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The motion of a self-propelled body excites internal waves that modulate wind-induced microscale waves and affect the radar scattering cross section of rough sea surfaces. This process is closely related to factors such as stratification, propulsion effect, and radar parameters. Based on this, this study establishes and partially verifies a computational model for the scattering cross section of the internal wave wake left by an underwater self-propelled body. The model incorporates the first-order resonant internal waves of the stratified flow field as the dominant component of the wake-effect internal waves and determines the equivalent source size using the wake evolution model, thereby effectively simulating the characteristics of the surface flow field when the net momentum of the underwater vessel is nonzero. By solving the wave-action conservation equations, the wave spectrum of the modulated surface is derived, and the tilt and convergence/divergence effects caused by internal waves are comprehensively considered through the facet scattering model to assess their impact on the synthetic aperture radar (SAR) scattering cross section. Overall, this study systematically elucidates the correlation mechanism between the flow field and the radar system. • Obtaining the internal wave wake field of a nonstationary moving object based on quality and equivalent momentum sources. • Probing the modulation of microscale waves at the sea surface by the velocity field of the internal wave wake based on the conservation of wave action. • Investigating the scattering fieldby considering the Bragg effect of short wavesand the tilted effect of internal and surface long waves. [ABSTRACT FROM AUTHOR]

This paper conducts an experimental study to investigate the effects of immersion water depth on the dynamic stability performance of vertical cantilevered pipe aspirating fluid. Two cantilevered pipes about 4 m long with different diameters are partially immersed in water at eight different depths. The pipe experiences clear dynamic instability when the internal flow exceeds critical velocity. The dynamic instability is in the manner of mixed regular large amplitude flutter and small amplitude shudder. Experimental data show that the deeper the pipe immersion depth, the bigger the difference between the critical and natural frequency of the pipe. It is found that increasing immersion depth can reduce the flutter amplitude in the post-critical range but has little effect in the pre-critical region. The critical velocity of the pipe increases significantly as the immersion depth increases. The trace of the pipe gradually shifts from expanding motion to periodical motion as immersion depth increases. A preliminary analytical study shows these phenomena can be accounted for by the fact that the external fluid supply damping to the fluid-pipe system and larger immersion water depth decreases pipe tension. • The immersion depth effects on the dynamic stability characteristics of aspirating cantilevered pipe vertically is studied experimentally. • Root mean square (RMS), Power spectral density (PSD) and phase portraits are used to analyze displacement–time history curve. • The pipe end trace gradually shifts from expanding motion to periodical motion as immersion depth increases. • The pipe critical velocity increases significantly as the immersion depth increases. [ABSTRACT FROM AUTHOR]

• Harmonic differential quadrature (HDQ) method is developed to analyze one dimensional vibration problem of pipes conveying fluid. • Numerical simulations show HDQ method has better computational efficiency and accuracy than other numerical models. • HDQ method is more suitable for rapid calculation of large number of numerical cases than other methods. Harmonic differential quadrature (HDQ) method is developed to analyze the one dimensional vibration problem of pipes conveying fluid with various boundary conditions. HDQ uses the trigonometric functions to formulate the harmonic test function and weighting coefficients are calculated explicitly. Unevenly spaced grid point distribution method is applied to discretize pipe domain. The high efficiency and accuracy of HDQ method are demonstrated by comparing with other methods for various internal flow induced pipe vibration problems. Numerical simulations show HDQ method holds better computational efficiency and accuracy than other numerical models. HDQ method is more suitable for rapid calculation of large number of numerical cases than other methods. [ABSTRACT FROM AUTHOR]

The suitability of unidirectional internal solitary wave (ISW) models in a two-layer fluid system is evaluated using an improved experimental method. A new method for generating internal solitary waves in the laboratory tank is proposed, utilizing a piston-type wave maker in a density stratified two-layer fluid. The prescribed velocities of the pistons are determined by the mean velocities derived from the adjusted High-order Unidirectional (aHOU) model for the upper and lower layers. Experimental conditions encompass a range of wave Reynolds numbers between 1. 8 × 1 0 5 and 2. 3 × 1 0 5 . The repeatability and amplitude control of the proposed wave-making method are verified. The unidirectional models considered in this study encompass the Korteweg–de Vries (KdV), Gardner and aHOU model. Laboratory experiments and theoretical computations have been systematically compared in this study to examine the wave characteristics inherent in typical unidirectional internal solitary wave models. It is found that Reynolds number (Re) and nonlinear parameter (α = | a | / h) serve as suitable criteria for delineating the range of applicability of unidirectional models. According to these criteria, the KdV theory is suitable for ISWs with amplitudes α < 0. 02 across all Reynolds number cases, while the Gardner model is valid for cases where α < 0. 02 and Re ω > 2. 2 × 1 0 5 , with α < L i m G , where L i m G represents the non-dimensional limiting amplitude. The aHOU model exhibits the capability to capture fully nonlinear ISWs across all Reynolds numbers considered in this study. • An improved method for generating ISWs using a piston-type wave maker is proposed. • The Re and α = | a | / h are suitable criteria for the applicability of ISWs models. • The aHOU model demonstrates robustness in capturing fully nonlinear ISWs. [ABSTRACT FROM AUTHOR]

