Effect of wave-directionality on second-order loads induced by the set-down

At first-order of approximation a sea-state may be considered as an infinite sum of Airy components with angular frequencies ω_i and wave-number vectors k_i. A second-order analysis shows the co-existence of long waves appearing at the difference frequencies ω_i—ω_j with wave-number vectors k_i—k_j. In shallow water they become appreciable in amplitudes and may induce slow-drift motion of moored structures.For small values of ω_i—ω_j,k_i—k_j may take all kinds of directions for an angular-spread wave system. Then it may be questioned how the in-line and transverse second-order accelerations compare to those obtained for a mono-directional wave-system.This analysis is carried out here by relating the spectra of the second-order horizontal accelerations to the directional wave-spectrum. Numerical applications are first performed for deep water. They show that at low frequencies, even for very narrowly spread wave systems, the transverse component is larger than the in-line component. In shallow water both components are dratically reduced as compared to the mono-directional case. As a consequence one may question the validity of model-testings or numerical models which take no account of the directionality of the wave-system.     

Boundary layer approach in the modeling of breaking solitary wave runup

The boundary layer is very important in the relation between wave motion and bed stress, such as sediment transport. It is a known fact that bed stress behavior is highly influenced by the boundary layer beneath the waves. Specifically, the boundary layer underneath wave runup is difficult to assess and thus, it has not yet been widely discussed, although its importance is significant. In this study, the shallow water equation (SWE) prediction of wave motion is improved by being coupled with the k–ω model, as opposed to the conventional empirical method, to approximate bed stress. Subsequently, the First Order Center Scheme and Monotonic Upstream Scheme of Conservation Laws (FORCE MUSCL), which is a finite volume shock-capturing scheme, is applied to extend the SWE range for breaking wave simulation. The proposed simultaneous coupling method (SCM) assumes the depth-averaged velocity from the SWE is equivalent to free stream velocity. In turn, free stream velocity is used to calculate a pressure gradient, which is then used by the k–ω model to approximate bed stress. Finally, this approximation is applied to the momentum equation in the SWE. Two experimental cases will be used to verify the SCM by comparing runup height, surface fluctuation, bed stress, and turbulent intensity values. The SCM shows good comparison to experimental data for all before-mentioned parameters. Further analysis shows that the wave Reynolds number increases as the wave propagates and that the turbulence behavior in the boundary layer gradually changes, such as the increase of turbulent intensity.     

Effect of turbulence modelling on the computation of the near-wake flow of a circular cylinder

An evaluation of four well-known Reynolds-Averaged Navier-Stokes (RANS)-based turbulence models was performed in comparison with the results of a dedicated experimental measurement on the near-wake of a circular cylinder in a large water (cavitation) tunnel using a state-of-the-art two-dimensional Digital Particle Image Velocimetry (DPIV) device.The turbulence models investigated were Spalart-Allmaras (S-A), Realizable k-ε (RKE), Wilcox k-ω (WKO) and Shear-Stress-Transport k-ω (SST), which were assessed based on their comparative performances in predicting some important flow field characteristics of the near-wake region of the experimental circular cylinder flow. Within the flow range investigated in this study, which implied a cylinder diameter-based Reynolds Number of 41,300, the qualitative and quantitative comparisons revealed that the application of the SST model to the wall-bounded unsteady flow - that experienced severe adverse pressure gradient, massive flow separation and vortex shedding - presents more successful predictions compared to other models investigated for such challenging flow conditions.     

2DOF numerical investigation of a planing vessel in head sea waves in deep and shallow water conditions

Analysis of a craft with two degrees of freedom (2DOF) consumes time more than simulation of a craft with a fixed trim condition; therefore in most of the previous researches fixed trim condition is taken into account to analyze the flow field around a craft in shallow water and head sea wave conditions. In this paper numerical simulation of Reynolds Average Naiver Stokes (RANS) equations are used to analyze the motion of DTMB 62 model 4667-1 planing vessel in calm water and head sea waves in both deep and shallow water with two degrees of freedom (heave and pitch). For this purpose, a finite volume ANSYS-FLUENT code is used to solve the Navier-Stokes equations for the simulation of the flow field around the vessel. In addition, an explicit VOF scheme and SST k-ω model is used with dynamic mesh scheme to capture the interface of a two-phase flow and to model the turbulence respectively in the 2DOF model.Regarding the results, reducing the wavelength and also the depth of the water can increase the drag force. Also comparing the results of a fixed trim vessel with the results of a free to sink and trim one in calm water shows a difference of approximately 50% in the drag force in shallow water.     

