W Pastoor, Det Norske Veritas AS, Norway R van 't Veer, Maritime Research Institute Netherlands, The Netherlands E Harmsen, Royal Netherlands Navy, The Netherlands
SUMMARY
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The motion behaviour of a frigate-type trimaran was studied in a joint co-operation between the Royal Netherlands Navy (RNLN), the, Maritime Research Institute Netherlands (MARIN) and Det Norske Veritas (DNV). The starting point for the study is a series of model tests for a frigate-type trimaran conducted at MARIN. Frequency and time-domain linear and nonlinear hydrodynamic calculations are validated against the model tests. The overall seakeeping behaviour ofthe vessel is discussed and particular attention is paid to the roU motion. Parametric roU is discussed and test results are presented. The use of passive and active fins to reduce the roU motion is evaluated in stem quartering seas. The nonlinear effect on the roU motions of the intermittent wetting of the side hulls and the size of the side hull volume is evaluated. The paper ends with a discussion on seakeepmg and design load assessments for trimaran vessels.
NOMENCLATURE
a foil angle of attack (rad) (3 wave heading (rad) <f> roll angle (rad) y angle between horizon and line through CoG and
side hull keel (rad) K non-dimensional roU damping (-) p density (kg/m3) ¥ fluid potential (m/s) Afi» fin area (m2) A44 roU added mass (kg m2) B44 roll damping (Nms) C44 roU restoring coefficient (Nm) CL lift coefficient C„uy eddy damping coefficient C9 slamming coefficient F force (N) I44 roU inertia (kg m2) Lpp Length between perpendiculars (m) K control gain for active fin M moment (Nm) p pressure (N/m2) r radius (m) S wetted area (mz) U mean ship speed (m/s) V R vertical relative velocity
1. INTRODUCTION
In the past 10 to 15 years a significant amount of research and development has been devoted to the appUcation of the trimaran concept for both navy and commercial purposes and this has been reported in numerous puhtications. The trimaran looks simUar to a conventional monohuU, as the side-hulls are usuaUy very smaU. However these side-hulls can have a significant effect on the dynamic behaviour of the vessel and thus the seakeeping performance and the wave-induced structural loads. Being capable of using numerical tools in the design phase of trimaran vessels is of great importance in order to optimise the vessel for seakeeping
performance and to develop realistic structural designs and weight estimates.
The Royal Netherlands Navy, RNLN, operates a fleet of 12 modern frigates of different types with sizes fiom 3300 to 6000 tons. Consequentiy, there is a continuous process of study and development into new concepts and designs for frigate type ships, like SES, SWATH and trimaran vessels.
Model tests play a central role in vaUdating numerical tools, they provide insight in physical phenomena and they are used as verification of (final) design characteristics. Developing numerical prediction tools and providing advanced model test capabilities is key competence for the Maritime Research Institute Netherlands and have thus a long history of co-operation with the RNLN.
Since 1996 has DNV developed the nonlinear ship motion and load program WASUVL It is being used in seakeeping and design load assessments for aU kind of vessels including multihuUs. VaUdating the program and further developing the program is required to provide reliable seakeeping and wave load predictions. This is used in both ship specific design load assessments, with full hydrodynamic load transfer to FE models, as weU as the general development of Rules and guidelines for ship structural design.
Developing vaUdated numerical tools and increasing the competence on the dynamic behaviour of trimaran vessels is thus of common interest for the RNLN, MARIN and DNV. This formed the basis to start a cooperation between the three companies to use trimaran model tests, [1], to validate existing linear and nonlinear numerical tools. The paper starts with a summary of the model test program after which parametric roU, linear and nonlinear motion predictions are discussed. Of particular interest has been the roU motion and the effect of rudders, passive and active fins. AdditionaUy the effect of a variation of the side hull volume above the calm water on the roll motions was investigated.
In October 1996 the Royal Netherlands Navy commissioned MARIN to carry out a research project to investigate the hydrodynamic aspects of a trimaran. Powering and seakeeping aspects were considered in the test program. The test conditions were mainly based on the results of the calculations performed in advance of the tests with a trimaran version of a 2D linear strip-theory program, which indicated that large roU motions could be expected in stern quartering seas. The main uncertainties in these calculations were however the viscous roll damping and associated non-linearities in resulting large roU motions. Variation in huU spacing of the outriggers and appUcation of passive and active fins were studied mainly with the aim to reduce the roU motions in stem quartering seas.
2.1 MODEL DESCRIPTION
This paper focus on the seakeeping characteristics ofthe bare hull (configuration 0), the bare hull with passive fins (configuration 1) and with active fins (configuration 2). Model tests were conducted using different outrigger spacing and design, but these results are classified, and the only numerical results will be discussed. Since the model was free-sailing in aU test conditions, a twin rudder with auto-puot was instaUed.
Model tests were conducted in the former seakeeping towing tank of MARIN, with dimensions 100 by 24 meters. The research design measured 165.0 m Lpp prototype, and was tested to a scale of 1:35. The ship characteristics are summarized in Table 1. A lines plan of the trimaran in seen in Figure 1.
