Gap Resonance Research Articles

The Impact of Heave Motion on Gap Resonance in Floating Structures: A Numerical Investigation

The phenomenon of gap resonance has increasingly captured the attention of researchers due to its significant impact on offshore and coastal structures. Despite extensive studies, the effect of the heave motion of floating structures on gap resonance has lacked thorough investigation. This paper addresses this gap by using a two-dimensional numerical wave tank in OpenFOAM (version v1812) to compare both fixed-box and floating-box systems. Our findings reveal that the inclusion of the heave motions of structures shifts the resonance frequency to higher values (larger kh) and significantly reduces wave amplification compared with fixed-box systems. Furthermore, while gap resonance can induce extreme wave forces, its impact on the rear box in floating-box systems is minimal. These results underscore the necessity of considering the motion of floating structures in gap resonance studies to enhance the stability and design of offshore and coastal structures, a factor that has been insufficiently addressed in previous research.

Effects of gap entrance configuration on gap resonances between two free-heaving barges: Vortex shedding behaviors

This paper mainly concentrates on the influences of the vortex shedding pattern and the behaviors of the generated vortex bubbles on the hydrodynamic performances of two identical side-by-side barges when encountering the linear and nonlinear gap resonances. The vortex shedding pattern around the entrance of the gap is highly influenced by the gap entrance configuration, and thus, two kinds of gap entrance configurations, i.e., round edge and square edge, are taken into account. The vortex shedding patterns are identified during the linear and nonlinear gap resonances for all conditions. Meanwhile, the effects of incident-wave height and barges' heave responses are considered when interacting with different edge shapes. Numerical results demonstrated that both the gap resonances and barges' heave responses are influenced by the vortex generation pattern. Significantly, the magnitudes of the wave elevation at gap during the linear and nonlinear gap resonances are influenced by the coupling effect between the vortex bubbles' pre-behaviors, i.e., vortex shedding pattern, and their post-behaviors, i.e., vortex bubbles' behaviors post-shedding from shear layers, underscoring the importance of understanding vortex shedding patterns and the behaviors of vortex bubble in investigating the gap resonances.

Evaluation of oscillating water column efficiency in the presence of multiple bottom-standing breakwaters under oblique waves

This study proposed an array of bottom-standing breakwaters (BSBs) in the presence of an oscillating water column (OWC) for a better understanding of physical mechanisms, under the framework of a linearized potential flow theory. The free water regions are provided between the multiple BSBs to utilize the gap resonance for energy extraction by OWC. The multi-domain boundary element method is adopted to conduct the parametric study, and the validation of the proposed model is presented. The effect of BSB physical properties, OWC, and incident wave properties are reported on the variation of OWC efficiency, radiation susceptance, conductance, force on the wall, and wave reflection by BSBs against the relative wave frequency and water depth. A comparative study on the variation of coefficients is presented between three types of BSB and flat seabed. The higher number of BSBs enhances the intensity of harmonics and subharmonics of coefficients and strengthens the harmonic trough of efficiency. The Bragg reflection by multiple BSBs diminishes the efficiency of OWC for particular wavelength, and the Bragg peak is suppressed by adopting the permeable property for BSBs. The enlargement of OWC efficiency toward the higher frequencies is observed with an increase in BSB height, width, and chamber length. This study suggests a pair of BSBs with a chamber length equal to water depth for optimal efficiency. Overall, the seaside inclined lip-wall, moderate chamber length, and double BSBs are recommended to diminish the Bragg peak (nearly 18%) and extract the maximum renewable energy for a wider frequency, from the OWC device against the incident waves.

