Experiments on the synchronous sloshing in suspended containers described by shallow-water theory

2017

Phys. Rev. Fluids

This paper investigates the coupled motion between the dynamics of N vessels coupled together in a one-dimensional array by springs, and the motion of the inviscid fluid sloshing within each vessel. We develop a fully-nonlinear model for the system relative to a moving frame such that the fluid in each vessel is governed by the Euler equations and the motion of each vessel is modelled by a forced spring equation. By considering a linearization of the model, the characteristic equation for the natural frequencies of the system is derived, and analysed for a variety of non-dimensional parameter regimes. It is found that the problem can exhibit a variety of resonance situations from the 1 : 1 resonance to (N + 1)-fold 1 : · · · : 1 resonance, as well as more general r : s : · · · : t resonances for natural numbers r, s, t. This paper focuses in particular on determining the existence of regions of parameter space where the (N + 1)-fold 1 : · · · : 1 resonance can be found.

Section: Introductionsupporting

confidence: 79%

“…Therefore the system (3.10) has a non-trivial solution if D N (ω) = det(A) = 0, which for a tridiagonal matrix occurs when 12) where K N (ω) is the N th continuant [26] which for the notation in A is defined recursively as…”

Section: Natural Frequencies and The Characteristic Equationmentioning

confidence: 99%

Dynamic fluid sloshing in a one-dimensional array of coupled vessels

Huang

2017

Phys. Rev. Fluids

“…Alemi Ardakani et al (2012) demonstrated a 'resonance' effect in the rectangular container system, where anti-symmetric fluid eigenmodes, which couple to the container motion, can have the same oscillation frequency as the symmetric fluid eigenmodes, which exhibit zero force on the container. Weidman & Turner (2016) also conducted experiments on multi-compartment rectangular containers and showed that measured frequencies were in good agreement with those obtained from the baffled container theory of Turner et al (2013). Herczynski & Weidman (2012) produced potential flow theory and experiments for the freesloshing motion (l → ∞) of fluid-filled boxes, cylinders, wedges, cones, and cylindrical annuli containers.…”

Section: Introductionsupporting

confidence: 58%

“…This may thus explain why the theoretical wedge frequencies presented in Weidman & Turner (2016) underestimated the experimentally measured frequencies for short pendulum lengths, because the vessel motion also contained a moderate contribution from the asynchronous mode, thus rendering measurement of the frequencies more difficult.…”

Section: The Initial Value Problemmentioning

confidence: 94%

“…In this case the sole driving force is the fluid sloshing against the container walls. Weidman & Turner (2016) also investigated the initial value problem for both rectangular and cylindrical containers suspended as bifilar pendulums. That study was motivated by experimental results showing that the frequency of container oscillations switch to higher frequency modes as M → 0.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Coupled sloshing in hyperbolic containers suspended as a bifilar pendulum

Weidman

2016

Phys. Rev. Fluids

Self Cite

The coupled interaction between a sloshing fluid in a partially-filled container suspended as a bifilar pendulum is investigated. The sloshing fluid has a free-surface upon which waves are generated this fluid contributes a restoring force to the container motion by its weight through the wire suspensions and the free-surface waves may either enhance or diminish the restoring force through hydrodynamic interaction with the container walls. Results are presented for inviscid, irrotational sloshing in both a two-dimensional hyperbolic container and a threedimensional hyperboloid container. Frequency results for the coupled system are presented for various pendulum lengths and fluid fill heights. It is found that for long pendulum lengths the container and the fluid oscillate in a synchronous motion when the vessel is released with typical experimental initial conditions, but for pendulum lengths below a given threshold the container and fluid oscillate asynchronously from the same initial condition.

Coupled shallow-water fluid sloshing in an upright annular vessel

Rowe

2019

J Eng Math

The coupled motion of shallow-water sloshing in a horizontally translating upright annular vessel is considered. The vessel's motion is restricted to a single space dimension, such as for Tuned Liquid Damper systems. For particular parameters, the system is shown to support an internal 1:1 resonance, where the frequency of coupled sloshing mode which generates the vessel's motion is equal to the frequency of a sloshing mode which occurs in a static vessel. Using a Lagrangian Particle Path formation, the fully nonlinear motion of the system is simulated using an efficient numerical symplectic integration scheme. The scheme is based on the implicit-midpoint rule which conserves energy and preserves the energy partition between the fluid and the vessel over many time-steps. Linear and nonlinear results are presented, including those showing the system transitioning to higher-frequency eigenmodes as the fluid depth is reduced.