Designation Length between perpendiculars [m] Breadth centre hull on waterline [m] Draught center hull [m] Length side hull Breadth side hull [m] Draught side hull [m] Position of side hull wrt centre hull, XfromAP Y from centre line Displacement [tonnes] KG KM (main + outriggers) [m] RoU radius of gyration (k^) [m] Pitch radius of gyration 0%) [m] Yaw radius of gyration (km) [m]
Value 165.0 12.0 6.0 50.0 1.50 3.50
63.0 15.0 6323 8.35 10.1 7.9 36.4 39.7
mounted at 3 m from the base line, and at midship location with respect to the outriggers centre station. A NACA 65-015 profile with span 4.0 m and mean chord of 2.0 m was appUed. The active fin responded witii a gain of 4 deg/deg/s to the roU velocity of tiie trimaran.
The twin rudders were located at about 2.7 m from the centreline and orientated 10 degrees from vertical pointing outwards. The rudder mean chord was 4.25 m and the span was 5.5 m so that the rudder tip was slightly below the keel line. The propeUer shafts were supported by V-brackets to the main hull.
Table 1 Main particulars ofthe trimaran
The stabiliser fins were attached to the outriggers and pointed inwards, see Figure 1. They were horizontaUy
Figure 1 Bodylines of the trimaran with original and increased side-hull
2.2 MODEL TESTS
Prior to model tests, seakeeping calculations are often carried out to determine the test conditions. If such calculations are performed with a linear frequency domain tool one need to be careful, since non-linear effects can introduce important operability limitations such as parametric roU which wiU not be predicted.
If the ship speed is known, a contour plot showing the encounter frequency as a function of heading and wave frequency can be prepared. From this plot the worst heading with respect to resonant roll can be depicted. Figure 2 presents the results for the trimaran at 22 knots and with a natural roll period of 12 seconds. It indicates that in stern quartering seas with a heading of 65 degrees resonant roU can be expected over a large range of wave frequencies.
At zero wave encounter frequency (the shaded area in Figure 2) seakeeping calculations should be distrusted when low-frequency (viscous) damping is not introduced. The restoring forces in the horizontal plane are zero, and with vanishing potential damping unrealistic large yaw motions can be expected, which most likely will influence the roU motions.
The model (configuration 0, 1 and 2) was tested in regular stern quartering waves of 75 and 65 degrees heading at 22 and 35 knots. The wave ampUtude varied from about 0.4 to 1.2 m, which led to significant roll amplitudes of about 10 degrees. In beam wave condition the roll response is significantly reduced compared to stern quartering condition, and at this heading the model was tested in regular waves of about 2 m ampUtude.
— Natural pottd in «r ■ 1 U 0 Isf H—?—>—i > ■. ■'.— ' ^
\ -, V\'\\V* • \ I \ '+ \ \ \ \Y '
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OS 0-8 1 1.3 WAVE FREQUENCY |r»B»]
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Figure 2 Wave encounter period as function of heading and wave frequency at 22 knots forward speed
The model was freesailing in all tests and appUed with a twin rudder and propeUer arrangement including an autopilot. The autopilot responded to the yaw amplitude and turning rate, as weU as to the sway motion to keep the vessel at track in the basin. Default autopUot settings were appUed.
23 PARAMETRIC ROLL
A nonlinear phenomenon that can occur for trimaran vessels is parametric roll in head seas conditions. When large periodic GMt variations occur, due to for example pitch motions, autoparametric roU motions can be initiated. The probability for parametric roU is difficult to estimate since it is associated with a threshold value; below a certain wave height the GMt variations wiU be too smaU to initiate the roU motions. From past accidents with container ships severe consequences are described so that it should be investigated when relevant [2].
The aft body shape ofthe main hull has a rather Umited draught which is prone for large stability variations. However, the outriggers contribute significantly to the overaU stability and even then the mainhuU experiences large variations in the wetted surface the outriggers will prevent large parametric roU angles, when they are not emerging out of the water. In this respect the trimaran behaves differently than the monohull. When bom outriggers will become dry in more sever seastates, loss of stability occurs to a significant extent The main hull has a KM value of 6.4 m and with a KG of 8.35 m the trimaran with emerging outriggers has a negative transverse stability. Figure 3 shows probable critical conditions for a GMt of 1.75 m. The contour lines are isoencounter period lines [s]. The figure shows that around 9 to 15 knots parametric roU conditions are met, considering the stability condition and the ship speed. The threat for stability loss due to outrigger emerging is associated with the shorter waves.
Table 2 presents an overview of the model test results in different conditions. The wave length associated with the
\mmmMXmmSBBSBWG3E*
15 20 25
Speed [Knots)
Figure 3 Parametric roU in head seas is more likely to occur when the natural period of the wave encounter is half the natural roU period (this is the soUd line) combined with large pitoh motions (shaded area "pitch") or loss of stability due to the outrigger (shaded area "outriggers")
peak ofthe spectrum in sea state 7 was 225 m, which is the 'shortest' possible sea condition within the definition of sea state 7 (significant wave height 8 m, PM spectrum type). The tests reveal that parametric rolling occurred to a smaU extent and it is concluded that it does not impose a severe operability limitation for this trimaran.
Wave condition Sea state SS5 SS6 SS7 SS7
Heading rdegl 180 180 180 0
Tp
9.7 11.0 12.0 12.0
Ship speed
M 22 15 9 10
RoU motions rdegl St.
