Theoretical and experimental study of motion characteristics of high-speed catamaran hull forms

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Abstract

In the new millennium, significant changes can be seen in the form of novel hull forms suitable for high-speed operation. Several authors have made significant

contri-butions over the last few years to the evaluation and analysis of hydrodynarnic performance of high-speed multihull forms.

In this paper, an attempt has been made to present the seakeeping characteriStics for a range of high-speed catamaran hull forms based on the typical geometry used in practice by the Australian high-speed ferry in-dustry.

It has been shown that., although experimental analysis would still continue to play a major role, the theoretical approaches are fast becoming robust enough to attract serious attention for the preliminary design stagç, where several different hull forms need to be evaluated within limited time to suit a specific requirement.

Keywords

Catamarans; Hydrodynamics; Motions

Introduction

In this paper, we present results for heave and pitch motions in head seas for typical catamaran hull forms generally used in the high-speed ferry industry. In the first instance, the two-dimensional strip theory method (using Lewis-form sections) has been used to predict the heave and pitch motions in head seas. In the second instance, use has been made of HYDROS to predict these motion characteristics, using an exact analysis of the ship sections. An overview of two-dimensional strip theory and the HYDROS approach are given in later

sections of this paper.

Deift University of Technology

Ship Hydromechanics laboratory

Library

Mekelweg 2

26282 CD Deift

Phone: +31 (0)15 2786873

E-mail: p.w.deheertudelft.nI

Theoretical and Experimental Study of Motion Characteristics of

High-Speed Catamaran Hull Forms

Prasanta K. Sahoo' and Lawrence J. Doctors2

Senior Lecturer (Hydrodynamics), Department of Maritime Engineering Australian Maritime College, Launceston, Tasmania, Australia

2)

Professor and Head of Naval Architecture, The University of New South Wales Sydney, New South Wales, Australia

Literature Review

Lee et al (1973) proposed an analytical method for pre-dicting the catamaran motions and hydrodynamic loads in head seas. The analytical prediction of motion ap-peared to be adequate, except near the resonant frequen-cies where the magnitude of motion amplitudes is over-estimated with increasing forward speed. The discrep-ancies in the correlation are a result of the inadequacy of the theory, which did not account for the viscous effects as well as the three-dimensional hydrodynamic interac-tion effects between the demihulls at higher Froude numbers. It was also concluded that the separation dis-tance between the demihulls does not play a significant role, except in the case of roll motions.

Miii et al (1993) carried out a seakeeping study on the development of a mid-size high-speed catamaran ferry based on the theoretical methods of strip theory and a three-dimensional soUrce distribUtion. Although the study concluded that strip theory is inaccurate in the high-speed region, no noticeable differences have been observed in both methods. The authors emphasize that the strip-theory method could be utilized as a practical tool to estimate seakeeping performance of catamarans. The paper by Fang et al (1996) presented an analytical technique based on the two-dimensional Green function method associated with a cross-flow approach to ac-count for the viscous effects in order to estimate the motion responses in the frequency domain. Experiments conducted by the authors showed that reasonable pre-dictions are achievable at low fôrward speed, although discrepancies do set in at higher forward speed, where motion responses are overestimated by the

potential-flow theory.

A further paper by Fang et al (1997) introduced an ex-tension of the linear frequency domain theory to a quasi-non-linear time-domain technique to compute the large-amplitude motions in regülar waves. The authors have solved the coupled heave and pitch equations in the time domain by the Runge-Kutta method and have

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experimented with a catamaran in head seas to compare the linear and non-linear methods. Both methods over-predict the motions at resonant frequencies, although the non-linear approach shows better validation agaiìist

experimental results. Non-linear effects are quite

sig-nificant in the higher Froude number range and at

higher wave amplitudes. It has been recommended by the authors that the abOve-water form of the hull should be included in the numerical simulations for large-amplitude motions, where the classical concept of fre-quency-dependent added-mass and damping coefficients are to be replaced by non-linear hydrodyiwmic forces in the time domain.

Bailey et al (1999) have adopted a three-dimensional potential-flow analysis procedure to investigate the

dynamic behavior of the NPL hull form in both

monohull and catamaran configurations in head waves. The different numerical formulations demonstrated very good agreement for the response amplitude operator (RAO) in heave and pitch. For the catamaran configura-tion,

the predicted RAOs showed a better overall

agreement with experimental results than those derived from strip-theory methods. The authors clearly state that further theoretical and experimental work needs to be carried out for a better understanding of the dynamic behavior of multihull configurations.

