Numerical Simulation of Two-Dimensional Free-Surface Flow and Wave Transformation Over Constant-Slope Bottom Topography

2007 ◽  
Author(s):  
Aggelos S. Dimakopoulos ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Numerical Solution ◽  
Euler Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Transformation ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Time Step ◽  
Good Agreement

A numerical model is presented for the simulation of the two-dimensional, inviscid, free-surface flow developing by the propagation and breaking of water waves over a flat bottom of steep slope. The simulation is based on the numerical solution of the unsteady, two-dimensional, Euler equations subject to the fully-nonlinear free-surface boundary conditions, the non-penetration condition at the bottom and appropriate inflow and outflow conditions. A boundary-fitted transformation, which includes both the time-dependent free surface and the arbitrary bottom shape, is applied. For the numerical solution of the Euler equations, a two-stage fractional time-step method is employed for the temporal discretization, while a hybrid scheme is used for the spatial discretization. Finite differences are used in the streamwise direction and a pseudo-spectral method in the vertical direction. An absorption zone is placed at the outflow region in order to minimize wave reflection by the outflow boundary. Wave breaking is modeled by a surface roller breaking model, which modifies the dynamic free-surface condition. The simulation results are in very good agreement with available experimental results for the wave propagation and breaking over bottom with slope 1:35. Results, from the simulations over bottom with steeper slopes of 1:15 and 1:10, which generate strong spilling and mild plunging breakers, respectively, are also in very good agreement with available predictions for the breaking depth and wave height. In all cases, a vortex is formed under the breaking wave front and convected in the surf zone.

Minimising wave drag for free surface flow past a two-dimensional stern

2011 ◽  
Vol 23 (7) ◽  
pp. 072101 ◽  
Author(s):  
Osama Ogilat ◽  
Scott W. McCue ◽  
Ian W. Turner ◽  
John A. Belward ◽  
Benjamin J. Binder
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Wave Drag ◽  
Surface Flow ◽  
Two Dimensional ◽  
Flow Past

SPLASH Free-Surface Flow Code Methodology for Hydrodynamic Design and Analysis of IACC Yachts

1993 ◽  
Author(s):  
Bruce S. Rosen ◽  
Joseph P. Laiosa ◽  
Warren H. Davis ◽  
David Stavetski
Keyword(s):  
Free Surface ◽  
High Performance ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Surface Boundary ◽  
Induced Drag ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
America’S Cup ◽  
Areas Of Interest

A unique free-surface flow methodology and its application to design and analysis of IACC yachts are discussed. Numerical aspects of the inviscid panel code and details of the free-surface boundary condition are included, along with enhancements developed specifically for the '92 America's Cup defense. Extensive code validation using wind tunnel and towing tank experimental data address several areas of interest to the yacht designer. Lift and induced drag at zero Froude number are studied via a series of isolated fin/bulb/winglet appendages. An isolated surface piercing foil is used to evaluate simple lift/free­surface interactions. For complete IACC yacht models, upright wave resistance is investigated, as well as lift and induced drag at heel and yaw. The excellent correlation obtained for these cases demonstrates the value of this linear free-surface methodology for use in designing high performance sailing yachts.

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.

Numerical Simulation of Nonlinear Wave Propagation and Breaking Over Constant-Slope Bottom

2006 ◽  
Author(s):  
Aggelos S. Dimakopoulos ◽  
Athanassios A. Dimas
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Surface Boundary ◽  
Nonlinear Wave Propagation ◽  
Large Wave ◽  
Slope Bottom ◽  
Wave Heights ◽  
Constant Slope

The numerical simulation of the two-dimensional free-surface flow resulting from the propagation of nonlinear gravity waves over constant-slope bottom is presented. The simulation is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. Wave breaking is accounted for by a surface roller model. The formulation includes a boundary-fitted transformation and is suitable for future extension to incorporate large-eddy and large-wave simulation terms. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:50, and three different inflow wave heights. Over the bottom slope, waves of small wave heights are modified according to linear theory. For nonlinear waves, wavelengths are becoming shorter, the free surface elevation deviates from its initial sinusoidal shape and wave heights increase with decreasing depth. Breaking is observed for the cases with the larger initial wave height and the smaller outflow depth.

Unstructured Grid Based Reynolds-Averaged Navier-Stokes Method for Liquid Tank Sloshing

2005 ◽  
Vol 127 (3) ◽  
pp. 572-582 ◽  
Author(s):  
Shin Hyung Rhee
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Governing Equations ◽  
Reconstruction Scheme ◽  
Geometric Reconstruction ◽  
Membrane Type ◽  
Tank Sloshing ◽  
Good Agreement

The present study is concerned with liquid tank sloshing at low filling level conditions. The volume of fluid method implemented in a Navier–Stokes computational fluid dynamics code is employed to handle the free-surface flow of liquid sloshing. The geometric reconstruction scheme for the interface representation is employed to ensure sharpness at the free surface. The governing equations are discretized by second order accurate schemes on unstructured grids. Several different computational approaches are verified and numerical uncertainties are assessed. The computational results are validated against existing experimental data, showing good agreement. The capability is demonstrated for a generic membrane-type liquefied natural gas carrier tank with a simplified pump tower inside. The validation results suggest that the present computational approach is both easy to apply and accurate enough for more realistic problems.

The Free Surface Flow Around a TLP

2010 ◽  
Author(s):  
A. Yalpaniyan ◽  
M. Goodarzi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Turbulent Flow ◽  
Numerical Solution ◽  
Flow Pattern ◽  
Symmetry Plane ◽  
Free Surface Flow ◽  
Inviscid Flow ◽  
Surface Flow ◽  
Wave Heights

A TLP is a buoyant platform containing four cylindrical columns. The purpose of this study was to consider the effects of different model solvers in the numerical solution on the flow pattern around the TLP. The flow around the TLP was numerically simulated with inviscid, laminar, and turbulent solvers. Three Froude numbers were run for each case. There was a symmetry plane that allowed simulating just one half of the flow field. Therefore, two columns along the symmetry plane were considered in the results discussion. Beside the generated surface waves there was a pair of vortex behind each column none of them were actually symmetric. The vortex behind the first column significantly affected the flow pattern around the second one in the manner that the vortex behind the first column was larger than the next one. In all cases the outer vortex was larger than the inner one. The obtained results showed that the generated waves of the inviscid flow were smoother than the turbulent flow, and also those of the turbulent flow were smoother than the laminar ones. Compared to the mentioned results, the influence of the flow velocity on the wave heights was more significant.

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