Small Deadrise Angles Research Articles

Hydrodynamic performance comparison of planing catamarans with mono-hulls using numerical and experimental methods

This study addresses the hydrodynamic performance of high-speed planing catamarans compared to equivalent mono-hulls using numerical simulations and experimental validation. The study includes computational fluid dynamics (CFD) simulations to analyse the hydrodynamic behaviour of the catamarans under various operating conditions, such as different speeds, deadrise angles, and static trim angles. Comparison of the numerical simulation results with model tests reveals that the numerical results for the resistance of planing catamarans at high speeds deviate significantly from the experimental data due to strong spray. This discrepancy is systematic (rather than random) and has been recognised and modified. The modified numerical results are sufficiently accurate for further pursuit. Generally, the resistance of a planing catamaran compared to an equivalent planing mono-hull is significantly larger, approximately 25–60 %, while the absolute sinkage is lower. A positive feature of the catamaran is its ability to prevent porpoising instability, especially in boats with a small deadrise angle. Choosing a planing catamaran over a mono-hull must offer other substantial advantages, such as better seakeeping performance, which compensate the higher resistance.

Fluid–structure interaction analysis of curved wedges entering into water

The water entry of wedges with curvature differs significantly from that of linear wedges, which have been fully investigated and formulated. The safety and integrity of structures prompt an urgent investigation into the mechanism by which the curvature affects slamming loads and structural responses during water entry. This study examines the slamming force characteristics, pressure distributions, fluid jet evolutions, and structural response behaviors of two-dimensional curved wedge sections, considering five different curvatures and two panel thicknesses. A two-way coupling fluid–structure interaction (FSI) solver has been proposed within an open-source framework. The FSI solver was validated against published literature to ensure its high-fidelity. The small deadrise angle results in a more complicated time-domain characteristics for the slamming pressure, with a gradual transition from a single peak to a double peak. The half-peak pressure duration time were defined, and the quantitative results reveal that the hydroelastic effect of the linear wedge is significantly higher than the curved wedges. When considering the geometric curvature, the elastic wedges do not consistently reduce the peak slamming pressure and lengthen the pulse time. Additionally, large deformations generated by the panel vibrations alter the evolutionary pattern of the fluid jet. In contrast to the linear wedge, the structural responses of the curved wedges show distinctive two-stage behaviors.

Motion response induced by air cushioning effect during the water impact of a plate at small deadrise angles

Motion response induced by air cushioning effect during the water impact of a plate at small deadrise angles

Water entry of an elastic conical shell

The axisymmetric problem of a conical shell impact onto an inviscid and incompressible liquid of infinite depth is studied. The shell is thin, and its deadrise angle is small. The problem is inertia dominated. Gravity, surface tension and viscous effects are not taken into account. The hydrodynamic loads acting on the shell and the shell displacements are determined at the same time. The model by Scolan (J. Sound Vib., vol. 277, issue 1–2, 2004, pp. 163–203) is used to find the flow and hydrodynamic pressure caused by the shell impact. This model is based on the Wagner theory of water impact, which was generalised to axisymmetric problems of hydroelastic slamming. Dry and wet modes of the conical shell, as well as the corresponding frequencies, are calculated. It is shown that a conical shell can be approximated by a circular plate only for a very small deadrise angle. Deflections and strains in the conical shell during the impact stage, when the wetted part of the shell increases at high rate, as well as the hydrodynamic loads, are determined and analysed.

Hydroelastic analysis of slamming induced impact on stiff and flexible structures by two-way CFD-FEA coupling

ABSTRACT In rough seas, ships may be subject to wave-induced slamming loads.Thus, modelling of fluid and structural mechanics, and their dynamic interactions can help with the evaluation of fluid actions and the prediction ofwave-induced loads for use in ship design. In this paper a partitioned two-way coupled CFD-FEA fluid–structure interaction (FSI) method is usedto study the water entry of flat plates with different impact velocities and wedges with different deadrise angles. Results show that when flexibleplate dynamics prevail, at relatively low to medium impact velocity a negative correlation between the nondimensional pressure and water entryvelocities is evident near plate centre areas. A steady correlation exists when only stiff plate dynamics prevail. Pressure differences between stiffand flexible wedges become evident at small deadrise angles. The similarity of the pressure distribution during water impingement of ideally stiffwedge structures is not valid when structural flexibility prevails.