Dev. 0.68 0.97 1.75 2.36
Max. +
2.9 2.7 6.2 9.8
Max
2.7 3.1 6.3 7.7
Table 2 Parametric roU investigations in irregular waves
3. NUMERICAL SIMULATION
3.1 SHIP MOTION PROGRAMS
Numerical simulations for a trimaran ship impose additional requirements to the appUed tool. Apart from general geometry aspects as hydrostatic properties, the hydrodynamics of a multihuU ship require dedicated calculation schemes.
Strip theory calculations are based on 2D hydrodyriamic coefficients and with forward speed an unrealistic overprediction of the interaction effects between the main hull and the outriggers should be avoided. Clearly the wave excitation experienced by the outriggers can be easUy included as weU as the hydrostatic restoring terms. But since the method is 2D, hydrodynamic interaction effects can not be taken into account properly. Neglecting tiie hydrodynamic interaction effects is justifiable by reasoning that the outriggers are small and that the pressure distribution on the main hull will not be influenced largely by the waves generated by the
outriggers assuming the distance between the main hull and the outriggers is not too small and forward speed is relatively high. Since a trimaran ship is designed to sail at high forward speed the hulls wiU be relatively slender, which is beneficial in tiie above reasoning.
In a 3D method the hydrodynamics can be included correctly, accounting properly for the hydrodynamic interaction effects at different speeds and headings. The 3D linear frequency domain seakeeping program PRECAL has been developed over the last years within the Co-operative Research Ships framework of MARIN. The boundary integral equation is solved using a free surface Green's function to calculate the influence coefficients between all panels on the wetted part ofthe hull. The panel code can be appUed in seakeeping studies of monohulls, twinhuUs and trimarans, with or without taking tiie hydrodynamic interaction between the different hulls into account The latter one involves the use of Green's function that satisfies the exact forward speed boundary conditions. The method appUed in PRECAL is the steepest-descent implementation, which still requires long calculation time compared to the zero forward speed Green function.
Additional viscous roll damping can be included based on the Ikeda-Himeno approach [3] combined with eddy Hamping following Tanaka [7], or one can implement measured viscous roll damping data. Advanced motion control functionality is implemented by means of passive or active stabilizer fins and rudders. The forces on the rudders and fins are taken into account using a stochastic linearisation procedure. The lift slope is calculated based on 3D theory and empirical data from extensive model tests series were used accounting for the presence ofthe free-surface and hull in the vicinity of the lifting device. The contributions on tiie flow velocity due to the incident, diffracted and radiated wave are accounted for when calculating the angle of attack ofthe fin with the flow.
The computer program DNV-WASIM (previously known as DNV-SWAN) is a 3-dimensional time domain program for arbitrary shaped ships (including multi-huUs) or other marine structures in waves. The ship may have an arbitrary forward speed, the waves can come from any direction and the responses can be computed in aU six degrees of freedom. The program is based on a three-dimensional Rankine Panel method, where also the free surface is modeUed. The steady flow around the ship is first solved and tiie coupling witii the body motions in the ship motion problem is incorporated. Radiation conditions are treated by including a zone where the free surface condition is modified such that the waves are absorbed, i.e. a numerical beach on the outskirts of the free surface domain. DNV-WASIM was origjnaUy developed in a co-operation between MTT and DNV until 1996. DNV- WASIM can be run in both a fuUy linear mode and in a non-linear mode. Transfer functions are derived from linear computations by harmonic analysis of output time series. The implemented non-linear option
solves the radiation and diffraction problem stul in a linear way. The Froude-Krylov and hydrostatic forces are calculated by integration of the incident wave pressure over the instantaneous wetted surface of the hull and gives thus a nonlinear contribution. This instantaneous wetted surface can be defined by the instantaneous position and orientation ofthe ship in the incident wave or the disturbed wave profile, which is built up by the incident waves and the radiated and tuffracted waves. Rudders and fins can be added both passive or actively controUed. Viscous damping can be specified as an additional linear or nonlinear damping term, the latter is then given as a linear function ofthe roU ampUtude. The motion equations are solved in an Eulerian frame thus aUowing for large ampUtude motions. The incident waves are modeUed according to linear wave theory. Irregular waves both long and short-crested can be simulated. The included non-Unearities can give significant contributions to both global loads and motions in large waves. Further developments of the program include slamming and hull flexibility analysis, i.e. whipping and springing. More details on the slamming integration are given paragraph 3.3.5.
AppUcation of a time domain code gives the opportunity to include the non-linear effect of the stabilizer fins directly into the motion equations, and to account for the non-linear hydrostatics and wave excitation forces. However, for large amplitude roU motions or high forward speed it will be difficult to account properly for aU hydrrxrynamic fin effects which become important, such as stall due to large angles of attack, cavitation due to high forward speed or ventilation due to the influence of the free-surface, see [4]. Current state-of-art knowledge is not sufficient to model aU aspects correctly for a new design. But, using time domain simulations, in combination witii linear frequency domain results and, above aU, model test data can provide detaUed understanding of the hydrodynamic aspects involved in trimaran analysis.
