Search Results (40)

This paper applies physics-informed neural networks (PINNs) to laterally excited liquid sloshing in a two-dimensional rectangular tank, where near-resonant forcing (${\omega }_e/{\omega }_1=0.9$) produces a multi-frequency beating response with a period of approximately $10T_1$. Linearized potential flow theory governs the problem; the network learns the velocity potential $\phi (x,z,t)$ while the free-surface elevation $\eta$ is injected analytically. Two training obstacles specific to forced sloshing are analyzed. First, a zero-solution trap arises because the trivial solution $\widehat{\phi }=0$ satisfies all equations except the free-surface conditions, whose residuals are roughly ${10}^{-4}$ times smaller than the Laplace residual; characteristic-scale normalization combined with loss weighting (${\lambda }_D={\lambda }_K=100$) breaks this trap. Second, spectral bias prevents standard MLPs from resolving the three co-existing frequencies (${\omega }_1$, ${\omega }_e$, $\mathsf{\Delta }\omega$); a Fourier time embedding that augments the input from 3 to 9 dimensions overcomes this limitation. Two additional techniques further reduce errors: a hard-wall boundary condition enforced exactly via a $\cos (\pi x/B)$ spatial embedding, which eliminates wall collocation points; and a gradient-enhanced Laplace regularizer (${\parallel \nabla \left({\nabla }^2\widehat{\phi }\right)\parallel }^2$) that constrains velocity smoothness through third-order automatic differentiation. An ablation study shows that these four techniques progressively reduce the horizontal velocity error from ${\epsilon }_u=12.46\%$ to $0.84\%$. Results are validated against a viscous finite-difference benchmark. Over one beating cycle the errors are ${\epsilon }_{\eta }=0.15\%$, ${\epsilon }_u=0.84\%$, and ${\epsilon }_w=1.65\%$. A frequency parameter study across ${\omega }_e/{\omega }_1$ = 0.5–1.1 gives ${\epsilon }_{\eta }<0.25\%$ and ${\epsilon }_u<2.3\%$ for all near-resonance cases. For long-time simulation, a time-domain decomposition strategy with transfer learning partitions the domain into one-beat windows; extending to five beating cycles ($50T_1$) yields ${\epsilon }_u=3.43\%$ and ${\epsilon }_{\eta }=0.30\%$ with no monotonic error accumulation across windows. The methodology is then extended to a three-dimensional rectangular tank ($B\times W\times H$) with bi-directional lateral excitation. The 3-D formulation introduces the y-dimension into the Laplace equation (${\nabla }^2\phi ={\phi }_{xx}+{\phi }_{yy}+{\phi }_{zz}=0$), adds transverse wall boundary conditions ($\partial \phi /\partial y=0$) enforced exactly via a $\cos (\pi y/W)$ embedding, and extends the Fourier time embedding from 9 to 16 dimensions to accommodate six physical frequencies. The bi-directional excitation excites both $(m,0)$ and $(0,n)$ modal families, producing a genuinely three-dimensional beating response. Experimental results verify that the proposed methods can be well generalized to three-dimensional scenarios. Within a single beating cycle, the relative errors reach ${\epsilon }_{\eta }=0.24\%$, ${\epsilon }_u=1.31\%$, ${\epsilon }_v=1.78\%$ and ${\epsilon }_w=2.32\%$, with a total training time of 2499 s. By applying time domain decomposition to carry out two-cycle three-dimensional simulations, the model can steadily maintain satisfactory prediction precision across segmented time intervals, achieving overall errors of ${\epsilon }_{\eta }=0.30\%$ and ${\epsilon }_u=1.32\%$. Full article