Theoretical Investigations on Slamming of Cone-Shaped Bodies

A general expression for the pressure distribution on a cone penetrating the water surface is derived from the similar procedure developed by Wagner for a wedge. The effect of trapped air between the falling body and the water is ignored for this investigation. The pressure distributions, velocity potentials, stream functions, and piled-up water phenomenon are summarized and compared with those for the wedge. Wagner provided a theoretical analysis on the slamming of a wedge [1,2,3].3 His approach was to approximate the wedge as an equivalent flat plate provided that the wedge had a small deadrise angle. By means of the velocity potential technique and the Bernoulli equation, he derived equations for determining the pressure distributions on the impact surface of the wedge. A cone piercing the water surface has been studied experimentally by Watanabe [4] and theoretically by Shiffman and Spencer [5]. However, their work provided only the total force acting on the impact surface of a cone. The purpose of the present work is therefore to determine theoretically the slamming pressure distribution of a cone. The similar approaches developed by Wagner for his wedge equations are used for this investigation.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method.
 Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Numerical and Theoretical Study on the Varying Speed Impact of Wedge Bodies on a Water Surface

Abstract The varying speed impact of wedge bodies on a water surface is studied numerically and theoretically to provide a fast and accurate prediction of the pressure on the wedge surface and the motion of wedge bodies during the free impact, which can be a two-dimensional (2D) model for the strip theory or 2D + t strategy. The fluid is assumed to be incompressible, inviscid, with negligible gravity effect and surface tension effect. The computational fluid dynamics (CFD) method is based on the volume of fluid (VOF) method and global moving mesh (GMM) method. Various cases of a varying speed impact are shown for the CFD method, and a linear relationship between the pressure coefficient Cp and a dimensionless variable K is observed. To clearly explain the linear relationship between Cp and K, we follow the potential theory to derive the Cp expression based on several assumptions on the free surface drawn from the CFD results. The Cp expression and the motion of wedge bodies for a free impact derived from it are considered as an approximate solution for a varying speed impact. The approximate solution is compared with the existing analytical models and the published experimental data. The approximate solution can work well for different deadrise angles, while the existing analytical models can only be used for small deadrise angles. Good agreement is also obtained between the approximate solution and the experimental test results, including the time history of wedge acceleration and the pressure on the wedge surface.

Experimental study on the propagation characteristics of the slamming pressures

The ship slamming pressure may exhibit a propagating feature and would have a significant influence on the local response of ship structure. This paper presents an experimental investigation on the characteristics of the slamming pressure, such as the slamming pressure coefficient, time duration, spatial pressure distribution and propagation speed. A series of experiments on the water entry of rigid and elastic wedges have been carried out for deadrise angles ranging from 0° to 45° and for drop heights ranging from 0.1 m to 1.0 m. Wedge plates with varying thicknesses are tested in the experiments to study the effect of structural elasticity on the propagating feature of the slamming pressure. Based on the experimental results, the spatial variation of the slamming pressure is analyzed. Besides, the effects of the water entry velocity, deadrise angle and wedge plate's structural elasticity on the propagating feature of the slamming pressure is studied. For the flat bottom slamming with a deadrise angle of 0°, the slamming pressure instantaneously acts on the structure, which shows no propagating feature and is close to the uniformly distributed pulse load. The propagation of slamming pressure is found to occur when the deadrise angle exceeds 0.2°. When the deadrise angle is between 4° and 45°, the pressure pulse shape is nearly unchanged during the propagation of the slamming pressure, and the ratio between the experimental speed of propagation and Wagner's theoretical speed is about 0.8. The effect of wedge plate flexibility on the slamming pressure is mainly observed in the cases with small deadrise angles. The wedge plate flexibility causes the duration of the slamming pressure to increase and the pressure coefficient to increase or decrease depending on the ratio between pressure duration and the structure's natural period.

