Oscillatory Free Surface Displacement of Finite Amplitude in a Small Orifice

2004 ◽  
Vol 126 (5) ◽  
pp. 818-826
Author(s):  
Brian J. Daniels ◽  
James A. Liburdy
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Surface Displacement ◽  
Experimental Results ◽  
Significant Shift ◽  
Curvature Effect ◽  
Modal Frequency ◽  
Large Curvature ◽  
Curvature Effects ◽  
Free Surface Displacement

The oscillatory free-surface displacement in an orifice periodically driven at the inlet is studied. The predictions based on a potential flow analysis are investigated in light of viscous and large curvature effects. Viscous effects near the wall are estimated, as are surface viscous energy loss rates. The curvature effect on the modal frequency is shown to become large at the higher modal surface shapes. Experimental results are obtained using water for two orifice diameters, 794 and 1180 μm. Results of surface shapes and modal frequencies are compared to the predictions. Although modal shapes seem to be well predicted by the theory, the experimental results show a significant shift of the associated modal frequencies. A higher-order approximation of the surface curvature is presented, which shows that the modal frequency should, in fact, be reduced from potential flow predictions as is consistent with the large curvature effect. To account for the effect of finite surface displacements an empirical correlation for the modal frequencies is presented.

CFD Modeling of Fully Nonlinear Water Wave Tank

2009 ◽  
Author(s):  
Guangyu Wu ◽  
Owen H. Oakley
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Wave Breaking ◽  
Water Wave ◽  
Surface Displacement ◽  
Wave Steepness ◽  
Wave Tank ◽  
Fully Nonlinear ◽  
Free Surface Displacement ◽  
Time Histories

In this study, we use CFD simulations to model a fully nonlinear water wave tank. Firstly, for validation purpose, regular waves with different wave steepness are simulated and the results are compared with the second-order potential flow solution for the free surface displacement time history at fixed locations, the instantaneous free surface spatial profiles, and the velocity and pressure fields under the free surface. It is shown that for small wave steepness, the CFD solutions agree very well with the second-order potential flow solutions while for large wave steepness, apparent differences between these two solutions are observed. The validation and fully nonlinear feature of the CFD solutions are therefore demonstrated. Secondly, plunging breaking waves are simulated using the CFD wave tank by focusing a large number of linear wave components at a prescribed time and location. The time histories and normalized variance of free surface displacement at various locations along the tank are obtained from the CFD simulation and compared to the lab experiments. In particular, the CFD results predict reasonably well the wave breaking location and the loss of energy flux due to wave breaking. Finally, a vertical circular cylinder is placed in the CFD wave tank to simulate the breaking wave impact on a fixed structure. The pressure time histories at various points on the cylinder surface are obtained for several cylinder locations with respect to the prescribed wave breaking point. The CFD results are compared with previous experiments and discussed.

Nonlinear Helmholtz oscillations in harbours and coupled basins

1981 ◽  
Vol 104 ◽  
pp. 407-418 ◽  
Author(s):  
John W. Miles
Keyword(s):  
Free Surface ◽  
Additional Assumption ◽  
Phase Plane ◽  
Surface Displacement ◽  
Elliptic Functions ◽  
Forced Oscillations ◽  
Amplitude Parameter ◽  
Spatial Uniformity ◽  
Open Sea ◽  
Free Surface Displacement

Free and forced oscillations in a basin that is connected through a narrow canal to either the open sea or a second basin are considered on the assumption that the spatial variation of the free-surface displacement is negligible. The free-surface displacement in the canal is allowed to be finite, subject only to the restriction (in addition to that implicit in the approximation of spatial uniformity) that the canal does not run dry. The resulting model yields a Hamiltonian pair of phase-plane equations for the free oscillations, which are integrated in terms of elliptic functions on the additional assumption that the kinetic energy of the motion in the basin(s) is negligible compared with that in the canal or otherwise through an expansion in an amplitude parameter. The corresponding model for forced oscillations that are limited by radiation damping yields a generalization of Duffing's equation for an oscillator with a soft spring, the solution of which is obtained as an expansion in the amplitude of the fundamental term in a Fourier expansion. Equivalent circuits are developed for the various models.

scholarly journals Three dimensional numerical simulations for non-breaking solitary wave interacting with a group of slender vertical cylinders

