Hydroelastic Response Research Articles

Experimental and numerical investigation of hydroelastic response of a flexible hydrofoil in cavitating flow

The objective of this paper is to investigate the hydroelastic response of a flexible NACA66 hydrofoil in cavitating flows by combined experimental and numerical studies. Experimental results are presented for rigid/flexible NACA66 hydrofoils fixed at α0=8° for subcavitating (σ=8.0) and cavitating flows (σ=1.4). The high-speed video camera and Laser Doppler Vibrometer are applied to investigate the flow patterns and vibration characteristics. The multiphase flow is modeled with the incompressible and unsteady Reynolds Averaged Navier–Stokes (URANS) equations. The k−ω SST turbulence model with the turbulence viscosity correction and the Zwart cavitation model are introduced to the present simulations. The results showed that the cavitation has significant effect on the foil deformation and the unsteady characteristics of the hydroelastic response. The bending deformation is enhanced when the cavitation occurred. Meanwhile, the hydroelastic response has also affected the cavitation development and the vortex structure interactions. The cavity shedding frequency and vortex shedding and interacting frequency for the flexible hydrofoil are higher than that for the rigid hydrofoil. Compared to the periodic development of the hydrodynamic coefficients for the rigid hydrofoil, the hydrodynamic load coefficients of the flexible hydrofoil fluctuate more significantly, and the chaotic response of the flexible hydrofoil is mainly attributed to the disturbance caused by the flow-induced flutter and deformation of the foil. The evolution of the transient cavity shape and the corresponding hydrodynamic response can be divided into three stages: During the development of the attached cavity, the partial sheet cavity is formed and develops with the lift and drag coefficients increasing, while the maximum attached cavity formed on the suction side of the flexible hydrofoil is larger than that of the rigid hydrofoil, which is caused by the increase of the effective angle of attack due to the twist deformation. During the vortex structure interaction and cavity shedding process, the hydrodynamic loads for the flexible hydrofoil fluctuate because of the foil deformation, leading to a more complex cavitation pattern. During the residual cavity shedding and partial sheet cavity formation process, the cavities, together with the counter-rotational vortex structures, shed downstream totally and are followed by the formation of partial sheet cavities in next period, which is in advance for the flexible hydrofoil due to the larger effective angle of attack.

Hydroelastic analysis of a very large floating structure edged with a pair of submerged horizontal plates

This paper is concerned with the hydroelastic problem of a very large pontoon-type floating structure (VLFS) edged with a pair of submerged horizontal plates, which is a combination of perforated and non-perforated plates attached to the for-end and back-end of the VLFS. For the hydroelastic analysis, the fluid is assumed to be ideal and its motion is irrotational so that a velocity potential exists. The VLFS is modeled as an elastic plate according to the classical thin plate theory. The fluid-structure interaction problem is separated into conventional hydrodynamics and structure dynamics by using modal expansion method in the frequency-domain. It involves, firstly, the deflection of the VLFS, which is expressed by a superposition of modal functions and corresponding modal amplitudes. Then the boundary element method is used to solve the integral equations of diffraction and radiation on the body surface for the velocity potential, whereas the vibration equation is solved by the Galerkin’s method for modal amplitudes, and then the deflection is obtained by the sum of multiplying modal functions with modal amplitudes. This study examines the effects of the width and location of the non-perforated horizontal plates on the hydroelastic response of the VLFS, then the performance of perforated plates is investigated to reduce the motion near the fore-end of the VLFS. Considering the advantages and disadvantages of submerged plates without and with cylindrical holes, we propose a simple anti-motion device, which is a combination of a pair of perforated and non-perforated plates attached to the for-end and back-end of the VLFS. The effectiveness of this device in reducing the deformation and bending moment of the VLFS has been confirmed, and is compared with the results in cases without and with the submerged horizontal plates by the analysis in this paper.

Numerical investigation of the hydroelastic response in cavitating flow around a flexible hydrofoil

The objective of this paper is to investigate the hydroelastic response of cavitating flows around a flexible hydrofoil. The numerical simulations are performed by solving the incompressible and unsteady Reynolds Average Navier-Stokes (URANS) equations via the commercial CFD software ANSYS CFX. The k-ω SST turbulence model with the turbulence viscosity correction and the Kubota cavitation model are introduced to the present simulations. The results showed that the cavitation has significantly affected the foil deformation and the evolution of the transient cavity shape and the corresponding hydrodynamic response with time can be divided into three stages: during the development of the attached cavity, the cavity formed on the suction side of the flexible hydrofoil is much larger with a steeper slope of the cavity area, which is caused by the increase of the effective angle of attack due to the twist deformation. During the vortex-cavitation interaction process, the hydrodynamic loads for the rigid hydrofoil remain relatively flat, while that for the flexible hydrofoil fluctuates with high frequency because of the foil deformation, leading to a more complex cavitation pattern due to the interaction with the foil vibration. During the cavity shedding process, both the primary and the residual cavities shed downstream totally, together with the counter-rotational vortex structures, corresponding to a sharp drop in the hydrodynamic loads. The larger effective angle of attack leads to the advanced cavity inception of the next cavitation period.

