Piston-type Wavemaker Research Articles

Experimental and numerical determination of the optimum configuration of a parabolic wave extinction system for flumes

In this work the phenomenon of the wave reflection has been studied using a self-developed passive extinction system. Twenty one type of waves were generated in the laboratory using a piston-type wave maker. The variation of the reflection coefficient, Kr, was studied at several depths (h [m] of 0.3, 0.4, and 0.5), periods (0.636 < T [s] < 1.526), wave heights (0.010 < H [m] < 0.064), slopes (3 < α [°] < 17) and vertical end positions of the extinction system (y1 [m] and y2 [m] defined by y1 [m] and α [°]), covering the linear and non-linear regions of the “Le Méhauté” chart. In parallel, an unsteady numerical model based on the Eulerian multiphase VOF was designed and validated according to the free surface displacement, ɳi, and the calculation of the Kr values. Both type of validations were successful so this model was used in order to determine Kr values at slopes [°] that could not be physically reached by the extinction system. The obtained results allowed to determine the minimum Kr values for each set of experiments and finding a useful non-dimensional relationship of Kr,(h-y1)/λ and Ir as a function of the dispersion parameter, kh.

Experimental study on the effect of second order wavemaker theory on the response of a flexible large diameter monopile in irregular sea

Motivated by the need for larger offshore wind turbines, large diameter monopile foundations are being developed. To ensure safe design, there is a need for model testing and validation of hydrodynamic load models. Scaled model tests with a piston-type wavemaker commonly apply first order wavemaker theory for irregular waves. This approach results in the generation of second (and higher) order spurious (also known as parasitic) free waves in the tank. In this study, the effect of superharmonic spurious waves on the response of a monopile with eigenfrequency close to three times the wave peak frequency is examined experimentally. The bending moment response statistics are not found to be significantly affected by the wavemaker correction. Different wave breaking patterns are observed for individual events, but our results do not indicate any clear relation between breaking waves and the wave generation technique.

Nondimensionalized semi-empirical equation to predict secondary load cycles on vertical cylinders of different diameters

Theoretical solutions including the Morison equation have been widely used to estimate the wave forces exerted on offshore structures of vertical cylindrical configuration. However, none of those methods can accurately predict the wave force of the secondary load cycle induced by a steep wave acting on the cylinder. In this study, regular waves of different wave steepness are generated using an experimental wave flume with a piston-type wavemaker, and the forces exerted on the cylinders of three different diameters are investigated. Using the data-fitting method, the difference between the experimentally measured wave force and that calculated by the Morison equation is empirically formulated, and the effects of key non-dimensional parameters on the force difference function are analyzed. The results show that the amplitude and phase of the force difference function are mainly governed by the incident wave condition including the relative depth, relative amplitude, and relative elevation. On the other hand, the effect of the relative radius is negligible when the diameter-to-wavelength ratio satisfies the small-scale structure condition. The proposed equation is valid for predicting the non-breaking regular wave forces exerted on a vertical cylinder when the secondary load cycle occurs and can be utilized in wave-structure interaction problems.

A generalized second-order 3D theory for coupling multidirectional wave propagation from a numerical model to a physical model. Part II: Experimental validation using an I-shaped segmented wavemaker

This paper provides the experimental validation of the generalized second-order three-dimensional (3D) coupling theory outlined by Yang et al. [Z. Yang, S. Liu, X. Ji, and H.B. Bingham, 2020. A generalized second-order 3D theory for coupling multidirectional nonlinear wave propagation from a numerical model to a physical model. Part I: Derivation, implementation and model verification, submitted for publication] using multidirectional nonlinear 3D irregular waves. Based on the second-order theory for two-dimensional (2D) irregular waves described by Yang et al. (2014a), this work provides a second-order dispersive correction for the physical wavemaker signal which improves the nonlinear 3D wave information transfer between the numerical and physical models compared to the first-order method of Zhang et al. (2007). The important coupling equation and its discretization schemes were presented in detail in Part I. For further validating the performance of the second-order 3D coupling model under complex waves and bathymetry conditions, in this Part II, a careful experimental validation has been carried out by establishing a flat coupling basin and a concave-convex coupling basin. In addition, a sequence of progressively more complex numerical target waves has been used and an I-shaped segmented piston-type wavemaker system has been considered for verification of the theory. The effectiveness, adaptability, and precision of the second-order 3D coupling model have been discussed in detail. The effects of the wave parameters and its nonlinearity on the coupling simulation have also been evaluated from the discrepancy error and a wave harmonic analysis. By defining a space synchronization error, the overall error of the spatial wave field has been analyzed. Coupling simulation experiments using oblique regular and irregular waves, unidirectional irregular waves, and multidirectional irregular waves show that the traditional first-order coupling model has limitations when coupling complex waves with strong nonlinearity. When controlling the waves using the second-order 3D coupling signal, the higher harmonics underlying the numerical waves are accurately captured and transferred into the physical model, and the unwanted second-order spurious free waves are substantially reduced. Results obtained from the experimental verification described in this paper demonstrate the strengths of the second-order 3D coupling theory, which are more evident with increased wave nonlinearity.