In this study, a refined and improved theoretical model was proposed for calculating the synthetic aperture radar (SAR) images of internal wave wakes. This model was based on an equivalent source model of internal wave wakes and the velocity-bunching principle. Wake field, scattering field, and SAR image characteristics were systematically calculated for multiple scenarios. The model described the transfer and solution processes by inputting the background flow field temperature and salinity profiles to map the radar image intensity distribution. The physical mechanisms of the internal wave wake generation and its capture by SAR were comprehensively explained. The effects of various parameters on the internal wave wake SAR images were analyzed comprehensively. The SAR image features containing internal wave wakes were determined based on the gray-level co-occurrence matrix and image power spectrum, which revealed that the maximum surface current induced by the internal wave modes of the same amplitude was considerably larger than that induced by surface-wave mode. When traveling far from the water surface, the rate of change in the total scattering coefficient because of the Bragg effect was approximately 20 times that of the slope effect. In SAR images, the recognizability of wakes depends primarily on the maximum intensity rather than the average disturbance on the sea surface. Therefore, SAR images exhibit considerable differences during downwind radar observations, with the most prominent contrast differences occurring at the maximum spreading angle of wake scattering and 1500 m behind underwater objects. In the image power spectrum, the frequency range of the first modal internal waves was approximately 10–30 Hz, whereas the higher-order modal internal waves had frequencies lower than 10 Hz. Furthermore, the frequency range of the surface-wave mode was larger than that of internal-wave modes, approximately 50–60 Hz. • A comprehensive theoretical and simulation model are developed to accurately depict the synthetic aperture radar (SAR) imaging of internal wave wakes generated by underwater moving objects. • The physical process of exciting internal wave wakes by moving objects in real sea environments and their significant influence on SAR image modulation is thoroughly elucidated. The modulation effects of factors such as wake magnitude and flow velocity on SAR images are thoroughly analyzed, leading to the determination of optimal navigation and radar parameters for observation. • Leveraging the flow field characteristics of internal wave wakes, the contrast features and power spectrum information of wake signals are successfully extracted from SAR images. [ABSTRACT FROM AUTHOR]

• A new geometric VOF method called isoAdvector is modified to be compatible with the simulations of sloshing flow with using the dynamic mesh. • The buoyancy-modified k − ω SST turbulence model is used to avoid the excessive turbulence level induced by classical RANS turbulence closure models. • RANS simulations of resonant sloshing flow are carried out and compared with the experiments and the ones by using other methods. • The methods adopted in the present paper improve the accuracies of wave elevations and hydrodynamic loads. • The effects of the sharp interface and the effects of the excessive turbulence level on the results are analyzed. Sloshing is an interfacial-flow phenomenon which brings two challenges on how to locate the position of the interface and avoid the unphysical motion of the interface. In order to locate the the position of the interface, a new geometric Volume-of-Fluid (VOF) method called isoAdvector is adopted to pursue a sharp interface. Aiming to make the isoAdvector method compatible with the dynamic mesh adopted to handle the tank motion, the motion-flux correction is introduced, and a moving-velocity correction for face-interface intersection line (FIIL) is proposed. An approximation formula is adopted to effectively reconstruct the moving-velocity field of the meshes at each cell center based on the motion fluxes on each cell face. In order to avoid the unphysical motion of the interface due to the excessive turbulence level in the transition region at the interface, the buoyancy-modified k − ω SST model is adopted. The numerical results of wave elevations and forces are compared with the experiments. The comparisons suggest that (i) the moving-velocity correction for FIIL is important to update the volume fraction; (ii) the modified isoAdvector method can capture the the position of the interface more accurately than the algebraic VOF method; (iii) the unphysical motion of the interface can be avoided by using the buoyancy-modified k − ω SST model in long-time simulations. In addition, a new post-processing approach is proposed to evaluate the interface thickness. The decrease of interface thickness improves the accuracies of wave elevations by using the modified isoAdvector method. The adoption of both the modified isoAdvector method and the buoyancy-modified k − ω SST model improves the computational accuracies of wave elevations and hydrodynamic loads in long-time simulations. [ABSTRACT FROM AUTHOR]

Abstract Two dimensional freely floating body motion responses induced by wave and current are investigated in seabed conditions. This problem is solved by boundary integral method, which is formulated by a combination of steady, diffraction/radiation and reflection potential problems accounting for current, incoming wave and seabed effects respectively. All the three potential problems are solved using a boundary element model involving a continuous Rankine source method subject to appropriate boundary conditions. The presence of incoming wave, current and seabed causes an asymmetric fluid domain. Numerical simulations show that water depth, seabed slope angle, current speed, current direction and cross coupling effects are significantly important for surge, heave and roll motion responses. Highlights 1 Both coupled and uncoupled body motion equations are developed. 2 Steady potential, diffraction/radiation potential and reflection potential are included in the numerical model 3 Roll viscous damping is interpolated into the potential theory model. 4 Mathematical model is validated by comparing with published numerical and model test data. All the three body motion modes (surge, heave and roll) are investigated. [ABSTRACT FROM AUTHOR]