This study presents a comprehensive numerical investigation of a modified backward bent duct buoy (BBDB) floating oscillating water column (FOWC) system, with emphasis on coupled hydrodynamic response and power take-off (PTO) representation. A fully integrated computational framework is developed using SIEMENS STAR-CCM+, ANSYS AQUA and ANSYS CFX, and three-dimensional CFD, incorporating free-surface wave modeling (VOF), six-degree-of-freedom (6-DOF) body motion, and mooring system interaction under realistic offshore wave conditions (H_s = 3.0 m, T = 9.0 s). A key contribution of this work is the development of an orifice-based PTO surrogate calibrated to replicate turbine-equivalent pressure-drop behavior. Comparative analysis demonstrates that the selected 0.30D orifice reproduces turbine response with deviations below 10% in pressure and flow characteristics, while maintaining superior numerical stability. Hydrodynamic analysis confirms that the modified BBDB-FOWC exhibits stable and bounded motion, with dominant heave-driven response and controlled pitch behavior. The influence of viscous damping is quantified through free-decay analysis and incorporated into the coupled simulations. Results show that damping enhances pressure development by ~25% and flow throughput by ~20%, leading to a significant increase in energy extraction potential. Dimensionless analysis further reveals that the system operates in a turbulent, inertia-dominated regime, governed by nonlinear oscillatory flow dynamics. The combined results demonstrate that the proposed methodology enables accurate, stable, and computationally efficient modeling of floating OWC systems with realistic PTO behavior. The findings provide a scalable framework for future optimization and support the development of high-performance offshore wave energy converters. Full article

In this study, the energy harvesting mechanism of a two-degree-of-freedom (2-DOF) oscillating foil under near-surface conditions and the underlying influence of structural parameters are systematically investigated. Numerical simulations are conducted using the open-source CFD platform OpenFOAM and the waves2Foam toolbox. The free surface is captured using the volume of fluid (VOF) method, while the heave and pitch motions of the foil are simulated via the overWaveDyMFoam solver, coupling 6-DOF dynamic equations with the overset grid technique. The results demonstrate that the periodic evolution and shedding of the leading-edge vortex (LEV) fundamentally drive the self-sustained oscillation of the foil. Moreover, the phase synchronization between the fluid-induced force and the kinematic response serves as the core mechanism for efficient energy extraction. Structural parameters critically regulate these characteristics: stiffness coefficients dictate the natural frequency and phase coordination, thereby modulating the overall motion response. Notably, a local resonance occurs when the system’s natural frequency approaches the fluid’s vortex shedding frequency, inducing the maximum kinematic response. Within the investigated parameter space, the system achieves a peak energy harvesting efficiency of 45.6% and a maximum average power coefficient of 1.15. Finally, the damping coefficients are found to primarily govern the response amplitude and the viscous dissipation of the system. Full article

Mesh generation is a critical preprocessing step in Computational Fluid Dynamics. In ship hydrodynamics, existing mesh generation methods lack adaptability to complex hull surface geometries, necessitating repeated optimization. To address these issues, a new hybrid mesh generation strategy was proposed, integrating Non-Uniform Rational B-Spline surface interpolation, advancing front technique, hull surface curvature features, and mesh quality evaluation parameters. Firstly, the ship hull surface was partitioned into multiple regions, and each region was assigned a specific mesh type. Subsequently, the adaptively sized mesh was generated based on local curvature variations. Finally, the angle skewness was employed as an objective function to improve the mesh quality. In addition, considering the actual ship model as an example, the mesh generated by our method and conventional Laplacian smoothing method were used to perform first-order potential flow simulations, and the results were compared against the convergence values. The results indicated that our method has lower root mean square errors in computing the total non-viscous force, steady drift force and ship hull free floating Response Amplitude Operator. This method is applicable to numerical simulations of the ship potential flow, providing high-quality hull meshes for hydrodynamic analysis. Full article

