การประช มว ชาการเคร อข ายว ศวกรรมเคร องกลแห งประเทศไทยคร งท 18 18- ต ลาคม 547 จ งหว ดขอนแก น A Nuerical Prediction of Wash Wave and Wave Resistance of High Speed Displaceent Ships in Deep and Shallow Water Sattaya Chandraprabha 1 and A.F. Molland 1 Departent of Marine Engineering, Royal Thai Naval Acadey, Thailand, E-ail: sattaya88@yahoo.co.uk School of Engineering Sciences, University of Southapton, UK, E-ail: a.f.olland@soton.ac.uk Abstract In recent years, the design concept of high speed displaceent craft, including concerns of safety and the environent due to the ipact of ship generated wash wave, has received considerable attention. The influences on wave resistance and wash wave generated by high speed displaceent craft have been investigated using a nuerical ethod. Thin ship theory was used and developed in order to predict the wave pattern resistance and wave wash of slender hulls with transo sterns. In particular, the theory was extended to cover the supercritical speed range. The theory was validated for the physical wave patterns and profiles, especially in shallow water and at supercritical speeds using the experiental results. The validation included the effects of hull for paraeters and depth Froude nuber on wave pattern resistance and wave profiles. It is found that the nuerical ethod, based on the thin ship theory, can be satisfactorily eployed as a siple and effective eans of estiating wave pattern resistance and wave profiles with low coputational effort. 1. Introduction The introduction into service of ferries and other arine vehicles with higher service speeds has led to a new range of probles. The wash waves generated by such craft can ipact upon safety and the environent in ters of the safety of saller craft, people on beaches, coastal erosion and changes in the local ecology. As a result, there is a need to develop tools for predicting the ship generated near-field waves and their propagation to the far field, both for applications at the design stage and during ship operation. The work described in this paper focuses on the prediction of the near field wave syste, assued to be within.5 to 1. ship lengths fro the vessel. An extensive aount of research into the resistance and powering of high speed displaceent onohulls and cataarans has been carried out at the University of Southapton for soe years [1] [5]. This work, which uses experiental and nuerical techniques, has been extended to cover the prediction of the wash produced by such craft, and early results are reported in [6], [7]. Further experiental and nuerical work has been carried out to provide design and validation data and a better understanding of the creation of wash, with particular ephasis on higher ship speeds in shallow water, [8]. Thin ship, or slender body, theory [5], [6] is used to describe the wave wash syste. The thin ship approach provides an alternative to higher order panel ethods for estiating wave resistance and, when applied strictly to slender hulls, has been found to provide a siilar degree of accuracy at a fraction of the coputational effort, [5]. The theory can provide a description of the coponent long-crested waves of the wave syste in ters of their height, period and direction. These waves ay then be used as input conditions for nuerical wave propagation and transforation odels, or applied directly to wave decay relationships which have been derived experientally, such as those in [9], [1] and [11]. The basic thin ship theory requires odification which relate particularly to transo stern corrections. Developents and iproveents in the estiation of this effect are described in the paper, together with the use of easured shallow water wave cuts to validate the nuerical ethods and provide exaple applications.. Basic Thin Ship Theory The thin ship theory of wave resistance was originally introduced as a purely theoretical approach for predicting the wave resistance of a ship by J.H. Michell in 1898 [1]. The