The coalescence and interaction of two inline bubbles in viscous ambient liquids are explored using axisymmetric computations. The incompressible Navier–Stokes equations for gas-liquid flow are solved numerically through a tree-based finite volume method. Starting from spherical shape, the deformation and evolution of bubbles are simulated by a volume-of-fluid (VOF) method that combines a balanced surface tension force calculation and a height function curvature estimation. High mesh resolution is achieved by dynamic, adaptive mesh refinement to finely resolve the local topological evolutions during coalescence. The influence of liquid viscosity, for which Galilei number G a ranges from 1 to 150, is studied under different Eötvös numbers E o . It is discovered that the outcome of coalescence is determined by the competition between the two liquid circulations (vortex rings) around bubbles. We find that the inter-bubble interaction is always enhanced by reducing liquid viscosity. However, the effect of liquid viscosity on bubble coalescence is dual and the minimum coalescence time is obtained at a moderate G a with other parameters fixed. A comprehensive map of coalescence regime is provided, where four distinct coalescence regimes are identified and three critical Galilei numbers are defined. The motion of bubbles in different coalescence regimes are also analyzed and compared. Our work contributes to a further understanding of the coalescence and interaction of bubbles. [ABSTRACT FROM AUTHOR]

Vortex-induced vibration (VIV) of a riser considering both internal and external flows is investigated numerically. The model is firstly verified based on the comparison of the experimental data and numerical results. Then the internal flow is taken into account while VIV of a riser subjected to external flow in the subcritical regime of the Reynolds number is studied. Correspondingly, typical VIV characteristics such as the dominating mode and frequency in the in-line (IL) and cross-flow (CF) directions are analyzed, as well as the Root Mean Square (RMS) of the amplitudes, standing and traveling waves for the IL and CF responses. The results indicate that the IL and CF dominating modes are obviously influenced by the internal flow while the dominating frequency and RMS in both IL and CF directions are slightly changed during the investigation. The dominating modes for both IL and CF responses increase with the internal flow velocity increasing. Moreover, conspicuous traveling wave response is detected for both IL and CF responses while the internal flow interacts with the external flow for VIV. [ABSTRACT FROM AUTHOR]

On the basis of the two-dimensional Navier–Stokes equations, a new numerical method is proposed to generate internal solitary waves (ISWs) of expected parameters by adding a source term above the interface and a sink term below the interface into the continuity equation. Fluxes between the source and the sink are balanced to assure mass conservation, and the source/sink regions (the spatial windows over which the sink/source terms are placed) are adjusted as functions of time with the interface motion. Thus, the nonphysical trailing waves can be eliminated, which makes it easy to assure the prescribed ISW parameters. Moreover, a new layout is presented to avoid the difficulty of sizing and positioning the source/sink region, which has been proved to be an intrinsic drawback of the traditional mass source method. Numerical experiments are performed to validate the proposed method by analyzing the wave displacements and vertical profiles of velocity fields. It is shown that the numerical waveform remains stable with much less trailing waves than previous methods, and the numerical results are in good agreement with theoretical and experimental results. In addition, through sensitivity analysis, a reasonable method to determine the width of source/sink region is recommended. [ABSTRACT FROM AUTHOR]

We study the global hydrodynamic performance of a semi-submersible floating platform unit in order to optimize the hull form in the future. The hydrodynamic problem is solved by employing potential flow theory and Morison equation for modelling of the viscous effects. The added mass and damping coefficients, as well as the first-order motion responses, second-order mean drift forces, diffracted and radiated wave field, and airgap are computed to examine the hydrodynamic behavior of the floating production unit. The computational results show that the motion responses in short-crested waves are mostly smaller than those in long-crested waves. The maximum wave elevation occurs at WP45 in 45 ° wave heading in long-crested waves. In addition, the minimum airgap occurs at AG45 in 45 ° wave heading in linear waves, while the worst airgap point in nonlinear waves is AG0 in 0 ° wave heading. Extensive parametric studies have been performed to examine the dependence of the motion responses and the other key design criteria on the principal dimensions including hull draft, column width, column spacing, column corner radius, pontoon height, pontoon width, and the size of cakepiece. By comprehensive and systematic hydrodynamic computations and analyses, it is revealed that the combined vertical motion at the worst airgap location is almost in phase with the wave elevation in extreme wave condition with a peak wave period around 14–15 s. Moreover, it is found that the most efficient way to reduce the motion is to increase the hull draft, though the airgap may also decrease. Besides, reducing the pontoon height can achieve better motion performance and larger airgap simultaneously. This paper aims to provide a benchmark for future studies on automatic hull form optimization. [ABSTRACT FROM AUTHOR]