Varyani et al (2000) have presented the behavior of a catamaran hull form with and without forward speed. Like the previous authors, two different methods have been used, namely, strip theory and the

three-dimensional pulsating-source method. Minor differ-ences have been noted at zero forward speed in both methods, whereas these differences increase fUrther as the forward speed increases. It is the contention that increasing the number of panels in three dimensions

could improve the accUracy of motion prediction. Centeno et al (2000) have proposed a two-dimensional potential-flow theory in which viscous forces have been considered through a cross-flow drag approach to pre-dict catamaran motions in regular waves. Experiments conducted by the use of twin cylinders show good agreement with theory at zero forward speed. When viscous forces taken into account, the results showed a decrease in peak resonance amplitude, as was expected. Its influence is stronger at.higher forward speed. Duan et al (2001) presented a comparative study of two motion-prediction methods for high-speed displacement hull forms. A numerical method based on two-and-a-half-dimensional theory has been used where the three-dimensional free-surface condition is retained. The two-dimensional transient free-surface Green function is used to formulate the integral equation on the body surface. The notable conclusions were: a) at high for-ward speed, strip theory cannot accurately predict the motion responses resulting from standing waves be-tween the hulls, and b) the-two-and-half-dimensional theory appeared to be more rObust than a complete

three-dimensional method.

Centeno et al (2001) have presented their results of experiments carried out on hard-chine catamaran hull form configurations and have compared these against

the standard strip theory and a two-dimensional poten-tial theory which includes viscous forces through a cross-flow drag approach. This paper is similar to that of Centeno et al (2000). The results are complimentary to each other, in that inclusion of the viscous effects showed improved motion prediction at all speeds, espe-cially in the case of heave. At higher speeds, large reso-nance peaks have been obtained with wider hull con-figurations. Monohull and catamaran hull configurations showed similar responses at higher speeds and higher frequencies This was attributed to decreased interfer-ences between the demihulls at high speeds for certain values of the hull spacing and the wave frequency. Davis and Holloway (2003) illustrated a two-dimensional Green function solution in the time domain in order to predict the motions of catamaran hull forms in oblique seas in the high-Froude-number range. The authors have compared their theoretical approach against experimental results conducted on Series 64 and NPL Series hull forms in catamaran configurations. It has been claimed that the form and maximum value of the RAO in heave, roll and pitch show generally good agreement with theory.

Subramanian and Gururajan (2004) have presented a set of experimental results for single-chine catamaran hull forms at various separation ratios. The results have been compared with SEDOS, a computer program based on strip theory but incorporating interference effects and viscous cross-flow drag effects, which analyses catama-ran motions. For moderate wave heights, computational and experimental results have been shown to be encour-aging up to a Froude number of 1.12. Non-linear effects appear to be absent.

In summarizing the literature review, one can say that:

For practical applications two-dimensional strip theory compares favorably (within its stated limita-tions) with experimental results conducted by vari-ous authors.

Two-dimensional potential theory, which incorpo-rates viscous cross-flow drag effects, appears to

show improved results when compared with classic strip theory.

2-1/2 D theory may be more robust than a complete 3-D potential flow analysis but further experimental work is needed to validate both of these theoretical approaches.

lt appears that extensive experimental work and improvements in the theoretical formulation need to be carried out for a better understanding of motions of multihull vessels in both regular and irregular

seaways and for different headings.

Overview of Strip Theory and HYDROS

-Strip Theory

In this paper, the computer program SEAKEEPER (2003), which is based on strip theory, as exemplified iñ the landmark paper by Salvesen et al (1970), has been used to predict the motions of catamaran hull forms.

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The two relevant equations in coupled heave and pitch motions are given by:

HYDROS Approach

HYDROS firstly sets the vessel, which is represented by a surface mesh, at the required load waterline. A series of equally spaced sections is then computed. The hy-drodynamic added mass and damping of each section is obtained using the frequency-domain Galerkin bound-aiy -element approach. A mathematical "lid" is also used on the "internal" water surface in order to remove the problem of irregular frequencies. The details were pre-sented by Doctors (1988).

