Proper orthogonal decomposition of oscillatory Marangoni flow in half-zone liquid bridges of low-Pr fluids

Proper orthogonal decomposition (POD) using method of snapshots was performed on three different types of oscillatory Marangoni flows in half-zone liquid bridges of low-Pr fluid (Pr = 0.01). For each oscillation type, a series of characteristic modes (eigenfunctions) have been extracted from the velocity and temperature disturbances, and the POD provided spatial structures of the eigenfunctions, their oscillation frequencies, amplitudes, and phase shifts between them. The present analyses revealed the common features of the characteristic modes for different oscillation modes: four major velocity eigenfunctions captured more than 99% of the velocity fluctuation energy form two pairs, one of which is the most energetic. Different from the velocity disturbance, one of the major temperature eigenfunctions makes the dominant contribution to the temperature fluctuation energy. On the other hand, within the most energetic velocity eigenfuction pair, the two eigenfunctions have similar spatial structures and were tightly coupled to oscillate with the same frequency, and it was determined that the spatial structures and phase shifts of the eigenfunctions produced the different oscillatory disturbances. The interaction of other major modes only enriches the secondary spatio-temporal structures of the oscillatory disturbances. Moreover, the present analyses imply that the oscillatory disturbance, which is hydrodynamic in nature, primarily originates from the interior of the liquid bridge. (C) 2007 Elsevier B.V. All rights reserved.

How to determine critical Marangoni number in half floating zone convection

In the present paper, the coordinated measurements of the temperature profile inside the liquid bridge and the boundary variation of Free surface, in addition to other quantities, were obtained in the same time for the half floating zone convection. The results show that the onset of free surface oscillation is earlier than the one of temperature oscillation during the increasing of applied temperature difference, and the critical Marangoni numbers, defined usually by temperature measurement, are larger than the one defined by free surface measurement, and the difference depends on the volume of liquid bridge. These results induce the question, ''How to determine experimentally the critical Marangoni number?'' Copyright (C) 1996 Elsevier Science Ltd.

Fractal features of oscillatory convection in the half-floating zone

Unsteady and two-dimensional numerical simulation is applied to study the transition process from steady convection to turbulence via subharmonic bifurcation in thermocapillary convection of a liquid bridge in the half-floating zone. The results of numerical tests show clearly the fractal structure of period-doubling bifurcations, and frequency-locking at f/4, f/8, f/16 with basic frequency f is observed with increasing temperature difference. The Feigenbaum universal constant is given by the present paper as delta(4) = 4.853, which can be compared with the theoretical value 4.6642016.

Transition from steady to oscillatory convection with chaotic feature in thermocapillary convection

The transition process from steady to turbulent convection via subharmonic bifurcation in thermocapillary convection of half floating zone was studied by numerical simulation and experimental test. Both approaches gave structure of period doubling bifurcations in the present paper, and the Feigenbaum universal law was checked for the system of thermocapillary convection.

G-jitter effects on half floating-zone convection in intermediate-frequency range

The g-jitter influence on thermocapillary convection and critical Marangoni number in a liquid bridge of half-floating rone was discussed in the low frequency range of 0.4 to 1.5 Hz in a previous paper. This paper extended the experiments to the intermediate frequency range of 2 to 18 Hz, which htrs often been recorded as vibration environment of spacecrafts. The experiment was completed on the deck of a vibration machine, which gave a periodical applied acceleration to simulate the effects of g-jitter. The experimental results in the intermediate frequency range are different from that in the low frequency range. The velocity field and the shape of the free surface have periodical fluctuations in response to g-jitter. The amplitude of the periodical varying part of the temperature response decreases obviously with increasing frequency of g-jitter and vanishes almost when the frequency of g-jitter is high enough. The critical Marangoni number is defined to describe the transition from a periodical convection in response to g-jitter to an oscillatory convection due to internal instability, and will increase with increasing g-jitter frequency. According to the spectral analysis, it can be found that the oscillatory part of temperature is a superposition of two harmonic waves if the Marangoni number is larger than a critical value.

Influence of buoyancy on floating-zone convection of small bond number

Gravity may influence the velocity and temperature distributions, bouyancy may induce Rayleigh instability and the instability may be excited due to the change of free surface shape associating with gravity in the thermocapillary convection. These effects have been studied in the present paper. The results show that gravity may have an important effect in thermocapillary oscillatory convection even for the cases of small Bond number experiments either on the ground or in space.

