Ship Wave Resistance Research Articles

The study of float wave formation for the usage as heavy-duty catamaran bulbs

The large cargo catamaran ferries can increase speed freight transportation on inland waterways. However, an increase of vessel's speed entails the growth in the heights of ship waves when the ship, which in turn adversely affects both the hydrodynamic characteristics of the ship itself, enhances wave impacts on the catamaran bridge and the ecological state of water bodies. According some scientific articles one way to reduce wave resistance of large catamarans may be deployment а a float-bulb between it hulls. Ship's wave and wave resistance depend on the shape of the float-bulb, so it is advisable to study the parameters of the waves formed first on the bulb in free flow, and then together with the catamaran. In this paper presents analytical equations for the resistance of the "float-catamaran complex", as well as formulas that also allow one to calculate the main parameters of the float-bulb. The results of numerical simulation are presented for the three ellipsoid's length: 29,2m (Fr=0,414-0,691), 14,6m (Fr=0,585-0,978) and 7,3m (Fr=0,827-1,383), ball d=1,76m (Fr=1,685-2,816). The characteristics of the generated ship waves is determined. Conclusions about the feasibility of modifying the float-bulb shape for heavy catamarans is given.

Sampling method for hull form optimization based on the morphing method and its application

The intelligent optimization algorithm has been widely used in hull form optimization. The sampling method (SM) provides information on the optimization space in the initial stage, which can determine the accuracy and efficiency of the optimization algorithm. Hull form transformation methods determine the features of the optimization space, and the SM should fit the optimization space. Most optimization space is cubic space, although a unique type of space is observed, and it is unsuitable for most SMs, such as Latin hypercube sampling (LHS) and uniform design (UD). This paper proposes a special sampling method in simplex space (SMSS), which is different from cubic optimization space, for use with the morphing method (MM). This SM can provide uniformly distributed samples for hull form optimization based on the MM. The wave resistance of the 1300TEU container ship based on the MM is simulated to illustrate the efficiency of the SMSS.

Development of enhanced empirical-asymptotic approach for added resistance of ships in waves

This study aims to develop a practical and accurate prediction method for the added resistance of ships in regular wave conditions. To this end, the SNU formula proposed by Yang et al. (2018a) is enhanced for the diffraction-induced added resistance of ships in short waves with arbitrary wave headings. Notably, the SNU formula is simplified without loss of accuracy for its application in practical problems. Radiation-induced added resistance in long waves is predicted using the SNNM formula proposed by Liu and Papanikolaou (2016, 2020), and Wang et al. (2021). The two formulas are combined with a proper blending function. To validate the developed method, various tank-test data of existing ship models are collected, and a systematic comparative study including statistical analysis is performed. In particular, the accuracy of the developed numerical method is discussed considering the effects of ship speed and wave heading angle. Based on the present study, the reliability and fidelity of the proposed enhanced method are expressed by considering a variety of physics of added resistance.

Improvement of the prediction of the added resistance in waves of ships with extreme main dimensional ratios through numerical experiments

After a decade of development, the semi-empirical SNNM (SHOPERA-NTUA-NTU-MARIC) method for the prediction of the added resistance of ships in waves (Liu & Papanikolaou, 2020) was successfully developed and is being widely used by the maritime industry (IMO, 2021; ITTC, 2021). The method is herein updated by use of numerical simulations for the consideration of ships with extreme dimensional ratios, for which experimental data are scarce or non-existent. Numerical experiments are designed to investigate the joint effect of the variation of CB, L/B, and B/T using well-established numerical tools for the added resistance in waves. The patterns observed in the results are then correlated to the parameters through explicit, readily useable mathematical expressions. The improved formula is benchmarked with an experimental database of 11 ships with extreme dimensional ratios of various types. The validation study shows that the improved formula achieved a higher correlation coefficient and a smaller mean percentage error. Thus, the introduced expressions can significantly improve the prediction of the added resistance of various types of ships in waves, including those with extreme dimensional ratios. This study demonstrates how to combine the merits of both numerical and physical experiments to gain insight into complex physical problems.

