Reliable collision-risk warning during low-speed ship docking requires accurate and efficient hydrodynamic prediction. This study develops a physics-SVR (support vector regression) framework combining a three-degree-of-freedom maneuvering model with three SVR models that learn residuals in longitudinal force, lateral force, and yaw moment from computational fluid dynamics (CFD) data. The corrected loads support 120 s trajectory prediction and hull-envelope reconstruction. Minimum lateral and longitudinal clearances and their times to safety-threshold crossing distinguish normal, warning-alert, and emergency-alarm states. The database comprises 20 model-development conditions and three condition-level holdout tests representing unseen loading/draft, heading, and lateral-offset conditions. Across the holdout tests, overall relative errors decrease from 22.00–30.20% for the baseline model to 14.91–19.93%. In two hazardous cases, warning alerts precede contact by 154.9 and 172.09 s, while the non-hazardous control case triggers no alarm. The complete prediction-and-warning update requires 0.32 s on average, demonstrating potential for shore-based docking assistance under calm-water conditions.

This paper presents an investigation on steady motion of three-dimensional submerged bodies in water beneath an ice sheet. The detailed derivation of the Green's function for steady flow with ice cover is first provided, and its validity is confirmed through computations involving a moving point source and the ice deflection it produces. Then, based on the Green's function, a boundary element method, in conjunction with the corresponding numerical program, is established to evaluate the wave-making resistance and wave propagation on the ice cover. The results show that for the ice thickness tending to zero, the present computations are in close agreement with those obtained from free-surface Green's function method, as reported in the published literature. But as the ice thickness increases, the hydrodynamic performance with ice cover shows a significant difference. There exists a critical speed associated with ice parameters, below which the wave resistance on the submerged body is always equal to zero and the generated waves cannot propagate to infinity. Above the speed, additional waves are found to propagate upstream, along with those traveling downstream, which leads to a larger wave resistance in comparison to the open water. Comprehensive research and analysis are conducted on submerged bodies at various forward speeds, ice thicknesses, and submerged depths. Within the calculated range, it is revealed that the wave resistance and the wave amplitude increase as the submerged depth decreases or the ice sheet gets thicker at speeds exceeding the critical value.

The paper demonstrates a hybrid Green function method for investigating wave loads acting on a structure floating in polynya enclosed by an ice sheet. A vertically virtual surface, stretching from the ice edge to the seabed, is designated as the control surface to divide fluid domain into two subdomains. In the interior polynya with a free surface, an upper surface condition for diffraction potential is derived, and the simple Rankine source is employed to construct boundary integro-differential equation (BIE) over free surface, body surface and control surface. On the other hand, in the exterior fluid domain beneath ice, the Green function, which inherently satisfies ice-covered water surface, radiation and seabed conditions, is adopted. So the corresponding integro-differential equation is only imposed over vertically virtual surface. Interior and exterior BIEs are discretized and solved simultaneously through implementing the continuity condition between the two subdomains. In this solution, analytical and semi-analytical schemes are utilized to determine influence coefficients related to Rankine source and ice-covered Green function. Numerical simulations are carried out for the wave loads on a submerged sphere as well as a FPSO floating in polynya, and the effects of ice thickness and water depth are analyzed. The good concordance with available published results indicates that our developed approach is reliable for investigating wave interactions with structures in polynya.

The unwetted height E-dry, characterized by free-surface depression directly aft of the transom stern, is apparently affected by the intricate bubble flow observed within the transom-draft Froude numbers 1.3 < E-T < 1.7. To exclude measurement uncertainties caused by these multiphase flow interactions, the data corresponding to E-dry within this Froude range is omitted from subsequent analysis. Subsequently, a refined regression model for unwetted height prediction is developed to address this limitation. The proposed formulation improves the accuracy of total resistance predictions based on the Neumann-Michell potential flow theory, especially at low Froude numbers (E-T <1.3). Additionally, a novel methodology is proposed to analyze the wave pattern, explicitly accounting for the nonlinear effects of the free-surface hollow. This approach reveals that stern ship waves are predominantly governed by free-surface potential in the present case, which is directly influenced by the geometry of the hollow.