Theoretical method for generating solitary waves using plunger-type wavemakers and its Smoothed Particle Hydrodynamics validation

ABSTRACT Although solitary wave generation using a piston-type wavemaker has been common, the method cannot be applied to all wave tanks because many of them have been or will be equipped with plunger-type wavemakers. How to use a plunger to generate solitary waves as good as those generated by a piston is an unsolved but practically significant problem. Herein, a theoretical method is proposed. New formulae for the precise descent of an arbitrary-geometry plunger are derived and constraints on the produced wave height are given. Taking wedge-shaped, box-shaped, and cylinder-shaped plungers as examples, the generic wave-making theory and constraints are then specified. On their bases a Smoothed Particle Hydrodynamics (SPH) model is applied to simulate the solitary wave generation, and its reliability is validated in advance by reproducing available experiments. The SPH-simulated wave profiles, velocity fields, and pressure fields are examined by comparing SPH results with analytical solutions. In addition, plunger-type and piston-type as well as Rayleigh-based and Boussinesq-based solitary wave generation are compared. The results show that the solitary wave generated by a plunger-type wavemaker can be as accurate as the one generated by a piston-type wavemaker, provided that the plunger does not have a sharp corner or an incompatible surface with the wave profile. It is therefore anticipated that the proposed theory will extend the functionalities of existing plunger-type wavemakers and benefit plunger design in the future.

Dynamic and kinematic characterization of the impulsive wavemaker system in a numerical wave tank

We study the dynamical response of a piston-type wavemaker in a numerical wave tank. The two-dimensional, fully viscous unsteady Navier–Stokes equations are solved on a two-phase flow configuration using the volume of fluid method to capture the free surface dynamics. The wavemaker is a moving wall driven by an arbitrary signal waveform. The step response of the wavemaker may generate pulse-like waves similar to an undular bore propagating along the tank. Wave elevation at the piston wall has close similarity to the time response of second order systems found in feedback theory. The scaling found for water elevation at the piston wall for different step velocities and mean still water levels is in agreement with that in the available theory at low Froude numbers. The results along the tank for continuous waves agree with those of potential theory. The power input during the step response was determined during the whole wave generation process showing that net piston forces are predominantly hydrostatic. A power scaling for different mean still water levels and step velocities as a function of the Froude number was obtained. An active absorption strategy based upon a feedback controller driving a secondary piston was implemented. Wave absorption was successfully achieved on regular and irregular waves.

Numerical Investigation of Wave Generation Characteristics of Bottom-Tilting Flume Wavemaker

Motivated by the recently developed bottom-tilting wavemaker specially designed for tsunami research, we propose to investigate numerically the wave generation mechanism of this new wave generator. A series of numerical experiments is carried out using a RANS-based computer model to evaluate the effects of wavemaker length, bottom displacement, motion duration, and water depth on the wavelength, wave amplitude, phase speed, and waveform of the leading waves produced by the bottom-motion wave generator. Numerical results fit well with the existing laboratory data. Explicit equations for the wavelength and wave amplitude are developed and can serve as the guideline for wave generation. Encouraging results suggest that bottom-tilting wavemaker is a good alternative to the traditional piston-type wavemaker for tsunami research.

New nonlinear theory for a piston-type wavemaker: The classical Boussinesq equations

In this study, we present a new nonlinear theory for a moving boundary wavemaker of piston-type based on a nonlinear dispersive shallow water model, where the classical Boussinesq equations are employed as a starting point. The new theory is inherently different from the traditional wavemaker theories, such as the usual theories employed for solving the Laplace equation equipped with the free surface boundary conditions by using the perturbation approach. To verify the wavemaker theory proposed in this study, the ratio of the wave height relative to the stroke characterizing the performance of the wavemaker was observed and compared with numerical, experimental, and Havelock's theoretical results, thereby confirming that the results obtained with the proposed theory were in significant agreement. Furthermore, a comparison of the solitary wave generated by the proposed theory and the known exact solution showed that they were in good agreement.

