Fluid–structure interaction of water filled tanks during the impact with the ground

Crashworthiness of subfloor-integrated tank is fundamental for the survivability of an impact with the ground in emergency. In this paper, numerical models for the analysis of the water sloshing in a tank during the impact with the ground have been developed and validated using experimental data. Specific drop tests were carried out using simulacra of a tank integrated in the subfloor of a small dimension helicopter and reproduced in detail using LSTC LS-Dyna. In particular, four different models were developed for the water inside the tank—namely: Finite Element (FE), Eulerian, Arbitrary Lagrangian Eulerian, and Smoothed Particles Hydrodynamics (SPH) model. Advantages and disadvantages of these models were evaluated and the results show that the FE model of the water is the most feasible for the analysis of the tank structure damages whereas the SPH model of the water, despite the large required CPU time, is the most feasible for the analysis of the sloshing of the water.     

圆柱贮箱液体"平面"晃动波的稳定性研究

应用Floquet-Lyapunov方法研究了作水平横向运动圆柱贮箱中液体"平面"晃动波的稳定性问题.首先利用Narimanov-Moiseev三阶渐近假设关系,推导出描述液体作非线性共振晃动的5维渐近模态系统.根据此模态系统,推导出液体"平面"晃动波的频率响应方程并应用Floquet-Lyapunov方法研究了其稳定性和稳定区间.数值仿真结果表明虽然其频率响应方程与Duffing方程的频率响应方程具有相同的结构,但两者的稳定性范围有明显的不同.此外,当经过某一临界充液比时,液体的"平面"晃动将由"软"弹簧特性转变为"硬"弹簧特性.理论分析结果与实验有很好的吻合.     

飞机机翼油箱晃振仿真与全尺寸试验验证

飞机飞行过程中,机翼油箱受晃振激励易发生结构破坏,造成经济损失和人员伤亡,因此,飞机适航审定有必要合理评估机翼油箱晃振响应。现行飞机适航审定基于全尺寸试验,经济代价高且费时;数值分析多考虑规则油箱开展趋势影响研究,无法有效反映非规则油箱的晃振响应。该文以某全复合材料机翼油箱为研究对象,基于VOF法和模态叠加法描述非规则油箱液体晃动和结构振动,考虑流固耦合和晃振解耦获取油箱壁面应变信息,采用最大应变准则进行机翼油箱复合材料壁面结构失效分析,开展机翼油箱全尺寸晃振试验验证数值仿真的有效性。该文给出油箱壁面应变幅值和分布随油箱载液量、晃动幅值与频率、振动幅值与频率变化的时域响应,指出晃动破坏多发生于油箱下蒙皮近翼梢侧,振动破坏多出现在油箱下蒙皮近翼根处,晃振响应由振动因素主导。该文验证了数值仿真代替全尺寸试验的可行性,并基于数值仿真和物理实验研究油箱壁面应变水平和载液量、晃动和振动激励的非线性关系,为飞机适航审定提供有效指导性意见。     

匀加速激励下的液体晃动力解析计算

针对矩形容器在匀加速运动下的液体晃动问题,采用基于非线性振动的解析方法求出容器所受液体晃动力的解析近似解,并分析其非线性效应以及加速度大小和充液率的影响作用。根据流体速度势的解析解计算边壁处的流体压力,而对于部分边壁区域的流体压力则采用线性分布的近似估计。对流体压力沿边壁做积分即可获得边壁处液体晃动力的解析近似解。计算结果表明,非线性因素并不会对容器所受晃动力产生较大影响,晃动力非线性项与加速度立方成正比;充液率的变化会使得线性晃动固有频率的数值发生改变,进而对晃动力线性项造成影响,其影响程度与固有频率曲线的变化趋势较为一致。     