The South China Sea is rich in mineral resources, and the prospect of developing seabed mineral resources in the South China Sea is bright. However, the South China Sea is also famous for the active internal solitary waves, the researchers detected an internal solitary waves with an amplitude of 240 m and a peak velocity of 2.55 m/s in this area, which may severely impact the deep sea mining system. In this paper, we first simplify the vector finite element method's calculation process. Then the improved vector form intrinsic finite element method is used to simulate the installation process and normal working state of the deep sea mining systems under the action of internal solitary waves. The influence of the internal solitary waves on the deep sea mining systems in the installed state is limited, and its displacement and internal force changes are controllable. Still, the internal solitary waves may cause extensive movement or 180° bends in deep sea mining systems during installation. Necessary measures must be taken during installing deep sea mining systems to reduce the effects of internal solitary waves. • In this paper, the vector form intrinsic finite element method is improved, and the calculation process is simplified. • The internal solitary waves will cause large-scale movements of the deep sea mining system under normal operating conditions, but the impact is limited. • The internal solitary waves will cause 180° bending and a sudden increase in top tension to the deep sea mining system in the installed state, which may cause the failure of installation. • It is necessary to consider the effects of the internal solitary waves during the installation of the deep sea mining system. [ABSTRACT FROM AUTHOR]

Based on Lagrangian integral technique and Lagrangian particle-tracking technique, a numerical model is developed to simulate the underwater transport and fate of oil spilled from deepwater. This model consists of two submodels: the plume dynamics model and advection–diffusion model. The former is used to simulate the stages dominated by initial jet momentum and plume buoyancy of the spilled oil while the latter is used to simulate the stage dominated by ambient current and turbulence. The model validity is verified through comparing model predictions with data observed from a field experiment. The model is applied to simulating a hypothetical oil spill taking place at the seabed of a deepwater oil/gas field in the South China Sea, wherein the fate of spilled oil within the first 48 h after spill starts is investigated in terms of the oil budget and its underwater distribution. [ABSTRACT FROM AUTHOR]

Vortex-induced vibration (VIV) of flexible risers with both internal and external flows has received much attention recently. Hence, VIV dynamics of a fluid-conveying flexible riser subjected to external shear current is investigated. The effect of internal flow velocity and fluid density on VIV response is mainly examined and analyzed. A time domain model is introduced and elaborated. Then the finite element method is adopted to discretize the governing equations. Firstly, the model is validated based on the comparison between the numerical and experimental results. Then the influence of the internal flow velocity and fluid density on VIV dynamics is studied. The results show that multi-frequency response occurs when the flexible riser with various internal flow velocities and densities is subjected to external shear current. Under same shear current velocity, the IL mean deflection is enlarged with the increase of the internal flow velocity and fluid density. In addition, the internal flow velocity and fluid density have an evident effect on the vibrating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions. Moreover, mode and frequency transitions can be observed under different internal flow velocities and fluid densities. • Multi-mode and multi-frequency VIV response of the fluid-conveying riser occurs under external shear current. • The IL mean deflection is amplified obviously with the increase of internal flow velocity and fluid density. • The CF RMS displacement is magnified while the IL RMS displacement decreases due to the increase of internal flow velocity and fluid density. • The IL and CF vibrating frequencies are decreased while the internal flow velocity and fluid density are increased. [ABSTRACT FROM AUTHOR]

Three dimensional Rankine source model is utilized to investigate the hydrodynamic responses for wave radiation problems under arbitrary seabed condition in time domain. The free surface, seabed surface and body surface are presented by layer of continuous panels rather than a discretization by isolated points. These panels are positioned exactly on the fluid boundary surfaces and no desingularization technique required. To accommodate the sloping seabed profile, a straightforward source panel distribution on seabed surface is newly developed with two parameters determined by numerical tests. The accuracy and efficiency of the numerical solutions are validated by comparison with published data. The influences of flat seabed, uneven seabed and sloping seabeds are examined. Numerical simulations demonstrate that various seabed profiles have significant and complicated effects on the body hydrodynamic response characteristics. • Layer of Rankine source panel is applied to simulate free surface, body surface and seabed surface respectively. • A straightforward seabed source distribution is newly developed to accommodate sloping seabed profiles. • The proposed model is validated extensively by comparison with published data. • Effect of sloping sebed on wave radiation is studied by Rankine source panel method. [ABSTRACT FROM AUTHOR]