Active infrared tuning of metal–insulator-metal resonances by VO2 thin film

VO2 is a promising phase change material offering a large contrast of electric, thermal, and optical properties when transitioning from semiconductor to metallic phase. Here we show that a hybrid metamaterial obtained by proper combination of a VO2 layer and a nanodisk gold array provides a tunable plasmonic gap resonance in the infrared range. Specifically, we have designed and fabricated a metal–insulator-metal gap resonance by inserting sub-wavelength VO2 film between a flat gold layer and a gold nanodisk resonator array. The resonance of the hybrid metamaterial is centered in the useful 3–5 μm range when VO2 is in its semiconductor state. The experimental study highlights a monotonical spectral tuning of the resonance when increasing temperature up to 50 °C above the room temperature, providing a continuous resonance shift of almost 1 μm in the mid-infrared range. Wavelength range and intensity tunability can be further optimized by modifying the thicknesses of the layers and metamaterial parameters.

Effects of gap entrance configuration on gap resonances between two free-heaving barges: Higher-order harmonics

The hydrodynamic characteristics of linear and nonlinear gap resonances between two identical side-by-side free-heaving barges are investigated in a numerical wave tank based on the constrained interpolation profile method. This study focuses on the influence of the gap entrance configuration on key hydrodynamic parameters during gap resonances, comparing conditions of round and square edges. Additionally, the effects of incident wave height and the barge's heave responses are examined. The distributions of the first four harmonic components of the key parameters are illustrated, including the wave elevation at the gap, wave run-up on each barge, and wave forces. Numerical results reveal that the gap entrance configuration influences more on the linear gap resonance rather than the nonlinear gap resonances. The higher-order components of the wave elevation at the gap are more sensitive to the incident wave height rather than the edge shape. The influences of the edge shape on the wave forces are mainly manifested in the magnitude of the wave forces rather than in their tendencies. Furthermore, the response time during the development stage of gap resonance is analyzed. The findings indicate that gap resonance develops more quickly with square edges or when the incident wave height increases.

Two-dimensional viscous study of coupled nonlinear fluid resonances in two narrow gaps

The wave-induced hydrodynamics of coupled nonlinear piston-mode fluid resonances within two narrow gaps between three barges are numerically investigated using a two-dimensional viscous wave flume. This study aims to explore the time-dependent nonlinear interactions between fluid oscillations in the two gaps. The coupled synchronous dynamic behaviors of fluid oscillations during the transient evolution stage are first examined in terms of amplitude and frequency modulation. It is shown that phase dynamics, including phase slipping, trapping, and locking, play significant roles in establishing the coupled synchronous dynamic evolutions of fluid oscillations in the two gaps. The quasi-steady state of the amplitude- and phase-frequency responses of fluid oscillations within the gaps, along with the reflection and transmission waves in front of and behind the three-barge system, are further analyzed. This analysis clarifies the significance of viscous damping energy dissipation and radiation damping energy transfer involved in gap resonance problems. This clarification also explains the performance of fully nonlinear potential flow solvers in predicting fluid resonances in the two narrow gaps. Finally, the nonlinear dynamic features of fluid oscillations are examined. The effects of incident wave nonlinearity, i.e., wave steepness, on resonant frequencies, response amplitudes, energy dissipation, and reflection and transmission coefficients are investigated. Harmonic analysis via Fourier transformation reveals the contributions of first-, second-, and third-order harmonics to the overall response amplitudes. The physical insights gained from this study provide a deeper understanding of the coupled nonlinear dynamics of piston-mode fluid resonances in multiple narrow gaps.

Hydrodynamics of fluid resonance in a narrow gap between two boxes with different breadths

Violent fluid oscillations occur inside narrow gaps between closely side-by-side structures, threating the safety of the operations. In the current study, fluid resonance in the gap between two side-by-side different boxes is investigated by a two-dimensional viscous-flow numerical wave tank, which can simultaneously predict the viscous damping and free-surface nonlinearity. The accuracy of the established numerical model is fore validated by the published experimental data. The upstream box keeps fixed and has six varied breadths, the downstream box heaves freely under wave actions and remains a constant breadth. The current work aims to study the effects of the breadth ratio and heave motion of the lee-side box on the hydrodynamics of gap resonance. The wave amplification in the gap, the heave motions of the lee-side box, the reflection, transmission, and energy loss coefficients, and the response time and damping time are concerned. Results show that the gap resonance frequency is insensitive to the variation of the breadth ratio. As the breadth ratio increases from 0.4 to 1.4. The maximum wave height amplification in the gap reduces more than 25%. The maximum response time of the fluid resonance occurs when two boxes have equal breadth.

