流动聚焦及射流不稳定性

流动聚焦是一种有效的微细射流产生方法,其原理可以描述为从毛细管流出的流体由另一种高速运动的流体驱动,经小孔聚焦后形成稳定的锥–射流结构,射流因不稳定性破碎成单分散的液滴.自从1998年流动聚焦被提出以来,陆续发展了单轴流动聚焦、电流动聚焦、复合流动聚焦和微流控流动聚焦等毛细流动技术.这些技术稳定、易操作、没有苛刻的环境条件的要求,能够制备单分散性较好的微纳米量级的液滴、颗粒和胶囊,在科学研究和实际应用中具有重要价值.流动聚焦涉及了多尺度、多界面和多场耦合的复杂流体力学问题,其中稳定的锥形是形成稳定射流的先决条件,过程参数是影响射流界面扰动发展的关键因素,而射流不稳定性分析是揭示射流破碎的最主要理论工具.该文回顾了近二十年来不同结构流动聚焦的研究进展,概述这些技术涉及的过程控制、流动模式、尺度律和不稳定性分析等关键力学问题,总结射流不稳定性的研究方法和已取得的成果,最后展望流动聚焦的研究方向和应用前景.     

Flow focusing and jet instability

流动聚焦是一种有效的微细射流产生方法,其原理可以描述为从毛细管流出的流体由另一种高速运动的流体驱动,经小孔聚焦后形成稳定的锥–射流结构,射流因不稳定性破碎成单分散的液滴.自从1998年流动聚焦被提出以来,陆续发展了单轴流动聚焦、电流动聚焦、复合流动聚焦和微流控流动聚焦等毛细流动技术.这些技术稳定、易操作、没有苛刻的环境条件的要求,能够制备单分散性较好的微纳米量级的液滴、颗粒和胶囊,在科学研究和实际应用中具有重要价值.流动聚焦涉及了多尺度、多界面和多场耦合的复杂流体力学问题,其中稳定的锥形是形成稳定射流的先决条件,过程参数是影响射流界面扰动发展的关键因素,而射流不稳定性分析是揭示射流破碎的最主要理论工具.该文回顾了近二十年来不同结构流动聚焦的研究进展,概述这些技术涉及的过程控制、流动模式、尺度律和不稳定性分析等关键力学问题,总结射流不稳定性的研究方法和已取得的成果,最后展望流动聚焦的研究方向和应用前景.     

Dynamics and Breakup of Pulse Microjets of Polymeric Liquids

The possibilities of controlling the dynamics and breakup of pulsed low-viscosity liquid microjets by means of small amounts of polymeric additives are considered. Significant differences between the breakup of pulse jets of Newtonian and viscoelastic polymeric liquids are recorded by means of high-speed photography. In flight a standard Newtonian fluid jet fragments into many secondary droplets. Depending on the molecular parameters, for a polymeric liquid three variants of the behavior of the jet in flight are possible: (1) the jet tail fragments into several secondary droplets; (2) the entire tail flows into the leading drop without loss and a single drop is formed; (3) the drop ejected from the nozzle returns to the nozzle under the action of elastic internal stresses in the tail. Criteria for the transition from one regime of jet motion to another are proposed.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 45–63.Original Russian Text Copyright © 2005 by Bazilevskii, Meyer, and Rozhkov.     

