Hideaki Miyata

Finite-difference simulation of breaking waves

Abstract A finite-difference simulation method for breaking water waves is developed. The Navier-Stokes equations in finite-difference form are solved by time-marching scheme in an inflexible rectangular staggered mesh system. Ingenious techniques are particularly focussed on the implementation of the nonlinear free-surface conditions so that overturning and impinging waves can be simulated. It is demonstrated that this method is applicable to three water wave problems that involve breaking phenomenon, namely, bow waves of an advancing floating body, a shallow water flow over a bump, and waves on a submergible. The simulated results show fairly good resemblance to the actual nonlinear wave motions including overturning and breaking of waves, occurrence of impact pressure, and generation of vortices.

Fully non‐linear free‐surface simulations by a 3D viscous numerical wave tank

A finite difference scheme using a modified marker-and-cell (MAC) method is applied to investigate the characteristics of non-linear wave motions and their interactions with a stationary three-dimensional body inside a numerical wave tank (NWT). The Navier-Stokes (NS) equation is solved for two fluid layers, and the boundary values are updated at each time step by a finite difference time marching scheme in the frame of a rectangular co-ordinate system. The viscous stresses and surface tension are neglected in the dynamic free-surface condition, and the fully non-linear kinematic free-surface condition is satisfied by the density function method developed for two fluid layers. The incident waves are generated from the inflow boundary by prescribing a velocity profile resembling flexible flap wavemaker motions, and the outgoing waves are numerically dissipated inside an artificial damping zone located at the end of the tank. The present NS-MAC NWT simulations for a vertical truncated circular cylinder inside a rectangular wave tank are compared with the experimental results of Mercier and Niedzwecki, an independently developed potential-based fully non-linear NWT, and the second-order diffraction computation

Difference solution of a viscous flow with free-surface wave about an advancing ship

Abstract A finite-difference solution method is described for a 31) viscous flow with free-surface waves about an advancing ship in steady course. A Navier-Stokes equation of finite-difference form is solved by a time-marching scheme in a boundary-fitted curvilinear coordinate system which is deformed to fit the moving free-surface at each time step. A sub-grid-scale turbulence model is introduced to achieve computations at higher Reynolds numbers. It is demonstrated that the computations by this method simulate fairly well free-surface waves, viscous flows and their interactions including three-dimensional separation under the influence of the free-surface.

Finite difference simulation of nonlinear waves generated by ships of arbitrary three-dimensional configuration

Abstract A modified marker-and-cell method is developed in order to simulate nonlinear wave making in the near-field of ships of arbitrary three-dimensional (3D) configuration advancing steadily in deep water. The 3D Navier-Stokes equations are solved by a finite difference scheme under proper boundary conditions. Efforts are particularly focused on the treatment of the boundary conditions on the body surface and free surface which have complicated 3D configurations. An orthogonal cell system with more than 70,000 cells is used for the computation of the waves and flow field of ships. The agreement of computational results with experiment is good, and it promises effectiveness for engineering purposes.

Direct numerical simulation of wall turbulent flows with microbubbles

The marker-density-function (MDF) method has been developed to conduct direct numerical simulation (DNS) for bubbly flows. The method is applied to turbulent bubbly channel flows to elucidate the interaction between bubbles and wall turbulence. The simulation is designed to clarify the structure of the turbulent boundary layer containing microbubbles and the mechanism of frictional drag reduction. It is deduced from the numerical tests that the interaction between bubbles and wall turbulence depends on the Weber and Froude numbers. The reduction of the frictional resistance on the wall is attained and its mechanism is explained from the modulation of the three-dimensional structure of the turbulent flow. Copyright

Finite-difference simulation of nonlinear ship waves

A finite-difference solution method for nonlinear wave generation in the near field of ships of arbitrary three-dimensional configuration is developed. Momentum equations of finite-difference form in a fixed rectangular cell system are solved by a time-marching scheme. The exact inviscid free-surface condition is approximately satisfied at the actual location of the free surface, and the free-slip body boundary condition is implemented by use of approximation of the body configuration and a special pressure computation in body boundary cells. The degree of accuracy is raised by employing a variable-mesh system in the vertical direction. Computed results are presented for three hull forms: a mathematical and two practical hull forms. Agreement with experiment seems to be fairly good. In particular, the computed wave profiles and contour maps of bow waves show excellent resemblance to the measured ones, having some typical characteristics of nonlinear ship waves.

Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures

Abstract A finite-difference scheme and a modified marker-and-cell (MAC) algorithm have been developed to investigate the interactions of fully nonlinear waves with two- or three-dimensional structures of arbitrary shape. The Navier–Stokes (NS) and continuity equations are solved in the computational domain and the boundary values are updated at each time step by the finite-difference time-marching scheme in the framework of a rectangular coordinate system. The fully nonlinear kinematic free-surface condition is implemented by the marker-density function (MDF) technique developed for two fluid layers. To demonstrate the capability and accuracy of the present method, the numerical simulation of backstep flows with free-surface, and the numerical tests of the MDF technique with limit functions are conducted. The 3D program was then applied to nonlinear wave interactions with conical gravity platforms of circular and octagonal cross-sections. The numerical prediction of maximum wave run-up on arctic structures is compared with the prediction of the Shore Protection Manual (SPM) method and those of linear and second-order diffraction analyses based on potential theory and boundary element method (BEM). Through this comparison, the effects of non-linearity and viscosity on wave loading and run-up are discussed.

Nonlinear Ship Waves

Publisher Summary This chapter discusses about nonlinear ship waves. The waves generated by ships advancing steadily in deep water have been considered as typical linear dispersive ones. Many wave-making resistance theories have been proposed by mathematicians and naval architects, most of which are based on this linear postulation. Miyata and co-workers supposed that the complicated nonlinear free surface phenomena called breakdown of waves or necklace vortices were consequent results of nonlinear wave making in the near field, and over a period of five years they carried out experimental investigations into the characteristics and structure of nonlinear waves, as well as numerical analyses of nonlinear wave formation by a finite-difference method. The chapter deals with the studies they made at the experimental tank of the University of Tokyo. In Section II of the chapter, characteristics of nonlinear waves around ship models are experimentally studied, and in Section III more detailed characteristics and structure are clarified with simple wedge models. A numerical method of simulating nonlinear wave formation around the bow is described in Section IV, and the computed results are discussed and compared with experimental results in Section V.

Forces on a circular cylinder advancing steadily beneath the free-surface

Abstract Experimental and numerical study is made of the forces and flow about a circular cylinder steadily advancing beneath the free-surface. Force measurements at a Reynolds number of 4.96 × 104 show that the drag coefficient abruptly decreases from 1.3 to 1.0 and the Strouhal number simultaneously increases from 0.19 to 0.30 at the depth-radius ratioof 1.7 when the depth of submergence of the circular cylinder is gradually reduced. Pressure measurements, flow visualization and numerical simulations indicate that at the shallowly-submerged condition the difference of the flow in the vacinities of the top and bottom of the cylinder causes asymmetric vortex generation and that this results in a smaller pressure reduction on the backward face of the cylinder, a lower drag coefficient of the cylinder, and a higher frequency of vortex shedding.

Application of CFD simulation to the design of sails

Abstract: A finite-volume method was applied to a simulation of the flow about the sail system of IACC sailing boats. The interface boundary technique was employed to generate a proper grid system for the two-sails system, which is composed of head and main sails. The turbulence model was carefully chosen by numerical test, and the most reliable simulation method was completed and used to design the sails. The suitability of the method is demonstrated by some examples of design applications.