg for the

rest of the test. The damped roll period is about 11.9 sec during the test which is larger compared to previous

cases as expected due to larger roll damping. The time history of active fins angle describes how the roll is

controlled. Once the ship is released the fins are controlled by D controller on the roll i.e. thus the

fin angle changes by changing the roll rate. When the ship starts rolling the roll angle decreases to zero

(upright position) and then overshoots to starboard. At the same time, the fin angle would be negative as the

roll rate is positive i.e. the starboard fin is at nose up position while the portside one is at nose down position

inducing significant negative roll moment. The induced roll moment counteracts the hydrostatic roll moment

to reduce the roll speed and consequently the overshooting. Once the ship overshoots the upright position the

hydrostatic moment changes its sign and assists the fins to reduce the next roll peak. Thus fins control the rollby roll speed reduction first and then providing extra restoring moment for each half of roll cycle. Note that

the maximum fin angle is limited to 25 deg in the test and that occurs when the roll overshoots the upright

position as that is the point where the roll rate is at its peak. The pitch time history shows that the ship is at

0.12 deg bow down position at t=0 and then oscillates one cycle at pitch natural period to reach to about 0.04

deg after the roll is damped. For heave motion, the ship is pushed down into water for about 6.5% of the

design draft to enforce the initial roll. The ship moves upward and oscillates at heave natural/hydrostatic

frequency Tzh= 5.7 sec around a water line at 3% lower than the design draft. For yaw angle, the ship starts

moving to East for a short time after releasing and then turns to West attaining 0.7 deg yaw angle. However,

the yaw angle reduces to 0.28 deg as the ship is steered by the rudders. The rudders' trailing edge turn 1 deg to

starboard causing the ship turns to East as mentioned earlier. At t=8 sec the rudders turns -3 deg to portside

attempting to control the heading of 0.7 deg at that time. To keep the ship at heading of 0.28 deg, the rudders

stay at -1.2 deg for the rest of the test. The heading of 0.28 produces 0.5 m side motion to East after traveling3.3L to North. Note that the side motion shows oscillations induced by large roll angle at beginning of the

simulation showing coupling between roll and the side motion. The ship speed throughout the test is changed

1% i.e. it is nearly constant and it corresponds to desired Fr=0.248. This ship speed is achieved by propellersrotating at 115.8 rpm and producing averaged thrust of about 569 kN for each propeller. The loads on rudders

show high frequency oscillations on rudder surge force at propeller rotation frequency. The side force shows

oscillations at damped roll period with maximum value of about 400 kN for max rudder deflection condition.



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The resistance force induced by fins show oscillations at Td/2 with maximum of 210 kN for max fin angle.

The mean value of fin surge force is about 20 kN for small fin angle. The fin side force is two times larger for

max fin angle and reaches to about zero as it is expected for small fin angle. The bilge keel side force and roll

moment show damped oscillations at Tdwith peaks where the roll rate is maximum. The bilge keel side force

is 20% of the side force induced by fins.

The prediction for CFDShip-Iowa indicates that the roll damping is under predicted and roll period is over

predicted. The damped roll period is about 12.4 sec throughout the simulation i.e. it is over predicted by 4%D.

Also, the roll peak after second cycle is 4.4 deg compared to 2 deg for EFD. The source of the discrepancy

between CFD and EFD is probably due to the simplification performed on the grid generation for active fins

geometry. There is a gap between the hull and the fins giving the fins capability to have their own moves. The

original gap was too narrow for overlap grid setup thus the gap was modified by reducing the span size of the

fins. That would cause under estimation of fins roll moment i.e. over prediction of roll angle. The pitch time

history agrees fairly well with experiment. The pitch motion starts oscillating at damped roll period afterreleasing the ship and then stays at 0.024 deg trim angle. The heave time history clearly shows the oscillations

at heave natural frequency after the roll is released similar to EFD. The oscillations also have fairly similar

amplitude with EFD but the averaged value is under predicted. The yaw angle shows the ship advancestoward East for a very short time because the negative roll is induced negative yaw moment. Then the ship

turns to West as the roll gets positive and consequently the induced yaw moment applies in the oppositedirection. Thus the yaw motion shows oscillations at damped roll period. Since the heading is under the

control of rudders, the ship finally sails at 0.28 deg set as target heading for the heading controller. The CFD

rudders are at initial positive angle i.e. they produce positive yaw moment to counteract the roll induced yaw

moment to turn the ship toward 0.28 deg heading. Once the roll induced yaw moment changes its sign, both

the rudders and roll induced bare hull yaw moment assist the ship to reach to the target such that after one rollcycle the ship is fairly located at target heading. Comparing EFD and CFD fins motion, CFD over predicts the

peaks and period similar to those for roll as fin motion prediction is correlated with roll motion prediction.

