受径向振荡激励的黏弹性液滴稳定性分析

当液滴受到外部周期性的径向激励时, 在其表面会形成驻波模式的不稳定, 这就是在球面上的Faraday不稳定问题. 不稳定的表面波的振荡频率根据流体物性参数和所施加激励条件的不同呈现为谐波或是亚谐波模式的振荡. 本文基于线性小扰动理论, 研究了受径向振荡体积力的黏弹性液滴表面波的不稳定性. 振荡的体积力导致动量方程为含有时间周期系数的Mathieu方程, 系统因此变成参数不稳定问题, 采用Floquet理论进行求解. 本模型中将黏弹性的特征处理为与流变模型参数相关的等效黏度, 从而简化了问题的求解. 基于对中性稳定曲线及增长率的分析, 研究了黏弹性参数对液滴稳定性的影响. 结果表明零剪切黏度和应变驰豫时间的增加具有抑制液滴表面波增长的作用, 提高了使液滴表面发生谐波不稳定的激励幅值. 随着振荡幅值的增加, 增长率不稳定的区域减少, 且随着振荡频率的增加, 液滴表面波增长率减小. 通过对增长率的分析可以得出, 应力松弛时间的增加使得增长率增加, 从而促进了液滴表面波的增长.      

DROP FORMATION FROM A CAPILLARY TUBE IN THE PRESENCE OF SURFACTANT 1)

本文研究了竖直毛细圆管出口表面活化剂包覆液滴的形成过程。基于泰勒展开和润滑近似理论, 建立了液滴形成过程的一维动力学模型,并且通过坐标变换和有限差分的方法进行了数值求解。结果显示, 液滴自由面上表面活化剂包覆层可促进液滴颈部断裂,加快液滴头部与尾部锥形区的分离过程。与此同时, 还可增大颈部断裂前液滴下落的极限位移。与表面活化剂的活性相比, 液滴自由面上表面活化剂浓度的变化对液滴形成过程以及液滴形貌变化的影响更为显著。     

毛细管出口表面活化剂包覆液滴形成过程研究

本文研究了竖直毛细圆管出口表面活化剂包覆液滴的形成过程。基于泰勒展开和润滑近似理论,建立了液滴形成过程的一维动力学模型,并且通过坐标变换和有限差分的方法进行了数值求解。结果显示,液滴自由面上表面活化剂包覆层可促进液滴颈部断裂,加快液滴头部与尾部锥形区的分离过程。与此同时,还可增大颈部断裂前液滴下落的极限位移。与表面活化剂的活性相比,液滴自由面上表面活化剂浓度的变化对液滴形成过程以及液滴形貌变化的影响更为显著。     

镓铟锡液滴撞击泡沫金属表面的运动学特性研究

常温下为液态的镓铟锡合金以其优异的导热性能在具有特殊要求的传热领域有着重要的应用价值,与传统流动介质相比较大的表面张力使得其产生的流动现象必有所区别.本文研究镓铟锡所形成的液滴撞击泡沫金属表面后所产生的铺展、回缩及回弹现象.采用高速相机拍摄液滴投影轮廓随液滴运动的变化过程,并通过图像处理获得不同撞击速度、底板表面孔径下的液滴铺展系数、中心位置轮廓高度以及液滴回弹后在空中的振动特性.研究结果表明:具有较高表面张力的镓铟锡液滴的铺展系数随无量纲时间的变化在铺展初始阶段仍满足常规流体的1/2次幂关系,只在铺展后期与底板的无量纲孔径有关系;液滴的最大铺展系数在较小无量纲孔径底板大于在光滑镍板,且随底板无量纲孔径增大而逐渐减小;在回弹过程,由于底板孔隙结构的存在使得液滴回弹后在空中的振动呈现3种形态:规则的横向和纵向振动、带旋转的横向和纵向振动以及旋转振动;最后,通过对振动频率的拟合和分析,进一步拓展了传统振动频率理论公式在非规则振动过程预测中的应用.      

镓铟锡液滴撞击泡沫金属表面的运动学特性研究

常温下为液态的镓铟锡合金以其优异的导热性能在具有特殊要求的传热领域有着重要的应用价值,与传统流动介质相比较大的表面张力使得其产生的流动现象必有所区别.本文研究镓铟锡所形成的液滴撞击泡沫金属表面后所产生的铺展、回缩及回弹现象.采用高速相机拍摄液滴投影轮廓随液滴运动的变化过程,并通过图像处理获得不同撞击速度、底板表面孔径下的液滴铺展系数、中心位置轮廓高度以及液滴回弹后在空中的振动特性.研究结果表明:具有较高表面张力的镓铟锡液滴的铺展系数随无量纲时间的变化在铺展初始阶段仍满足常规流体的1/2次幂关系,只在铺展后期与底板的无量纲孔径有关系;液滴的最大铺展系数在较小无量纲孔径底板大于在光滑镍板,且随底板无量纲孔径增大而逐渐减小;在回弹过程,由于底板孔隙结构的存在使得液滴回弹后在空中的振动呈现3种形态:规则的横向和纵向振动、带旋转的横向和纵向振动以及旋转振动;最后,通过对振动频率的拟合和分析,进一步拓展了传统振动频率理论公式在非规则振动过程预测中的应用.     

