Free Surface Pressure Research Articles

Study on the free surface evolution and slamming pressure of curved-wedge water entry using a Riemann-smoothed particle hydrodynamics method

The present study aims to provide a deep understanding of curved wedge water entry. It involves a numerical simulation investigation into the kinematic and dynamic properties of water entry for two curved wedges with deadrise angles of 25° and 35°. The meshless Riemann-smoothed particle hydrodynamics (SPH) model embedded with an acoustic damper is developed to simulate these violent water entries. The validation of the Riemann-SPH accuracy is confirmed through comparison with experimental data, and subsequently, we make a systematical simulation study on curved wedge water entry, including a comparative study of free surface evolution and pressure distribution at different curvatures and drop heights. Furthermore, the kinematics analysis of velocity and displacement of curved wedges and time domain characteristics of slamming pressure loads on both sides of the wedge are investigated. It is revealed that the pressure distribution is symmetrical, with high-pressure regions forming near the bottom of the wedge and gradually propagating outward. The free surface profiles are symmetrical, with deeper depressions formed by sharper wedges. The entry depth and velocity are correlated with the initial theoretical entry velocity, and the rate of speed decline varies with the curvature of the wedge. The slamming pressure loads exhibit distinct time-domain patterns, with lower pressure loads by sharper wedges.

Cavity flow characteristics of a curved hull section impacting a free surface with inclined postures

The water entry of structures is a complex gas–liquid flow. This paper studies the asymmetrical flow characteristics of a curved hull section entering water through numerical and experimental methods. The free-falling test from drop heights of 250–900 mm and inclination angles from 0° to 20° is carried out. Compared to a smooth hull section (cutting the bottom appendage), the experimental results observe some special asymmetrical flow phenomena (i.e., flow separation, jet impact, bubble flows, and bubble expansion). The physical mechanisms behind these flows are explained through combing the free surface flow and pressure distribution obtained by the numerical method. The effects of the inclination angle and impact velocities on these flow phenomena are further discussed, and they increase the degree of flow separation, bubble volume, and fragmentation. The load characteristics before and after cavity formation are analyzed based on a volume-of-fluid method. The high pressure caused by bubble closure can produce an instantaneous impulse pressure that even be 34% larger than the conventional impact pressure and is worth noting. This study clarifies some complex asymmetrical impact flow characteristics of curved hull sections and thus reveals the evolution mechanism of gas–liquid flows for complex geometries during oblique water entry.

Experimental and numerical investigation of focused wave interactions with a vertical truncated dumbbell-shaped cylinder

A new type of vertical truncated dumbbell-shaped cylinder is commonly adopted as the cap or cofferdam in sea-crossing bridges and may be subject to large typhoon waves. Focused waves can be employed to simulate typhoon-induced waves, which produce longer periods and larger wave heights. In this study, a series of wave flume tests of focused wave interactions with a vertical truncated dumbbell-shaped cylinder are conducted. The influences of the maximum wave amplitude, peak frequency and frequency range of focused waves are considered experimentally and numerically. Based on the verified numerical model, the influence of the focusing position is analyzed. Furthermore, the flow patterns, including the free surface, velocity and hydrodynamic pressure distribution around the structure, are given numerically to better explore the interactions between the focused waves and the cylinder. The results show that the maximum wave amplitude, peak frequency, and focusing locations have significant impacts on the flow field characteristics and focused wave forces. However, the influence of the frequency range on the flow patterns and wave forces seems very slight. This study will enhance the understanding of the interaction mechanics between focused waves and a vertical truncated dumbbell-shaped cylinder under various working conditions.

An Unorthodox Arrangement of Boussinesq-Type Wave Equations for Accurate and Robust Numerical Treatment

A set of Boussinesq-type wave equations with enhanced dispersion characteristics is presented for accurate, efficient, and robust numerical treatment. New arrangement uses three different velocity variables simultaneously in order to keep continuity and momentum equations in simplest conservation forms while improving the dispersion characteristics. This approach allows us to retain all the nonlinear contributions with minimum number of terms. Spatial and time-dependent variations of the seabed are fully accounted for and the effect of external free surface pressure is included. A numerical scheme based on finite differences is developed, and various well-known experimental cases are simulated for testing the performance of the proposed set of equations. Comparisons of simulations with measurements reveal quite satisfactory agreements and, hence, bolster confidence in the wave model.

Numerical analysis of water entry under ocean currents with smoothed particle hydrodynamics method

Water entry is a fluid–structure interaction process closely related to the ocean environment. Repeated water entries take place when ships are sailing in an ocean environment, e.g., ocean currents, which greatly affect the ship's safety and stability in navigation. In this paper, we adopt a smoothed particle hydrodynamics method to numerically study the water entry of a bow-flare ship body section under ocean currents. We simulate the process of water entry under different current velocities and analyze in detail the fluid field regarding the free surface evolution, the velocity and pressure distributions, and the body's forces and motions. It is revealed that the ocean current can induce multidirectional fluid impacts, and a stagnation point with zero velocity occurs at the upstream side. Asymmetric fluid fields including the evolution of the free surface and the velocity and pressure distributions around the body can also be found. In addition, discrepancies are caused in the formation time and the range of the high-pressure region. These fluid field changes greatly affect the ship body's dynamic responses. However, the effects of the ocean current are mainly reflected in the direction of the current flow and are relatively small in the direction perpendicular to the flow.

Insights from sloshing experiments in a rectangular hydrophobic tank

The wave impingement on the side walls due to the oscillation of a rectangular tank under harmonic sway motion is analysed experimentally with hydrophobic coated and uncoated tank surfaces. Impact pressures and free surface deformations are compared in three water filling levels over an excitation frequency range encompassing the first natural frequency. The reduced hydrodynamic loads acting on the tank walls are observed under hydrophobic effects and discussed in detail. Experimental observations clearly indicate that there is a strong effect of the solid surface properties on the free surface elevation, wave generation and pressure distribution. In particular, major changes have been traced around the resonance frequency due to more dominant tangential flow and altered wave form, which results in lower peak pressure values with increased water movement within the tank under the hydrophobic effects.

Numerical study on the water entry of two-dimensional airfoils by BEM

Hydrodynamics of the traditional wedges, cylinders, and cones entering water have been heavily studied. However, the hydrodynamic characteristics of airfoils are practically unknown; the problem is inspired by the recently widely developed fixed-wing unmanned aerial-underwater vehicle, which can fly in the air, cruise in water and frequently enters and exits free water surface. In this study, the hydrodynamic characteristics and fully nonlinear free surface deformation for the water entry of airfoils have been investigated by the time domain boundary element method. First, convergence study based on the NACA0012 airfoil is considered. The time step and element size are adjusted, and the results show that the free surface elevation and pressure distribution agree well with those obtained through Reynolds-averaged Navier–Stokes equations. The results show that the higher the entry velocity, the greater the peak hydrodynamic force. Furthermore, the higher thickness ratio causes greater added mass. Gravity and velocity are found to significantly influence the hydrodynamic behavior, including the time-varying force, while thickness ratio has a great impact on added mass and pressure.

Analysis of fluid dynamic behavior and impact load on oblique water entry of a two-dimensional seaplane based on VOF method

Seaplane landing is a typical water entry impact phenomenon. However, our understanding on the development of jet flow and air cavity, and corresponding load characteristic is still limited. In this paper, the impact problem of oblique water entry of a two-dimensional seaplane is studied to clarify the relationship between theses complex flows and loads. A gas-liquid two-phase model is established to model these complex fluid flows, where the air-water interface is captured based on a VOF algorithm. The accuracy is validated by the published experimental data. Some hydrodynamic impact characteristics related to seaplane model under different oblique water entry postures, including air-water free surface and local impact pressure are discussed. Complicated flows (air cavity and jet flow impact) are the internal cause to some unusual load characteristics such as multiple pressure peaks, negative pressure, simultaneity of impact load on the airfoil, and great difference of load at different positions on the cabin. The evolution of jet flow and air cavity is further discussed through combing free surface and pressure distribution. Results clarified the mechanism of complex flows under the influence of bottom cabin and inclined postures, which will be helpful to further understand the impact phenomenon of seaplane landing.