2009 ◽  
Vol 1 (1) ◽  
Author(s):  
Weihua Mo ◽  
Philip L.-F. Liu
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Dynamic Pressure ◽  
Laboratory Data ◽  
Three Dimensional ◽  
Time History ◽  
Surface Displacement ◽  
Numerical Results ◽  
Finite Volume Scheme ◽  
Free Surface Displacement

AbstractIn this paper we validate a numerical model for-structure interaction by comparing numerical results with laboratory data. The numerical model is based on the Navier-Stokes(N-S) equations for an incompressible fluid. The N-S equations are solved by two-step projection finite volume scheme and the free surface displacements are tracked by the slender vertical piles. Numerical results are compared with the laboratory data and very good agreement is observed for the time history of free surface displacement, fluid particle velocity and force. The agreement for dynamic pressure on the cylinder is less satisfactory, which is primarily caused by instrument errors.

Equilibrium and oscillations of liquid fuel free surface in coaxial-cylindrical vessels under microgravity conditions

2021 ◽  
Author(s):  
Y. Zhaokai ◽  
A.N. Temnov
Keyword(s):  
Contact Angle ◽  
Free Surface ◽  
Liquid Fuel ◽  
Outer Space ◽  
Surface Displacement ◽  
Ideal Liquid ◽  
Intermolecular Forces ◽  
Hydrodynamic Characteristics ◽  
Free Surface Displacement ◽  
Microgravity Conditions

In the absence of significant mass forces, the behavior of liquid fuel under microgravity conditions is determined by surface tension forces, which are intermolecular forces at the interface of two phases. The paper posed and solved the problem of equilibrium and small oscillations of an ideal liquid under microgravity conditions, and also quantified the influence of various parameters: the contact angle α0, the Bond number, the ratio of the radii of the inner and outer walls of the vessel and the depth of the liquid. For the coaxial-cylindrical vessels, there were obtained expressions in the form of a Bessel series for the potential of the fluid velocities and the free surface displacement field. The study relies on the analytical and experimental data available in the literature and proves the reliability of the developed numerical algorithm. Findings of research show that for and r, with the physical state of the wetted surface being unchanged, the shape of the free surface tends to be flat and the contact angle has little effect on the intrinsic vibration frequency of the free surface of the liquid. The results obtained can be used to solve problems of determining the hydrodynamic characteristics of the movement of liquid fuel in outer space.

On free-surface oscillations in a rotating paraboloid

1963 ◽  
Vol 17 (2) ◽  
pp. 257-266 ◽  
Author(s):  
John W. Miles ◽  
F. K. Ball
Keyword(s):  
Free Surface ◽  
Second Harmonic ◽  
Harmonic Component ◽  
Surface Displacement ◽  
Wave Number ◽  
Rigid Displacement ◽  
Axisymmetric Solution ◽  
Axisymmetric Mode ◽  
Azimuthal Wave ◽  
Free Surface Displacement

Lamb's analysis of small-amplitude, shallow-water oscillations in a rotating paraboloid, interpreted by him in the inconsistent context of an approximately plane free surface, is re-interpreted to obtain results that are valid for $0 \le \omega^2l|2g \; \textless \;1$ (ω = rotational speed, l = latus rectum of paraboloid); no equilibrium is possible for ω2l/2g > 1. It is shown that the frequencies of the dominant modes for the azimuthal wave numbers 0 (axisymmetric motion) and 1 are independent of ω for an observer in a non-rotating reference frame and that the frequencies of all other axisymmetric modes are decreased by rotation (Lamb concluded that they would be increased). An axisymmetric mode of zero frequency, which was over-looked by Lamb, also is found.Exact solutions to the non-linear equations of motion, which reduce to the aforementioned dominant modes for small amplitudes, are determined. The axisymmetric solution is inferred from similarity considerations and is found to contain all harmonics of the fundamental frequency. The finite motion of azimuthal wave-number 1 is a quasi-rigid displacement of the liquid and is found to be simple harmonic except for a second-harmonic component of the free-surface displacement (but the horizontal velocity at a given point remains simple harmonic).

