Counter- and co-directed swirling-type waves due to orbital excitations of a square-base tank

Reports of the National Academy of Sciences of Ukraine ◽

10.15407/dopovidi2021.06.045 ◽

2021 ◽

pp. 45-51

Author(s):

O.E. Lagodzinskyi ◽

A.N. Timokha

Keyword(s):

Steady State ◽

Numerical Experiments ◽

Elliptic Orbit ◽

Orbital Forcing ◽

Circular Orbits ◽

Sloshing Frequency ◽

Resonant Waves

The analytic technique and numerical experiments are employed to show that the orbital elliptic translational ex citations of a square-base container can, depending on the ratio of the semiaxes of the elliptic orbit, lead, when the forcing frequency is close to the lowest natural sloshing frequency, to both the counter- and co-directed (relative to the orbital forcing direction) stable swirling-type steady-state resonant waves. For a non-zero damping in the hydrodynamic wavy system, the passage to circular orbits makes the stable counter-directed swirling impossible.

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The effects of boundary conditions on the steady-state response of three hypothetical ground-water systems; results and implications of numerical experiments

10.3133/wsp2315 ◽

1987 ◽

Keyword(s):

Steady State ◽

Boundary Conditions ◽

Ground Water ◽

Numerical Experiments ◽

Water Systems ◽

Steady State Response ◽

State Response

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Steady-state sloshing for the orbital forcing

Sloshing in Upright Circular Containers ◽

10.1201/9780429356711-7 ◽

2020 ◽

pp. 111-122

Author(s):

Ihor Raynovskyy ◽

Alexander Timokha

Keyword(s):

Steady State ◽

Orbital Forcing

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Numerical Experiments of Coolant Mixing in a Lower Plenum of PWR Under Asymmetric Thermal- Hydraulics Conditions

Volume 4: Computational Fluid Dynamics, Neutronics Methods and Coupled Codes; Student Paper Competition ◽

10.1115/icone14-89447 ◽

2006 ◽

Cited By ~ 1

Author(s):

Masanori Ohtani ◽

Akito Kozuru ◽

Yasuyuki Kashimoto ◽

Mitsuto Montani ◽

Koutaro Takeda ◽

...

Keyword(s):

Steady State ◽

Temperature Distribution ◽

Turbulent Mixing ◽

Numerical Experiments ◽

Time Dependent ◽

Inlet Temperature ◽

Velocity Fluctuations ◽

The Core ◽

State Calculation ◽

Lower Temperature

Asymmetric thermal-hydraulic conditions among primary loops during a postulated steam line break (SLB) induce a non-uniform temperature distribution at a core inlet. When coolant of lower temperature intrudes into a part of core, it leads to a reactivity insertion and a local power increase. Therefore, an appropriate model for the core inlet temperature distribution is required for a realistic SLB analysis. In this study, numerical experiments were conducted to examine the core inlet temperature distribution under the asymmetric thermal-hydraulic coolant conditions among primary loops. 3D steady-state calculations were carried out for Japanese standard Pressurized Water Reactor (PWR) such as 2, 3, 4 loop types and an advanced PWR. Since the flow in a reactor vessel involves time-dependent velocity fluctuations due to a high Reynolds number condition and a complicated geometry of flow path, the turbulent mixing might be enhanced. Hence, the turbulent thermal diffusivity for the steady-state calculation was examined based on experimental results and another transient calculation. As a result, it was confirmed that (1) the turbulent mixing in a downcomer and a lower plenum were enhanced due to time-dependent velocity fluctuations and therefore the turbulent thermal diffusivity for steady-state calculation was specified to be greater, (2) the core inlet temperature distribution predicted by a steady-state calculation reasonably agreed with a experimental data, (3) the patterns of core inlet temperature distribution were comprehended to be dependent on the plant type, i.e. the number of primary loop and (4) under a low flow rate condition, the coolant of lower temperature appeared on the opposite side of the affected loop due to the effect of a natural convection.

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On the existence of steady-state resonant waves in experiments

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.658 ◽

2014 ◽

Vol 763 ◽

pp. 1-23 ◽

Cited By ~ 21

Author(s):

Z. Liu ◽

D. L. Xu ◽

J. Li ◽

T. Peng ◽

A. Alsaedi ◽

...

