Theoretical and Experimental Study of Motion Characteristics of High-Speed Catamaran Hull Forms

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1 Deift University of Technology Ship Hydromechanics laboratory Library Mekelweg 2 Phone: +31 (0) p.w.deheertudelft.ni CD Deift 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 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 contributions 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 industry. 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. Literature Review Lee et al (1973) proposed an analytical method for predicting the catamaran motions and hydrodynamic loads in head seas. The analytical prediction of motion appeared to be adequate, except near the resonant frequencies where the magnitude of motion amplitudes is overestimated with increasing forward speed. The discrepancies 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 interaction effects between the demihulls at higher Froude numbers. It was also concluded that the separation distance 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 account for the viscous effects in order to estimate the motion responses in the frequency domain. Experiments conducted by the authors showed that reasonable predictions are achievable at low fôrward speed, although discrepancies do set in at higher forward speed, where motion responses are overestimated by the potentialflow theory. A further paper by Fang et al (1997) introduced an extension 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

2 - experimented with a catamaran in head seas to compare the linear and non-linear methods. Both methods overpredict the motions at resonant frequencies, although the non-linear approach shows better validation agaiìist experimental results. Non-linear effects are quite significant 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 largeamplitude motions, where the classical concept of frequency-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 configuration, 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 threedimensional pulsating-source method. Minor differences 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 predict 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-ahalf-dimensional theory has been used where the threedimensional free-surface condition is retained. The twodimensional transient free-surface Green function is used to formulate the integral equation on the body surface. The notable conclusions were: a) at high forward speed, strip theory cannot accurately predict the motion responses resulting from standing waves between 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 potential 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, especially in the case of heave. At higher speeds, large resonance peaks have been obtained with wider hull configurations. Monohull and catamaran hull configurations showed similar responses at higher speeds and higher frequencies This was attributed to decreased interferences between the demihulls at high speeds for certain values of the hull spacing and the wave frequency. Davis and Holloway (2003) illustrated a twodimensional 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 catamaran motions. For moderate wave heights, computational and experimental results have been shown to be encouraging up to a Froude number of 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 limitations) with experimental results conducted by various authors. Two-dimensional potential theory, which incorporates 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.

3 The two relevant equations in coupled heave and pitch motions are given by: (M + A33»i + B333 +C373 +A35i75 +ß C35i5 = F3e (1) (15 + A55)jj5 + B555 +C A53q3 + B527+C537 = F5e"»' (2) 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 hydrodynamic added mass and damping of each section is obtained using the frequency-domain Galerkin boundaiy -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 presented by Doctors (1988). Figure 1: Round-Bilge Catamaran Demihull (Mi-RB) 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 previous application of this computer program, together with a comparison with experimental data on a semi-smallwaterplane-area twin-hull (semi-swath) vessel. Figure 2: Semi-SWATH Catamaran Demihull (M2-SS) Catamaran Models Table 1 below shows the paranielric range of seven catamaran hull form, which were subjected to heaveand-pitch-motion prediction in the theoretical computations. 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 MOJ Mi-RB M2-SS M3-SS M4-SS M5-CHM6-CRM7-CH Draft (m) Lw,.(m) j) Figure 3: Semi-SWATH Catamaran Demihull (M3-SS) BWL(m) C (t) Vt í LIB BIT It has been the intention to keep the displacement identical for all the models in order to illustrate the effects of hull fonti influence on the motion characteristics. Computer 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 Figures 1 through 7 below depict the body plans for the various catamaran hull form configurations. Figure 4: Semi-SWATH Catamaran Demihull (M4-SS)

4 Figure 5: Single Chine Catamaran Demihull (MS-CH) The following definitions have been used to present the various motion characteristics: Heave Transfer function H' = 'o In order to test the results of the present research work seakeeping tests were performed at the Australian Mautime College Ship Hydrodynamics Centre (AMCSHC). The table below shows the geometrical parameters of the tested model. Table 2: Model Particulars and Sea State Full Scale Model Scale Waterline length (m) Waterline beam (m) )raught(m) Load displacement (tonnes) kg Radius of gyratión 0.25L 6 Q75 Speed of vessel (m/s) Seaway Head seas Modal wave height (m) Encounter freqúency (radis) The hull form configuration of the above tested catama- (3) ran model is shown in Figure 8 below. Pitch Transfer function p' = (4) kç0 22r where wave number k = - = - g L (5) Figure 8: Body Plan of Tested Catamaran Demihull Figure 6: Chine Catamaran Demihuli (M6-CH) z- - //,. /_ / Figure 9: Profile View of Tested Catamaran Model Figure 10: Plan View of Tested Catamaran Model Results of Numerical Simulation Figure 7: Chine Catamaran Demihull (M7-CH) Model Testing 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 limitations of space only a selected few results wilï be presented. 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-

