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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 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.

The 3D frequency-domain analysis of the flow around a ship advancing in regular waves, in deep water, via the Green-function and boundary-integral method requires a practical and reliable way of evaluating the flow due to an arbitrary distribution of singularities (sources and dipoles) over the (flat or curved, quadrilateral or triangular) panels that are commonly used to approximate a ship hull-surface. This crucial element of the Green-function method, also widely called panel method, in a 3D analysis of ship motions is classically performed via a two-step procedure that involves evaluation of the Green function G and its gradient ∇ G as a first step, and their subsequent integration over hull-surface panels. This usual direct method, widely studied and applied in the literature, involves notorious well-documented mathematical and numerical complexities. A novel alternative method, based on the Fourier–Kochin approach, is expounded in the study. In this method, evaluation of G and ∇ G is bypassed, i.e. G and ∇ G are not evaluated, and the flow due to a distribution of singularities is evaluated directly, in the manner already expounded for the particular cases of steady flow around a ship advancing in calm water and diffraction-radiation of regular waves by an offshore structure or a ship at zero forward speed. The method expounded in these previous studies and extended here is based on an analytical representation of the flow due to a distribution of singularities (including the special case of a Green function and its gradient) that yields a formal decomposition into a wave component, given by single Fourier integrals along the dispersion curves associated with the dispersion relation, and a non-oscillatory local-flow component given by a double integral that has a smooth integrand mostly dominant within a compact region of the Fourier plane. An important aspect of this analytical flow decomposition is that the wave and local-flow components are smooth, unlike the wave and local-flow components in the expressions for G and ∇ G given in the literature. Moreover, the analytical representation of the flow due to a distribution of singularities given in the study provides a practical mathematical basis that is well suited for accurate and efficient numerical evaluation, as is demonstrated via the illustrative applications reported previously for steady flow around a ship advancing in calm deep water and diffraction-radiation of regular waves by an offshore structure in deep water, and reported here for the more general case of a ship advancing in deep water at a constant speed V through regular waves of frequency ω in the regime τ ≡ V ω ∕ g 1 ∕ 4 where g denotes the acceleration of gravity.

Diffraction-radiation of regular waves by offshore structures and flows around ships advancing in calm water or in regular waves are commonly analyzed via potential-flow methods based on the Green functions that satisfy the corresponding free-surface boundary conditions. This realistic, practical, and widely-used approach requires evaluation of free-surface flows due to arbitrary (notably constant, linear or quadratic) distributions of singularities (sources and dipoles) over (flat or curved) panels of various shapes (notably rectangles and triangles). Indeed, reliable, efficient and practical methods to evaluate the flows due to arbitrary singularity-distributions over hull-surface panels is a crucial core-element of the Green-function method in ship and offshore hydrodynamics. This core-issue is the object of the study. Free-surface flows due to singularity-distributions over panels (and related ‘influence coefficients’) are ordinarily evaluated via a two-step procedure that involves evaluation of a Green function G and its gradient ∇ G (a Fourier integration) and subsequent integration of G and ∇ G over a panel (a space integration). This common approach involves notorious analytical and numerical complexities related to the complicated singularities of the Green functions in ship and offshore hydrodynamics. An alternative general approach, applicable to generic dispersion relations and arbitrary distributions of singularities, is expounded. This alternative approach is based on a Fourier–Kochin representation of free-surface effects, in which the space integration over hull-panels is performed first and the Fourier integration is performed subsequently. Thus, the Green function and its gradient are not evaluated in this approach. Indeed, this usual first step is bypassed, and the flow due to a singularity distribution is evaluated directly. A major advantage of the Fourier–Kochin method is that the panel-integration is a trivial task as it merely involves integration of an exponential–trigonometric function. A crucial element of the approach expounded in the study is a general analytical decomposition of free-surface effects into waves and a local flow. The waves in this fundamental flow decomposition are expressed as single integrals along the dispersion curves defined by the dispersion relation in the Fourier plane, and the local flow is given by a double Fourier integral that has a smooth integrand dominant within a compact region of the Fourier plane. This analytical flow representation does not involve approximations, i.e. is mathematically exact, as is verified via numerical applications for two main classes of flows in ship and offshore hydrodynamics: ships advancing in calm water, and diffraction-radiation of regular waves by offshore structures. These applications also demonstrate that the general approach expounded in the study provides a practical, remarkably simple, basis that is well suited for accurate and efficient evaluation of flows due to arbitrary singularity-distributions. Indeed, the approach yields a smooth wave and local-flow decomposition that avoids the complexities related to the evaluation and subsequent hull-panel integration of the singular wave and local-flow components in the classical Green functions of ship and offshore hydrodynamics. The general approach expounded in the study is applicable to other classes of flows, notably wave diffraction-radiation by ships advancing through waves in deep water and by offshore structures in finite water-depth, and these important particular applications will be considered in sequels to the study.

