To meet the demand for efficient propulsion across a broad speed range, waterjet-propeller hybrid propulsion (WPHP) has emerged as a promising solution combining high propulsive efficiency with favorable cavitation performance under multi-speed operating conditions. This study proposes a sequential WPHP design methodology for a large high-speed displacement vessel, prioritizing propeller design for economical-speed operation, followed by adjustment of propeller rotational speed and pitch coupled with waterjet matching for high-speed conditions. A preliminary scheme with twin controllable-pitch propellers (CPPs) and twin waterjets was developed. RANS-based numerical methods, validated against model tests in the towing tank of the Science and Technology on Water Jet Propulsion Laboratory, were developed for performance prediction. Simulations determined multiple rotational speed combinations at the self-propulsion point under maximum-speed conditions (Fn = 0.428). Results indicate that overall propulsive efficiency peaks at a propeller thrust or power share of approximately 0.6. The total thrust deduction factor ranges from 0.055 to 0.073 across various rotational speed combinations, showing low sensitivity to load allocation. Nominal wake fractions of 0.0546–0.0583 exhibit slight variation with waterjet speeds.

This paper presents an optimization design method for wake-adapted propellers, combining the vortex lattice model based on lifting surface theory with a multi-objective genetic algorithm. By defining a comprehensive circulation variation index that characterizes the time-varying intensity of the pressure distributions on blade surfaces, and incorporating it alongside hydrodynamic efficiency and the pulsation amplitude of unsteady thrust as optimization objectives, a balanced optimization of multiple propeller performance metrics is achieved. The optimization is specifically conducted for a propeller operating in a nine-cycle wake, and the resulting performance improvements are validated by solving the unsteady Reynolds-Averaged Navier-Stokes equations. The findings indicate that the proposed circulation variation index is strongly correlated with the unsteady pressure distribution and can serve as an effective indirect measure of its quality. Additionally, it is observed that there may be a constraint relationship between the unsteady pressure distribution and thrust pulsation, suggesting that these factors need to be considered comprehensively during the design process. Ultimately, the optimized propeller demonstrates superior performance across all three metrics—hydrodynamic efficiency, unsteady thrust pulsation, and pressure distribution—compared to the original design.

A method is presented for optimizing the radial circulation distribution of the marine propeller operating in a radially non-uniform inflow. The optimum circulation distribution is obtained by searching a BPNN surrogate model with the PSO algorithm. The BPNN model establishes the nonlinear relationship between the radial circulation distribution and the thrust loading coefficient as well as the hydrodynamic efficiency. An in-house lifting-surface VLM code is employed to generate the performance data of sample propellers for the purpose of training, validating, and testing the surrogate model. The camber surface geometry and pitch distribution corresponding to the optimum circulation distribution are designed by the VLM-based method developed by the authors previously. Numerical examples are presented for a five-bladed propeller subject to a radially non-uniform inflow and a seven-bladed propeller in open water to assess the performance of the present design method, and the numerical validation results yielded from an in-house surface panel code indicate that the design requirements are fulfilled with reasonable accuracy. In addition, the effect of the hub on the optimum circulation distribution is investigated. (c) 2026 THE AUTHORS. Published by Elsevier B.V. on behalf of Shanghai Jiao Tong University. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

The Azimuth Waterjet Propulsor (AWP) is a special type of waterjet propulsor, which offers better adaptability to shallow water environments. Improved Delayed Detached Eddy Simulation (IDDES) is an enhanced hybrid numerical modeling method, which combines Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES). It leverages the advantages of both methods which can effectively simulate flow separation with relatively low computational resources. In this study, IDDES was employed to develop an unsteady numerical method for predicting the hydrodynamic performance of AWP, and the results are in good agreement with experimental values. The unsteady method was used to investigate the hydrodynamic performance, flow characteristics, entropy generation and pressure pulsation of the AWP at different water depths, and it was found that when the water depth is less than 0.53D, the hydrodynamic performance of AWP undergoes significant alteration, with increased losses inside and noticeable peaks of low-frequency components emerge in internal flow channel. When the water depth is less than 0.15D, the AWP flow rate decreases dramatically, inflow non-uniformity intensifies, and hydrodynamic performance deteriorates quickly, leading to enhanced indirect entropy generation caused by turbulence inside the AWP, and low-frequency components becomes dominant in internal flow field.