The estimation of a ship’s displacement volume, ∇, from remote sensing data is of considerable practical value for maritime surveillance and vessel characterization. This paper introduces a practical framework for the inverse estimation of displacement volume from Kelvin ship waves, building upon a prior study through two key extensions. First, the wave amplitude function is recovered using Fourier series expansions combined with the stationary phase method. The displacement volume is then estimated via a two-step procedure: an initial estimate is obtained by identifying a hull with similar amplitude characteristics from a database, followed by a refinement that incorporates discrepancies between the target and candidate wave amplitude functions. In the case studied, the proposed approach achieves a prediction error of 4.02%, demonstrating its potential for non-invasive extraction of hull information from remote sensing data.

A multi-domain boundary element method (BEM) is originally proposed to address hydrodynamic challenges associated with a structure floating in a polynya. This approach utilizes a control surface vertically extended from the interface of polynya and ice cover to seabed to separate entire fluid domain into two subregions. Ice-covered Green's function is adopted to establish boundary integral equation (BIE) in the outer region beneath ice sheet. And to enhance computational stability and efficiency, a semi-analytical scheme based on vertical line source distributing over vertical control surface is formulated to evaluate corresponding influence coefficients. Within inner polynya region, free-surface Green's function is employed, so BIE is merely imposed on structure and control surfaces. By discretizing the integral boundaries into a series of panels and enforcing the continuous conditions between the ice-covered and polynya regions, a coupled system of equations is formulated to solve velocity potentials on fluid domain boundaries of polynya. The efficacy of the multi-domain BEM is verified through calculations involving hydrodynamic coefficients of a cylinder structure that is submerged in the polynya, considering scenarios of negligible ice thickness as well as very small ice thicknesses. Then based on the multi-domain BEM, an extensive array of results and analyses are presented for a realistic offshore structure FPSO operating in polynya. Various configurations involving differing ice thicknesses, water depths and body drafts are thoroughly investigated.

An extension of the Neumann–Michell theory is given here — a more practical and efficient numerical approach is proposed , which only relates with the flow potential (instead of the related derivatives) and the related coefficients do not need to be updated repetitively during the iterative computations. A practical method is subsequently proposed to decompose the ship waves into the local, transverse or divergent wave components. The near-field ship waves along the ship hull and its effects of the wave interference on the wavelength, the wave drag and the hydrodynamic pressure are then considered. Clear relations between the near-field wavelength of the transverse or divergent ship waves and the Froude number are found, and the unfavorable or favorable interference relations in the near-field are given, which can predict the peaks or valleys of the wave drag more reasonable than the traditional far-field wave interference relations. Moreover, the effects of the transverse wave interference in the near-field is found more important than it conventionally believed, and it could be partially cancelled out by the wave interference of the divergent ship waves around the ship hull.

A practical decomposition of the pressure drag for the transom-stern monohull ships is proposed here, where the pressure drag is decomposed into four different components, including the hydrodynamic drags CS∗, CTS∗ for the side surface or the wetted transom-stern surface, the hydrostatic drags CTSdry, CTSwet for the unwetted or wetted transom-stern surface. The influence of the transom-stern on these drag components are researched here, and practical approaches to predict these drag components are subsequently proposed. This research finds that accurately predicting the unwetted height ηdry at low Froude numbers, which is usually thought unimportant in the conventional researches, is actually important for the drag prediction.

This study examines the impact of the ship’s principal dimensions on the steady waves generated by the ship, and practical approaches are subsequently proposed to reverse-predict the ship’s length, width, draught, and related parameters. The ship length Ls and the related Froude number Fr=Vs/gLs are found to relate with the quasi-period of the divergent wave amplitude function. The ship length can be predicted within an accuracy of ±5% overall based on the two-point wake model considered here. The effects of the ship width and the ship draught are different, and a practical method is proposed here to predict the ship width and the ship draught based on the simplification of the Hogner theory. A noteworthy discovery of this research is that the hull form details have a more pronounced impact on the trough of the divergent waves compared to the transverse waves and the peaks of the divergent waves.

