Damping computation of liquid sloshing in containers aboard spacecraft

Under the non-rotating assumption, a method for the calculation of damping of fuel sloshing with small amplitude in containers aboard spacecraft is proposed in the present paper. And we have presented an eigen-value equation for sloshing damping and frequency computation. This equation may be solved by Ritz or Galerkin methods for a container of simple geometry or by finite element method for a container of arbitrary geometric shape even with rigid baffles. The simulated results show that the equivalent damping coefficients is directly proportional to fuel‘s viscosity, whereas it almost exhibits no influence on sloshing frequencies. The drawback of the proposed method lies in expensive computation cost. Thus far, it hasn‘t yet be applied to a container with elastic baffles.     

Damping computation of liquid sloshing with small amplitude in rigid container using FEM

An FEM (Finite Element Method) based damping estimation method of liquid sloshing with small amplitude in rigid container is proposed. Damping of the sloshing is affected by many factors and some of them are very complicated. Therefore, this paper aims to provide an estimation range, instead of computing the exact value of damping. This method will consider the dissipation at wall, in the interior, and at the contaminated free surface. Owing to the complexity of viscous damping at the free surface, damping of two extreme conditions are computed to estimate the range of actual damping. An iterative algorithm is designed to solve a special general eigenvalue problem. Comparing the computation results with experimental results, it is found that most of the experimental results are within the range of the numerical estimation. Therefore, the method is effective in estimating the range of the damping of liquid sloshing with small amplitude in rigid container. The project supported by the National Natural Science Foundation of China (10172048) The English text was polished by Keren Wang.     

Dripping retardation with corrugated ceiling

The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.     

Inertia effects in TLD sloshing with perforated screens

Rectangular tanks equipped with perforated screens and partly filled with water have been proposed as Tuned Liquid Dampers (TLDs) to mitigate the vibratory response of slender buildings. In a previous paper (Molin & Remy 2013)an experimental campaign was reported and its results compared with a numerical model, based on linearized potential flow theory. Good agreement was generally obtained for the added mass and damping coefficients. In these experiments the screen had numerous circular openings, 4 mm in diameter, and it was assumed in the numerical model that the screen created a pressure drop proportional to the square of the relative traversing velocity. In this subsequent paper complementary experiments are described where the screen openings are increased in size, keeping constant the open-area ratio, and varied in shapes (vertical slots then circular holes). As a result of the solid parts of the screen getting larger, inertia effects come into play resulting in a shift of the resonant frequencies of the odd sloshing modes. With a proper modification of the discharge law in the numerical model, ccounting for inertia effects, good agreement is recovered between experimental and numerical hydrodynamic coefficients.     

Damping of tubes due to internal two-phase flow

Two-phase internal flow is present in many piping system components. Although two-phase damping is known to be a significant constituent of the total damping, the energy dissipation mechanisms that govern two-phase damping are not well understood. In this paper, damping of three different clamped–clamped tubes subjected to two-phase air–water internal axial flow is investigated. Experimental data are reported, showing a strong dependence of two-phase damping on void fraction, flow velocity and flow regime. Data-points plotted on two-phase flow pattern maps indicate that damping is greater in a bubbly flow regime. The two-phase damping ratio reaches a maximum value at the highest void fraction before the transition to a churn flow regime. An analytical model that relates the two-phase damping ratio to the interface surface area is proposed. The model is based on rigid spherical bubbles in cubic elementary flow volumes. The analytical results are well correlated with the experiments.     

Darcyan flow with relaxation effect

The equation for the flow of a liquid through a porous medium is either elliptic or parabolic which implies that a disturbance in pressure or head is transmitted with infinite velocity. This is unsatisfactory from a physical viewpoint, although not necessarily from a practical one. If Darcy's law is completed with an inertial term the flow equation becomes a strongly damped wave equation. The proposed additional term can be identified from experiments with confined flow and free surface flow when the pressure or head varies harmonically with time.Symbols c ₀ characteristic speed - c ₁ characteristic speed - c _w characteristic speed - C auxiliary parameter - d diameter of a bead - E modulus of elasticity - F auxiliary function - h piezometric height - H height of groundwater table - I ₀(x) modified Bessel function - I ₁(x) modified Bessel function - k permeability - K hydraulic conductivity - L tube length or channel length - L ₀ reference length - m auxiliary parameter - n porosity - p pressure - Q mass flux - r=(x, y, z) Cartesian coordinates - dimensionless Cartesian coordinates - r(p) tube radius - r ₀ tube radius - R ₀ tube radius - r _p equivalent pore radius - t time - velocity vector - V volume - coefficient of compressibility - coefficient of compressibility - coefficient of compressibility - expansibility - relaxation time - dynamic viscosity - Poisson's ratio - density - dimensionless time - angular frequency     