The trajectory of ship predictions show that CFD under predicts the side motion but shows very similar trend

with EFD i.e. oscillations at damped roll period for large roll angles are observed on side motion. The surge

motion indicates very good agreement with EFD as ship speed is predicted close to EFD. The propeller rpm isfixed at 118.7 during the simulation providing 2.5%D error compared with EFD data. The average of the

propeller thrust is about 507 kN, the same for both propellers. The forces and moments on bare hull, rudders,

bilge keels and active fins are integrated to study the role of such parts on the total forces and moments

applied on the ship. Note that Fig. 6 shows some selected loads on the bilge keels (Xbk,Ybk,Kbk,Nbk), rudders

(Xr,Yr,Kr,Nr) and fins (Xf,Yf,Kf,Nf). The other components of loads on appendages, the bare hull forces, the

propeller forces and total forces are not shown here and reported in [52]. The rudders surge force is about 100

kN which is about 14% of the resistance of bare hull and 10% of the total resistance of the appended hull. The

bilge keels create only 25 kN resistance throughout the simulation. The active fins provide 200 kN resistance

(20% of the total resistance of the appended hull) when they are at the maximum angle (25 deg) showing their

significant role on the resistance. Therefore the fin motion causes the propeller thrust to change slightly to

keep the ship at desired speed as shown in Fig. 6. The contribution of fins to total resistance for small fin

angles is the same as bilge keels i.e. 20 kN, close to EFD value. For side force, the combination of rudders andfins side forces counteract the hull side force. The side force of rudders is over predicted and it is in phase

with EFD data. The maximum rudder side force is 500 kN for maximum rudder deflection. The fins side force

is under predicted and it is 400 kN for maximum fin deflection. The induced side force by bilge keels is about

200 kN for maximum roll angle i.e. it is over predicted. The propeller side force is zero during the test because

of the nature of body force propeller model as mentioned earlier. The total heave force and roll moment are

mainly induced by hydrostatic force applied on the hull such that the role of the appendages are not dominant.

The roll moments induced by appendages explain that in each half roll cycle the fins reduce the roll speed as


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they counteract hydrostatic roll moment first and then assist that after overshooting the upright position. The

order of the induced roll by rudders is similar with the fins moment. The bilge keels, however, provide one

order magnitude smaller moment which agrees well with EFD data. The pitch moment indicates that the hull

itself, bilge keels and propellers produce a bow up moment while rudders mainly and fins partially counteract

those moments. It is interesting that the propellers pitch moment is 14% of the moment induced by the hull.The yaw moment time histories show the rudders working against the yaw moment induced by the hull and

bilge keels to control the heading. The yaw moment applied on the ship due to fins is negligible even for

maximum fin deflection. This is due to the fact that the fins are located close to center of gravity of the ship.

The results for different methods are also shown in Fig. 6. ISIS-CFD is not used for this case. The roll decay

time history indicates that the roll damping is under predicted by all methods. SWAN2 shows the most under

prediction for roll damping. The roll period is pretty well predicted by all methods. The pitch motion agrees

well with EFD only for CFDShip-Iowa. The results of LAMP and SWAN2 show over prediction of dynamic

trim while Fredyn under predicts that. The SB methods are not used to predict the heave and pitch. The heave

motion is predicted fairly well by CFDShip-Iowa, LAMP and SWAN2 while Fredyn under predicts the steady

state value. The yaw response is estimated well by CFDShip-Iowa following closely the EFD data while other

methods show large prediction errors even though the trend is relatively predicted. This is because the yawmotion is controlled and reduced to target heading after awhile due to active rudders. The rudder angle time

history is correlated with yaw motion such that the rudder angle is over predicted by LAMP and Fredyn and