Vortex-induced vibration (VIV) can be inevitably encountered in deep ocean mining. As the internal flow is transported axially in the flexible riser, complicated VIV dynamics occurs undergoing both the internal and external flows. Therefore, the object here is to explore the effect of the internal flow with different velocities and densities on VIV response under various uniform current. In this study, a semi-empirical time domain prediction method for VIV dynamics of flexible risers considering both internal and external flows is introduced and adopted. The governing equations are discretized and solved by using finite element method. Firstly, validations are made for VIV without internal flow based on the numerical results and experimental data. Comparisons prove that the simulation could reproduce the VIV dynamics of a flexible riser. Then with the increase of the internal flow velocities and densities, the effect of the internal flow on VIV response is examined. It is found that the dominating frequency and the root mean square (RMS) displacement in both in-line (IL) and cross-flow (CF) directions are notably influenced by the internal flow velocity and density. Besides, the drag coefficient and IL mean deflection are detected magnified while the internal flow velocity and density are increased under different external flow velocities. It should be noted that the change of the internal flow velocity and density could trigger new mode response of the flexible riser, leading to mode transition for the IL and CF dominating modes. In addition, VIV dynamics shows a similar changing trend with the increase of the internal flow velocity and density when the flexible fluid-conveying riser is subjected to different external flow velocities. • With the increase of the internal flow velocity and density: • The CF RMS displacement is magnified while the IL RMS displacement shows a decreasing trend. • The drag coefficient and IL mean deflection are enlarged obviously. • The IL and CF dominating frequencies are decreased. • VIV dynamics shows a similar changing trend under different external flow velocities. [ABSTRACT FROM AUTHOR]

In this study, a dynamic model of a two-joint manipulator used in underwater robots considering the influence of ocean waves was derived based on the Lagrange principle and Newton–Euler method. The Morison equation was employed to calculate the inertial force and water resistance of ocean waves acting on the manipulator. The ocean force terms in the new model vary with time, which makes trajectory tracking control more complicated than in models used in land and still-water environments. The ideal trajectory of the manipulator was tracked using proportional-derivative (PD) control and sliding mode control (SMC). The PD control proved weak in trajectory tracking, whereas the sliding mode control could quickly and accurately track the ideal trajectory. Three reaching laws were compared, and variable exponential reaching law 2 was the most suitable for trajectory tracking. To test the sliding mode control ability, an experiment was conducted in an ocean-wave environment with varying ocean wave heights, wave frequencies, and water depths. In addition, variations in input torque were observed. It was also found that the input torque required in an ocean-wave environment was higher than that required in land and still-water environments. • The two-joint manipulator dynamic model in ocean wave environment is derived by Lagrange and Newton–Euler method. • The hydrodynamic drag force and added mass force of the ocean waves acting on the manipulator are calculated by Morison equation. • PD control and sliding mode control of three reaching laws are tested for the trajectory tracking ability. • Ocean waves of different property are applied and the variation of input torque is studied. [ABSTRACT FROM AUTHOR]

The flows around two tandem circular cylinders in the subcritical and supercritical flow regimes are studied through three-dimensional numerical simulations. Different spacing ratios L / D (where L is the center-to-center distance between the two cylinders with D being the diameter of the cylinders) from 2.0 to 5.0 is considered. The instantaneous flow structures, pressure distributions and hydrodynamic forces on two tandem cylinders are analyzed at subcritical (R e = 2.2 × 10 4 ) and supercritical (R e = 3.0 × 10 6 ) Reynolds numbers. The present numerical solutions demonstrated that at the two R e , for L / D < 3.5 , the shear layer from the upstream cylinder reattaches on the surface of the downstream cylinder and vortex street is only formed behind the downstream cylinder, while the shear layer from the upstream cylinder rolls up alternately for L / D ≥ 3.5 , and vortex shedding occurs from both upstream and downstream cylinders. Compared with the flow characteristics at R e = 2.2 × 10 4 , for R e = 3.0 × 10 6 , the flow separation positions on the upstream cylinder move backward and the width of the wake behind the upstream cylinder becomes narrower, which leads to forward movement of the reattachment position. At the supercritical Reynolds number, the mean drag and fluctuating lift coefficients of the upstream cylinder are nearly independent of L / D while the sharp increase of force coefficients of the downstream cylinder occurs for L / D = 3.5. Comparing to the case at the subcritical Reynolds number, higher vortex-shedding frequencies from the upstream and downstream cylinders are identified. It is also revealed that the slope of the best fit line for φ (the phase lag of the fluctuating lift force between two cylinders) and L / D increases at the supercritical Reynolds number. In addition, for L / D = 2.5 , the mean drag coefficients of the upstream cylinder decrease sharply for R e > 1.0 × 10 5 , while those of the downstream cylinder rise slightly with the growing R e. Moreover, the fluctuating lift coefficients of the upstream cylinder are almost independent of R e , but those of downstream cylinder drop as R e increases. • The flow patterns on each cylinder at the supercritical Re are different from those at the subcritical Re. • The lift coefficient of the upstream cylinder is almost independent of L/D at the supercritical Re. • For L/D = 3.5, the force on the downstream cylinder increases sharply at the supercritical Re. • The mean convection velocity of the vortices increases at the supercritical Re. [ABSTRACT FROM AUTHOR]