3.2 LINEAR SHIP MOTION ANALYSIS
Figure 4 presents the heave and pitch RAO in head seas at 22 knots. The model tests were performed in sea state 5. The calculated results compare weU with the model tests. The pitch resonant response occurs around 0.6 rad/s, associated with the natural pitch period in water determined by restoring, mass inertia and added mass inertia.
The roU motion behaviour in stern quartering seas depends on the prediction of the viscous roU damping since roU resonant conditions are encounter as concluded from Figure 2.
In PRECAL the empirical roU damping method of Bceda-Himeno-Tanaka is included [3]. This method was based on roU damping data for monohulls and might not be appticable for fast sailing trimarans. However, no other
Figure 4 Heave and pitch response in head seas condition, 22 knots
damping data than based on model test results was available. The IkedaHimeno roU damping for a ship without bilge keels results in mainly lift damping and eddy damping, of which the lift damping ofthe main hull is most important
Other important roU Hamping contributions will be due to active or passive fins, or due to the rudder activity. The rudders on the trimaran will respond to the yaw motions to keep the vessel on its track and course, but the forces on tiie rudder will lead to a roU moment as weU. When the rudder actions increase in stern quartering seas, tins effect will be more and more visible in the roU response ampUtude operator.
Figure 5 presents the PRECAL calculated results with passive and active rudders and the model test data. Default autopilot coefficients were used of 8 deg/(deg/s) yaw rate, and 4 deg/deg yaw; no realistic rudder actuator coefficients were known or reported. The results show the effect ofthe active rudder on the RAO's, which are closer to the measured data which include active rudders as weU. With active rudders the yaw motions decrease and roU motions increase, but in absolute sense the difference (in yaw response) is small. The motion response in the vertical plane is hardly influenced.
In the physical tests effects like lift damping of the outriggers and viscous roU damping due to yaw motions wiU be present which are not included in PRECAL. Thus it was not expected to obtain an exceUent agreement witii tiie model test. However, the results so far indicate tiiat with a linear potential seakeeping program trimaran motions can be reasonably weU predicted.
A comparison between tiie model tests and linear PRECAL calculations is shown in Figure 6 for 65 deg heading (from the stern) and 22 knots forward speed. The trend in the roU motion response using passive or active fins agrees weU with the model test data. The span ofthe fins was set to 2.0 m in the PRECAL calculations which
lead to a lift slope of 2.28 1/rad. The model test results indicate a somewhat lower lift slope since roU motions are slightly larger. The effect of the hull on the fin lift
■ P n c a ■ Pajaree nostra ■ o * Piccal - Active racttra
■+•■* E*&-Acfcv*HHKfeft
. . . 1 . . .
i
HAVE f aEOlSMtWJWHS WAVE FREQUEHCrirctlfel
Figure 5 Motion response from model tests (regular waves) and PRECAL calculations with passive and active rudders for 22 knots in heading 65 degrees
slope is difficult to estabUsh. The PRECAL implementation is based on a fin near a ship hull, which increases the effective spaa The outriggers are smaU and the tins are located near the keel line, so the actual span of the fin (4.0 m) will introduce a too large effective fin. The effect on the roU motions is significant; with 4.0 m span the roll motions with fins reduce a factor 2.
The model test where performed in waves of about 0.5 m ampUtude, so that the roU angles were about 10 deg. Such roU motions will introduce large angles of attack on the fins, and if ventilation and or staU occur, the lift slope will be less than in the PRECAL calculations which neglect these effects.
Linear calculations were conducted with the DNVWASIM program using passive rudders for 22 knots in 65 degrees heading. The motion transfer functions are shown in figure 7 and are similar to the results obtained with the PRECAL code. Most deviations occur for the sway and the yaw motion, which of course are most affected by the rudder control in the model tests.
-B-expnofins -"-Precalnofins - * - Exp Passive fins — - Preca! Passive 6ns - A - Exp Active fins - * - Preca! Active fins
1
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0.3 0.5 0.8 1.0 Wav« Frequency [recite]
1.3
Figure 6: RoU response with no fins, passive and active fins. Fin span input is 2.0 m in PRECAL.
20
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e 0.7 OS 1.1 13
0.7 09 1.1 » f c i m | i n . ) | i M |
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Figure 7 Motion response from model tests (regular waves) and linear WASIM calculations with passive rudders for 22 knots in heading 65 degrees
3.3 NONLINEAR ROLL MOTION ANALYSIS
RoU damping is an important aspect in seakeeping predictions and assessments and for a trimaran no validated prediction tools are present In general the roU damping consists of wave damping, skin friction damping, eddy damping, bare hull lift damping and appendage damping. In the present paper no attempt is made to develop vaUdated prediction methods for the various components. Instead, existing methods are used or reformulated and appUed for this trimaran case. The
objective is to evaluate the effect of the various components.
With the main huU being slender and not fitted with bilge keels the main roU damping part ofthe hull is assumed to be wave damping, eddy damping from the side hulls, rudder damping and side-hull fin damping. In the subsequent section the effects of these contributions are discussed and evaluated by nonlinear calculations. No variations of wave damping are studied, but the volume ofthe side hull above the still water level is varied.
