Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

scholarly journals Free surface flow past topography: A beyond-all-orders approach

2012 ◽  
Vol 23 (4) ◽  
pp. 441-467 ◽  
Author(s):  
CHRISTOPHER J. LUSTRI ◽  
SCOTT W. MCCUE ◽  
BENJAMIN J. BINDER
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Numerical Solutions ◽  
Power Series Expansion ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Asymptotic Results ◽  
Stagnation Points ◽  
Flow Past ◽  
Stokes Lines

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck, (2006) Exponential asymptotics and gravity waves. J. Fluid Mech.567, 299–326, the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of inclination. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

scholarly journals Influence of the hydrofoil inclination angle at free surface flow around junctions

2020 ◽  
Vol 43 ◽  
pp. 103-108
Author(s):  
Costel Ungureanu ◽  
Costel Iulian Mocanu
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Bluff Body ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Breaking Waves ◽  
Surface Flow ◽  
Vortex Structures ◽  
The Body ◽  
Flow Topology

"Free surface flow is a hydrodynamic problem with a seemingly simple geometric configuration but with a flow topology complicated by the pressure gradient due to the presence of the obstacle, the interaction between the boundary layer and the free surface, turbulence, breaking waves, surface tension effects between water and air. As the ship appendages become more and more used and larger in size, the general understanding of the flow field around the appendages and the junction between them and the hull is a topical issue for naval hydrodynamics. When flowing with a boundary layer, when the streamlines meet a bluff body mounted on a solid flat or curved surface, detachments appear in front of it due to the blocking effect. As a result, vortex structures develop in the fluid, also called horseshoe vortices, the current being one with a completely three-dimensional character, complicated by the interactions between the boundary layer and the vortex structures thus generated. Despite the importance of the topic, the literature records the lack of coherent methods for investigating free surface flow around junctions, the lack of consistent studies on the influence of the inclination of the profile mounted on the body. As a result, this paper aims to systematically study the influence of profile inclination in respect to the support plate."

Nonlinear Wave Forces Acting on Submerged Horizontal Cylinders

1988 ◽  
Vol 110 (1) ◽  
pp. 62-70 ◽  
Author(s):  
R. Inoue ◽  
Y. Kyozuka
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Nonlinear Wave ◽  
Wave Breaking ◽  
Nonlinear Effects ◽  
Second Order ◽  
Experimental Results ◽  
Wave Forces ◽  
Regular Perturbation ◽  
Horizontal Cylinders

This paper is to present experimental results of the first and second-order wave forces acting on three kinds of horizontally submerged cylinders. Wave height, wave frequency and the models’ submergence were varied in the experiments. These results are compared with the numerical calculations based on the regular perturbation theory. Through this study, it was found that the calculations of both the first and second-order wave forces coincide with the experiments when the cylinders are submerged at a sufficient depth. However, in the case that the cylinders are close to the free surface and/or wave amplitudes are relatively large, the experimental results become small compared with the calculations because of nonlinear effects, such as wave breaking observed in the experiments.

On Marangoni drying: nonlinear kinematic waves in a thin film

1993 ◽  
Vol 254 ◽  
pp. 649-670 ◽  
Author(s):  
S. B. G. M. O'Brien
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Order Approximation ◽  
Nonlinear Partial Differential Equation ◽  
Free Surface Flow ◽  
Wave Theory ◽  
Alcohol Concentration ◽  
Surface Flow ◽  
Singular Perturbation Theory ◽  
Higher Derivative

In the field of industrial drying, a recent innovation has exploited the occurrence of Marangoni effects in such a way that the resultant free-surface flow enhances the drying process. To this end, alcohol vapour, soluble in water, is introduced above a drying film and as a result of diffusion through the air and water phases a favourable concentration gradient gives rise to the required shear flow. We consider here a simple process driven by this mechanism, and by means of asymptotic simplification and the concepts of singular perturbation theory a leading-order approximation is obtained in which the alcohol concentration in the water is a specified function of space and time. The evolution of the free surface thus reduces to a single nonlinear partial differential equation of a similar form to the Korteweg–de Vries and Burgers equations, higher-derivative terms corresponding to surface tension and gravity effects. Numerical solutions of this equation are obtained and are compared to the application of first order nonlinear kinematic wave theory with corresponding shock solutions.

