Twenty-Third Symposium on Naval Hydrodynamics (2001)

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lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line INVESTIGATION OF GLOBAL AND LOCAL FLOW DETAILS BY A FULLY THREE-DIMENSIONAL SEAKEEPING METHOD 355 Investigation of Global and Local Flow Details by a Fully Three- dimensional Seakeeping Method V.Bertram (HSVA, Germany) H.Yasukawa (Mitsubishi Heavy Industries, Japan) ABSTRACT A fully-three-dimensional Rankine panel method in the frequency domain is validated for local pressures, motions, and added resistance. Previous formulae for added resistance contained errors resulting in large differences to experiments. This has now been remedied. The method is linearized with respect to wave height. The steady flow contribution is captured completely by solving the fully nonlinear wave-resistance problem first and linearizing the seakeeping problem around this solution. The same grids on the hull are taken for both steady and seakeeping computation. On the free surface different grids are used, either following quasi-streamlined grids or rectangular grids with cut-outs for the hull. The results from the steady solution are interpolated on the new free-surface grid. The method is applied to various test cases. Motions are in good agreement with experiments, but this is also the case for strip method results. Local pressures, especially for shorter waves, are much better predicted than by strip method. The added resistance is sensitive to higher derivatives of the potential and a numerical differentiation of these terms may be preferable to using higher-order panels. 1. INTRODUCTION The most commonly used tools to determine seakeeping properties are based on strip theory. The strip method approach is cheap, fast, and for most cases also quite accurate. However, strip methods do not perform so well for high- speed ships, full hullforms (tankers), ships with strong flare, and generally for low encounter frequencies which typically occur in following seas. They are also questionable with regard to local pressures which are needed as input for finite- element analyses. Approaches to improve predictions of seakeeping properties should capture: – 3-D effects of the flow 3-D effects are important for low encounter frequencies and full hull forms. 3-D diffraction at the bow region of tankers contributes considerably to added resistance, [1]. – Forward-speed effects Strip methods include forward speed by the change in encounter frequency. But forward speed enters the ship motion problem in additional ways: the local steady flow field, the steady wave pattern of the ship, and the change of the hull form and wetted surface due to squat (dynamic sinkage and trim). We will present here a 3-d Rankine singularity method (RSM) which captures all forward-speed effects. The method is ‘fully three-dimensional', i.e. both steady and unsteady flow contributions are captured three-dimensionally. For a recent survey of Rankine singularity methods for forward-speed seakeeping, we refer to [1], [2]. 2. THEORY 2.1. Physical model We consider a ship moving with mean speed U in a harmonic wave of small amplitude h. We assume an ideal flow. Then the fundamental field equation is Laplace's equation. In addition, boundary conditions are postulated: 1. No water flows through the ship's surface. 2. At the trailing edge of the ship, the pressures are equal on both sides. (Kutta condition) 3. No water flows through the free surface. (Kinematic free-surface condition) the authoritative version for attribution. 