background and developent of the theory is described in [1], [4] and [8]. In the theory, it is assued that the ship hull(s) will be slender, the fluid is inviscid, incopressible and hoogeneous, the fluid otion is steady and irrotational, surface tension ay be neglected and that the wave height at the free surface is sall copared with the wave length. For the theory in its basic for, Ship bodies are represented by planar arrays of Kelvin sources on the local hull centreline, together with the assuption of linearised free surface conditions. The theory includes the effects of a channel of finite breadth and shallow water. The strength of the source on each panel ay be calculated fro the local slope of the local waterline, Equation(1) U dy σ = da (1) π dx πy W dy, where is the slope of the waterline. The hull waterline dx offsets in the current procedures can be obtained directly and rapidly as output fro a coercial lines faring package, such as ShipShape, [13]. The wave syste is described as a series using the Eggers coefficients, Equation (). The wave coefficients ξ and η can be derived theoretically using Equations (3), noting that they can also be derived experientally fro physical easureents of ζ in Equation(). The wave pattern resistance ay be calculated fro Equation (4) which describes the resistance in ters of the Eggers coefficients. The scheatic overview of the odeling procedure is shown in Fig.1. ζ= [ ξ cos( xk cosθ ) + η sin( xk cosθ )] cos () = ξ 16π U = η Wg 1+ sin θ k + k cos θ k σ σ σe [ k H + zσ ] ( ) π σ θ W H cosh ( ) { (3) k Hsech k H sin( k x y cos ) σ σ πy σ cos( k x cosθ ) cos sin W R WP M ρgw = + k H + + cos θ ( ξ η )(1 ) ( ξ η ) 1 1 + 4 sinh(k H) = sinh 1 k H ( ) k H (4) dcw.14.1.1.8.6.4. -. Fn=. 4 6 8 Wave Angle Cwp.5..15.1.5..4.6.8 1 Fn Fig.1 Scheatic overview 3. Transo Stern Corrections As described above, thin ship theory represents a body with a source-sink distribution over the centreplane of the hull. The calculated source strength in each panel depends on the slope of the waterline (dy/dx). For a ship with a transo stern, the waterline slope on the transo is, therefore, undefined causing Wave elevation.4.3..1 -.1 -. -.3 -.4 NPL cataaran S/L=.4 Fn=.3 4 6 8 1 1 X the under-prediction of wave resistance and wave wash. As a result, there is need for a transo correction to iprove the potential for predicting wave resistance and wave wash. The use of sources / sinks placed in the vicinity of the transo, [14], [15], has been used with reasonable success, whilst the creation of a virtual stern and associated source strengths, [4] and [5], has been found to provide the best results in ters of wave pattern resistance. In order to confir y=1
that this would also be the case for the prediction of wash waves, an investigation was carried out to verify the use of a virtual stern and/or the alternative use of source/sink placeents, [8]. It was found that the use of virtual stern can provide satisfactory wave wash predictions. With regard to a single source ethod, the effect of the position of a single source on the wave profile and wave pattern resistance was investigated. Source strength of a single source is equated to the strength necessary to bring the total integration of source/sink strength over the hull to zero. The best results were obtained using a single source near the base of the transo, when the correlation with the experiental results was seen to be good [8]. This approach is uch sipler to apply than a virtual stern. A single source approach was, therefore, used for validation of the theory to odel transo correction. 4. Validation of the Theory and Exaple Applications 4.1 General Exaples are presented to validate the theory and to illustrate its applications and scope. The theory has been well validated for wave pattern resistance in deep water, [4], [5] and [15]. Validation of the theory was required for the physical wave patterns and profiles, especially in shallow water and at supercritical speeds. This has been facilitated using the new shallow water experiental data presented in [8]. The hull fors used in the investigations are shown in Fig. and their particulars are given in Table 1. 4. Round bilge cataaran hull, Series 64, Deep water: theoretical and experiental A nuber of physical wave cuts for the Series 64 odel had been carried out in the Southapton Institute test tank. Coparisons of the theoretical and experiental wave cuts are shown in Fig.3. It is seen that there is reasonable agreeent between the theoretical and experiental results. Fig. 3 Coparison of wave profiles 4.3 Round bilge onohull, NPL Series, Shallow water: subcritical - theoretical and experiental Fig.4 shows the coparison of easured and predicted wave cuts for odel 5b at Froude Nubers Fn of. and.38 at a water depth of.4. It is seen that acceptable agreeent is achieved. NPL Series 64 Fig. Hull Bodyplans Model 4b 5b 6b 5s L [] 1.6 1.6.1 1.6 L/ 1/3 7.4 8.5 9.5 8.5 L/B 9. 