2-D numerical wave Tank by boundary element method using different numerical techniques (original) (raw)
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Modelling of wave generation in a numerical tank by SPH method
Journal of Ocean Engineering and Marine Energy, 2020
There have been many mathematical and physical modelling strategies to represent a numerical wave tank that can generate the desired wave spectrums. Presently, one of the recent methodologies that have certain intrinsic capabilities for the investigation of free-surface hydrodynamic problems, namely, Smoothed-Particle-Hydrodynamics (SPH) technique, has been utilized for the modelling of a numerical wave tank. The Navier-Stokes and continuity equations are utilized for governing the fluid motion through Weakly Compressible SPH (WCSPH) approach which couples pressure and density by an equation of state. As one of the major numerical treatments, kernel gradient normalization is included into the present SPH method together with the numerical treatments, namely, well-known density smoothing algorithm, hybrid velocity variance-based free surface (VFS), and artificial particle displacement (APD) algorithms. The generation of regular and irregular waves is performed by a moving boundary at the inlet where natural damping is targeted by utilizing a dissipative beach at the end of numerical wave tank. A wide range of test cases in terms of wavelengths and steepness ratios have been investigated for the regular wave simulations. Although the wave-maker is forced linearly to oscillate sinusoidally at the inlet of the tank, due to the relatively high wave steepness ratios applied, the non-linear character of the free-surface has been clearly observed with the performed Fast Fourier Transform analyses. Wave energy densities of the SPH results have also been compared with the linear theory expectations per unit wavelength. To scrutinize the conditions for the wave-breaking inception, three additional wave steepness values have been simulated at a single wavelength value. As a further examination of the proposed SPH scheme, JONSWAP irregular wave spectrum has been utilized with both flap and piston type moving boundaries. In the light of performed simulations, the proposed SPH numerical scheme can provide robust and consistent results while generating regular and irregular wave systems in deep water conditions. Furthermore, it is observed that it has the capability of capturing the non-linear characteristics of generated waves with high sensitivity, including the wave-breaking phenomenon. Keywords SPH method • Regular/irregular wave generation • Wave breaking • Wave energy • Free surface hydrodynamics List of symbols c 0 Reference speed of sound in water c w Celerity of the generated waves d Depth of water f Frequency of waves
Computational Modeling of a Regular Wave Tank
2009 3rd Southern Conference on Computational Modeling, 2009
This paper presents two different numerical methodologies to generate regular gravity waves in a wave tank. We performed numerical simulations of wave generation through the FLUENT ® package, using the Volume of Fluid (VOF) multiphase model to reproduce the wave propagation in the tank. Thus it was possible to analyze two methods for generating regular waves that could be used in future work, especially in the study of devices of energy conversion from ocean waves into electrical energy.
Wave Generation in a Numerical Wave Tank
2017
Article History: Received: 10 May. 2016 Accepted: 15 Mar. 2017 Developing numerical tanks to study wave structure interaction drew engineers’ attention in last decade. Numerical wave tanks are absolutely essential for investigating wave-structure interaction. This paper presents two different numerical software capabilities to generate regular gravity waves in a wave tank. The wave generation was performed using the FLUENT package and Flow-3D. Both models are based on Navier-Stokes and VoF equations. The results of the mentioned models were compared with theoretical results. Free surface elevation and horizontal component of wave particle velocity were the two parameters which have been considered for comparison. Results indicate that Flow-3D in some cases is a bit more accurate than Fluent in capturing free surface elevation. In numerical models it is important to dissipate wave energy and prevent wave reflection. In this way four different slopes were evaluated to determine the mi...
A comparison of methods in fully nonlinear boundary element numerical wave tank development
We present the development and validation of an efficient numerical wave tank (NWT) solving fully nonlinear potential flow (FNPF) equations. This approach is based on a variation of the 3D-MII (mid-interval interpolation) boundary element method (BEM), with mixed Eulerian-Lagrangian (MEL) explicit time integration, of Grilli et al., which has been successful at modeling many phenomena, including landslide-generated tsunami, rogue waves, and the initiation of wave breaking over slopes. The MEL time integration is based on a second-order Taylor series expansion, requiring to compute high order time and space derivatives. In order to solve wave-structure interaction problems with complex geometries, we reformulate the model to use a 3D unstructured triangular mesh, building on earlier work, but presently only working with linear elements. The added flexibility of arbitrary meshes is demonstrated by modeling the longitudinal forces on a truncated (surface-piercing) vertical cylinder, comparing to theory and experiment. In order to improve the computational efficiency of the BEM, we apply the fast multipole method (FMM), in the context of the new unstructured mesh. A detailed study of the resulting computational time shows both the efficiency of the earlier 3D-MII approach and the proposed one, and also what is necessary to scale such results up to larger grids.
