Period-doubling bifurcations of the thermocapillary convection in a floating half zone

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d0=3.00 mm and the aspect ratio A=l/d0=0.72 in terrestrial conditions.The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements.The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection,similar in some way to one of the routes to chaos for buoyant natural convection.The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transfor-mation(FFT).The projections of the trajectory onto the reconstructed phase-space were also provided.Furthermore,the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J.Phys Lett A,1979,74:375-378].     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

The onset of convection in a finite container due to surface tension and buoyancy

A method for predicting instabilities which combines recent techniques from bifurcation theory with the finite-element method is described. It is applied to the prediction of the onset of convection driven by both surface tension and buoyancy in rectangular containers. For zero buoyancy, the critical values of the Marangoni number for the first two bifurcations from the trivial solution are found for a two-dimensional cavity of aspect ratio 2. The variation of these critical values with aspect ratio is obtained by continuation methods and this reveals an interlacing of modes as the container size increases. It is established that the bifurcation to an even number of cells is transcritical rather than pitchfork and the turning point on the subcritical branch is located as a function of aspect ratio. The hysteresis associated with the transcritical bifurcation is small. As the surface tension forces decrease to zero, so that the convection is driven by buoyancy alone, the amount of hysteresis associated with the transcritical bifurcation becomes vanishingly small. The reason for this is not fully understood.     

3D Analysis of Crystal/Melt Interface Shape and Marangoni Flow Instability in Solidifying Liquid Bridges

Solidification of gallium (Pr=0.02) in liquid bridges in zero-gravity conditions is investigated by numerical solutions of the three-dimensional and time-dependent flow-field equations. A single region (continuum) formulation based on the enthalpy method is adopted to model the phase-change problem. This paper analyzes the influence of the azimuthally asymmetric and steady first bifurcation of the Marangoni flow on the shape of the solid/melt interface during the crystal growth process. The numerical results show that this interface is distorted in the azimuthal direction. The distortion is related to the sinusoidal three-dimensional temperature disturbances due to the instability of the Marangoni flow. The three-dimensional flow field organization, related to the wave number, changes during the solidification process; this behavior is explained according to the variation of the aspect ratio of the solidifying liquid bridge. A correlation law is found for the azimuthal wave number of the instability as function of the melt zone aspect ratio.     

新型分离结晶法的三维数值模拟研究

本文借助三维数值模拟的方法,对微重力条件下新型分离结晶Bridgman生长过程中熔体内部的热毛细对流进行模拟计算。结果表明:(1)Ma数较小时,流动为稳态流动;当Ma数超过一定数值后,流动发展为非稳态热毛细对流。(2)狭缝宽度越大,流动越容易失稳。(3)随着高径比的增大,狭缝处流胞的流动范围增大。     

分离结晶过程中熔体热毛细对流的转变

为了了解微重力条件下新型分离结晶生长过程中熔体热毛细对流的基本特征,利用有限差分法进行了数值模拟,熔体深径比A取1和2,自由界面无因次宽度B分别取0.05、0.075和0.1.当熔体上表面为自由表面时,得到了分离结晶Bridgman生长过程中熔体热毛细对流的流函数和温度分布.计算结果表明:当Ma数较小时,在上下两个自由表面的表面张力的驱动下,熔体内部产生了两个流动方向相反的流胞,流动为稳态流动,随着Ma数的增加,上下自由表面速度增大,温度分布的非线性增加;当Ma数超过某一临界值后,流动将转化为非稳态流动;与熔体上表面为固壁时相比,A=1时的临界Ma数减小,而A=2时的临界Ma数增大;流动失稳的物理机制是流速的变化和阻力的变化之间存在滞后.     

Threshold onset of Marangoni convection in narrow channels

There are several experimental studies where the Marangoni convection begins only at a certain difference in the surface tension, i.e. in a threshold way. This effect contradicts a traditional point of view according to which the surface flow in Newtonian fluids should begin at an arbitrary small difference in surface tension. To explore this phenomenon in detail we investigated the initiation of the Marangoni convection at a free liquid surface caused by injection of a droplet of surfactant. It was found that the surface motion occurs in a threshold manner, i.e. when a surfactant concentration in the droplet approaches a certain critical value. The described phenomenon is more important in narrow channels and essentially depends both on the purity of the basic liquid and on the surfactant used. Based on the experimental results, a hypothesis about an important role of residual impurities contained in basic liquids which can thoroughly change a surface rheology was suggested. The theoretical model taking into account special rheological properties in the free surface is considered. The results of the numerical simulation are in a good agreement with the experimental observations.     

