液滴对爆炸冲击波的衰减作用

为分析液滴对舰船舱内爆炸冲击波的耗散与衰减作用,通过有限元分析方法,建立冲击波作用于不同尺寸单个液滴和多排液滴的模型,分析冲击波与单个及多个液滴的作用过程及液滴形态变化,对冲击波衰减规律进行分析总结。得到结论如下:单个液滴模型中,小液滴破碎更迅速,破碎的规律性强;大液滴抛撒现象发生较早,抛撒出的小液滴数目多,但整体变化规律性偏差;不同尺寸单个液滴对冲击波有一定的衰减作用,衰减率随液滴尺寸增大而增大,线性规律较明显;成排液滴对冲击波有明显的衰减作用,相同液滴密度下衰减率随着液滴数量的增多而增大,呈现明显的线性特性。     

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 m and on the order of 10¹² particles/m³, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.     

Attenuation of a shock wave passing through a cloud of water droplets

The mitigation of a planar shock wave caused by a cloud of calibrated water droplets was studied both experimentally and numerically. Experiments were carried out, with different shock wave Mach numbers ranging from 1.1 to 1.8, in a vertical shock tube coupled with a droplet generator which produced a well-characterized cloud of droplets of 120, 250 and 500 μm in diameter. By exploiting such an experimental set-up, we successfully measured the attenuation of a normal shock wave when passing through the water droplet cloud. This series of experiments allowed to identify the main parameters of this investigation and a clear dependence between the attenuation of the shock wave and terms governing the regimes of droplet breakup has been found. On the other hand, to support this experimental approach, 1D unsteady calculations were performed in similar configurations. Although the mathematical model based on an Eulerian/Eulerian approach was actually incomplete, the first comparisons between the experiments and the simulations were rather interesting and pointed out the need to improve the physical model, by taking into account the fragmentation and the vaporization of the droplets submitted to the shock wave as well as the size distribution of the water spray.     

Study of the shock-induced acceleration of hexane droplets

An experimental study of the interaction of a shock wave with a hexane droplet is presented. The main goal of the experiments was to record images of the process and measure basic parameters describing movement, dispersion and evaporation of the droplets engulfed by a shock wave propagating in air. A shock tube with a visualization section was used for this research. Photography of the process allowed one to measure the positions, velocities and sizes of mist clouds created by the interaction processes. Analysis of the pictures shows that there is no qualitative difference between cases for different size droplets, but shock Mach number had a significant effect on the process. Quantitative analysis shows that under certain conditions, a catastrophic breakup mechanism of dispersion occurred. The droplets are shattered into a mist cloud before they achieve mechanical equilibrium with the surrounding gas. The approximate time for the complete dispersion and acceleration of the fuel droplet varies from 300 to 500 μs, and depends both on the droplet diameter and shock velocity. The dispersion time is controlled principally by the droplet diameter, and to a lesser extent, the shock Mach number. This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

液滴在激波冲击下的破裂过程

对液滴在入射激波作用下的变形破碎过程进行了实验研究和数值模拟,得知数值模拟结果与实验结果基本吻合,以及在什么情况下两者出现分歧。结果显示,液滴在激波的作用下要经历从压缩变形、RM不稳定性变形、细小液雾剥离到全部雾化破碎等过程。结果还表明,不同液滴直径、入射激波马赫数和液滴介质等参数下的液滴变形破碎的发展趋势是一致的,而其发展速度明显则不同。其中Weber数的增加加速了液滴的破碎,而Ohnesorge数和黏性的增加则抑制了液滴的破碎。     

竖直振动无黏液滴的法拉第不稳定性分析

由于外部周期性的振动而在液滴表面产生的Faraday不稳定效应广泛存在于超声雾化、喷涂加工等应用中,对Faraday不稳定性进行分析对研究振动液滴的表面动力学有着重要意义.本文将Faraday不稳定性问题从径向振动拓展到竖直振动,研究了竖直振动无黏液滴表面波的不稳定性.竖直方向的振动使得液滴动量方程为含有空间相关项和时...     

Modeling of droplet collision-induced breakup process

The present article proposes a new droplet collision model considering droplet collision-induced breakup process with the formation of satellite droplets. The new model consists of several equations to investigate the post-collision characteristics of colliding droplets and satellite droplets. These equations are derived from the conservations of droplet mass, momentum, and energy between before and after collision, and make it possible to predict the number of satellite droplets, and the droplet size and velocity in the analytical way. To validate the new collision model, numerical calculations are performed and their results are compared with experimental data published earlier for binary collision of water droplets. It is found from the results that the new model shows good agreement with experimental data for the number of satellite droplets. It can be also shown that the predicted mean diameter by the new model decrease with increasing the Weber number because of the collision-induced breakup, whereas the O’Rourke model fails to predict the size reduction via the binary droplet collision.     

Shock wave structure in a mixture of gas,vapour and droplets

The structure of the relaxation zone behind a shock wave of moderate strength in a mixture of gas, vapour and droplets is analysed. A model is presented for shock induced evaporation, which is based on wet-bulb equilibrium and on the absence of relative motion between droplets and gas. Experimental and numerical data on heterogeneous condensation induced by an unsteady rarefaction wave and on re-evaporation due to shock wave passage are reported for a mixture of water vapour, nitrogen gas and condensation nuclei. Pressure, temperature, saturation ratio and droplet size are experimentally obtained and are very well predicted by a numerical simulation based on the non-linear quasisteady wet-bulb model for phase transition, as well for the expansion wave as for the shock wave. During expansion, droplet number density decays much faster than predicted, which is not yet satisfactorily explained. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5×10^–3 to 0.2, corresponding to shock Mach numbers of 1.2 to 1.9. The evaporation times are well predicted by the theoretical model. No evidence is found for droplet break-up for Weber numbers up to 13, and droplet radii of the order of 1m.On leave at Institute of Fluid Science, Shock Wave Research Center, Tohoku University, Sendai 980, JapanThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

平面激波冲击并排液滴的三维数值模拟研究

采用三维守恒清晰界面数值方法, 研究平面激波冲击并排液滴的动力学过程. 研究的焦点在于激波接触液滴后的复杂波系结构生成, 以及并排液滴相互耦合作用诱导的单个液滴非对称界面演化. 首先, 分析并排液滴之间界面通道内的波系结构发展, 发现在冲击初期由于反射激波相交而形成新的反射激波以及马赫杆; 这些流动现象与液滴另外一侧 (非通道侧) 由激波反射所形成的弯曲波阵面截然不同, 而且所导致的液滴横向两侧流场差异是中后期冲击过程液滴两侧界面非对称演化的主要原因. 其次, 研究冲击中期时, 特别是入射激波已运动至液滴下游并远离并排液滴, 界面形态的演化过程和规律, 揭示通道下游出口处由于气流膨胀导致的界面闭合、以及随后气流阻塞导致的界面破碎等新的流动现象. 最后, 研究液滴间距对并排液滴相互作用的影响规律, 发现液滴间距大小与通道内压力峰值具有明显的关联关系. 研究表明, 更小的液滴间距不仅带来更大的压力峰值, 而且使得峰值出现的时间更早.      

煤油液滴直径对两相旋转爆轰发动机流场的影响

为探究煤油液滴不同初始直径对气液两相旋转爆轰发动机流场的影响,假设初始注入的煤油液滴具有均匀直径,考虑雾化破碎、蒸发等过程,建立了非定常两相爆轰的Eulerian-Lagrangian模型,进行了液态煤油/高温空气爆轰的非预混二维数值模拟。结果表明：在初始液滴直径为1～70μm的工况范围,燃烧室内均形成了单个稳定传播的旋转爆轰波;全局当量比为1时,爆轰波前的空气区域大于液滴煤油的蒸气区域,导致波前燃料空气混合不均匀,波前均存在富油区和贫油区,两相速度差导致分离出的空气形成低温条带;当煤油液滴的初始直径较小时,波前的反应物混合过程主要受蒸发的影响,爆轰波可稳定传播;当直径减小至1μm时,煤油液滴在入口处即蒸发,旋转爆轰波表现为气相传播的特性,爆轰波结构平整;当煤油液滴的初始直径较大时,波前的反应物混合过程主要受液滴破碎的影响;对于相同的燃料质量流量,在不同初始煤油液滴直径工况下,煤油液滴最大的停留时间均占爆轰波传播时间尺度的80%以上;爆轰波前燃料预蒸发为气相的占比越高,爆轰波的传播速度越高;初始液滴直径为10～70μm的工况范围内,爆轰波的速度随初始直径的增大先升高后降低。     