Keyword(s):

Experimental Investigation ◽

Steady State ◽

Multiple Solutions ◽

Wave Spectra ◽

Ocean Engineering ◽

System Error ◽

Exact Resonance ◽

Wave Trains ◽

Theoretical Results ◽

Resonant Waves

AbstractThis paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

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Quenching Vibration on a Harmonically Excited Symmetric Laminated Composite Plate

Journal of Vibration and Acoustics ◽

10.1115/1.4052683 ◽

2021 ◽

pp. 1-35

Author(s):

Jiawang Chen ◽

Philip Cha ◽

Yichang Shen ◽

Xiang Zhou

Keyword(s):

Steady State ◽

Efficient Method ◽

Composite Plate ◽

Numerical Experiments ◽

Laminated Composite ◽

Governing Equations ◽

Laminated Composite Plate ◽

Constraint Equations ◽

Damped Oscillators ◽

Damped Oscillator

Abstract In this paper a simple and efficient method is developed to quench the steady state vibration of a harmonically excited, damped and symmetric laminated composite rectangular plate. This is achieved by enforcing points of zero displacement, or nodes, at some specified locations on the laminated composite plate using properly tuned damped oscillators. Using the assumed-modes method, the governing equations of the laminated composite plate carrying the damped oscillators are first formulated. A set of constraint equations is established by enforcing nodes at user-specified locations on the plate. Two attachment scenarios are considered: when the attachment and node locations coincide, and when they are distinct. Numerical experiments show that for both cases, the damped oscillator parameters can be readily determined and the desired node locations can be successfully imposed. More importantly, enforcing nodes can suppress vibration in the vicinity of the node locations, thereby keeping that region of the laminated composite plate nearly stationary.

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The expulsion of magnetic flux by eddies

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1966.0173 ◽

1966 ◽

Vol 293 (1434) ◽

pp. 310-328 ◽

Cited By ~ 239

Keyword(s):

Magnetic Field ◽

Steady State ◽

Magnetic Flux ◽

Characteristic Time ◽

Numerical Experiments ◽

Uniform Magnetic Field ◽

Conducting Fluid ◽

Central Field ◽

The Sun ◽

Lines Of Force

A convective eddy imposed on an initially uniform magnetic field in a highly conducting fluid distorts the lines of force and amplifies the field. Flux is concentrated outside the eddy; within it, the field grows and its scale of variation decreases until resistive effects become important. Closed lines of force are then formed by reconnexion. The central field decays and a steady state is reached. Within a period, small compared with the characteristic time for resistive decay, magnetic flux is almost entirely expelled from regions of rapid motion and concentrated at the edges of convection cells. This process is demonstrated from numerical experiments. The results are applied to the sun, where the concentrated fields are strong enough to inhibit convection locally.

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Steady-state resonance of multiple wave interactions in deep water

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.2 ◽

2014 ◽

Vol 742 ◽

pp. 664-700 ◽

Cited By ~ 31

Author(s):

Zeng Liu ◽

Shi-Jun Liao

Keyword(s):

Steady State ◽

Parameter Space ◽

Gravity Waves ◽

Deep Water ◽

Wave Energy ◽

Two Dimensions ◽

Physical Parameters ◽

Wave System ◽

State Resonance ◽

Resonant Waves

AbstractThe steady-state resonance of multiple surface gravity waves in deep water was investigated in detail to extend the existing results due to Liao (Commun. Nonlinear Sci. Numer. Simul., vol. 16, 2011, pp. 1274–1303) and Xu et al. (J. Fluid Mech., vol. 710, 2012, pp. 379–418) on steady-state resonance from a quartet to more general and coupled resonant quartets, together with higher-order resonant interactions. The exact nonlinear wave equations are solved without assumptions on the existence of small physical parameters. Multiple steady-state resonant waves are obtained for all the considered cases, and it is found that the number of multiple solutions tends to increase when more wave components are involved in the resonance sets. The topology of wave energy distribution in the parameter space is analysed, and it is found that the steady-state resonant waves indeed form a continuum in the parameter space. The significant roles of the near-resonance and nonlinearity were also revealed. It is found that all of the near-resonant components as a whole contain more and more wave energy, as the wave patterns tend from two dimensions to one dimension, or as the nonlinearity of the steady-state resonant wave system increases. In addition, the linear stability of the steady-state resonant waves is analysed. It is found that the steady-state resonant waves are stable, as long as the disturbance does not resonate with any components of the basic wave. All of these findings are helpful to enrich and deepen our understanding about resonant gravity waves.

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