Spray Formation and Structural Deformation During the Oblique Impact of a Flexible Plate on a Quiescent Water Surface

The oblique impact of a flexible and a nearly rigid plate on a quiescent water surface is studied experimentally. Both plates are 122 cm long by 38 cm wide and are mounted with a 5° upward pitch angle and a 10° lateral roll angle. The plates are attached to a dual-axis instrument carriage. The horizontal and vertical components of the carriage (plate) motion are driven by servo motors and controlled by a single computer-based feedback system, which is set with a single trajectory that is traversed for all impact speeds. The transient strain at multiple locations on the upper surface of the plate is measured with optical fiber Bragg grating sensors and the out-of-plane deformation is measured with a photographic method. A cinematic laser-induced fluorescence technique is used to measure the water spray generated during the impact. Two types of spray are observed and several aspects of the spray behavior are found to be noticeably affected by the deformation of the plate. The maximum deflection along the plate's upper long edge is found to increase almost linearly with impact velocity. 1. Introduction In rough seas, planing boats moving at high speed frequently slam into the water surface. The slamming process involves large highly transient pressures and forces on the hull, rapid accelerations of the boat and the water, the generation of water spray, and significant structural responses. This phenomenon is difficult to study numerically and experimentally because of the large motions of the hull and the violent motions of the water free surface, including the formation of spray sheets and the structural responses coupled with the flow dynamics. The problem of slamming (water entry) has received significant attention in the past. Many of the previous studies on this subject examine fundamental problems, such as the impact of a wedge or a flat plate on water surface. Some early theoretical studies on the water entry of a rigid wedge include, e.g., Von Karman (1929) and Wagner (1932). Wagner's model considers the water rising adjacent to the surface of a vertically moving wedge with small deadrise angle. This model was later extended to higher order (e.g., Oliver 2007) and other geometries (e.g., Howison et al. 1991). Based on Wagner's theory, Dobrovol'Skaya (1969) derived a similarity solution to the water entry of a wedge and the solution at small deadrise angles (down to 4°) was computed numerically by Zhao and Faltinsen (1993) using a nonlinear boundary element method. De Divitiis and de Socio (2002) studied the water entry of symmetric and asymmetric wedges. In their method, the flow field is represented by potential flow singularities whose intensities are determined as part of the solution. Moore et al. (2012) did a numerical study of normal and oblique water entry of a threedimensional rigid body with its bottom surface nearly parallel to the water surface.

A comparison of pre-impact gas cushioning and Wagner theory for liquid-solid impacts

The normal impact of a symmetric rigid body with an initially quiescent liquid half-space is considered using both Wagner theory and a model of viscous gas pre-impact cushioning. The predictions of these two theories are compared for a range of different body shapes. Both theories assume that the impactor has small deadrise angle. Novel solutions of the Wagner normal impact problem for a symmetric body with a power-law shape are presented, which generalize the well-known results for a parabola and a wedge. For gas cushioned pre-impacts, it is shown that a pocket of gas is entrained even for body shapes with a cusp at the body minimum. A scaling law is developed that relates the dimensions of the trapped gas pocket to the slope of the body. For pre-impact gas cushioning, surface tension is shown to smooth the liquid free-surface and delay the instant of touchdown for a smooth parabolic body, while for a wedge, increasing surface tension initially delays touchdown, before hastening touchdown as the importance of surface tension is increased further. For a flat-bottomed wedge, gas entrainment is again predicted in the gas-cushioning model although the location of initial touchdown, either on the transition between the wedge and the flat bottom or along the side of the wedge, now depends upon the parameters of the body shape.

Numerical Analysis of the Pressure Peak Position Shift With Deadrise Angle in Two-Dimensional Wedge Water Entry

This study deals with the pressure peak position shift with deadrise angle during the initial phase of a two-dimensional (2D) wedge water entry. The finite volume method with volume of fluid (VOF) and dynamic mesh technique is used to simulate the water entry process of the 2D wedges with the moderate deadrise angles within the range α = 20 deg–60 deg. The results show that with the increasing deadrise angle, the pressure peak position shifts from the spray root to the wedge apex. And, the critical deadrise angle of pressure peak position shift is identified in the range between 40.8 deg and 41 deg, which is more precise than previous studies. In the initial stage of water entry of a 2D wedge, the pressure on wedge side is determined by the dynamic pressure term and unsteady term simultaneously. For the spray root position, at small deadrise angles, the unsteady term is stronger than the dynamic pressure term; at large deadrise angles, the former is weaker than the later.