The Nonlinear Hydroelastic Response of a Semi-Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves

The nonlinear hydroelastic response of very large floating structures (VLFSs) or an ice sheet floating on the surface of deep water, idealized as a semi-infinite thin elastic plate, is investigated analytically in the case of nonlinear incident waves. Assuming that the fluid is inviscid and incompressible and the motion is irrotational, we consider incident progressive waves with a given angular frequency within the framework of potential flow theory. With the aid of the homotopy analysis method (HAM), the convergent analytical series solutions are derived by solving the simultaneous equations in which we apply a convergence-control parameter to obtain convergent solutions with relatively few terms. The clear calculation results are represented to show nonlinear wave-plate interaction. The effects of different physical parameters, including incident wave amplitude, Young’s modulus, the thickness and density of the plate on the wave scattering, and the hydroelastic response of the floating plate, are considered. We find that the variations of the plate stiffness, thickness, and density greatly change amount of wave energy which is reflected into the open water region and is transmitted into the plate-covered region. Further, the hydroelastic response of the plate also can be affected by the amplitude of incident wave.

FEM Hydroelastic Models with Application to the Nonlinear Response of Large Floating Bodies in Shallow Wave Conditions

Abstract A higher order finite element scheme is presented for the study of the transient hydroelastic response of a floating, thin, nonlinear strip in shallow wave conditions. First, nonlinear effects are introduced only in the elasticity model, where large deflections and non-negligible normal stress variation in the lateral direction are assumed. The nonlinear beam is initially coupled with the linearized and subsequently with the full nonlinear Shallow Water equations, introducing nonlinearity in both the hydrodynamics and the elasticity model. The effects of the incorporated nonlinear effects are assessed through a numerical example featuring an elevation pulse of increasing steepness.

Experimental and Numerical Analysis of Hull Girder Vibrations and Bow Impact of a Large Ship Sailing in Waves

It is of great importance to evaluate the hull structural vibrations response of large ships in extreme seas. Studies of hydroelastic response of an ultra large ship have been conducted with comparative verification between experimental and numerical methods in order to estimate the wave loads response considering hull vibration and water impact. A segmented self-propelling model with steel backbone system was elaborately designed and the experiments were performed in a tank. Time domain numerical simulations of the ship were carried out by using three-dimensional nonlinear hydroelasticity theory. The results from the computational analyses have been correlated with those from model tests.

Hydro-structural issues in the design of ultra large container ships

The structural design of the ships includes two main issues which should be checked carefully, namely the extreme structural response (yielding & buckling) and the fatigue structural response. Even if the corresponding failure modes are fundamentally different, the overall methodologies for their evaluation have many common points. Both issues require application of two main steps: deterministic calculations of hydro-structure interactions for given operating conditions on one side and the statistical post-processing in order to take into account the lifetime operational profile, on the other side. In the case of ultra large ships such as the container ships and in addition to the classical quasi-static type of structural responses the hydroelastic structural response becomes important. This is due to several reasons among which the following are the most important: the increase of the flexibility due to their large dimensions (Lpp close to 400 m) which leads to the lower structural natural frequencies, very large operational speed (> 20 knots) and large bow flare (increased slamming loads). The correct modeling of the hydroelastic ship structural response, and its inclusion into the overall design procedure, is significantly more complex than the evaluation of the quasi static structural response. The present paper gives an overview of the different tools and methods which are used in nowadays practice.

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.

Global hydroelastic model for springing and whipping based on a free-surface CFD code (OpenFOAM)

The theoretical background and a numerical solution procedure for a time domain hydroelastic code are presented in this paper. The code combines a VOF-based free surface flow solver with a flexible body motion solver where the body linear elastic deformation is described by a modal superposition of dry mode shapes expressed in a local floating frame of reference. These mode shapes can be obtained from any finite element code. The floating frame undergoes a pseudo rigid-body motion which allows for a large rigid body translation and rotation and fully preserves the coupling with the local structural deformation. The formulation relies on the ability of the flow solver to provide the total fluid action on the body including e.g. the viscous forces, hydrostatic and hydrodynamic forces, slamming forces and the fluid damping. A numerical simulation of a flexible barge is provided and compared to experiments to show that the VOF-based flow solver has this ability and the code has the potential to predict the global hydroelastic responses accurately.

