Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Numerical Partition of Energy Absorption of Foam-filled Top-Hat and Double-Hat Sections

The interaction effect, i.e., the contribution of each component to the total energy absorption of an axially crushed foam-filled hat section was investigated quantitatively via numerical simulation. The FE results were first verified by experimental work of aluminum foam-filled top-hat and double-hat sections, then the contribution of foam-fillers and that of hat sections to the overall energy absorption were quantitatively obtained, respectively. When foam-filled, increase in energy absorption was found both in hat section component and foam-filler component, whereas the latter contributes predominantly to the interaction effect.

Liquid-filled microstructured polymer fibers as monolithic liquid-core array fibers

Liquid-filled microstructured polymer optical fibers (MPOFs) as monolithic liquid-core array fiber are proposed and prepared by injecting high-refractive-index liquid into the holes array of the MPOFs. One example for potential applications is demonstrated as a new kind of coherent imaging fiber. It provides great potential for applications in chemical sensing, biosensors, and endoscopy, particularly in bifunctional detection. (C) 2009 Optical Society of America

失重条件下对称充液陀螺的不稳定行为研究

对于质心固定的，充满粘性均匀液体的旋转对称陀螺在失重条件下绕对称长轴旋转态的小扰动不稳定及其极限行为进行了研究，所给出的定理3比以往的不稳定定理[4]为强，且反映的信息量多很多。关于初始大扰动后的渐近行为，对文[8]已给出但未严格证明的两条定理给出了严格证明，它由定理1和定理2所描述。

Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

刚性充液容器内竖直激励表面波研究进展

受外激励的充液刚性容器中流体的波动问题有实际的工程应用背景.竖直方向的受周期性外激励的充液容器的自由表面波问题--Faraday波问题是流体力学三大不稳定性难题之一(另外两个不稳定性问题是RayleighBénard对流和Taylor-Couette流).本文综述了在理想流体中和弱粘性流体中Faraday波的研究成果;介绍了作者在底部垂直激励的圆柱形容器中流体表面波图谱的实验研究和理论分析的结果.最后提出有待进一步研究的问题.

Pool boiling heat transfer of ultra-light copper foam with open cells

High speed visualizations and thermal performance studies of pool boiling heat transfer on copper foam covers were performed at atmospheric pressure, with the heating surface area of 12.0 mm by 12.0 mm, using acetone as the working fluid. The foam covers have ppi (pores per inch) from 30 to 90, cover thickness from 2.0 to 5.0 mm, and porosity of 0.88 and 0.95. The surface superheats are from -20 to 190 K, and the heat fluxes reach 140 W/cm(2). The 30 and 60 ppi foam covers show the periodic single bubble generation and departure pattern at low surface superheats. With continuous increases in surface superheats, they show the periodic bubble coalescence and/or re-coalescence pattern. Cage bubbles were observed to be those with liquid filled inside and vented to the pool liquid. For the 90 ppi foam covers, the bubble coalescence takes place at low surface superheats. At moderate or large surface superheats, vapor fragments continuously escape to the pool liquid. Boiling curves of copper foams show three distinct regions. Region I and II are those of natural convection heat transfer, and nucleate boiling heat transfer for all the foam covers. Region III is that of either a resistance to vapor release for the 30 and 60 ppi foam covers, or a capillary-assist liquid flow towards foam cells for the 90 ppi foam covers. The value of ppi has an important effect on the thermal performance. Boiling curves are crossed between the high and low ppi foam covers. Low ppi foams have better thermal performance at low surface superheats, but high ppi foams have better one at moderate or large surface superheats and extend the operation range of surface superheats. The effects of other factors such as pool liquid temperature, foam cover thickness on the thermal performance are also discussed.

Effect of liquid bridge volume on the instability in small-Prandtl-number half zones

A perturbation method is used to examine the linear instability of thermocapillary convection in a liquid bridge of floating half-zone filled with a small Prandtl number fluid. The influence of liquid bridge volume on critical Marangoni number and flow features is analyzed. The neutral modes show that the instability is mainly caused by the bulk flow that is driven by the nonuniform thermocapillary forces acting on the free surface. The hydrodynamic instability is dominant in the case of small Prandtl number fluid and the first instability mode is a stationary bifurcation. The azimuthal wave number for the most dangerous mode depends on the liquid bridge volume, and is not always two as in the case of a cylindrical liquid bridge with aspect ratio near 0.6. Its value may be equal to unity when the liquid bridge is relatively slender.