Three-dimensional Effects on Gap-Resonances in Twin-Hull Vessels in Time-Harmonic Vertical Oscillations

Three-dimensional effects induced by dimensional ratios on the gap resonances happening in twin hull vessels oscillating in forced vertical motion have been analyzed. They can lead to relevant consequences, such as the amplification of the inner radiated waves or the generation of standing waves in between the demi-hulls, that can have a direct effect on the operating profile of the vessel. The response of twin hull vessels in waves can be strongly affected by these resonant phenomena. Also, some of these behaviors can be exploited in the framework of wave energy conversion systems. The present analysis is carried out by using an open-source, linear, Boundary Element Method (BEM), based on the Green function approach. Mathematical backgrounds of the added mass and damping coefficients computation for a floating body under harmonic vertical oscillation are provided as well as details of the numerical discretization used in the BEM. A panel mesh sensitivity study is carried out and the numerical prediction is validated by comparison against available experimental data, another CFD solution obtained by a high-fidelity viscous solver based on the open-source libraries Open-FOAM and approximate analytic formulations. The effect of the beam ratio and the length-to-beam ratio on the resonant phenomena has been analyzed. This has been achieved by systematic variations of the geometric dimensions of the hull, focusing on the trends of the hydrodynamic coefficients, the amplitude of the radiated waves, and the location of the resonant frequencies over the analyzed range.

Experimental investigation on gap resonance between two floating vessels

This paper explains the influence of gap resonance phenomena in floating vessels having unequal draughts. Two separate model configurations are considered here: one is a vessel having a shallow draught at the weather side (SW), and the other is a deep draught vessel that comes at the weather side. An experimental investigation was carried out in beam sea conditions, where the vessel could only move freely in the heave and roll directions. By beam sea, we mean the incident waves come at a right angle to the broadside of the vessels. Regular wave tests reveal that even though only a slight difference in the gap resonance frequency is observed for the two configurations, the wave amplification at resonance is 57% higher for SW. The reason for this behavior is explained using the instantaneous velocity and vorticity obtained from the particle image velocimetry analysis for a selected test case. Furthermore, the turbulent characteristics of the flow inside the gap for the configurations are compared at different time instances. The horizontal force acting on the vessels and motions (heave and roll) of the vessels in the beam sea condition are also reported in the study.

Transient gap resonance between two closely-spaced boxes triggered by nonlinear focused wave groups

A two-dimensional (2D) viscous numerical wave flume is developed based on OpenFOAM® to investigate the transient gap resonance problem triggered by nonlinear focused wave groups. The narrow gap is formed by two closely-spaced boxes, where the weather-side box is allowed to heave freely under wave actions, but the rear one is firmly fixed. The overset mesh method is introduced in the numerical model to capture the weather-side box's large-amplitude motion accurately. This work mainly focuses on the coupled effects of free-surface nonlinearity and heave-freedom of the weather-side box on the fluid oscillations in the gap and heave motions of the weather-side box. The heave-freedom of the weather-side box is demonstrated to play an important effect on the period in which the maximum value of non-dimensional amplitude of fluid oscillation in the gap occurs. It is revealed that the free-surface nonlinearity significantly affects the nonlinear fluid oscillations in the gap but has a limited effect on the heave motions of the weather-side box. The four-phase combination method is further employed to conduct the higher harmonic component analysis to clarify the effects of higher harmonic components on the nonlinear response of fluid and box.

