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24th Symposium on Naval Hydrodynamics Fukuoka, JAPAN, 8-13 July 2002 Validation of Numerical Method for Predicting Hydrodynamic Characteristics of a High-speed Ship H. Orihara (Hitachi Zosen Corporation, Japan) ABSTRACT The capability of a CFD code is validated for predict- ing the hydrodynamic characteristics of a high-speed ship advancing in calm water. The CFD code WISDAM-VIII is used for the validation study. practical high-speed ship hulls advancing in calm water over a Froude number range from 0.4 to 1.0. The validation of the code is conducted by comparing the computed results with a set of experimental data for a number of mono-hull type hull forms. Theses comparison include ship running attitudes, wetted surface at running condition, total resistance coefficients and surface pressure distributions. Also the code is validated for the prediction of the effects of hull shape on the hydrodynamic characteristics of the ship and the results are compared with the available experimental data. method. These methods were capable of treating the change of running attitudes and computing the flow about a hull in the free to sink and trim condition. It was reported that the computed results from these methods agreed qualitatively well with the experimental data. In this study, simulations are carried out for More recently, with the development of computer - ~ ~~ ~ ~ ~~ ~ ~~ ~ ~ ~ ~ hardware and the numerical solution methods, CFD simulation methods have been developed, which is applicable for the prediction of flows about a high-speed ship, such as Subramani et al (2000), Lin and Percival (2000), Orihara and Miyata (2000~. These methods were based on the solution of Reynolds-Averaged Navier-Stokes (RANS) equations. In contrast to the above-mentioned theoretical methods, these methods had the advantages in that they could treat the nonlinear free-surface conditions without any linearized approximations and that the viscous effect can be taken into account. The computed results from these CFD simulation methods showed that the trends in the measured running attitudes data could be predicted correctly and the quantitative agreement between the computations and the experimental were generally well. However, these computations were conducted mainly for low speed cases in the context of a high-speed ship, i.e. at Froude number (Fn) below 0.65. The principal objective of the present study is to validate a CFD code for predicting the hydrodynamic characteristics of a high-speed ship advancing in calm water. In the present study, WISDAM-VIII code is selected for the validation. WISDAM-VIII was originally developed at the University of Tokyo by Orihara and Miyata (2000) for the performance prediction of a high-speed ship. The code has been used for the performance prediction for practical high-speed ships in Hitachi Zosen Corp. The code solves the Reynolds-Averaged Navier-Stokes (RANS) equation and continuity equation with the nonlinear free-surface conditions. The code has already validated for some cases of high Froude number flows about high-speed ship models, including wave height near INTRODUCTION The prediction of hydrodynamic characteristics of a high-speed boat advancing in calm water has been challenging task due to the complex flow features around a hull. From a hydrodynamic point of view, these complexities are consisted of two distinctive features. One is the highly nonlinear waves generated about a hull, and the other is the change of running attitude with the increase of ship speed. Due to these flow features, there has been little work on the development of the prediction method of flows and performance of a high-speed ship, and the performance prediction of a high-speed ship has been made almost all cases by means of model tests. In recent years, several theoretical prediction methods for high-speed ships has been developed, such as Xia (1986), Larson and Xia (1987), Wang et al (1996), Eguchi (1998), Kawashima (1998), Brizzolara et al. (1998~. Most of these method were based on the linear potential theory and using the Rankine-source
the semi-planing boat at Fn = 0.513 and the running attitudes and resistance coefficient of semi-planing boats at Fn = 0.6. Most of these validation cases, however, are mainly concerning the cases of relatively lower speeds. The systematic validation of the predicted running attitude and resistance attitudes, which is of great importance for the evaluation of the performance of high-speed ships, has been conducted as yet. Also the validation of surface pressures have not been conducted. So in the present study, the validation of the surface pressures, running attitudes and resistance coefficients are conducted for a number of mono-hull type hull forms over a wide range of Fn from O.4to 1.0. In the next section, the outline of WISDAM-VIII will be briefly described. The descriptions of experimental data used for the validation study will be followed. Then, comparisons of computed results and experimental data are presented. Finally, some conclusions will be mentioned. NUMERICAL METHOD In the present study, computations of flows around high-speed hull forms are carried out using WISDAM-VIII (Orihara and Miyata, 2000~. Since details of the computational procedure used in the code can be found in Orihara and Miyata (2000), the outline of the code is described in the following. The code solves the RANS equation and continuity equation. These can be written in the following conservative form for time-dependent arbitrary control volume Q(t) as: ~' A,) u dV = im( ) dS - T. 0t [ea(,)dS-(U-V), (2) where u is the velocity vector, v is the velocity vector of the face of the control volume. All the variables are made dimensionless with respect to the constant reference velocity Uo and the ship length on waterline Let . The stress tensor Tis written in ALE form as: T = -¢I-tU-v~u+[VU+(Vu) ]-U'u (3) where I is the identity tensor, v is the gradient opera- tor, ()T denotes the transport operator, -utu' is the Reynolds stress. ~ is the nondimensionalized pressure excluding the hydrostatic pressure defined as: Fn2 (4) where z is the vertical position. The stress term which comes from the Reynolds stress is incorporated in the diffusion term using the turbulence model of eddy viscosity type. In the present study, the algebraic Baldwin-Lomax turbulence model is used. A finite-volume method is used to discretize the governing equations (1) and (2~. Except for the convective term, all the terms of Eq. (2) are approximated with second-order accurate central differencing, while the convective term is approximat- ed with third-order accurate upwind differencing. The code employs a body fitted coordinate system and uses single-block H-O grid topologies. The computational grid are generated algebraically. One of the principle features in grid generation of WISDAM-VIII is specifying the grid point clustering along both the hull surface and the undisturbed free surface such that the grid spacing near these boundaries is sufficiently small for resolving free surface waves and flow separation behind the transom stern. For a time-accurate solution of the incompressible flow, pressure and velocities are coupled by a MAC- type solution algorithm and a Rhie-Chow interpolation scheme is employed to avoid the checkerboard type oscillations of the pressure field. The free-surface treatment is based on the density-function method (Miyata et al. 1988, Kawamura and Miyata, 1994), which is a kind of a so-called front capturing method and corresponds to a generalized interpretation of the VOF method. In WISDAM-VIII, the kinematic condition is satisfied by solving the following transport equation for the density function Pm t(') ~ U dV |~(,)dS Pm (u v) (5) where Pm is the density function which is defined as ;~1, in fluid region m tO, in external region This implies that Pm is unity at any point occupied by the fluid and the value of Pm changes from unity to zero at the free surface. In WISDAM-VIII, Eq. (5) is descretized by the finite-volume method and solved in a time marching manner and the free surface location