A Computational Fluid Dynamics Investigation of a Numerically Simulated Wave Tank
American journal of mechanical engineering, 2020
In this paper, a two-dimensional Numerical Wave Tank (NWT) is proposed to calculate the static pressure variation along the lower wall of an experimental wave-flume. The experimental setup was a 4.72m long wave flume with a flap-type wave-maker. The experiments were carried out at various water heights of 100mm, 80mm, and 60mm, with a motor speed of 60 rpm. The numerical simulations were completed using ANSYS™ Fluent, with two sets solutions: 1) the unsteady, three-dimensional Reynolds Averaged Navier-Stokes (URANS) equations coupled with a k-e turbulence model; 2) unsteady 3-D Euler equations. In both computations, the volume of fluid (VOF) method was used to capture the free surface and a grid independence study was completed. The unsteady Euler simulations showed the best agreement to the experimental results. Several cases were run to complete validation and verification of the numerical model, and the CFD results are in good agreement with the experiment. Thus, for small two-di...
Generation of linear and nonlinear waves in numerical wave tank using CT-VOF method
In this paper, a two-dimensional numerical model is developed for wave simulation and propagation in a wave flume. The fluid flow is assumed to be viscous and incompressible and Navier-Stokes and continuity equations are used as governing equations. Standard k-ε model is used to model turbulent flow. The Navier-Stokes equations are discretized using staggered grids finite difference method and solved by SMAC method. Waves are generated and propagated using a piston type wave maker. An open boundary condition is used at the end of numerical flume. Some standard tests such as lid-driven cavity, constant unidirectional velocity field, shearing flow and dam-break on dry bed are performed to valid the model. To demonstrate the capability and accuracy of the present method, the results of generated waves were compared with available wave theories. Finally, clustering technique (CT) is used for mesh generation and the best condition is suggested.
A Modified Wavemaker Boundary Condition for a Numerical Wave Tank Based on the WCSPH Method
Jurnal Teknologi, 2016
In this paper a space-averaged Navier-Stokes approach was deployed to Modified Wavemaker Boundary condition for a numerical wave tank. The developed model is based on the smoothed particle hydrodynamic (SPH) method which is a pure Lagrangian approach and can handle large deformations of the free surface with high accuracy. In this study, the large eddy simulation (LES) turbulent model was coupled with the weakly compressible version of the smoothed particle hydrodynamics (WCSPH) method to Modified Wavemaker Boundary condition for a numerical wave tank. An absorbing wavemaker boundary condition was developed to absorb the second reflecting waves from the wavemaker. The capacity of absorbing secondary reflecting waves and incoming waves in absorbing wavemaker was validated through comparisons of the numerical results with general wavemaker.
Journal of Computational Physics, 2021
A fully nonlinear potential Numerical Wave Tank (NWT) is developed in two dimensions, using a combination of the Harmonic Polynomial Cell (HPC) method for solving the Laplace problem on the wave potential and the Immersed Boundary Method (IBM) for capturing the free surface motion. This NWT can consider fixed, submerged or wall-sided surface piercing, bodies. To compute the flow around the body and associated pressure field, a novel multi overlapping grid method is implemented. Each grid having its own free surface, a two-way communication is ensured between the problem in the body vicinity and the larger scale wave propagation problem. Pressure field and nonlinear loads on the structure are computed by solving a boundary value problem on the time derivative of the potential. The stability and convergence properties of the solver are studied basing on extensive tests with standing waves of large to extreme wave steepness, up to H/λ = 0.2 (H is the crest-to-trough wave height and λ the wavelength). Ranges of optimal time and spatial discretizations are determined and high-order convergence properties are verified, first without using any filter. For cases with either high level of nonlinearity or long simulation duration, the use of mild Savitzky-Golay filters is shown to extend the range of applicability of the model. Then, the NWT is tested against two wave flume experiments, analyzing forces on bodies in various wave conditions. First, nonlinear components of the vertical force acting on a small horizontal circular cylinder with low submergence below the mean water level are shown to be accurately simulated up to the third order in wave steepness. The second case is a dedicated experiment with a floating barge of rectangular cross-section. This very challenging case (body with sharp corners in large waves) allows to examine the behavior of the model in situations at and beyond the limits of its formal application domain. Though effects associated with viscosity and flow separation manifest experimentally, the NWT proves able to capture the main features of the wave-structure interaction and associated loads.
Validation of a hydrodynamic model for a curved, multi-paddle wave tank
Applied Ocean Research, 2014
ABSTRACT Obtaining a hydrodynamic model for a wave tank has many benefits, from allowing the useable test zone to be identified, to helping with the tuning of the wavemaker controllers. This paper explores a first-order, boundary element method (BEM) that has been previously proposed for modelling wave tanks, applying the method to a tank with a unique, curved geometry. In a series of experiments, the model is shown to provide a good representation of the wave profile across the tank. Inherent limitations in the method are also identified: in the case when only a single paddle is moved, significant, un-modelled second-order spurious waves are found to emerge. Moreover, the representation of the wave absorbers by a simple, partially reflecting surface does not adequately reproduce the measured spatial variation in the reflection coefficient.