An investigation into the spreading of a thin liquid drop under gravity on a slowly rotating disk

The axisymmetric spreading of a thin liquid drop under the influence of gravity and rotation is investigated. The effects of the Coriolis force and surface tension are ignored. The Lie group method is used to analyse the non-linear diffusion-convection equation modelling the spreading of the liquid drop under gravity and rotation. A stationary group invariant solution is obtained. The case when rotation is small is considered next. A straightforward perturbation approach is used to determine the effects of the small rotation on the solution given for spreading under gravity only. Over a short period of time no real difference is observed between the approximate solution and the solution for spreading under gravity only. After a long period of time, the approximate solution tends toward a dewetting solution. We find that the approximate solution is valid only in the interval t∈[0,t∗), where t∗ is the time when dewetting takes place. An approximation to t∗ is obtained.     

由三平行轴惯量求重心的一种方法

为了求得复杂刚体重心的位置, 根据转动惯量平行轴定理, 由已知轴转动惯量和一定的几何 关系推导出用于求重心的关系式, 从理论上给出两个可能重心坐标值, 再实际判断取舍.只要 用实验仪器先测量刚体对3个平行转轴的转动惯量, 就可由该关系式计算得到刚体重心的位 置. 这一方法有时要比直接测量重心更为简单.     

Effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids by using the Lord-Shulman and dual-phase-lag models

The effects of rotation and gravity on an electro-magneto-thermoelastic medium with diffusion and voids in a generalized thermoplastic half-space are studied by using the Lord-Shulman(L-S) model and the dual-phase-lag(DPL) model. The analytical solutions for the displacements, stresses, temperature, diffusion concentration, and volume fraction field with different values of the magnetic field, the rotation, the gravity, and the initial stress are obtained and portrayed graphically. The results indicate that the effects of gravity, rotation, voids, diffusion, initial stress, and electromagnetic field are very pronounced on the physical properties of the material.     

Note on buble motion in a rotating liquid under residual gravity

The motion of a small gas bubble, presumed to retain its geometrical shape and contained in a rotating liquid, has been investigated. The fluid system liquid-gas is subject to the influence of a reduced gravitational field. It is demonstrated that under certain conditions (spin axis and direction of gravity are perpendicular to each other) the bubble travels on a circular path about the axis of rotation, as seen from an observer moving with the bulk of the liquid.     

Stability of Solutal Convection in a Rotating Mushy Layer Solidifying from a Vertical Surface

We consider the effects of rotation in a mushy layer being cast from a vertical surface where the effects of Coriolis acceleration, gravity and centrifugal effects are included. It is demonstrated that the Coriolis acceleration and gravity play a passive role in convection and are excluded from the stability criteria. The stability criteria is presented as the critical centrifugal Rayleigh numbers referenced for locations far away (start of solidification) and close to (nearing end of solidification) the axis or rotation.     

Mobility performance of a rigid wheel in low gravity environments

To investigate influences of gravity on mobility of wheeled rovers for future lunar/planetary exploration missions, model experiments of a soil-wheel system were performed on an aircraft during variable gravity maneuvers. The experimental set-up consists of a single rigid wheel and a soil bed with two kinds of dry sands: lunar soil simulant and Toyoura sand. The experimental results revealed that a lower gravity environment yields higher wheel slippage in variable gravity conditions. In addition to the partial gravity experiments, the same experiments with variable wheel load levels were also performed on ground (1 g conditions). The on-ground experiments produced opposite results to those obtained in the partial gravity experiments, where a lower wheel load yields lower slippage in a constant gravity environment. In low gravity environments, fluidity (flowability) of soil increases due to the confining stress reduction in the soil, while the effect of the wheel load on sinkage decreases. As a result, both of these effects are canceled out, and gravity seemingly has no effect on the wheel sinkage. In the meantime, in addition to the effect of wheel load reduction, the increase of the soil flowability lessens the shear resistance to the wheel rotation, as a result of which the wheel is unable to hold sufficient traction in low gravity environments. This suggests that the mobility of the wheel is governed concurrently by two mechanisms: the bearing characteristics to the wheel load, and the shearing characteristics to the wheel rotation. It appears that, in low gravity, the wheel mobility deteriorates due to the relative decrease in the driving force while the wheel sinkage remains constant. Thus, it can be concluded that the lunar and/or Mars’ gravity environments will be unfavorable in terms of the mobility performance of wheels as compared to the earth’s gravity condition.     