To investigate the air layer drag reduction and the related flow field characteristics of ships, the gas–liquid two-phase numerical model using the VOF solver in STAR-CCM+ has been established, considering the effects of free surface and surface tension. The numerical model is first validated through experimental results for the drag reduction by air-injection on a simplified ship model. Then, the numerical simulations for the KVLCC2 at varying speeds and air-injection rates are conducted, considering different ship attitudes and air-injection surface configurations. The impacts of flow velocity, air-injection rates, ship attitude and air-injection configurations on air layer drag reduction are analyzed. The distributions of air and pressure around the ship and their influence mechanisms on drag reduction are discussed. The simulation results show that the drag reduction exhibits a positive correlation with air-injection rate until it reaches an optimal peak value. The combined action of the incoming flow and injection velocities causes the vortex recirculation of the air layer under the ship, leading to its disruption and the subsequent formation of air-free zones on the hull bottom. High air-injection rates and the stern trim induce air layer lateral spillage, increasing frictional resistance on the hull side surfaces. An air layer on the stern surface will reduce the viscous pressure resistance by changing the flow separation near the ship stern. Air-layer coverage area is closely correlated with inflow velocity and injection surface configurations. The reasonable configurations of the air-injection surfaces can significantly improve the drag reduction. Full article

In this study, a correction procedure for ship mass and its longitudinal location of center of gravity suitable for a simulation environment is proposed in OpenFOAM v6.0. The concept is implemented ensuring static equilibrium and an approximately zero-pitch moment on the ship before the simulation. The viscous flow field around the ship in calm water is simulated using the VOF (Volume of Fluid) free surface two-phase and SST (Shear Stress Transport) k–ω turbulence models. Using static mesh, the resistance error of medium and fine grids is 4%, on average, against the experimental value. As the sinkage and trim are predicted using dynamic mesh, the increasing ship’s resistance causes larger errors, except for the container ship. Through the proposed correction, the ship’s vertical motions are significantly improved, and the resistance error decreases for the dynamic simulation. For the container ship, the error of resistance and motion achieved is less than 1%. The sinkage and trim errors improve tremendously for the tanker and bulk carrier, and the resistance errors are reduced slightly, by less than 3%. In the end, the detailed flow field is analyzed, as well as the ship wave-making pattern and the nominal wake velocity distribution, and these are compared with the measurement data available. The characteristics of the flow phenomena are successfully modeled. The resistance value for each hull form satisfies the requirement of Verification and Validation, and the uncertainty values are estimated. Full article

This study investigates the WAM-V (Wave Adaptive Modular Vessel) catamaran configuration, focusing on the hydrodynamic interaction between its articulated hulls. The unique hinged connection mechanism induces a relative angular displacement between the demihulls during operation, significantly modifying the calm water resistance characteristics. Such resistance variations critically influence both vessel maneuverability and the operational effectiveness of onboard acoustic detection systems. This study using computational fluid dynamics (CFD) technology, the effects of varying demihull spacing and the angles of the demihulls on resistance were calculated. Numerical simulations were performed using STAR-CCM+, employing the Reynolds-averaged Navier–Stokes equations (RANS) method combined with the k-epsilon turbulence model. The study investigates the free surface and double body viscous flow at different Froude numbers in the range of 0.3 to 0.75. The analysis focuses on the effects of the demihull spacing ratio (B_S/L_PP, Demihull spacing/Length between perpendiculars) on calm water resistance. Specifically, the resistance coefficient at B_S/L_PP = 0.2 is on average 14% higher than that at B_S/L_PP = 0.5. Additionally, the influence of demihull angles on resistance was simulated at B_S/L_PP = 0.42. The results indicate that inner demihull angles result in higher resistance compared to outer angles, with the maximum increase in resistance being approximately 9%, with specific outer angles effectively reducing resistance. This study provides a scientific basis for optimizing catamaran design and offers valuable insights for enhancing sailing performance. Full article

This work numerically investigates the fully nonlinear evolution of the free surface of a deep non-conducting liquid in a strong tangential electric field based on the method of dynamic conformal transformations. Direct numerical simulation revealed two possible scenarios for the evolution of nonlinear surface electro-hydrodynamic waves: collapse at finite time (in the non-viscous case) and turbulence generated by strongly nonlinear shock-like waves (taking into account both dissipation and pumping of energy). In the process of wave breaking, regions with a steep wave front arise, in which the curvature of the boundary increases infinitely. The inclusion of viscosity prevents the formation of singularities, and the system transfers to a strongly turbulent mode of motion. The spectrum of surface disturbances is very well described by the Kuznetsov spectrum $k^{-4}$, which corresponds to the second-order singularities in the liquid boundary. The measured probability density functions demonstrate a high level of intermittency in the turbulent regime, i.e., extreme events such as shocks play a dominant role in the evolution of the system. The results of calculations such as the turbulence spectrum, type of surface singularity, and the presence of intermittency are in good qualitative agreement with recent experiments carried out by Ricard and Falcon for a ferrofluid in a magnetic field. Full article