Effects of nonlinearities on the gap resonances between two free-heaving barges

The hydrodynamic characteristics of the gap resonances between two identical side-by-side barges are investigated in a constrained interpolation profile method-based numerical wave tank. Each barge can heave freely under the excitation of the incident waves. This paper mainly concentrates on the influences of the nonlinearities during the gap resonances on their hydrodynamic performance, via the parameter study of the incident-wave height. Numerical results demonstrated that the nonlinear gap resonances' magnitudes may reach close to or exceed that of the linear gap resonance and naturally contain strong nonlinearities when considering the heave responses of the side-by-side barges. Meanwhile, the effects of the heave responses on the key hydrodynamic parameters cannot be ignored as well. Therefore, the wave run-ups of the barges are of significant importance for the investigation. On the one hand, the wave run-ups directly reflect the coupling effects between the gap resonances and the twin barges' heave responses. On the other hand, the nonlinearities of the wave run-ups perform stronger than the wave elevation at the gap. Moreover, the linear wave run-ups are proposed via the linear formulas to qualitatively and quantitively investigate the effects of the nonlinearities on the inner process of the wave run-ups by comparison. Based on the harmonic analysis, the features of the distributions of the first four order harmonics of the wave elevation at the gap, the wave run-ups, and the wave loads are illustrated.

A visible light driven photocatalyst Ag/AgBr/SrSb2O6 for removal of model organic contaminants and hexavalent chromium

A single plausible solution to multi-environmental issues is an efficient photocatalyst. The SrSb2O6 with a band gap of 2.72 eV was successfully tailored to 1.99 eV by deposition of Ag/AgBr. The synergistic effect of reduced band gap and surface plasmon resonance (SPR) effect of Ag0 could enhance the photocatalytic efficiency to a greater extent. This work attempts to explore a composite photocatalyst Ag/AgBr/SrSb2O6 for the photodegradation of organic wastes such as dyes, organic solvents, drugs, and antibiotics. In addition, the photo remediation of heavy metal waste such as Cr6+ is also investigated. The propitious results promise Ag/AgBr/SrSb2O6 to be a wide-range photocatalyst that can eliminate both organic and inorganic waste from water. The photodegradation of RhB dye, phenol, and tetracycline reached up to 80.8%, 76.8%, and 64.5%, respectively. Notably, the Ag/AgBr/SrSb2O6 catalyst effectively converted 97.3% of lethal Cr6+ to benign Cr3+. The better electron hole pair separation of the composite was evidenced by PL spectra.

The potential of end-of-life ships as a floating seawall and the methodical use of gap resonance for wave attenuation

This study examines the potential of a new type of floating seawall, made up of retired large-scale oceangoing vessels, to be used in open water and exposed coastal areas. The main objectives of the research are to assess the effectiveness of the floating seawall concept, to determine the contribution of the gap resonance to wave attenuation, and to compare the results of physical tests with those obtained numerically using ANSYS-AQWA. The use of end-of-life ships in this way provides a unique opportunity to extend their life cycle and reduce the environmental and human health risks associated with the current practice of shipbreaking. The research focuses on a multimodule floating seawall configuration, where each module is composed of two hulls that are rigidly connected side by side, with a small gap to induce gap resonance. The results suggest that end-of-life ships can be used as a resource for the construction of floating seawalls for various marine applications. Furthermore, the results demonstrate the positive influence of the gap resonance on the wave attenuation capacity of the seawall, as well as the limitations of the numerical tool in providing realistic values in this region.

Effects of multi motion responses and incident-wave height on the gap resonances in a moonpool

The hydrodynamic characteristics of a free-floating moonpool encountering the gap resonances are investigated based on the constrained interpolation profile method in numerical wave tank. This paper mainly concentrates on the influences of the moonpool's motion responses and the incident-wave height on the gap resonances in the free-floating moonpool. Numerical results demonstrated that the heave response significantly changes the frequency and the magnitude of the linear gap resonance, while the roll motion influences more on the vertical wave loads and the wave responses in the fluid field. The heave and roll response of the free-floating moonpool are generally independent. Moreover, the magnitudes of the nonlinear gap resonances have the tendency of catching up and exceeding the linear gap resonance as the incident-wave height increasing for the free-floating moonpool, which is the consequence of the higher-order harmonics driven by the nonlinear processes and the linear secondary resonant region induced by the heave response. Based on the wavelet transform, it could be observed that the amplified harmonic component usually takes more time to be fully developed than other harmonic components during the development of its corresponding nonlinear gap resonance.

