CFD Modeling of Regular and Irregular Waves Generated by Flap Type Wave Maker

The improvement of wave generation in numerical tanks represents the key factor in ocean engineering development to save time and effort in research concerned with wave energy conversion. For this purpose, this paper introduces a numerical simulation method to generate both regular and irregular waves using Flap-Type wave maker. A 2D numerical wave tank model is constructed with a numerical beach technique, the independence of the numerical beach slope is tested to reduce the wave reflections. The different governing parameters of the Flap type wave maker were studied such as periodic time dependency and length of the flap stroke. The linear wave generated was validated against the wave maker theory WMT, the numerical results agreed with WMT. The Pierson-Moskowitz model is used to generate irregular waves with different frequencies and amplitudes. The numerical model succeeded to generate irregular waves which was validated against published experimental data and with Pierson-Moskowitz spectrum model using Fourier expansion theory in the frequency domain. Useful results are presented in this paper based on the numerical simulation to understand the characteristics of the waves. This paper produces a full guide to generate both regular and irregular waves numerically using ANSYS-CFX approach to solve the 2D Unsteady Reynolds Averaged Navier-Stokes Equation (URANS).

A NUMERICAL STUDY OF WAVE-CURRENT INTERACTION IN THE BOTTOM BOUNDARY LAYER

In the present work, a numerical wave-current flume has been developed, based on a standard k-ε model. The numerical flume was 12.86m in length, with a numerical beach at one end of the flume. The Volume of Fluid (VOF) method was used to capture the free surface in the flume. The velocity profile obtained at the test section from the numerical simulation has then been compared with experimental data and good agreement found. Periodic velocities in the bottom boundary layer have been obtained which agree well with the experimental data. The model provides an insight to the changes in bed shear stress time histories that characterise wave current interaction.

A 3D Numerical Wave Tank for Coastal Engineering Studies

This paper presents the validation of active and passive, made by a dissipation beach, numerical absorbing methods implemented in RANS-VOF FLUENT® code for modelling long time series of wave propagation interacting with coastal structures. Verification of both numerical techniques was performed in 2D – wave flume, and 3D – wave tank, this one using a multiple active absorption wave makers. The active absorption wave maker allows maintaining the incident wave generation and the mean water level along the time. Good results were obtained for 2D and 3D applications for active absorption wave maker at the generation boundary and both numerical beach and active absorption at the end of the flume/tank.

Regular and Irregular Wave Propagation Analysis in a Flume with Numerical Beach Using a Navier-Stokes Based Model

This paper describes the analysis of the propagation of regular and irregular waves in a flume by using Fluent® model, which is based on the Navier-Stokes (NS) equations and employs the finite volume method and the Volume of Fluid (VoF) technique to deal with two-phase flows (air and water). At the end of the flume, a numerical beach is used to suppress wave reflections. The methodology consists of adding a damping sink term to the momentum equation. In this study, this term is calibrated for three cases of regular incident waves (H = 1 m, T = 5, 7.5, and 12 s) by varying the linear and quadratic damping coefficients of the formulation. In general, while lower values of damping coefficients cause residuals on the free surface elevation due to wave interactions with the outlet boundary, reflection occurs on the numerical beach when higher values are used. A range of optimal damping coefficients are found considering one of them null. In one of these cases, temporal series of free surface elevation are compared with theoretical ones and very good agreement is reached. Afterwards, an irregular wave propagation, characterized by a JONSWAP spectrum, is investigated. Several gauges along the flume are evaluated and good agreement between the spectrum obtained numerically and the ones imposed at beginning of the flume is verified. This study shows the capacity of NS models, such as Fluent®, to simulate adequately regular and irregular wave propagations in a flume with numerical beach to avoid reflections.

A Nonlinear Numerical Wave Tank and its Applications

A two-dimensional fully nonlinear numerical wave tank is developed by using a boundary element method (BEM). The water depth can be shallow or deep. The waves are generated by simulating a piston wave maker or by specifying the input velocity at the upstream boundary. Fully nonlinear free surface conditions are satisfied in the numerical simulations. In the downstream region, a numerical beach is employed to dissipate the wave energy to avoid waves reflecting from the vertical downstream boundary. When there is a body piercing the free surface, another numerical beach is applied upstream the body to damp out only the reflected waves from the body. Two different applications are presented in this paper. The first one is to compute the pressure and velocity at any point inside the wave field. The other application is to calculate the forces on a horizontal cylinder fixed on the free surface. This second application is related to the investigation of the hydrodynamic forces on the pontoon of a fish farm. Nonlinearities are significant since the wave amplitudes can be large relative to the wavelength and the dimension of the cylinder.

Time Domain Simulation of Two Interacting Ships Advancing Parallel in Waves

A 3D Rankine source method is developed to solve the initial-boundary value problem of two ships advancing in waves. Linear wave effects are considered. The two ships are assumed advancing parallel with identical forward speed, with or without stagger, and the Neumann-Kelvin flow is chosen as the steady basis flow. An artificial numerical beach is applied to satisfy the radiation condition. A fourth order Runge-Kutta method is used for the 12 degree of freedom dynamic solver of the two ships. The present solver is validated through studying linear radiation and diffraction problem of one or two ships by comparing with analytical or model test results. The coupled motion solver is applied to a single S-175 ship advancing in waves and two parallel advancing ships which were tested in the MARINTEK towing tank (Ronæss, 2002) and promising agreements are obtained.

Studies in the Stability of a Numerical Wave Tank Model for Generation and Propagation of Steep Nonlinear Long-Crested Surface Waves

We are studying numerically the problem of generation and propagation of gravity long-crested waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed which gives a realistic “continuity condition”, since it tracks the entire fluid domain at all times. A depth profile of the potential is assumed, and employed to perform a waveform relaxation algorithm to decouple the discrete Laplacian along dimensional lines, thereby reducing it’s computation over this total fluid domain. In addition, the full nonlinear kinematic and dynamic free surface boundary conditions are utilized in the algorithm, and a suitably tuned numerical beach is used to avoid reflections. It is well known that instability, in the form of generated spurious “sawtooth waves”, plagues this problem, leading to numerical overflow. This makes it very difficult to generate steep waves for sufficiently long simulation times. The authors have struggled with this problem for some time, with significant success, by employing an “aliasing filter”. This paper outlines our ongoing study of the stability of the model, including an analysis of the possible nature of the underlying causes including compatibility conditions. We conclude by giving a simple practical technique for greatly improving the stability.

The Nonlinear Interaction and Resonance of Steep Long-Crested Bichromatic Surface Waves in a Numerical Wave Tank

We are studying numerically the problem of generation and propagation of long-crested gravity waves in a tank containing an incompressible inviscid homogeneous fluid initially at rest with a horizontal free surface of finite extent and of infinite depth. A non-orthogonal curvilinear coordinate system, which follows the free surface is constructed which gives a realistic “continuity condition”, since it tracks the entire fluid domain at all times. A depth profile is assumed and employed to perform a waveform relaxation algorithm to decouple the discrete Laplacian along dimensional lines, thereby reducing its computation over this total fluid domain. In addition, the full nonlinear kinematic and dynamic free surface conditions are utilized in the algorithm. A bichromatic deterministic wave maker using a Dirichlet type boundary condition and a suitably tuned numerical beach is utilized. This paper pays special attention to satisfying the full nonlinear free surface conditions and presents the nonlinear interaction of the higher order components, especially near resonance.