Floating breakwaters (FBs) play an important role in protecting coastlines, marine structures, and ports due to their simple construction, convenient movement, cost-effectiveness, and environmental friendliness. However, the traditional box-type FBs are flawed due to their requiring large sizes for wave attenuation and their overly high level of wave reflection. In this paper, a novel partial T special-type FB with wave attenuation on the surface and flow blocking below the water has been presented. First, the User-Defined Function (UDF) feature in ANSYS Fluent was employed to compile the six degrees of freedom (6-DOF) motion model. A two-dimensional viscous numerical wave flume was developed using the velocity boundary wave-generation method and damping dissipation wave-absorption method, with fully coupled models of the FBs developed. A VOF multiphase flow model and a RANS turbulence model were employed to capture the free flow of gas–liquid two-phase flow. Then, the performance of wave attenuation of the new FB was compared with that of the traditional box-type FB of the same specifications. The simulation results showed that the transmission coefficient of the new FB is significantly lower than that of the box-type FB, and the dissipation coefficient is notably higher, demonstrating excellent performance of wave attenuation, particularly for long-period waves. As wave height increases, the novel FB benefits from its wave attenuation mechanism, with a lower reflection coefficient compared to the box-type FB. Finally, through parametric analysis, some design recommendations of the novel FB suitable for practical engineering applications in deep-sea aquaculture are presented. Full article

We investigated the hydrodynamic characteristics of a dual-chamber oscillating water column (OWC) wave energy converter (WEC) using the OpenFOAM-v1912 open-source platform and waves2Foam solver. The numerical simulations were conducted using incompressible viscous fluid theory, applying the two-dimensional Stokes equation to describe fluid motion. The displacement of the free surface was accurately captured using the volume of fluid (VOF) methodology, and the governing equations were solved using the finite volume method (FVM). The dependability of the computational method was shown by validating the numerical model, which was based on a 2D representation, against experimental data. Within the resonance zone, the energy conversion efficiency of a dual-chamber OWC was approximately 25% greater than that of a single-chamber OWC. Moreover, the dual-chamber design displayed a broader resonance bandwidth, owing to the presence of multiple resonant frequencies, which enhance the stability and energy conversion over a wider range of wave conditions. The dual-chamber OWC generated stronger internal wave dynamics and higher chamber pressures, enabling superior energy capture compared to the single-chamber variant. Additionally, the formation and persistence of vortices within the chamber are key in sustaining efficient energy conversion by promoting continuous airflow. These results offer valuable information for constructing and optimizing dual-chamber OWC systems for more efficient wave energy collecting. Full article

This study examines the influence of drift angle on the wave and flow field generated by a submarine navigating through a density-stratified fluid. Employing a numerical methodology, this research computed the viscous flow field around the SUBOFF bare hull under conditions of oblique shipping maneuvers. The analytical framework relies on the Reynolds-Averaged Navier–Stokes (RANS) equations, supplemented by the Re-Normalization Group (RNG) k-ε turbulence model and the Volume of Fluid (VOF) method. The initial phases of this study involved verifying grid convergence and the accuracy of the numerical methods used. Subsequently, numerical simulations were performed across a spectrum of drift angles while maintaining a fixed Froude number of F_n = 0.5, with submergence depths set at 1.1 D and 2.0 D. The analysis focused on the wave profiles at both the free surface and the internal surface. The results indicate that the presence of a drift angle produces significant alterations in the characteristics of the free surface and internal surface when compared with straight-ahead motion. Specifically, the asymmetry in the flow field is enhanced, and the variability in the roughness of the free surface is pronounced. Full article

