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

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.

Tuned Sloshing Dampers With Large Rectangular Core Penetrations

Space restrictions at the top of tall buildings may necessitate using tuned sloshing dampers (TSD) tanks with large rectangular penetrations to accommodate the structural core of the tower. A finite element model is employed to predict the natural sloshing frequencies and mode shapes of liquid sloshing in a rectangular tank with a rectangular core. Equivalent mechanical properties are determined to predict the sloshing response. Frequency response predictions of wave heights, sloshing forces, and energy-dissipation per cycle agree with results from shake table testing conducted on a rectangular tank with a rectangular core. Energy dissipation due to flow around the core adds considerable damping to the liquid and is proportional to the response velocity-squared. Nonlinear coupling among sloshing modes results in multiple peaks in the frequency response plots near the fundamental resonant frequency. An interior core with a broad dimension in one direction substantially reduces the fundamental sloshing frequency and equivalent mechanical mass in the perpendicular direction; however, the fundamental sloshing frequency and equivalent mechanical mass in the parallel direction are only influenced marginally. Large rectangular cores reduce the proportion of the total water mass that is effective in controlling tower motion. A TSD with a rectangular penetrating core may enable a TSD option to be considered for the control of a tall building in cases where a traditional rectangular TSD is infeasible.

Vibration Analysis of a Horizontal Partially Fluid-Filled Cylindrical Shell Considering Sloshing Effect of Free Surface

The free and forced vibrations of a horizontal partially fluid-filled cylindrical shell with sloshing effect are studied based on the finite element method. The structure and inner fluid taking into account the sloshing effect of the free surface are simulated by the shell and acoustic elements respectively. The natural frequencies of sloshing fluid and shell structure are calculated simultaneously by the FEM. To verify the accuracy of the results, the shell’s natural frequencies are compared with published results. The effects of the structural parameters and fluid depth on the vibration of the coupled system are discussed. The natural frequencies of a sloshing fluid can be divided into low-frequency and high-frequency part, and the low-frequency part refers to the pressure fluctuation caused by the sloshing of the free surface, while the high-frequency part corresponds to the pressure fluctuation of the particles below the free surface. The thinner the shell thickness is, the lower the sloshing frequency of free surface and coupled modal frequency of the shell are. With the increase of the liquid depth, the natural sloshing frequency of the free surface increases slightly while the coupled modal frequency of the shell decreases. The impact of the free surface effect on the coupled vibration cannot be omitted when the shell’s natural frequencies are close to the sloshing frequencies.

An inviscid analysis of the Prandtl azimuthal mass transport during swirl-type sloshing

An inviscid analytical theory of a slow steady liquid mass rotation during the swirl-type sloshing in a vertical circular cylindrical tank with a fairly deep depth is proposed by utilising the asymptotic steady-state wave solution by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608–645). The tank performs a periodic horizontal motion with the forcing frequency close to the lowest natural sloshing frequency. The azimuthal mass transport (first observed in experiments by Prandtl (Z. Angew. Math. Mech., vol. 29(1/2), 1949, pp. 8–9)) is associated with the summarised effect of a vortical Eulerian-mean flow, which, as we show, is governed by the inviscid Craik–Leibovich equation, and an azimuthal non-Eulerian mean. Suggesting the mass-transport velocity tends to zero when approaching the vertical wall (supported by existing experiments) leads to a unique non-trivial solution of the Craik–Leibovich boundary problem and, thereby, gives an analytical expression for the summarised mass-transport velocity within the framework of the inviscid hydrodynamic model. The analytical solution is validated by comparing it with suitable experimental data.

Steady-State Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion

The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio h>1). This behavior type is supported by the existing experimental data. The wave elevations at the vertical wall are satisfactorily predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.

Resonant Steady-State Sloshing in Upright Tanks: Effect of Three-Dimensional Excitations and Viscosity

Bearing in mind recent experimental and theoretical results showing that viscous damping can qualitatively affect resonant sloshing in clean tanks, the Narimanov-Moiseev multimodal sloshing theory for an upright circular container is revised to analytically analyze steady-state surface waves when the container performs a small-amplitude sway/roll/pitch/surge prescribed periodic motion with the forcing frequency close to the lowest natural sloshing frequency. The revised theory is applicable for the radius-scaled mean liquid depths h > 1 providing the secondary resonance phenomenon does not occur at the primary resonance zone. A focus is on how the damping influences the phase lag as well as on the amplitude response curves versus the forcing type, which can in the lowest-order approximation be treated as if the container translatory moves along an elliptic orbit in the horizontal plane. The analytical results are compared with existing experiments for longitudinal and circular orbital tank excitations. Whereas a good agreement is found for longitudinal excitations, a discrepancy is detected for the circular orbital forcing. The discrepancy may, most probably, be explained by the wave breaking and mean angular mass-transport (Ludwig Prandtl, 1949) phenomena. Occurrence of the Prandtl phenomenon makes inapplicable the existing analytical inviscid sloshing theories, even if they are modified to account for damping.

Investigation of Soil Structure Interaction and Wall Flexibility Effects on Natural Sloshing Frequency of Vessels

The main purpose of this study is to establish the effects of vessel walls flexibility on its natural sloshing frequency considering soil-structure-fluid interaction theory. Furthermore, two new efficiently relations to find both of wall flexibility and soil-structure interaction effects on natural frequency are developed. Regarding the aim of current study three different conditions of elevated tanks are applied. Fixed base condition with an emphasis on recommendations of international code ACI-350, analytical FSSI regarding equivalent mass spring method, and the numerical direct method regarding theory of finite element are taken into consideration. Results indicate that there is no significant effect of walls flexibility on natural sloshing frequency regarding fixed base assumptions of vessels. On the contrary, significant effects of wall flexibility are achieved considering SSI theory. Results of international code ACI-350 show that, the international codes assumptions have imprecise estimations of natural sloshing frequency in the range of hard to very soft soil categories. On the other hand, it is observed that the wall flexibility has a more highlighted effect on natural frequency in soft soils rather than soil-structure interaction. The significance of wall flexibility effect on natural frequency is more than that of SSI considering soil softening.

The design of the floating baffle for Cassini tank and the analysis of restraining sloshing

In this article, a new floating plate structure with “drive ring” is presented, which breaks the traditional idea of installing fixed baffle in a tank. In order to analyze the performance of this anti-sloshing structure, the effect of sloshing suppression and the liquid sloshing dynamics of this structure in a Cassni tank with numerical simulation is investigated. Liquid sloshing frequencies of the floating plate with different fill ratio under the circumstances of normal weight and micro-gravity were studied. At last aiming at the liquid sloshing amplitude, the suppression effect of the floating plate and rigid ring baffle was also studied under the circumstances of instantaneous angular and “Bang-Bang” transverse acceleration incentives with different fill ratios. The result of the numerical simulation shows that the movable-type floating plate structures can increase the liquid sloshing frequency and can effectively absorb the kinetic energy of the liquid sloshing and reduce liquid sloshing amplitude.