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This technique is known to give better results for full hulls than streamlining a grid around the hull. The fully nonlinear method used 3 iterations which reduced the error at the free surface by 4 orders of magnitude. The same grid for the hull was employed for the seakeeping computations (at the dynamic trim and sinkage). Pressure integrations considered only the area submerged in the steady case. The free surface in the seakeeping computations was discretised with typically 1400 elements. Again the ‘cut-out' technique was employed and the steady results interpolated from the ‘steady' grid to the ‘unsteady' grid. Test computations for two wave lengths with free-surface grids involving approximately 4200 elements yielded results that were only 5% different. This may be interpreted as that the coarser discretisation is sufficient. The computational results are compared to measurements of [12] and MHI strip method results. The strip method is based on standard STF method with Lewis section representation, but includes an empirical correction [13]. The results include motions and pressures on the hull at a location x= −0.078Lpp (23.95m behind amidships). The motions agree rather well for both head sea and oblique sea with µ=150°, Figs. 1 and 2. However, strip method also predicts heave and pitch motions well. In fact, for long waves strip methods gives better results than the RSM. This is not surprising. Strip methods are known to predict heave and pitch motions well for usual ships and ship speeds. The present RSM uses the shifting technique which deteriorates in performance for τ<0.4…0.5. Sway and yaw are also well predicted, the maximum of the roll motion is underpredicted. This may be due to the deterioration of the shifting technique, as for a fast containership with Fn=0.275 Bertram [2] obtained significant overprediction for roll resonance as expected for a method that does not include empirical corrections for nonlinear roll damping. Figs. 3 and 4 compare pressures. Starboard is the weather side. For head waves the computed pressures are of course symmetrical to the midship plane (90°). One point on the port side was then plotted on its corresponding position on the starboard side. Pressures computed by the RSM agree well with measured pressures for λ/L<1.25 for µ=180° and λ/L<1.0 for µ=150°. These limits correspond for the investigated low Froude number to τ-values around 0.35…0.4. For short waves, the computations underpredict the pressures at the bottom of the ship compared to measurements. However, as the pressures should decay exponentially with depth like all wave effects, for short waves the near-zero values of the computation appear to be more plausible and we assume that they reflect in this case reality better than the measured values. For waves of moderate length 0.5<λ/L<0.75, measured and computed pressures at the ship bottom agree well. The strip method results for pressures are worse for short waves λ/L=0.2, 0.3 where diffraction effects are stronger than radiation effects. In summary, the RSM predicted pressures and motions well, the strip method predicted pressures in short waves badly, but motions well. The RSM is currently limited in practice to approximately τ>0.4. Unless techniques are developed to extend it to smaller τ-Values, the RSM will remain a research tool of limited functionality. We see hybrid methods matching an inner RSM solution to an outer Green function method or Fourier-Kochin solution as most promising approach to extend the method to low τ-values, but at present no such research is planned due to lack of funds. Table I: Test case VLCC Lpp 307.00 m zg 4.333 m B 54.00 m kx 19.193 m T 19.50 m ky 73.987 m CB 0.813 kz 76.750 m KG 15.17 m kxz 0m xg 10.045 m 3.2. Added resistance We show here applications to the ITTC standard test case S-175 containership in head seas. Computations are compared to experiments of Mitsubishi Heavy Industries. Fig. 5 shows results for Fn=0.25 and Fig. 6 for Fn=0.3. For all three motions the agreement is good. In fact, the computational results for heave for long waves appear to be more plausible, as they tend as expected monotonously to 1. The discrepancies between experiments and computations for the higher Froude number Fn=0.3 are most likely due to nonlinear damping effects in the experiments. For Fn=0.275, [2] showed that the phase information is also correctly captured, at least the authoritative version for attribution. 

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line INVESTIGATION OF GLOBAL AND LOCAL FLOW DETAILS BY A FULLY THREE-DIMENSIONAL SEAKEEPING METHOD 363 for wave lengths where the RAOs are not approximately zero. The added resistance is similarly well captured. The differences for the higher Froude number are explained by the differences in capturing the motions. The derived formula seems to be debugged now and can be recommended for other ‘fully three-dimensional' methods. ACKNOWLEDGMENT We are grateful for the support of our younger colleagues Shuji Mizokami and ‘Cowboy' Tanaka in preparation of the results. REFERENCES 1. Bertram, V. and Yasukawa, H., “Rankine source methods for seakeeping problems,” Jahrbuch der Schiffbautechnischen Gesellschaft, Springer, 1996, pp. 411–425 2. Bertram, V., “Numerical investigation of steady flow effects in 3-d seakeeping computations”, 22. Symp. Naval Hydrodyn., Washington, 1998 3. Bertram, V. and Thiart, G., “A Kutta condition for ship seakeeping computations with a Rankine panel method”, Ship Technology Research 45, 1998, pp. 54–63 4. Bertram, V., “Fulfilling open-boundary and radiation condition in free-surface problems using Rankine sources”, Ship Technology Research 37, 1990, pp. 47–52 5. Iwashita, H. and Ito, A., “Seakeeping computations of a blunt ship capturing the influence of the steady flow”, Ship Technology Research 45, 1998, pp. 159–171 6. Jensen, G., “Berechnung der stationären Potentialströmung um ein Schiff unter Berücksichtigung der nichtlinearen Randbedingung an der freien Wasseroberfläche”, IfS Report 484, Univ. Hamburg, 1988 7. Nakatake, K. and Ando, J., “Rankine source method using rectangular panels on water surface”, 11. Workshop Water Waves and Floating Bodies, Hamburg, 1996 8. Bertram, V., “Vergleich verschiedener 3D-Verfahren zur Berechnung des Seeverhaltens von Schiffen”, Jahrbuch Schiffbautechnische Gesellschaft, Springer, 1997, pp. 594–600 9. Bertram, V. and Thiart, G., “A Rankine panel method for ships in oblique waves”, Euromech 374, Poitiers, 1998, pp. 221–229 10. Bertram, V. and Thiart, G., “Fully three-dimensional ship seakeeping computations with a surge-corrected Rankine panel method”, J. Marine Science and Technology, 1998, pp. 94–101 11. Bertram, V. and Thiart, G., “Fully 3-d seakeeping computations for real ship geometries”, Jahrbuch Schiffbautechnische Gesellschaft, Springer, 1998, pp. 244–249 12. Tanizawa, K., Taguchi, H., Saruta, T. and Watanabe, I., “Experimental study of wave pressure on VLCC running in short waves”, J. Soc. Nav. Arch. Japan 174, 1993, pp. 233–242 13. Mizoguchi, S., “Exciting forces on a high speed container ship in regular oblique waves—Frequency selections for calculating exciting forces by the strip method—”, J. Kansai Soc. Nav. Arch. Japan 187, 1982, pp. 71–83 the authoritative version for attribution. 