Numerical modeling of wave runup and forces on an idealized beachfront house

In this paper, a numerical wave model based on the incompressible Reynolds-averaged Navier–Stokes (RANS) and k–ε equations is used to estimate the impact of a solitary wave on an idealized beachfront house located at different elevations on a plane beach. The locations of the free surface are reconstructed by volume of fluid (VOF) method. The model is satisfactorily tested against the experimental data of wave runup, and the analytical solution of wave forces on vertical walls. The time histories of wave profiles, forces, and overturning moments on the idealized house are demonstrated and analyzed. The variations of wave forces and overturning moments with the elevation of the idealized beachfront house are also investigated.     

A coupled model of submerged vegetation under oscillatory flow using Navier–Stokes equations

This work presents a new model for wave and submerged vegetation which couples the flow motion with the plant deformation. The IH-2VOF model is extended to solve the Reynolds Average Navier–Stokes equations including the presence of a vegetation field by means of a drag force. Turbulence is modeled using a k–ε equation which takes into account the effect of vegetation by an approximation of dispersive fluxes using the drag force produce by the plant. The plant motion is solved accounting for inertia, damping, restoring, gravitational, Froude–Krylov and hydrodynamic mass forces. The resulting model is validated with small and large-scale experiments with a high degree of accuracy for both no swaying and swaying plants. Two new formulations of the drag coefficient are provided extending the range of applicability of existing formulae to lower Reynolds number.     

Numerical modeling of flow and scour below a pipeline in currents: Part I. Flow simulation

The performance of the standard k–ε, Wilcox high-Reynolds-number k–ω, Wilcox low-Reynolds-number k–ω and Smagorinsky's subgrid scale (SGS) turbulence models is examined against the flow around a circular cylinder 0.37 diameter above a rigid wall. The governing equations are solved using finite difference method in a non-orthogonal boundary-fitted curvilinear coordinate system. A mesh dependence study for the four turbulence models is carried out on computational meshes with different densities. In addition, the performance of the k–ω models with either wall function or no-slip boundary condition on the cylinder surface is examined on the finest mesh. It is found that the SGS model over-predicts the shedding of vortices from the cylinder and is sensitive to the computational mesh and the model constant C_s used. The standard k–ε and the Wilcox k–ω models predict the mean velocity field quite well but generally under-predict the velocity and hydrodynamic force oscillations using wall functions on the cylinder surface. It is also found that the Wilcox k–ω models with the no-slip boundary condition on the cylinder surface give better predictions on the shedding of vortices than their counterparts using the wall function boundary condition.     

Numerical simulation of random wave slamming on structures in the splash zone

The numerical investigation of random wave slamming on superstructures of marine structures in the splash zone is presented in this paper. The impact pressures on the underside of the structure are computed based on the improved volume of fluid method (VOF). The governing equations are Reynolds time-averaged equations and the two equation k– model. The third order upwind difference scheme is applied to the convection term to reduce the effect of numerical viscosity. The numerical wave flume with random wave-maker suitable for VOF is established. Appropriate moving contact-line boundary conditions are introduced to the model wave in contact with and separated from the underside of structure. Parametric studies have been carried out for different incident waves, structure dimensions and structure clearance. The numerical results are verified by the experimental results.     

An Irregular Wave Generating Approach Based on naoe-FOAM-SJTU Solver

In this paper, a wave generating approach for long-crest irregular waves in a numerical tank by our in-house solver naoe-FOAM-SJTU is presented. The naoe-FOAM-SJTU solver is developed using an open source tool kit, OpenFOAM. Reynolds-averaged Navier?Stokes (RANS) equations are chosen as governing equations and the volume of fluid (VOF) is employed to capture the two phases interface. Incoming wave group is generated by imposing the boundary conditions of the tank inlet. A spectrum based correction procedure is developed to make the measured spectrum approaching to the target spectrum. This procedure can automatically adjust the wave generation signal based on the measured wave elevation by wave height probe in numerical wave tank. After 3 to 4 iterations, the measured spectrum agrees well with the target one. In order to validate this method, several wave spectra are chosen and validated in the numerical wave tank, with comparison between the final measured and target spectra. In order to investigate a practical situation, a modified Wigley hull is placed in the wave tank with incoming irregular waves. The wave-induced heave and pitch motions are treated by Fourier analysis to obtain motion responses, showing good agreements with the measurements.     