The standard strip theory as developed by Salvesen et al (1970) is next employed to compute the motion of the vessel. In the present work, specifically, head seas only were considered. Numerical tests on the method were also conducted. This test showed thàt 20 stations, each defined by 20 surface points, were more than adequate to provide essentially converged results.

Doctors, Holloway, and Davis (1996) published previ-ous application of this computer program, together with a comparison with experimental data on a semi-small-waterplane-area twin-hull (semi-SWATH) vessel.

Catamaran Models

Table 1 below shows the paranielric range of seven catamaran hull form, which were subjected to heave-and-pitch-motion prediction in the theoretical computa-tions. It may be noted that RB stands for round bilge, SS stands for semi-SWATH and CH for chine form.

Table 1: Parametric Range of Catamaran Models Tested in Both Theories

It has been the intention to keep the displacement iden-tical for all the models in order to illustrate the effects of hUll fonti influence on the motion characteristics. Com-puter simulations on all these catamaran hull forms have been condUcted with separation ratios sIL of 0.2 and 0.3 with Froude numbers being 0.35, 0.55 and 0.85. Figures 1 through 7 below depict the body plans for the various catamaran hull form configurations.

Figure 1: Round-Bilge Catamaran Demihull (Mi-RB)

Figure 2: Semi-SWATH Catamaran Demihull (M2-SS)

4j)

MOJ Mi-RB M2-SS M3-SS M4-SS M5-CHM6-CRM7-CH Draft(m) 1.5 1.7 1.8 1.8

1.41.3

1.3 Lw,.(m) 47.7 47.7 47.6 47.5 47.5 45.8 45.8 BWL(m) 3.2 3.1 3.2 3.2 3.1 3.1 3.1 C8 0.55 0.49 0.46 0.46 0.60 0.66 0.66 (t) 127.5 127.4 127.4 127.4 127.4 127.5 127.5 11Vt13 _9.56 _9.55 _9í3 _9.52 _9.51 _9.17 _9.17 - LIB 150 15.2 15.1 15.0 15.2 14.8 14.8 BIT 2.1 1.8 1.8 1.7 2.2 2.3 2.3

(M + A33»i + B333 +C373 +A35i75 +ß35175 +C35i5 = F3e° (1)

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Figure 5: Single Chine Catamaran Demihull (MS-CH) The following definitions have been used to present the various motion characteristics:

Pitch Transfer function p' = (4)

kÇ0 22r

where wave number k = =

-g L

Figure 6: Chine Catamaran Demihuli (M6-CH)

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Figure 7: Chine Catamaran Demihull (M7-CH)

Model Testing

In order to test the results of the present research work seakeeping tests were performed at the Australian

Mau-time College Ship Hydrodynamics Centre (AMCSHC). The table below shows the geometrical parameters of

the tested model.

Table 2: Model Particulars and Sea State

Figure 8: Body Plan of Tested Catamaran Demihull

Results of Numerical Simulation

z-- __//,. ____/_ /

Figure 9: Profile View of Tested Catamaran Model

Figure 10: Plan View of Tested Catamaran Model

The authors would like to present and share the data obtained from numerical simulations by both the strip theory and HYDROS methods. However due to limita-tions of space only a selected few results wilÏ be pre-sented. In the first instance, results of catamaran models as depicted by Mi-RB, M2-SS, M5-CH and M7-CH hull forms have been presented at three different Froude numbers of 0.35, 0.55 and 0.85, respectively, to

illus-Full Scale Model Scale

Waterline length (m) 23.53 1.5

Waterline beam (m) 2.293 0.146

)raught(m) 1.19 0.075

Load displacement (tonnes) 40.11 19.6 kg

Radius of gyratión 0.25L 6

Q75

Speed of vessel (m/s) 3.65-10.13 0.92-2.56

Seaway Head seas

Modal wave height (m) 1.24 0.078

Encounter freqúency (radIs) 0.25-10 0.5-1.5 The hull form configuration of the above tested catama-(3) _{ran model is shown in Figure 8 below.}

Heave Transfer function H' = 'o

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trate the close correlation between both methods. Fig-ures 11 to 13 depict the non-dimensional heave

re-sponses plotted against non-dimensional encounter frequency for both methods.