Abstract An Innovative Semi-submersible platform Optimization Program (ISOP) has been developed to solve the multi-objective optimization problem for semi-submersible platforms (SEMI). Three types of SEMIs, including semi-submersible floating production unit (SEMI FPU), heave and vortex induced motion (VIM) suppressed semi-submersible (HVS) and semi-submersible floating drilling unit (SEMI FDU) are selected for case studies. The hydrodynamic performances of three types of semi-submersible platforms are analyzed by using panel method and Morison's equation. In order to improve the computing efficiency, the hydrodynamic performances for different hull forms during optimization process are estimated by the surrogate models, which are built by artificial neural network prediction method and Inverse Multi-Quadric (IMQ) radial basis function (RBF). The accuracy of surrogate models is ensured by performing leave-one-out cross validation (LOOCV). The most probable maximum (MPM) heave motion and total weight, representing the safety and economy, respectively, are chosen as the two objectives for optimization. The transverse metacentric height, the MPM surge motion, and the most probable minimum (MPMin) airgap are selected as constraints. Based on surrogate models, multi-objective particle swarm optimization (MOPSO) is employed to search for the Pareto-optimal solutions. A Computational Fluid Dynamics (CFD) tool is adopted to validate the proposed model for the prediction of the motion responses. By comparing the obtained Pareto-optimal solutions with the initial design using simple panel method plus Morison's equation, it is confirmed that the MPM heave motions for SEMI FPU, HVS and SEMI FDU can be suppressed by up to 12.68%, 11.92%, and 14.96%, respectively, and the total weights can be reduced by up to 12.16%, 13.00%, and 24.91%, respectively. Through the detailed analyses of optimization results, the most efficient design strategies for semi-submersible platforms are discussed and proposed. Highlights • Surrogate models are adopted to evaluate the stability, motion responses and airgap for semi-submersible platforms. • The multi-objective particle swarm optimization is used for the multi-objective optimization of SEMIs. • The most efficient design strategies for three types of semi-submersible platforms are proposed and discussed. [ABSTRACT FROM AUTHOR]

A new mathematical model is developed to investigate the vibration stability of a lifting pipe induced by solid–liquid two phase flow. Three different slip models and the momentum conservation theorem are introduced to describe the slip characteristics of solid particles in two phase flow, which are coupled with the pipe vibration equations to establish a new governing equation and solved using the harmonic differential quadrature method. The mathematical model is validated by published data for the single-liquid flow case. Numerical results show that the slip model has noticeable effects on two phase flow-induced pipe vibration performance. The transport concentration of solid particles has a significant effect on the stability characteristic; however, the effect of particle size is very limited. The pipe flow mass ratio and the gravity coefficient are also key parameters affecting two phase flow-induced pipe vibration performance. • A new governing equation is formulated by coupling pipe vibration equation and slip model together with momentum conservation theorem. • The transport concentration of solid particle has significant effect on the pipe stability performance while particle size has very limited effect. • The pipe flow mass ratio and the gravity coefficient are also key parameters affecting the two phase flow induced pipe vibration performance. [ABSTRACT FROM AUTHOR]

An Innovative Tension Leg Platform (TLP) Optimization Program, called ITOP, has been developed to solve the multi-objective optimization problem for TLP. We first examine the hydrodynamic behavior of a base TLP for wave headings between 0 ∘ and 45 ∘ . The numerical results show that the maximum heave and surge motion responses occur in 0 ∘ wave heading in long-crest waves. It is found that the dynamic tension of No. 8 tendon is larger than the other tendons and reaches its maximum in 45 ∘ wave heading. It can be attributed to the fact that heave and pitch motions are almost out of phase for wave periods between 10 and 15 s. Because the maximum wave elevation occurs near the northeast column and the vertical motion is very small, the minimum airgap occurs there. Moreover, a surrogate model based on radial basis function (RBF) has been built and adopted to estimate the hydrodynamic performance of TLP. A multi-objective evolutionary algorithm, Non-dominated Sorting Genetic Algorithm II (NSGAII), is employed to find the Pareto-optimal solutions. By comprehensive and systematic computations and analyses, it is revealed that the maximum dynamic tension shows positive correlation with pontoon height and width, but negative correlation with hull draft, column spacing, and column diameter. The most efficient modification strategy for design is proposed to reduce the maximum dynamic tendon tension. According to the strategy, the column spacing, draft, and column diameter should be increased in sequence. By applying this strategy, the maximum dynamic tendon tensions can be reduced while the total weight of the platform is minimized as much as possible. [ABSTRACT FROM AUTHOR]