Towards the uncertainty quantification of semi-empirical formulas applied to the added resistance of ships in waves of arbitrary heading

The present paper examines a semi-empirical framework for the estimation of added resistance in arbitrary wave heading under consideration of uncertainty quantification. In this respect, the calibration of the formula’s parameter vector is conducted based on particle swarm optimization as well as a database of model test results comprising 25 different ships and around 1100 samples. In the first iteration, the minimization of reducible systematic uncertainty is of interest and the effect of four objective functions on prediction accuracy is evaluated. Moreover, two different parameter combinations were obtained for blunt (CB≥0.70) and slender-type ships. Conversely, the irreducible statistical uncertainty, i.e. the inherent noise of the experimental data, is taken into account by a quantile regression procedure. Applying this approach, a 90% prediction interval for the formula’s estimates is implemented using the skewed version of the superior loss function in the previous iteration. The practical relevance of an uncertainty estimate for the prediction of the added resistance is emphasized in the final part, in which the proposed approach is validated in regular waves against model test data and other well-established prediction methods. In general, the validation studies suggest satisfactory performance and reliability of the adapted semi-empirical formulation.

A DFN-based method for fast prediction of ships' added resistance in heading waves

The added resistance of ships in waves has been of great concern in recent years. In some engineering scenarios, rapid prediction of ships' added resistance is required. In this study, given the complexity of developing semi-empirical formulas and the small learning capacity of single hidden layer artificial neural networks, a method based on deep feedforward neural networks (DFNs) for fast prediction of ships' added resistance in heading waves is proposed. The proposed DFN-based method takes into account the particularity of added resistance prediction and makes innovations and optimizations in input vector parameters, the design of the input layer, the number of hidden layers, and the activation function of the output layer. A DFN-based model based on the proposed method, called DFN-AW, is constructed, achieving satisfactory results. Furthermore, the prediction accuracy of the DFN-AW model is better than generic DFN models, which proves the feasibility and advantage of the proposed method. Finally, the generalization ability of the DFN-AW model on new ships and speeds is investigated.

Investigation into the direct calculation of added wave resistance of ship in forward motion with reflection ratio correction

Affected by the minimum power assessment requirements of the newbuilding energy efficiency design index (EEDI), added resistance of ships navigating in waves has been attracted more and more attention. By using the Green's function of three-dimensional translating pulsating source (3DTP), radiation/diffraction problems and ship motions are solved and good results are obtained. Based on these, the three-dimensional (3D) scattered energy approach to evaluate added wave resistance is proposed, which is combined with the radiated energy method and the Salvesen's weakly scattering assumption. It is reported in previous studies the computed added wave resistance is in reasonable agreement with experiment results on fine ship in medium wavelength waves. But for short-waves, the direct calculation cannot give precise result due to the limitation of the theory assumption. It is also question for long-waves case. A semi-empirical formula is proposed to correct the added wave resistance due to diffraction in short-waves. Considering the reflection attenuate phenomenon of waves with various wave length, a new approach with reflection ratio correction is hired in the formula. Finally, the modified formula is achieved that can be applied to directly calculate ship advancing in waves of various wavelength or full frequency range. With the comparison of calculation and model test results, the new correction method is verified and validated. It is also proved it fits not only for fine ship, but also for large blunt ship.

Salvesen’s Method for Added Resistance Revisited

Abstract Almost 4 years after the appearance of Salvesen–Tuck–Faltinsen (STF) strip theory (Salvesen et al., 1970, “Ship Motions and Sea Loads,” Annual Meeting of the Society of Naval Architecture and Marine Engineers (SNAME), New York, Nov. 12–13), Salvesen in 1974 published his popular method for calculation of added resistance (Salvesen, 1974, “Second-Order Steady State Forces and Moments on Surface Ships in Oblique Regular Waves,” Vol. 22; Salvesen, 1978, “Added Resistance of Ships in Waves,” J. Hydronautics, 12(1), pp. 24–34). His method is based on an exact near-field formulation; however, he applied the long-wave and the weak-scatterer assumptions to present his approximate method using the integrated quantities (hydrodynamic and geometrical coefficients). Considering the available computational powers in the 1970s, both of these assumptions were absolutely justifiable. The intention of this paper is to disseminate the results of a recent study at the Technical University of Denmark, whereby the Salvesen’s formulation has been revisited and the added resistance is computed from the original exact equation without invoking the weak-scatterer or the long-wave assumptions. This is performed using the solutions of the radiation and the scattering problems, obtained by a low-order boundary element method and the two-dimensional free-surface Green function inside our in-house STF theory implementation (Bingham and Amini-Afshar, 2020, DTU_Strip Theory Solver). The weak-scatterer assumption is then removed through a direct calculation of the x-derivatives of the velocity potentials and the normal vectors along the body. Knowing the velocity potentials over each panel, the long-wave assumption is also avoided by a piece-wise analytical integration of sectional Kochin Function (Kochin, 1936, “On the Wave Resistance and Lift of Bodies Submerged in Fluid,” Transactions of the Conference on the Theory of Wave Resistance, Moscow.). The presented results for five ship geometries testify that the correct treatment of the original equation is achieved only after both of the above-mentioned assumptions are removed. Implemented in this manner, Salvesen’s method proves to be relatively more accurate and robust than has been generally perceived during all these years.