Regulation of band gap and localized surface plasmon resonance by loading Au nanorods on violet phosphene nanosheets for photodynamic/photothermal synergistic anti-infective therapy.

In the face of the serious threat to human health and the economic burden caused by bacterial antibiotic resistance, 2D phosphorus nanomaterials have been widely used as antibacterial agents. Violet phosphorus nanosheets (VPNSs) are an exciting bandgap-adjustable 2D nanomaterial due to their good physicochemical properties, yet the study of VPNS-based antibiotics is still in its infancy. Here, a composite of gold nanorods (AuNRs) loaded onto VPNS platforms (VPNS/AuNR) is constructed to maximize the potential of VPNSs for antimicrobial applications. The loading with AuNRs not only enhances the photothermal performance via a localized surface plasmon resonance (LSPR) effect, but also enhances the light absorption capacity due to the narrowing of the band gap of the VPNSs, thus increasing the ROS generation capacity. The results demonstrate that VPNS/AuNR exhibits outstanding antibacterial properties and good biocompatibility. Attractively, VPNS/AuNR is then extensively tested for treating skin wound infections, suggesting promising in vivo antibacterial and wound-healing features. Our findings may open a novel direction to develop a versatile VPNS-based treatment platform, which can significantly boost the progress of VPNS exploration.

Wave energy conversion by an array of oscillating water columns deployed along a long-flexible floating breakwater

Large-scale spatial configurations combining Wave Energy Converters (WECs) and coastal attenuating-wave facilities have the potential to exploit marine renewable energy sustainably. In this study, an integrated concept of multiple Oscillating Water Columns (OWCs) and a very long floating breakwater is introduced. Associated energy extraction, gap resonance and hydroelastic interaction problems are examined. A coupled numerical simulation methodology consisting of a Finite Volume Method (FVM)based solver and a Finite Element Method (FEM) solver, is developed to investigate the strong fluid and structure coupled problem. The fluid-structure information is matched in real-time and the flexible modes of the floating breakwater are obtained by imposing a restrained beam inside the pontoon. The accurate time-domain model is validated against both simulated and measured data. Extensive parametric studies indicate that the energy conversion has a conflict with the wave attenuation in terms of determining the along-shore number of OWCs. The highest energy conversion in medium-period and long-period waves are observed in the OWCs near the end and middle locations, respectively. Besides, the constructive resonant gap effect between OWCs and the breakwater can amplify the peaks of energy conversion efficiency, leads to a sudden collapse in transmission coefficient curves. With an increased sidewall draft, OWCs closer to oblique incident direction generate stronger piston-type and sloshing oscillations. Additionally, compared with a rigid breakwater, the elastic deformation of the breakwater plays a destructive role in wave energy conversion, which is attributed to the out-of-phase interference of multi-mode radiated waves.

Experimental study on the wave-induced fluid resonance and suppression scheme in the narrow gap of two floating rectangular structures

An experimental study on the wave-induced gap resonance and resonant suppression scheme for two floating rectangular structures (TFRSs) is systematically presented. The instantaneous velocity fields for the present problem are measured using an enhanced underwater particle image velocimetry measurement system. Detailed experimental results have been presented to study the influences of the wave and structural parameters on the gap resonant characteristics. The resonant wave height and wave frequency were sensitive to the variation of the gap width but not very sensitive to the variation of the surface roughness on the rounded corner of TFRSs. The nonlinear effects of harmonic components on resonant free surface elevation are estimated. To analyze the vortex structures, different vortex identification methods in literature are analyzed and their merits and demerits are summarized based on a comparative analysis of the measured velocity data. The Ω-criterion vortex identification approach is then selected to evaluate the vortex intensity and capture the main vortex cores. Thanks to the adopted technique, the subsequent separation of the two quasi-symmetric vortex structures is considered to be a significant contribution to energy dissipation. The vortex shedding and dissipation modes of different TFRSs are very similar and exhibit slight variations in resonant responses. A formula of the modified Reynolds number for the gap resonance problem of TFRSs is proposed. The non-dimensional vortex strengths are nonlinearly dependent on the newly modified Reynolds number and linearly dependent on the Keulegan–Carpenter (KC) number. Finally, an optimal suppression scheme for the gap resonance problem of TFRSs is suggested.

