Liquid sloshing and wave breaking in circular and square-base cylindrical containers

2007 ◽  
Vol 577 ◽  
pp. 467-494 ◽  
Author(s):  
A. ROYON-LEBEAUD ◽  
E. J. HOPFINGER ◽  
A. CARTELLIER
Keyword(s):  
Natural Frequency ◽  
Wave Breaking ◽  
Wave Motion ◽  
Wave Amplitude ◽  
Variable Parameter ◽  
Frequency Offset ◽  
Vortical Flow ◽  
Wave Crest ◽  
Wide Range ◽  
Planar Wave

Near resonance sloshing in containers, filled with a liquid to a given depthh, depends on three parameters, which are the viscous damping, the frequency offset that contains the forcing amplitude and the fluid depth. Experiments have been conducted with low-viscosity liquids mainly in circular cylindrical containers of radiusRsubjected to harmonic horizontal forcing; complementary experiments on wave breaking have been performed in a square-base container. The fluid depth was kept large (h/R> 1) so that it was no longer a variable parameter. The bounds of existence of the different wave regimes, namely planar waves, swirling waves, chaotic sloshing as well as breaking waves, have been determined as a function of forcing frequencies relative to the lowest natural frequency ω1and for a wide range of forcing amplitudes. It is shown that when the forcing frequency ω is slightly larger than the lowest natural frequency ω1, planar wave motion bifurcates to a swirling wave mode at finite wave amplitude, the value of which depends on the offset parameter. The swirl wave amplitude grows exponentially and saturates at a certain value. The swirl has a hard-spring behaviour, is very robust and can generate a vortical flow of the liquid column. Chaotic sloshing and wave breaking occur quasi-periodically: growth of planar wave amplitude at a rate depending on the forcing amplitude, collapse, irregular swirl and again growth of planar wave amplitude. The details and periodicity of the chaotic behaviour and breaking depend on the frequency-offset parameter. Close to the natural frequency, chaotic wave motion is possible without breaking. Planar wave breaking is, in general, associated with spilling caused by the encounter of nearly freely falling lumps of fluid with the upward moving wave crest, in a way demonstrated previously in two-dimensional wave breaking. In three dimensions, the wave crest is destabilized in the crosswise direction so that spilling is not uniform along the wave crest and an irregular swirl is generated following breaking; free fall of fluid lumps occurs over many wave periods. The complementary experiments, performed in a square-base container of base dimensionL, show four different wave patterns of wavelengthsLandL/2 crosswise to the primary wave. This cross-wave instability is interpreted in terms of parametric instability.

Wide-Range and Fast-Tracking Non-Data-Aided Frequency Offset Estimator for QAM Optical Coherent Receivers

2016 ◽  
Vol E99.B (7) ◽  
pp. 1416-1425 ◽  
Author(s):  
Tadao NAKAGAWA ◽  
Takayuki KOBAYASHI ◽  
Koichi ISHIHARA ◽  
Yutaka MIYAMOTO
Keyword(s):  
Frequency Offset ◽  
Fast Tracking ◽  
Wide Range ◽  
Coherent Receivers

Density Wave Measurements in a Rectangular Clarifier

1983 ◽  
Vol 18 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Mark K. Watson ◽  
R.R. Hudgins ◽  
P.L. Silveston
Keyword(s):  
Power Spectrum ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Motion ◽  
Wave Amplitude ◽  
Suspended Solids ◽  
Small Volume ◽  
Density Wave ◽  
Measure Concentration ◽  
Wave Measurements

Abstract Internal wave motion was studied in a laboratory rectangular, primary clarifier. A photo-extinction device was used as a turbidimeter to measure concentration fluctuations in a small volume within the clarifier as a function of time. The signal from this device was fed to a HP21MX minicomputer and the power spectrum plotted from data records lasting approximately 30 min. Results show large changes of wave amplitude as frequency increases. Two distinct regions occur: one with high amplitudes at frequencies below 0.03 Hz, the second with very small amplitudes appears for frequencies greater than 0.1 Hz. The former is associated with internal waves, the latter with flow-generated turbulence. Depth, velocity in the clarifier and inlet suspended solids influence wave amplitudes and the spectra. A variation with position or orientation of the probe was not detected. Contradictory results were found for the influence of flow contraction baffles on internal wave amplitude.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

2016 ◽  
Vol 33 (3) ◽  
pp. 323-329 ◽  
Author(s):  
S.-S. Zhou ◽  
S.-J. Zhou ◽  
A.-Q. Li ◽  
B.-L. Wang
Keyword(s):  
Residual Stresses ◽  
Natural Frequency ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Transition Range ◽  
Biochemical Sensors ◽  
Tension Parameter ◽  
Wide Range

AbstractResonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Estimating energy dissipation in internal solitary waves breaking on slopes

2021 ◽  
Author(s):  
Kateryna Terletska ◽  
Vladіmir Maderich ◽  
Tatiana Talipova
Keyword(s):  
Energy Dissipation ◽  
Solitary Waves ◽  
Wave Breaking ◽  
Wave Amplitude ◽  
Hot Spot ◽  
Slope Angle ◽  
Bottom Layer ◽  
Internal Solitary Waves ◽  
Coastal Zones ◽  
Waves Interaction

<p>The shoaling mechanisms of internal solitary waves that propagate horizontally are an important source of mixing and transport in the coastal zones. Numerical modelling, llaboratory experiments and observations are needed for understanding wave energetics, especially energy transformation during waves interaction with the slopes. Two shoaling mechanisms are important during interaction with the slope: (i) wave breaking that results in mixing and dissipation, (ii) changing of the polarity of the initial wave of depression on the slope. Classification based on regimes of interaction with the slope was presented in [1]. Four zones were separated in αβγ (γ - is slope angle, α-  is the non-dimensional wave amplitude (wave amplitude normalized on the thermocline thickness) and β – is the blocking parameter that is the ratio of the height of the bottom layer on the shelf to the incident wave amplitude) classification diagram: (I) without changing polarity and wave breaking, (II) changing polarity without breaking; (III) wave breaking without changing polarity; (IV) wave breaking with changing polarity. It was shown that results of field, laboratory and numerical experiments are in good agreement with proposed classification.  In the present study we estimate energy dissipation for all the types of interaction and present the algorithm for building a zone map with a ‘hot spot’ of energy dissipation for real slopes in the ocean.</p><p> </p><p>[1] K Terletska, BH Choi, V Maderich, T Talipova  Classification of internal waves shoaling over slope-shelf topography RUSSIAN JOURNAL OF EARTH SCIENCES vol. 20, 4, 2020, doi: 10.2205/2020ES000730</p>

scholarly journals REFLECTIONS FROM COASTAL STRUCTURES

1988 ◽  
Vol 1 (21) ◽  
pp. 58 ◽  
Author(s):  
N.W.H. Allsop ◽  
S.S.L. Hettiarachchi
Keyword(s):  
Wave Motion ◽  
Significant Contribution ◽  
Numerical Models ◽  
Coastal Structures ◽  
Wave Reflections ◽  
Reflected Waves ◽  
Sea Bed ◽  
Wide Range ◽  
Alternative Structure ◽  
General Reduction

Wave reflections at and within a coastal harbour may make a significant contribution to wave disturbance in the harbour. Reflected waves may lead to danger to vessels navigating close to structures, and may reduce the availability of berths within the harbour. Wave reflections may also increase local scour or general reduction in sea bed levels. In the design of breakwaters, sea walls, and coastal revetments, it is therefore important to estimate and compare the reflection performance of alternative structure types. In the use of numerical models of wave motion within harbours, it is essential to define realistically the reflection properties of each boundary. This paper presents results from a study of the reflection performance of a wide range of structures used in coastal and harbour engineering.

On Categorization of Seismic Load As Primary or Secondary for Piping Systems With Hardening Capacity

2018 ◽  
Author(s):  
Pierre B. Labbé
Keyword(s):  
Natural Frequency ◽  
Response Spectrum ◽  
A Priori ◽  
Effective Stiffness ◽  
Linear Oscillator ◽  
Seismic Load ◽  
Wide Range ◽  
Non Linear ◽  
Piping Systems ◽  
Non Linear Oscillator

The concept of primary/secondary categorization is first reviewed and generalized for its application to a non-linear oscillator subjected to a seismic load. Categorizing the seismic load requires calculating the input level associated with the oscillator ultimate capacity and comparing it to the level associated with the plastic yield. To resolve this problem, it is assumed that the non-linear oscillator behaves like a linear equivalent oscillator, with an effective stiffness (or frequency) and an effective damping. However, as it is not a priori possible to predict the equivalent stiffness and damping, a wide range of possibilities is systematically considered. The input motion is represented by its conventional response spectrum. It turns out that key parameters for categorization are i) the “effective stiffness factor” (varying from 0 for perfect damage behaviour to 1 for elastic-perfectly plastic) and the slope of the response spectrum in the vicinity of the natural frequency of the oscillator. Effective damping and spectrum sensitivity to damping play a second order role. A formula is presented that enables the calculation of the primary part of a seismically induced stress as a function of both the oscillator and input spectrum features. The formula is also presented in the form of a diagram. This paper follows-up on a similar paper presented by the author at the PVP 2017 Conference [1]. The new development introduced here is that the oscillator exhibits hardening capacity, while no hardening was assumed in [1]. It appears that the conclusions are slightly modified but the trend is very similar to the non-hardening case. Regarding piping systems, it appears that even when experiencing large plastic strains under beyond design input motions, their observed effective frequency is very close to their natural frequency, decreasing only by a few percents (experimental data from USA, Japan and India are processed). These observations lead to the conclusion that the seismic load, or the seismically induced inertial seismic strains, should basically be regarded as secondary.

Ambulance Stretcher Suspensions

1985 ◽  
Vol 199 (2) ◽  
pp. 151-160 ◽  
Author(s):  
C W Stammers ◽  
D Leysbon
Keyword(s):  
Natural Frequency ◽  
Vibration Isolation ◽  
Coil Spring ◽  
Electric Actuator ◽  
Initial Testing ◽  
Load Variation ◽  
Simple Mechanism ◽  
Wide Range ◽  
Patient Load

Existing methods for vibration isolation of patients transported by ambulance are discussed. Some alternative suspensions are outlined and a relatively simple mechanism analysed. This can give virtually constant vertical natural frequency over a wide range of patient load. Variation in pitch natural frequency can also be minimized at the expense of some variation in vertical natural frequency. The elements used are a coil spring, load arm and an electric actuator. Initial testing of the mechanism has been made to confirm the feasibility of the concept.

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