scholarly journals Computational Estimation And RANS Simulation of Free Surface Flow Around A Ship Hull

2012 ◽  
pp. 118-121
Author(s):  
Katuri Samarpana
Keyword(s):  
Free Surface ◽  
Complex Geometry ◽  
Computational Prediction ◽  
Breaking Waves ◽  
Surface Flow ◽  
Ship Hull ◽  
Operating Conditions ◽  
Surface Phenomenon ◽  
Hydrodynamic Behaviour ◽  
Different Shapes

Ship hydrodynamics present many unique challenges due to complex geometry, environment, and operating conditions, which results in many complex physics and modelling issues. This is commonly studied through experiments in a towing tank and experiments in a sea keeping and manoeuvring basin. Recently hydrodynamicists have begun to venture into computational prediction of hydrodynamic behaviour of surface ships. Free surface phenomenon around a ship hull plays an important role in its resistance. Wave making resistance comes from the very presence of free surface. Therefore its accurate prediction is very essential for ship design. The flow problem to be simulated is rich in complexity and poses many modelling challenges because of the existence of breaking waves around the ship hull involving two-phase flow, and because of the resolution of thin turbulent boundary layer. The paper aims to computationally estimate the effect of free surface for a moving ship. Commercial software is used for grid generation and flow solution. 1. Solution of a Rudder of a ship in submerged condition. Few different shapes of the rudders are examined. 2. Solution of flow- around a complete ship with free surface. In the present work, flow through the ship hull is computed using a finite volume commercial code, ANSYS 12.1. The ship geometry is modelled using solid modelling software, CATIA V5R9. A three-dimensional structured hexahedral grid is generated using grid generating code, ICEM-CFD V10.0 .Turbulence is modelled with Reynolds Stress model. The resistance of the ship is predicted, and compared against the experimental values. The rudder of the ship is also analyzed. Two different shapes, one wedge shaped and a standard NACA0012 foil, for which experimental results are available in literature, are analyzed. The lift coefficients and flow separation are predicted for different angles of attack using various turbulence models.Computational results are in good agreement with the experimental ones.

scholarly journals Explosive ripple instability due to incipient wave breaking

2019 ◽  
Vol 863 ◽  
pp. 876-892
Author(s):  
Alexei A. Mailybaev ◽  
André Nachbin
Keyword(s):  
Free Surface ◽  
Wave Breaking ◽  
Surf Zone ◽  
Asymptotic Expression ◽  
Nonlinear Effects ◽  
Finite Depth ◽  
Breaking Waves ◽  
Theory Model ◽  
Intrinsic Frequency ◽  
Strong Compression

Considering two-dimensional potential ideal flow with a free surface and finite depth, we study the dynamics of small-amplitude and short-wavelength wavetrains propagating in the background of a steepening nonlinear wave. This can be seen as a model for small ripples developing on the slopes of breaking waves in the surf zone. Using the concept of wave action as an adiabatic invariant, we derive an explicit asymptotic expression for the change of ripple steepness. Through this expression, nonlinear effects are described using the intrinsic frequency and intrinsic gravity along Lagrangian (material) trajectories on a free surface. We show that strong compression near the tip on the wave leads to an explosive ripple instability. This instability may play an important role in the understanding of fragmentation and whitecapping at the surface of breaking waves. Analytical results are confirmed by numerical simulations using a potential theory model.

Nonlinear water waves generated by an accelerated circular cylinder

1979 ◽  
Vol 92 (4) ◽  
pp. 767-781 ◽  
Author(s):  
H. J. Haussling ◽  
R. M. Coleman
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Water Waves ◽  
Numerical Solutions ◽  
Nonlinear Effects ◽  
Surface Boundary ◽  
Nonlinear Water Waves ◽  
Pressure Distributions ◽  
Surface Boundary Conditions ◽  
Surface Profiles

Numerical solutions for the irrotational flow of an incompressible fluid about a circular cylinder accelerated from rest below a free surface are presented. The usual restriction to linearized free-surface boundary conditions has been avoided. The transient period from the start to a local steady state or to the development of a very steep wave slope is investigated in terms of free-surface profiles and body-surface pressure distributions. Linear and nonlinear results are used to illustrate the transition from deep submergence when nonlinear effects are small to shallow submergence when linearized analysis is inaccurate.

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