基于超导的全张量重力梯度敏感头设计

基于超导的迈斯纳效应与超导量子干涉技术,结合柔性并联机构理论,设计一种基于超导的全张量重力梯度敏感头。敏感头采用6个完全相同的同时具有移动与转动自由度的敏感结构,对称的布置在正六面体外,对称面的两个敏感结构相对旋转90°成垂直状态。轴向间距使两个敏感结构直接测量重力梯度轴向分量,相互垂直使两个敏感结构既可以测量重力梯度交叉分量,也可以测量共模角加速度。利用超导线圈的电感变化响应质量块位移,进一步通过超导回路将其转变为磁场变化,并由超导量子干涉器进行检测。敏感结构采用8分支的柔性并联机构支承,构成空间对称的形式,可以实现对称的力学特性,保证各处的柔性铰链产生均匀变形,减少非对称的偏移,避免单一铰链的应力集中,具有沿轴移动刚度与绕轴转动刚度小、非设计的寄生误差方向刚度大的优势。在惯性系下的全张量重力梯度值可由坐标变换得到,可以预期得到1E的测量精度。     

On permanent nonlinear waves in a rotating fluid

The governing equation for long nonlinear gravity waves in a rotating fluid changes with the value of the Coriolis parameter f. (1) When f is large, i.e. in the strong rotation case, in an infinite ocean, there are only Sverdrup waves; in a semi-infinite ocean or in a channel, there are either solitary Kelvin waves, for which the governing equation is a KdV equation, or Poincaré waves, which can be obtained by superposition of two Sverdrup waves. (2) When f is small, i.e. in the weak rotation case, in an infinite ocean there are solitary or cnoidal waves governed by the Ostrovskiy equation, and we provide an explicit solution for both solitary and cnoidal Ostrovskiy progressive waves; and in a semi-infinite ocean or a channel, there are Sverdrup waves, which are governed either by Ostrovskiy equations or by the Grimshaw-Melville equation. (3) When f is very small, i.e. in the very weak rotation case, in an infinite ocean, or in a channel, there are solitary waves with a horizontal crest, but with a velocity component or a pressure gradient, which are governed by KdV equations as in the non-rotating case. Physically, that means that the most determining factor is the ratio of the Rossby radius of deformation over a characteristic length of the wave.     

激光陀螺捷联惯导系统参数稳定性与外场自标定

惯导系统参数稳定性是决定系统精度的重要因素。基于激光陀螺捷联惯导系统参数稳定性统计分析,建立了适合激光陀螺捷联惯导系统外场自标定的加速度计组件误差参数模型。以惯性组合转动后重新调平的水平姿态修正量以及静态下重力测量误差为观测量,不依赖外界方向姿态转角等基准信息,实现了加速度计组件主要误差参数在外场条件下的自标定,并给出了标定参数的修正方法。实验表明,常温下加速度计组件的标定参数发生明显变化,采用外场标定方法可对其进行修正,相应的水平姿态最大误差由65″减小到10″。该方法标定精度好,标定时间短,操作简便,且对基座不稳造成的瞬时姿态小扰动影响有抑制能力。     

Dynamics of disk-like particles in turbulent vertical channel flow

The dynamical behavior of inertial disk-like particles in turbulent vertical channel flow is investigated by an Eulerian–Lagrangian point-particle approach. Gravity effects on distribution, translation, rotation and orientation statistics of non-spherical particles modeled as oblate spheroids have been studied both in an upward and a downward flow and compared with results obtained in the absence of gravity. Altogether 12 different particle classes have been studied, with inertia and shape parameterized by means of Stokes number St and aspect ratio λ ≤ 1. The St = 5 disk-like particles distribute more evenly across the channel in upward than in downward flow. The gravity effect on the particle concentration diminishes with large inertia and the spheroid shape has only a modest influence. Although the gravity significantly affects the streamwise and wall-normal mean slip velocities with increasing inertia, the particle shape rarely has any impact on the translational motion, except for the mean wall-normal velocity. The fluctuations of the velocity of disk-like particles are mainly ascribed to inertia, whereas the gravity and shape only have marginal effects. The presence of gravity is moreover found to have a negligible effect on the particles’ orientation and rotation, in spite of the striking effect of λ on the orientation and rotation seen in the near-wall region. The tendency of the disks to align their symmetry axis orthogonal to the fluid vorticity in the channel center is stronger for particles with modest inertia. In the near-wall region, however, oblate spheroids preferentially align with the fluid vorticity for St >> 1. The observed behavior is believed to be caused by the influence of the gravity force on the turbophoresis; i.e. that inertial particles move towards low-turbulence regions.     

Coriolis Effect on Convection in a Rotating Porous Layer Subjected to Variable Gravity

We consider the effects of rotation in a porous layer heated from below and subjected to a variable gravity field. The study is presented for large Vadasz numbers where no oscillatory convection is possible. It is demonstrated that the Coriolis acceleration stabilizes the convection in a variable gravity field, whilst the effect of gravity parameter stabilses the convection when reduced and destabilizes the convection when increased.     

Flow structures,nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.     

Effect of rotation in generalized thermoelastic solid under the influence of gravity with an overlying infinite thermoelastic fluid

The present problem is concerned with the study of deformation of a rotating generalized thermoelastic solid with an overlying infinite thermoelastic fluid due to different forces acting along the interface under the influence of gravity.The components of displacement,force stress,and temperature distribution are first obtained in Laplace and Fourier domains by applying integral transforms,and then obtained in the physical domain by applying a numerical inversion method.Some particular cases are also discussed in the context of the problem.The results are also presented graphically to show the effect of rotation and gravity in the medium.     