This study investigates the morphology of a free-falling liquid jet by using a computational approach with an experimental validation. Numerical simulations are developed by means of the Finite Element Method (FEM) for solving the viscous fluid flow and the level set method in order to track the interface between the fluid and air. Experiments are conducted in order to capture the shape of a free-falling jet of viscous fluid via circular orifice, where the shape is measured optically. The numerical results are found to be in agreement with the experimental data, demonstrating the validity of the proposed approach. Furthermore, we analyze the role of the surface tension by implementing linear as well as nonlinear surface energy models. All computational codes are developed with the aid of open-source packages from FEniCS and made publicly available. The combination of experimental and numerical techniques provides a comprehensive understanding of the morphology of free-falling jets and may be extended to multiphysics problems rather in a straightforward manner. Full article

In the present study, the added resistance, heave, and pitch of the KRISO Container Ship (KCS) in waves, at both model scale and full scale, are predicted numerically in regular head waves, for four wavelengths and three wave heights. The ISIS-CFD viscous flow solver, implemented in the Fidelity Fine Marine software provided by CADENCE, was employed for the numerical simulations. The spatial discretization was based on the finite volume method using an unstructured grid. The unsteady Reynolds-averaged Navier–Stokes (RANS) equations were solved numerically, with the turbulence modeled by shear stress transport (k-ω) (SST). The free-surface capturing was based on the volume-of-fluid method. The computed solutions were validated through comparisons with towing test data available in the public domain. To predict the uncertainties in the numerical solution, a systematic grid convergence study based on the Richardson extrapolation method was performed for a single wave case on three different grid resolutions. Specific attention was given to the free-surface and wake flow in the propeller plane. The purpose was to compare the numerical results from the model- and full-scale tests to examine the scale’s effect on the ship’s performance in regular head waves. The comparison between the model scale and full scale showed obvious differences, less accentuated for the free-surface topology and clearly observed in terms of boundary layer formation in the propeller’s vicinity. Full article

In this paper, a numerical assessment of the effect of shallow water on the total resistance of the solar catamaran SolarCat is carried out using computational fluid dynamics within the software package STAR–CCM+. The unsteady viscous fluid flow was modelled based on the Reynolds-averaged Navier–Stokes (RANS) equations with the application of the $k-\omega$ SST ($k-\omega$ Shear Stress Transport) turbulence model. The RANS equations were discretized by the finite volume method, and the position of the free surface is determined by the volume of fluid method. In shallow water conditions, a mesh morphing algorithm is applied. Numerical simulations were carried out for the deep water and limited depths corresponding to $h/T=7.6$, $h/T=4$, and $h/T=2$ at two speeds. The verification study was carried out and the total numerical uncertainty was calculated for the total resistance and sinkage of the catamaran. A detailed analysis of the flow around the catamaran was carried out. Full article

High-speed planetary mixers can rapidly and efficiently combine rheological liquids, such as polymer resins and paste materials, because of the large centrifugal forces generated by the planetary motion of the mixing vessel. Only a few attempts have been made to computationally model and analyze the intricate mixing patterns of highly viscous substances. This paper presents meshless flow simulations of the planetary mixing of polymeric fluids. This research utilized the smoothed particle hydrodynamics (SPH) approach for numerical calculations. This method has advantages over the finite-volume method, which is a grid-based computational technique, when it comes to modeling interfacial and free surface flow problems. Newtonian rheology and interfacial surface force models were used to calculate the dissipative forces in the partial differential momentum equation of fluid motion. Simulations of the flow of an uncured polyurethane resin were carried out while it was mixed in a planetary mixer, under various operating conditions. Simulations using SPH were able to accurately reproduce the intricate flow and blending pattern, providing insight into mixing mechanics and mixing index evolution characteristics according to operating conditions for the planetary mixing of polymeric fluids. The simulation results showed that the spiral band, which promotes the mixing performance, is densely and distinctively formed under high-speed operation conditions. Full article