The tip-clearance flow in a pump-jet propulsor exerts great impacts on the fluctuating pressures and resultant unsteady forces, which are important sources of structural vibrations and radiated noise underwater. The blade geometry close to the tip is an important factor determining the vortex strength in the tip-clearance flow. In the open-water condition, the effects of raking the rotor tips on the duct-surface fluctuating pressures and the resultant unsteady forces acting on different components of the propulsor are investigated via physical model experiments and the numerical solution of Reynolds-averaged Navier-Stokes (RANS) equations coupled with the SST k - ω turbulence model. The measured and simulated results of hydrodynamic pressures are consistent to each other, and the simulated flows help better understand why the fluctuating pressures change with the tip geometry. The strong fluctuations of duct-surface pressures are caused by intensive tip separation vortices. The duct-surface pressure fluctuations are effectively reduced by using the rake distribution near the tip towards blade back side and, for the combination of the five-bladed rotor and the seven-bladed stator, the resultant unsteady horizontal (and vertical) forces acting on the duct and stator are also reduced; while increasing rake leads to negative effect on pressure fluctuations and unsteady horizontal (and vertical) forces acting on all the components of the propulsor.

Potential flow computations, based on a weakly singular integral equation, are considered in the infinite-gravity limit g=∞ and the zero-gravity limit g=0. The weakly singular integral equation, obtained via a straightforward and rigorous application of Green's basic identity, involves a distribution of weak dipoles that is continuous across the body surface. The integral equation is solved via a low-order panel method, which is validated for a half sphere and applied to the S60 ship model in translation along the x, y or z-axis. A systematic numerical analysis of the convergence of numerical predictions shows that the number of panels that is required to obtain a 0.1% accuracy is significantly different for the infinite-gravity or zero-gravity flows, and for translation of the S60 hull along the x, y or z-axis. In particular, a very large number of panels is required for translation of the S60 ship model along the horizontal x or y-axis in the zero-gravity limit.

在喷水推进器进口流道内外流场数值模拟的基础上,通过在Star CCM+软件中编制宏命令,在一条从获流区顶部中点发出的射线上用二分法取点,生成经过该点的流线,并判断其是否进入流道内部,逐次逼近止于喷水推进器进口唇口的流线,可快速、准确地确定获流区的边界,提高喷水推进器推力预报的精度.考察进口流道几何、来流条件等参数对获流区形状的影响,其中进速比、船底边界层的影响较大.

Wave diffraction-radiation by large bodies such as offshore structures and ships advancing in regular waves or in calm water is widely analyzed via panel methods based on a boundary integral flow representation and a Green function that satisfies the relevant free-surface boundary condition. The boundary integral flow representations solved in existing panel methods express the flow potential in terms of distributions of sources and dipoles, related to a Green function and its gradient, over the body surface. Other notable features of existing boundary integral flow representations are that they can be ill-posed for a set of irregular frequencies, and that – for a ship advancing in calm water or in regular waves – they involve a troublesome line integral around the ship waterline. Several alternative boundary integral flow representations that are well suited for wave diffraction-radiation by offshore structures or by ships advancing in regular waves or in calm water are given in this study. These representations, based on an alternative linear flow model (given previously) and an alternative vector Green function (not previously considered), are weakly singular and do not involve a waterline integral. The influence coefficients related to these new flow representations consist of Rankine components associated with complementary types of weakly singular Rankine singularities, and Fourier components defined by a Fourier superposition of elementary waves. Both the Rankine and Fourier components of the influence coefficients can be evaluated simply and efficiently. In particular, the Fourier component can be evaluated via the Fourier–Kochin (FK) method, in which the dominant computational task is independent of the number of panels that approximate the body surface. Thus, the new boundary integral flow representations given in this study and the FK method expounded previously provide a practical new basis for the evaluation of three main classes of wave diffraction-radiation by ships and offshore structures via panel methods.

The dominant computational task involved in the methods, widely called panel methods, currently used to compute 3D potential flows around large floating bodies such as ships and offshore structures (and other classes of dispersive waves such as flexural-gravity waves in very large floating structures or ice sheets) consists in evaluating N-2 coefficients, called influence coefficients. These coefficients are associated with the flows created by distributions of singularities (sources, dipoles) over the N panels that approximate the surface of the body (ship, offshore structure) at every panel of the body surface. In contrast to the O(N-2) computations required in existing panel methods, the dominant part of the computations of influence coefficients are independent of N in the Fourier-Kochin (FK) method if the Kochin functions in the FK flow representation are approximated by means of Fourier series and Chebyshev polynomials. The numerical analysis reported in this study shows that Fourier-Chebyshev approximations to the Kochin functions are feasible and indeed practical. In particular, the analysis shows that the number N-F of basic Fourier integrals (the major and most difficult computational task) that must be evaluated within the approach to the numerical implementation of the FK method considered in the study is given by N-F approximate to (600)(2), i.e. is smaller than N-2 if 600 < N. Thus, one has N-F << N-2 for typical panel numbers N = O(10(4)), and the FK approach opens the way for a class of panel methods in which the dominant computations are independent of the number N of panels instead of O(N-2) in existing panel methods. Another major advantageous feature of the FK method is that this approach circumvents the notorious difficulties involved in the numerical evaluation and the panel-surface-integration of the complicated Green functions associated with ship and offshore hydrodynamics.