Analysis of soliton gas with large-scale video-based wave measurements

An experimental procedure for studying soliton gases in shallow water is devised. Nonlinear waves propagate at constant depth in a 34\,m-long wave flume. At one end of the flume, the waves are generated by a piston-type wave-maker. The opposite end is a vertical wall. Wave interactions are recorded with a video system using seven side-looking cameras with a pixel resolution of 1\,mm, covering 14\,m of the flume. The accuracy in the detection of the water surface elevation is shown to be better than 0.1 mm. A continuous monochromatic forcing can lead to a random state such as a soliton gas. The measured wave field is separated into right- and left-propagating waves in the Radon space and solitary pulses are identified as solitons of KdV or Rayleigh types. Both weak and strong interactions of solitons are detected. These interactions induce phase shifts that constitute the seminal mechanism for disorganization and soliton gas formation.

Forces on a semi-submersible in internal solitary waves with different propagation directions

Experiments were conducted to study the forces acting on a semi-submersible platform induced by internal solitary waves (ISWs) with different propagation directions. The ISW propagation directions range from 0 deg to 180 deg at the interval of every 30 deg. A series of depression ISWs were generated by a laboratory piston-type wave-maker in a two-layer fluid system. Conductivity probes are used to obtain the ISW profiles at the interface of the two-layer fluid. Experimental results show that the force peak on both columns and pontoons part induced by ISWs increases linearly with wave amplitude under all the propagation directions. The force peak is also influenced significantly by propagation direction. The inline force peak on the pontoons part reaches the maximum in the 90 deg direction, while that of the columns part is the largest in the 30 deg direction at the same wave amplitude. The transverse force on pontoons part is almost zero in the 0 deg and 90 deg direction. The force peaks of 30 deg and 150 deg have no obvious difference because of the symmetrical semi-submersible, so are 60 deg and 120 deg. Besides, effects of propagation direction on the vertical force peak are negligible.

Olatu-kanal baten balioztatze esperimentala eta konputazionala

BiMEP-Biscay Marine Energy Platform- eta Mutriku Wave Energy Plant-eko azpiegituretan itsas energiaren inguruko ikerkuntza egiten da, itsas baldintza errealetan. Bilboko Ingeniaritza Eskolako Fluidoen Mekanikako laborategian dagoen olatu-kanala (12,5 × 0,6 × 0,7 m, luzera × zabalera × sakonera) azpiegitura horietan izaten diren baldintzak erreproduzitzeko gai da, eskala txikiago batean. Olatu-kanal horrek, pistoi motako olatu-sorgailu bat erabiliz, olatu monokromatiko eta pankromatiko mota desberdinekin lan egiteko aukera eskaintzen du. Ultrasoinuak erabiltzen dituzten zenbait zundak ur-gainazalaren desplazamendu bertikala neurtzen dute, eta tankearen amaieran kokatuta dagoen hondartzak, parabola-formadunak, olatuaren energia disipatzen du horren islapena murriztuz. «Reynolds Averaged Navier Stokes» (RANS) ekuazioetan oinarritutako zenbakizko modelo bat sortu da Star-CCM+ kode komertziala erabiliz, gainazal askean gertatzen diren fenomenoak simulatzeko. Zenbakizko modelo horren balioztatzea aurkezten da artikulu honetan, sakonera, olatu-altuera, uhin-luzera eta periodo desberdinak bateratuta eta egindako esperimentu sortarekin konparatuta. Emaitza guztiak fluxu potentzialaren teoriatik lortutako emaitza analitikoekin batera aztertu dira. Lan honetan aurkezten diren esperimentuek kanal horren eraginkortasunaren mugak ezartzen dituzte, olatuen sorkuntzari, hedapenari eta suntsipenari dagokienez. Etorkizunean egingo diren ikerkuntza-lanetako parametroak ezartzeko ere baliogarria izan da lan hau: egitura flotagarrien eta olatuen arteko interakzioa, olatu energiaren bihurgailuak eta ainguratze- eta amarradura-sistemak aztertuko dira.