Background: The blackhole infection can affect the collaborative communication in mobile networks. It is man-in-middle attack that seizes and deflects the route and avoids packet-forwarding in the network. The occurrence of collaborative-blackhole reduces the trust and trustworthiness over the network. Objective: A probabilistic and weighted analysis based protocol is proposed in this research for detection of cooperative blackhole nodes and generating the preventing route over the network. The aim of the work is to improve the communication reliability. Methods: In this paper, the communication behaviour is analyzed under associated and probabilistic measures using Data Routing Information (DRI) table to discover the blackhole attack. It applies a dual check based on participation and communication constraints to estimate the node criticality. The evaluation is performed by neighbours and neighbour-on-neighbour nodes with weights and threshold specific decisions. These measures are evaluated through composite and integrated measures and presented as decision metrics. The parametric and probabilistic checks are conducted as a comprehensive evaluation within the proposed PSAODV (Probabilistic Secure Adhoc On Demand Distance Vector) protocol. Results: The simulation of PSAODV protocol is conducted in NS2 environment on various scenarios with mobility, density and traffic type variations. The scenarios are defined with a higher density of blackhole nodes within the network. The adaptive weights are identified by simulating the network with different weight combinations. These weights are employed within the PSAODV protocol to configure it with the maximum benefits. The analytical evaluations are taken against AODV and SAODV protocols and identified the performance enhancement in terms of Packet Delivery Ratio (PDR) Ratio, delay, attack detection ratio parameters. Conclusion: A significant improvement in attack detection is achieved by this proposed PSAODV protocol. The proposed protocol improved the reliability and effectiveness of mobile network.

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.

In situ soil properties exhibit spatial variability, which is often described using a three-dimensional (3D) random field. With site investigations, soil properties at some specific locatio...

The pump-jet propulsor consists of a duct, a rotor and stators which are installed upstream of the rotor to provide pre-swirl flow or downstream of rotor to absorb the kinetic energy in the flow. The strong interactions between the three components and the vehicle are closely related to their design and exert great effect on noise and hydrodynamic performance. This paper attempts to develop an effective and efficient method for the optimal design of the duct and the pre-swirl stators under the influence of vehicle and rotor via viscous flow CFD simulations. In this paper, the two key parameters, attack angle of the duct and pitch angle of pre-swirl stators, are investigated. The numerical simulations are based on the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations using a two-layer realizable k-ε model for turbulence closure. The computational domain is discretized into mixed unstructured cells. The software package STAR-CCM+ is used for both grid generations and flow simulations. The rotor is replaced by the body-force model which is proposed according to the load distribution of the rotor in pump-jet propulsor. Total thrust of body force balances the resistance of a fully-appended underwater vehicle and its propulsor in the self-propulsion simulations and torque is determined by assuming that the propulsive efficiency is 80%. To the end of the optimal design, the total resistance, as the main consideration, and detailed flow field, such as pressure distribution, are numerically investigated for varied attack angles of the duct and pitch angles of pre-swirl stator. It is shown that the two parameters have significant impact on the performance of the propulsor and the recommended design is given.

The turbulent flow around a cavitating controllable pitch propeller (CPP) is simulated by solving the Reynolds-Averaged Navier-Stokes (RANS) equations, to investigate the dynamic effects on cavitation when the pitch of propeller blades is changed at different pitch adjustment velocities (PAVs). The process of changing the pitch at prescribed PAVs is controlled by a user-defined function (UDF) in the software FLUENT, and during the process, the time-dependent flow domain is re-discretized at each time step with dynamic meshes. The SST k-ω turbulence model and the cavitation model proposed by Schnerr and Sauer are employed in the simulation. The numerical simulation approach is first validated against model experiments for a fixed pitch propeller (FPP) working in the open water. A grid dependence study is carried out to determine a proper mesh resolution for the simulation of such cavitating flows; then the hydrodynamic performance as well as the extent and volume of the sheet cavities obtained from the RANS simulations are compared with experimental data. Then influences of the PAV on the hydrodynamic performance and cavity geometry are investigated. The CPP blades are rotated around the spindle axes to change the pitch, and the movement is controlled by a UDF. The PAV is prescribed and kept constant in the process of adjusting the pitch. At different PAVs, the unsteady thrust and torque, pressure distributions on blade surfaces and propeller disk, cavity geometry, as well as cavitation volume of the cavitating flow are compared with each other to assess the dynamic effects of the PAV.

Compared with open propellers, the impeller of a tunnel thruster is more vulnerable to cavitation and structural vibration problems because the impeller is typically subject to severe non-uniformity of inflow produced by the blunt gearbox. Model tests and numerical simulations are carried out in the cavitation tunnel of Shanghai Jiao Tong University for a tunnel thruster using a “flat plate” impeller and a tip-unloaded one. The characteristics of fluctuating pressures on the tunnel wall and the resultant excitation forces are investigated. It is found that although unloading the blade tips of an impeller is effective in reducing the fluctuating pressures in a local tunnel wall area near the tips, the same trend does not apply to the case of the excitation forces. The results show that care should be taken when the experimentally measured fluctuating pressures are utilized as the input to the analysis of structural vibrations.

A numerical method is proposed to predict the effective wake profiles of high speed underwater vehicles propelled by contra-rotating propellers (CRPs), in which the hydrodynamic effects of the CRPs are simulated by distributed body forces. First, Reynolds-averaged Navier-Stokes (RANS) simulations are conducted for identical body-force distributions in open-water and self-propulsion conditions. The effective wake profiles at the CRP disks are then obtained by subtracting the velocities induced by the body forces in the open water from those induced by the body forces in the self-propulsion condition. The effective wake profiles were then predicted for a generic underwater vehicle with an established CRP design. Next, the hydrodynamic performance of the CRPs in the effective wake was computed using an in-house vortex-lattice code. The potential-flow results agree well with those provided by the RANS simulation under the self-propulsion condition, indicating that the proposed method can predict the effective wake profiles for CRPs with reasonable accuracy. The influences of different wake components on the blade forces were investigated, determining that for CRPs, and especially for the aft propeller, the circumferential wake cannot be neglected in the design.

High-voltage and high-power voltage source converters (VSCs) are usually operated at low switching frequencies to minimise the switching losses. This study presents a new control method suitable for low switching frequencies. It consists of two stages. In the first stage, a simple proportional controller is used to suppress any overvoltage or overcurrent during the transients. Then, after the control variables have settled to steady-state values, the iterative controller is activated to finely adjust the modulation index and firing angle of the converter to fulfil the control objectives. To justify the proposed control method, various control objectives are realised in a 10 MVA VSC system, and the results are validated by PSCAD/EMTDC and hardware-in-the-loop simulation. The results show that state variables converge within a few iterative steps, and the transient response is sufficiently fast. The proposed method is shown to perform better than the conventional PI control for eliminating the power imbalance and DC second harmonics due to the imbalance at the grid voltage.