5 trate the close correlation between both methods. Figures 11 to 13 depict the non-dimensional heave responses plotted against non-dimensional encounter frequency for both methods Ml RB MCH M5-CH I A FSS=O Noo.dA,mtomI Emsm,md,r Frsq,rny (L ID-LS AmiovalaS La.)SSlp Nmonil EnmWr Frqq (IJg)" (.IL.}SbtpTh, ftsu)hyd Figure 14: P' -Strip Theory and HYDROS at Fn 0.35 Figure 11: H' -Strip-Theory and HYDROS at Fn MS-CH MI-CH OES N.-dm1onI E,,coI,r Frquy Ug)" fc.0 Sm, Th..(LS.EYDSOS Nolmslm1 Et,r Fooqom,my (0Jg>' 1200 Figure 15: P' -Strip Theory and HYDROS at Fn 0.55 Figure 12: H' -Strip-Theory and HYDROS at Fn M2 SS 3.0 MI-CH -Mi-CH MI-RB 2.0 A NLSS.dlmosmkmml Eno.msg,r Fo,qsmmoy,(LI8I ' WhStD.) Nom.dlmirmI Emomm1s Fftqy (L/g) Figure 13: H' -Strip Theory and HYDROS at 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 earlier, in head seas. In order to validate these results, expeiirñental 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. Figure 16: P' -Strip Theory and HYDROS at Fn 0.85 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 eliminating the deficiencies of the strip theory. In the following figures, the non-dimensional heave and pitch responses at three Froude numbers namely 0.430, and have been plotted, which are representative of

6 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 predicted by SEAKEEPER and HYDROS are quite consistent with experimental results. However, HYDROS tends to correlate considerably better with experimental results than the former program o Expt-H SENÇEE PER-If HYOROS-I-f Ei-P. -SEAKEEPER-P HYDROS-P' F, a Z I.0 J 0.5 o.o 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 following: 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 program suggest that it is better than SEAKEEPER at both the lower and the higher Froude numbers of interest. Indeed, the predictions of the peak responses 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 conditiöns be carried out in future in order to test the limits of, and build confidence in, these two programs. O Eopt-H O Expt.. -SEAXEEPER-H SEAKEEPER-P HYDROS-H.I-IYDROS-P NdIrno,o1 Eotor Foqq (1Jg)" Figure 18: Experimental validation against SEAKEEPER andhydros at Fn Figure 19: Experimental validation against SEAKEEPER and HYDROS at Fn Acknowledgements The authors would like to take this opportunity to express 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. References Bailey, P.A., Hudson, D.A., Price, W.G., Temarel, P. (1999). "Theoretical and Experimental Validation of the Seakeeprng Characteristics of High Speed Mono- and Multi-hulled Vessels", Proc. Fifth International Conference on Fast Sea Tra nsport atiön (FAST '99), Seattle, pp Centeno, R., Fonseca, N., and Guedes-Soares, C. (2000). "Prediction of MotiOns of Catamarans Accounting for Viscous Effects", International Shipbuilding Progress, Vol. 47, No. 451, pp Centeno, R, Varyani, K.S., and Guedes-Soares, C. (2001). "Experimental Study on the Influçnce of Hull Spacing on Hard-Chine Catamaran Motions", J. Ship Research, Vol. 45, No. 3, pp Davis, M.R., and Holloway, D.S. (2003). "Motion and Passenger Discomfòrt on High Speed Catamarans in Oblique Seas", International Shipbuilding Progress, Vol. 50, No. 4, pp Doctors, U. (1988). "Application of the Boundary- Element Method to Bodies Oscillating near a Free Surface", Computational Fluid Dynamics - Proc. International Syiizposium on Computatiònal Fluid Dynamics ISCFD-Sydney, Elsevier Science Publishers B.V., Amsterdam, pp Doctors, U., Holloway, D., and Davis, M.R. (1996).

7 "The Effect of Huliform on Ship Motions", Proc. Twenty-Sixth Israel Conference on Mechanical Engineering, Technion, Haifa, Israel, pp 5-9 Fang, C.C., Chan, H.S. and Incecik, A. (1996). "InvestigatiOn of Motions of Catamarans in Regular Waves - I", Ocean Engineering, Vol: 23, No 1, pp Fang, C.C., Chan, H.S. and Incecik, A. (1997). "Investigation of Motions of Catamarans in Regular Waves - H", Ocean Engineering, Vol. 24, No. 10, pp Lee, C.M., Jones, H.D., and Curphey, R.M. (1973). "PredictiOn of Motion and Hydrodynamic Loads of Catamarans", Marine Technology, Vol. 10, No. 4, pp Mm, K.S., Yum, D.J., and Song, K.J. (1993). "A Study on the Prediction Method of Motion Characteristics for the High-Speed Catamaran Ship", Proc. Second International Conference on Fast Sea Transportation (FAST '93), Yokohama, Vol. 1, pp Sâlvesen, N., Tuck, O.E., and Faltinsen,O. (1970). "Ship Motions and Sea Loads", Trans. Society of Naval Architects and Marine Engineers, Vol. 78, pp , Discussion: SEAKEEPER (2003), User Manual, Formation Design Systems Pty. Ltd, Fremantle, Western Australia Subramanian, V.A., and Gururajan, N. (2004). "Parametric Studies on Motion Behaviour of High Speed Planing Catamarans", Ship Technology Research, Vol. 51, No. 1, pp 3-8 Varyani, K.S., Gitiganti, R.M., and Gerigk, M. (2000). "Motion and Slamming Impact on Catamaran", Ocean Engineering, Vol. 27, pp