well predicted by CFDShip-Iowa. Note that the rudders are passive for SWAN2 simulations. The loads of

propellers are underestimated by all methods as before with best agreement observed for CFDShip-Iowa. The

resistance of rudders is under predicted by all methods except CFDShip-Iowa which over predicts that. The

rudder resistance is predicted fairly constant while EFD shows large oscillations on rudders resistance due to

existence of rotating propellers. The side force on the rudders is over predicted by SB methods and under

predicted by PF methods. For the SB methods, the over prediction shown is caused by the inclusion of the fin

forces in the overall rudder forces. If the EFD rudder and fin forces are summed, the agreement between the

EFD and SB results is much better. The resistance of the fins shows harmonics at Td/2 for all methods similar

to EFD. The amplitude of oscillations is under predicted by PF methods while CFDShip-Iowa shows the best

agreement with EFD data. The side force of fins for all of the methods shows similar trend as EFD but theamplitude is under predicted for most of the methods. PF methods significantly under predict the loads on

bilge keels as the nature of bilge keel forces is eddy making force and PF methods should be tuned to capture

properly the bilge keel forces. The results for CFDShip-Iowa show over prediction of bilge keel forces.

6.2.4 Effects of Fins

The roll decay results of the model appended with passive, active, or no fin stabilizers provide the opportunity

to investigate the effectiveness of the fin stabilizers as roll reduction device. Therefore herein the reduction

rate of the roll motion for different cases is studied by comparing the linear and nonlinear dampingcoefficients. The damping coefficients are obtained based on quadratic and cubic fits to the roll decay

extinction curves.

Tables 6-8 show damping coefficients for no fin, passive fin and active fin roll decay cases. Each tableincludes the damping coefficients estimated based on quadratic and cubic fitings. Based on quadratic fitting to

EFD data, the dimensional linear damping coefficient for no fin case is 68.1103 kNms/rad while the

quadratic term is 4.3103kNms2/rad2. The prediction error for damping coefficient is between 4% and

40%D in which the minimum is for FreSim and the maximum is for ISIS-CFD. The quadratic term is

predicted by an error between 10% for SurSim and 85%D for SWAN2. For the case with passive fin the EFD

damping coefficient increases to =68.9103 kNms/rad and =14.38 kNms2/rad2, as shown in Table 7.



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Therefore, the nonlinear damping is increased 230% compared with the case with no fin while linear damping

is increased only 1%. The nonlinear roll damping is originated from eddy making damping which is increased

due to the eddies induced by passive fins. The prediction errors for andare in a range of 2-40%D and 10-

100%D, respectively. The large errors for quadratic damping coefficient are for all SB and PF methods as they

might not include the eddy making forces induced by viscosity using proper empirical formula. The estimatedquadratic damping is negative for Fredyn and LAMP. For CFD cases, the quadratic damping prediction error

is about 10%D for both CFD simulations which is better than other methods as vortical structures can be

predicted. The CFDShip-Iowa over predicts while ISIS-CFD under predicts the quadratic damping.

Comparing the results with no fin case shows that the linear damping is increased by 35% from no fin to

passive fin case for some PF and SB methods compared to 1% change for EFD data. For the case with active

fins (Table 8) the EFD linear damping coefficient increases to 202 kNms/rad and the quadratic term increases

to =20.8 kNms2/rad2. Thus, the linear damping is three times larger compared with passive fin case due to

the increase of lifting forced induced by active fins with large attack angle. Also the quadratic damping is

increased by 45%. The prediction errors for andare in a range of 25-72%D and 8-195%D, respectively.

Most of the predictions show significant increase of linear damping compared to passive fin case as expected.

For nonlinear damping, among all the methods only CFD simulations could predict the quadratic damping

coefficients.