Global hydroelastic analysis of ultra large container ships by improved beam structural model

Some results on the hydroelasticity of ultra large container ships related to the beam structural model and restoring stiffness achieved within EU FP7 Project TULCS are summarized. An advanced thin-walled girder theory based on the modified Timoshenko beam theory for flexural vibrations with analogical extension to the torsional problem, is used for formulation of the beam finite element for analysis of coupled horizontal and torsional ship hull vibrations. Special attention is paid to the contribution of transverse bulkheads to the open hull stiffness, as well as to the reduced stiffness of the relatively short engine room structure. In addition two definitions of the restoring stiffness are considered: consistent one, which includes hydrostatic and gravity properties, and unified one with geometric stiffness as structural contribution via calm water stress field. Both formulations are worked out by employing the finite element concept. Complete hydroelastic response of a ULCS is performed by coupling 1D structural model and 3D hydrodynamic model as well as for 3D structural and 3D hydrodynamic model. Also, fatigue of structural elements exposed to high stress concentration is considered.

Stochastic procedures for extreme wave induced responses in flexible ships

Different procedures for estimation of the extreme global wave hydroelastic responses in ships are discussed. Firstly, stochastic procedures for application in detailed numerical studies (CFD) are outlined. The use of the First Order Reliability Method (FORM) to generate critical wave episodes of short duration, less than 1 minute, with prescribed probability content is discussed for use in extreme response predictions including hydroelastic behaviour and slamming load events. The possibility of combining FORM results with Monte Carlo simulations is discussed for faster but still very accurate estimation of extreme responses. Secondly, stochastic procedures using measured time series of responses as input are considered. The Peak-over-Threshold procedure and the Weibull fitting are applied and discussed for the extreme value predictions including possible corrections for clustering effects.

Structural Safety Assessment of a 1100 TEU Container Ship, Based on a Enhanced Long Term Fatigue Analysis

This paper is focused on an enhanced integrated method for structural safety assessment of maritime ships under extreme random wave loads. In this study is considered an 1100 TEU container test ship, with speed range 0 to 18 knots. The most comprehensive criteria for ships structural safety evaluation over the whole exploitation life is based on the long term ship structures analysis, that includes: stress hot-spots evaluation by 3D/1D-FEM hull models, computation of short term ship dynamic response induced by irregular waves, long term fatigue structure assessment. The analysis is enhanced by taking into account the ships speed influence on hydroelastic response. The study includes a comparative analysis on two scenarios for the correlation between the ships speed and waves intensity. The standard constant ship speed scenario and CENTEC scenario, with total speed loss at extreme waves condition, are considered. Instead of 20 years ship exploitation life estimated by classification societies rules from the long term structural safety criteria, the enhanced method has predicted more restrictive values of 14.4-15.7 years. The numerical analyses are based on own software and user subroutines. The study made possible to have a more realistic approach of ships structural strength assessment, for elastic and faster ships as container carriers, in compare to the standard one based only on naval rules, delivering a method with higher confidence in the designed structural safety.

Hydroelastic response of a circular plate in waves on a two-layer fluid of finite depth

The hydroelastic response of a circular, very large floating structure (VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the plate-covered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.

Stochastic hydroelastic analysis of a very large floating structure using pseudo-excitation method

This paper is concerned with the linear hydroelastic response of a pontoon-type very large floating structure (VLFS) in short-crested irregular waves. The linear potential theory is employed for the analysis of VLFS in frequency domain. To decouple the fluid–structure interaction, the higher-order boundary element method (HOBEM) combined with the finite element method (FEM) is adopted. VLFS is modeled as a Mindlin plate, and the mode superposition method is used to reduce the dimension of dynamic equations. The pseudo-excitation method (PEM) is adopted to analyze the stationary stochastic response of the floating structure. The efficiency of this new calculation scheme with the application of PEM is investigated in comparison with the conventional method for stochastic response by analyzing the computational complexity theoretically. Finally, the new calculation scheme is validated by comparing with the experimental data as well as the existing numerical results calculated in the conventional way. In addition, the efficiency of the present numerical approach is also testified which indicates that the proposed numerical scheme is time-saving.