Анализ волновых полей свободной поверхности воды от движущейся пластины, пары последовательно расположенных стоек и обсуждение возможных составляющих их волнового сопротивления

The paper presents and compares photographs of wave patterns from a moving plate with pointed and full ends, from which, with the exception of a cylindrical insert, there develops a post with a teardrop-shaped cross-section, as in a pair of tandem posts. The plate length equals to the overall size of the specified pair of consecutive posts. The conclusion is made about the possibility of selecting a unified wave resistance component from the total resistance, which can be determined experimentally based on the results of the study of a combination of individual posts and/or other objects of the specified shape. Possible variants of wave resistance components are being discussed. Besides, a variant of modeling the ship's wave resistance by representing two pairs of such wave systems rather than two Kelvin wave systems on a free surface is proposed. Additional fore and aft Kelvin wave systems are proposed to be shifted against the course of motion by half the wavelength. These additional wave systems are intended to describe internal intermediate waves located between the main transverse waves. There have been presented the expressions for wave resistance that contain some proportionality coefficients, possible components of wave resistance from smoothing diverging waves within the smoothing zone of wave structures, starting from the bow extremity and other unaccounted components of wave resistance. The photos proposed were taken in the experimental pool of Siberian State University of Water Transport (Novosibirsk State Academy of Water Transport) in 2006

횡단면선 위치 변화에 따른 여객선박의 선형 설계에 관한 연구

The purpose of this study is to investigate the interrelationship of how the ship's wave resistance performance changes with the change of the longitudinal position of the section line in the ship's lines, and to find a way to use it in the hull-form design. To this end, we developed a hull-form automatic change algorithm that can maintain the proper hull-form while moving the section lines in the longitudinal direction, and the computer program for a numerical analysis was developed to apply the developed algorithm. By applying the developed hull-form automatic change algorithm and the wave resistance performance prediction program, the numerical analysis package was constructed. The numerical analysis was carried out for the passenger ship. Numerical analyzes were carried out by moving the section lines of the passenger ship in the longitudinal direction, and the results were compared with each other. Based on the numerical results, we attempted to investigate the correlation between the section line movement and the wave resistance performance.

Environmental Aspects of Total Resistance of Container Ship in the North Atlantic

The total resistance of ship in waves is composed of calm water resistance and added resistance in waves. The added resistance in waves is one of the main causes of an involuntary speed reduction of a ship. It may cause a significant increase in ship resistance and consequently increased fuel consumption and CO2 emission, especially at heavier sea states. Thus, the added resistance is very important from both an economic and environmental point of view. In this paper, an increase in fuel consumption is calculated for container ship on a typical North Atlantic route. The calm water resistance is calculated utilizing Computational Fluid Dynamics (CFD) based on the viscous flow theory at model scale and the obtained results are extrapolated to full scale. The added resistance in waves is calculated using three-dimensional panel code based on the free surface Green function, for the sake of simplicity. It is calculated at regular waves and the mean value of the added resistance at certain sea states is obtained by means of spectral analysis. Two-parameter Bretschneider wave spectrum recommended for the North Atlantic, defined by significant wave height and zero crossing period, is used in the spectral analysis. The obtained results may provide valuable insight into important environmental issue of pollution reduction.

Numerical Study on Change of Added Resistance due to Incident Waves in Finite Water Depth

AbstractIn this study, the effect of water depth on vertical motion responses and added resistance of ships in waves was numerically examined. The applied numerical method corresponded to the time ...