The damping coefficients based on cubic fitting to all EFD and predicted results show larger linear damping

coefficients for all cases compared with those estimated from quadratic fits. The EFD linear damping is

71.4103kNms/rad for no fin case increasing to 74.9103kNms/rad for the case with passive fins, as shown

in Tables 6 and 7. The trend of linear damping from no fin to passive fin is the same as before. However, the

rate of the increase of the linear damping is 5%, which is larger than what quadratic fitting shows. This ismore reasonable as the lift force induced by passive fins is not negligible and should increase clearly the linear

damping. The EFD cubic damping coefficient is 1.1103 kNms3/rad3 for no fin case increasing to 6.5103

kNms3/rad3for the passive fin case as expected. The prediction errors for and for no fin case are in range

of 2-34%D and 20-85%D, respectively. Also, the prediction errors for and for passive fin case are in rangeof 0.3-30%D and 31-103%D, respectively. The large errors for linear damping are for ISIS-CFD, SWAN2 and

LAMP. For active fin case (Table 8), the EFD linear damping increases to 209 kNms/rad and cubic dampingincreases to 11103kNms3/rad3. The prediction errors for and are in range of 28-73%D and 34-138%D,

respectively. The prediction error for cubic damping coefficient is minimum for CFD simulations as before.

For both quadratic and cubic methods, it should be mentioned that the EFD roll decay analysis itself is prone

to an uncertainty. Depending on the number of oscillations considered, different damping coefficients will be

obtained. The authors noticed that the uncertainty in is 19% using quadratic fitting and 13% using cubic

fitting. Also, the uncertainties in and are 160% and 131%, respectively. Therefore, part of the large

prediction errors for nonlinear damping coefficients could be due to the uncertainties in EFD data analysis.

6.2.5 Motions Coupling

The total forces and moments on the ship can be investigated in frequency domain using 6DOF mathematical

model discussed in Sadat-Hosseini et al.[21] ( refer to equations 4-9 in the paper) to analyze the coupling

between all modes of motion. As discussed earlier, surge motion is not under any discernable oscillations

while side motion oscillates noticeably at fdfor large roll angle. Heave and pitch asymptote to their dynamic

calm water values with small amplitude oscillations mostly at fd/2 and 2fd. Roll and yaw are under damped

harmonic oscillations at fd. The rudder angle oscillates at fd similar to yaw angle as it is defined by PID

controller using yaw angle input. The active fins also show harmonics at fd as they are based on the PID

controller on the roll angle. The CFDShip-Iowa total surge force shows harmonic amplitudes at 2fdat large


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roll angle and fd/2 at small roll angles. The first one is mainly induced by second order surge and roll

coupling term expressed as in the mathematical model and partially induced by second order surge

and sway/yaw coupling and

. The second one should be induced by first order surge and

heave/pitch coupling as heave and pitch oscillate at fd/2. The total side force shows large harmonic

amplitudes at fd and 3fd which are originated from the first and third order coupling with roll and yawmotions and first order coupling with rudder and fin motions. The heave force and similarly the pitch moment

show noticeable harmonics at about 2fdwhich could be because of first order heave and pitch coupling and/or

second order coupling of heave and pitch with sway, roll and yaw motions. The roll moment shows large

harmonic amplitudes at fdwhich is originated from the first order coupling of roll with sway, yaw, rudder and

fin motions. Lastly, the yaw moment indicates harmonics at fdand 3fddue to first and third order coupling of

yaw with roll and sway motions and due to first order coupling of yaw with rudder and fin motions.

6.3 Forced Roll in Calm Water

6.3.1 Rudder Induced Roll with Passive Fins

The results for rudder induced roll with passive fins are shown in Fig. 7 and Table 9. The rudders' trailing

edges are at 4 deg to starboard at the beginning of the test, as shown in Fig. 7. Then the rudders are moved

under forced oscillations at TR=11.42 sec close to natural roll period. The amplitude of oscillations is about

13.4 deg compared to the desired value of 15 deg, as shown in Table 9. Throughout the test, the rudders

oscillate around an average value of -4 deg which is similar to the initial deflection value inducing negative

average yaw moment on the ship. The time history of roll shows that the roll is about zero at t=0 but once the

rudders' trailing edge turns to portside the ship starts rolling to portside as the acting point of the net lift force

on the rudders are below the center of gravity of the ship. For first couple of rudder oscillation cycles the roll

amplitude eventually raises until it reaches to stable oscillation. The roll response oscillates at rudder

excitation frequency with amplitude and average value of 6.216 deg and 0.17 deg, respectively. The phase lag

between roll and rudder is 137 deg. The pitch motion shows the model is at 0.1 deg bow up condition when

the rudders start harmonic turning. The pitch angle decreases to average value of 0.02 deg in first couple of

oscillations. The stable amplitude of pitch response is about 0.06 deg at T R and 0.015 deg at TR/2. It is

interesting that the pitch oscillates mainly at TRwhile it was expected to fluctuate at TR/2. In other words, thepitch angle is positive for negative rudder angle and negative for positive rudder angle while the pitch is

supposed to be same for both positive and negative rudder angles. The source of pitch motion oscillations at