液滴自发运动的微粗糙结构梯度表面参数研究

采用多体耗散粒子动力学(MDPD)方法,研究液滴在微结构粗糙梯度表面上的自发运动现象.表面微结构的构成影响液滴自发运动速度和距离.对相关的具体参数如构成微结构表面立柱的截面形状、排布、边长、面积等参数进行系统研究.研究表明,微结构表面的排布影响液固接触区域的边缘大小和形状,进而影响液滴自发运动输送效果;不对称结构立柱朝向对液滴运动也有影响,其中先宽后窄截面形状的立柱上液滴运动速度较快;对于对称的立柱组成的梯度表面,定义周长和面积的比值为长积比,该参数越大,液滴自发运动速度越快.本文可为微流控表面设计提供一定的数值模拟依据.     

双液滴热毛细迁移的实验研究

在地面实验中,研究在竖直向上温度梯度流场中,双液滴的热毛细迁移运动和它们间的相互 作用. 豆油和硅油分别作为实验系统的母液和液滴. 液滴迁移轨迹被记录和分析. 实验结果 表明,大小液滴的实验迁移速度均小于理论迁移速度;两个液滴之间的相互作用对小液滴的 影响更为明显,使之出现倾斜``8'字的迁移轨迹;两个液滴的运动速度都出现了振荡现象, 小液滴可能出现短时反向迁移. 实验结果与数值模拟结果较为相似,但尚有差异,需要进一 步进行研究.     

基于扰动波的HVAS液滴耦合振动特性分析

高速电弧喷涂过程中熔融金属液滴的振动特性对喷涂涂层性能具有决定性作用,但限于实验技术很难检测液滴的动力学行为,因而利用扰动波理论建立了气流和液滴的耦合振动方程组,并数值求解获得了喷涂气流最不稳定波数,与Bradley的数据曲线进行了比较,二者呈现出较好的吻合性,误差在士2％之间,验证了所建立的HVAS小扰动液滴模型是有效的;根据HVAS液滴耦合振动模型分析了不同喷涂气流及其速度对不同熔融金属的相应HVAS液滴振动特性。结果表明,HVAS过程中用N2具有一定的优势,且增加气流速度有利于提高喷涂涂层的结合强度,从而为HVAS过程中的材料选择与工艺控制提供了基本的理论依据。     

非等温粗糙表面液滴撞击特性试验与仿真研究

非等温固体表面液滴碰撞现象广泛存在于航空航天领域机械零部件中,液滴碰撞动力学行为的研究对提升机械零部件传热换热以及润滑性能具有重要意义.为获得液滴在非等温粗糙表面的撞击特性,研究了硅油在金属表面撞击、铺展和回缩的动力学行为,并着重分析了硅油黏度、撞击速度、油滴初始直径、金属表面粗糙度及温度对硅油撞击特性的影响.结果表明,在等温表面,液滴最大铺展直径与撞击速度、基体表面温度及液滴初始直径正相关,与基体表面粗糙度、硅油黏度负相关;当表面粗糙度介于6.3～25μm时,其对液滴最大铺展直径影响较小;在非等温表面,液滴回缩过程中少量液体残留并形成尾迹,且残留尾迹随基体温度升高而愈发明显;随后数值模拟了硅油在非等温粗糙表面的碰撞过程,并揭示了基体温度和表面粗糙度的影响机制.本文中研究成果为理解非等温粗糙金属表面液滴的撞击行为提供了丰富的理论和试验依据.     

椭球液滴撞击超疏水表面反弹过程数值分析

液滴在自由落体或受外力作用时常发生椭球形变,对其撞击超疏水壁面的运动形态及形成二次液滴有较大影响.本文假定具有不同轴向半径比值(AR)的椭球形液滴,采用耦合水平集-体积分数(CLSVOF)方法对椭球形液滴撞击超疏水平壁面进行数值模拟研究,对椭球形液滴撞击超疏水平壁面反弹过程运动形态和AR对二次液滴形成的影响进行分析.研究表明,不同AR液滴撞击超疏水壁面后反弹过程具有一定相似性,同时存在明显差异.液滴反弹过程中会拉伸形成长液柱,其未扰动界面直径随AR的增大而减小.在Plateau-Rayleigh不稳定性影响下,长液柱会发生破碎形成二次液滴,但较低的AR对二次液滴的形成有较明显的抑制作用,当AR小于临界值0.6时,反弹过程中液滴内部压力均匀稳定,最终不产生二次液滴.     