A 3D multi-domain high order boundary element method to evaluate time domain motions and added resistance of ship in waves

A newly developed three dimensional multi-domain high order boundary element method (MDHOBEM) is applied to solve time domain ship motions in waves for ships advancing with forward speed, as well as the corresponding added wave resistances. By the method, fluid domain is decomposed by a regular control surface into inner and outer parts, in which Rankine panel method and transient Green function method are adopted respectively. By the MDHOBEM, the problem of highly oscillatory nature of transient Green function near waterline can be avoided due to substitution of Rankine source in inner domain. Fewer discrete quantities than in Rankine panel method is needed as transient Green function is employed in outer domain, and the radiation condition can be analytically satisfied as well. Boundary value problem of velocity potential is solved in a translational and inertial frame without use of moving mesh, implying it is a highly efficient approach. A mixed form of ship wave linearized or double body flow linearized free surface condition, and the according m-terms are employed in inner domain to treat the steady flow effects more accurately. The yielding hybrid boundary integral equations are discretized with bi-quadratic isoparametric high order elements to minimize discretization error.A Fortran code is originally developed, and is used to simulate wave-body interactions of both the wall-sided and flared hulls including mathematical Wigley-3 hull, Series60, and more realistic hull forms of KCS and S175. Convergence of spatial and temporal discretization, and size of inner domain are detailedly investigated beforehand. Results indicate the present numerical scheme has quite good robustness, and the inner free surface can be reduced to a rather small region comparing to Rankine panel method. The computed hydrodynamic coefficients, added wave resistance and ship motions by MDHOBEM are compared with model test data and results of classic boundary element methods including Rankine panel method, transient Green function method, and translating and pulsating Green function method. It manifests the MDHOBEM has quite good accuracy and needs less computational cost.

Solving Wave Flow Energy Propagated by Twin-Hull Ships (Catamarans)

The main objective of this paper is to put forward a method of solution of wave flow energy propagated by twin-hull ships utilizing ship wave resistance integral equation by Tuck-Lazauskas [8]. The underlying principle of the governing equation is based on the linear thin ship theory pioneered by Michell. The ship wave resistance integral equation by Tuck-Lazauskas is improvised in which the upper limit of the mathematical integration of the governing equation is set to the final root instead of π/2 as in the original equation to eliminate the problem of solving such a divergent improper integral. The method of solution and the theoretical results are validated against works of others experimentally and theoretically. The results obtained by the proposed method are found to be very consistent and more closely fit to the experimental results in comparison with those obtained by other theoretical method as presented in this paper.

Estimation of the drift forces and added resistance in waves of the KVLCC2 tanker

The present research explores different numerical techniques for the estimation of the drift forces, the yaw moment and the added resistance of ships in waves. The estimation of these forces and moment is of interest for a variety of marine engineering applications, including the numerical simulation of the maneuvering of ships in adverse weather conditions. The numerical tools to estimate these forces and moment herein are an in-house 3D panel code based on potential theory, namely NEWDRIFT and a CFD URANS commercial solver. Obtained numerical results for the KVLCC2 standard tanker ship are compared with available experimental data from the EU funded project SHOPERA. The paper critically assesses the potential of the employed numerical methods, while the obtained results are generally satisfactory for practical applications.

Selection and substantiation of the relative position of the central hull and outriggers for the trimaran ship

The relative position of the central hull and the outriggers of the ship with outriggers has been considered in this article. The volume of the outrigger as a part of the central hull volume, stagger and horizontal clearance are determined. The simplified optimization methods are used and the minimization of the wave resistance of the outrigger ship is taken as a criterion. In general, for determining the stagger and horizontal clearance, the stability of a damaged and non-damaged ship, buoyancy of a damaged ship, volumes, roll in beam waves and effects, connected with roll, course stability and also heave and pitch in head waves are taken into account. In this article, only the wave resistance, stability of a non-damaged ship and green water and slamming, connected with the roll in beam waves are numerically considered. Other factors are to be numerically analyzed later. According to the theoretical determination of the wave resistance and some another factors, the bow, middle and stern positions of the outriggers are compared. It is showed, that the bow and stern positions of outriggers are approximately equal to wave resistance. But, considering some other factors, the bow position of the outriggers is bed. Than, it is also shown that according to the wave resistance, the volume of the outrigger as a part of the central hull volume is not connected with the stagger. It is shown that the influence of the horizontal clearance on the wave resistance is small. So, the horizontal clearance is determined as a function of the stability of non-damaged ship, necessary volumes and effects, connected with roll in beam waves. The frequencies of slamming and green water, connected with the roll are also considered.