Free surface oscillation of thermocapillary convection in liquid bridge of half-floating-zone

Free surface deformations of thermocapillary convection in a small liquid bridge of half floating-zone are studied in the present paper. The relative displacement and phase difference of free surface oscillation are experimentally studied, and the features of free surface oscillation for various applied temperature differences are obtained. It is discovered that there is a sort of surface waves having the character of small perturbation, and having a wave mode of unusually large amplitude in one corner region of the liquid bridge.

Experimental study on oscillatory thermocapillary convection

The transition processes from steady flow into oscillatory flow in a liquid bridge of the half floating zone are studied experimentally. Two methods of noncontacted diagnoses are developed to measure the distribution of critical Marangoni numbers described by the onset of the oscillation st the free surface of the liquid bridge.The experimental results obtained for both cases of the upper rod heated and the lower rod heated agree with the prediction by Rayleigh's instability theory.The sensitive relations between the relatively fat or slender liquid bridge and the onset of oscillatory convection are also discussed to reveal the insight of the pressure distribution near the free surface. The experiments have been performed in a small liquid bridge, where the Bond number is much smaller than 1, and the results can be used to simulate the experiment in the microgravity environment.

蒸发液层对流稳定性理论与实验研究进展

综述了蒸发液层稳定性理论分析和蒸发对流实验研究方面的最新进展．首先回顾历史上经典的单层流Marangoni不稳定性分析．利用经典的单层流模型可以很好解释无蒸发液层的稳定性特性，但是由于经典的单层流模型没有考虑蒸汽层与液层之间的动力学耦合关系，所以不能完全解释蒸发液层的Marangoni不稳定性特性．有的学者建立了考虑蒸汽层与液层的热耦合与动力学耦合关系的两层流模型，并采用了界面温度连续这样的假设．而在实验的观测中，蒸发界面处的温度是不连续的，特别是在蒸发量比较大的情况下，汽／液界面处温度跳跃很明显．由于界面温度连续假设在处于非平衡状态的系统中是不成立的，所以这些模型虽然能给出一些新的有关系统稳定性的特性，但还是不能完全解释蒸发液层的Marangoni不稳定性的特性，特别是为什么从底部冷却液层的时候，在实验中仍然能够观察到Marangoni对流涡胞的出现的原因．本文总结了前人的研究成果，同时给出了蒸发系统的动力学建模过程和实验研究方法，并对各种模型的稳定性特性进行了总结．最后，指出了现有理论中存在的问题和有待进一步研究的问题．

Oscillatory Instability of Rayleigh-Marangoni-Benard Convection in Two-Layer System

The convective instabilities in two or more superposed layers heated from below were studied extensively by many scientists due to several interfacial phenomena in nature and crystal growth application. Most works of them were performed mainly on the instability behaviors induced only by buoyancy force, especially on the oscillatory behavior at onset of convection (see Gershuni et. Al.(1982), Renardy et. Al. (1985,2000), Rasenat et. Al. (1989), and Colinet et. Al.(1994)) . But the unstable situations of multi-layer liquid convection will become more complicated and interesting while considering at the same time the buoyancy effect combined with thermocapillary effect. This is the case in the gravity reduced field or thin liquid layer where the thermocapillary effect is as important as buoyancy effect. The objective of this study was to investigate theoretically the interaction between Rayleigh-Bénard instability and pure Marangoni instability in a two-layer system, and more attention focus on the oscillatory instability both at the onset of convection and with increasing supercriticality. Oscillatory behavious of Rayleigh-Marangoni-Bénard convective instability (R-M-B instability) and flow patterns are presented in the two-layer system of Silicon Oil (10cSt) over Fluorinert (FC70) for a larger various range of two-layer depth ratios (Hr=Hupper/Hdown) from 0.2 to 5.0. Both linear instability analysis and 2D numerical simulation (A=L/H=10) show that the instability of the system depends strongly on the depth ratio of two-layer liquids. The oscillatory instability regime at the onset of R-M-B convection are found theoretically in different regions of layer thickness ratio for different two-layer depth H=12,6,4,3mm. The neutral stability curve of the system displaces to right while we consider the Marangoni effect at the interface in comparison with the Rayleigh-Bénard instability of the system without the Marangoni effect (Ma=0). The numerical results show different regimes of the developing of convection in the two-layer system for different thickness ratios and some differences at the onset of pure Marangoni convection and the onset of Rayleigh-Bénard convections in two-layer liquids. Both traveling wave and standing wave were detected in the oscillatory instability regime due to the competition between Rayleigh-Bénard instability and Marangoni effect. The mechanism of the standing wave formation in the system is presented numerically in this paper. The oscillating standing wave results in the competition of the intermediate Marangoni cell and the Rayleigh convective rolls. In the two-layer system of 47v2 silicone oil over water, a transition form the steady instability to the oscillatory instability of the Rayleigh-Marangoni-Bénard Convection was found numerically above the onset of convection for ε=0.9 and Hr=0.5. We propose that this oscillatory mechanism is possible to explain the experimental observation of Degen et. Al.(1998). Experimental work in comparison with our theoretical findings on the two-layer Rayleigh-Marangoni-Bénard convection with thinner depth for H<6mm will be carried out in the near future, and more attention will be paid to new oscillatory instability regimes possible in the influence of thermocapillary effects on the competition of two-layer liquids

