Enhanced Numerical Modeling of Breaking Waves

The prediction of wave resistance in naval architecture is an important aspect especially at high Froude numbers where a great percentage of total resistance of ships and submerged bodies is caused by waves. In addition, during hull form optimization, wave resistance characteristics of a ship must closely be observed. There are potential, viscous and experimental methods to determine the wave resistance of a ship. Reynolds-averaged Navier-Stokes equation-based methods usually follow the experimental method that determines the form factor first. However, it is proven in recent studies that the form factor changes with the Reynolds number. As the Reynolds number increases, this change in the form factor is being neglected. In this study, a Reynolds-averaged Navier-Stokes equation-based prediction of wave resistance is presented that overcomes this flaw. The methodology is validated with the benchmark problems of submerged and surface-piercing bodies to determine the effectiveness of the proposed method. The method is also validated by experiments carried out at the Ata Nutku Ship Model Testing Laboratory of Istanbul Technical University for a totally submerged ellipsoid and the benchmark KRISO Containership. Results reveal the robustness of the present methodology.

Physics of Fluids, 2004

The focus of the present work is on the numerical simulation of steady flows with spilling breaking waves. In particular, the breaker is modeled through a hydrostatic pressure and a shear stress exerted on the free-surface. Many elements of the exposed model are derived by Cointe and Tulin's theory of steady breaker. The model has been implemented in a RANSE code in a simple but effective way through a modification in the free-surface boundary conditions. At present, the resulting code is valid for two-dimensional flows, and has been accordingly tested against the experimental data obtained by Duncan for the flow generated by a hydrofoil towed under the free-surface at different velocities and depths. 36-1 Paper presented at the RTO AVT Symposium on "Reduction of Military Vehicle Acquisition Time and Cost through Advanced Modelling and Virtual Simulation", held in Paris, France, 22-25 April 2002, and published in RTO-MP-089.

1996

Numerical simulations describing plunging breakers including the splash-up phenomenon are presented. The motion is governed by the classical, incompressible, two-dimensional Navier-Stokes equation. The numerical modelling of this two-phase flow is based on a piecewise linear version of the volume of fluid method. Capillary effects are taken into account as a stress tensor computed from gradients of the volume fraction function. Preliminary results concerning the time evolution of liquid-gas interface and vorticity field are given for short waves, showing how an initial steep wave undergoes breaking and successive splash-up cycles. Different evolutions of the wave energy are observed during the breaking stage. The energy dissipation due to viscosity becomes significantly important at each time of the impact of jet and the formation of splash-up. It is found that nearly 70% of the wave energy is lost after about three periods. Plunging breakers are due to the formation of a jet at the crest of the wave or in its vicinity. Under the influence of gravity the jet plunges down into the water generating a splash-up phenomenon and important turbulence generation (see for example Bonmarin 1 ). Generation of bubbles and spray is observed. Numerical experiments describing the evolution of breaking waves up to the time of impact of the jet have been developed successfully by numerous investigators using methods based on potential flows. Among the main contributions are the works of Longuet-Higgins and Cokelet, 2 Vinje and Brevig, 3 Baker et al., 4 and New et al.. 5 This list is not exhaustive (see for more detailed reviews Peregrine, 6 and Banner and Peregrine 7 ). The process of the initiation of spilling breakers is less well understood. Two main mechanisms have been proposed. Computations of overturning waves by New et al. 5 demonstrated that there is no essential difference between spilling and plunging

2003

Applications of Computational Fluid Dynamics 5 8.3. Potential flow 8.3.1. Guidelines on definition of non-linear problems 8.3.2. Guidelines on integration of viscous effects 8.3.3. Guidelines on definition of geometry 8.3.4. Guidelines on boundary conditions 9. REFERENCES Best Practice Guidelines for Marine Applications of Computational Fluid Dynamics Best Practice Guidelines for Marine Applications of Computational Fluid Dynamics 2. Overview of equations and methods in marine CFD 2.1. Fluid equations of motion In marine CFD we are chiefly concerned with problems in hydrodynamics. In the majority of problems being solved, we are attempting to calculate global pressures and fluid velocity components in a 3 dimensional space surrounding the submerged portion of the marine vehicle or platform of interest. In this way, it is possible to further calculate the forces and moments acting on the vessel, whether steady or unsteady. It is customary to treat the working fluid, in this case water, as incompressible and isothermal. However, it is also possible to make further assumptions regarding the behaviour of the flow, depending upon the nature of the problem in hand and the leading order effects of interest. Therefore here, we start from the beginning and provide definitions of the general fluid equations of motion, from which such special cases (such as gravity driven, incompressible, inviscid and irrotational free surface waves-potential flow) can be derived. The majority of commercial CFD software tools have been written to solve the more general cases of compressible, viscous, turbulent flows with heat transfer, but may be applied to problems in hydrodynamics, so long as the correct choices are made regarding equations of state, fluid properties, and boundary conditions. The definitions given below should provide those attempting problems in hydrodynamics with a guide to how the equations of most interest are derived. 2.1.1. General Fluid Dynamic Equations The general equations of fluid flow represent mathematical statements of the conservation laws of physics, such that: Best Practice Guidelines for Marine Applications of Computational Fluid Dynamics 55 7.2. Example of viscous stern flow calculations Application example calculated with SHIPFLOW/XVISC supplied by FLOWTECH International AB, Gothenburg, Sweden.

Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 2015

The prediction of wave resistance in naval architecture is an important aspect especially at high Froude numbers where a great percentage of total resistance of ships and submerged bodies is caused by waves. In addition, during hull form optimization, wave resistance characteristics of a ship must closely be observed. There are potential, viscous and experimental methods to determine the wave resistance of a ship. Reynolds-averaged Navier–Stokes equation–based methods usually follow the experimental method that determines the form factor first. However, it is proven in recent studies that the form factor changes with the Reynolds number. As the Reynolds number increases, this change in the form factor is being neglected. In this study, a Reynolds-averaged Navier–Stokes equation–based prediction of wave resistance is presented that overcomes this flaw. The methodology is validated with the benchmark problems of submerged and surface-piercing bodies to determine the effectiveness of t...

The availability of robust commercial Computational Fluid Dynamics (CFD) software and the rapid growth in processing power have lead to an increasing use of CFD for the solutions of fluid engineering problems across all industrial sectors. The marine industry is no exception: computational methods are now routinely used, for example, to examine vessel boundary layer and wake, to predict propeller performance and to evaluate structural loads. There has been a growing awareness that computational methods can prove difficult to apply reliably i.e. with a known level of accuracy. This is in part due to CFD being a knowledge-based activity and, despite the availability of the computational software; the knowledge base embodied in the expert user is not available. This has lead to a number of initiatives that have sought to structure existing knowledge in the form of best practice advice. Few notable examples are the best practice guidelines developed by ERCOFTAC, the European Thematic network QNET-CFD and of course the best practice guideline applied to the marine applications, MARNET-CFD. The guidelines presented here build on the work of these initiatives and particularly update the MARNET-CFD Best Practise Guidelines with recent results and conclusions obtained during the VIRTUE project – The Virtual Tank Utility in Europe. The guidelines provide simple practical advice on the application of computational methods in hydrodynamics within the marine industry. It covers both potential and viscous flow calculations.

The paper concerns modeling of two-phase flow with the volume of fluid method (VOF) and two high-resolution advection schemes based on the normalized variable diagram (NVD). Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) and High Resolution Interface Capturing scheme (HRIC). Both considered schemes are used to discretize convective term in the scalar equation for the transport of the volume fraction. High-resolution schemes are employed to minimize influence of the artificial numerical dissipation and to keep the shape of the step interface profile. Original contribution of this work is a detailed comparison of the two high-resolution schemes CICSAM and HRIC in the case of the breaking wave phenomenon. It is shown that using relatively simple to apply, high-resolution schemes it is possible to obtain good agreement with an experimental evidence and other authors results. However, some difficulties connected with optimal size of the local Courant number are adre...

In this study, approaches for calculating the hydrodynamics of breaking waves were examined and the impact of hydrodynamic model errors on the prediction of radar backscatter was assessed. Reynolds-averaged Navier-Stokes (RANS) computations of stationary hydrofoil-generated breaking waves were carried out, including the modeling of the breaking region. These results were compared to experimental data. A subset of these results was used as input to the Veridian scattering model (VSM) and the results were also compared to available data. The results were then used define the research needs in this area.

Applied Mathematical Modelling, 2004

In this paper, a numerical two-phase flow model for incompressible viscous fluid is presented for the simulation of wave propagation in shallow water, including the processes of wave shoaling, wave breaking, wave reflection and air movement. The model consists of the continuity equation, the Navier–Stokes equations, the fractional VOF function equation, and the equations of density and viscosity. The turbulent eddy viscosity is evaluated by using the Smagorinsky's sub-grid scale model. The VOF method with an advection algorithm following [Int. J. Numer Meth. Fluids 35 (2001) 151] is employed for tracking the free surface. To solve the time evolution of the governing equations, the SMAC method and iteration technique are used. The convective terms in the momentum equation are approximated using a high accuracy CIP scheme proposed in [Comput. Phys. Commun. 66 (1991) 219]. A numerical test with dam break problem was conducted and compared with experimental data to verify the validity and stability of the model. The model was then applied to simulate the wave breaking on a sloping bottom and the numerical results were compared with experimental data. The results demonstrated that the present model is capable of simulating wave deformation in shallow water, as well as wave breaking problem.

Journal of Marine Science and Technology

The objective of the present work is to illustrate the performances of the numerical wave models in ocean and coastal environment. Third generation wave models are considered nowadays the most appropriate for such task. These are full spectral models based on the integration on the wave energy (or alternatively wave action) balance equation. In order to cover more aspects related with the modelling process hindcast, nowcast and forecast schemes are discussed and illustrated along six case studies. The major model used was SWAN (acronym for Simulating Waves Nearshore) which is a very flexible model that can be applied in a wide range of coastal applications being effective from high resolution coastal areas up to quasi oceanic scales. In both hindcasts and forecasts the wave forcing was provided by generation models (WAM and WW3), while in nowcast schemes buoy data were used. Various coastal environments that are rather different from the point of view of the bathymetric features and of the characteristics of the environmental matrix were considered. These are the Portuguese continental nearshore with higher resolution sub domains, Madeira Archipelago, the nearshore of Sardinia Island in the Mediterranean Sea and the Black Sea. A general conclusion of this work would be that, despite some limitations, the wave models provide an effective framework in predicting wave conditions in ocean and coastal environment.