Effect of sloshing on the mechanics of dewar systems in low-gravity

The mechanics of a spacecraft or space module, that contains a dewar system, is affected by sloshing of the cryogen. When a spacecraft is in orbit the acceleration level is very low and sloshing differs in several ways from that on Earth. Surface tension replaces gravity as the restraining force. The liquid–gas interface is curved and the depth is variable. Cryogens have low surface tension and this causes the resonant frequencies of sloshing to be very low. Programs were developed to calculate sloshing in low-g in dewars with annular and circular cross sections and with segmented and ring baffles. The programs correct for surface curvature and variable depth. The driving force for sloshing is the motion of the wall of the dewar. Dewar motion is an unknown because the sloshing force contributes to the motion of the support structure. Programs were also written for the dynamics of the system treating the motion of the dewar as an unknown. The combined program for sloshing and dynamics is called LOWGSLOSH. The calculations are carried out in the frequency domain so that both coherent and random driving forces can be used as input. The output is the motion of the spacecraft if the dewar is firmly attached to the vehicle. For modules suspended by a vibration-isolation interface, the output is the acceleration spectrum of the module. The calculations show the conditions when sloshing has an appreciable effect on the spacecraft or module. The timeline of spacecraft maneuvers is very important in determining the sloshing amplitude. In many cases, it is possible to reduce sloshing drastically by timing a maneuver properly. The results are illustrated using calculations on two NASA projects: the Space Infrared Telescope Facility spacecraft (SIRTF) and the Low Temperature Microgravity Physics Facility (LTMPF), a module for the International Space Station.     

The motion of bubbles in a sinusoidally oscillating liquid in microgravity

The sinusoidal motion of single, spherical bubbles in microgravity was studied experimentally aboard the U.S. Space Shuttle. Tests were performed to determine the effect of frequency, acceleration amplitude, bubble size, and fluid viscosity on bubble motion. Five test cells each containing a single bubble were subjected to rectilinear, sinusoidal oscillations. Three nominal bubble sizes and three liquids were used to cover a range of Stokes numbers from 1.3 to 21 and Reynolds numbers from 0.6 to 75. Bubble motion was recorded by video. The ratio of bubble motion amplitude to container motion amplitude was found to be essentially independent of the actual container motion amplitude. Therefore, this ratio could be plotted against frequency to obtain a frequency response for each case. This ratio was found to rise sharply from zero at zero frequency and then approach an asymptote at high frequencies. The strong effect of the walls in these experiments caused the amplitude of bubble motion to be reduced somewhat from that expected for an infinite fluid.     

容器内液体晃动的变分有限元方法

提出了用变分有限元方法计算容器内液体晃动谐振频率的方法和步骤。这种方法可适用于各种形状复杂的容器内液体晃动问题，按照此方法对二维矩形容器问题进行了实际计算，对计算结果和解析方法获得的解进行了比较。     

微幅晃动下考虑地基效应的矩形贮液结构动力响应研究

一般情况下矩形贮液结构通过底板直接坐落在地基上,有必要在考虑地基效应的基础上研究其动力特;定义微幅晃动波高限值,并建立矩形贮液结构的简化模型。采用人工边界模拟地基效应,建立了有限元计算模型,对比两类模型对应的晃动波高以验证简化模型的合理性,基于势流理论在微幅晃动范围内研究在不同边界条件、不同地震波和不同地震加速度幅值下矩形贮液结构的动力响应。结果表明,两类模型得到的晃动波高趋势一致,且最大晃动波高相差较小。在微幅晃动范围,液体最大晃动波高和地震加速度幅值成线性关系,考虑土-结构相互作用后,壁板水平位移、壁板有效应力和液体晃动压力有较大程度的的减小,而地基效应对液体晃动波高影响很小。     

Reduced order modeling of liquid sloshing in 3D tanks using boundary element method

This paper presents the application of reduced order modeling technique for investigation of liquid sloshing in three-dimensional tanks. The governing equations of sloshing are written using a boundary element formulation for incompressible potential flow. Then, the governing equations are reduced to a more efficient form that is represented only in terms of the velocity potential on the liquid free surface. This particular form is employed for eigen-analysis of fluid motion and the sloshing frequencies and mode shapes are determined. Then, the sloshing frequencies and the corresponding right- and left-eigenvectors are used along the modal analysis technique to find a reduced order model (ROM) for fluid motion. Using a rectangular and a cylindrical tank, the results of the ROM are verified in comparison with the analytical results. Then some example tanks are used to examine the ROM in comparison with the full boundary element model for determination of the free surface motion under the angular and lateral motion of the tank. The obtained results demonstrate the capability and accuracy of the reduced order modeling technique for analysis of sloshing using a few modes.     