11. 13.1 1.8 B/T.... C B.397.397.397.537 C P.693.693.693.633 C M.565.565.565.848 A [ ].338.76.41.61 LCB [%] -6.4-6.4-6.4-6.4 Table 1: Principal particulars of odels Fig. 4 Coparison of wave profiles 4.4 Round bilge cataaran hull, NPL Series, Shallow water: supercritical - theoretical and experiental Fig.5 shows a coparison of the easured and predicted wave cuts for odel 5b for different water depths (H=. and.4) and two hull separations (S/L=. and.4). In general, the theory provides an acceptable agreeent with the experients, especially at very high speeds. The theory with no transo correction underestiates the wave height, whilst the theory with a single source correction gives better results, including the prediction of the leading bow waves. It is however found that, at supercritical speeds, the theory with a single
source tends to create a hollow in front of the bow wave, although the size of the hollow decreases with increase in Fn. Fig. 7 Coparison of wave profiles 4.6 Effect of Cataaran hull separation (S/L), in shallow water Fig.8 shows the influence of cataaran hull separation on the wave pattern resistance. It is seen that as the separation is increased, there is a reduction in resistance, which is in line with the experiental results. Fig.9 shows good agreeent between the experiental and theoretical wave cuts for the two separations. Fig.5 Coparison of wave profiles. 4.5 Effect of Length/Displaceent ratio (L/ 1/3 ) Fig.6a shows the influence of L/ 1/3 on the wave pattern resistance. It is seen that an increase in L/ 1/3 causes a reduction in wave pattern resistance, which is in line with the experiental results in Fig.6b. Fig.7 shows good agreeent between the experiental and theoretical wave cuts for odel 4b (L/ 1/3 = 7.4) and odel 5b (L/ 1/3 = 8.5). Fig. 8 Experiental and theoretical wave resistance: effect of hull separation, Model 5b, H=.4 Fig. 6a Theoretical wave pattern resistance: effect of length to displaceent ratio, H=.4 Fig. 6b Experiental wave resistance: effect of length to displaceent ratio, H=.4. Fig. 9 Coparison of wave profiles 4.7 Theoretical wave pattern resistance Fig.1 shows the theoretical estiates of the wave pattern resistance ratio (wave pattern resistance shallow water/wave pattern resistance deep water) for odel 5b cataaran with S/L =. at water depths of H =. and.4 for a range of depth Froude Nuber. It is seen that the trend agrees with the experiental results, although the theoretical ratio at about
critical speed is uch higher than the experiental results. It is noted that the effects of shallow water are significant in the critical speed region, where there are large increases in resistance, whilst the resistance decreases again at supercritical speeds. Fig.1 Experiental and theoretical wave resistance ratio: Model 5b cataaran S/L=. 4.8 Divergent wave angle Fig.11 shows the change in divergent wave angle with change in speed, derived using Kofoed-Hansen theory, [11], the thin ship theory and the experiental results [8]. It is seen that there is good agreeent between the thin ship theory and the experiental results. Fig.11 Diverging wave angle 4.9 Distribution of wave energy Predicted wave patterns and the distribution of the wave pattern resistance coponents (or wave energy) at different water depths are shown in Fig.1. It is seen that at supercritical speeds, since a gravity wave cannot travel at speeds > (gh) 1/, the transverse waves disappear and waves can only be propagated at angles greater than θ = Cos -1 (gh/u) 1/. These results, which describe wave patterns and their associated distribution of wave coponents (or energy) within that pattern, together with the prediction of the wave propagation angles (Fig.11), are of value as input to wave propagation odels. Fig. 1 Wave pattern & distribution of wave pattern resistance: change in depth Froude nuber at a given speed (Fn=.5), Model 5b onohull.