3.3(a) Eddy damping
The work by Zhang and Andrews [5] predicted that eddy damping is the main contribution to the roll damping together witii appendage damping for their trimaran design. The eddy damping was determined vising the model as proposed by Schmifke [6] based on the work from Tanaka [7]. The latter conducted roll experiments with various ship sections to assess the effect of section shape on eddy-making roU damping. The roll resisting force is expressed as,
F^pirtfsC, eddy (1)
Taking the roU centre at the centre of gravity and decomposing the force, the roU resisting moment is written as,
M ^^pirjsmrfsCvUy =BMjd p2 (2)
The estimation of the coefficient Ceddy depends on the section shape and is a rather uncertain factor to estimate. Secondly, the effect of the fluid velocities due to the incident and disturbed waves is not considered, only the roll motion induced relative velocity at the bilges or keel is taken into account This model is used here as well but no attempt is made to predict the eddy damping as accurately as possible but instead a lower and upper value were estimate for the eddy coefficient, resulting in two damping values, which are used to evaluate the influence on the roll motions.
In the DNV-WASIM program the viscous roll damping can be added by using a non-dimensional damping curve as a function ofthe roU ampUtude,
With the roll damping formulation in equation 2 and the estimated upper and lower values for C^ , two K
curves are obtained, with K2 =0.005, K2- 0.012 and
KX = 0.0 . When using both K curves in a nonUnear
DNVWASIM analysis the roU ampUtude RAOs are derived and shown in figure 8. As seen the variation of the roU response varies from a few percent up to 20%, mainly due to different roil velocities, encounter frequencies and a timedependent added mass formulation' in DNVWASIM. In the lemaining calculations ofthe paper tc2 was set to 0.0085.
i
M:'-T-
0.9 0-6 0.7 0.« <LS 1.0 1.1 t.» 1.4
Figure 8 Eddy damping variation on WASIM first harmonic RAO, 22kn 65 degrees
3.3 (b) Autopilot model
The model was selfpropeUed with rudders acting on an autopilot. The exact settings of the autopUot gains were not reported. The DNVWASIM calculations are most often conducted with an autopUot model based on an ordinary PDtype controUen
Sfy^kflr + kiW (5)
The values ofthe gain coefficients are of arbitrary choice as usuaUy no specific values are available for the vessel under investigation. Figure 9 demonstrates that the effect of the gains on the roU motions is significant. Two different set of gains with both stable autopilot settings gave an average difference of 15%. If the autopUot model is extended with a proportional sway term the effect can even be larger depending on the motion reference point as roU contributes to the sway motion. The comparison between DNVWASIM and tiie model tests for this 35 knots case is not as good as for the 22 knots case of figure 8. Possibly the side hulls, being very slender, give extra roU damping by acting as lowaspectratio wings upon asymmetric inflow due to occurring drift angles and sway and yaw motions. Secondly, the average number of measured oscillations for the tests at 35 knots was just 4, whue for the 22 knots case this was over 9 giving more reliable harmonic results.
AUUSIM
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Figure 9 WASIM first harmonic RAOs with two sets of autopUot gains, 35kn 75 degrees
3.3 (c) Passive and active fins
The modelling of a stabitising fin in the DNVWASIM program is done by a lift formulation,
M'^Q^pt/^XO (6)
Here a is the angle of attack, which is determined by the relative velocity normal to the lifting surface. In case of active fin control tiie demand angle is determined by a control model. In the present calculations a simple term proportional to roU velocity is used,
a^,{t) = K j(t)
with K = 4 deg/ deg/ s
(7)
The Uft coefficient is user input and it is a rather difficult task to select a value as a lot of aspects have an influence on the fin performance:
Profile thickness Aspect ratio Fin submergence BUge radius Boundary layer thickness Finhull interaction Fin osciUation (Theodorsen function)
The fins were defined by a NACA 65015 profile with a 2D Uft coefficient of 6.02. In the nineties a 3years R&D project was carried out by the MARINCooperative Research Ships programme on motion control of ships, [8]. Based on this work, an estimate has been made ofthe lift coefficient, compensating for the effects as listed above. However the present fin configuration is not easily comparable witii fins instaUed at the bUges of ordinary ships. When taking the aspect ratio as s/c or 2s/c (based on the actual dimension, or assuming the hull as an end plate) the estimated lift coefficient varies from 2.2 to 3.2. An average of 2.7 was used in the DNVWASIM calculations.
In figure 10 the roU motion RAOs are shown for the vessel sailing at 22 knots in 65 degrees waves. Good predictions are obtained for the bare hull and the hull fitted with passive fins. An under prediction of 30% is seen for the active fin modelling. In the WASIM calculations no delay was modeUed for the behaviour of the active fins, to what extent a delay was present in the model tests is unknown. In contrast to the linear predictions shown earlier a nonlinear simulation does capture the trend in the model test results. The two clear response peaks are weU predicted.
Why the results for the active fins are not as good as the passive fins is not known. The interaction between the huU and the fins can possibly be important. Van Walree [9] has shown that the interaction between the hull and control surfaces can be large. If important, this would recjuire a modification of the DNV WASIM program to include a lifting surface model in the boundary value problem.