This paper proposes the modification of the propulsion system of the surface ship ONRT and the optimization strategy for the stern propulsion system of the modified ship. Specifically, this paper proposes a blade design scheme of a semi-elliptical projection profile with zero skew, zero rake, and equal pitch. An in-house code for autonomous three-dimensional reconstruction is employed to recreate the thruster. Next, a presentation of the ship's propeller optimization design process based on the CAD, CFD, DOE, and Optimization frameworks ensues. In this approach, four surrogate models are applied. The study also performs optimization research and examines the optimization approach for updated designs. The results demonstrate that the Kriging surrogate model provides more accurate and reliable predictions. Compared with the original model, the total resistance of the optimized modified design is reduced by 23.99 %, and the power of the single thruster is reduced by 3.35 %. In addition, the volume occupied by the modified design is only 44% that of the original model. The results of this paper provide effective technical support for the optimization and upgrading of the shaftless rim-driven system of surface ships.

The wave interference and the corresponding effects on the wave drag of the leader–follower ship fleet are researched here, via a 4-point model and the Neumann-Michell potential flow computation. A simple analytical relation of the dominant wake angle is given, which considers both the wave interferences between the ship bow and the stern, and the wave interferences between the leader ship and the follower ship. Moreover, a simple relation of the destructive interference region (where the wave drag of the follower ship decreases) for the wave drag is given based on the research on the effects of the ship distance ℓ2 and the Froude number F on the wave drag of the leader ship or the follower ship. An interesting finding is that the destructive interference relation is invalid at low Froude numbers or very high Froude numbers, since the constructive interference of the divergent waves is apparent at low Froude numbers and the transverse waves is relatively small at high Froude numbers. These findings can be used to decrease the wave drag of ship fleets or ship formations.

A magnetic lead screw (MLS) is a device that can help a wave energy converter (WEC) to transform the low-speed linear wave motion into high-speed rotary motion with no frictional contact. However, the dynamic performance of the MLS is insufficient because only the permanent magnet (PM) is used to couple the magnetic field between the rotor and mover. To improve the dynamic performance of the MLS, a novel structure of an electromagnetic lead screw (EMLS) for the application of a WEC is proposed in this paper. In the proposed EMLS, a helical-shaped PM is mounted on the inner side of the rotor, which is as same as the traditional MLS. However, helical-shaped slots are grooved on the surface of the mover, and two-phase helical-shaped AC winding is placed in these slots to generate the controlled helical-shaped magnetic field. In this paper, the topology and the operating theory are introduced firstly. Then, the three- and its corresponding two-dimensional axis-symmetric finite element analysis model is developed to analyze the performance of the proposed EMLS. Moreover, the design aspects are presented for the realization of the proposed EMLS. Then, the performance of the proposed EMLS is compared with that of the traditional EMLS. From the results, the proposed EMLS shows larger maximum thrust force than the traditional one. Finally, the potential use value and applications in WECs of the proposed EMLS are mentioned.

The Fourier–Kochin representation of the oscillatory part of the flow pressure at the hull surface of a ship that travels at a constant speed in calm water of large depth – and the related Fourier–Kochin representations of the wave drag, hydrodynamic lift and pitch-moment experienced by the ship – are considered within the framework of the potential flow theory based on the Green function that satisfies the Kelvin–Michell linear boundary condition at the free surface. The convergence of the Fourier integrals in these Fourier–Kochin representations of the flow pressure, the wave drag, the lift and the pitch-moment are studied via a parametric numerical analysis, based on Hogner’s approximate theory, for two families of 120 simple ship models at Froude numbers F within the range 0.15≤F≤2. The analysis shows that the cutoff wavelength λ∞ associated with negligible short waves is significantly influenced by the Froude number and the hull shape, and yields an analytical relation that explicitly determines λ∞ in terms of F and three major hull-shape parameters: beam/length ratio, draft/length ratio, and (nondimensional) bow or midship lengths.