A successive boundary element model for investigation of sloshing frequencies in axisymmetric multi baffled containers

This study presents a developed successive Boundary Element Method to determine the symmetric and antisymmetric sloshing natural frequencies and mode shapes for multi baffled axisymmetric containers with arbitrary geometries. The developed fluid model is based on the Laplace equation and Green's theorem. The governing equations of fluid dynamic and free surface boundary condition are also applied to proposed model. A zoning method is presented to model arbitrary arrangement of baffles in multi baffled axisymmetric tanks. The influence of each zone on neighboring zones is applied by introducing interface influence matrix which correlates the velocity potential of interfaces to their flux. By discretizing the flow boundaries, the integral equation governed on the boundary is formulated into a general matrix eigenvalue problem. The proposed method has a considerable effect on decreasing computational cost and a good accuracy in determining the sloshing natural frequencies. The obtained results for different types of container based on the application of the presented study are validated in comparison with the literature and very good agreement is achieved. Finally, the effect of baffle parameters on the sloshing natural frequencies was investigated and some conclusions are outlined.     

Linear sloshing frequencies in the annular region of a circular cylindrical container in the presence of a rigid baffle

Sloshing in any type of container may invite instability to it. If some part of the free liquid surface in the annular region of a specially designed circular cylindrical container is covered with an annular baffle, the natural frequencies and the response of the liquid in the container undergo a drastic change. A partly covered free surface shifts the natural frequency above and away from the control frequency of the vehicle, in which the liquid-filled container is placed, which results in the reduction of sloshing mass participating in the dynamic motion of the system. The fundamental natural frequency of an inviscid and incompressible liquid is determined for increasing width of the baffle that is attached to the outer tank wall on the free surface. It is observed that by increasing the width of the baffle, natural frequencies can be significantly increased. Investigations are also carried out for different values of Bond number, which depicts different states of surface tension, and for varying values of the part of the radius in the fluid region. It is also observed that by increasing the fluid height inside the container, the natural frequencies can be increased, which results in reduction of sloshing.     

一种采用激振器激励的扬声器振动部件共振频率测量方法及系统

提出了一种采用激振器激励方式的扬声器振动部件共振频率测量方法及系统。采用激振器作为激励被测部件振动的激励源,并通过加速度传感器实时检测夹具的振动加速度（包括幅度和相位）,以确保被夹具夹持住的被测部件在测量频率范围内上下平稳振动;通过激光位移传感器测量被测部件在不同频率点振动时的振动位移,可得到被测部件振动的频率响应（被测部件振动加速度和夹具振动加速度的比值的频率响应）;根据该频率响应进行计算最后可得到被测部件的共振频率。实验结果表明,实测频率响应的曲线与理论分析相一致,测量结果的可重复性和准确性良好,可测量的振动部件的种类和范围更广。     

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.     

变曲率滚动隔震动力学分析及在球形储罐中的应用

根据力平衡原则推导了椭圆轨道滚动隔震装置恢复力力学模型,并分析了其不同椭圆函数参数及滚动摩擦系数时的力学性能。得出滚球半径及椭圆轨道短轴尺寸一定时,随着长轴的增加,刚度系数逐渐减小,且刚度函数及周期函数的变化率逐渐变小,地震作用时可调节范围也逐渐变小。建议椭圆长轴值的选取综合考虑上部结构自振频率及有可能产生的最大水平位移优化设计。采用速度势刚性理论推导球形储罐考虑储液晃动的变曲率滚动隔震简化力学模型,并进行了地震动响应研究。结果表明:考虑滚动基础隔震后能够有效地减小球形储罐地震动响应,尤其对基底剪力及倾覆弯矩有较好的减震控制作用。同时对储液的晃动响应也能起到一定的抑制作用。球形轨道滚动隔震与椭圆形轨道滚动隔震各工况均值减震率相差较小,且变曲率滚动隔震能在一定程度上限制隔震层位移。     

Discussion related to Watson and Evans: “Resonant frequencies of a fluid in containers with internal bodies”

Some recent authors have studied sloshing frequencies of fluid in a container, but have ignored the well-established literature on the asymptotic structure of the modes of linear oscillations. The present discussion draws attention to the more efficient solution methods thus suggested and relates the results to known asymptotic forms.     

The pulse width effect on the shock response of the hard disk drive

A finite element model (FEM) of the ST drive from Seagate is developed in ANSYS to investigate the shock response of the hard disk drive (HDD). The FEM includes the pivot bearing, the head stack assembly (HSA) and the disk. The free state of the HSA is determined by an iterative procedure to produce the prescribed preloading force at the head–disk interface. The FE model is then verified by conducting a modal analysis over the HSA. The obtained mode shapes and resonant frequencies are compared with the modal testing results. An acceleration pulse is applied to the shaft and the whole disk surface at the same time to study the shock response of the HDD. The head slap behavior is examined at the slider–disk interface. The effect of the pulse width on the head slap behavior is studied. The duration of the acceleration pulse varies from 0.3 to 1 ms. It is found that the lift-up height of the slider reaches a peak value at different pulse widths when the amplitude of acceleration pulse changes. This is due to the nonlinear behavior introduced by the contact surfaces.     