The influence of the hull representation for modelling of primary ship waves with a shallow-water equation solver

Long-period ship-generated loads have become design-relevant in many shallow and confined waterways. Numerical methods based on depth-averaged equations have conceptually proven successful to provide the ship wave parameters required for waterway management and design. Yet, the validation of these models remains challenging, due to variations in hull shapes, transient ship-motion during field data collection, and the dearth of published experimental benchmark data. The present study makes use of a new experimental data set to validate novel ship-modelling options in the shallow water equations solver REEF3D::SFLOW, using its free surface pressure extension for predicting long-period ship-generated load. The model predicts the primary wave field and the maximum return current with sufficiently low errors (MAPE) of 9.09% and 23.48%, respectively. A sensitivity study reveals that a simple slender body pressure assumption yields comparable simulation performance compared to a more complex hull-derived pressure distribution. The cross-sectional area of the respective pressure function, rather than the exact pressure function shape, is found to be decisive for the correct prediction of the design parameters primary wave height and maximum return current. Based on a systematic investigation of the ship draft to water depth relation, concise guidance on the choice of appropriate pressure functions is presented.

Verification of a Free-Surface Pressure Term Extension to Represent Ships in a Nonhydrostatic Shallow-Water-Equations Solver

Abstract In recent years, increasing ship sizes and associated increasing wave loads have led to a demand for prediction tools quantifying the ship-induced loads on waterways. Depth-averaged numerical models, using a free-surface pressure term, are a prominent method to obtain the relevant design parameters. These models incorporate the wave deformation processes due to attributes of complex bathymetries, while allowing for an efficient simulation of large computational domains. The nonhydrostatic shallow-water-equations (SWE) model REEF3D::SFLOW uses a quadratic pressure approximation and high-order discretization schemes. This paper presents the implementation of a pressure term to account for the displacement of the free surface by solid moving objects. Two test cases verifying the implementation are shown based upon the analytical one-dimensional solution of the wave propagation due to surface pressure and the estimation of Havelock angles. These verification tests are the first step toward a holistic model, combining a large scale model with computational fluid dynamics (CFD) simulations near waterway banks.

High-fidelity simulation of ship and linear shear current interaction

In this paper, the hydrodynamic performance of KCS (KRISO Container Ship) in the presence of a non-uniform shear current is investigated for the first time using high-fidelity CFD (Computational Fluid Dynamics) simulations. Various shear current strength conditions Frs with different directions were considered and results were compared to the ones with no shear current. The studies were conducted for the ship advancing at Fr = 0.26, 0.367. The focus is laid on the shear current effects on the ship resistance as well as the free surface elevation, pressure distribution, vortex structures, boundary layer, and nominal wake. Results showed that the presence of the shear current affects the hydrodynamic performance of the ship profoundly such that it increases/decreases the ship resistance in heading/following shear current with the largest change for the cases with the strongest shear current. The viscous resistance is dominant at Fr = 0.26 for all shear current conditions while the wave resistance is dominant for most cases at Fr = 0.367. The wave resistance reduces as the shear current direction varies from head to following shear current, similar to the theoretical model predictions. The viscous component follows a similar trend. The lateral resistance generated by the cross flow in beam shear current increases with the increase of Frs and the reduce of Fr and it is strongly dominated by the lateral pressure resistance. The Kelvin angle reduces in the head shear current and increases in the following shear current while the beam shear current reduces the Kelvin angle on the windward side of the ship and increases on the leeward side. The shear current also altered the transverse wavelength such that it increased in head shear current and reduced in following shear current. The predicted Kelvin angles and transverse wavelengths confirmed the finding of simplified theories on ship-shear current interaction. The presence of shear current also significantly affects the boundary layer, vortical structures, and the wake field.

