液滴在气体介质中剪切破碎的数值模拟研究

液滴变形和破碎是燃料抛撒问题的重要过程。本文将VOF方法和标准k-ε湍流模型组合,建立了计算液滴在气流中变形破碎过程的数值方法。数值模拟了相关的实验,计算得到的液滴破碎过程与实验结果符合较好。在此基础上,分析了几个关键参数(Weber数、Ohnesorge数、液气密度比)对液滴破碎过程的影响。计算结果表明,Weber数对液滴变形破碎起促进作用,而Ohnesorge数和液气密度比起阻碍抑制作用。  

Rheological behavior of compatibilized and non-compatibilized PA6/EPM blends

The rheological properties of PA-6/EPM polymer blends, non-compatibilized and compatibilized with grafted ethylene propylene rubber (EPM-g-MA), have been investigated. Linear and non-linear (relaxation both in shear and extension) experiments were realized. Stress relaxation experiments coupled with scanning electron microscopy (SEM) analysis showed the existence of one relaxation time and non-deformed droplets for the immiscible blend, and two relaxation times and deformed droplets for the compatibilized ones, the second relaxation being more pronounced for higher compatibilizer contents. These results clearly indicate that, despite the high viscosity and elasticity ratios, if high amounts of compatibilizer are added to the blend, interfacial slip is suppressed and a high-enough adhesion between the phases is achieved for the high-viscosity dispersed phase to be deformed. Paper presented at the 3rd Annual European Rheology Conference, April 27–29, 2006, Crete, Greece  

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.  

Consistency issues of Lagrangian particle tracking applied to a spray jet in crossflow

Numerical simulations are performed for multiphase jets in crossflow. The flow solver uses an Eulerian/Lagrangian approach. Turbulence in the gas phase is modeled in the framework of large eddy simulation. The dispersed phase is handled using Lagrangian particle tracking. The model assumptions of solvers for Lagrangian particle tracking are critically assessed for typical flow conditions of spray jets in crossflow. The droplets are assumed to be spherical and isolated. It is shown that several model assumptions are apparently inconsistent in larger portions of the flow field. Firstly, average Weber numbers can be so large that the model assumption to regard droplets as spherical is questionable, not only near the nozzle, but also in the far-field. Secondly, the average droplet spacing can be so low that droplets directly interact with each other, again also in the far-field. Thirdly, the average Stokes numbers in the jet region can be so large that the phase coupling between the dispersed and continuous phase is weak. Some remedies to these deficiencies are proposed.  

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对于微型设备中的低雷诺数流动,毛细力和黏性力起主导作用.应用相场方法,引入自由能泛函,研究了二相流体在微型管中流动问题及表面浸润现象,并给出了微型管中二相流体的无量纲输运方程.针对方形微管道,利用差分法给出了输运方程的数值求解方法.最后,模拟了方形直管中的液滴流动和变形的过程,并给出了液滴前后压力差与其它主要物理参数之间的变化关系.结果表明,压力差随液滴半径增大而增加,而随毛细管系数的增大而减小.  

Numerical prediction of droplet dynamics in turbulent flow,using the level set method

In the present article, the droplet dynamics in turbulent flow is numerically predicted. The modelling is based on an interfacial marker-level set (IMLS) method, coupled with the Reynolds-averaged Navier–Stokes (RANS) equations to predict the dynamics of turbulent two-phase flow. The governing equations for time-dependent, two-dimensional and incompressible two-phase flow are described in both phases and solved separately using a control volume approach on structured cell-centred collocated grids. The topological changes of the interface are predicted by applying the level set approach. The kinematic and dynamic conditions on the interface separating the two phases are satisfied. The numerical method proposed is validated against a well-known computational fluid dynamics problem. Further, the deformation and breakup of a single droplet either suddenly moved in air or exposed to turbulent stream are numerically investigated. In general, the developed numerical method demonstrates remarkable capability in predicting the characteristics of complex turbulent two-phase flows.  

Effect of confinement on droplet deformation in shear flow

The dynamics of a single droplet under shear flow between two parallel plates is investigated by using the immersed boundary method. The immersed boundary method is appropriate for simulating the drop-ambient fluid interface. We apply a volume-conserving method using the normal vector of the surface to prevent mass loss of the droplet. In addition, we present a surface remeshing algorithm to cope with the distortion of droplet interface points caused by the shear flow. This mesh quality improvement in conjunction with the volume-conserving algorithm is particularly essential and critical for long time evolutions. We study the effect of wall confinement on the droplet dynamics. Numerical simulations show good agreement with previous experimental results and theoretical models.  

Non‐conforming finite elements for axisymmetric charged droplet deformation dynamics and Coulomb explosions

The deformations of both electrically charged and uncharged incompressible axisymmetric Newtonian viscous liquid droplets acting under the effects of surface tension (but not gravity) are studied using a non‐conforming, discontinuous Galerkin finite element procedure with moving meshes. The full Navier–Stokes equations are discretized and solved in an Eulerian manner with a simple predictor–corrector Lagrangian updating of the free boundary location coincident with the droplet surface at each solution iteration. By using linear Crouzeix–Raviart basis functions for the velocity and piecewise constant pressures, results are presented both for the simple (oscillatory) relaxation of elongated electrically charged/uncharged droplets to a sphere and for the deformation to steady state/Coulomb explosions of initially slightly oblate/prolate spheroidal droplets charged beyond/to the Rayleigh limit. Copyright © 2012 John Wiley & Sons, Ltd.  

FEM‐BEM coupling for the exterior Stokes problem with non‐conforming finite elements and an application to small droplet deformation dynamics

A non‐conforming, discontinuous Galerkin finite element–boundary element coupling procedure is presented for the exterior planar Stokes problem. The novel coupled formulation is developed using that for the conforming case as a guide to the introduction of extra mortar variables used to couple a discontinuous interior finite element solution with a continuous exterior boundary element solution. Convergence results for the new scheme are presented, for a range of different interior penalties, on computational domains discretized with regular structured meshes. To illustrate an application, the excitations required to model two‐phase droplet deformations in an extensional flow, under simple surface tension, with the new scheme are also presented. For a selection of different drop viscocities and exterior flows, with and without a rotational component, the progression to a steady‐state deformation of initially undeformed circular drops is calculated and the results compared with those from both a conforming FEM‐BEM equivalent scheme and from a small perturbation analysis where available. Copyright © 2011 John Wiley & Sons, Ltd.  

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

In this paper we present a three‐dimensional Navier–Stokes solver for incompressible two‐phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third‐order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second‐order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first‐order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three‐dimensional results with those of quasi‐two‐dimensional and two‐dimensional simulations. This comparison clearly shows the need for full three‐dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd.