微型管中液滴流动的三维数值模拟

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.     

Direct numerical simulation of a freely decaying turbulent interfacial flow

Whereas Large Eddy Simulation (LES) of single-phase flows is already widely used in the CFD world, even for industrial applications, LES of two-phase interfacial flows, i.e. two-phase flows where an interface separates liquid and gas phases, still remains a challenging task. The main issue is the development of subgrid scale models well suited for two-phase interfacial flows. The aim of this work is to generate a detailed data base from direct numerical simulation (DNS) of two-phase interfacial flows in order to clearly understand interactions between small turbulent scales and the interface separating the two phases. This work is a first contribution in the study of the interface/turbulence interaction in the configuration where the interface is widely deformed and where both phases are resolved by DNS. To do this, the interaction between an initially plane interface and a freely decaying homogeneous isotropic turbulence (HIT) is studied. The densities and viscosities are the same for both phases in order to focus on the effect of the surface tension coefficient. Comparisons with existing theories built on wall-bounded or free-surface turbulence are carried out. To understand energy transfers between the interfacial energy and the turbulent one, PDFs of the droplet sizes distribution are calculated. An energy budget is carried out and turbulent statistics are performed including the distance to the interface as a parameter. A spectral analysis is achieved to highlight the energy transfer between turbulent scales of different sizes. The originality of this work is the study of the interface/turbulence interactions in the case of a widely deformed interface evolving in a turbulent flow.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.     

Numerical simulation of droplet ejection of thermal inkjet printheads

In this study, we present a method to predict the droplet ejection in thermal inkjet printheads including the growth and collapse of a vapor bubble and refill of the firing chamber. The three‐dimensional Navier–Stokes equations are solved using a finite‐volume approach with a fixed Cartesian mesh. The piecewise‐linear interface calculation‐based volume‐of‐fluid method is employed to track and reconstruct the ink–air interface. A geometrical computation based on Lagrangian advection is used to compute the mass flux and advance the interface. A simple and efficient model for the bubble dynamics is employed to model the effect of ink vapor on the adjacent ink liquid. To solve the surface tension‐dominated flow accurately, a hierarchical curvature‐estimation method is proposed to adapt to the local grid resolution. The numerical methods mentioned earlier have been implemented in an internal simulation code, CFD3. The numerical examples presented in the study show good performance of CFD3 in prediction of surface tension‐dominated free‐surface flows, for example, droplet ejection in thermal inkjet printing. Currently, CFD3 is used extensively for printhead development within Hewlett‐Packard. Copyright © 2015 John Wiley & Sons, Ltd.     

Fundamental equations of turbulent two-phase flow

A new set of Reynolds equations for predicting turbulent two-phase flows has been developed by means of Reynolds averaging method on the unsteady laminar equations of two-phase flow. These equations involve average terms of products of turbulent fluctuations in some physical parameters in a large degree. The interaction forces between two phases, the pressures for dispersed phase, extra stresses except for pressure and the expressions for energy interchange between two phases have been discussed.     

Turbulent forced convective heat transfer in two-phase evaporating droplet flow through a vertical pipe

A physical model was developed to study heat transfer in turbulent dispersed flow at very high vapor quality in a vertical pipe by numerically solving the coupling governing differential equations for both phases. Major heat transfer mechanisms included in the model were the thermal nonequilibrium effects, droplet vaporization, droplet deposition on the duct wall and thermal radiative transfer. The predicted results indicated that vapor superheating is dominant for the cases with high wall superheat, otherwise droplet vaporization dominates the energy transport processes. Heat transfer during the droplet-wall interaction only exists at low wall superheat but in small amounts.     

油-水两相湍浮力回流双流体模型

在自然界和工程技术的许多领域,常遇到这样一类物理性质相差悬殊的两相复杂湍流,其特点是流场中包含有回流和因两相间的密度差而产生的浮力,在一定条件下,流场的密度分布会发生突变,使数学模拟和数值计算的难度大大增加。本文把研究精细的油污染预报模型作为基本目标,广泛地涉及了两相湍流精细模拟的理论和方法。用Eulerian坐标系中多流体模型统一描述油和水两相各自的运动,并分别对油和水本身的湍流输运规律以及相间相互作用规律进行模拟,建立了油-水两相湍浮力回流双流体模型及相应的数值计算方法。选定了包含有浮力和回流的两相复杂湍流作为模拟对象,对模型进行了数值验证,并与实测资料作了对比。然后,对油-水两相湍流进行了预报。结果表明,模型的模拟效果非常满意。     

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.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.