贮箱内液体小幅晃动的频率和阻尼计算

根据小幅晃动条件下利用速度势函数推导的计算液体晃动频率和内部Rayleigh阻尼的特征值方程,利用简化处理转化为一般的广义特征值问题,并针对这种非对称大型稀疏矩阵采用了Arnoldi迭代方法,求解得到晃动频率和内部阻尼。将利用Stokes边界层理论计算得到边界上的阻尼与内阻尼之和作为晃动的等效阻尼,通过两个算例比较计算结果接近实验结果。这种方法可以计算任意形状贮箱内液体的小幅晃动频率和晃动阻尼。     

Iron Burning in Pressurised Oxygen Under Microgravity Conditions

An investigation of cylindrical iron rods burning in pressurised oxygen under microgravity conditions is presented. It has been shown that, under similar experimental conditions, the melting rate of a burning, cylindrical iron rod is higher in microgravity than in normal gravity by a factor of 1.8 ± 0.3. This paper presents microanalysis of quenched samples obtained in a microgravity environment in a 2.0 s duration drop tower facility in Brisbane, Australia. These images indicate that the solid/liquid interface is highly convex in reduced gravity, compared to the planar geometry typically observed in normal gravity, which increases the contact area between liquid and solid phases by a factor of 1.7 ± 0.1. Thus, there is good agreement between the proportional increase in solid/liquid interface surface area and melting rate in microgravity. This indicates that the cause of the increased melting rates for cylindrical iron rods burning in microgravity is altered interfacial geometry at the solid/liquid interface.     

Spectral analysis of vibrational harmonic motion by use of a continuous-wave CO2 Doppler lidar

Vibrational motion of a harmonic oscillator was investigated with a focused continuous-wave (cw) CO2 Doppler lidar at 9.1-microm wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation. For vigorous vibration of the oscillator, the observed spectra may be indicating nonlinear motion.     

Verification of the Microgravity Active Vibration Isolation System based on Parabolic Flight

The Microgravity active vibration isolation system (MAIS) is a device to reduce on-orbit vibration and to provide a lower gravity level for certain scientific experiments. MAIS system is made up of a stator and a floater, the stator is fixed on the spacecraft, and the floater is suspended by electromagnetic force so as to reduce the vibration from the stator. The system has 3 position sensors, 3 accelerometers, 8 Lorentz actuators, signal processing circuits and a central controller embedded in the operating software and control algorithms. For the experiments on parabolic flights, a laptop is added to MAIS for monitoring and operation, and a power module is for electric power converting. The principle of MAIS is as follows: the system samples the vibration acceleration of the floater from accelerometers, measures the displacement between stator and floater from position sensitive detectors, and computes Lorentz force current for each actuator so as to eliminate the vibration of the scientific payload, and meanwhile to avoid crashing between the stator and the floater. This is a motion control technic in 6 degrees of freedom (6-DOF) and its function could only be verified in a microgravity environment. Thanks for DLR and Novespace, we get a chance to take the DLR 27th parabolic flight campaign to make experiments to verify the 6-DOF control technic. The experiment results validate that the 6-DOF motion control technique is effective, and vibration isolation performance perfectly matches what we expected based on theoretical analysis and simulation. The MAIS has been planned on Chinese manned spacecraft for many microgravity scientific experiments, and the verification on parabolic flights is very important for its following mission. Additionally, we also test some additional function by microgravity electromagnetic suspension, such as automatic catching and locking and working in fault mode. The parabolic flight produces much useful data for these experiments.     

The effects of gravity on the features of the interfacial waves in annular two-phase flow

A physical model of interfacial waves in annular two-phase flow was studied in both microgravity and normal gravity. The wave structure was obtained for local film thickness and velocity measurements using a conductance probe technique. It was found that the wave height, and not its width, is strongly affected by changing the gravity level. In fact, the wave height in normal gravity is more than twice that in microgravity. Using an analogous approach to a turbulent, single-phase flow in a rough tube, a preliminary mathematical model was proposed to calculate the wave amplitude. The model fits well with the experimental data and shows that the wave height in normal gravity is approximately 1.7 times the combined thickness of the viscous sublayer and transition zones in the turbulent gas stream. The wave height in microgravity was estimated to be approximately 80% of the total thickness.     

Development of a valved linear compressor for a satellite borne J-T cryocooler

The provision of temperatures below 12 K is essential for sub-mm and FIR observations from satellite instruments. Historically this has been achieved with stored cryogens, however mechanical coolers could potentially provide higher reliability and flexibility. These cryocoolers typically incorporate a regenerative cold-finger, such as a pulse-tube, however this can be replaced by a recuperative Joule-Thompson stage to obtain the lowest temperatures required. The major change to the compressor is the requirement for steady flow. This paper describes the development of such a compressor using reed valves, based on space-qualified hardware. Long life potential was demonstrated by measuring the motion of the valves during operation. A model was also developed and validated to optimize performance.     

Bubble rupture in a vibrated liquid under microgravity

The response of an air bubble surrounded by a liquid in a sealed cell submitted to vibrations was investigated experimentally under microgravity conditions and compared to experiments under normal gravity conditions. As in normal gravity [1], it was observed that the bubble split into smaller parts when the acceleration of the vibrations reached a threshold. This threshold in microgravity is substantially smaller than that in normal gravity. Experimental results are presented in terms of an acceleration based Bond number which has been found to characterize the bubble behaviour in the laboratory experiments [1].     

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.