The effect of surfactants on the instability of a rotating liquid jet

It has long been known that the presence of surfactants on the free surface of a liquid jet can create surface tension gradients along the interface. The resulting formation of tangential stresses along the surface lead to Marangoni type flows and greatly affect the resulting dynamics of rupture. In this way surfactants can be used to manipulate the breakup of a liquid jet and control the size of droplets produced. In this paper we investigate the effects of insoluble surfactants on the breakup of rotating liquid jets with applications to industrial prilling. Using a long wavelength approximation we reduce the governing equations into a set of one-dimensional equations. We use an asymptotic theory to find steady solutions and then carry out a linear instability analysis on these solutions. We show that steady state centreline solutions are independent of viscosity to leading order and that the most unstable wavenumber and growth rate of disturbances decrease as the effectiveness of surfactants is increased. We also numerically solve these equations using a finite difference scheme to investigate the effects of changing the initial surfactant concentration and other fluid parameters. Our results show that differences in breakup lengths between rotating surfactant-laden jets and surfactant-free jets increase with the rate of rotation. Moreover, we find that satellite droplet sizes decrease as the rate of rotation is decreased with the effect of surfactants amplifying the reduction in sizes. Furthermore, the presence of surfactants at fixed rotation rates is shown to produce larger main droplets at low disturbance wavenumbers whilst satellite droplets are smaller for moderate disturbance wavenumbers κ≈0.7.     

水动力作用下低速射流碎化的数值模拟

为研究射流在水动力作用下的碎化特性,采用有限体积法对轴对称坐标下Navier-Stokes方程进行了求解,考虑重力和表面张力的影响,并通过Volume-of-Fluid法与Level-Set法成功捕捉到界面的不稳定发展、变形及射流碎化过程,分析了流场内部速度场和压力场分布,结果表明,射流碎化长度随Re/We“5数呈指数型增加,最后探讨了射流速度、直径及周围流体密度、粘性等参量对射流的碎化过程的影响规律.     

Thermal modulation and breakup of liquid jets

In this paper, we study the breakup behavior of Newtonian liquid and non‐Newtonian liquid jets with an arbitrary variation surface tension imposed along its length. The effect of duty cycle, fluid properties, and the various profiles of the surface tension is investigated. It is shown that the breakup behavior of a jet can be constructed by using the Fourier expansion of the surface tension profile. When the dimensionless wavenumber k is larger than 0.5, the jet breakup behavior is determined by the lowest frequency of the Fourier series expansion of the surface tension profile. As k decreases, higher frequency Fourier modes come to play. In general, for k between, 1∕(n+ 1) and 1∕n,n Fourier modes are needed to determine the jet breakup behavior. The current nonlinear model differs from the existing linear slender jet model in the literature in several ways. While the principle of superposition is valid for the linear model, it is not generally valid for the current nonlinear model. For the linear model, the jet will never break up when the wavenumber is larger than 1. The current model, however, shows clearly that the jet can indeed break up when the wavenumber is larger than 1. Furthermore, the current nonlinear model predicts a breakup time substantially higher than that from the linear model.Copyright © 2011 John Wiley & Sons, Ltd.     

液体环轴对称抛洒首次破碎的理论分析

对于水和无水乙醇环形轴对称抛洒实验的首次破碎结果的分析表明，在给定实验条件下，液体密度大约是气体的1000倍，液体首次破碎的过程分2个阶段:首先，界面不稳定性非线性发展，液体尖钉在惯性力和空气阻力的作用下，拉伸变细变长；然后在射流不稳定性的作用下，断裂成液体珠串。这个理论分析给出的首次破碎的平均液体直径与实验结果基本一致。理论分析表明，无水乙醇破碎液滴的平均直径比水液滴小，是无水乙醇表面张力值仅为水的1/3的一个必然结果。     

单液滴内空化气泡的生长及溃灭研究

超空化燃油射流使得喷雾中部分燃油分裂液滴内含有空化气泡;空化气泡的生长及溃灭对液滴的分裂与雾化具有重要影响. 基于VOF 方法首次对超空化条件下燃油液滴内空化气泡的生长及溃灭过程进行了数值模拟. 通过研究发现,单液滴内空化气泡的生长过程可以按控制机理划分为表面张力控制阶段、综合竞争阶段和惯性力控制阶段;在第I 阶段,空泡的生长主要受表面张力的控制作用,惯性力对空泡生长的促进作用及黏性力对空泡生长的抑制作用可以忽略;在第II 阶段,空泡的生长受表面张力、惯性力及黏性力三者的综合作用,空泡的生长速率是促进空泡生长的惯性力和抑制空泡生长的表面张力及黏性力相互竞争、共同作用的结果;在第III 阶段,空泡的生长主要受惯性力的控制作用,抑制空泡生长的表面张力及黏性力的作用基本可以忽略. 单液滴内空化气泡的溃灭过程由多个溃灭阶段和反弹阶段构成,类似于有阻尼弹簧振子的振动过程;根据每个溃灭周期结束时空泡半径随时间的变化历程,可以将空泡的溃灭分为快速溃灭期、缓慢溃灭期以及稳定期;溃灭初期空泡溃灭压力的变化非常剧烈,但空泡溃灭体积的变化则要相对平缓得多;空泡反弹压力随时间的变化与空泡反弹体积随时间的变化基本对应.      