W n h « « v l ^
Figure 10 WASIM first harmonics RAOs, 22kn 65 degrees, without and with passive and active sidehuU fins
3.3 (d) Varying side hull volume
The model test program used a preliminary trimaran design with side hulls being very slender up to the cross deck structure. An actual design will most likely have more volume in the abovewater part for proper load transfer between the side hull and cross deck structure and for other reasons based on stability or design characteristics. In a later model test series, the present hullform was tested with side hulls having more volume above the still water level Although this provides a significant increase of the GZ stability curve, a significant increase of tiie roll motion was observed. Apparently the wave excitation on the side hulls, inducing roU motions, can be dominant over the restoring and damping effect due to the extra volume. If analysing the motion behaviour of a trimaran with a nonlinear seakeeping tool such a phenomenon can be quantified. No detailed data was available of the actual hullform with increased side hull volume, therefore a modified hullform was developed as part of this study, see figure 1.
For the regular tests at 22 knots in stern waves from 65 degrees tins hull form was simulated with WASIM and the roU motion RAO is shown in figure 11.
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Figure 11 Nonlinear WASIM first harmonic RAOS, 22kn65 degrees
The increase of the side hull volume clearly shows a reduction of the roU motion amplitudes. The benefit is however small for wave frequencies around 1 rad/s. For these wave frequencies the corresponding wave length is about twice the ship's beam. It then happens that one side hull is wetted in a wave crest while the other is dry or nearly dry in an opposite wave trough not giving any restoring or damping effect A snapshot of this moment is shown in figure 12.
Figure 12 WASIM Snapshot of trimaran with increased side hull volume, heading=75deg from the stern, £,=1.02, COFO.90 rad/s
With the heading changing more towards beam seas the effect becomes more pronounced as figure 13 shows for 75 degrees heading. Around 1.0 rad/s almost a doubling ofthe roU motion is calculated.
Figure 13 Nonlinear WASIM first harmonic RAOs, 22kn 75 degrees
3.3 (e) A nonlinear damping model in DNVWASIM
An additional option in the DNV WASIM code is to include slamming loads. A preprocess calculation is then conducted for a set of 2dimensional strips of the hull using a 2D BEM program, developed by Skeie and Helmers [10], as part of the MARINCooperative Research Ships programme [11]. The theory of this program is based on work carried out at NTNU in Trondheim including verification by experiments, see [12]. The results from the 2DBEM program are subsequently used in the nonlinear WASIM simulation. Thus nonlinear contributions for damping and added mass are incorporated for tiie *abovestiUwaterpart\ The total pressure is then formulated as,
1 p(x,t) = /> VR V(x ,h)+pC, (x,h)Vj (8)
Here the invariant potential solution and the slamming coefficient are only functions ofthe position on the hull and the immersion depth. During the WASIM simulation the relative velocities and the immersion ofthe section in the wave are calculated. The slamming coefficients and the potential solutions are extracted from the slamming database and the pressure is calculated and mapped on the panel model. Experience has shown that some nonlinear simulations with only the FroudeKrylov and hydrostatics as nonlinear components show unrealistic ship motion behaviour as the motion behaviour lacks an amount of nonlinear damping. Sometimes this behaviour can be characterised by a "chttd on a trampoline" as the nonlinear FroudeKrylov and hydrostatic term are spring terms and insufficient damping is present in the dynamic system. Experience with the integrated slamming has shown that for cases where no slarnming occurs this model can give an improved motion behaviour of the vessel as it adds nonlinear damping to the motion equations. This model is used here for the side huUs to add nonlinear damping due to the intermittent wetting of side hulls. When evaluating the results, only a few percent less roU ampUtudes are obtained and thus irrelevant to show in an additional figure. As the encounter frequency is rather large, above 9 seconds, the
velocities are too small to cause any substantial nonlinear damping due to the side hulls.
3.3.(1?) Summarising discussion
The calculations in the previous paragraphs show that linear and nonlinear calculations can predict the motions of a trimaran vessel weU. The roU motions as observed in tiie tests were large and for distinct heading and wave length very large. RoU motion control is thus of paramount importance for a trimaran vessel. The model tests and calculations proved that the active use of roU damping fins gave the largest reduction of the roU motions. Increasing the volume of the side hulls can reduce the roU motions in some conditions while it can increase it at other distinct headings and wave period combinations. In addition to tiie use of side hull fins are other Uft devices possible, like Tfoils or foils extending from the main hull to tiie side hull. The work by Grafton, see [13], addresses these different configurations as well as variations in the dimensions and aspect ratios. This is of importance for improved modelling of Uft devices in numerical ship motion predictions for trimaran vessels.
4. MOTION AND LOAD ASSESSMENT
The final goal with numerical simulations of trimaran motions and loads is to support the design of these vessels, to provide sufficient documentation to prevent the risk of violent motions, to optimise the seakeeping performance and to provide reliable predictions of structural design loads. Based on the previous studies a discussion on the application of linear and nonlinear snip motion analysis is given for both seakeeping and wave load studies as part of a trimaran design development
4.1 SEAKEEPING PERFORMANCE ASSESSMENT
EspeciaUy in case of a combatant trimaran development the seakeeping behaviour is an important aspect, as the performance or availability of sensors, weapons or personnel deteriorates with increasing motions. In an early stage critical response characteristics are to be identified and properly addressed in order to optimise the seakeeping behaviour. As shown in the paper a linear ship motion tool can assist in tiiis process. RoU stabilising fins can provide a significant reduction in roU motions and good results were obtained with the modelling of these devices in Linear ship motion analyses. Nonlinear prediction tools can provide additional predictions for phenomena not captured in linear theory. EspeciaUy the side hull volume above the calmwater level showed to have a surprisingly large influence on the roU motion response. Increasing the side hull volume gives increased static stability however for distinct headings and wave lengths the intermittent wetting ofthe side hulls shows a dominant behaviour of the roll excitation giving a significant increase of roU motions.