Numerical approach for predicting the slamming loads in oblique long waves considering the wave-body interface

Ship slamming is quite common for ongoing ships, which involves complex wave-body interaction. However, our understanding on the ship slamming is limited to symmetrical cases. In this paper, a numerical approach was established to predict the asymmetric slamming loads in oblique long waves through combining the seakeeping theory and CFD technology. A reference coordinate system located on the wave surface was applied to transfer the ship slamming problems into asymmetrical water entry cases, where the inclination wave-body interface and asymmetrical ship motions were included. Numerical verifications including the CFD method, different water entry models, 3D effects and wave effects were carried out to discuss the applicability. Taking a 21K TEU container ship as an example, the characteristics of slamming loads under oblique long waves were further discussed through combining the free surface evolution and pressure distribution. The results demonstrate that the wave direction has significant influence on the slamming loads. This method can provide a high-efficiency prediction for slamming loads in oblique long waves with reasonable accuracy, which is quite useful at present to serve the impact strength design.

On applicability of von Karman’s momentum theory in predicting the water entry load of V-shaped structures with varying initial velocity

The water landing of an amphibious aircraft is a complicated problem that can lead to uncomfortable riding situation and structural damage due to large vertical accelerations and the consequent dynamic responses. The problem herein is investigated by solving unsteady incompressible Reynolds-averaged Navier–Stokes equations with a standard k−ω turbulence closure model. The theoretical solutions established by the von Karman’s momentum theory are also employed. In order to validate the relationships between the initial vertical velocity and the peak value of vertical acceleration, free fall test cases of 2D symmetric wedge oblique entry and 3D cabin section vertical entry are presented first. The other parameters at which the maximum acceleration occurs, such as time, penetration depth, velocity, are also evaluated. Hence, the quantitative relations are investigated to water landing event for amphibious aircraft. Detailed results in terms of free surface shape and pressure distribution are provided to show the slamming effects. The results show that a linear dependence of the maximal acceleration from the square of initial vertical velocity can be derived for two-dimensional wedge, three-dimensional cabin section and seaplane with V-shaped hull. Moreover, the ratio between the corresponding velocity and the initial vertical velocity tends to a constant threshold value, 5/6, derived from the theoretical solution, when increasing the initial vertical velocity in all three cases.

Fast 3D Simulation of Nonhydrostatic Flows Using a Modified Ghost-Cell Free-Surface Pressure Treatment

Fast 3D Simulation of Nonhydrostatic Flows Using a Modified Ghost-Cell Free-Surface Pressure Treatment

Nonlinear liquid sloshing dynamics: Post-processing of conventional finite element solutions by digital filters

The aim of this study is to develop a robust finite element procedure for solving 2D and 3D nonlinear liquid sloshing dynamics modelled by standard potential theory. A computational problem encountered in almost all of the nonlinear simulations of inviscid free-surface flows is the appearance of “saw-tooth” spurious oscillations on the free surface as the waves become steep. The proposed post-processing, based on the moving least-squares smoothing algorithm, allows robust recovering more accurate nodal values of potential velocity gradients from conventional finite element solutions. Sloshing motions induced by harmonic and El-Centro seismic excitations are presented for small to steep non-overlapping waves in rectangular containers. The paper compares between various techniques to enhance stability and mitigate numerical oscillations, both common and innovative for sloshing problems. We explore the influence of these techniques on the free surface and velocity and pressure profiles, and choose the most robust stabilized finite element formulation for potential flow sloshing models.

Improving ocean modeling software NEMO 4.0 benchmarking and communication efficiency

Abstract. Communications in distributed memory supercomputers are still limiting scalability of geophysical models. Considering the recent trends of the semiconductor industry, we think this problem is here to stay. We present the optimizations that have been implemented in the 4.0 version of the ocean model NEMO to improve its scalability. Thanks to the collaboration of oceanographers and HPC experts, we identified and removed the unnecessary communications in two bottleneck routines, the computation of free surface pressure gradient, and the forcing in the straight or unstructured open boundaries. Since a wrong parallel decomposition choice could undermine computing performance, we impose its automatic definition in all cases, including when subdomains containing land points only are excluded from the decomposition. For a smaller audience of developers and vendors, we propose a new benchmark configuration, which is easy to use while offering the full complexity of operational versions.