This paper presents numerical studies on vortex-induced motions (VIM) of a multi-column floating oil and gas exploration platform. Numerical computations are performed using an improved delayed detached eddy simulation (IDDES) together with a moving grid approach. The transverse (sway) and yaw motion responses, motion trajectories, motion frequencies and power spectral density of motions are computed and analyzed systematically. After extensive comparisons with experiments, it is confirmed that the present numerical solutions using IDDES agree well with the experimental results and are better than those via delayed detached eddy simulation (DDES). The differences of transverse motion responses between computational results and experiments are less than 10% in the lock-in region. The numerical simulations reveal that the transverse VIM responses occur in a range of reduced velocities from 7.0 to 14.0 at H / D = 1.44 ( H and D are the column height and width, respectively). The largest nominal transverse amplitude, around 35 % of the column width, occurs for 22 . 5 ∘ current incidence. It is found that the VIM responses mainly perform along the platform diagonals for 1 5 ∘ , 22 . 5 ∘ and 4 5 ∘ current incidences. The transverse and yaw motion frequencies for 1 5 ∘ , 22 . 5 ∘ and 4 5 ∘ current incidences are higher than those for 0 ∘ current incidence. The energy levels of the yaw motion responses for 1 5 ∘ , 22 . 5 ∘ and 4 5 ∘ current incidences are about 10% of that for 0 ∘ current incidence. Moreover, parametric studies have been performed to examine the effect of submerged column height on VIM. It demonstrates that VIM in transverse direction grows significantly when submerged column height H / D is greater than 1.0. To be more specific, compared to the case with H / D = 1.44, VIM in transverse direction at H / D = 3.0 increase by around 120%. [ABSTRACT FROM AUTHOR]

The paper presents experimental studies on the effects of draft conditions, current headings and mooring stiffnesses on the Vortex-Induced Motion (VIM) responses of a Tension-Leg Platform (TLP) with four circular columns. The nominal transverse and yaw amplitudes, and the corresponding spectra obtained by fast Fourier Transform (FFT) and continuous wavelet transform (CWT) are analyzed to examine the characteristics of the motion responses. Four current headings in the range of 0° to 45° are adopted in the model test. The results show that the maximum response amplitude in both transverse and yaw directions are achieved at 0° current incidence. For the transverse response, the maximum nominal amplitude decreases and the lock-in range narrows as the current heading increases. The spectral analyses for the transverse and yaw motions at 0° current heading show that the dominant peak frequencies increase as the reduced velocity increases. It is observed that the low-frequency spectral peak of the in-line motion amplitude spectra increases as reduced velocity increases. A color band or a ribbon concentrates stably around the frequency of f < 0. 05 in the wavelet analysis. It is primarily caused by the initial acceleration of the model in the towing tank. The absolute values of correlations between the spring tensions and the transverse motion of the platform are much larger than those between the spring tensions and the in-line or yaw motions. Moreover, it is found that the VIM trajectories of the TLP are primarily always along the direction perpendicular to the current heading. • A model test was conducted to study the VIM responses of a TLP. • Amplitude spectra analysis was performed to examine the performances of motion and spring tension. • Wavelet analysis was performed to examine the transient effect. • The correlations between the mooring tension and the VIM are analyzed. • The motion trajectories of the TLP for different conditions are analyzed. [ABSTRACT FROM AUTHOR]

• Vessel motion and internal flow are simultaneously considered for investigating CF VIV of a flexible riser. • Vessel motion can lead to intermittent VIV, amplitude modulation, hysteresis, mode jump and frequency transition. • Both vessel motion and internal flow can exert an obvious impact on top tension and CF VIV characteristics. • Vessel motion plays a dominated role in affecting top tension and CF VIV features. As vessel motion and internal flow can exert impact on vortex-induced vibration (VIV) of flexible risers, it is of great significance to take these two factors into consideration while VIV is investigated. Therefore, crossflow (CF) VIV of a flexible fluid-conveying riser is studied when vessel motion is considered. The governing equation is firstly discretized based on finite element method and solved by Newmark-β method. Then, validation is conducted by comparing with experimental data. Subsequently, CF VIV response of a flexible riser is explored with consideration of both vessel motion and internal flow. The results show that regardless of low and high Keulegan-Carpenter (KC) numbers, vessel motion can have a notable effect on top tension and CF VIV characteristics. Variations of CF VIV amplitude, vibration frequency as well as top tension frequency are affected by both vessel motion and internal flow. With the increase of internal flow velocity, CF VIV amplitude is changed while mode jump occurs concomitant with frequency transition. Besides, both vessel motion and internal flow velocity can have an impact on energy allocation along the flexible fluid-conveying riser. Noteworthy is that although both vessel motion and internal flow can exert an impact on top tension and VIV response, the effect induced by vessel motion still plays a dominated role. [Display omitted] [ABSTRACT FROM AUTHOR]