A two-dimensional Reynolds averaged Navier–Stokes investigation on gap resonance and wave elevation around two side-by-side bodies with motions

The coupled dynamics of wave elevation and motions around bodies floating in proximity may be sensitive to radiation and diffraction effects. In this paper, the influence of radiation on wave elevation is examined for two side-by-side boxes subject to forced sway, heave, and roll oscillations in a two-dimensional numerical wave tank. The effects of diffraction on wave elevation and the joint influence of radiation and diffraction are investigated in regular waves assuming free heave motions. Heaving of one or two boxes and single-box sway or roll excites a piston mode of water motions in the proximity gap. Synchronous sway or roll induces sloshing. The close relationship between gap resonance and rapid water exchange in and out of the gap is confirmed. Vortices within the gap drive water exchange and influence the gap wave elevation. Their impact is determined by both spatial and temporal distributions.

Generalized hydrodynamic coefficients of twin connected circular cylinders in finite water depth

In this work the generalized hydrodynamic coefficients of connected twin circular cylinders are studied. Firstly, a matched boundary element method with eigen-function expansion is applied to study the generalized hydrodynamic coefficients of floating and submerged tunnels with twin horizontal cylinders in finite water depth. By numerical examination it is found that gap resonance problem can be neglected for the submerged floating tunnels with a certain submergence depth, and the axial wave number play an important role for the added mass. Then, analytic solutions are derived for the high frequency approximations of the generalized added masses of twin connected cylinders by the eigenfunction expansion in the polar coordinate system with aid of their images about the x-axis in the infinite fluid domain. The high frequency approximations of generalized added masses decrease with increasing vibration wave number. When T/a and B/a are larger than 3 (where T is the cylinder submergence, B is the spacing distance between the twin cylinders and a is the radius of the cross-section of the cylinder), the hydrodynamic interference between the two cylinders can be neglected and the generalized added mass coefficients of connected twin cylinders can be derived from these of single isolated cylinders.

Numerical modelling of a catamaran float-over deck installation for a spar platform with complex hydrodynamic interactions and mechanical couplings

Multi-body system is becoming common in engineering practice, such as the catamaran float-over installation for a Spar platform, one of the most complex marine systems. Gap resonance phenomenon occurs in the catamaran float-over system due to strong hydrodynamic interactions, inducing inaccuracy in evaluations of the hydrodynamic coefficients. To obtain reasonable hydrodynamic coefficients, the damping lid method in AQWA, which provide viscous correction for the potential flow theory, is first validated and then applied to the model in this study. It is found that the damping lid is capable of dealing with the gap resonance phenomenon. With the introduction of the damp lid method in the catamaran float-over system with α = 0.20, the relative error between frequency-domain and time-domain declined from 690% to 1.7%. Based on the corrected frequency-domain results, a time-domain model, considering various types of mechanical coupling components in the float-over system, including LMUs, DSUs, steel-to-steel impacts on LMUs, lateral constrains of LMUs and DSUs, sway fenders, hawsers and the mooring system. Simulations for first contact stage and last contact stage under different incident wave angle are performed. It is observed that the relative motions under quartering sea in first contact stage are the largest. Furthermore, in order to reveal the coupling mechanism, different configurations of the barges and Spar are investigated for the first contact stage under irregular waves. It is found that the relative heave motions on the LMUs are larger when the deck and barges are rigidly connected to form a catamaran-barge.