is determined as the iso-surface of Pm=O.S. The dynamic condition, which denotes the stress equilibrium at the free surface, is approximately satisfied by the extrapolation of the pressure and velocity components above the free surface. The change of running attitude is treated by combining the solution of the equation of the rigid motion of the hull with the flow solution. This is performed by calculating the solution of flows and rigid motions iteratively. At each time step, the force and moment acting on the hull were obtained by integrating the pressure and shearing stress on the whole wetted surface. Then the equation of motion for heave and pitch motions are integrated in time and the new position of the hull is obtained. After obtaining the ship position, computational grid is regenerated in accordance with the movement of the hull surface. The effect of grid movement is accounted for in the flow solution by including the velocity vector of the face of the control volume v in Eqs. (2), (3) and (5). These procedure are repeated until the motion in heave and pitch are converged. Then the running attitudes of the hull are obtained as the converged solution of the heave and pitch motion. RESULTS AND DISCUSSION In the present study, the WISDAM-VIII code is validated for surface pressure distributions, running attitudes and hull resistance. The validation of the code is conducted by comparing the computed results with a set of experimental data for selected mono-hull type high- speed ship hull forms. Computations are carried out for the hulls advancing over a range of Froude number, based on the length on waterline, from 0.4 to 1.0. Also the code is validated in terms of the capability of predicting the effect of the change in hull shape on the running attitudes and resistance of the hull. The details of the Experimental data, the condition of computations and the representative validation results are described in the following. Experimental data In the present study, experimental data for two selected hull forms of high-speed ships are used for the code validation. For the validation of computed running attitudes and resistance coefficients, experimental data for NPL round bilge series hull forms (Marwood and Bailey 1969, Bailey, 1974) is used. The body plan and principal dimensions of the basic form of the series, NPL Model lOOA, are given in Table 1 and Fig.1, respectively. Table 1 Principal dimensions of NPL Model lOOA. Length on water line ( L'`, ) Breadth ( B ~ ~ , . Draft ( ~ ) ~ , Block Coefficient (c ) ~ h . Longi. Cent. of Buoyancy ( LOB ) 2.54 m 0.4064 m 0.140 m 0.397 6.4% Lo, aft NPL series models were derived by producing geometric variations of the basic form (NPL Model lOOA) and all have constant block coefficient, prismatic coefficient, maximum section area coeffi- cient and longitudinal center of buoyancy. In the present study, the basic form (1OOA) and two derived forms, 80A and 150A are selected for the validation study. 80A and 150A are the forms having a same Length to Breadth ratio (L/B = 6.25) as lOOA, L, and a displacement of 80 and 100 tons for a 30.48 m ship length, respectively. The comparisons of principal dimensions between the three models are shown in Table 2. Table 2 Comparisons of dimensions between selected NPL series models. Model number 80A l OOA _150A UB B/d Llvil3 6.25 3.63 7.09 6.25 2.90 6.59 6.25 1.93 5.76 cb _ 0.397 . 0.397 . _ 0.397 In Table 2, d denotes the draft of the ship, and L/V/3 denotes the length to displacement ratio where V is the volume of displacement. In the validation study, the experimental data for NPL series models obtained in No. 3 tank of Ship Division at the National Physical Laboratory (NPL) is used, which is reported in Marwood and Bailey (1969) and Bailey (1974). In the experiments, the models were tested in the bare hull condition. The models were tested in calm water over a En range from 0.1 to 1.2. The maximum model Reynolds number based onLwLwas 1.3x107. Each model of the series was given a level trim at rest and towed horizontally at the position of the longitudinal center of buoyancy. For each run, model speed, resistance and running attitudes were measured. Photographs of the wave profile along the hull were taken to assist for the assessment of the
running wetted surface. Further details of the model tests of NPL series can be found in Marwood and Bailey (1969~. For the validation of computed surface pressure distributions, the pressure measurements on the hull surface are conducted in this study. The pressure measurements are carried out at the Akashi Ship Model Basin (ASMB) Co., Japan. The towing tank at ASMB has a length of 200m and a section of 13m wide and 6.5m depth with a maximum carriage speed of 6.0 m/sec. The tank tests are carried out with a 4.0 m model of a mono-hull type high-speed ship with a transom stern, which is designated as Hull B in the following description. The picture of the model towing in the tests is shown in Fig.2. The model is fitted with 12 static pressure gauges on the keel line. The pressure gauges are placed closely near the bow and stern so that the pressure peaks can be measured in the tests. The locations of the pressure measurements are shown in Fig. 3. Initially, the model is given a level trim at rest. The pressure measurements are carried out at five different speeds (Fn = 0.434, 0.514, 0.612, 0.685, 0.787~. To check the accuracy of the measurements, surface pressure distributions measured three times at each speed. The scattering of the measured data were within + 1% of the static head at the bottom. The running attitudes were obtained by measuring the bow and stern sinkage with two potentiometers mounted on the bow and stern of the model. Condition of computations The computations of models of three NPL series (80A, lOOA and 150A) and Hull B are performed on the O-O type structured grid with a total of 168,000 grid points, with 80 points in the axial direction, 30 points in the direction normal to the hull and 70 points in the girth direction. A partial view of the gird for NPL model lOOA and Hull B model are shown in Fig. 4 and Fig. 5, respectively. In these figures, grids on the hull surface, still water plane and the center plane are shown. The minimum grid spacing normal the hull surface is set 0.001 LO . The outer boundary extends eight ship lengths from the center of the hull. In order to make comparison exactly of the computed results with the experimental data, the Reynolds number in the computations should be set the same value as the experiment. For the case of high-speed ships with a transom stern, however, since the flow detaches smoothly at the corner of the transom stern and stern waves formed continuously from the bottom of the hull, the boundary layer does not become so thick as