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Fig. 2: Like Fig. 1, but for µ=150° Fig. 1: Motions for VLCC, Fn=0.131, µ=180°; • experiment, ○ RSM, · strip method INVESTIGATION OF GLOBAL AND LOCAL FLOW DETAILS BY A FULLY THREE-DIMENSIONAL SEAKEEPING METHOD 364 

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Fig. 4: Like Fig. 3, but for µ=150° Fig. 3: VLCC, Fn=0.131, µ=180°; unsteady pressure angle; 90°=bottom, 0° starboard CWL; • exp., ○ RSM, · strip method INVESTIGATION OF GLOBAL AND LOCAL FLOW DETAILS BY A FULLY THREE-DIMENSIONAL SEAKEEPING METHOD at x=−0.078Lpp plotted over circumference 365 

About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Fig. 6: As Fig. 5, but for Fn=0.3 Fig. 5: RAOs for motions and added resistance for S175, Fn=0.25, µ=180°, • exp., ○ RSM INVESTIGATION OF GLOBAL AND LOCAL FLOW DETAILS BY A FULLY THREE-DIMENSIONAL SEAKEEPING METHOD 366 

lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line INVESTIGATION OF GLOBAL AND LOCAL FLOW DETAILS BY A FULLY THREE-DIMENSIONAL SEAKEEPING METHOD 367 DISCUSSION H.Chun Pusan National University, Korea 1) I think that you solved iteratively the nonlinear free surface boundary condition. In that case, how did you treat the coefficients (such as added mass, damping, restoring force) of the motion equation? 2) You mentioned that the panel shift method can not meet the radiation condition for some cases. Do you have any alternative idea to satisfy the radiation condition for such cases? AUTHORS' REPLY 1) We treated the linearized (unsteady) ship motion problem based on fully nonlinear steady flow[2]. Then, since the ship motion problem is linearized, we can define all coefficients such as added mass, damping, restoring force and exciting forces. Of course, the effect of steady wave elevation and flow on the coefficients is included in the computations. 2) We see so-called hybrid methods matching an inner RSM solution to an outer Green function method or Fourier- Kochin solution as most promising approach to extend the method to low values. DISCUSSION M.Kashiwagi Kyushu University, Japan Firstly I wish to commend you for completing complicated calculations of the added resistance with the pressure integration method. I have a couple of questions concerning the grids. I understand that what you call ‘cut-out' technique is used for a tanker and possibly S-175 container ship as well. Why do you think the ‘cut-out' technique goes well? If you use the alternative quasi-streamline grid, how is the result going to be? Does the computation break down or are obtained results much different from experiments? Are there some criteria of which grid should be used for given values of the block coefficient and the Froude number? AUTHORS' REPLY We used ‘cut-out' method for the computation of VLCC. The reason is that quasi-streamlined grids either give very distorted grids near the bow and stern or do not locate collocation points on the water surface near the ship ends. Distorted cells lead to problems with the radiation condition. The ‘cut-out' method is robuster in this respect for full waterline forms. We recommend the cut-out method for ships with block-coefficients above 0.7. DISCUSSION M.Ohkusu Kyushu University, Japan Apparently, a pressure transducer is located on the water line in your experiment. This transducer is naturally out of water some duration during one period of the motion. Then the time history of the pressure measured will be of not a sinusoidal but a truncated sinusoidal curve. So I wonder how you treated with the truncated curve to derive your value of pressure. If you take the first harmonic components of this curve, you will obtain much smaller amplitude of the pressure. Nevertheless, your pressure at the water line looks consistent with the pressure at other locations. AUTHORS' REPLY As you pointed out, we observed the time history of a truncated sinusoidal curve in the pressure measurement in the vicinity of the water line. From the time history data, amplitude was defined as variation between zero-level and the positive peak value[12]. So the experimental data plotted in Figs. 3 and 4 is not the first harmonic components of the curve. In the computations, we do not take the truncated effect into account. The reason why the calculated accuracy is insufficient in the vicinity of water line may be due to treatment of the truncated effect. the authoritative version for attribution.