The classical Neumann–Kelvin (NK) linear potential flow theory of ship waves in calm water and the related Neumann–Michell (NM) theory are considered. Five alternative boundary integral representations are given: (1) the classical NK integro-differential representation, called “classical NK formulation”, which corresponds to an inconsistent linear flow model, (2) a modification of the classical NK flow formulation that corresponds to a consistent linear flow model and is called “consistent NK formulation”, (3) a flow representation, called “NM potential and velocity formulation”, that involves the flow potential ϕ and the velocity components ϕd and ϕt along two unit vectors d and t tangent to the ship hull surface, and yields an integro-differential equation for determining ϕ, (4) a flow representation, called “NM velocity formulation”, that only involves ϕd and ϕt and yields a pair of coupled integral equations for determining (ϕd,ϕt), and (5) a flow representation called “NM potential formulation” that only involves the flow potential ϕ and yields an integral equation for determining ϕ. The two NK formulations involve both a surface integral over the ship hull surface and a line integral around the ship waterline, whereas the three NM formulations do not involve a waterline integral. All flow representations other than the classical NK representation are based on a consistent linear flow model.

The Neumann–Michell (NM) theory – a practical linear potential flow theory – is applied to four freely-floating ship models (Wigley, S60, DTMB5415, KCS), assumed to advance at a constant speed in calm water of large depth, to investigate nonlinear effects on the wave drag, the sinkage, the trim, and the wave profile along the hull, and to approximately account for these effects via simple corrections of the linear theory. Nonlinear effects are found to be relatively small. However, an important exception to this general finding is that the wave drag of a bulbous ship (DTMB5415, KCS) is greatly reduced due to the nonlinear component of the pressure in the Bernoulli relation. This important nonlinear effect is readily included in the NM theory. The nonlinear component of the pressure in the Bernoulli relation also yields a small increase of the sinkage, likewise readily included in the NM theory. Moreover, free-surface nonlinearities can have appreciable, although not large, effects on the wave profile. These nonlinear effects can also be approximately taken into account via a simple transformation of the linear wave profile. Indeed, the flow computations for the four ship models considered here suggest that simple (post-processing) nonlinear corrections (that require no additional flow computations) of the NM theory yield numerical predictions of the wave drag, the sinkage, the trim and the wave profile that agree well with experimental measurements, and compare favorably with predictions given by more complex computational methods.

Numerical simulations of free roll decay are carried out for the DTMB 5512 based on computational fluid dynamics (CFD) theory and adoption of overset mesh technology. The numerical time history of the ship roll shows good quantitative agreement with the experimental time history in the case of Fr = 0.138 with an angle of list of theta(a0) =10 degrees. The natural period is well estimated, there is less than 2% error. According to the time history of the roll angle and the corresponding angular velocity, the nonlinear ship roll damping and restoring force of the hull are identified by solving the nonlinear Volterra integral equation of the first kind with Tikhonov's regularization method. The results indicate that the numerical method in the paper is feasible, and the choice of regularization parameter is proper. Additionally, the influences of angle of list, model scale and ship speed on free roll decay are investigated. Roll damping and nonlinear restoring force increase as model scale decreases. Keeping the same scale of ship model, roll damping increases with ship speed while nonlinear restoring force decreases.

The far-field waves, and the related far-field wave drag, predicted by the Michell or Hogner theories are considered. These two classical theories are found to predict nearly identical transverse waves for all practical cases. However, the Michell and Hogner models predict divergent-waves dominant at high Froude numbers-that can differ significantly. Differences between the far-field waves predicted by the Michell and Hogner models are much smaller for catamarans, for which lateral interferences between the twin hulls overwhelm lateral interferences between the port and starboard sides of the hulls, than for monohull ships. Moreover, differences between the divergent waves predicted by the Michell and Hogner theories are larger for higher Froude numbers, bigger beam/length ratios, smaller draft/length ratios, or larger separation distances between the twin hulls of a catamaran. (C) 2017 Elsevier Ltd. All rights reserved.

