Amini Afshar, Mostafa

Bingham, Harry B.

Online Research Database In Technology

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Downloaded from orbit.dtu.dk on: Dec 20, 2017A note on added resistance for slow shipsBingham, Harry B.; Amini Afshar, MostafaPublication date:2013Link back to DTU OrbitCitation (APA):Bingham, H. B., & Amini Afshar, M. (2013). A note on added resistance for slow ships.A note on added resistance for slow ships ∗Harry B. Bingham and Mostafa Amini Afshar†Mech. Engineering, Tech. Univ. of DenmarkE-mail: hbb@mek.dtu.dk, maaf@mek.dtu.dkIntroductionRising fuel costs and increased environmental regulation of emissions, combined with a currentover-capacity in the global shipping fleet, have provided a strong incentive for a dramatic reduc-tion in the operating speed of cargo ships. In particular, many ships are routinely sailing at 10knots and under these days, which translates to an engine load of as little as 10 to 20% of thedesign operating load. This trend towards slow and ultra-slow steaming is expected to continue,and thus lead to new ship designs with smaller engines and possibly auxiliary wind-propulsionsystems. One consequence of slower design speeds and a reduction in installed engine power isan increased concern about the ship’s ability to maintain maneuverability and escape a lee shoreunder heavy weather conditions. While the calm water resistance of a ship tends to increase ata rate proportional to ship speed raised to a high power (typically somewhere from 4 to 6), theadded resistance due to waves generally increases only linearly with increasing ship speed. Thusthe lower the design speed the more important an accurate prediction of the added-resistancebecomes.This abstract reviews the existing methods for predicting the added resistance of a sailing ship,and highlights the large uncertainties involved in both calculating and measuring this sensitivequantity. This serves to motivate a recently begun PhD project with the goal of an improvedadded resistance tool based on the high-order finite difference approach described by [9, 10], andreferences therein.Methods for Computing Added ResistanceWe adopt a Cartesian coordinate system xi = [x1, x2, x3] with origin on the still water level andthe x3 axis vertically upwards. When a ship sails along the x1 axis at a given speed U throughcalm water it experiences a constant forceF1 = −R (1)where R is the calm water resistance. If the ship now sails through a seaway, it will experiencean unsteady force in the x1-direction F1(t). The mean value of this unsteady force over sometime-period T isF1 =1T∫T0F1(t) dt = −(R+Rw +Ra) (2)where Rw is the added resistance due to waves and Ra is the added resistance due to wind whichis typically at least an order of magnitude smaller than Rw.There are basically three methods for predicting F1:1. Near-Field Pressure integration:F1 =∫Sbp n1 dS (3)where p is the fluid pressure and n1 is the x1-component of the unit normal vector to thebody surface Sb.∗The authors wish to thank the EU 7th Framework Programme (grant # 266030, ULYSSES) for funding, andthe Danish Center for Scientific Computing for supercomputing resources.†Presenting author0 0.5 1 1.500.511.522.5  N=6400, Mom.N=1600, Mom.N=800, Mom.N=6400, Pres.N=1600, Pres.N=800, Pres.λ/LCw=LRw/ρgA2B2Figure 1: Convergence for calculations of the added resistance of a Wigley hull at zero forwardspeed using WAMIT and both near-field pressure integration and far-field momentum conserva-tion.2. Momentum Conservation:F1 =∫Sc(p n1 + ρu1 niui) dS (4)where ui is the fluid velocity vector and Sc is a control surface away from the body. Herethe summation convention applies to repeated indices.3. Energy Conservation: The work done by the ship on the undisturbed waves (per waveperiod) equals the average energy flux removed from the wave propagation direction andsent in other directions.F1[c+ U cos (β)] = Ave. energy flux sent sideways. (5)where c is the wave phase speed and β the wave heading angle measured from the x1-axis.Many particular forms for these relations have been derived over the years depending on theapproximations and assumptions made, and on the numerical methods applied. Common to allforms however, is the assumption that higher-order potentials do not contribute to the mean forcewhich can therefore be computed from the first-order solution alone. Most existing solutions arebased either on the strip theory of Salvesen, Tuck & Faltinsen [12] or on 3D Boundary ElementMethods (BEMs).At zero forward speed, the added resistance (or drift force) can be robustly computed using3D panel methods and either near-field pressure integration or far-field momentum conservation.However, much finer resolutions are required to show convergence for drift forces than are necessaryfor strictly linear quantities, at least when using near-field pressure integration methods. Anexample is shown in Figure 1 which shows the convergence of the drift force on a Wigley hullcomputed using the 3D BEM code WAMIT [8] and both near-field pressure integration and far-field momentum conservation. Here quantities have been non-dimensionalized using the fluiddensity ρ, the gravitational acceleration constant g, the ship length L and beam B, and theincident wave length λ and amplitude A. These results have