Physical Wave Tank Research Articles

Modelling physical wave tank with flap paddle and porous beach in OpenFOAM

The capability of a numerical model to mimic the operation of a physical wave tank allows us to carry out complementary numerical tests to explore various aspects or to investigate the insights of the physical tests, which are otherwise not feasible with limited measured data. The numerical model could also be extended beyond the physical limitation of a laboratory facility, such as “full-scale” tests with realistic conditions at lower cost and shorter turnaround time. In this paper, we present a construction of such a numerical model of a physical wave tank with flap paddles and porous beaches. The model is built based on the Navier-Stokes solver and the Volume of Fluids method in the open-source software Open Field Operation and Manipulation (OpenFOAM). The paddles and the beaches are explicitly modelled to mimic the behaviours of the physical counterparts in the tank. High quality laboratory experiments of regular and focused waves were conducted for the validation of the numerical model. Extension of the numerical model to a three-dimensional wave tank with individually controlled paddles is also demonstrated.

Experimental and numerical measurements of wave forces on a 3D offshore stationary OWC wave energy converter

In this paper, wave forces on a 1:50 model–scale of an offshore stationary Oscillating Water Column (OWC) device are studied in 3D physical and numerical wave tanks. In total 310 physical experiments including repetition were performed in a wave tank for regular waves of different heights and periods, and several turbine–induced pneumatic damping conditions simulated via orifice plates. A Computational Fluid Dynamics (CFD) model based on the RANS equations and the VOF surface capturing scheme was constructed and validated against the tank measurements. The validated CFD model was then utilized to investigate the effects of tank sidewalls on the predicted wave forces. It was found that the horizontal wave force acting on the OWC device was always larger than the vertical force. The total horizontal and vertical forces were maximum and minimum, respectively at the intermediate wavelength. In addition, the pneumatic damping had a significant impact on the measured vertical force, whereas negligible effects were observed on the horizontal force. Increasing the wave height increased nonlinear effects on the forces measured, especially the vertical force. It was concluded that a tank width of less than five times the OWC device breadth will likely provide misleading wave forces due to blockage effects.

Wave shoaling over steep slopes-An experimental investigation

Shoaling characteristics of waves on steep slopes are unique due to significant reflections. Wave heights on steep slopes are altered in a way that is different from wave interaction with mild slopes. Studies on detailed characterization of such phenomenon on steep slopes are scanty. In this study, an attempt has been made to quantify the wave shoaling coefficient (Ks) on steep slopes. Wave shoaling and reflection characteristics are studied on steep sloped (1/2.8, 1/3.8, 1/5.6), smooth and impermeable beaches a physical wave tank facility. The thorough analysis of experimentally measured wave heights along the steep slopes revealed that Ks is influenced by relative depth which is the ratio of shoaling depth (dsh) and shoaling wave length (Lsh) as well as surf similarity parameter (ξ) and this led to an empirical formula between Ks and other important parameters related to initial wave and beach slope conditions. Through this study, application of linear wave theory (LWT) has been extended for the estimation of shoaling coefficients on steep slopes, which otherwise reported to be not applicable. The derived empirical relations were also tested for the results obtained from experiments performed on a gentle slope (1/100) for similar test conditions. The details of experimental program, analyzing methodology and results are discussed in this paper.

Experimental Investigation of Motion and Wave Induced Forced On Semi-Submersible in Regular Wave

For the design of safe and economic offshore structure the knowledge of the wave environment and related wave-structure interactions is required. In general, frequency domain analysis has been regarded as an adequate tool for the assessment of motion and loads which are needed to derive the stress and hydrodynamics forces as well as operational limitations. For investigating the behavior of response to specific sea conditions, this research analyzes the behavior of the response due to motion and wave forces as well as hydrodynamics with focus on a type square column. The frequency domain investigation has used to provide the response behaviors on the wetted body of the semi-submersible in regular waves. For investigation,, the selected sea condition for regular wave is generated in a physical wave tank, and the behavior of the response on the semi-submersible is evaluated at model scale. GumusutKakap model has been choosing as a case study in this research. Equation of motion was formulated to evaluate the mass, damping and stiffness at every frequency step. In frequency domain analysis, the hydrodynamics responses were obtained. The motion response results were obtained as Response Amplitude Operators (RAO) in heave, roll and pitch.

Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part I: Formulation, implementation and numerical properties

In this series of two papers, we report on the irregular wave extension of the second-order coupling theory of numerical and physical wave model described in [Z. Yang, S. Liu, H.B. Bingham and J. Li. Second-order theory for coupling numerical and physical wave tanks: Derivation, evaluation and experimental validation. Coast. Eng. 71, 37–51]. We also correct several errors which unfortunately appeared in that manuscript. In the present part I, the full second-order coupling theory for irregular wave is described in detail. The new second-order coupling signal is presented including both superharmonics and subharmonics and covering wavemaker configurations of the piston- and flap-types. The second-order dispersive correction allows for an improved nonlinear transfer of wave information between the two models. For practical implementation, the coupling equations are solved by a combined five-point Lagrange interpolation and the fourth-order Runge–Kutta scheme, with a numerical velocity time series which is decomposed by the Newton–Raphson iterative method. Analytical evaluations on the suppression of spurious free waves and the relative errors of the resultant bound waves have been conducted by considering a 2nd-order, bi-chromatic wave over a range of dimensionless water depth and oscillation frequency combinations, indicating that the resultant wave quality is significantly improved using the second-order coupling theory. A separate verification combining numerical and experimental model of the theory will be presented in Part II by the same authors.

Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part II: Experimental validation in two-dimensions

This paper provides an experimental validation of the second-order coupling theory outlined by Yang et al. (Z. Yang, S. Liu, H.B. Bingham and J. Li., 2013. Second-order coupling of numerical and physical wave tanks for 2D irregular waves. Part I: Formulation, implementation and numerical properties, submitted for publication) using 2D irregular waves. This work provides a second-order dispersive correction for the physical wavemaker signal which improves the nonlinear transfer of information between the numerical and physical models compared to the first-order method of Zhang et al. (2007). The important nonlinear parameters and numerical performance were theoretically investigated in Part I. In the present Part II, careful experimental validation is carried out using a sequence of progressively more complex analytical and numerical target waves. The results demonstrate clearly that improved performance is achieved by using the second-order correction. When controlling with a second-order coupling signal, two key points are notable: (i) The higher harmonics underlying the numerical waves are accurately captured and transferred into the physical model. (ii) The second-order behavior leads to an unwanted spurious freely propagating second harmonic that is substantially reduced when compared to an identical wave paddle operating with a first-order coupling signal. Using nonlinear regular (monochromatic), bi-chromatic and irregular wave cases as well as varying coupled wave tank bathymetries, both these aspects are verified over a broad range of wave frequencies and shown to be extensively applicable to physical wave tanks.

A Load Cell for the Measurement of Slack Mooring Forces

A load cell for the measurement of mooring forces is designed using the load-strain principles and the same is verified for its efficiency by structural modeling. A model load cell is fabricated and calibrated through laboratory experiments using three axes loading as well as mooring chain catenary principles. Experiments are also conducted in the physical wave tank to measure the mooring forces exerted on a disc shaped data buoy by using the designed load cell. The details of the design concepts, structural modeling, instrumentation, calibration, wave tank experiments and the results are discussed in this paper.

Force-controlled absorption in a fully-nonlinear numerical wave tank

An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank.In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain.The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

Second-order theory for coupling 2D numerical and physical wave tanks: Derivation, evaluation and experimental validation

A full second-order theory for coupling numerical and physical wave tanks is presented. The ad hoc unified wave generation approach developed by Zhang et al. [Zhang, H., Schäffer, H.A., Jakobsen, K.P., 2007. Deterministic combination of numerical and physical coastal wave models. Coast. Eng. 54, 171–186] is extended to include the second-order dispersive correction. The new formulation is presented in a unified form that includes both progressive and evanescent modes and covers wavemaker configurations of the piston- and flap-type. The second order paddle stroke correction allows for improved nonlinear wave generation in the physical wave tank based on target numerical solutions. The performance and efficiency of the new model is first evaluated theoretically based on second order Stokes waves. Due to the complexity of the problem, the proposed method has been truncated at 2D and the treatment of regular waves, and the re-reflection control on the wave paddle is also not included. In order to validate the solution methodology further, a series of nonlinear, periodic waves based on stream function theory are generated in a physical wave tank using a piston-type wavemaker. These experiments show that the new second-order coupling theory provides an improvement in the quality of nonlinear wave generation when compared to existing techniques.