in the case of displacement-type ships. Thus, it could be considered that the flows about the hull are not so sensitive to the Reynolds number. For this reason, in the present study, a smaller value of Reynolds number, Rn =l.Ox106, is specified for all the computations to avoid the numerical instability and save computational expense. Surface pressure distributions The computed surface pressures are shown in Figs. 6 - 19. The Froude number is varied from 0.434 to 0.785, and the Reynolds number is set at Rn = 1.0 x 1 o6 . All the computations are performed with the hull free to sink and trim. In these figures, pressure is shown in the nondimensional coefficient c. c. is the (Da - (Da pressure coefficient excluding the hydrostatic com- ponents and made dimensionless with respect to the hydrostatic pressure at the bottom of the midship as follows: c" = ~ P d ]. ~ (6) where do is the midship draught at rest; g is the acceleration due to gravity, ~ is dimensionless pressure defined in Eq. (4~. As shown in Eq. (6), ascot is scaled with Fn, the effect of Fn on surface pressure distributions can be shown more directly with Cal than the ones shown in ~ Computed pressure contour plots on the hull surface are shown in Fig. 6. Since the surface pressure is only measured on the keel line, surface pressure distributions are only qualitatively examined for Fn = 0.511 and 0.787. It is seen that surface pressure decreases rapidly near the stern for all the Froude numbers. This shows that the surface pressure decreases to the atmospheric pressure, i.e. c,k =zS``rnlFn2 ~ where A, is the vertical position of the transom stern. It is also shown that the smooth flow detachment at the transom stern is reasonably predicted by the computation. Also seen in these figures is that the increased positive pressure region exist at higher Froude numbers. The comparison of computed surface pressure distributions on the keel line for Hull B with the experimental data are shown in Figs. 7 - 11. In general, the computed surface pressures agree well with the . . exit perimental data, indicating the capability of WISDAM-VIII for predicting the flow about a high-speed ship hull form is excellent over a wide range of Froude number. In particular, computed surface pressures in the aft part of the hull agree quite well with experimental data. This may show that the viscosity has minor effect on the surface pressure
distributions on the high-speed ships considered. On the fore part of the hull, however, the computed results deviate from the experimental data with the increase of Froude number, as shown in Figs. 10 and 1 1. A probable cause of this disagreement is that the computed grid used is not sufficiently fine for capturing the pressure. The effect of Froude number on surface pressure is shown in Figs. 12 - 15. In these figures, pressure coefficient Cal is plotted as a function of Fn at four points on the hull surface. The locations of these points are shown in Fig. 3. It is seen that the computed results agree qualitatively well with the experimental data. At point Pi which is located 0.025 ~ from the transom stern corner, c,~ value is nearly constant at speeds Fn > 0.6. This may implies that the vertical position at the stern is almost constant at these speeds. At points P5, P6 and P8, which are located 0.2~, 0.3 ~~ and 0.8 ~ from the transom stern corner, respectively, c,k values increase with the increase of Fn. This is consistent with the increase of rise of the hull shown in Fig. 19, which is considered to be due to the increase in dynamic lift acting on the hull. Running attitudes The prediction of running attitude of the ship is made for NPL hull 80A, 1 00A, 1 50A and Hull B. The comparisons of computed running attitudes, which include running trim angle and rise at the longitudinal center of gravity (LCG), with the experimental data are shown in Figs. 16 - 19. The computed running attitudes agree fairly well with experimental results. In particular, the computed running attitudes for Hull B agree quite well with the experimental data. Since computed surface pressure distributions correlate fairly well with the experimental data as shown in Figs. 7-11, the agreement of running attitudes between the computation and the experiment is considered to be reasonable. For the NPL series cases, however, some discrepancies are seen in the rise at LCG, which is shown in lower graph in each figure. Except for the case of NPL 80A at Fn>0.8, computations underpredict the rise at LCG by about 0.001. While no detailed investigation for this discrepancy is conducted, one of the probable cause is measurement errors since the trend in the computed rise is almost same as the experiment. Wetted surface area The computed wetted surface areas are compared with the experimental data as shown in Figs. 20 - 22. The computed wetted surface area So is obtained by integrating the density function over the wetted surface of the hull as follows: so = f Pm~ dS H (7) where SH denotes the surface of the hull; Pm iS the density function; n =(nx, ny, n ~ is the unit normal vector to the hull surface. Due to a change in running attitude and large- amplitude bow waves developed along the hull surface, the wetted surface area of high-speed ships changes with Fn. As described earlier, since the measured wetted surface area were obtained from photographs and it is difficult to measure the edge locations of bow spray on the hull, it is difficult to make direct comparison of the wetted surface area between the measurements and computations. Thus the comparisons are made only qualitatively. The computed wetted surface areas correlate fairly well with the experimental data. Resistance coefficient To make a direct comparison of computed resistance coefficients with the measured ones, total resistance coefficient CTM] was estimated from the computed flow data. Since the computations were conducted at smaller Reynolds number than the experiment, the correction of the difference of Reynolds number had to be made on the computed results. To this end, the model-scale total resistance coefficient of the hull CTML is divided into two parts, frictional resistance coefficient CFM! and residuary resistance coefficient A, respectively. These coefficients are obtained by the following resistance breakdown: RTM C = = CRL + CF.~L (8) where RTM is the total resistance; p is the density; u is the velocity of the ship; So is the wetted surface of the hull. It is noted that the frictional resistance Coefficient CFMZ is made dimensionless with the reference area of ~,,7' The residual resistance coefficients C.R1 is obtained by integrating the longitudinal component of the static pressure p over the hull wetted surface as follows: CRL = PU2LWL I PmPnx dS (9)