A new predictive model for fragmenting and non-fragmenting binary droplet collisions

A new predictive model for collisional interactions between liquid droplets, which is valid for moderate to high Weber numbers (>40), has been developed and validated. Four possible collision outcomes, viz., bouncing, coalescence, reflexive separation and stretching separation, are considered. Fragmentations in stretching and reflexive separations are modeled by assuming that the interacting droplets form an elongating ligament that either breaks up by capillary wave instability, or retracts to form a single satellite droplet. The outcome of a collision, number of satellites formed from separation processes and the post-collision characteristics such as velocity and drop-size are compared with available experimental data. The comparisons include colliding mono- and poly-disperse streams of droplets of different fuels under atmospheric conditions, and the results agree reasonably well.     

Impaction of spray droplets on leaves: influence of formulation and leaf character on shatter,bounce and adhesion

This paper combines experimental data with simple mathematical models to investigate the influence of spray formulation type and leaf character (wettability) on shatter, bounce and adhesion of droplets impacting with cotton, rice and wheat leaves. Impaction criteria that allow for different angles of the leaf surface and the droplet impact trajectory are presented; their predictions are based on whether combinations of droplet size and velocity lie above or below bounce and shatter boundaries. In the experimental component, real leaves are used, with all their inherent natural variability. Further, commercial agricultural spray nozzles are employed, resulting in a range of droplet characteristics. Given this natural variability, there is broad agreement between the data and predictions. As predicted, the shatter of droplets was found to increase as droplet size and velocity increased, and the surface became harder to wet. Bouncing of droplets occurred most frequently on hard-to-wet surfaces with high-surface-tension mixtures. On the other hand, a number of small droplets with low impact velocity were observed to bounce when predicted to lie well within the adhering regime. We believe this discrepancy between the predictions and experimental data could be due to air layer effects that were not taken into account in the current bounce equations. Other discrepancies between experiment and theory are thought to be due to the current assumption of a dry impact surface, whereas, in practice, the leaf surfaces became increasingly covered with fluid throughout the spray test runs.     

Shock wave induced evaporation of water droplets in a gas-droplet mixture

A model is presented for the droplet evaporation process induced by a shock wave propagating in a fog. The model is based on the existence of a quasi-steady wet bulb state of the droplets during evaporation. It is shown that for moderate shock strength, Ma = < 2, and droplet radii in the range of 1–5 the, the major part of the evaporation process is governed by a balance between heat conduction and vapour diffusion. The formation of a fog by means of an unsteady adiabatic expansion of humid nitrogen is described. Experimental results of shock induced evaporation are shown for shock Mach numbers from 1.2 to 2.1, droplet mass fraction of 5 · 10^-3, and initial droplet radii of 1–1.4 m. The expected linear relation between droplet radius squared and time during evaporation is observed. Characteristic evaporation times appear to be strongly dependent on shock strength. A variation of about two decades, predicted by theory, was experimentally observed for the Mach number range studied.     

Combustion of a liquid fuel droplet in the process of non-equilibrium surface evaporation

As a rule, mathematical combustion and evaporation models are proposed for a single droplet under the assumption that the phase transition is in equilibrium. From theoretical and experimental results it follows that this assumption is valid in the case of large droplets and flat surfaces, but leads to essential errors in the case of small droplets. The aim of this paper is to develop a mathematical model for the droplet combustion with consideration of non-equilibrium evaporation and to evaluate the effect of the non-equilibrium condition imposed on the phase transition at the interface.     

Numerical study of global rainbow technique: sensitivity to non-sphericity of droplets

The measurement of droplet temperature and size distribution in sprays is a difficult task. To reach this aim, the global rainbow technique (GRT) has been developed on the assumption that the synthetic rainbow created by a large number of droplets is insensitive to the non-sphericity of droplets if the droplets’ orientations were sufficiently random. In order to test this assumption, numerical as well as experimental analyses of GRT are carried out by our team. As a companion to the work done in experiments, the objective of this work is to quantify the sensitivity of the GRT to the non-sphericity of droplets from a numerical aspect. Light scattering properties around the rainbow angle are investigated by using the Null-field method within a T-matrix formulation, both for a single spheroid in an arbitrary orientation and for an ensemble of spheroids in random orientations illuminated by a plane wave. Refractive index and size distribution of droplets are extracted from simulated global rainbow signals so as to quantify the sensitivity of the GRT to the non-sphericity. Exemplifying results are compiled and presented. Additionally, comparisons between the Null-field method and the generalized Lorenz-Mie theory for spheroids are also provided in this paper.     