Liquid sloshing in partly-filled laterally-excited circular tanks equipped with baffles

Linear potential theory in conjunction with the conformal mapping technique are employed to develop rigorous mathematical models for two-dimensional transient sloshing in non-deformable baffled horizontal circular cylindrical vessels, filled with inviscid incompressible fluids to arbitrary depths, and subjected to arbitrary time-dependent lateral accelerations. Three common baffle configurations are considered, namely, a pair of free surface-touching horizontal side baffles, and a central surface-piercing or bottom-mounted vertical baffle of arbitrary extension. The first few normalized antisymmetric/symmetric sloshing frequencies of the partially-filled tanks are tabulated for selected baffle extension and fill depth ratios. Also, the effects of liquid fill depth or baffle length parameter on the impulsive, total and modal convective mass ratios are examined. A ramp-step function is used to replicate the lateral acceleration excitation encountered in an idealized turning maneuver. Durbin's numerical Laplace transform inversion scheme was applied to solve the resulting truncated linear sets of ordinary differential equations in the time-domain. The effects of excitation input time, fill level, and baffle configuration/extension on the force and moment amplification factors are illustrated through appropriate design charts. Furthermore, the transient hydrodynamic responses to a real seismic event are calculated and the effectiveness of baffle configuration/length on suppression of the induced destabilizing lateral forces are examined. Limiting cases are considered and rigorous verifications are made by comparison with the available data as well as with the numerical simulations performed by using a commercial CFD software package.     

Non-linear sloshing analysis of liquid in tanks with arbitrary geometries

A method is newly proposed for calculating the non-linear dynamic behavior of liquid in tanks with arbitrary geometries. The formulation uses the orthogonality of the linear mode shapes and the numerical perturbation technique. The problem is reduced to the non-linear coupled ordinary differential equations describing the timewise trend. Numerical examples carried out on the sloshing in rectangular and axisymmetric tanks demonstrate the versatility of the present method.     

Liquid sloshing in a horizontally forced vessel with bottom topography

This paper presents a numerical study of the free-surface evolution for inviscid, incompressible, irrotational, horizontally forced sloshing in a two-dimensional rectangular vessel with an inhomogeneous bottom topography. The numerical scheme uses a time-dependent conformal mapping to map the physical fluid domain to a rectangle in the computational domain with a time-dependent aspect ratio Q(t), known as the conformal modulus. The advantage of this approach over conventional potential flow solvers is the solution automatically satisfies Laplace's equation for all time, hence only the integration of the two free-surface boundary conditions is required. This makes the scheme computationally fast, and as grid points are required only along the free-surface, high resolution simulations can be performed which allows for simulations for mean fluid depths close to the shallow water water regime. The scheme is robust and can simulate both resonate and non-resonate cases, where in the former, the large amplitude waves are well predicted.Results of nonlinear simulations are presented in the case of non-breaking waves for both an asymmetrical ‘step’ and a symmetric ‘hump’ bottom topography. The natural free-sloshing mode frequencies are compared with the small topography asymptotic results of Faltinsen and Timokha (2009) (Sloshing, Cambridge University Press (Cambridge)), and are found to be lower than this asymptotic prediction for moderate and large topography magnitudes. For forced periodic oscillations it is shown that the hump profile is the most effective topography for minimizing the nonlinear response of the fluid, and hence this topography would reduce the stresses on the vessel walls generated by the fluid. Results also show that varying the width of the step or hump has a less significant effect than varying its magnitude.     

带有可渗透隔板的液舱内流体晃荡的时域模拟

针对液舱内隔板的可渗透特性,采用多域边界元方法,对流体晃荡问题进行了非线性时域模拟计算与分析。计算研究表明,多域边界元方法能够准确地模拟带有可渗透隔板的液舱内流体晃荡现象。对应于没有隔板和有完全不可渗透隔板情形的计算结果与相应的实验和理论结果吻合良好,带有不同渗透率的隔板在一定程度上改变了结构的固有振荡频率,隔板的可渗...     

Fluid sloshing in an ice-hole of arbitrary shape

A numerical method is proposed for determining the natural frequencies and modes of the small oscillations of an ideal fluid in a half-space bounded above by a rigid plane with an aperture of arbitrary shape. Considering the monotonic dependence of the eigenvalues on the geometry, it can be stated that the eigenvalues for a half-space are universal upper limits for the corresponding eigenvalues of tanks with an arbitrary boundary but the same free surface.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 108–112, July–August, 1992.     