A numerical study of water entry of asymmetric wedges using a CIP-based model

The two-dimensional water entry of wedges with different inclination angles is numerically investigated using a constrained interpolation profile (CIP)-based model, which is developed on the ground of a fixed Cartesian grid and governed by the Navier-Stokes (N-S) equations. A high-order finite difference method is employed as the flow solver, where the CIP method is used to discretize the convective term. The tangent of hyperbola for interface capturing/slope weighting (THINC/SW) is adopted to capture the free surface/interface, and an immersed boundary method is applied to simulate the motion of bodies. The present numerical model involving symmetric water entry is verified in comparison with the previous numerical and experimental results in the literature. The results of the asymmetric water entry are provided in terms of the penetration depth, velocity, pile-up coefficients, impact force of wedges, and velocity and pressure distributions of fluid. Considerable attention is paid into the effects of deadrise and inclination angles. It is found that the presence of the inclination angle significantly influences both the velocity and pressure field, and further regulates the penetration depth, velocity, pile-up coefficients, and impact force on the wedge. Specifically, wedges entering into the water with small deadrise angles are found to be more sensitive to the inclination angle than those with large deadrise angle.

Challenges on the numerical prediction of slamming loads on LNG tank insulation panels

The load assessment in water impacts problems involving complex geometries is generally a quite challenging task for numerical solvers. Indeed, the occurrence of large free-surface deformation, air cushioning and possible compressibility effects strain the standard Computational Fluid Dynamics (CFD) codes to their limits. In the present work, an enhanced Smoothed Particle Hydrodynamics (SPH) model is adopted to evaluate the pressures acting on the surface of smooth and corrugated panels impacting water and the numerical outcomes are compared to experimental data and analytical solutions. Specifically, the water entry of a flat panel at 4° is firstly studied in order to highlight the main critical aspects underlying the numerical solution of water impacts with small deadrise angles. Then, the water impact of a Mark III type panel (a corrugated insulation panel) adopted in LNG tanks is considered. Experimental data involving wet drop tests of both flat and corrugated panels have been performed and the pressures during the impact have been measured at several points along the panel surface. Complex features of the flow, such as 3D effects and air-cushioning, have been addressed by a developing the numerical study in steps of increasing complexity.

Improved numerical solution of Dobrovol'skaya's boundary integral equations on similarity flow for uniform symmetrical entry of wedges

Dobrovol'skaya [1] presented a similarity solution for the water entry of symmetrical wedges with constant velocity. The solution involves an integral equation that becomes increasingly harder to numerically solve as the deadrise angle decreases. Zhao and Faltinsen [2] were able to present reliable results for deadrise angles down to 4°. In this paper, Zhao and Faltinsen's results are improved and reliable results for deadrise angles down to 1° are confirmed by comparing to the asymptotic solutions at small deadrise angles and the solutions by the traditional boundary element method at relatively large deadrise angles. The present similarity solution results provide a reference solution in theoretical studies of water entry problems and in developing accurate numerical solvers for simulating strongly nonlinear wave–body interactions, which flows are governed by Laplace equation or Euler equation.

Model tests on resistance and seakeeping performance of wave-piercing high-speed vessel with spray rails

The resistance and seakeeping performance of a high-speed monohull vessel were investigated through a series of model tests in a towing tank. The hull had a slender wave-piercing bow, round bilge, and small deadrise angle on stern. Tests on the bare hull in calm water were first conducted and tests on spray rails followed. The spray rails were designed to control the flow direction and induce a hydrodynamic lift force on the hull bottom to reduce trim angle and increase rise of the hull. The maximum trim of the bare hull was 4.65° at the designed speed, but the spray rails at optimum location reduced trim by 0.97°. The ship motion in head seas was examined after the calm water tests. Attaching the rails on the optimum location effectively reduced the pitch and heave motion responses. The vertical acceleration at the fore perpendicular reduced by 11.3%. The effective power in full scale was extrapolated from the model test results and it was revealed that the spray rails did not have any negative effects on the resistance performance of the hull, while they effectively stabilized the vessel in calm water and waves.