A practical method to account for the influence of sinkage and trim on the drag of a freely floating (free to sink and trim) common monohull ship at a Froude number F≤0.45 is considered. The sinkage and the trim are estimated via two alternative simple methods, considered previously. The drag is also estimated in a simple way, based on the classical Froude decomposition into viscous and wave components. Specifically, well-known semiempirical expressions for the friction drag, the viscous pressure drag and the drag due to hull roughness are used, and the wave drag is evaluated via a practical linear potential flow method. This simple approach can be used for ship models as well as full-scale ships with smooth or rough hull surfaces, and is well suited for early ship design and optimization. The method considered here to determine the sinkage and the trim, and their influence on the drag, yields theoretical predictions of the drag of the Wigley, S60 and DTMB5415 hulls that are much closer to experimental measurements than the corresponding predictions for the hull surfaces of the ships in equilibrium position at rest. These numerical results suggest that sinkage and trim effects, significant at Froude numbers 0.25<F, on the drag of a typical freely floating monohull ship can be realistically accounted for in a practical manner that only requires simple potential flow computations without iterative computations for a sequence of hull positions.

A practical method well suited for early ship design and hull form optimization for estimating the sinkage, the trim and the drag of a freely-floating common monohull ship at moderate Froude numbers F <= 0.45 is considered. The sinkage and the trim are realistically estimated via two alternative simple methods: an experimental approach based on an analysis of experimental measurements (involving no flow computations), and a numerical approach based on a practical linear potential-flow theory (the Neumann-Michell theory) that only requires simple flow computations for the hull surface Sigma(H)(0) of the ship at rest. The drag is also estimated in a simple way, based on the classical Froude decomposition into viscous and wave components: well-known semi empirical expressions for the friction drag, the viscous drag and the drag due to hull roughness are used, and the wave drag is evaluated via the Neumann-Michell theory. The drag is more sensitive to the hull position than the sinkage and the trim. Accordingly, it must be computed for a 'dynamic' ship hull surface Sigma(H)(st) that accounts for sinkage and trim effects, although the hull surface Sigma(H)(st) does not need to be very precise. In fact, the total drag computed for the hull surface Sigma(H)(st) chosen as the hull surface qi predicted by the numerical approach, or as the hull surface Sigma(H)(alpha) predicted by the even simpler experimental approach, are nearly identical. Moreover, the drag of the hull surface Sigma(H)(1) and the (nearly identical) drag of the hull surface Sigma(H)(alpha) are significantly higher, and also in much better agreement with experimental measurements, than the drag of the hull surface Sigma(H)(0) of the ship at rest at high Froude numbers.

Highlights and main conclusions • At high Froude numbers, constructive interference among the divergent waves created by sources and sinks distributed over the hull surface of a monohull ship, or a catamaran, steadily advancing in calm water of large depth results in highest waves along ray angles located inside the cusps of the Kelvin wake. • These highest waves are much shorter than the transverse and divergent waves along the cusps of the wake. E.g., for Froude numbers 1.5 < F , the waves along the cusps of the Kelvin wake of a ship are more than ten times longer than the highest waves created by the ship. • The highest waves created by a fast ship are also significantly shorter than the ship length. E.g., the wavelength of the highest waves created by a catamaran is equal to the distance between the twin bows of the catamaran if 1 < F . • The ray angles of the highest ship waves are only weakly influenced by the hull shape. Similarly, the wavelength of the highest waves is not significantly affected by the hull shape. Thus, the location (ray angle) and the wavelength of the highest ship waves mostly are kinematic flow features. • The ray angles where the highest-waves are found, and the corresponding wavelengths, are determined via simple analytical relations in terms of the Froude number and, for a catamaran, the distance between the twin bows of the catamaran. These relations hold for all monohull ships and catamarans. • These general results about the highest waves created by a fast ship widely expand the classical results about far-field ship waves obtained by Kelvin in 1887 for a ship modeled as a one-point wavemaker.