A study of sloshing absorber geometry for structural control with SPH

A liquid sloshing absorber consists of a container, partially filled with liquid. The absorber is attached to the structure to be controlled, and relies on the structure's motion to excite the liquid. Consequently, a sloshing wave is produced at the liquid free-surface within the absorber, possessing energy dissipative qualities. The primary objective of this work is to numerically demonstrate the effect of a sloshing absorber's shape on its control performance. Smoothed Particle Hydrodynamics (SPH) is used to model fluid–structure interaction of the structure/sloshing absorber system in two dimensions. The structure to be controlled is a lightly damped single degree-of-freedom structure. The structure is subjected to a transient excitation and then allowed to respond dynamically, coming to rest either due to its own damping alone or with the added control of the sloshing absorber. It is identified that the control performance of the conventionally used rectangular container geometry can be improved by having inward-angled walls. This new arrangement is robust, and of significant advantage in situations when the external disturbance is of uncertain magnitude.     

Lagrangian modelling of fluid sloshing in moving tanks

The paper considers the problem of sloshing of incompressible fluid in a moving 2-D rectangular tank under horizontal and vertical excitation. The problem is solved in Lagrangian variables by applying two approaches. First, a third-order asymptotic solution for resonant sloshing with a dominant mode is derived using a recursive technique. Then, fully nonlinear set of equations in the material coordinates is solved numerically by employing a finite difference method. Both methods are applied to a problem of high amplitude resonant Faraday waves and the obtained results are compared with experimental data known from the literature and a good agreement between the results of the two methods and the empirical data is demonstrated.     

Neural network-based reduced-order modeling for nonlinear vertical sloshing with experimental validation

In this paper, a nonlinear reduced-order model based on neural networks is introduced in order to model vertical sloshing in presence of Rayleigh–Taylor instability of the free surface for use in fluid–structure interaction simulations. A box partially filled with water, representative of a wing tank, is first set on vertical harmonic motion via a controlled electrodynamic shaker. Accelerometers and load cells at the interface between the tank and an electrodynamic shaker are employed to train a neural network-based reduced-order model for vertical sloshing. The model is then investigated for its capacity to consistently simulate the amount of dissipation associated with vertical sloshing under different fluid dynamics regimes. The identified tank is then experimentally attached at the free end of a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the overall structure. The experimental free response and random seismic excitation responses are then compared with that obtained by simulating an equivalent virtual model in which the identified nonlinear reduced-order model is integrated to account for the effects of violent vertical sloshing.

     

Damping in ceramic matrix composites with matrix cracks

The paper presents an analytical solution capable of predicting the effect of matrix cracking in ceramic matrix composites (CMC) on damping. The cracking scenarios considered in the paper include through-the-thickness cracks and cracks terminating at the layer interfaces. The increase in damping associated with matrix cracking is mostly due to the frictional energy dissipation along the damaged fiber–matrix interfaces adjacent to the bridging cracks whose plane of propagation intersects the fiber axis. Damping increases with a higher density of matrix cracks. The loss factor is affected by the angle of the lamina relative to the direction of the applied load. The loss factor is also influenced by the frequency and magnitude of local dynamic stresses. Examples of distributions of the local loss factor along the axis of a CMC beam subject to pulsating loads of various frequencies are shown in the paper.     

Damping associated with porosity and crack in solids

When a material is subjected to alternating stresses, there are temperature fluctuations indicative of damping. Temperature effects give rise to entropy production. An analysis is made to obtain the entropy produced for a vibration cycle. This corresponds to the reciprocity of temperature rise and strain yielded that alter the material damping factor (MDF) as a function of shape and magnitude of material porosity or existing cracks. A homogeneous, isotropic, elastic bar is considered. It consists of uniformly distributed cavities or a single-edge crack subjected to alternating axial stresses. Dynamic characteristics of the porous or cracked medium are determined to evaluate the damping factor of the bar and/or of the material. The experimental data correlate well with the analytical results. The calculated damping factor in this work can be used as an indicator of structural integrity.     

A boundary element method for small-amplitude viscous fluid sloshing in couple with structural vibration

A boundary element method is presented for the coupled motion analysis of structural vibration with small-amplitude fluid sloshing in two-dimensional space. The linearized Navier-Stokes equations are considered in frequency domain and transformed into boundary integral equations. An appropriate fundamental solution for the Helmholtz equation with pure imaginary constant is found. The condition of zero-stress is imposed on the free surface, and non-slip condition of fluid particles is imposed on the walls of the container. For rigid motion models, the expressions for added mass and added damping to the structural motion equations are obtained. Some typical numerical examples are presented.     

Linear and nonlinear sloshing in a circular conical tank

Linear and nonlinear fluid sloshing problems in a circular conical tank are studied in a curvilinear coordinate system. The linear sloshing modes are approximated by a series of the solid spheric harmonics. These modes are used to derive a new nonlinear modal theory based on the Moiseyev asymptotics. The theory makes it possible to both classify steady-state waves occurring due to horizontal resonant excitation and visualise nonlinear wave patterns. Secondary (internal) resonances and shallow fluid sloshing (predicted for the semi-apex angles >60) are extensively discussed.