Time-domain numerical and experimental analysis of hydroelastic response of a very large floating structure edged with a pair of submerged horizontal plates

This paper is concerned with the hydroelastic problem of a pontoon-type, very large floating structure (VLFS) edged with the perforated plates, non-perforated plates or their combination anti-motion device both numerically and experimentally. A direct time domain modal expansion method, taking amount of the time domain Kelvin sources in hydrodynamic forces, in which the fluid flows across the perforated anti-motion plate by applying the Darcy's law, is applied to the fluid–structure interaction problem. A quarter of numerical model is built based on the symmetry of flow field and structure in hydrodynamic forces, and special care is paid to the rapid and accurate evaluation of time domain free-surface Green functions and its spatial derivatives in finite water depth by using interpolation–tabulation method. Using the developed numerical tools and the model tests conducted in a wave basin, the response-reduction efficiency of the perforated plates is systematically assessed for various wave and anti-motion plate parameters, such as plate width, porosity and submergence depth. As a result of the parametric study, the porosity 0.11 is selected as the optimal porosity, and the relationship between the porosity and the porous parameter is developed by using the least-squares fitting scheme. After simulation and verification, the dual anti-motion plates which are the perforated-impermeable-plate combination attached to the fore-end and back-end of the VLFS, are designed for more wave energy dissipation and added damping. Considering variation of the water depths in offshore, discussion on the effectiveness of these anti-motion devices at different water depths is highlighted.

Influence of cavitation on the hydroelastic stability of hydrofoils

This work numerically examines the effect of turbulent and cavitating flow on the hydroelastic response and stability of a hydrofoil. A cantilevered, rectangular, chordwise rigid hydrofoil is modeled as a 2-degrees-of-freedom structure for its spanwise bending and torsional flexibilities. The fluid flow is modeled with the incompressible, Unsteady Reynolds Averaged Navier–Stokes equations using an eddy-viscosity turbulence closure model that is corrected for the presence of cavitation, and with a transport equation based cavitation model. The results show that, in general, massive cavitation tends to: (i) reduce the mean lift, (ii) increase the mean drag, (iii) lower the mean deformations, and (iv) delay static divergence, while unsteady sheet/cloud cavitation promotes flow induced vibrations. Such vibrations and load fluctuations could be as large as (and even greater than) the mean values for cases with unsteady cavitation, so dynamic and viscous fluid–structure models are needed to simulate flexible hydrofoils in cavitating flows. In general, the flow induced vibrations, and hence the drag force, are higher with decreasing stiffness. For small leading edge partial cavitation, increasing foil flexibility increases the maximum cavity length and reduces the cavity shedding frequency; however, the influence of foil flexibility is limited for cases where the maximum cavity length is near or beyond the foil trailing edge, because of the relocation of the center of pressure at the elastic axis, near the mid-chord. The results show that the mean deformations are generally limited by stall, and by the quasi-steady linear theory predictions at the fully-wetted and supercavitating limits. Furthermore, frequency focusing can occur when the cavity shedding frequency is near the fundamental system resonance frequencies, and broadening of the frequency spectrum can occur due to excitation of the sub-harmonics and/or modulation induced by the fluctuating cavities, if the cavity shedding frequency is away from the fundamental system resonance frequencies.

A study on the proximity interference and synchronization between two side-by-side flexible cylinders

In this paper, we present the results of a study of the effects of proximity interference on the hydro-elastic responses of two pre-tensioned flexible cylinders in side-by-side arrangement subjected to uniform cross-flow (CF). Two flexible cylinders of the same size, properties, and pretensions were tested with two different vertical separation distances. It was found that at a small center-to-center separation distance (2.75 diameters), the upper cylinder showed no upper branch in the first CF lock-in region. With the increase in the initial vertical separation, both cylinders exhibited amplitude responses similar to the isolated cylinder. At this small separation distance, the upper cylinder showed a CF frequency response (higher values) quite distinct from both the lower cylinder and the single cylinder. For the reduced velocity range of 1.82≤Ur≤5.1, strong phase synchronization was detected. Anti-phase synchronization was even detected within the region of the collapsed classical vortex-induced vibration (VIV) amplitude response. It was also found that even for a separation of 5.5 diameters, the wakes of the cylinders were strongly synchronized within the region of high cylinder vibration amplitudes (2.91≤Ur≤5.1). From the analysis of the synchronization, no synchronization was built up for very small amplitudes for the large separation case, in contrast to the small separation case. The mean drag and the fluctuating components of the drag and lift forces of both cylinders showed quite different behaviors.