Alternative boundary-integral representations of linear potential flow around a ship that travels at a constant speed in regular (time-harmonic) waves in deep water are considered. In particular, the Neumann–Michell (NM) boundary-integral representation of steady flow around a ship traveling in calm water is extended to ship motions in regular waves. This extension is straightforward, but points to a complicated and unresolved fundamental issue that is essentially related to the formulation of a linear flow model. Indeed, the NM boundary-integral flow representation for ship motions in regular waves given in the study suggests that the classical Neumann–Kelvin (NK) flow model may be inadequate at a ship waterline. Alternative NM boundary-integral representations of time-harmonic ship waves that are consistent with the previously given NM representation of ship waves in calm water, and yield Fourier–Kochin representations of ship waves that are well suited for numerical computations, are given.

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 ϕ d and ϕ t 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 ϕ d and ϕ t and yields a pair of coupled integral equations for determining ( ϕ d , ϕ t ) , 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.

Short-wave approximations are obtained within the framework of the Neumann–Michell (NM) linear theory of potential flow around a ship that travels at a constant speed in calm water. Specifically, the integral over the ship hull surface – that determines ship waves within the Fourier–Kochin representation related to the NM theory – is approximated as a line integral around the ship waterline via Laplace’s method. This waterline-integral approximation is further approximated via Kelvin’s method of stationary phase. The short-wave asymptotic approximations obtained via successive applications of Laplace’s method and Kelvin’s method of stationary phase provide theoretical insight into short (transverse and divergent) waves created by ships that travel at low Froude numbers, and short divergent waves created by ships traveling at moderate or high Froude numbers. In particular, these analytical approximations show that short ship waves are related to the Froude number and the hull form in a fairly complicated manner.

A vortex-lattice modeling approach is proposed for investigating the free-surface effects on the hydrodynamics of submerged moving bodies and the propeller in the frame of the potential flow theory. The bodies, the propeller, and the free surface waves generated by them are modeled uniformly by vortex lattices. By fulfilling simultaneously the non-penetration boundary condition on the body surface (or on the camber surface for a propeller) and the linearized free-surface boundary condition, a set of linear algebraic equations can be established and solved for the vortex strengths. The vortex lattices for modeling the body- or propeller-generated waves are located slightly above the still water surface, while those for modeling the body are located on the exact body surface. In the case of the propeller, the vortex-lattice lifting-surface model is employed at present and combined with the vortex-lattice free-surface model. A number of test cases are given to investigate the convergence property and accuracy of the proposed approach, in terms of body-surface velocity or pressure distributions, as well as the lift and the wave-making resistance. Then the free-surface effects on quasi-steady propeller hydrodynamics are simulated and investigated at different submerged depths.

This paper presents our numerical study of the scale effects on a tip-rake propeller, the PPTC-II, based on the RANS simulations using software FLUENT 6.3. The low Re option in SST k–ω model is adopted at model scale, together with fine prism grids to resolve the viscous sub-layer. At full scale, standard wall function is adopted. The scale-effect corrections yielded by our RANS simulations are compared with those obtained from the ITTC method. To explain the CFD results, an analysis of sectional forces is performed. To investigate how the tip rake influences propeller scale effects, the geometry of PPTC-II is modified by removing the tip rake only, and the RANS-predicted scale effects for the modified propeller, PPTC-II-m, are compared with those for the PPTC-II. The study indicates that the scale effect on propeller thrust can be as important as that on the torque; somehow the RANS- and ITTC-based predictions for full-scale efficiency agree quite well; the tip-rake reduces tip loading and tip vortex strength, and brings about large differences in the scale effects as compared with the propeller without tip-rake. Keywords: Propeller, Tip rake, Open water, Scale effect, RANSE

Tunnel thrusters are more vulnerable to cavitation due to the tip clearance flow, blockage effect of the gearbox, and heavy blade loads as compared with open propellers, which makes the problems of...

The tonal noise prediction of non-cavitating seven-bladed propellers in effective wake are conducted based on Farassat's formulation 1A in this article. First, the noise characteristics of a seven-...

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-ω 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.