内置有水平挡板的矩形储液器非线性晃动分析

该文以内置有水平挡板的矩形储液器为研究对象,对储液器的非线性晃动问题展开研究。利用势流理论和虚功原理,推导了由水平挡板引起的储液器非线性阻尼比(非线性体现于波高有关)的计算公式,同时考虑水平挡板对储液器晃动频率的影响而对非线性阻尼比计算公式进行了修正。结合液体晃动的非线性分析理论,研究了水平挡板处于不同位置、挡板长度不同时储液器的液面波高与晃动力变化情况。利用Fluent软件进行了数值模拟,并与理论模型分析的结果进行对比。结果表明：当水平挡板靠近储液器底部或长度较小时,储液器内液体的非线性晃动现象较明显,利用非线性三阶模态方程推导得到的波高、晃动力与数值模拟结果较接近,而仅考虑一阶线性响应会明显低估储液器液面波高,但其求解的晃动力却与考虑非线性值的状况基本一致;随着挡板到自由液面距离的变小或挡板长度的增大,储液器液面波高、晃动力幅值减小,液体晃动呈线性变化,说明水平挡板靠近自由液面或增大其长度时能够提高储液器的阻尼比,进而也更能抑制液体的非线性晃动。同时水平挡板逐渐靠近自由液面或长度逐渐增大时,储液器晃动频率逐渐减小,减小的幅度分别可达到5.7%～28%。     

截面任意形状的柱形和环形容器内液体晃动特性的精确解法

本文研究截面任意形状的柱形和环形容器内液体的晃动特性，利用Ｆｏｕｒｉｅｒ级数匹配法将液体速度势沿容器壁面展开得频率方程，由行列式搜根法数值计算各阶固有振动频率，结果是精确的，方法具有通用性。     

Computational slosh dynamics: theory and industrial application

 The effect of liquid sloshing upon the performance, control, and acoustics of vehicles is becoming more pronounced with the increasing size of fuel tanks. Especially the fundamental natural frequency and the viscous damping rate are important quantities from an engineering point of view. Theory and industrial application for calculating numerically sloshing effects of viscous liquids within fuel tanks are presented for various container geometries. The numerical treatment uses the volume-of-fluid method for calculating the free surface flows. The efficiency and the error level of the chosen numerical approach are evaluated by academic benchmark tests. The industrial application presented covers a typical contemporary automotive fuel tank and its sloshing problems. Received: 27 May 2002 / Accepted: 6 January 2003 This work has been performed as a part of the automotive slosh research at KAUTEX TEXTRON GmbH & Co. KG, Bonn. In addition, the author expresses his thanks for submitting helpful papers by W. Eidel and H. Bauer, Neubiberg.     

液舱晃荡的CIP法数值模拟

数值模拟是求解液舱晃荡问题的重要方法。基于CIP方法,该文建立了有限差分法求解二维不可压缩流体的Navier-Stokes方程的数值模型,使用对时间积分的分步算法求解流场,利用THINC格式捕捉自由液面,将液舱晃荡问题视为包括气体、液体和固体的多相流问题。分别模拟了无隔板和带纵隔板的液舱晃荡。该模型可以模拟晃荡过程中自由面破碎、翻卷和对舱壁的冲击压力以及隔板附近涡的生成与脱落,模型在不同网格的计算结果一致,并将计算结果与试验结果进行了对比。结果表明：该模型可以较好地模拟液舱晃荡问题并且纵隔板对液舱晃荡有明显的抑制作用。     

Analytical modeling of liquid sloshing in a two-dimensional rectangular tank with a slat screen

Potential-flow theory is employed with linear free-surface conditions, multimodal method, and a screen-averaged pressure-drop condition to derive an analytical modal model describing the two-dimensional resonant liquid motions in a rectangular tank with a vertical slat-type screen in the tank middle. The tank is horizontally excited in a frequency range covering the two lowest natural sloshing frequencies. The model consists of a system of linear ordinary differential [modal] equations responsible for liquid sloshing in compartments, as well as a nonlinear ordinary differential equation describing the liquid flow between the compartments. New experimental model tests on steady-state wave elevations near the tank wall are reported for the solidity ratios 0.328 ?? Sn ?? 0.963 where Sn is the ratio between the solid area and the full area of the screen. The experiments generally support the applicability of the model. The discrepancy can be explained by the free-surface nonlinearity. The screen acts as a damping mechanism for low and intermediate solidity ratios, but it causes an increase in the lowest resonant sloshing frequency at higher solidity ratios as if the screen had been replaced by an unperforated wall.     

Compression Frequency Choice for Compression Mass Gauge Method and Effect on Measurement Accuracy

It is a difficult job to gauge the liquid fuel mass in a tank on spacecrafts under microgravity condition. Without the presence of strong buoyancy, the configuration of the liquid and gas in the tank is uncertain and more than one bubble may exist in the liquid part. All these will affect the measure accuracy of liquid mass gauge, especially for a method called Compression Mass Gauge (CMG). Four resonance resources affect the choice of compression frequency for CMG method. There are the structure resonance, liquid sloshing, transducer resonance and bubble resonance. Ground experimental apparatus are designed and built to validate the gauging method and the influence of different compression frequencies at different fill levels on the measurement accuracy. Harmonic phenomenon should be considered during filter design when processing test data. Results demonstrate the ground experiment system performances well with high accuracy and the measurement accuracy increases as the compression frequency climbs in low fill levels. But low compression frequencies should be the better choice for high fill levels. Liquid sloshing induces the measurement accuracy to degrade when the surface is excited to wave by external disturbance at the liquid natural frequency. The measurement accuracy is still acceptable at small amplitude vibration.     

On the hysteresis phenomenon in the directly excited nonlinear resonant sloshing waves in a tank

Summary Steady nonlinear resonant standing waves obtained in a rectangular tank by a direct excitation are studied in detail both experimentally and numerically. The experimental study demonstrates the existence of a well defined hysteresis between two quite different wave distributions in the tank. The dissipation coefficient at the wavemaker is estimated from the present experimental results. Numerical simulations based on the solution of the nonlinear Schrödinger equation, with the dissipation coefficient at the wavemaker obtained experimentally, show that this hysteresis may be reproduced in calculations when a nonlinear boundary condition at the wavemaker is adopted. Such a boundary condition is indeed supported by experimental evidence.     

Transient analysis of the DSIFs and dynamic T-stress for particulate composite materials—Numerical vs. experimental results

The fracture behavior of particulate composite materials when subjected to dynamic loading has been a great concern for many industrial applications as these materials are particularly susceptible to impact loading conditions. As a result, many numerical and experimental techniques have been developed to deal with this class of problems. In this work, the fracture behavior of particulate composites under impact loading conditions is numerically studied via the two most important fracture parameters: dynamic stress intensity factors (DSIFs) and dynamic T-stress (DTS), and the results are compared with the experimental data obtained in Refs. [1,2]. Here, micromechanics models (self-consistent, Mori–Tanaka, …) or experimental techniques need to be employed first to determine the effective material properties of particulate composites. Then, the symmetric-Galerkin boundary element method for elastodynamics in the Fourier-space frequency domain is used in conjunction with displacement correlation technique to evaluate the DSIFs and stress correlation technique to determine the DTS. To obtain transient responses of the fracture parameters, fast Fourier transform (FFT) and inverse FFT are subsequently used to convert the DSIFs and DTS from the frequency domain to the time domain. Test examples involving free–free beams made of particulate composites are considered in this study. The numerical results are found to agree very well with the experimental ones.     

单边碰撞悬臂梁系统的实验研究和数值模拟

针对基础激励下单边碰撞悬臂梁系统进行详细的实验研究。在实验中,测量悬臂梁自由端的响应信号以及碰撞力信号。从实验结果中可以看到在不同的激励频率下,系统响应会表现出周期运动和混沌运动。在混沌运动的功率谱中发现悬臂梁的高阶模态频率,而在周期运动时这一特征并不明显。利用集中质量法和碰撞条件建立该系统的动力学方程,并运用 Runge-Kutta法直接积分得到系统的动力学响应。从时域和频域两方面分析比较仿真结果与实验结果,两者有较好的吻合度。     

Noise due to sloshing within automotive fuel tanks

The effect of liquid sloshing upon the acoustics of automotive vehicles is becoming more pronounced with the increasing size of fuel tanks and the recent progress in minimising tyre, engine and aero-acoustical noise generation. This paper deals with experiments and numerical simulations of sloshing in automotive fuel tanks. A correlation between recorded slosh noise and simulated pressure fluctuations within the sloshing liquid is derived. The presented numerical simulations are based on the volume-of-fluid method and are able to track the free-surface-flow within complex fuel tank shapes subjected to arbitrary outer acceleration profiles. Some typical applications of the numerical approach are presented, too.     