A numerical study of an annular liquid jet in a compressible gas medium

An annular liquid jet in a compressible gas medium has been examined using an Eulerian approach with mixed-fluid treatment. The governing equations have been solved by using highly accurate numerical methods. An adapted volume of fluid method combined with a continuum surface force model was used to capture the gas–liquid interface dynamics. The numerical simulations showed the existence of a recirculation zone adjacent to the nozzle exit and unsteady large vortical structures at downstream locations, which lead to significant velocity reversals in the flow field. It was found that the annular jet flow is highly unstable because of the existence of two adjacent shear layers in the annular configuration. The large vortical structures developed naturally in the flow field without external perturbations. Surface tension tends to promote the Kelvin–Helmholtz instability and the development of vortical structures that leads to an increased liquid dispersion. A decrease in the liquid sheet thickness resulted in a reduced liquid dispersion. It was identified that the liquid-to-gas density and viscosity ratios have opposite effects on the flow field with the reduced liquid-to-gas density ratio demoting the instability and the reduced liquid-to-gas viscosity ratio promoting the instability characteristics.     

运动状态下液体轴对称抛撒首次破碎的实验研究

在实验室条件下利用组合式激波管设备,对运动状态下液体轴对称抛撒进行了实验研究。通过纹影装置获得其所形成雾化场的外形轮廓照片,测量获得了液核发生首次破碎的位置与对称轴之间的距离。通过对抛撒过程中R-T不稳定性与K-H不稳定性的分析认为,轴向气流作用下液体轴对称抛撒的首次破碎点与对称轴的距离主要由轴向气流的速度、轴向气流的密度、液体轴对称抛撒的出口速度、抛撒液体的表面张力系数、环形喷口的宽度等参数所决定。在此基础上,利用相似性理论和无量纲分析,获得了运动状态下液体轴对称抛撒首次破碎点与对称轴之间的距离与相关参数的无量纲关系式。     

A regularised one-dimensional drop formation and coalescence model using a total variation diminishing (TVD) scheme on a single Eulerian grid

The breakup of an axisymmetric viscous jet is considered in the lubrication approximation. The discretised equations are solved on a fixed equidistant one-dimensional Eulerian grid. The governing equations are implemented in a conservative second order accurate total variation diminishing (TVD) scheme, preventing the numerical diffusivity. Singularities that occur at pinchoff and coalescence are regularised by a small modification on the surface tension. The modification is of the order of the spatial step Δx. This regularisation ensures that the solution of the presented numerical model converges to the exact solution of the breakup of a jet in the lubrication approximation. The results of the presented numerical model agree quantitatively with the analytical solution of the Rayleigh–Plateau instability, and with experimental results on the final stage of the Rayleigh–Plateau instability.     

