Large-Wave Simulation of Surface Tension Effect on Weak Spilling Breakers

2005 ◽  
Author(s):  
Athanassios A. Dimas
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Wave Height ◽  
Weber Number ◽  
Surface Profile ◽  
Surface Flow ◽  
Surface Tension Effect ◽  
Time Step ◽  
Large Wave ◽  
Spilling Breakers

The effect of surface tension on the evolution of weak spilling breakers is studied by performing large-wave simulations (LWS) of the free-surface flow developing by the interaction of a gravity free-surface wave and a surface shear-layer current. The flow models the evolution of gravity waves under the influence of wind shear. The surface tension modifies the dynamic free-surface condition and its effect depends on the dimensionless Weber number. The Euler equations are filtered according to the LWS formulation and solved numerically by a spectral method and a fractional-time-step scheme. The results indicate a stronger surface tension effect with decreasing Weber number values and increasing initial wave height. Specifically, decreasing the Weber number alters the size and shape of the characteristic bulge of spilling breakers and the toe position resulting in sharper slopes and angles of the free surface profile. The spiller wave height is reduced with decreasing Weber number.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

Two methods of surface tension treatment in free surface flow simulations

2018 ◽  
Vol 86 ◽  
pp. 236-242 ◽  
Author(s):  
Kirill D. Nikitin ◽  
Kirill M. Terekhov ◽  
Yuri V. Vassilevski
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Flow Simulations

Étude de formation de vortex au voisinage de l'aspiration verticale inversée dans un puits de pompage

1983 ◽  
Vol 10 (3) ◽  
pp. 369-383
Author(s):  
Tilena Kougnima ◽  
René Kahawita
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Laboratory Investigation ◽  
Relative Position ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Inertia Forces

The purpose of the laboratory investigation reported here has been to study the conditions under which vortices appear in the free surface flow upstream of a vertically inverted intake in a circular sump. The influence of geometry, approach conditions, size, and relative position of the intake in the sump has been studied. The effect of viscosity, surface tension, and inertia forces on the formation of vortices has been examined. A discussion of the results and the principal conclusions drawn permit certain recommendations to be made at the conceptual stage of pumping pits.

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.

Free-surface flow past oscillating singularities at resonant frequency

1982 ◽  
Vol 120 ◽  
pp. 139-154 ◽  
Author(s):  
G. Dagan ◽  
T. Miloh
Keyword(s):  
Free Surface ◽  
Resonant Frequency ◽  
Free Surface Flow ◽  
Generalized Solution ◽  
Surface Flow ◽  
Third Order ◽  
Large Wave ◽  
Drag Forces ◽  
Flow Past ◽  
Lift And Drag

This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(ε½) and O(εlogε) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.

Sign in / Sign up

Export Citation Format

Share Document