垂直参数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Rayleigh-B\'enard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.图13,参74      

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.     

DAMPING OF VERTICALLY EXCITED SURFACE WAVE IN WEAKLY VISCOUS FLUID

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.     

Instability of an Axisymmetric Vortex in a Stably Stratified, Rotating Environment

We investigate the stability of a barotropic vorticity monopole whose stream function is a Gaussian function of the radial coordinate. The model is based on the inviscid Boussinesq equations. The vortex is assumed to exist on an $f$-plane, in an environment with constant, stable density stratification. In the unstratified, nonrotating case, we find growth rates that increase monotonically with increasing vertical wave number, the so-called “ultraviolet catastrophe” characteristic of symmetric instability. This type of instability leads to rapid turbulent collapse of the vortex, possibly accompanied by wave radiation. In the limit of strong background stratification and rotation, the vortex exhibits a scale-selective instability which leads to the formation of stable lenses. The transition between these two regimes is sharp, and coincides approximately with the centrifugal stability boundary. Received 6 December 1996 and accepted 1 November 1997     

Effect of Heat Supply on the Stability of the Supersonic Swept Atiachment-Line Boundary Layer

The stability of a boundary layer with volume heat supply on the attachment line of a swept wing is investigated within the framework of the linear theory at supersonic inviscid-free-stream Mach numbers. The results of numerical calculations of the flow stability and neutral curves are presented for the flow on the leading edge of a swept wing with a swept angle χ=60° at various free-stream Mach numbers. The effect of volume heat supply on the characteristics of boundary layer stability on the attachment line is studied at a surface temperature equal to the temperature of the external inviscid flow. It is shown that in the case of a supersonic external inviscid flow volume heat supply may result in an increase in the critical Reynolds number and stabilization of disturbances corresponding to large wave numbers. For certain energy supply parameters the situation is reversed, the unstable disturbances corresponding to the main flow-instability zone are stabilized but another zone of flow-instability with small wave numbers and a significantly lower critical Reynolds number appears.     

Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet

This paper describes the implementation of the instability analysis of wave growth on liquid jet surface, and maximum entropy principle (MEP) for prediction of droplet diameter distribution in primary breakup region. The early stage of the primary breakup, which contains the growth of wave on liquid–gas interface, is deterministic; whereas the droplet formation stage at the end of primary breakup is random and stochastic. The stage of droplet formation after the liquid bulk breakup can be modeled by statistical means based on the maximum entropy principle. The MEP provides a formulation that predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. The deterministic aspect considers the instability of wave motion on jet surface before the liquid bulk breakup using the linear instability analysis, which provides information of the maximum growth rate and corresponding wavelength of instabilities in breakup zone. The two sub-models are coupled together using momentum source term and mean diameter of droplets. This model is also capable of considering drag force on droplets through gas–liquid interaction. The predicted results compared favorably with the experimentally measured droplet size distributions for hollow-cone sprays.     

Nonlinear faraday waves in a parametrically excited circular cylindrical container

IntroductionIn 1 83 1 ,Faraday[1]reportedhisexperimentalobservationofsurfacewavesindifferentfluidscoveringahorizontalplatesubjectedtoaverticalvibration ,andheobservedthesurfacestandingwavesoffluidsliketheteethofaveryshortcoarsecomb .Heremarksthatthesesurfacewaveshaveafrequencyequaltoonehalfthatoftheexcitation .ThisisthefamousFaradayexperiment.WedesignatethosefluidsurfacewavesformedbyverticallyexcitationandhaveafrequencyequaltoonehalfthatoftheexcitationasFaradaywaves.FollowingthisproblemMatth…     

CAPILLARY EFFECT ON VERTICALLY EXCITED SURFACE WAVE IN CIRCULAR CYLINDRICAL VESSEL

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions was developed in inviscid fluids to investigate the motion of single free surface standing wave including the effect of surface tension. A nonlinear slowly varying amplitude equation, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from potential flow equation. The results show that, when forced frequency is lower, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is higher, the surface tension can not be neglected. This proved that the surface tension causes free surface returning to equilibrium location. In addition, due to considering the effect of surface tension, the theoretical result approaches to experimental results much more than that of no surface tension.