An irregular wave generating approach based on naoe-FOAM-SJTU solver

In this paper, a wave generating approach for long-crest irregular waves in a numerical tank by our in-house solver naoe-FOAM-SJTU is presented. The naoe-FOAM-SJTU solver is developed using an open source tool kit, OpenFOAM. Reynolds-averaged Navier-Stokes (RANS) equations are chosen as governing equations and the volume of fluid (VOF) is employed to capture the two phases interface. Incoming wave group is generated by imposing the boundary conditions of the tank inlet. A spectrum based correction procedure is developed to make the measured spectrum approaching to the target spectrum. This procedure can automatically adjust the wave generation signal based on the measured wave elevation by wave height probe in numerical wave tank. After 3 to 4 iterations, the measured spectrum agrees well with the target one. In order to validate this method, several wave spectra are chosen and validated in the numerical wave tank, with comparison between the final measured and target spectra. In order to investigate a practical situation, a modified Wigley hull is placed in the wave tank with incoming irregular waves. The wave-induced heave and pitch motions are treated by Fourier analysis to obtain motion responses, showing good agreements with the measurements.     

A simple two-way coupling method of BEM and VOF model for random wave calculations

A numerical method, which combines the boundary element method (BEM) and the volume of the fluid method (VOF method), has been presented to solve wave–structure interactions; the intense wave motion at the proximity of the structure is modeled by the VOF method and the rest of the fluid region is modeled by the BEM. The combined method can considerably reduce the time-consuming VOF domain, and thus practically makes it possible to apply the VOF method for random wave calculations, in which long time computations are usually required to obtain statistically meaningful results, and therefore the use of the single-VOF model often becomes prohibitive in terms of computational time and storage memories. A VOF model CADMAS-SURF, which is based on SMAC scheme and had been constructed by a number of VOF researchers in coastal engineering in Japan, is used in the combined BEM–VOF model. The two-way coupling treatment, which enables us to deal with bidirectional wave propagations, which was originally given for the SOLA-VOF model by Yan et al. (2003a) and later improved by Kim et al. (2007), was modified for the SMAC scheme. The coupling treatments are described in detail in the paper. The validity of the combined BEM–VOF model was investigated by comparing the numerical results with the theoretical results for the propagations of Stokes 5th order waves and random waves.     

Analysis of second-order resonance in wave interactions with floating bodies through a finite-element method

A time-domain method is employed to analyse the resonant oscillations of the liquid confined within the two floating bodies. The velocity potentials at each time step are obtained through a finite-element method (FEM) with quadratic shape functions. The matrix equation of the FEM is solved through an iteration. The radiation condition is satisfied through a combination of the damping zone method and the Sommerfeld–Orlanski equation. A detailed analysis is made for two rectangular floating cylinders undergoing forced oscillation. The first-order potential reveals the resonant behaviour of the wave motion at certain frequencies ω_i, which is similar to sloshing in a tank. More interestingly, the second-order theory further reveals that when the oscillation frequency is at ω_i/2 or half of the resonant frequency, no first-order resonance is observed as expected, but the second-order resonant motion becomes evident, which does not seem to have been extensively investigated so far. Detailed results for two rectangular cylinders are provided to show some insights into the resonant effect due to the interaction between the bodies. The first- and second-order resonant phenomena have been observed and the result has shown that the second-order components have significant influence on the wave and force in some cases, especially at the second-order resonance.     

Numerical and simplified methods for the calculation of the total horizontal wave force on a perforated caisson with a top cover

The VOF method and the k–ε model, combined with the equation of state of air at constant temperature, have been used to calculate the total horizontal wave force caused by monochromatic waves acting on a perforated caisson with a top cover. From comparison of various parameters, such as the total horizontal force, the pressure difference on the front wall, the pressure on the back wall and the pressure on the top cover, between the numerical results and test data, it can be seen that the numerical results agree well with the test data. It is concluded that the method described in this paper can be utilized to calculate wave forces acting on perforated caissons with a top cover in the case of nonovertopping, nonbreaking waves. A simplified method to calculate the total horizontal force has been developed, based on test data, using a least-squares method. A comparison between the numerical results and the values calculated from the simplified equations shows good agreement. Therefore the simplified equations can be used in engineering applications to evaluate the total horizontal force on a perforated caisson with a top cover.     