The frictional resistance coefficient CAM] is obtained by using the frictional resistance coefficient of a flat plate CFO as follows: CT7I~. = ()CFO ,where CFO is evaluated using the Schoenherr line as: = loge (Rn x CFO ~ (10) (1 1) The comparisons of resistance coefficients bet- ween the computations and experiments for NPL models 80A, 100A and 150A are shown in Figs. 23 - 25. In these figures, the computed total resistance coefficients estimated using Eqs. (7) - (11) are compared with the measured total resistance coeffi- cients. Also shown in these figures is the computed frictional resistance coefficient CFM] estimated using Eqs. (10) and (11). As can be seen from Figs. 23 - 25, the computed results correlate fairly well with the experimental data for all the three different models selected. This is surprising since the present computations are carried on relatively coarse grid consisting of 168,000 grid points. In the case of computations for low-speed displacement type ships, the resistance coefficient, in particular, the residual (or wave-making) resistance is known to be quite difficult to predict. In general, the use of fine grid consisting of nearly million grid points is considered to be required for the accurate prediction of the resistance coefficients for this type of ships. The reason for this may be considered as follows. For high-speed ships running with the dry transom, since the pressure increase in the aft part of the hull are not occurred as shown in Fig. 6, so the pressure integral in Eq. (9) can be made accurately on the coarse grid. Also seen from Figs 23 - 25 is that the frictional resistance component becomes predominant in the total resistance with the increase of En and that the resistance coefficient is almost same over a En range from 0.6 to 1.0. From the results described above, it may be considered that the resistance prediction method used in the present study which is based on Eqs. (7) - (l l), is valid for high-speed ships of mono-hull type. Also it may be considered that the effect of viscosity on the residual resistance is relatively small and that the resistance coefficients can be estimated with certain degree of accuracy from computations conducted at Reynolds numbers lower than the experiment. From a practical point of view, this is advantageous in that the time required for computations can be reduced and design alternations by means of computations can be made more easily. Effect of hull shape on running attitudes and Resistance coefficient To validate the capability of predicting the effect of the change in hull shape on the running attitudes and resistance coefficients, the variations of the running attitudes and resistance coefficient with the hull form factor are considered. Since the NPL series models cover a wide variety of hull form parameters, e.g. L/B, B/d, LIV~'3, validations can be conducted on the effect of these hull form parameters. Among theses factors, the length to displacement ratio LIV~'3, which is known to be the predominant factor on the running attitudes and resistance of high-speed ships, are selected for this validation study. The effect of LIV"3 on the running attitudes and resistance coefficients are shown in Figs. 26 - 31 for the selected Froude numbers of 0.6, 0.8 and 1.0. Running attitudes, running trim angle and rise at LCG, are plotted functions of LIV"3 and compared with the experimental data in Figs. 26 to 28. In general, the computed results show well agreement with the experimental data for all the Froude numbers. Although some discrepancies are observed in rise, the trend in the experimental data, i.e. the variations of running attitudes with LIV"3 are predicted favorably well by the computations. In Figs. 29 - 31, total resistance coefficient c, is plotted as a function of LIV"3 and compared with the experimental data. As shown in these figures, the computed results agree quite well with the experimental data as in Figs. 22 - 24 shown earlier. From these comparisons, it may be considered that the present code has capability of predicting the effect of change in hull shape for high-speed ships considered. CONCLUSIONS Validation of the CFD code WISDAM-VIII is carried out for a number of mono-hull type high-speed ship hull forms. Between the computed results and experimental data, comparisons are made of surface pressure distributions, running attitudes and resistance coefficients. The computed surface pressure distributions agree well with the experimental data. The computed running attitude also agree well with the experimental data, except that the computed rise at LCG for NPL series models are slightly underpredicted. The estimated total resistance coefficients correlate well with the experimental data. The running attitudes and the resistance coefficient are also validated in
terms of the effect of the length to displacement ratio LIVE, and it is shown that the code can predict the effect of L/V~'3 on these quantities with reasonable accuracy. From these results, although the degree of accuracy of the code is not completely satisfactory, and further study is needed to improve the code, it is confirmed that the capability of the present code is generally sufficient to analyze the flow about a mono-hull type high-speed ship over a En range from 0.4 to 1.0 and that the present code is very promising as a design tool for predicting the still-water performance of mono-hull type high-speed ships. ACKNOWLEDGEMENTS The author would like to thank Mr. Mitsuyasu Na- gahama and Mr. Kazuya Hatta of Hitachi Zosen Corp. for their valuable help and discussions provided during this research. The author wishes to express his gratitude to the member of the test section of Akashi Ship Model Basin Co. for conducting the model test of Hull B. REFERENCE Bailey, D., "The NPL High Speed Round Bilge Displacement Hull Series," Maritime Technology Monograph, No.4, RINA, London, 1974. Brizzolara, S., Bruzzone,D., Cassela,P., Scamardella, A., and Zotti, I., "Wave Resistance and Wave Patterns for High-Speed Crafts; Validation of Numerical Results by Model Tests," Proceedings of the Twenty-Second Symposium on Naval Hydrodynamics, Washington, D.C., 1998, pp. 69-83. Eguchi, T. "On the Prediction of High-Speed Boats by a Rankine-Source Method," Transaction of the West-Japan Society of Naval Architects, No. 95, Mar. 1998, pp. 9-16 (in Japanese). Kawamura, T., and Miyata, H., "Simulation of Nonlinear Ship Flows by Density-Function Method," Journal of the Society of Naval Architects of Japan, Vol. 176, Dec. 1994,pp. 1-10. Kawashima, T., and Suzuki, S., "Development of Program based on Rankine-Source Method for Transom-Stern Hull Forms," Bulletin of National Research Institute of Fishery Engineering, No. 19, Mar. 1998, pp. 61-70 (in Japanese). Larsson, L., and Xia, F., "Numerical Hydrodynamics - A Useful Complement to Model Testing," Proceedings of the Third Symposium on Practical Design of Ships, London, 1987, pp. 171-183. Lin, C.W., and Percival, S., "Free Surface Viscous Flow Computation Around A Transom Stern Ship By Chimera Overlapping Scheme," Proceedings of the Twenty-Third Symposium on Naval Hydrodynamics, Rouen, 2000. Marwood, W.J., and Bailey, D., "Design data for high- speed displacement hulls of round-bilge form," NPL Ship Report, No. 99, 1969. Miyata, H., Katsumata, M., Lee, Y.,G., and Kajitani, H., "A Finite-Difference Simulation Method for Strongly Interacting Two-Layer Flow," Journal of the Society of Naval Architects of Japan, Vol. 163, Dec. 1994, pp. 1-16. Orihara, H., and Miyata, H., "Numerical Simulation Method for Flows about a Semi-Planing Boat with a Transom Stern," Journal of Ship Research, Vol. 44, No. 3, Sep. 2000, pp. 170-185. Subramani, A.,K., Paterson, E.,G., and Stern, F., "CFD Calculation of Sinkage and Trim," Journal of Ship Research, Vol. 44, No. 1, March 2000, pp. 59-82. Wang, Y., Sproston, J.,L., and Millward. A. "Calculations of Wave Resistance for a High-Speed Displacement Ship," International Shipbuilding Progress, Vol. 43, No. 435, 1996, pp. 189-207. Xia, F., "Numerical Calculations of Ship Flows, With Special Emphasis on the Free Surface Potential Flow," PhD thesis, Chalmers University of Technology, Gothenburg, 1986.