Droplet-based flows in serpentine microchannels: Chemical reactions and secondary flows

Mixing is an essential operation in many microfluidic devices. Droplet-based micromixers utilize droplets for mixing enhancement. In the present study, a novel three-dimensional simulation is conducted which has the ability to capture not only the mixing process, but also the chemical reactions inside liquid droplets. This two-phase model is used for simulating the reacting flow inside a serpentine microchannel and explores the effects of droplet size and reaction rate on the production and consumption of species in droplets. It is observed that the chemical reaction in each droplet, begins from its front area. Furthermore, it is shown that the production of species does not depend on water fraction (ratio of water flow rate to total flow rate) and for all droplet sizes, only depends on the reaction rate. Moreover, different transient generated vortices and secondary flows are studied in the presence and absence of droplets and explained in details based on the position of droplets. It is found that during the passage of droplets through a microchannel bend, the number of cross-sectional vortices changes and the velocity magnitude in these secondary flows increases dramatically.     

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。     

Numerical modeling and experimental measurements of water spray impact and transport over a cylinder

This study compares experimental measurements and numerical simulations of liquid droplets over heated (to a near surface temperature of 423 K) and unheated cylinders. The numerical model is based on an unsteady Reynolds-averaged Navier–Stokes (RANS) formulation using a stochastic separated flow (SSF) approach for the droplets that includes submodels for droplet dispersion, heat and mass transfer, and impact on a solid surface. The details of the droplet impact model are presented and the model is used to simulate water spray impingement on a cylinder. Computational results are compared with experimental measurements using phase Doppler interferometry (PDI). Overall, good agreement is observed between predictions and experimental measurements of droplet mean size and velocity downstream of the cylinder.     

Modeling of binary droplet collisions for application to inter-impingement sprays

In this paper, we focused on modeling the collision phenomenon between two liquid droplets for application in spray simulations. It has been known that the existing O’Rourke collision model widely used in CFD codes is inaccurate in determining collision outcomes and droplet behavior. In addition, since the collision probability of the model follows a statistical approach involving computational cell geometry, the prediction results should be strongly dependent on the cell size. As a result, to more accurately calculate droplet collisions, the technique for predicting the droplet velocity and its direction after collision must be extended for use in spray modeling. Further, it is also necessary to consider all the possible collision outcomes, such as bouncing, stretching separation, reflexive separation and coalescence. Therefore, this paper describes the appropriateness of a composite concept for modeling collision outcomes and the implementation of deterministic collision algorithms into a multidimensional CFD code for the calculation of post-collisional droplet movements. Furthermore, the existing model does not consider the formation of satellite droplets. For this reason, our present modeling concept includes a fragmenting droplet collision model. Using the present model, we have validated the collision interactions between liquid droplets under high Weber number conditions by comparing our calculations with experimental results from a binary droplet collision. This paper also deals with the application of the model to inter-impingement sprays by analyzing the atomization characteristics, such as mean droplet size and velocity, spray tip penetrations and spray-shapes of the impinging spray using the suggested collision algorithms and then comparing the results with available experimental data.     

Numerical simulations of drop size evolution in a horizontal pipeline

A population balance model using a standard method of moments ($S-\gamma$) in an Eulerian–Eulerian framework has been used for oil and brine two-phase flow simulations in pipelines. Results have been compared to both numerical and experimental data from the literature. The effects of the forces constituting the momentum transfer term at the interphase between droplets and the continuous phase (drag, lift, turbulent dispersion and virtual mass), turbulence modelling, break-up and coalescence parameters are analysed; they are shown to be important for droplet mean diameter evolution. It has been demonstrated that a correct combination of models and parameters improves (47% for the best case) simulated results when compared to experimental data. Interactions between the different components of the whole model are discussed and their corresponding effects on the droplet diameter predictions are explained. In particular, the addition of the lift force tends to push the droplet toward the walls of the computational domain where turbulence and shear stress are the strongest, therefore leading to an increased break-up rate. Based on the findings of this study, recommendations for further population balance-based modelling with a standard method of moments are provided.