Cross-flow (CF) vortex-induced vibration (VIV) of a flexible riser considering both internal flow and external oscillatory flow is numerically investigated with consideration of combining the structural model with semi-empirical hydrodynamic force model by using Finite Element Method. The accuracy of the applied model is firstly examined by comparing the numerical results with the experimental data, which proves that the model can reproduce typical characteristics of CF VIV of a flexible riser undergoing external oscillatory flow. Then CF VIV of a flexible fluid-conveying riser subjected to external oscillatory flow is studied while the non-dimensional internal flow velocity and density ratio between internal and external flows are changed. The results show that regardless of the non-dimensional internal flow velocity and density ratio, typical VIV features of a flexible riser, such as intermittent VIV, amplitude modulation, hysteresis, mode and frequency transitions as well as standing and travelling wave responses, can be captured with variation of external oscillatory flow velocity. Moreover, VIV developing process, including building-up, lock-in and dying-out, can be detected for CF VIV. With the increase of the non-dimensional internal flow velocity and density ratio, high mode response can be effortlessly triggered for CF VIV, which is accompanied with occurrence of new vibrating frequencies. In addition, the vibrating frequency of CF VIV decreases while the non-dimensional internal flow velocity and density ratio are increased. • Complicated VIV dynamics can be captured with variation of external oscillatory flow velocity by using EM. • VIV developing process, including building-up, lock-in and dying-out, can be detected while external flow velocity varies. • With non-dimensional internal flow velocity and density ratio increasing, high mode response can be triggered for CF VIV. • The vibrating frequency of CF VIV decreases while the non-dimensional internal flow velocity and density ratio increase. [ABSTRACT FROM AUTHOR]

Time–frequency analysis is widely applied in Kelvin ship waves. However, limited studies have been conducted on the time–frequency features of internal waves. In this study, spectrograms used to visualize the frequencies of the internal waves generated by a submerged body are studied using a short-time Fourier transform. A linear dispersion curve and numerical model are introduced considering an idealized situation. The linear dispersion curve indicates wave frequency variation with time. The effects of parameters on the dispersion curve are discussed for a linear density profile and three-layer density profile. The dispersion curve presents upper and lower branches corresponding to the divergent and transverse wave components, respectively. In contrast to surface waves, the upper-branch curve for internal waves continues to increase and finally levels to the middle Brunt–Vaisala (BV) frequency N m of the density profile, whereas the lower branch curve continues to decrease and finally approaches a constant value. The numerical simulation provides idealized spectrograms of the linear internal waves. The linear dispersion curve provides an excellent prediction of the dominant wave signals. The high-intensity portion in the spectrograms is confined to the lower branch for a low Froude number, whereas for a larger Froude number, the high-intensity portion follows the upper branch but decays rapidly over time. The spectrograms obtained by the model test reveal that the high-color-intensity portion can be categorized into leading, reflected, nonlinear, and low-frequency regions. The experimental results also reveal that the model travel length is a critical factor affecting internal waves. • Analyze internal waves generated by a submerged body by short-time Fourier transform. • A new dispersion curve in the stratified fluid is discussed. • Several high-intensity portions in the experimental spectrogram are explained. • The travel length in the experiment is a critical factor and its effect is discussed. [ABSTRACT FROM AUTHOR]

The variable-coefficient modified Gardner equation is proposed to describe large amplitude internal solitary waves (ISWs) propagating over slope-shelf topography. The model is adapted from weakly nonlinear Gardner equation by adjusting its original coefficients such that the model is capable of representing the crucial characteristics of large amplitude ISWs, including the effective wavelength and wave speed. To numerically solve the nonlinear equation, the fourth-order Runge-Kutta method is applied for temporal discretization, second-order central finite difference numerical scheme is implemented for the space discretization and the iterative scheme is applied to treat the coupling term of time and space. The numerical method is then verified by comparing fairly with laboratory experiments. It's found the variable-coefficient modified Gardner model is a reliable theoretical tool to describe the behavior of large amplitude internal solitary waves passing through bottom topography. • The modified Gardner equation (vmG) model is originated from weakly nonlinear Gardner equation by adjusting its original coefficients. • The vmG can describe the characteristics for large amplitude internal solitary waves (ISWs) over slope-shelf topography. • The experiments provide the verification of vmG model in prediction of wave profiles and dynamic behaviors. [ABSTRACT FROM AUTHOR]

• The effect of a vertical wall on rising bubble is numerically investigated. • Special attentions are paid to the bubble with a spiral trajectory. • The onset of bubble path oscillation is found to occur earlier than for a freely rise counterpart and also at a lower Galilei number. • The sensitivities of Galilei number and initial bubble-wall distance are checked. The dynamics of a single rising bubble in the vicinity of a vertical wall is explored via three-dimensional numerical simulations. A finite volume method is used to solve the incompressible Navier–Stokes equations. The gas–liquid interface is reconstructed by volume-of-fraction (VOF) method. The trajectory, velocity, shape and vorticity of the bubble are analyzed in detail. The numerical results show that the presence of the wall imposes a repulsion on the bubble and that the bubble migrates away from the wall upon release. The onset of bubble path oscillation is found to occur earlier than for a freely rise counterpart and also at a lower Galilei number. Interestingly, we find that the vertical wall serves as a destabilizing factor in the wall-normal direction but a stabilizing factor in the spanwise direction. The increase of bubble inertia is discovered to enhance the influence of the wall. Furthermore, the bubble oscillations seem insensitive to the variation of the initial bubble-wall distance. [ABSTRACT FROM AUTHOR]