(mm) 30 NPL-1 OGA loo o ` t t~D.W.L._ _ -200 0 200 ( mm ) Figure 1: Body plan of NPL model l OOA. - :~ 1 11'1~f Cat Figure 5: Computational grid for NPL Model lOOA. Figure 2: Model of Hull B towing at En = 0.687. W.L. at rest | P' i.L. at rest ~0 Q- 0 0 0 0 PtOP`1~ ~ A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S.S. Figure 3: Locations of pressure measurements for Hull B. i__ _ ~ Il111J,1Jr i_ ~ . I B. 111'/~ Figure 4: Computational grid for Hull B. A.P. 1 ~ ( Cody 10 ): ~ 3 4 3g~ 6 7 8 9 F P S.s. Figure 6: Computed surface pressure distributions for Hull c. o., o.` 0.1 o.. o.' . . ~ W.L. at rest | ~ F~W/.L. at nest ,.~ - - ~ _ .~ J ~ ~ : Mes. (ASMB) I _: Cal. (WISDA - Va) ..J · ,1 , , , , I , , , , _ A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S S Figure 7: Comparison of pressure distribution along the keel line for Hull B. Fn=0.434.
-'-~1 GAL o.ol 4A _ ~ ,r · : Mes. tAsMs) t Cal. (WISDAM-V~) - .R . .' . . . . ~ . . . · . . A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S. Figure 8: Comparison of pressure distribution along the keel line for Hull B. Fn=0.5 11. cod us o.~. : O.t _ 4.4 4.8 _n.2 , . , ., . . P1 -0.4 _ -0.6 I l V.Q Fn - 0.590 ' ' ' ' ' ' ' ' ' ~ Fn , / W.L. at neat ~W.L. at test 1 _ ~- 9- ~- · : Mes. (ASMB) : Cal. (WISDAM-VUg I, , , , , I , , , A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S. , , , Figure 9: Comparison of pressure distribution along the keel line for Hull B. Fn=O.S90. O.' . Fn - 0.688 , ' __~ it' / W.L at rest _ ~ ~.L 8t rest 0.0 _ - ~ ~ . 4.4 ~ _ · : Mes. (ASMB) · : Cal. (\NISDAM-VUg 4.8 , ,~, , , , ~ , , , , , _ A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S Figure 10: Comparison of pressure distribution along the ke- el line for Hull B. Fn=0.688. u ~ o.` 4.~- f · : Mes. (ASMB) : Cal. (WISDAM-V00 A.P. 1 2 3 4 ~ 6 7 8 9 F.P. S. S Figure 11: Comparison of pressure distribution along the ke- el line for Hull B. Fn=0.787. Figure 12: Effect of Fn on surface pressure for Hull B. at Pi. 0.2 0.0 -0.2 7 Fn Figure 13: Effect of Fn on surface pressure for Hull B. at PS. 0¢0.0 0.2 ''0.4 0.6 0.8 Fn Figure 14: Effect of Fn on surface pressure for Hull B. at P6.
_3.0 ~ NPL-1 OOAF 2 5 ~ = _ _ : _ `, r · _ _ _ _ _ _ ~ ~ ~ ~ 1 ~ ~ ~ .5 _ _ _ _ _ _ _ _ _ _ _ _ _ ., _ _ _ _ _ _ _ _ _ _ _ _ _ ~ 10 _ _ _ _ _ _ _ _ _ _ _ _ _ .= _ _ _ _ _ _ _ _ _ _ _ _ _ ~ l =0R _ _ _ _ _ _ _ _ _ _ _ _ _ ~ V ~ .- _ _ _ _ _ _ _ _ _ _ _ _ _ ~ZC ~ _ _ _ _ _ _ _ _ _ _ _ _ Z ~ O. O _ _ ~ . _ _ _ ~ ~ ~ ~; ~ ~ (T ~ 0.0 0.2 0.4 0.4~ 02L o.o ~70.4 0 6 0.8 Fn 1 4.0 1 ~ 2.0 J 0.0 Figure 15: Effect of Fn on surface pressure for Hull B. at P9. ~ ~ 20 _3.t~ cn O 25 ~ I I I I Ttll T _ _ _ _ _ _ 1 1 1 1 O On _ _ _ _ _ 1 1 1 1 =^ v fLFI : 5 _ _ 1 1 1 1 1 ~ _ _ _ _ _ T 1 r T ~ .