Extending the k–ω turbulence model towards oceanic applications

Four different two-equation turbulence models for geophysical flows are compared: The k–ϵ model, two new versions of the k–ω model, and the Mellor–Yamada model. An extension of the k–ω model for buoyancy affected and rotating flows is suggested. Model performance is evaluated for a few typical oceanic flows. First, new analytical solutions of the models for the surface layer affected by breaking surface waves are discussed. The deficiencies of earlier attempts are high-lighted, and it is demonstrated why the Mellor–Yamada model and the k–ϵ model fail. It is illustrated that only one version of the k–ω model computes correct decay rates for turbulent quantities under breaking waves. Second, it is demonstrated that all models predict almost identical mixed layer depths and profiles for the turbulent kinetic energy in a classical stratified shear-entrainment experiment if the buoyancy term in the second equation is appropriately weighted. Third, the accuracy and numerical robustness of the new k–ω model in realistic oceanic situations is confirmed by comparison with the data-set of the Ocean Weather Ship ‘Papa’.     

Numerical simulation of wave transformation and runup incorporating porous media wave absorber and turbulence models

A numerical wave tank is first established using the Navier–Stokes equations and the VOF method assuming laminar flow. The standard k–ε, realizable k–ε and RNG k–ε turbulent models are then incorporated to the numerical tank. An effective numerical method for wave absorption utilizing the energy-dissipating property of porous media is also included. To validate the accuracy of the proposed models, the propagation of a solitary wave, where analytical solution is available for comparison, is first simulated. This is followed by the simulation of irregular wave runup on a composite seawall, wave propagation over submerged bars and wave refraction and diffraction over an elliptic shoal, where experimental data are available for comparison. All computed results agree well with either the analytical solution or the experimental data.     

Numerical investigation of the scale effect of hydrodynamic performance of the hybrid CRP pod propulsion system

The scale effect of hydrodynamic performance of the hybrid CRP pod propulsion system was investigated numerically using the RANS method combined with SST k − ω turbulence model and moving mesh method. The pod resistance influence factor was introduced to represent the effect of wake field of CRP on the pod resistance. Results showed the pod resistance influence factor to be a function of the Reynolds number and revolution ratio. Representative function expression can be obtained by regression analysis using multiplication of multinomial polynomials and linear function. The standard ITTC 1978 extrapolation procedure can be utilized to predict hydrodynamic performance of forward propeller because of the slightness of the influence of the pod unit on the forward propeller. The thrust and torque coefficient influence factors of aft propeller were introduced, and they were found to represent the effect of wake field of forward propeller and blockage effect of the pod on the hydrodynamic performance of aft propeller. It shows that thrust and torque coefficient influence factors are independent of the Reynolds number and have a linear relationship with the revolution ratio. On this basis, a method of estimating the hydrodynamic performance was proposed for full scale propulsion system.     

Investigation of drag crisis phenomenon using CFD methods

When fluid flow passes a cylinder, the drag crisis phenomenon occurs between the sub-critical and the super-critical Reynolds numbers. The focus of the present studies was on the numerical prediction of the drag crisis based on CFD methods. In this work, block structured meshes with refined grids near the cylinder surface and in the downstream were employed. Both 2D and 3D simulations were performed using various turbulence models, including the SST k − ω model, the k − ϵ model, the SST with LCTM, the DES model, and the LES model. In the convergence studies, the effects of the grid size, the time step, the first grid size and the aspect ratio (for 3D simulations) on the solutions were examined. The errors due to spatial and time discretizations were quantified according to a V&V procedure. Validation studies were carried out for various Reynolds numbers between Re = 6.31 × 10⁴ and 7.57 × 10⁵. The averaged drag force, the RMS of lift force and the Strouhal number were compared with experimental data. The studies indicated that standard 2D and 3D RANS methods were inadequate to capture the drag crisis phenomenon. The LES method however has the potential to address the problem.     

Tsunami-like solitary waves impinging and overtopping an impermeable seawall: Experiment and RANS modeling

This study investigates tsunami-like solitary waves impinging and overtopping an impermeable trapezoidal seawall on a 1:20 sloping beach. New laboratory experiments are performed for describing three typical cases: a turbulent bore rushes inland and subsequently impacts and overtops the seawall (Type 1); a wave directly collapses on the seawall and then generates overtopping flow (Type 2); and, a wave straightforwardly overtops the seawall crown and collapses behind the seawall (Type 3). A two-dimensional volume of fluid (VOF) type model called the COBRAS (COrnell BReaking And Structure) model, which is based on the Reynolds-Averaged Navier–Stokes (RANS) equations and the k–ε turbulence closure solver, is validated by experimental data and then applied to investigate wave dynamics for which laboratory data are unavailable. Additionally, a set of numerical experiments is conducted to examine the dynamic wave acting force due to waves impacting the seawall. Effects of wave nonlinearity and freeboard are elucidated. Special attention is given to a distinct vortex evolutionary behavior behind the seawall, in which the dynamic properties of entrapped air-bubbles are briefly addressed experimentally and numerically.