On an invariant property of water waves

1971 ◽  
Vol 49 (2) ◽  
pp. 385-389 ◽  
Author(s):  
T. Brooke Benjamin ◽  
J. J. Mahony
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Horizontal Plane ◽  
Wave Motion ◽  
Surface Displacement ◽  
Heavy Liquid ◽  
Invariant Property ◽  
Finite Region ◽  
Free Wave ◽  
Free Surface Displacement

The discussion concerns free wave motions generated from rest in a finite region of an ocean of heavy liquid lying on a horizontal plane. It is shown that the horizontal fist moment of the free-surface displacement varies linearly with time. Hence, if the total volume displaced is not zero and therefore the centroid of the displacement is definable, the centroid travels with a constant horizontal velocity as the wave motion evolves. This conclusion holds exactly for waves of any amplitude and even remains applicable subsequent to the breaking of waves.

scholarly journals Weak formulation of free-surface wave equations

2001 ◽  
Vol 5 (2) ◽  
pp. 75-85
Author(s):  
A. D. Sneyd
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Wave Equations ◽  
Evolution Equations ◽  
Surface Displacement ◽  
Wave Dispersion ◽  
The Body ◽  
Weak Formulation ◽  
Free Surface Displacement ◽  
Free Surface Wave

An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion, η=∑n=1∞αn(t)En where the αn(t) are time-dependent coefficients. For a tank with vertical sides the En are eigenfunctions of the eigenvalue problem, ∇2+λ2E=0,  ∇E⋅n^=0 on the tank side walls. Evolution equations for the αn(t) can be obtained by taking inner products of the linearised equation of motion, ρ∂v∂t=−1ρ∇P+F with the normal irrotational wave modes. For unforced waves each evolution equation is a simple harmonic oscillator, but the method is most useful when the body force F is something more exotic than gravity. It can always be represented by a forcing term in the SHM evolution equation, and it is not necessary to assume F irrotational. Several applications are considered: the Faraday experiment, generation of surface waves by an unsteady magnetic field, and the metal-pad instability in aluminium reduction cells.

scholarly journals Simulation of Partially Filled Liquid in a Moving Tank

2020 ◽  
Vol 8 (6) ◽  
pp. 1941-1944
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Unsteady Flow ◽  
Numerical Simulations ◽  
Dynamic Pressure ◽  
Surface Displacement ◽  
Volume Of Fluid ◽  
Two Dimensional ◽  
Ansys Software ◽  
Free Surface Displacement

Numerical simulations have been carried out on a rectangular tank filled partially with liquid using volume of fluid technique. The tank has been given to and fro motion in one direction. Numerical simulation has been carried for a two dimensional case having laminar and unsteady flow. The changes in free surface displacement and dynamic pressure at different times has been observed using ANSYS software. The study was conducted for two sec. It was observed that free surface displacement of fluid increases with velocity. Also, with an increase in volume of liquid the sloshing effect decreases.

Surface waves due to resonant horizontal oscillation

1988 ◽  
Vol 192 ◽  
pp. 219-247 ◽  
Author(s):  
M. Funakoshi ◽  
S. Inoue
Keyword(s):  
Surface Waves ◽  
Evolution Equations ◽  
Period Doubling ◽  
Surface Displacement ◽  
Nonlinear Evolution Equations ◽  
Experimental Results ◽  
Weakly Nonlinear ◽  
Irregular Wave ◽  
Free Surface Displacement ◽  
Slow Evolution

Experiments on surface waves were made using a cylindrical container oscillated horizontally with the period T close to that associated with the two known degenerate modes. Outside a certain region in the (T,x0)-plane, where x0 is the amplitude of the forcing displacement, surface waves exhibit either of the two kinds of regular motions whose amplitudes are constant. Within this region, however, the wave amplitude slowly changes, expressing the irregular or periodic motion of surface waves. In order to analyse these motions in detail, the slow evolution of four variables associated with the amplitudes and phases of the two modes is computed from the free-surface displacement at two measuring points. It is shown that the most common attractor corresponding to the irregular wave motion is the strange attractor with a positive maximum Liapunov exponent and a correlation dimension of 2.1–2.4. Furthermore, another kind of chaotic attractor and a few periodic orbits are found in a small parametric region. The route to chaos associated with period-doubling bifurcation is also observed. The above experimental results are compared with the solutions to weakly nonlinear evolution equations derived by Miles. We find that the equations can explain well many of the experimental results on regular and irregular wave motions. In particular, the most common chaotic attractors both in the experiments and in the theory have similar shapes in a phase space, and also yield similar values for maximum Liapunov exponents and correlation dimensions.

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