Robust Sliding Mode Control for Tokamaks

Nuclear fusion has arisen as an alternative energy to avoid carbon dioxide emissions, being the tokamak a promising nuclear fusion reactor that uses a magnetic field to confine plasma in the shape of a torus. However, different kinds of magnetohydrodynamic instabilities may affect tokamak plasma equilibrium, causing severe reduction of particle confinement and leading to plasma disruptions. In this sense, numerous efforts and resources have been devoted to seeking solutions for the different plasma control problems so as to avoid energy confinement time decrements in these devices. In particular, since the growth rate of the vertical instability increases with the internal inductance, lowering the internal inductance is a fundamental issue to address for the elongated plasmas employed within the advanced tokamaks currently under development. In this sense, this paper introduces a lumped parameter numerical model of the tokamak in order to design a novel robust sliding mode controller for the internal inductance using the transformer primary coil as actuator.

Instability Analysis Of Torsional Mems/Nems Actuators Under Capillary Force

The static and dynamic instabilities of a torsional MEMS/NEMS actuator caused by capillary effects are studied, respectively. An instability number, eta, is defined, and the critical gap distance, g(cr), between the mainplate and the substrate is derived. According to the values of eta and g, the instability criteria of the actuator are presented. The dimensionless motion equation of the MEMS/NEMS torsional actuator is derived when it makes nonlinear oscillation under capillary force. The qualitative analysis of the nonlinear equation is made, and the phase portraits are presented on the phase plane. In addition, the bifurcation phenomena in the system are also analyzed. (C) 2008 Elsevier Inc. All rights reserved.

On the origin of shear banding instability in metallic glasses

To uncover the physical origin of shear-banding instability in metallic glass (MG), a theoretical description of thermo-mechanical deformation of MG undergoing one-dimensional simple shearing is presented. The coupled thermo-mechanical model takes into account the momentum balance, the energy balance and the dynamics of free volume. The interplay between free-volume production and temperature increase being two potential causes for shear-banding instability is examined on the basis of the homogeneous solution. It is found that the free-volume production facilitates the sudden increase in the temperature before instability and vice versa. A rigorous linear perturbation analysis is used to examine the inhomogeneous deformation, during which the onset criteria and the internal length and time scales for three types of instabilities, namely free-volume softening, thermal softening and coupling softening, are clearly revealed. The shear-banding instability originating from sole free-volume softening takes place easier and faster than that due to sole thermal softening, and dominates in the coupling softening. Furthermore, the coupled thermo-mechanical shear-band analysis does show that an initial slight distribution of local free volume can incur significant strain localization, producing a shear band. During such a localization process, the local free-volume creation occurs indeed prior to the increase in local temperature, indicating that the former is the cause of shear localization, whereas the latter is its consequence. Finally, extension of the above model to include the shear-induced dilatation shows that such dilatation facilitates the shear instability in metallic glasses.

Self-organized generation of transverse waves in diverging cylindrical detonations

Self-organized generation of transverse waves associated with the transverse wave instabilities at a diverging cylindrical detonation front was numerically studied by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. After solution validation, four mechanisms of the transverse wave generation were identified from numerical simulations, and referred to as the concave front focusing, the kinked front evolution, the wrinkled front evolution and the transverse wave merging, respectively. The propagation of the cylindrical detonation is maintained by the growth of the transverse waves that match the rate of increase in surface area of the detonation front to asymptotically approach a constant average number of transverse waves per unit length along the circumference of the detonation front. This cell bifurcation phenomenon of cellular detonations is discussed in detail to gain better understanding on detonation physics.