Simulating multi-phase sloshing flows with the SPH method

In this paper, the intense sloshing flow is simulated by Smoothed Particle Hydrodynamics (SPH) method successfully. First, the traditional SPH method is used for the simulation of sloshing process; and the obtained results for free surface shape and pressure evolution are in good agreement with the experimental data. Then, the δ-SPH method and particle shifting technique (PST) are introduced in the traditional SPH model to improve its stability and accuracy in simulating sloshing flow. Air phase does have an inescapable influence on water phase in intense sloshing process. Thus, an improved multiphase SPH model with pressure correction algorithm is utilized for interfacial sloshing simulation. The stability, accuracy and conservation of pressure correction algorithm are validated by the cases of hydrostatic test and dam breaking test. Besides, the comparison results show that unphysical pressure transmission at the interface between two fluids with large density ratio is effectively suppressed. Finally, the effect of air is considered in the multiphase flow simulation of sloshing process with presented multiphase δ-SPH and pressure correction utilized. The phenomenon that air phase is involved into inner water flow and then moves, rolls and rises in it is replicated accurately. It is found that both the shape of free surface and the air cavities during the slamming phase are well captured, which proves that the integrated multiphase SPH is effectively utilized for the simulation of such multiphase problem as sloshing.

Second-order sum- and difference-frequency bichromatic wave forces on three-dimensional bodies in a channel

In Huang and Teng (2020), the effects of the channel walls on the second-order hydrodynamic characteristics of three-dimensional bodies in monochromatic incident waves were investigated. To ensure the high accuracy and efficiency of the calculation, robust numerical algorithms have been developed to treat the troublesome integrals over the free surface, body surface and up- and down-wave vertical surfaces involved in the second-order analysis. In the present study, Huang and Teng (2020)'s work is extended to the cases of bichromatic incident waves, and some improvements in the numerical algorithms are made. The expressions of the locked potentials including both the propagating and evanescent modes are derived. Since the up- and down-wave vertical surfaces are allowed to be placed close to the body, the calculation of the free surface integral can be performed in a small region, and an analytical method is developed to directly evaluate the up- and down-wave vertical surface integrals. After solving the boundary integral equation, the sum- and difference-frequency radiation and diffraction potentials are obtained explicitly. Numerical results for the quadratic transfer functions of the second-order free surface elevation, pressure and force are given for a series of geometries in channels.

Parametric studies on sloshing in a three-dimensional prismatic tank with different water depths, excitation frequencies, and baffle heights by a Cartesian grid method

This paper aims to numerically investigate violent sloshing in a partially filled three-dimensional (3D) prismatic tank with or without a baffle, further to clarify the suppressing performance of the baffle and the damping mechanism of sloshing. The numerical model is based on a Cartesian grid multiphase flow method, and it is well validated by nonlinear sloshing in a 3D rectangular tank with a vertical baffle. Then, sloshing in an unbaffled and baffled prismatic tank is parametrically studied. The effects of chamfered walls on the resonance frequency and the impact pressure are analyzed. The resonance frequencies for the baffled prismatic tank under different water depths and baffle heights are identified. Moreover, we investigated the effects of the baffle on the impact pressure and the free surface elevation. Further, the free surface elevation, pressure and vortex contours are analyzed to clarify the damping mechanism between the baffle and the fluid.

Numerical Investigation on the Water Entry of Several Different Bow-Flared Sections

The bow-flared section may be simplified in the prediction of slamming loads and whipping responses of ships. However, the difference of hydrodynamic characteristics between the water entry of the simplified sections and that of the original section has not been well documented. In this study, the water entry of several different bow-flared sections was numerically investigated using the computational fluid dynamics method based on Reynolds-averaged Navier–Stokes equations. The motion of the grid around the section was realized using the overset mesh method. Reasonable grid size and time step were determined through convergence studies. The application of the numerical method in the water entry of bow-flared sections was validated by comparing the present predictions with previous numerical and experimental results. Through a comparative study on the water entry of one original section and three simplified sections, the influences of simplification of the bow-flared section on hydrodynamic characteristics, free surface evolution, pressure field, and impact force were investigated and are discussed here.