Focused waves and wave–structure interaction in a numerical wave tank

Sustainable and efficient design solutions are the aim for any engineer. In offshore engineering forces resulting from extreme wave impact are of special interest as these challenge the structure and the crew working in this harsh environment. Theoretical models tend to be limited to linear or weakly non-linear situations and are unable to predict the violent and turbulent effects of breaking waves in combination with wave run up on structures or green water loading. The classic approach for such cases is to carry out scale model tests in a physical wave tank and measure the forces, water levels and flow velocities at some chosen locations.Another approach is to use fully non-linear calculations, such as Computational Fluid Dynamics, which have the potential to investigate the design in different conditions at full scale. This paper deals with the generation and behaviour of extreme focused wave groups in a numerical wave tank. Non-linear effects of these extreme waves are shown and the implications for a numerical wave tank are discussed. Also the forces on horizontal and vertical cylinders, which represent simple models of offshore structures, are calculated. All numerical results are compared with measured data from physical experiments.

Estimating ocean wave directional spreading from an Eulerian surface elevation time history

The directional spreading of sea states is an important design parameter in offshore engineering. Wave directionality affects the resulting wave kinematics, which affects the forces exerted on offshore structures. In this paper, we develop a method for estimating the amount of spreading, when the only information available is the time history of free surface elevation at a single point in space. We do this by predicting the second-order bound waves that occur at the difference in frequency of two freely propagating waves. The magnitude of these second-order bound waves is a function of the angle between the interacting waves. Thus, it is possible to infer some information about spreading from a single-point time history. We demonstrate that this approach works for wave groups in a fully nonlinear numerical wave tank. We create a synthetic random sea state and introduce noise into the analysis and thus show that our approach is robust and insensitive to noise, even with a signal-to-noise ratio of unity in the difference waves. This approach is also applied to random waves in a physical wave tank where spreading was directly measured and also to a storm recorded in the North Sea. In all cases, we find our estimate of spreading is in good agreement with other measurements.

A fully-spectral 3D time-domain model for second-order simulation of wavetank experiments. Part A: Formulation, implementation and numerical properties

In this series of two parent papers, we report on the development and validation of a 3D second order numerical wave tank (NWT) model, SWEET. In the present part (A), the fully spectral time domain formulation is described in detail. Among other original aspects, the resulting scheme is based on a resolution achieved by fast Fourier transforms (FFTs) only, leading to very interesting properties in terms of computational efficiency. An extensive verification study of the model accuracy and convergence properties is reported in the context of both local and global quantities. The efficiency and fast-convergence offered by the proposed spectral method allow one to accurately account for the shortest wavelengths in the wavetank, while keeping computational times within affordable limits. The practical capabilities of the model are reported in length in the parent paper [Bonnefoy F, Le Touzé D, Ferrant P. A fully-spectral 3d time-domain model for second-order simulation of wavetank experiments. Part B: Validation, calibration versus experiments and sample applications. Appl Ocean Res 2005 [submitted for publication]], in which various 2D and 3D complex wave system simulations are compared with experiments and detailed analysis, examples given of the use of SWEET in assisting the design of experiments in a physical wavetank, and more validation results provided.

Numerical Modeling of Wave Absorbers for Physical Wave Tanks

A 3D numerical solution was derived to determine the wave field in a physical wave tank equipped with a porous wave absorber of variable width and draft. The solution was achieved by applying the boundary element method. The model was applied to analyze the effect of the geometry and material of wave absorbers on wave reflection to eventually equip a wave tank with a proper wave absorber. The results show that absorber geometry has a complex, often surprising and nonintuitive effect on wave reflection. A more pronounced effect on wave reflection possesses physical and hydraulic properties of the material used to build a wave absorber. A reduction of wave reflection can usually be achieved by increasing absorber length and simultaneously decreasing its slope, and often a reduction of wave reflection can be achieved by increasing absorber draft or width. Moreover, a reduction of wave reflection, often substantial, can be achieved by increasing porosity and the damping coefficient. The results and additional analysis show that a reasonable wave reflection level can already be achieved for fairly short absorbers, and the model can be applied to select an optimal wave absorber for any prespecified conditions. Theoretical results are in reasonable agreement with experimental data.