An Eulerian–Lagrangian hybrid model for the coarse-grid simulation of turbulent liquid jet breakup

In this paper we present a numerical model for the coarse-grid simulation of turbulent liquid jet breakup using an Eulerian–Lagrangian coupling. To picture the unresolved droplet formation near the liquid jet interface in the case of coarse grids we considered a theoretical model to describe the unresolved flow instabilities leading to turbulent breakup. These entrained droplets are then represented by an Eulerian–Lagrangian hybrid concept. On the one hand, we used a volume of fluid method (VOF) to characterize the global spreading and the initiation of droplet formation; one the other hand, Lagrangian droplets are released at the liquid–gas interface according to the theoretical model balancing consolidating and disruptive energies. Here, a numerical coupling was required between Eulerian liquid core and Lagrangian droplets using mass and momentum source terms. The presented methodology was tested for different liquid jets in Rayleigh, wind-induced and atomization regimes and validated against literature data. This comparison reveals fairly good qualitative agreement in the cases of jet spreading, jet instability and jet breakup as well as relatively accurate size distribution and Sauter mean diameter (SMD) of the droplets. Furthermore, the model was able to capture the regime transitions from Rayleigh instability to atomization appropriately. Finally, the presented sub-grid model predicts the effect of the gas-phase pressure on the droplet sizes very well.     

Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow

We employ detailed numerical simulations to understand the physical mechanism underlying the surface breakup of a non-turbulent liquid jet injected transversely into a high pressure gaseous crossflow under isothermal conditions. The numerical observations reveal the existence of shear instability on the jet periphery as the primary destabilization mechanism. The temporal growth of such azimuthal instabilities leads to the formation of interface corrugations, which are eventually sheared off of the jet surface as sheet-like structures. The sheets next undergo disintegration into ligaments and drops during the surface breakup process. The proposed instability mechanism is inherently an inviscid mechanism, contrary to the previously suggested mechanism of surface breakup (known as “boundary layer stripping”), which is relied on a viscous interpretation. The numerically obtained length and time scales of the shear instabilities on the jet laterals are compared with the results of Behzad et al. (2015) on temporal linear stability analyses of a jet in crossflow at near the nozzle. The stability characteristics of the most amplified modes (i.e., the wavenumber and the corresponding growth rate) obtained from the numerical simulations and the stability analyses are in good agreement.     

Simulation of the primary breakup of a high-viscosity liquid jet by a coaxial annular gas flow

The conversion of low-grade fossil and biogenic energy resources (petcoke, biomass) to a synthesis gas in a high pressure entrained flow gasification process opens a wide spectrum for high efficient energy conversion processes. The synthesis gas can be used for production of methane (SNG), liquid fuels (BtL, CtL) or as fuel for operation of a gas turbine in a combined cycle power plant (IGCC). The production of a tar free high quality syngas is a challenging objective especially due to the fact that typical liquid or suspension fuels for entrained flow gasifiers feature viscosities up to 1000 mPas. Fuel droplet conversion at typical entrained flow gasification conditions is characterized by heat up, evaporation and subsequent degradation of the vapour phase. To guarantee a high fuel conversion rate in the gasifier an efficient atomization of the fuel is required. Mainly twin-fluid burner nozzles are used for atomization of those typically high viscous fuels. The present study is focused on the assessment of the accuracy of CFD computations for the primary breakup of high-viscosity liquids using an external mixing twin fluid nozzle. In a first step experiments were performed with a Newtonian glycerol-water-mixture featuring a liquid viscosity of 400 mPas. Jet breakup was investigated using a high speed camera as well as PIV and LDA-System for a detailed investigation of the flow field. In a second step the experimental results serve as reference data to assess the accuracy of CFD computations. Compressible large eddy simulations (LES) were performed to capture the morphology of the primary breakup as well as the important flow field characteristics. A Volume of Fluid (VOF) approach was used to track the unsteady evolution and breakup of the liquid jet. Comparison of experimental and numerical results showed good agreement with respect to breakup frequency, velocity fields and morphology.     