Numerical and Experimental Analysis of Added Resistance of Ships in Waves

Two Reynolds-Averaged Navier–Stokes (RANS) based field methods numerically predicted added resistance in regular head waves for a 14,000 TEU containership and a medium size cruise ship. Long and short waves of different frequencies were considered. Added resistance was decomposed into diffraction and radiation force components, whereby diffraction forces were obtained by restraining the ship in waves and radiation forces by prescribing the motions of the ship in calm water. In short waves, the diffraction part of total resistance was dominant as almost no ship motions were induced. In long waves, the sum of diffraction and radiation forces exceeded total resistance, i.e., the interaction of these two force components, which caused the reduction of total resistance, needed to be accounted for. Predictions were compared with model test measurements. Particular emphasis was placed on the following aspects: discretization errors, frictional resistance as part of total added resistance in waves, and diffraction and radiation components of added resistance in waves. Investigations comprised two steps, namely, a preliminary simulation to determine calm water resistance and a second simulation to compute total resistance in waves, always using the same grids. Added resistance was obtained by subtracting calm water resistance from total averaged wave resistance. When frictional resistance dominated over calm water resistance, which holds for nearly all conventional ships at moderate Froude numbers, high grid densities were required in the neighborhood surrounding the hull as well as prism cells on top of the model's surface.

An investigation into added resistance of vessels advancing in waves

The hydrodynamic forces and motions of ship advancing in waves are estimated by using 3D frequency domain potential flow theories. The 3D translating and pulsating (3DTP) source panel method is employed to solve the radiation and diffraction potential problems, in which a semi-analytical scheme is established to get more robust results of integration of Green's function over panels. Added wave resistance is mainly categorized into the contributions of radiation and diffraction. The added wave resistance due to radiation motion of ship is evaluated by the radiation energy principle according to 3D hydrodynamic coefficients and ship motions, while the one due to diffraction is calculated based on steady-state force formula. The motions and added wave resistances of Wigley III hull and S175 containership advancing in waves with various forward speed are calculated and analyzed in frequency domain based on the above mentioned methods. The numerical results are validated for the models by comparing them with experimental data. The results by classic methods commonly used in engineering and the data from published papers are plotted together for comparison and discussion. Better agreement with experimental data in the prediction of peak value and its frequency of added resistance is achieved by present method. It also indicates that the correction of relative motion amplitude should be taken into account so as to improve the accuracy. Component analyses of added wave resistance are carried out and the results show the percentages of radiation part and diffraction part at various frequency respectively. The present method is of satisfactory accuracy and efficiency, which provides a rapid and robust approach to predict added wave resistance of ships voyaging in waves.

On the prediction of the added resistance of large ships in representative seaways

ABSTRACTThe importance of the sufficiently accurate prediction of the added resistance and powering of large ships in representative seaways is discussed. We introduce an updated empirical formula that may be used by engineers for the fast estimation of the added resistance of ships in waves and validate this formula for ships with LPP > 250 m operating in realistic sea conditions. The importance of the accurate prediction of added resistance of large ships is demonstrated by numerical and experimental studies on both full and fine hull forms. It is shown that for large ships sailing in representative seaways, properly quantifying the spectral contribution of the added resistance in the region of λ/LPP ≈ 0.1∼0.5 is of paramount importance and further studies are necessary to resolve this issue for large ships. This also leads to a critical discussion about the ITTC recommended experimental procedure, when assessing the overall seakeeping performance of large size ships in representative seaways.

Added resistance of ships in waves†

Added resistance of ships in waves is determined by a newly developed potential flow method, a Rankine source method, a strip method, and by RANS (Reynolds-averaged Navier-Stokes) equations solvers. For 10 ships, results of all these methods are compared with each other, with published computed and experimental results, and with approximation formulae submitted to IMO (International Maritime Organisation). The focus is on waves that are short relative to ship length. In spite of the large scatter of results, existing prediction methods appear useful for practical application.