4.1 Suary The chosen exaples have illustrated the wide scope and usefulness of theoretical ethods in the prediction of wave patterns and wave wash and, in particular, the relative effects due to changes in the design and operational features. This has allowed the developent of a robust nuerical ethod, based on thin ship theory, suitable for the estiation of near field wash waves in ters of wave period, height, direction of propagation and energy distribution, in a for suitable for use in wave propagation/transforation odels. 5. CONCLUSIONS 5.1 The nuerical ethod which has been developed offers a practical tool for assessing the likely wave wash of new designs, together with operational effects on the wash of ships in service. 5. The theoretical results, validated by experients, provide the facility to develop low wash guidelines for operational features such as speed, tri and shallow water, and low wash design features such as the influences of L/ 1/3, S/L and hull shape. 5.3 Overall, it is found that the nuerical ethods developed and described provide very realistic predictions of wave wash and wave resistance. 6. Acknowledgeents The work described in this report covers part of a research project on wash (SWIM) funded by EPSRC and industry and anaged by Marinetech South Ltd. Sattaya Chandraprabha acknowledges the support of the Royal Thai Navy during his respective study period at the University of Southapton. References 1. Insel, M., An Investigation into the Resistance Coponents of High Speed Displaceent Cataarans, PhD Thesis, Ship Science, University of Southapton, 199.. Insel, M., and Molland, A.F., An Investigation into the Resistance Coponents of High Speed Displaceent Cataarans, Transactions of RINA, Vol. 134, 199. 3. Molland, A.F., Wellicoe, J.F., and Couser, P.R., Resistance Experients on a Systeatic Series of High Speed Displaceent Cataaran Fors: Variation of Length Displaceent Ratio and Breadth Draught Ratio, Transactions of RINA, Vol. 138, 1996. 4. Couser, P.R., Wellicoe, J.F. and Molland, A.F. An Iproved Method for the Theoretical Prediction of the Wave Resistance of Transo Stern Hulls using a Slender Body Approach, International Shipbuilding Progress, 45, No.444, 1998. 5. Couser, P.R. An Investigation into the Perforance of High- Speed Cataarans in Cal Water and Waves Ph.D. Thesis, University of Southapton, 1996. 6. Molland, A.F., Wilson, P.A., and Chandraprabha, S., The Prediction of Ship Generated Near-Field Wash Waves Using Thin Ship Theory, Proc. of International Conference on Hydrodynaics of High Speed Crafts: Wake wash and Motion Control, RINA, London, Noveber. 7. Molland, A.F., Wilson, P.A., Turnock, S.R., Taunton,D.J. and Chandraprabha, S. The Prediction of the Characteristics of Ship Generated Near-Field Wash Waves. Proc. of Sixth International Conference on Fast Sea Transportation, FAST 1, Southapton, Septeber 1. 8. Chandraprabha, S., An Investigation into Wave Wash and Wave Resistance of High Speed Displaceent Ships, Ph.D. Thesis, School of Engineering Sciences, University of Southapton, UK., 3. 9. Macfarlane, G.J. and Renilson, M.R., Wave Wake - A Rational Method for Assessent. Proc. of International Conference on Coastal Ships and Inland Waterways. R.I.N.A., London, February, 1999. 1. Karfoed-Hansen, H., Jensen, T, Kirkegaard, J. and Fuchs, J. Prediction of Wake Wash fro High-Speed Craft in Coastal Areas. Proc. of International Conference on the Hydrodynaics of High-Speed Craft. R.I.N.A., London, Noveber, 1999. 11. Doyle, R., Whittaker, T.J.T. and Elsasser, B., A Study of Fast Ferry Wash in Shallow Water. Proc. of Sixth International Conference on Fast Sea Transportation, FAST 1, Southapton, Septeber 1. 1. Michell, J.H., Wave Resistance of A ship, Philosophical Magazine and Journal of Science, vol. XLV, 5 th Series, January June, V.1, 1898. 13. ShipShape User Manual. Wolfson Unit M T I A, University of Southapton. 14. Yi, B. Analysis of Waves and Wave Resistance due to Transo Stern Ships. Journal of Ship Research, June 1969. 15. Lee, A.R., A Theoretical and Experiental Investigation of the Effect of Prisatic Coefficient on the Resistance of High Speed Cataarans. M.Phil. Thesis, University of Southapton, 1995.