Analysis of loads, motions and cavity dynamics during freefall wedges vertically entering the water surface

In this paper, theoretical models are developed and numerical methods are used to analyze the loads, motions and cavity dynamics for freefall wedges with different deadrise angles vertically entering the water surface at Froude numbers: 1≤Fn<9. The time evolutions of the penetration depth, the velocity and the acceleration are analyzed and expressed explicitly. The maximum and average accelerations are predicted. The theoretical results are compared with numerical data obtained through a single-fluid BEM model with globally satisfactory agreement. The evolution of the pressures on the impact side is investigated. Before flow separation, gravity and the acceleration of the wedge have negligible influence on the pressure on the impact side for large Froude numbers or small deadrise angles; with increasing the deadrise angle or decreasing Froude number, the effects of gravity and the acceleration of the wedge tend to become more important. Global loads, with the main emphasis on the drag coefficient, are also studied. It is found that for the light wedge, the transient drag coefficient has slow variation in the first half of the collapse stage and rapid variation in the last half of the collapse stage. For the heavy wedge, the transient drag coefficients vary slowly during the whole collapse stage and can be treated as constant. The characteristics of the transient cavity during its formation are investigated. The non-dimensional pinch-off time, pinch-off depth and submergence depth at pinch-off scale roughly linearly as the Froude number.

A comparison study of water impact and water exit models

In problems of global hydroelastic ship response in severe seas including the whipping problem, we need to know the hydrodynamic forces acting on the ship hull during almost arbitrary ship motions. In terms of ship sections, some of them can enter water but others exit from water. Computations of nonlinear free surface flows, pressure distributions and hydrodynamic forces in parallel with the computations of the ship motions including elastic vibrations of the ship hull are time consuming and are suitable only for research purposes but not for practical calculations. In this paper, it is shown that the slamming forces can be decomposed in two components within three semi-analytical models of water entry. Only heave motion is considered. The first component is proportional to the entry speed squared and the second one to the body acceleration. The coefficients in these two components are functions of the penetration depth only and can be precomputed for given shape of the body. During the exit stage the hydrodynamic force is proportional to the acceleration of the body and independent of the body shape for bodies with small deadrise angles.

Elastic wedge impact onto a liquid surface: Wagner's solution and approximate models

The problem of elastic wedge impact onto the free surface of an ideal incompressible liquid of infinite depth is considered. The liquid flow is two-dimensional, symmetric and potential. The side walls of the wedge are modelled as Euler beams, which are either simply supported or connected to the main structure by linear springs. The liquid flow, the deflection of wedge walls and the size of wetted region are determined simultaneously within the Wagner theory of water impact. We are concerned with the impact conditions of strong coupling between the hydrodynamic loads and the structural response. The coupling is well pronounced for elastic wedges with small deadrise angles. This is the case when the fully nonlinear models fail and approximate models based on the Wagner approach are used. In contrast to the existing approximate models, we do not use any further simplifications within the Wagner theory. Calculations of the velocity potential are reduced to analytical evaluation of the added-mass matrix. Hydrodynamic pressures are not evaluated in the present analysis. In order to estimate the maximum bending stresses, both stages when the wedge surface is partially and totally wetted are considered.Three approximate models of water impact, which are frequently used in practical computations, are examined and their predictions are tested against the present numerical solution obtained by the normal mode method within the Wagner theory. It is shown that the decoupled model of elastic wedge impact, which does not account for the beam inertia, provides a useful formula for estimating the maximum bending stress in thick wedge platings.

Three-dimensional oblique water-entry problems at small deadrise angles

AbstractThis paper extends Wagner theory for the ideal, incompressible normal impact of rigid bodies that are nearly parallel to the surface of a liquid half-space. The impactors considered are three-dimensional and have an oblique impact velocity. A formulation in terms of the displacement potential is used to reveal the relationship between the oblique and corresponding normal impact solutions. In the case of axisymmetric impactors, several geometries are considered in which singularities develop in the boundary of the effective wetted region. We present the corresponding pressure profiles and models for the splash sheets.