Numerical and experimental analysis of hydroelastic response on a very large floating structure edged with a pair of submerged horizontal plates

This paper aims to investigate the hydroelastic response of the very large floating structure (VLFS) with the perforated, non-perforated or the dual submerged horizontal plates both numerically and experimentally. A modal expansion approach is applied to the fluid–structure interaction problem in the frequency domain. The boundary element method solutions based on Kelvin sources are used for the hydrodynamic diffraction and radiation forces, in which the viscous effect of the perforated anti-motion plate is taken into consideration through the Darcy’s law. As a comparison of the data between calculations and experiments, the relationship between the porosity and the porous parameter is developed using the least-squares fitting scheme. The effectiveness of the attached non-perforated and perforated plates in reducing the motion of the VLFS is systematically assessed for various wave and anti-motion plate parameters, such as plate width, porosity and submergence depth. After simulation and verification, we propose a simple anti-motion device, which is the perforated-impermeable-plate combination attached to the fore-end and back-end of the VLFS. The performance of this anti-motion device has been confirmed as an optimal design. Considering variation of the water depths in offshore, discussion on the hydroelastic response of the VLFS with these anti-motion devices at different water depths is highlighted.

Hydroelastic slamming response in the evolution of a flip-through event during shallow-liquid sloshing

The evolution of a flip-through event [6] upon a vertical, deformable wall during shallow-water sloshing in a 2D tank is analyzed, with specific focus on the role of hydroelasticity. An aluminium plate, whose dimensions are Froude-scaled in order to reproduce the first wet natural frequency associated with the typical structural panel of a Mark III containment system, is used. (Mark III Containment System is a membrane-type tank used in the Liquefied Natural Gas (LNG) carrier to contain the LNG. A typical structural panel is composed by two metallic membranes and two independent thermal insulation layers. The first membrane contains the LNG, the second one ensures redundancy in case of leakage.) Such a system is clamped to a fully rigid vertical wall of the tank at the vertical ends while being kept free on its lateral sides. Hence, in a 2D flow approximation the system can be suitably modelled, as a double-clamped Euler beam, with the Euler beam theory. The hydroelastic effects are assessed by cross-analyzing the experimental data based both on the images recorded by a fast camera, and on the strain measurements along the deformable panel and on the pressure measurements on the rigid wall below the elastic plate. The same experiments are also carried out by substituting the deformable plate with a fully stiff panel. The pressure transducers are mounted at the same positions of the strain gauges used for the deformable plate. The comparison between the results of rigid and elastic case allows to better define the role of hydroelasticity. The analysis has identified three different regimes characterizing the hydroelastic evolution: a quasi-static deformation of the beam (regime I) precedes a strongly hydroelastic behavior (regime II), for which the added mass effects are relevant; finally, the free-vibration phase (regime III) occurs. A hybrid method, combining numerical modelling and experimental data from the tests with fully rigid plate is proposed to examine the hydroelastic effects. Within this approach, the measurements provide the experimental loads acting on the rigid plate, while the numerical solution enables a more detailed analysis, by giving additional information not available from the experimental tests. More in detail, an Euler beam equation is used to model numerically the plate with the added-mass contribution estimated in time. In this way the resulting hybrid method accounts for the variation of the added mass associated with the instantaneous wetted length of the beam, estimated from the experimental images. Moreover, the forcing hydrodynamic load is prescribed by using the experimental pressure distribution measured in the rigid case. The experimental data for the elastic beam are compared with the numerical results of the hybrid model and with those of the standard methods used at the design stage. The comparison against the experimental data shows an overall satisfactory prediction of the hybrid model. The maximum peak pressure predicted by the standard methods agrees with the result of the hybrid model only when the added mass effect is considered. However, the standard methods are not able to properly estimate the temporal evolution of the plate deformation.

Measurement of ship hydroelastic response using multiple wireless sensor nodes

A measurement system is required for the assessment of the structural and kinematic response of a free-running model, either at model or full scale. Tethered and optical measurements systems used in towing tanks and wave basins are unsuited to this application. A system of wireless sensor nodes with synchronised video capability has been developed which allows rigid body motions and three-axis accelerations to be obtained by a single nine degree of freedom sensor node whilst the structural deformation of the hull girder can be obtained from a minimum of three nodes in parallel. The system performance was assessed in a controlled towing tank environment in comparison to a tethered system, using three nodes mounted on a flexible, four segment model hull. Measurements from the wireless system were comparable to the tethered results with the same degree of accuracy. Further tests showed a single node to produce comparable measurements to an optical system. The additional synchronised video capability allows a visual image of an extreme wave encounter to be correlated to the magnitude of the responses experienced. Practical advantages of the wireless system demonstrate its viability for acquiring high quality model data; further development should allow its application to full scale.