Lifting-surface design methods are proposed for marine propellers based on genetic algorithms (GAs) and a two-layer back-propagation neural network (BPNN). For propellers with prescribed spanwise circulation distributions, the design problem is solved as GA-based optimization of camber surface geometry and pitch distribution which produce a circulation distribution to best fit the prescribed one. An in-house code based on the vortex lattice method (VLM) is employed to simulate circulation distribution and hydrodynamic performance of the propeller. Computer codes are developed in this research based on existing genetic algorithms, with a measure devised to accelerate convergence and improve the quality of solution. To optimize the spanwise circulation distribution, GAs are utilized again to explore the BPNN model established via the MATLAB toolbox and the in-house VLM code. Then the optimal circulation distribution is taken as the prescribed one for the GA-based design method mentioned above. Numerical tests are conducted to determine proper ranges of modeling parameters, such as the population size for GAs and the number of vortex lattices, and to assess the performance of the BPNN established. To numerically validate the proposed methods, viscous-flow simulation by solving the Reynolds-averaged Navier-Stokes equations is carried out for the propeller designed by using both methods mentioned above. The predicted pressure distributions over blade surfaces correlate consistently with the circulation distributions used to design the propeller, thus indicating that present design methods are effective and reasonably accurate.

Axial-flow pump is widely used in water-jet propulsion, and its hydrodynamic and cavitation performance have an important effect on the performance of the vessel. Therefore, the study of pump design is very important. In this work, a coupled viscous and potential flow three-dimensional design method for impeller of axial-flow pump with pre-swirl stator is developed. The body-force model (BFM) is used to solve the effective inflow field for impeller design by using a viscous Reynolds-averaged Navier-Stokes equations (RANS) commercial software, and the lifting-surface vortex lattice method (VLM) is used to design the impeller. The feasibility of the design scheme is verified by quasi-steady numerical simulation, and the uncertainty analysis of the numerical simulation is carried out according to the uncertainty analysis method recommended by International Towing Tank Conference (ITTC). The design and verification of axial flow pump are carried out in this paper, and the results show that the design method developed in this work is feasible. In addition, the cavitation performance can be improved by adjusting the load distribution reasonably.

This study considers the core issue of evaluating flows created by general distributions of sources and dipoles over panels (typically flat/curved triangles/quadrilaterals) used to approximate the surface of a body (ship or offshore structure) in usual implementations of the Green function and boundary integral method in marine hydrodynamics. This crucial basic issue is considered – within the framework of the Fourier–Kochin (FK) method – for four classes of flows in deep-water ship and offshore hydrodynamics: diffraction-radiation of regular waves by an offshore structure, and flow around a ship that advances at a constant speed V in calm water or in regular waves of (encounter) frequency ω in the regimes τ ≡ ω V / g < 1 / 4 or 0 . 3 ≤ τ where g is the acceleration of gravity; diffraction-radiation of regular waves by an offshore structure in water of uniform finite depth is also considered. Two notable features of the Green functions G used in the study of these five classes of flows are that (i) they are based on optimal decompositions into Rankine and Fourier components G R and G F , and that (ii) these Green functions are consistent . In particular, a new representation of the Green function for flows around ships advancing in regular waves at τ < 1 / 4 that is consistent with the Green functions for the special cases V = 0 or ω = 0 is given. The study also provides a complete and largely self-contained account of the FK method for evaluating the Fourier component ϕ F in the Rankine–Fourier decomposition ϕ R + ϕ F of the velocity potential ϕ (and the related velocity) of the flow created by a general distribution of singularities. An essential element of this FK theory is an optimal waves/local-effects (WL) decomposition ϕ F = ϕ W + ϕ L , given for a general dispersion relation associated with a broad class of dispersive waves, in which the component ϕ W represents the (far-field and near-field) waves contained in ϕ F and the component ϕ L corresponds to a non-oscillatory local disturbance that is mostly significant in a small near-field region. Applications of this general WL decomposition to the five classes of flows in marine hydrodynamics of primary interest in the study yield simple analytical flow representations – for general compact distributions of singularities – that offer two notable advantages over the classical direct Green function method: (i) Integration over hull-surface panels within the FK method only involves smooth ordinary functions , which are incomparably simpler than the highly singular functions G F and ∇ G F , and (ii) The computations related to G F and ∇ G F in the FK theory – implemented in the manner expounded in the study – are proportional to the number N of panels that approximate the body surface, whereas common panel methods require O ( N 2 ) computations. Thus, the Fourier–Kochin method and the optimal Rankine–Fourier decompositions and optimal waves/local-flow decompositions given in the study lay the foundation of a new type of computational methods, which offers two compelling advantages over the classical ‘direct Green function method’ steadfastly applied in the past fifty years.