TRcould be a sign of asymmetric condition of the model respect to x-z plane. Comparing pitch and roll time

histories reveals that pitch and roll motions are relatively in phase (4 deg phase lag). The same can beobserved for heave motion i.e. the heave motion is maximum at the moments when roll and pitch are

maximum. The stable heave motion amplitude induced by forced rudder motion is about 0.03 m at TR and 0.01

deg at TR/2. The yaw motion shows the model is at zero heading before rudders start harmonic turning. Once

the rudders start the oscillation by turning to portside the ship turns portside as well due to positive yaw

moment induced by rudders. Because of the ship inertia and lethargy, the ship keeps turning to portside evenafter the rudders reach to maximum deflection and turn to starboard. The ship starts eventually turning to

starboard as a result of negative rudder yaw moment. Thus the result is a harmonic motion for yaw with

amplitude of 0.23 deg and with a phase lag between yaw and rudders for about 236 deg. Throughout the test,the average of heading changes slightly from initial value of 0.4 deg to a negative value as a result of negative

mean value of rudder angles mentioned earlier. Therefore, the ship travels toward West for a short time and

then heads to East while moves toward North. The fluctuations on heading cause harmonic oscillations on

surge and side motions with amplitude of 33 m and 0.24 m at TRand with 50% of those amplitudes at T R/2.

The ship speed is 9.0 m/s ( 3% less than the desired speed corresponding to Fr=0.248) at the beginning of the

test but decreases for about 3% due to the ship drift angle of 4 deg and large rudder angles. The propeller rpm



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is fixed at 106.5 rpm as the test setup was planned. The thrust for each propeller is about 500 kN oscillating

with amplitude of 50 kN at forced rudder motions period. The resistance for rudders oscillates at T R/2 and TR

with amplitude of 40 kN and 43 kN, respectively. The rudders provide 60 kN resistance in average. The side

force induced by rudders show harmonics at TR with amplitude of 493 kN. The average resistance induced by

fins is about 15 kN which oscillates at TR with small amplitude of 1.8 kN. The amplitude of side force inducedby fins is 30 kN. The recorded side force and roll moment on bilge keels show oscillations at TR with

amplitude of 19 kN and 163 kNm for Y and K, respectively. The forces on bilge keels are in phase with roll

velocity as it is expected.

Comparing CFDShip-Iowa results with EFD indicates that the CFD rudders oscillate under same conditions as

EFD i.e. same amplitude, mean and phase to mimic EFD test setup as close as possible. The prediction of roll

response agrees very well with EFD in terms of the phase and the period but not the amplitude. The stable roll

amplitude is predicted 8.08 deg compared to 6.216 deg for EFD suggesting under prediction of roll damping

and/or over prediction of rudders yaw moment. The CFD pitch motion confirms the fact that the pitch should

oscillate mainly at TR/2 unlike what was observed in EFD. Also the pitch shows oscillations at 2TR=2T

similar to the roll decay cases. The pitch oscillates with amplitude of 0.015 deg and 0.05 deg at T R/2 and 2TR,

respectively, and with average of 0.02 deg bow down position. The similar behavior is also observed forheave motion with amplitude of 0.011 m and 0.02 m at TR/2 and 2TR. The mean value of heave is about -0.16

m i.e. the ship sinks more into the water for about 2.6% of its design draft. The yaw motion shows that CFD

ship is located at zero heading at t=0, similar to EFD. The yaw motion oscillation happens for each cycle ofrudder motion producing a harmonic yaw motion with amplitude of 0.38 deg and fairly constant mean value

of 0.7 deg. Therefore, the yaw motion amplitude is over predicted probably due to over prediction of rudder

induced yaw moment which might be the source of roll over prediction as well. The yaw motion creates

harmonics on surge and side motions similar

cfd potential flow and system-based simu

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