Seakeeping operability studies are often conducted and usuaUy based on linear ship motion results. Further studies into the roU motion predictions should evaluate to what extent linear ship motion theory can be appUed in a seakeeping operability assessment depending on the actual side hull configuration. Nonlinear simulations are very time consuming for the simulation and postprocessing of a complete scatter diagram for all relevant heading and speed combinations.
4.2 DESIGN LOAD ASSESSMENT
Considering the prediction of design loads more guidance is available on how to apply nonlinear prediction tools and this is necessary as no rules for trimaran vessels are available. DNV provides a separate chapter on "Direct Calculation Methods" in the High Speed Light Craft Rules. As there are no rules available for trimarans it is recommended that a trimaran will have to be evaluated foUowing a so-called "level 3- alternative rule analysis". Nonlinear hydrodynamic analyses are then required with load transfer to a FE model for structural strength analysis. A principal issue for high speed craft is the use of a speed/sea state curve describing the maximum operational limits of the vessel. This speed/sea state curve forms the basis of tiie nonlinear load assessments. A priori it is not known, which speed/sea state combination is most critical nor which wave period gives worst responses. For some vessels/responses a linear ship motion and load analysis can be sufficient to identify the worst heading, speed and sea state combinations, which is subsequently used in a nonlinear design load analysis. However in case of unknown behaviour or significant nonlinear responses it is advised to perform a nonlinear analysis to identify the most critical sea state, which serves then as design sea state. Preferably irregular nonlinear analyses are conducted and used to derive the load statistics from the time series, from which expected extremes in 3 hours can be estimated. The appUcation of a regular design wave approach is to be Umited to cases, where this has proven to be reliable; tin's is not the case for a trimaran vessel. It is important to conduct the irregular simulation sufficiently long for reliable statistical post-processing; any extrapolation is preferably to be avoided. Most often the ship crew estimates the wave heights by visual observations, which introduces an uncertainty with respect to the operational limits set by the speed/sea state curve. In addition the design sea state might be encountered more often during the lifetime ofthe vessel. Consequently, the determined expected extreme in 3 hours cannot serve directly as basis for the structural design. Based on experience and studies a safety margin is therefore introduced, by demanding a design value at 1% exceedance ofthe extreme probability curve. In case of a linear response process this would imply a safety factor of approximately 1.25 on top of the expected extreme in 3 hours. This factor is adopted for nonlinear responses a weU. The use of this direct load procedure is weU-estabUshed over the years and supported by
operational experience and measurements. However the needs are changing and future developments are likely on several areas. First of aU DNV is aiming at the development of risk based rules and tiiis affects the direct load procedures as weU. More attention should then be focused on the statistical distributions of both the extreme loads and the ultimate capacity in combination with acceptance criteria. Secondly, the use of a speed/sea state curve is rather arbitrary and perhaps can be replaced in the future by directly accounting for the operator behaviour in wave load analyses. EspeciaUy in case of an unusual ship like the trimaran, where comparative data is lacking a speed/sea state curve is difficult to specify. A procedure to account directly for the operator behaviour in severe weather is then preferred and a summary is given hereafter.
4.2 (a) Ship behaviour assessment using realistic operational profiles
At MARIN simulating realistic operational behaviour is conducted to provide design assistance and decision support for designers and owners. This technique evaluates the progress of a ship on its route on the basis of historical wind-wave information. The results give a detailed insight into the nature of fuel consumption, efficient sailing strategies and the risk of exceeding a target trip duration, see DaUinga [15].
At DNV pUot studies have been conducted to evaluate design load analyses using reaUstic operational profiles, see Pastoor [14]. The basis ofthe procedure is to define ship response criteria and define environmental and operational conditions such tiiat these criteria are not exceeded. The foUowing steps are then foUowed:
a. Define critical responses Define which responses are used by the crew to change heading and or speed, for example: - Green water on over the bow or the cross deck - Slamming on the cross deck - Side hull emergence - Etc.
b. Define response criteria Criteria values are available for many responses and are used in seakeeping performance assessments. Consequently these can be used as a starting point. Another option is to use "expert opinion" from ship crews.
c. Define operator actions A definition is necessary on what actions ship personnel take. These actions depend not only on the primary parameters, i.e. responses, speed and heading, but also on secondary aspects like a possible delay on the voyage time schedule, possible manoeuvring restrictions, etc.
28 12004: The Royal Institution of Naval Architects
Design & Operation of Trimaran Ships, London, UK
d. Variation study of criteria values As the response criteria are most questionable they should be varied from low to large values in order to investigate there effect. Such results provide additional information to make proper choices for the criteria values. Even better would be to model the criteria as uncertain quantities with a probabilistic description. A simple approach would be to consult a group of experts to define a "maximum criterion value" and a "minimum criterion value" and use these to develop a standard normal distribution.'in this way the uncertainty of the criteria values can be evaluated in terms of design load variations, which in turn helps to evaluate whether appropriate criteria values can be selected or not
5. CONCLUSIONS
6. ACKNOWLEDGEMENTS
The authors would like to express their gratitude to the Royal Netherlands Navy for the permission to use and publish the model test data.