been computed using the low-order(constant-strength flat panel) version of the code and N indicates the total number of panels onthe hull. From this plot it is clear that the two methods are converging towards the same result0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 200.511.522.533.54  WAMITSalvesenG−Bλ/LCw=LRw/ρgA2B20 0.5 1 1.5 2 2.5 3024681012  Salvesen, U=15 knG−B, U=15Salvesen, U=10G−B, U=10Salvesen, U=5G−B, U=5λ/LCw=LRw/ρgA2B2Figure 2: Added resistance calculations for a tanker hull at various forward speeds using striptheory methods.for all relative wave lengths, but the momentum conservation method does so much faster thanthe pressure integration method.At non-zero forward speed the situation is less satisfying. Two methods are widely appliedto strip theory calculations: Salvesen’s method based on near-field pressure integration [11]; andthe energy conservation method first suggested by Gerritsma & Beukelmann [4]. Figure 2 showsan example of some converged strip theory calculations for a modern tanker hull at U = 0, 5, 10and 15 knots calculated using these two methods. WAMIT results for U = 0 are also shown forreference. Clearly both methods fail completely when U = 0, which is not surprising since themain assumptions of strip theory are violated in this case. At non-zero forward speed, there is goodagreement between the methods for where the peak response lies but the predicted magnitude ofthe force differs dramatically for all but the longest waves and can be almost a factor of two nearthe peak.3D BEM methods are also available for computing added resistance at forward speed; basedeither on the time-domain free-surface Green function e.g. [6, 1] or on the Rankine Green functione.g. [7, 5]. These calculations show a reasonable agreement with experiments in the sense thatuncertainties in the measurements can easily be a factor of two or more; but convergence of thecalculations has so far not been demonstrated. Presumably the quadratic scaling of the solutioneffort with increasing resolution associated with BEM methods prevents a true demonstration ofconvergence for this sensitive quantity.A High-Order Finite Difference Method for Added ResistanceBuilding on ongoing work discussed in [9, 10, 3, 2] we are developing a high-order finite differ-ence solver for the linear forward speed problem, using both Neumann-Kelvin and double-bodylinearizations, which will also give predictions of added resistance. Due to the combination ofhigh-order numerical accuracy and a linear scaling of the solution effort with increasing reso-lution, we hope to be able to show convergence for both pressure integration and momentumconservation methods. At this point we have validated the double-body flow solution and arecurrently implementing the radiation and diffraction solutions. Figure 3 shows the convergence ofthe double-body m-terms on a translating hemisphere along with a snapshot of the double-bodysurface elevation. The slopes of these convergence curves are approximately 4, consistent with theFigure 3: Convergence of the double-bodym-terms on a sphere and a snapshot of the double-bodyfree-surface elevation.fourth-order finite-difference schemes used in this test case. Further results will be presented atthe workshop.References[1] H. B. Bingham, F. T. Korsmeyer, and J. N. Newman. Predicting the seakeeping character-istics of ships. In 20th Symp. on Naval Hydrodynamics, Santa Barbara, Ca, 1994. Office ofNaval Res.[2] H. B. Bingham and H. Zhang. On the accuracy of finite difference solutions for nonlinearwater waves. J. Engineering Math., 58:211–228, 2007.[3] A. P. Engsig-Karup, H. B. Bingham, and O. Lindberg. An efficient flexible-order model for3D nonlinear water waves. J. Comput. Phys., 228:2100–2118, 2009.[4] J. Gerritsma and W. Beukelman. Analysis of the resistance increase in waves of a fast cargoship. Technical Report 334, Shipbuilding laboratory, Technological University - Delft, Delft,The Netherlands, 1971.[5] S. A. Joncquez, P. Andersen, and H. B. Bingham. A comparison of methods for computingthe added resistance. J. Ship Res., 56(2):106–119, 2012.[6] F. Kara. Time domain prediction of added resistance of ships. J. Ship Res., 55(3):163–184,2011.[7] K.-H. Kim and Y. Kim. Numerical study on added resistance of ships by using a time-domainrankine panel method. Ocean Engineering, 38:1357–1367, 2011.[8] J. N. Newman and C.-H. Lee. WAMIT; A radiation-diffraction panel program for wave-bodyinteractions. WAMIT, Inc, Chestnut Hill, MA, U.S.A, 2009. http://www.wamit.com.[9] R. Read and H. B. Bingham. An overset grid approach to linear wave-structure interaction.In 31stIntl. Conf. on Offshore Mech. and Arctic Eng., Rio di Janiero, Brazil, 2012.[10] R. Read and H. B. Bingham. Solving the linear radiation problem using a volume methodon an overset grid. In 27thIntl. Wrkshp. Water Waves and Floating Bodies, Copenhagen,Denmark, 2012.[11] N. Salvesen. Added resistance of ships in waves. J. Hydronautics, 12(1):21–34, 1978.[12] N. Salvesen, E. O. Tuck, and O. Faltinsen. Ship motions and sea loads. Soc. Nav. Arch. Mar.Eng., Trans., 78:250–287, 1970.

A note on added resistance for slow ships

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A note on added resistance for slow ships

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