方形颗粒在黏弹性流体中的沉降特性

采用有限元任意拉格朗日-欧拉(ALE)法对方形颗粒在黏弹性流体中的沉降特性进行研究。通过直接数值模拟得到了不同弹性数下方形颗粒的稳定取向角的变化情况,并讨论了颗粒长宽比和通道宽度对其沉降特性的影响。结果表明,当方形颗粒在黏弹性流体中沉降时,弹性数存在一个临界值。当弹性数小于临界值时,颗粒的稳定取向为长轴方向垂直于重力方向;当弹性数大于临界值时,颗粒的稳定取向为长轴方向平行于重力方向。颗粒长宽比和通道宽度对其沉降特性都有一定的影响。长宽比大的颗粒在沉降过程中的取向角和横向漂移的振幅更大。弹性数的临界值随着长宽比的增大而减小,随着阻塞比的增大而增大。     

Interaction between buoyant and solutocapillary convections induced by a surface-active source placed under the free surface

The onset and stability of solutal (buoyancy and Marangoni) convection induced by a localized source of surface-active substance placed under an interface were studied both experimentally and theoretically. It was shown that the competition between the buoyancy and solutocapillary convection can lead to the onset of oscillatory convection. The period of the observed oscillations appreciably depends on the relation of Grashof and Marangoni numbers and on the aspect ratio of the geometrical sizes of the problem. It was found out that an increase of the buoyancy contribution leads to the onset of stationary convection instead of oscillatory one.     

微重力条件下熔-固相变对流与浮区对流的耦合

本文以空间材料生长为背景,用有限元法研究微重力条件下的浮区单晶生长过程,考虑了表面张力对流与浮区对流的耦合作用,计算了凝固界面形状,结果表明,晶体的生长速度是个重要的影响因素,生长时,单晶-熔体界面比多晶-熔体界面更倾斜;当生长速度超过临界值时,多晶-熔体界面附近的Marangoni涡会分裂出二次涡。 关键词：     

过冷沸腾非均相汽泡界面特性分析

本文针对过冷沸腾中汽泡顶部射流现象进行分析与模拟。建立汽泡界面模型,考虑蒸发凝结以及Marangoni效应。利用CFD软件Fluent6.0对模型进行计算分析,成功模拟得到泡顶射流流场。模拟结果无论是流场结构,还是流场强度,都与实验一致吻合,充分证明泡顶射流由Marangoni效应引起。     

绕汽柱热毛细对流的稳定性分析

本文根据非平衡热力学理论,选取熵产作为F函数,以熵产随时间的变化率作F函数,采用Liapounov稳定性分析方法用数值法对绕汽柱热毛细对流进行了稳定性分析,得到了不同参数组合下的临界Marangoni数,并以工质水为例,得到了不同情况下的临界热负荷。     

EXPERIMENTAL STUDY OF MARANGONI-BENARD CONVECTION IN A LIQUID LAYER INDUCED BY EVAPORATION

Marangoni-Bénard instability and convection in evaporating liquid layers have been studied experimentally through flow visualization and temperature profile measurement. Bénard cells have been observed in an evaporating thin liquid layer whether it is heated, adiabatic, or cooled from below. This experimental study has revealed a different mechanism from the traditional Rayleigh-Bénard and Marangoni-Bénard instabilities and convections, which require a negative temperature gradient in the thin liquid layer. Evaporation rate and enthalpy of evaporation have been found to be important parameters of instability and convection in an evaporating liquid layer. A modified form of Marangoni number, Ma^*, is proposed and its critical values, Ma^* _c, for alcohol and Freon-113 evaporating layers are determined experimentally. A quantitative comparison between Ma^* and the traditional Marangoni number, Ma, shows that Ma^* is an adequate indicator of the stability status in evaporating liquid layers.     

The stability of simply supported tubes conveying a compressible fluid

This paper is concerned with establishing the conditions of static stability of a simply supported tube conveying a compressible fluid by application of Euler's method of equilibrium. Timoshenko beam theory is used to describe the tube motion whiler Euler's equations of motion govern the compressible flow through the tube. The eigenvalue problem associated with the linearized equations of motion first derived by Niordson is solved by using Muller's method. The effects on critical velocity of fluid sound speed, tube shear, and tube aspect ratio are parametrically studied. When the flow is subsonic, the aspect ratio increases the critical velocity predicted by the theory while increased aspect ratio decreases the critical velocity when the flow is supersonic. Reduced sound speed and tube shear modulus always reflect a reduced critical velocity for the onset of tube buckling or divergence instability.     