- _ _ _ _ _ - 1- ~ ~ 1.0 _ _ _ _ _ ~ ~ _ _ _ _ _ 1 1 1 1 ·co 1FT: : .5 _ _ _ _ _ 1 ~ 1 1 _ _ _ _ _ 1 1 1 1 . oo 1 1 1 1 0.0 0.2 0.4 (X10-3 ) 4.0 11 ~ 2.0 n I nc 4.O - : Mes. (NPL) · : Cal. ( WD-VIII ) ~ 0.6 0.8 1.0 1.2 Fn ~ : Mes. (NPL) I I I I I I I I Lll I I I · : Cal. (WD-VIII ) IITI IT~ ITTTIT~ E E 11.. a.o 02 0.4 0.6 0.8 1.0 1.2 Fn Figure 16: Comparison of running attitudes for NPL 80A. C| : Mes. (NPL) · : Cal. ( WD-VIII ) 0.6 0.8 1.0 | : Mes. (NPL) | · : Cal. (WD-VIII ) ll 1 .2 Fn II Figure 17: Comparison of running attitudes for NPL lOOA. ~3.0lr ~ H =2.5~ _ ~ O2.0R ~ 1.5 T 1.0 121 0.5 00 0.0 0.2 0.4 | NPL-1 50A|| | | |- | | | ~ 1 1 1 1 1 1 1 1 i ~ 1 1 1 1 1 1 l I r T7 [T7 [Tl ITTTTT7 1 1 llL111~ ll:FTT FTTItT FT -1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -lllTIITlllILLllillll T ~ T T 7 I T 7 ~ T 1 I T T T T I I I I 1 ITTI ITI ITI IT1 ITTI 1) l I T T I r T 7 r T l r T T T T I I 1~1 I I I I I 111 I T I TT1 ll 1 T~r T ~ T T 7 ~ T 1 ~ T 1 T T T T I T 1~1 1 ' I I I I I r1 T rT1 rTrTrr'TT 1111111111L1~111111 (X 10~ ) 4.0u 1 R =~2.0~ 0.0 L t ~~!-2.0~ C: Mes. (NPL) | · : Cal. (WD-VIII ) 0.6 0.8 1.0 : Mes. (NPL) : Cal. ( WD-VIII ) i 111111111~1 111111111~1 ~11111111111 T 1 1 T I I I I I T N~ 1 1 T I r 1 1 I T NPL-150A _401 1 1 1 1 · I I I I I ~ 1 1 1 1 1 1 1 1 1 1 1 1~1 1 1 1 1 1 1 1 1 11 ~ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Fn Figure 18: Comparison of running attitudes for NPL 1 SOA.
25 C~ 2.0 a) °0 1.5 .~ 1.0 ~ 0.5 ~ Hull B | 1 1 1 1 1 ~ _ IIITI 1 1 1 :1~1~ ~TTW2 _ I I rv _ _ 1 1 ~ _ ~ ~ _ _ ~ _ : Mes. ( ASMB ~ · : Cal. ( WISDAM-VIII ) 0.0 _ ,,,,, , ·,,,, ,- 0.4 0.5 0.6 0.7 Fn (X10 - ) 4.0 l ~ _ _ _ 1 l l : Mes. (ASMB ) ~ _ _ _ _ _ _ _ _ _ _ _ _ _ , 2.0 ~ · : Cal. ( WISDAM-VIII ) E _ _ _ _ _ = = = = = = _ 111111''' _ _ _ = _ _ = _ _ _ Z _ _ . _ _ _ _ _ I I I I I I I I I ~ , ~ _ _ _ _ _ _ _ _ _ 1 1 1 1 1 1 1 1 1 _ = _ _ = = _ _ ~ _ _ ~ o.o _ _ _ _ _ ~ _ ~ _ ~ _ ~ o5 ~^ _ _ _ _ _ _ _ ~ 1 ~ ~ ~ 1 1 1 1 ~ ~ _ _ _ = = = ~ = = 1 ~ ~.u _ _ _ _ = _ _ _ 1 1 1 1 1 1 L'-- _ _ = = = =F = ~ ._ _ _ _ _ _ _ _ _ 1 1 1 1 1 ~1 1 _ _ _ _ = _ _ = 1 _ _ 1 ~-4.0 _ _ ., _ _ = _ _ ~ 1~1 1 1 1 _ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ _ _ _ E11111111 _ _ _ _ _ _ ~ u _ ~ -60 _ _ _ ~ _ _ _ ~ 1 ~ ~ I 1 1 1 1 1 _ _ ~ _ ~ ~ _ _ ,1 · 0.4 0.5 0.6 0.7 Fn Figure 19: Comparison of running attitudes for Hull B. 0.2sp ~ 0.2t ~_ U. 3 0.1' ~J r ~ ° 3 01( ~ C .= 0.05 t ' t ~ 0.00 ~ : Mes. (NPL) l · : Cal. (W~V111) | ~ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Fn Figure 20: Comparison of wetted surface area for NPL 80A. a.) 0.25 ~ ~ NPL-100At O 0.2C' " _ ~0.1: ~J a)_ a) ~ 0.1C =~ r,, ,, I I ,, ~ ri r~e Ll 1 1 I nTT ·= U.~7tl 1 1 1 1 1 1 1 Ll I l ~ i I T I ~, r I I I I r I n r~ o.oorl rl I I ITl 0.0 0.2 ,, ~ 1 1 1 11 : Mes. (NPL) ~ : Cal. ( W~VIII ) |' 0.4 0.6 0.8 1.0 1.2 Fn Figure 21: Comparison ofwetted surface area for NPL lOOA. 0.2b 0) 0.20~ ~; ~ ~ ~ ~ ~ ~ ,` I ~ 1 1 1 1 1 1 1 1 1 =_ rl Ill I rTr c\' ~ 1 1 1 1 1 1 1 1 1 ~ ¢0.150~|~| 1 1 1 1 1 =' F11111111- , I 1 1 1 1 1 1 1 ~ 1 1 ~0.10llllllllI4l 005FlTIII nm IIIT7TIlllI rllllllllll ° °8' 1 " " ' 1 ' ~ ' .. ^~ ............. I NPL15nA~ 1 T1 T T I I ITITLL I T I T 1 1 TTTIT1 1 1 1 1 Tl~ I T I T I I ~ I I TT~ 1 1 1 1 1 1 iTTT ' 1llllllllIl!