Three alternatives to the classical boundary integral representation of diffraction-radiation of regular waves by large stationary bodies, such as offshore structures and moored ships, that underlies existing panel methods are defined. These three alternative flow representations are associated with two alternative linear flow models, called 'free waterplane flow model' and 'rigid waterplane flow model', of potential flow around an offshore structure in regular waves. As was shown previously, these two alternative linear flow models of diffraction-radiation of regular waves by stationary bodies yield identical boundary integral flow representations and are then consistent, although the rigid waterplane flow model precludes irregular frequencies. Moreover, this flow model – and mathematical transformations – yield two other boundary integral flow representations, so that three alternatives to the classical boundary integral flow representation used in existing panel methods are defined. These three alternative flow representations are weakly singular. The first of these flow representations, given previously, involves a surface integral over the waterplane inside the body, while the second flow representation involves a line integral around the waterline of the body, i.e. the intersection curve between the body and the undisturbed free surface. The third flow representation is of particular interest because it involves neither a surface integral over the waterplane nor a line integral around the waterline. Moreover, this boundary integral flow representation does not involve a distribution of dipoles over the body surface; indeed, it expresses the flow potential in terms of the normal and tangential components of the flow velocity at the surface of the body. It is also notable that this boundary integral flow representation is identical to the boundary integral representation previously obtained for flows around ships advancing at a constant speed in calm water or in regular waves, and thus provides a common basis for the analysis of three major classes of flows in ship and offshore hydrodynamics.

The Green-function and boundary-element method, widely used in ship and offshore hydrodynamics, requires accurate and efficient numerical evaluation of flows created by (typically polynomial) distributions of singularities (sources and dipoles) over (flat or curved) panels of various shapes (notably quadrilateral or triangular) that approximate the surface of a ship or offshore structure. This crucial core-element of the Green-function and boundary-element method is considered for the 3D theory of ship motions in regular waves in the regime 0.3≤τ≡Vω∕g where V and ω denote the ship speed and the (encounter) wave frequency, and g is the acceleration of gravity. In this regime, the dispersion relation yields two dispersion curves in the Fourier plane (α,β) that are conveniently defined in the Cartesian form α=α∗(β) with −∞<β<∞, whereas the polar representation k=k∗(γ) where k≡α2+β2 and −π≤γ≤π is convenient and used in a related study to represent the three dispersion curves associated with ship motions in the regime τ<1∕4. The complementary analytical representations given in this study for 0.3≤τ and previously for τ<1∕4 provide simple and practical expressions for the flow due to an arbitrary compact distribution of singularities that are suited for accurate and efficient numerical evaluation for all values of τ outside the relatively narrow range 0.25≤τ<0.3.

Cavitation inception and radiated noise of the pump-jet propulsor are closely related to the strength of vortical flows existing in the clearance between rotor-blade tips and duct surface, which is ultimately determined by blade geometry close to the tip. A method is proposed for weakening the tip-clearance flow in pump-jet propulsors by increasing section thickness and rake of rotor blades from 95% tip-radius to the tip. The impacts of the proposed tip-modification method are investigated via numerical simulations by solving the Reynolds-Averaged Navier-Stokes equations with the SST k-omega turbulence model. When the rotor-tip geometry is modified reasonably, the open-water performance of the pump-jet propulsor is barely influenced, though the efficiency of rotor decreases due to the reduction in thrust loading and lift-to-drag ratio close to the tip. Due to rotor/stator interactions, the thrust and torque of a rotor blade as well as pressures at the core of tip-leakage vortex (TLV) fluctuate at multiples of rotor shaft frequency times stator blade number. When the rotor tips are modified, the fluctuation amplitudes of thrust and torque are reduced by more than 35%, the formation of TLV is delayed, the strength of TLV is weakened, and the pressure fluctuation amplitudes at TLV core are almost reduced by 50% at dominating frequencies.