底部加热长方体腔内自然对流的非线性特性

采用SIMPLE算法,QUICK差分格式,对底部加热三维长方体腔内空气的自然对流进行了数值模拟。根据模拟结果,探讨了方腔内流体流动与换热的静态分岔与振荡等非线性现象。数值结果显示,在固定的几何尺寸和不同Ra的情况下,当初始场不同时,会出现若干不同的解,即存在解的静态分岔;在固定的几何尺寸和相同的初始场情况下,低Ra时流动和换热处于稳态,当Ra超过某一临界值时,流动和换热就会随时间振荡,并通过倍周期分岔过渡到混沌;当方腔的几何尺寸不同时,分岔点的特征值Ra也发生变化。     

微重力池沸腾现象中的汽泡脱落直径

本文报道了空间微重力池沸腾过程中的汽泡脱落现象,观测到微重力条件下小汽泡行为与常重力时相似,但在中等尺寸范围内,汽泡往往粘附在加热丝上做横向振动,并不断合并所碰到的小汽泡,直到超过临界尺寸后脱落.本文在Lee模型(1992)的基础上引入热毛细作用力,成功地解释了实验观测到的独特的汽泡动力学行为特征.     

Theoretical and experimental investigations of the dynamics of cantilevered flexible plates subjected to axial flow

In this paper, the dynamics of cantilevered flexible plates subjected to axial flow is investigated theoretically and experimentally. A nonlinear equation of motion of the plate based on the inextensibility assumption, coupled with an unsteady lumped vortex model for the aerodynamic part is used to analyze the instability and post-critical dynamical behaviour of this fluid–structure system theoretically. Experiments have been conducted in a 3 ft×2 ft (914 mm×610 mm) cross-section wind tunnel, using polypropylene carbonate (PPC) films, thin brass plates, polyethylene terephthalate (PET) sheets, and type 304 stainless steel sheets, with maximum dimensions 224 mm×168 mm. In the experiments, time traces, power spectral densities (PSDs), phase-plane plots, Poincaré maps, probability density functions (PDFs) and autocorrelations are used to characterize the motions of the system.Periodic and chaotic oscillations have been observed in the experiments. It has also been observed that flutter arises via a subcritical bifurcation involving hysteresis for large aspect ratio plates; this hysteresis does not occur for low aspect ratio plates. The hysteresis phenomenon is considered to be due to spanwise deformation of the plates. The effect of aspect ratio on critical flow velocity is investigated. The experimental critical flow velocities for flutter onset are in good agreement with the theoretically predicted values.     

Shape dependent full width at half maximum of the absorption band in gold nanorods

The dependence of full width at half maximum (FWHM) of the absorption peak in gold nanorods was investigated as a function of aspect ratio. Numerical calculations based on Drude model and quasi-static theory indicated that, the FWHM of longitudinal absorption peak is wider than that of transverse mode. Further more, with the increasing aspect ratio, the FWHM of longer wavelength absorption peak increasing in a nonlinear way, which is in agreement with the experimental results.     

Soret效应对具有自由表面的圆柱形浅池内双组分溶液热对流影响的实验研究

为了探究Soret效应对具有自由表面的圆柱形浅液池内双组分溶液热对流过程的影响, 通过实验观察了质量分数为50%的正癸烷/正己烷混合溶液在不同深宽比的液池内流动失稳后的自由表面耗散结构及液池内的温度波动. 结果表明, 双组分溶液流动失稳的临界热毛细Reynolds数小于纯工质的值, 且其随液层深宽比的变化规律与纯工质相同. 当深宽比小于0.0848时, 流动失稳后在自由表面观察到热流体波, 监测点处温度波动主频随热毛细Reynolds数增大而增加; 当深宽比大于0.0848时, 随热毛细Reynolds数的增大, 流动失稳后自由表面依次呈现轮辐状、花苞状、分离-合并-分离交替变化的条纹状结构.     

Numerical Simulation of Heat Transfer in Rectangular Microchannel

Numerical simulation of heat transfer in a high aspect ratio rectangular microchannel with heat sinks has been conducted, similar to an experimental study. Three channel heights measuring 0.3 mm, 0.6 mm and 1 mm are considered and the Reynolds number varies from 300 to 2360, based on the hydraulic diameter. Simulation starts with the validation study on the Nusselt number and the Poiseuille number variations along the channel streamwise direction. It is found that the predicted Nusselt number has shown very good agreement with the theoretical estimation, but some discrepancies are noted in the Poiseuille number comparison. This observation however is in consistent with conclusions made by other researchers for the same flow problem. Simulation continues on the evaluation of heat transfer characteristics, namely the friction factor and the thermal resistance. It is found that noticeable scaling effect happens at small channel height of 0.3 mm and the predicted friction factor agrees fairly well with an experimental based correlation. Present simulation further reveals that the thermal resistance is low at small channel height, indicating that the heat transfer performance can be enhanced with the decrease of the channel height.