~II ~1~1 1 l~l ' _ I I I T ~ T I I T _t_rl I I I I 1 I T 7 T I I T I I 1 1 ~ 1 ~ 1 1 1 1 1 1 1 1 i 1 1 1 17] r' I I I ~ l I l I T I ~ I I I I I I I I I I I ~ I I I I I Ll ~ I ~ I I f ~ I ~ ~ 1 1 ~ ~ TiT ~ ~ T' r~ ~ ~ l I l I T L T I I I ~ I i ~ T ~ ~ I I ~ I T I T I Ll I I T ~ I 1 ~ 1 I T I T I Ll I T ~ I 1 ~ ~ ~ Lj ~ ~ ~ ~ I I ~ I I I ~ I I I I I I i 11 ~ ~ I IIITlTIlllIITIlIIII 1 I I I 1 T I 171 I 1 T I 17 ii : Mes. (NPL) · : Cal. (W~V119) 0.6 0.8 1.0 12 Fn Figure 22: Comparison of wetted surface area for NPL 1 SOA. ( X 1 1, - - . _ c) C~ ~~ 7~r~ ~F~- `' ~ Mes. Cal. L~l Llil I I4lTL: ,,, ~ (NPL) (WD-VIII) II ;~ I ~ ~ I ~+l I l - ~ ~ I I I I ·_ Ll CTML ~ IL~ I ~ ~ ~ I ~ ~ ~ I ~ I ~ I ~ ~ I I ~ I ~ I cn ~ 1~ ~ I ~ ~ ~ I I ~ ~ I I ~ I ILlTI ~ I ~ I I I ~ IICF~ O II I I I I I I I I I i 11n 11111 I Ll I I I 011 111 1 1 1 1 1 1 T 1 1 1 1 1 111 1 I 1 1 1 1 1 I I 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Fn Mes. Cal. ( NPL ) (WD-VIII) CTML · CF~ O Figure 23: Comparison of resistance coefficients for NPL 80A. (X10 4' 1- c' .a o c' Mes. Cal. || |,`| | |,~| | |,`| | |~| | |~| | | | | | | | U) ~ (NPL) ~D-VIII) II lTI I l~l 1 ~TI 1 ITI I ITI I I I I I I I ·_ 11 CTI\L ~ I I I I I I I I I I I I I I I I I I I 11 11 1 1 1 1 1 1 1 1 1 1 1 1 1 11 L I I I I I I I I I I CFNL O Ll11 I I I I I I I I I I I I I I I I I I I I I I I I ol' Il I I I I rTI ~ ~ ~ I I I I ~ I I I I ~ I I I I ~ ~ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Fn Figure 24: Comparison of resistance coeff~cients for NPL 1 OOA.
(x~o-) ~e ~150; o o o o o 1 4 !11I!I!I!I1I !11!I1I1 11111 I ! 11 111111111 I I I I I I 111 ~ (~ ~ < ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . ~ CT~ ~ _ _ _ 11II[1II[T _ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 1 1 1 1 1 1 i I l? ° 1CF~ O ~ ~ ~ ~ ~ ~ ~ ~ 111.11II11 0.0 0.2 0.4 0.8 0.8 1.0 1.2 Fn . F1gure 25: Co~~son of ~si~ance coe~dents ~r NPL 1 30A. ~ 3 2.5 2 E1~ ~ ~ 1~ ~ ~ ~ o~ ~ ~ o.o _ _ _ ~ 1 1 1 1 1 1 1 1 I1 11 1 ~OI1 11 I 1 T 1 I 1 Ill illT11111d 11 I TI1I) 1I11[1T[11[ 1 1 1 1 1 1 1 1 1 1 1 ~ 1 1 + + LI 1 L1 1 11111111111 1 1 1 1 1 1 T 1 1 1 [ I I I 1 I 1 I ~ I 1 I 1 1 1 1 I 1 I I 1 1 T NPL UB=6.25, Fn=0.60 I ~BS.(NPL) :CS1.~D~II1) _ -~ 5~ 6~ 6~ ~ 7~ (X10~) L/V1~ ~{ q _: o e .s [NPL L/8=6.25, Fn=0.60 k H ~u ~ ~ ~ :C~]WD~I~ ~# NPL L/8=6.25, Fn=0.80 ,-I!I111IIII1I1i111iI ~PU e c8l. (WD~III) wu- 5.0 5.5 6.0 6.5 7.0 7.5 (X10~) L/V1 1NPL L/8=6.25, Fn=0.80 I :~eS.(NPL) 1 ~I ~ CaI.o - f f l l f 1 1 1 1 1 1 f l 1 I I I I I I I 1 1 ]~l~lT1 ol I 1 1 1 1 1 1 1 1 1 1 1 1 I! 1 1 lILllllH [--I-+-l--lIll+I -2~1 I 1 1 1 1 +1F ~IIII1TI) 5.0 5.5 6.0 ~u-vllI) I +IT1I11 llTlTF IIB1#I IllII~I 11lJlII 7.0 7.5 L/ P1gure 27: E~C1 of L/V 1~ on n~ning athtudes, Fn = 0.8. 30F 2.5~ k 2.0F ~ r ~ le5l |~[IIllIlIIllIlIIl I!!~ ~ I F+Er++ H+~ :~eS.(NPL) I F111111 I 1111 T 111 I 111 ~ C~l.~D-I'0 1 5.0 5.5 6.0 6.5 7.0 7.5 X10~) L/V1 4,. .. I NPL ~ F~1~0 ~ H :~eS.(NPL) H 2# @ :CB1.(WD^~1) ~ 6.5 7.0 7.5 L/V1 P1gure 26: E~ct of LV'/3 on nmning atti~dcs, Fn = 0.6. IlIII'lII L3I 1 1 1 1 1 1 1111111 1 1 1~111 1 1 ~1111E Illlllll? llllIFlI 111111111 5.0 5.5 6.0 6.5 7.0 7.5 L/V1 F1qure 28: E~ct of L/V 1~ on muning aui~des, Fn = 1.0.