Active Control of A Piston-Type Absorbing Wavemaker with Fully Reflective Structure

Multiple reflections of the waves between structure and wavemaker in hydraulic flumes could change the frequency content of the desired incident wave or result in resonance. A prominent approach to avoid multiple reflections is active control of the wavemaker. This paper proposes a simple and practical active control algorithm for piston-type wavemaker. The block diagram of the control system is presented in real time domain. It is shown that there is no need to use any transfer function or filter in the feedback and feed forward loops and the use of constant gains can yield acceptable results. In the operating frequency range (0.25–2 Hz), it is revealed that the proposed system is very effective at suppressing the excitation of resonant sloshing for regular wave. In the case of irregular waves, it is depicted that the experimental waves agree quite well with the desired wave elevation in frequency domain. In addition, comparison of the results obtained both with and without absorption discloses the good characteristics in time domain.

Piston-Driven Numerical Wave Tank Based on WENO Solver of Well-Balanced Shallow Water Equations

A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model.

MPS Method for Interaction Between Solitary Waves and Submerged Horizontal Plate

The interaction between structure and wave is a typical phenomenon in naval architecture and ocean engineering. In this paper, numerical simulation is carried out to study the interaction between a two-dimensional submerged, fixed, horizontal rigid plate and solitary wave with our in-house meshless particle CFD solver MLParticle-SJTU. First, the in-house CFD solver is verified by experimental results conducted at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. During the verification, the plate is submerged under water and the solitary wave with a given amplitude is generated by a piston-type wave maker. Free surface elevation of the wave and the pressure impacting on the plate is recorded and compared with experimental data respectively. The predicted pressure and surface elevation agree well with the experimental results. Then in order to further investigate factors affecting wave-structure interaction, wave height, submerged depth and plate length are analyzed.

Comparative study on the breaking waves by a piston-type wavemaker in experiments and SPH simulations

ABSTRACT The wave transfer function derived from the linear wavemaker theory has been widely applied to validate the accuracy of the regular wave. However, it is limited to analyze the waves with large wave steepness, short wavelength, or breaking wave generated right on the wave paddle. By introducing the piston stroke-to-water depth ratio, the empirical formula in the literature is modified to predict both regular and breaking waves according to the wave steepness. Using an experimental wave flume, regular and breaking waves are generated by manipulating the target wave steepness and stroke-to-water depth ratio. The proposed equation is verified in accordance with the experiment results, and optimal variables including energy loss coefficient and breaker index are presented by analyzing the root-mean-square errors. With the developed equation, wave heights and relative depths from any type of piston-type wavemaker can be predicted if the variables of the proposed equation are properly adjusted. Additionally, the numerical wave tank (NWT) is modeled by smoothed particle hydrodynamics (SPH), and the numerically calculated wave heights show good agreement with the proposed equation. The developed methodology can be employed as a guideline toward further studies including analyses of structural behavior under the breaking wave.

Generating stable solitary waves with a piston-type wavemaker

The generation of stable and pure solitary waves in large-scale experimental flumes and numerical models is the focus of this study. Such waves give a better description of the target wave amplitude, has minimal amplitude dissipation during propagation and has negligible trailing waves. In the present study, the two solitary wave generation methodologies, namely, Goring's Method (GM) and the Malek-Mohammadi and Testik Method (MMTM), described in Goring (1979) and Malek-Mohammadi and Testik (2010) respectively, have been used to examine the solitary wave solutions of Boussinesq, Rayleigh, Grimshaw and Fenton, both experimentally and numerically for three different relative wave height (ε), ratios of 0.1, 0.3 and 0.6. Numerical modeling is done within a Smoothed Particle Hydrodynamics (SPH) framework developed in Valizadeh and Rudman (2017). For each ε value, we have compared the experimental and numerical results in terms of the free surface profiles and the phase speeds to give recommendations for the solitary wave solution and the generation methodology that demonstrates the best performance. Our results indicate that the Rayleigh solitary wave solution gives more accurate profiles in both experiments and numerical simulations. With respect to wave generation methodology, the MMTM gives the best results in the experiments, whereas, the GM describes the target waves better in our numerical SPH simulations.

A Parametric Study of the Wave-Generation Performance of a Piston-Type Wave Maker

The wave-generation performance of a piston-type wave maker was analyzed using the numerical wave tank technique, and the numerical results were compared with theoretical solutions. A two-dimensional frequency domain analysis was conducted based on the Rankine panel method. Various parameters were used to examine the wave-generation performance, such as the width and gap of the wave board. The effects of the thickness of the wave board and of the gap from the bottom of the tank were evaluated. The difference in the amplitude of the generated wave between the analytical solution and the numerical result was examined, and its causes were addressed due to the gap flow between the bottom of the tank and the wave board. This parametric analysis can be utilized to design an optimum wave make parametric analysis to design an optimum wave maker that can generate waves with amplitudes that can be predicted accurately.