On the motion of a heavy dynamically symmetric rigid body with vibrating suspension point

The motion of a dynamically symmetric rigid body in a homogeneous field of gravity is studied. One point lying on the symmetry axis of the body (the suspension point) performs high-frequency periodic or conditionally periodic vibrations of small amplitude. In the framework of approximate equations of motion obtained earlier, we find necessary and sufficient conditions for the stability of the body rotation about the vertical symmetry axis and study the existence and stability of regular precessions of the body in the coordinate system translationally moving together with the suspension point.     

Vibrational dynamics of a light spherical body in a rotating cylinder filled with a fluid

The behavior of a light spherical body in a rotating horizontal cylindrical cavity filled with a low-viscosity fluid is experimentally investigated both in the absence and in the presence of transverse vibrations. The system is in a centrifuged state. Mean rotation of the sphere relative to the cavity is found to exist. In the absence of the vibrations slow lagging rotation of the body is due to the gravity field. With increase in the cavity rotation velocity the intensity of differential rotation reduces. The vibrations lead to the excitation of differential rotation of the body, either anticipating or lagging, due to the resonance excitation of its inertial oscillations. The differential rotation of the body leads to the formation of the cylindrical Taylor-Proudman column. With increase in the column rotation velocity the instability of its boundary manifests itself as an azimuthal two-dimensional wave.     

板壳有限变形精确理论及有限元列式

以位移型退化壳理论为基础,提出了板壳模型的有限变形精确理论.该理论引入转动伪矢量概念,充分发挥刚性线段的运动学模型和有限转动矩阵的作用,精确表达非线性位移-应变关系,抛弃以往的小位移、小应变、小转动增量乃至小加载步长等各种简化假设,并严格遵循能量共轭关系建立有限元平衡方程,能够可靠和有效地用于板壳结构的大位移、大转动分析.算例表明,该文列式在弹性范围内具明显的平方收敛效率,并且计算结果与加载步长无关.由于不受小加载步长、小转动增量等的限制,实现了板壳几何非线性问题的大步长加载 .     

Effect of weak rotation on natural convection in a horizontal porous cylinder

Natural convection in a fluid saturated porous medium confined in a horizontal circular cylinder and rotating about its axis, with isothermal boundary conditions and uniform internal heat sink, is studied by both numerical and perturbation methods. No symmetry with respect to the vertical diameter is expected for the flow and temperature fields and the whole region must be involved in the computation. Only the weak rotation regime, for which the centrifugal force is negligible compared to gravity, is considered. Governing equations for the two-dimensional flow field are solved in both rotating and non-rotating coordinate systems. Results indicate that rotation significantly decreases the radial amplitude of fluid particle trajectories in the radial direction and thus reduces the overall heat transfer.     

高精度加速度计分辨率的动态估算方法

高精度定位定向系统和重力测量系统需要高分辨率的加速度计,传统测试方法难以确定高精度加速度计的分辨率。对此,提出了一种使用双轴转台动态估算加速度计分辨率的方法,即匀速旋转调制法。将加速度计安装在双轴转台台面上,待转台调平,台面绕倾斜轴转过一个小角度后锁死,回转轴以一定的角速度旋转调制以对重力加速度分量进行细分,将加速度计的输出采样后进行FFT低通滤波,通过加速度计峰值与谷值处输出变化最大值的分析可以确定加速度计的分辨率。最后,对某型加速度计分辨率进行了实验验证,测试结果表明,当倾斜角度为0.001°,旋转调制角速率为10(°)/s,采样率为32 Hz时,输入的加速度最大变化为9.36×10-8g,加速度计敏感到的加速度变化量为1.05×10-7g。     

Stability of the cylindrical precession of a satellite in an elliptic orbit

We study the linear problem on the stability of rotation of a dynamically symmetric satellite about the normal to the plane of the orbit of its center of mass. The orbit is assumed to be elliptic, and the orbit eccentricity is arbitrary. We assume that the Hamiltonian contains a small parameter characterizing the deviation of the satellite central ellipsoid of inertia from the sphere. This is a resonance problem, since if the small parameter is zero, then one of the frequencies of small oscillations of the symmetry axis in a neighborhood of the unperturbed rotation of the satellite about the center of mass is exactly equal to the frequency of the satellite revolution in the orbit. We indicate a countable set of values of the angular velocity of the unperturbed rotation for which the resonance is even double. The stability and instability domains are obtained in the first approximation with respect to the small parameter.     

Flexural gravity wave motion over poroelastic bed

Using Biot’s consolidation theory, effect of poroelastic bed on flexural gravity wave motion is analyzed in both the cases of single-layer and two-layer fluids. The model for the flexural gravity waves is developed using linear water wave theory and small amplitude structural response in finite water depth. The effects of permeability and shear modulus of poroelastic bed and time period on flexural gravity wave motion are studied by analyzing the dispersion relation, phase speed, plate deflection, interface elevation and pressure distribution along water depth. Various results for surface gravity waves are analyzed as special cases. The study reveals that bed permeability retards the hydrodynamic pressure distribution along the water depth significantly compared to shear modulus whilst, floating plate deflection decreases significantly with change in shear modulus compared to permeability of the poroelastic bed. The present study can be generalized to analyze various wave–structure interaction problems over poroelastic bed.