7. REFERENCES 1. FEIKEMA, G.J., 'Seakeeping tests for a 165m
trimaran', MARIN report no. 2I3I82-3-ZT, Vol. I & It, 1996.
2. LEVADOU, M., PALAZ2J, L. 'Assessment of operational risks of parametric roU', Proceedings of World Maritime Technology Conference, SNAME, 2003.
A summary is presented of model tests conducted with a frigate type trimaran. Main attention has been given to the roU motion behaviour. Both linear and nonlinear ship motion calculations have been conducted to validate the numerical tools. These calculations showed that linear and nonlinear predictions give good comparisons with model test results and can thus be used in trimaran design and design load assessments.
Large roU motions were observed in the model testing and this needs to be addressed properly in the design process to achieve an acceptable level of roU motions. Lift devices seem most promising and reasonable to good predictions were made with the ship motion programs. However tiie modelling of the lift behaviour is an issue, which needs to be addressed further as the fin configuration and local flow behaviour on a trimaran side hull is not directly comparable to conventional bilge keel mounted fins. In addition it is expected that the side hull can give additional roll damping as it is very slender and asymmetric flow occurs when having a drift angle. It was shown that the side hull volume above the calm water level can have a significant effect on the roU motions, changing the conditions were and extreme response occurs.
For wave lengths in the order of twice the ship's beam the roU excitation is a dominant factor as tiie side hulls are opposite wet or dry. Further model testing with varying lift devices and side hull variations are recommended to increase the knowledge on the physics of these phenomena and their effects on the roU motion. Secondly, it is desirable to further develop calculation schemes for lifting devices and nonlinear excitation and damping for implementation in ship motion programs.
A discussion on the appUcation of these tools for trimaran seakeeping and wave load assessments completes this paper.
3. IKEDA, Y., HIMENO, Y., TANAKA, N., 'A prediction method for ship rolling', Technical report 00405, Department of Naval Architecture, University of Osaka Prefecture, Japan, 1978.
4. GAUARDE, G. 'Dynamic staU and cavitation of stabiliser fins and their influence on the ship behaviour', Proceedings of the FAST conference, Napels, 2003.
5. ZHANG, J.W., ANDREWS, DJ. 'RoU damping characteristics of a trimaran displacement ship', International Shipbuilding progress, Vol 46, no. 448, 1999.
6. SCHMITKE, R.T., 'Ship sway, roU and yaw motions in obUque seas', SNAME Transactions, Vol. 86,1978.
7. TANAKA, N. 'A study on the bflge keels (Part 4 - on the eddy making resistance to the rolling of a ship hull', Journal ofthe Society of Naval Architects of Japan, Vol. 109,1960.
8. DALLINGA, R.P., DOEVEREN, A.G. van, 'CRS Motion Control: Physics of fin stabilizers - empirical model of lift and drag', MARIN Report no. 211105-4-OE, 1994.
9. WALREE, F. van, 'Development, vaUdation and appUcation of a time domain seakeeping method for high speed craft with a ride control system', 24* Symposium on Naval Hydrodynamics, Fukuoka, Japan, July 2002
10. SKEIE, G., HELMERS, J.B. (1999) 'Slarnming in SWAN - using 2DBEM as a pre-processor', Technical report no. 99-2008 (internal), Det Norske Veritas.
11. SKEIE, G., KVALSVOLD, J., NESTEGARD, A., 'Computer program CRSLAM for prediction of slamming pressures', Technical report no. 96-2039, Det Norske Veritas, 1996.
12. ZHAO, R., FALTTNSEN, O., AARSNES, J.V. 'Water entry of arbitrary two dimensional sections with and without flow separation', Proceedings, 21th symposium on Naval Hydrodynamics, Trondheim, Norway, 1996
13. GRAFTON, T., "The trimaran concept and trimaran roll damping', Presentation held at the London branch ofthe RINA, 2003
14.PASTOOR, W. 'Rational determination of nonlinear design loads for advanced vessels', Proceedings of the FAST conference, Napels, 2003.
[15] DAIUNGA, R.P., DAALEN E.F.G. van, 'Design for service', IMTA Conference, October 2003, Rotterdam
8. AUTHORS BIOGRAPHY
Wouter Pastoor Ph.D. is working as a senior engineer at Det Norske Veritas. He is working on R&D projects to improve prediction and assessment methods for ship motions and loads for both fatigue, ultimate loading and seakeeping assessments. Other activities are concentrated on consultancy studies on behalf of clients and DNV Classification.
Riaan van ' t Veer PhJD, is working as project manager in tiie seakeeping group at the Maritime Research institute Netherlands. After graduation at Delft University on hydrocrynamics of catamarans, his PhD work was devoted to the same topic (1998). Currently he is involved in many research projects on advanced seakeeping and damage stability issues. His work combines model testing and numerical developments.
Eelco Harmsen M.Sc is working in the hydrodynamics group of the department MiUtary Maritime Technology ofthe Royal Netherlands Navy.