EXPERIMENTAL AND NUMERICAL CHARACTERISATION OF A 2D WAVE FLUME

A wave flume of 12.5 x 0.6 x 0.7 m (length x width x height) able to reproduce the ocean conditions of the most representative research facilities in the Basque Country (BiMEP-Biscay Marine Energy Platform and Mutriku Wave Energy Plant) has been recently installed at the laboratory of Fluid Mechanics of the Faculty of Engineering in Bilbao. This new facility has the capacity of producing a wide range of monochromatic and panchromatic waves by a piston-type wavemaker. Several ultrasonic wave probes measure the surface elevation, and the wave energy is dissipated in a passive parabolic beach in order to diminish significantly the reflection along the flume. A numerical model based on Reynolds Averaged Navier Stokes (RANS) equations has been developed to represent the turbulence and Eulerian Volume of Fluid (VOF) unsteady approach in STAR-CCM+ CFD code to track the evolution of the free surface. This numerical model has been validated with the corresponding experimental campaign covering a wide range of depths, wave heights, wavelengths and periods. Tests focused on the description of the basic hydrodynamic processes of wave generation and propagation, giving as a result the definition of the wavemaker to produce the required wave. Results were analysed together with the analytical solution based on potential flow theory. The experiments carried out in the present study establish the operational limits of the wave flume in terms of wave generation, propagation and extinction, defining the operational range of future experimental campaigns where wave interaction with floating structures, wave energy converters and mooring systems will be studied. Keywords: experimental wave flume, numerical wave flume validation, wave characterisation, BiMEP, renewable marine energy, CFD models

Hydrodynamic performance of a floating offshore OWC wave energy converter: An experimental study

To investigate the dynamic response of a floating moored oscillating water column device under realistic sea states, a focused wave technique was developed in this study to generate user-defined wave trains in a wave basin equipped with a piston-type wavemaker. The experimental setup allowed for simultaneous measurements of the designed focused wave trains, internal chamber wave elevations and air pressure, dynamic tendon response and the model's global motion responses. Based on the experimental results it was found that to accurately replicate the theoretical wave time series, a minimal focal reconstruction of 200 components was required which resulted in a focused wave regeneration accuracy greater than 93% with strong repeatability. The tested model showed typical motion responses to that of generalised tension leg platform systems with significant surge offsets along with stiff heave and pitch motions. Applying vertical tendons to the system allowed for the floating offshore device to be exposed to deeper waters, and hence the larger energy source associated with deep water ocean waves.

Vulnerability assessment of coastal bridge superstructure with box girder under solitary wave forces through experimental study

This study presented a vulnerability assessment of a selected coastal bridge located at Haitan Strait on the east China sea through experimental study. The extreme wave is simulated using the solitary wave that generated by piston-type wave maker in a medium-sized wave-flow flume at Southwest Jiaotong University's Deep-Water Long-span Bridge Laboratory. Horizontal and vertical wave forces acting on the deck with a box girder due to solitary wave are measured through laboratory experiments. Seventy-five cases included three water depths, five wave heights, and five submergence coefficients are conducted in the experiment. Although there is plenty of work addressing the extreme wave forces on the coastal bridge's superstructures, the experimental study that focuses on the vulnerability assessment of coastal bridge superstructures subjected to extreme wave forces, especially for the box girder geometry, are absent. Combined with the experimental data and snapshots, the effects of non-dimensional wave heights and submergence coefficients on wave forces are discussed in detail. The structural capacity is determined according to the structural parameters of the approach span of the selected prototype coastal bridges. In addition, the dominant structural failure modes of the simply support superstructures are assumed to be uplift and lateral displacement. The vulnerability assessment of the given coastal bridge superstructure is accessed by comparing wave forces with superstructure's capacities. The results indicate that: 1) compared to the submerged condition, the elevated superstructure suffers larger horizontal and vertical wave forces; 2) the impulsive wave force plays an important role in the vertical wave force on the deck with a box girder, especially for the high-elevated superstructure; 3) the failure probability of coastal bridge superstructure subjected to extreme wave conditions will be effectively reduced by increasing the elevation height of the superstructure. This study provides a further understanding of the fragility of the box-type superstructure under the extreme disaster.