Diffraction–radiation of regular waves by a body such as an offshore structure or a moored ship is considered within the classical framework of potential-flow theory, which is commonly used because it is realistic and practical. A simple analysis that is based solely on straightforward applications of Green's classical identity to a 'free-waterplane' flow-model and a 'rigid-waterplane' flow-model is expounded. These alternative flow-models and the related straightforward applications of Green's identity yield an elementary yet rigorous justification of the practical and effective method, called 'combined boundary integral equation method' (CBIEM), of Lau and Hearn for preventing irregular frequencies. This method is shown to be significantly more efficient, and arguably simpler and more logical, than the widely-used extended boundary integral method of Lee and Newman. A modification of the 'combined boundary integral equation method' is also given. This modification involves a pair of boundary integral equations that are mathematically equivalent to the pair of integral equations solved in the CBIEM, but are weakly singular.

The boundary-integral flow-representation associated with the boundary-value problem, commonly called Neumann–Kelvin (NK) problem, that corresponds to linear potential flow around a ship steadily advancing in calm water involves an integral around the mean waterline of the ship. This 'waterline integral' is a notorious source of numerical difficulties and has been extensively studied. The waterline integral in the NK theory is largely – but not fully – eliminated in the modification, called Neumann–Michell (NM) theory, of the NK theory. Specifically, the NM theory includes a residual waterline-distribution of weak Rankine singularities, ignored in practical applications. A crucial element of the NM theory is a mathematical transformation that is based on a vector Green function, which is associated with the common scalar Green function used in the NK theory. This transformation is revisited in the present study. A rigorous analysis yields an answer to a fifty-year old puzzle: an exact boundary-integral flow representation that does not include a waterline integral. A remarkable feature of this new flow representation, which is a modification of the NM flow representation given previously, is that it explicitly determines the flow potential and the flow velocity at a ship hull surface in terms of the flow velocity at the hull surface, rather than in terms of the hull-surface potential as in usual boundary-integral flow representations obtained via Green's classical identity.

基于重叠网格模型,通过非定常RANS数值模拟与结果分析,研究了块状冰的尺寸、轴向运动和冰桨位置对螺旋桨水动力性能的影响.选用切割体网格绘制整体静止计算域的背景网格,之后结合棱柱层网格绘制螺旋桨子计算域和冰块子计算域的重叠网格,不同的计算域之间通过两者的重叠区域进行数据传递和插值.计算结果显示,当冰块固定在桨前时,螺旋桨产生的非定常推力和扭矩均以叶频为基频进行周期性变化,而且两者的时间平均值和振幅主要受冰块在螺旋桨盘面内的轴向投影面积、冰桨轴向位置和冰桨水平位置的影响;当冰块在桨前沿轴向匀速靠近螺旋桨时,冰桨轴向距离逐渐变小,冰桨周向相对位置发生周期性的变化,使得推力和扭矩两者均以叶频振荡,而且两者的时间平均值和振幅均随着冰桨轴向距离减小而增加.

The behavior of an offshore structure in regular waves – and the related (linear and nonlinear) wave loads, added-mass and wave-damping coefficients, and body-motions – are commonly analyzed via the Green-function and boundary-integral method associated with potential-flow theory. This realistic, widely-used method requires accurate and efficient numerical evaluation of flows created by distributions of singularities (source, dipole) over (flat or curved) panels of various shapes (triangle, quadrilateral) that are used to approximate the surface of an offshore structure. This basic core element of the theory of diffraction–radiation of regular waves by an offshore structure is considered for water of uniform finite depth. The special case of deep water is also considered. An analytical representation of the flow created by a general distribution of singularities over a hull-surface panel is given. This flow-representation is based on the Fourier–Kochin (FK) approach, in which space-integration over the panel is performed first and Fourier-integration is performed subsequently, unlike the common approach in which the Green function (defined via a Fourier integration) is evaluated first and subsequently integrated over the panel. The analytical and numerical complexities associated with the numerical evaluation and subsequent panel integration of the singular Green function for wave diffraction–radiation by offshore structures are then avoided in the FK approach. In this approach, panel integration merely amounts to integrating an elementary (exponential–trigonometric) function, a trivial task that can be performed accurately and efficiently. The analytical flow-representation given in the study provides a mathematically-exact smooth decomposition of free-surface effects into a non-oscillatory local flow and waves. The waves in this flow decomposition are defined by a regular single Fourier integral, and the local flow is given by a double Fourier integral with a smooth integrand that only involves ordinary functions and is dominant within a compact region near the origin of the Fourier plane. Illustrative numerical applications for typical distributions of sources and dipoles over a panel show that the flow-representation given in the study is well suited for practical numerical evaluations.