Figure 11:H'-Strip-Theory andHYDROS at Fn 0.35

Figure 12: H'-Strip-Theory andHYDROS at Fn 0.55

Figure 13:H'-Strip Theory andHYDROSat Fn 0.85 Figures 14 to 16 depict the results of non-dimensibnal pitch responses against non-dimensional encounter frequencies for both methods. Once again, the results are only for the three Froude numbers mentioned ear-lier, in head seas. In order to validate these results, ex-peiirñental work was carried out at the AMCSHC on the catamaran model illustrated in Table 2, whose body plan, profile and plan view are shown in Figures 8 to lo.

A. A. 14 .2 I.0 0.2 0.4 0.2 0.0 0.00 2.00 4.00 6.00 8.00 0.00 1200

Noo.dA,mtomI Emsm,md,r Frsq,rny (L La .)SSlp ID-LS AmiovalaS

Figure 14: P' -Strip Theory andHYDROSat Fn 0.35

0.4 0.2 0.0 3.0 2.0 1.0 0.5 1.6 MS-CH MI-CH 1.4 .2 1.0 OES 2. 0.0

Experimental Validation

The authors have clearly summarized in the literature review that for all practical applications, strip theory would satisfy most requirements of a practising naval architect. However, HYDROS theory goes beyond in a way that it refines the motion characteristics by elimi-nating the deficiencies of the strip theory. In the follow-ing figures, the non-dimensional heave and pitch re-sponses at three Froude numbers namely 0.430, 0.524 and 0.667 have been plotted, which are representative of

0.05 2.00 4.00 6.00 8.00 10.00

Nolmslm1 Et,r Fooqom,my (0Jg>'

FSS=O.35

1200

0.00 2.00 4.00 6.00 8.00 10.00 1200

N.-dm1onI E,,coI,r Frquy Ug)"

fc.0 Sm, Th. .(LS.EYDSOS

0.00 2.00 4.00 6.00 8.00 10.00 12.00

Nmonil EnmWr Frqq (IJg)"

(.IL.}SbtpTh, ftSU)HYD

0.00 2.00 4.00 6.00 8.00 10.00 12.00

Nom.dlmirmI Emomm1s Fftqy (L/g)

Ml RB MCH 24200 - M5-CH 1200 0.0 0.00 2.00 4.00 6.00 8.00 10.00

NLSS.dlmosmkmml Eno.msg,r Fo,qsmmoy ,(LI8I°'

WhStD.) 1100505

-M2 SS

MI-CH MI-RB

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the speed regime, in which a high-speed catamaran

would most likely operate.

As can be seen from Figures 17 to 19 the trends as pre-dicted by SEAKEEPER and HYDROS are quite consis-tent with experimental results. However, HYDROS tends to correlate considerably better with experimental results than the former program.

25 2.0 11.5 1.0 0.5 Z 00 £25 20 11.5 I.0 J 0.5 o.o 10 1.0 3.0 5.0 7.0 9.0

No,..dII Emr F0eqooq (L/g)"

Figure 17: Experimental validation againstSEAKEEPER and HYDROS at Fn 0.43

Conclusions

In conclusion the authors would like to state the follow-ing:

For a practising naval architect, the SEAKEEPER predictions of motions are reasonably well within limits for low Froude numbers less than 0.5. Motions predicted by the HYDROS compùter pro-gram suggest that it is better than SEAKEEPER at both the lower and the higher Froude numbers of interest. Indeed, the predictions of the peak re-sponses by SEAKEEPER are genera]iy too high by at least a factor of 2.0.

Although experimental results have been presented for an arbitrarily chosen model, it is imperative that many more model tests in different seaway condi-tiöns be carried out in future in order to test the lim-its of, and build confidence in, these two programs.

O Eopt-H O Expt.. -SEAXEEPER-H SEAKEEPER-P

- - - HYDROS-H .I-IYDROS-P

3.0 5.0 7.0 9.0

NdIrno,o1 Eotor Foqq (1Jg)"

Figure 18: Experimental validation against SEAKEEPER andHYDROS at Fn 0.524 £2 20 11.5

_o

F,.0.667

a

3.0 5.0 7.0 9.0

Figure 19: Experimental validation against SEAKEEPER and HYDROS at Fn 0.667

Acknowledgements

The authors would like to take this opportunity to ex-press their gratitude to Mr Simon McGoldrick and Mr Luke Pretlove, who have devoted their precious time to the development of catamaran hull forms, analysis by use of strip theory and the experimental work carried out at the AMCSHC. The authors would also like to thank their two respective institutions for their in-kind support in undertaking this research work.

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