.O !t o a c cO . - ~n a ct - c .a c~ o - . - u) ........... >, `,,,, I,, I I L I I I I I I I _ ~ _ I I I I I I I I T 1 I T 1 I T 1 1~1 I T 1 I T 1 I T T I F _ = = _ = _ _ = _ _ 1 1 1 1 1 1 1 1 1 1 IU 1 1 1 1 1 1 1 1 1 1 _ _ _ _ _ _ _ _ _ _ I I I ~ I ~ r r I T I _ r 1ll 1: 1 1 ~ I ~ T _ : _ _ = = = I I 1 4~TT T 1 I T 1 I T ~ T 1 I T T I I ~ _ _ _ = = _ I I I I 11 I T 1 I T 1 I T 1 1011 T T It: ~ = _ _ _ _ _ I T 1 I T 1 I T 1 I T 1 I T 1 I T I`LI I I ~ = _ _ = = _ 1 T 1 I T 1 I T 1 I T 1 I T 1 I T 1 1 1~1tl ~ = _ _ _ _ _ r ', r r 7 T r ~ T r, T ~ I T r, T ~ I I I T _ _ _ _ = _ _ T., I,, T r 1 r,, T., r I j I I 1 1 1 T _ _ _ _ = = _ I T1 I T1 I T1 I T1 I T1 I T1 1 1 1 1 1 T r ~ r ~ 1 I T 1 I T 1 I T 1 I T 1 11 ~ I I 1 I T1 I T1 I T1 I T1 I LT 11 1 1 T1 1 T1 I T1 I T1 1 1 1 1 1 1 1 T1 I T1 I T1 I T1 1 1 1 1 1 _ _ _ _ _ _ IT1 I T1 I T1 I T1 I Tl Ll 2 NPL L/B=6.25, Fn=0 60 |1 I T I I T I I T I I T I I I I ~ :Mes.(NPL) 11 T I T1 ~ T1 I T1 ~ TT 11 1 111 I T1 I Tl I I Tll: · : Cal.(WD-V111) 11 1 1 1 ~ I ~ I i I I I ~ I I I 1l 1 I r 1 T r 1 T r 1 T r I I r: O , Illilid1~111161 i. 5.0 5.5 6.0 6.5 7.0 7.5 L/v1/3 Figure 29: Effect of L/V l/3 on total resistance coefficient, Fn=0.6. ( X104 ) 4O 14[ 1 1 1 L T 1 1 l l 11 1 10 8~ 6: 2 ~L 1 1 1 1 T 1 1 T I T 1 I T Tl 1~1 1 1 1 TT I T1 I T I 1 1 I T I 1 1 1 1 1 1 1 1 I T1 I T I 1~1 T1 TT I r7 1 1 1 I T1 1 T I I 11~1lEl I I I I ITT T T TTl T T~T 1 T r 1 1 1 ' ' ' ' ' I 1 1 1 1 1 1~ 1 1 1 1 1 _ 1 1 1 rr1 1 11 ~H ~3 1 1 1 I T I T r l T Pl ~H I r ~ I NPL UB=6.25, Fn=0.80 . : Mes. (NPL) · : Cal. (WD-VOf) i eF j ~ T 1 1 1 1 F j ~ ,F F T r r ~F T r r I I IT I I Ir T T r I rT I I I Trr T Ij jl T 1 1 1 1 1111 I IIT T T rr _LlL1 1 1 1 1 T I jl 1 1 1 1 1 1 1 1 T T r I Tr l l l l I I j I 5.0 5.5 6.0 6.5 7.0 7.5 L /v1/3 Figure 30: Effect of L/V "3 on total resistance coefficient, Fn=0.8. F I I I I I I I I I I I 11 1 1 1 1 1 1 1 ~ I I I I I I I I I I I I I I I I I I ~ _ ~ 6~1 1 1 1 1 1 1 1 1 1 1 ~1 171TIITI1 111 ITIITITII 01 1 1 11 ~: I- I I I I I I I I I I ~ I f I I I I I I I I r I ~ I I I rl I 111 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~1 1 1 1 1 1 1 1 1 1 1 4FI I T I I I I I I I I I I I I I I I I I I I I LPI 1 1~1 1 1 1 1 1 1 ~ r ~ F ' ' I 1 IF I I T 1 1 1 1 | I I I | | L | | 2|| NPL L/B=6.25, Fn=1.00 |1 1 | | T I 1 1 I T I I I I T I I I I : Mes. (NPL) : Cal. (\ND-VIll) U I I I I I I F 1 T j T F 1 F j T I 1 F ,] o n · . ~ 5.0 5.5 6.0 6.5 7.0 7.5 L /v113 N PL L/B=6.25, Fn=1.00 1 : Mes. (NPL) ~ ~ : Cal. (\ND-V111) | Figure 31: Effect of L/V 1/3 on total resistance coefficient, Fn= 1.0.
DISCUSSION Masashi Kashiwagi Kyushu University, Japan As validation for a wide variety of hull forms, you compared with the experiments of NPL series model. The data was published in the 1970's, and thus I guess those have been used for comparisons with other numerical models in the past. If this is true, what are the main differences between the present results and published results in the past? AUTHOR'S REPLY The comparison of the present computed results using WISDAM-VIII with the computed results of Wang et. al. are shown in Fig. A-1. In Fig. A- 1, two types of computed results of Wang et. al., the one is computed by the Rankine source method (RSM) and the other by the Tulin's theory (1986, cited below). Since only the comparison of wave making resistance coefficients (Cw) is shown in Wang et. al. (1996), comparison of residuary resistance coefficient (Crl) are shown in Fig. A-1 where computed Cw of Wang et. al. are compared with the experimental data along wit h the present computed data. As can be seen clearly from Fig. A-1, computed results of Wang et. al. fail to reproduce the Thank you for your kind remarks. trends, i.e. the slope of the experimental data, and the quantitative agreements with the experimental data seem to be poor. That is, the mean differences of computed Cw of Wang et. al. compared with the experiment are greater than 10% while that of the WISDAM-VIII result is about 4% for a speed range 0.6<Fn<1.0. As Prof. Kashiwagi points out, the experimental date of NPL hull form series are published in the 1970's. However, these data were originally published as the design data for the primary use in the calm water performance prediction at the design stage. Thus, the NPL hull forms have rarely been used for the comparison with the computations. To my best knowledge, the only published data of computed results of calm water performance for NPL hull forms is Wang et. al. (1996) (referenced in the present paper). REFERENCE Tulin, M.P. and Hsu, C.C., "Theory of High- Speed Displacement Ship with Transom Stern," Journal of Ship Research. Vol. 30 No. 3 pp. , , 186-193.