Partition Energy Absorption of Axially Crushed Aluminum Foam-Filled Hat Sections

The "interaction effect" between aluminum foam and metal column that takes place when foam-filled hat sections (top-hats and double-hats) are axially crushed was investigated in this paper. Based on experimental examination, numerical simulation and analytical models, a systemic approach was developed to partition the energy absorption quantitatively into the foam filler component and the hat section component, and the relative contribution of each component to the overall interaction effect was therefore evaluated. Careful observation of the collapse profile found that the crushed foam filler could be further divided into two main energy-dissipation regions: densified region and extremely densified region. The volume reduction and volumetric strain of each region were empirically estimated. An analytical model pertinent to the collapse profile was thereafter proposed to find the more precise relationship between the volume reduction and volumetric strain of the foam filler. Combined the superfolding element model for hat sections with the current model according to the coupled method, each component energy absorption was subsequently derived, and the influence of some controlling factors was discussed. According to the finite element analysis and the theoretical modeling, when filled with foam, energy absorption was found to be increased both in the hat section and the foam filler, whereas the latter contributes predominantly to the interaction effect. The formation of the extremely densified region in the foam filler accounts for this effect.

Experimental Investigation Of Thermocapillary Convection In A Liquid Layer With Evaporating Interface

Thermocapillary convection coupling with the evaporation effect of evaporating liquids is studied experimentally. This study focused on an evaporation liquid layer in a rectangular cavity subjected to a horizontal temperature gradient when the top evaporating surface is open to air, while most previous works only studied pure thermocapillary convection without evaporation. Two liquids with different evaporating rates are used to study the coupling of evaporation and thermocapillary convection, and the interfacial temperature profiles for different temperature gradients are measured. The experimental results indicate evidently the influence of evaporation effect on the thermocapillary convection and interfacial temperature profiles. The steady multicellular flow and the oscillatory multicellular flow in the evaporation liquid layer are observed by using the particle-image-velocimetry method.

Experimental Investigation Of Influence Of Interfacial Tension On Convection Of Two-Layer Immiscible Liquid

Benard-Marangoni convections of two-layer fluids heated from the bottom are investigated experimentally with a particle imagine velocimetry. The flows are visualized from the side, and various velocity fields near the onset of convection, such as three-layer vortex convective patterns, are observed when the depth ratio varies in a wide range. A new classification of the convective patterns is proposed with more detail than in previous studies. The analysis of the results indicates that the interface tension greatly influences the motion intensities of the bottom and top layers. The dimensionless wave number increases with the Bond number when the motion in the top layer is not more intense than that in the bottom layer, which agrees with the theoretical prediction.

Coupling Of Evaporation And Thermocapillary Convection In A Liquid Layer With Mass And Heat Exchanging Interface

We propose and analyse a new model of thermocapillary convection with evaporation in a cavity subjected to horizontal temperature gradient, rather than the previously studied model without evaporation. The pure liquid layer with a top free surface in contact with its own vapour is considered in microgravity condition. The computing programme developed for simulating this model integrates the two-dimensional, time-dependent Navier-Stokes equations and energy equation by a second-order accurate projection method. We focus on the coupling of evaporation and thermocapillary convection by investigating the influence of evaporation Biot number and Marangoni number on the interfacial mass and heat transfer. Three different regimes of the coupling mechanisms are found and explained from our numerical results.

Liquid encapsulated-melt zone processing of GaAs

A liquid encapsulated melt Bone process has been developed for single crystal growth of GaAs. Single crystals of 40 mm long have been grown with this technique. To avoid unwanted nucleation events and maintain a constant crystal diameter, from top to bottom growth using a short zone with a convex zone surface was found to give the best results. An arsenic overpressure was used to in conjunction with a B2O3 encapsulant in order to suppress arsenic dissociation from the melt and maintain the stoichiometry of the crystal.

Study on conical columns with different conical angles for semi-preparative liquid chromatography

The dynamic flow profiles and separation performances in conically shaped preparative liquid chromatographic columns (inlet i.d. larger than outlet i.d.) with three different angles (7, 10 and 15degrees) were studied and compared with cylindrical column of the same length and internal volume. The shapes of dynamic flow profiles were studied by on-column visualization method. The transparent chromatographic columns made of polymethyl methacrylate (PMMA), packed with C-18 bonded silica, were immerged into a cubic pool filled with glycerol to eliminate the cylindrical and conical lens effect. The flow profiles of colored iodine solution in the columns were observed clearly using cyclohexane as mobile phase since the refractive indices of C-18, column wall and the mobile phase are very close. In the conical column of 15degrees (20-7 mm i.d.) the mobile phase in the central region migrated slower than in wall region as it moved toward the column outlet, while in the conical column of 7degrees (17-11 mm i.d.) the mobile phase in the central region migrated faster than in wall region just like in cylindrical column. We found that a plug-like flow profile was generated in the conical column of 10degrees (18-9 mm i.d.) during the whole migration process. A carmine and brilliant blue mixture was used as a probe to test the separation ability of the columns. The resolutions of the two compounds on the conical column of 7, 10, 15degrees and on the cylindrical column were 0.6, 1.57, 1.29 and 0.8, respectively. (C) 2003 Elsevier B.V. All rights reserved.