Dramas of the sea: episodic waves and their impact on offshore structures

For the design of safe and economic offshore structures and ships the knowledge of the extreme wave environment and related wave/structure interactions is required. A stochastic analysis of these phenomena is insufficient as local characteristics in the wave pattern are of great importance for deriving appropriate design criteria. This paper describes techniques to synthesize deterministic task-related ‘rogue’ waves or critical wave groups for engineering applications. These extreme events, represented by local characteristics like tailored design wave sequences, are integrated in a random or deterministic seaway with a defined energy density spectrum. If a strictly deterministic process is established, cause and effect are clearly related: at any position the nonlinear surface elevation and the associated pressure field as well as the velocity and acceleration fields can be determined. Also the point of wave/structure interaction can be selected arbitrarily, and any test can be repeated deliberately. Wave–structure interaction is decomposable into subsequent steps: surface elevation, wave kinematics and dynamics, forces on structure components and the entire structure and structure motions. Firstly, the generation of linear wave groups is presented. The method is based on the wave focussing technique. In our approach the synthesis and up-stream transformation of arbitrary wave packets is developed from its so-called concentration point where all component waves are superimposed without phase-shift. For a target Fourier wave spectrum a tailored wave sequence can be assigned to a selected position. This wave train is linearly transformed back to the wave maker and—by introducing the electro-hydraulic and hydrodynamic transfer functions of the wave generator—the associated control signal is calculated. The generation of steeper and higher wave groups requires a more sophisticated approach as propagation velocity increases with wave height. With a semi-empirical procedure the control signal of extremely high wave groups is determined, and the propagation of the associated wave train is calculated by iterative integration of coupled equations of particle tracks. With this deterministic technique ‘freak’ waves up to heights of 3.2 m have been generated in a wave tank. For many applications the detailed knowledge of the nonlinear characteristics of the flow field is required, i.e. wave elevation, pressure field as well as velocity and acceleration fields. Using a finite element method the velocity potential is determined, which satisfies the Laplace equation for Neumann and Dirichlet boundary conditions. In general, extremely high rogue waves or critical wave groups are rare events embedded in a random seaway. The most efficient and economical procedure to simulate and generate such a specified wave scenario for a given design variance spectrum is based on the appropriate superposition of component waves or wavelets. As the method is linear, the wave train can be transformed down-stream and up-stream between wave board and target position. The desired characteristics like wave height and period as well as crest height and steepness are defined by an appropriate objective function. The subsequent optimization of the initially random phase spectrum is solved by a sequential quadratic programming method (SQP). The linear synthetization of critical wave events is expanded to a fully nonlinear simulation by applying the subplex method. Improving the linear SQP-solution by the nonlinear subplex expansion results in realistic rogue-waves embedded in random seas. As an illustration of this technique a reported rogue wave—the Draupner ‘New Year Wave’ is simulated and generated in a physical wave tank. Also a ‘Three Sisters’ wave sequence with succeeding wave heights H s,…,2 H s,…, H s, embedded in an extreme sea, is synthesized. For investigating the consequences of specific extreme sea conditions this paper analyses extreme roll motions and the capsizing of a RO–RO vessel in a severe storm wave group. In addition, the seakeeping behaviour of a semi-submersible in the Draupner New Year Wave, embedded in extreme irregular seas is numerically and experimentally evaluated.

A note on the difference in the speed of gravity waves in a physical and numerical wave tank

Precise measurements of gravity waves with very small wave slope in a physical wave tank are compared with an explicit linear inviscid wave maker theory. The main purpose is to measure the speed of the physical waves relative to those computed. We find that the wave speed in the physical wave tank is slightly less than in the computations. The small difference in the wave speed leads to a relative phase difference between the real waves and the inviscid computations of about 0.01±0.006 rad per wavelength (0.16±0.1%), which is comparable to an estimated phase delay due to the boundary layer at the tank walls. In this result, the estimated effects of weak non-linearity and surface tension in the experiments are subtracted. This relative phase difference is significantly smaller than what previous investigations in wave tanks of similar size have indicated. This means that physical wave tank simulations can effectively be applied as reference for numerical simulations of steep (non-linear) waves.