Experimental and numerical analyses of sloshing flows

Recently the demand for sloshing analyses is rising because of the construction of large LNG carriers and LNG platforms. This study considers the experimental and numerical observations of strongly nonlinear sloshing flows in ship cargo and their coupling effects with ship motion. Violent sloshing flows in experiments are observed, and two different numerical methods, the finite-difference method and smoothed-particle-hydrodynamics (SPH) method, are applied for the simulation of violent sloshing flows. Several physical issues are introduced in the analysis of sloshing flows, and the corresponding numerical models are described. This study demonstrates that physics-based numerical schemes are essential in the prediction of violent sloshing flows and sloshing-induced impact pressure. To study the sloshing effects on ship-motion, a ship-motion program based on an impulsive response function (IRF) is coupled with the developed numerical models for sloshing analysis. The results show that the nonlinearity of sloshing-induced forces and moments plays a critical role in the coupling effects.     

液固耦合内流问题及防晃研究进展

对液固耦合内流问题以及液体晃动特性的研究在宇航工程中有着十分重要的意义，大型液体运载火箭以及战略弹道导弹中的推进剂与储箱的藕合效应和推进刑的晃动特性对它们的飞行动力稳定性有着很大的影响。为了使导弹和航天运载器具有良好的飞行稳定性，就必须对其内部液体推进剂的晃动加以抑制，避免使液体的晃动与整体结构的固有振动发生耦合，防止结构的固有振动频率和液体的晃动频率落入控制系统的频带之中。本文概述了近年来在液固耦合作用以及在推进剂防晃研究方面所取得的进展。     

地震激励下储罐内液体的减晃试验研究及有限元分析

为了避免因液体晃动过大而引起的储罐"象足"型失稳破坏,采用减晃板作为抑晃装置并对其进行了减晃优化设计。分别采用缩尺模型试验(缩尺比1∶30)和有限元分析等手段对有、无安装减晃板的储罐内的液体晃动波高、罐底剪力及罐壁压应力等关键指标进行了实测和仿真模拟。研究结果表明:关键指标的模拟值与实测值较为接近,进而验证了储罐减晃有限元分析的可靠性;当减晃板在距液面0.125倍~0.225倍的储罐高度且其宽度在0.15倍的储罐半径附近时,减晃板对储液晃动波高、罐底剪力及罐壁压应力都具有较好的抑制效果;减晃优化设计后,"象足"失稳区(接近罐底处)的罐壁压应力峰值得到了较为显著的抑制。     

液体非线性晃动的同步Hopf分叉现象

针对受俯仰激励作用的圆柱形贮箱中液体非线性晃动,用变分原理建立了液体晃动的压力体积分形式的Lagrange函数;并将速度势函数在自由液面处作波高函数的级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;最后用四阶Runge-Kutta法求解非线性方程组。计算发现,在一定的激励频率内面外主模态和次生模态发生同步Hopf分叉,并给出了发生分叉的频率区域。     

Plastic deformation of impact loaded frames

The deflections of an elastic-plastic portal frame subject to impact loading is investigated, both numerically and experimentally. The numerical transient analysis accounts for the influence of large deflections and rotations in addition to elastic-plastic material behaviour. The experimental method is used to measure the time-dependent deflections of the frame when impacted by a steel hammer. The numerical results show good agreement with the experimental observations.     

Numerical investigation on steel fibre reinforced cementitious composite panels subjected to high velocity impact loading

Steel fibre reinforced cementitious composite (SFRCC) panels are numerically investigated for their performances under high velocity impact of short projectiles. Numerical responses are obtained using advanced constitutive material model of Riedel–Hiermaier–Thoma (RHT) for cementitious materials and adopting appropriate modelling techniques. Effects of steel fibre volume and the thickness of panels on the impact performance are mainly highlighted in this paper. Various characteristics phenomenon during impact on cementitious composite panels namely, spalling, cracking, scabbing and perforation, are captured which is a difficult task. Scabbing is likely to occur when tensile stresses at the back face of the panel exceed dynamic tensile strength of the material. Various critical aspects in numerical modelling like boundary conditions, material input parameters, and handling severe distortion of the Lagrangian based finite elements are appropriately explained. Design chart is also developed to determine optimum fibre volume and thickness for an impact energy level up to 2.2 kJ. The numerically predicted impact responses are found to corroborate well with experimental results.