On the instability of microjets

The instability of an axisymmetric viscous liquid jet in a gas or in a vacuum is examined using the interface formation theory. This model allows for variable surface tension at constant temperature, generalising the classical continuum formulation by using irreversible thermodynamics. Steady-state solutions are determined and found to be unstable to a travelling wave that propagates down the liquid jet, causing the jet to break-up into drops. The linear instability results are compared to those of the classical formulation. These are especially found to differ when the jets are on the micron scale. This will give rise to significantly revised predictions in some parameter ranges for the break-up length and droplet sizes produced by microjets. Comparisons with molecular dynamics simulations are also presented, with encouraging results. Finally, the dependence of the results on the initial conditions is discussed. PACS 68.03.Cd     

Simulation of electrically driven jet using Chebyshev collocation method

The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations (PDEs). Following the method of lines, the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations (DAEs). By differentiating constrains in DAEs twice, the system is transformed into a set of ordinary differential equations (ODEs) with invariants. Then the implicit differential equations solver “ddaskr” is used to solve the ODEs and post-stabilization is executed at the end of each step. Results show the distributions of radius, linear charge density, stretching ratio and also the horizontal velocity at a time point. Meanwhile, the spiral and expanding projections to X-Y plane of the jet centerline suggest the occurring of bending instability.     

A computational analysis of the hydrodynamic instability of a liquid jet focused into a converging microchannel

The instability of a focused liquid jet is studied by semi-analytical methods and by methods of computational fluid dynamics. The semi-analytical approach relies on earlier work on the instability of an extending liquid thread and is based on the Stokes flow regime and small-amplitude perturbations. The evolution of different excitation modes is evaluated and compared. Through hydrodynamic focusing and the corresponding extensional flow an initially stable mode may become unstable and it depends on the position away from the inlet which mode is to be regarded as the most unstable one. When plotting a hypothetical jet decay length against the excitation wave number, a comparatively broad minimum is exhibited. The CFD simulations based on the volume-of-fluid method show that the jet may break up either in the conical focusing zone or in the attached capillary, depending on the flow velocity. When the deformation of the jet surface reaches a certain amplitude, the jet assumes a “beads-on-a-string” structure instead of a shape derived from a harmonic perturbation. A jet decay within the capillary produces elongated droplets with cusped ends. When comparing the results of the CFD and the semi-analytical model, it turns out that the CFD simulations predict more stable jets with a larger decay length. An analysis of the flow velocity field shows that the increased stability might be due to the interaction of the jet with the channel walls.     

旋流喷嘴中空旋转射流近区域流动的研究

从理论上分析了旋流喷嘴喷出的中空射流近区域的液膜的运动,在只考虑液膜表面张力的作用下,应用质量守恒和动量定理,建立了描述液膜运动的非线性常微分（积分）方程组,该方程组可以用数值方法方便地求解,结果表明,液体离开旋流喷嘴后在自由空间形成的液膜呈葫芦形状,其速度和液膜厚度等都周期性地变化。本结果是在液厝受拓动失称碎成液滴前的最基本运动状态,可以在射流的近区域内实验观察到,也是进一步从理论液膜破碎雾化过     

Model validation image data for breakup of a liquid jet in crossflow: part I

We have applied three different imaging diagnostics: particle imaging velocimetry, high-speed shadowgraphy, and ballistic imaging, to observe the breakup of a liquid jet in a crossflow of air under a variety of conditions. The experimental system was designed to provide well-controlled conditions with minimal amounts of turbulence in the liquid jet and the gaseous crossflow. A variety of Weber numbers and momentum flux ratios were studied in order to provide a sizable data set for the validation of computational models. This paper briefly describes the three spray imaging techniques, outlines the results obtained to-date, and tabulates image statistics for each of ten spray conditions at varying distances from the spray nozzle orifice. The end result is a first installment in what will become a comprehensive model validation data set for jets in crossflow for use by computational fluid dynamics modelers.     

金属射流失稳断裂的理论分析

基于Hamilton原理,提出一个包含射流强度、剪切、应变率效应、动力学黏性、表面张力和速度梯度等多因素耦合的金属射流拉伸运动方程,具体分析了各种失稳因素,并由数值解定量给出其影响大小,以及最不稳定波长与初始应变率乘积\lambda_{m}\dot{\varepsilon}_{0} 值的变化范围;给出了射流断裂的时间判据和近似理论公式,计算得到的 t_{b}-\dot{\varepsilon}_{0}曲线与射流实验点、Chou\&Carleone拟合公式三者符合较好.