Predictions of the gas–liquid flow in wet electrostatic precipitators

Based on Computational Fluid Dynamics (CFD), the present paper aims to simulate several important phenomena in a wet type ESP from the liquid spray generation to gas-droplet flow in electric field. A single passage between the adjacent plates is considered for the simulation domain. Firstly, the electric field intensity and ion charge density are solved locally around a corona emitter of a barbed wire electrode, which are applied to the entire ESP using periodic conditions. Next, the Euler–Lagrange method is used to simulate the gas-droplet flow. Water droplets are tracked statistically along their trajectories, together with evaporation and particle charging. Finally, the deposition density on the plate is taken as the input for the liquid film model. The liquid film is simulated separately using the homogenous Eulerian approach in ANSYS-CFX. In the current case, since the free surface of the thin water film is difficult to resolve, a special method is devised to determine the film thickness.As parametric study, the variables considered include the nozzle pressure, initial spray spreading patterns (solid versus hollow spray) and plate wettability. The droplet emission rate and film thickness distribution are the results of interest. Main findings: electric field has strong effect on the droplet trajectories. Hollow spray is preferred to solid spray for its lower droplet emission. The liquid film uniformity is sensitive to the plate wettability.     

Lagrangian and Eulerian models for simulating turbulent dispersion and coalescence of droplets within a spray

Lagrangian and Eulerian modelling approaches are compared for simulating turbulent dispersion and coalescence of droplets within a spray. Both models predict similar droplet dispersion rates and shifts in droplet size distribution due to coalescence within the spray, over a wide range of droplet and gas flows, and for sprays with different droplet-size distributions at the nozzle exit. The computer time required for simulating coalescence within a steady axisymmetric spray is of a similar order of magnitude regardless of which formulation, Eulerian or Lagrangian, is adopted. However, the Lagrangian formulation is more practical in terms of the range of applicability and ease of implementation.     

Numerical modeling for compartment fire environment under a solid-cone water spray

A mathematical model was developed for simulating the fire environment of a compartment under the action of a solid-cone water spray such as those discharged from a water mist fire suppression system. A smoke layer was induced by a fire in the compartment. The solid-cone water spray was discharged to act on the smoke layer, but not on the burning object. Under this condition of having a stable smoke layer, the compartment was divided into three regions. Region 1 is the upper hot smoke layer, Region 2 is the lower cool air layer and Region 3 is the solid-cone spray. The effects on the smoke layer development due to spray-induced flow were considered on the basis of mass, momentum and heat conservation. Water droplets of the solid-cone spray were divided into four typical classes based on the droplet distribution function.

The parameters including the smoke layer interface height, smoke temperature and air temperature, smoke flow rate through the opening and oxygen concentration in the air layer were investigated under various heat release rates, water application rates and volume mean diameters of the solid-cone spray. Effective hot gas entrainment and water vapor production suggested that the water spray should contain a variety of droplet size. In this way, a compartment fire can be controlled effectively through indirect interaction such as oxygen concentration depletion.     

Numerical study on the effect of the injection pressure on spray penetration length

This paper investigates the fuel spray behavior and variation of the spray characteristics under different injection pressures in internal combustion engines. In diesel engines the fuel spray is affected by the cavitation phenomenon which occurs in the injector orifice. The cavitation is one of the important phenomena which has a significant effect on the fuel spray characteristics. In this paper, for a specified geometry of the nozzle and the combustion chamber, the effect of the cavitation phenomenon on the spray characteristics, i.e. spray penetration length, the Sauter main diameter and evaporation are studied numerically for different values of the injection pressures. High injection pressure causes high velocity of the fuel in the injector orifice which leads to an effective atomization process with small and dispersed fuel droplets. The fluid flow equations are calculated in the combustion chamber to obtain the spray model. Since it is known that, high injection pressure together with low discharge pressure leads to creation of cavitation phenomenon inside the injector orifice, then for having cavitation phenomenon inside the injector orifice and consequently for investigating the cavitation phenomenon effects on the spray characteristics, the injection pressure values of 10–150 MPa are considered while the discharge pressure remains constant. The injector and combustion chamber are simulated in separated regions and the results of the outlet of the nozzle are used as the boundary conditions for solving the fuel flow inside the combustion chamber to achieve the spray simulation. The results of this study show that by increasing the injection pressure, the value of the spray penetration length increases and the Sauter main diameter decreases for constant discharge pressure. The Hydraulic Flip phenomenon occurs after the injection pressure of 120 MPa on the base of the results of this work.     

Theoretical analysis of Rayleigh–Taylor instability on a spherical droplet in a gas stream

A linear analysis of the Rayleigh–Taylor (R–T) instability on a spherical viscous liquid droplet in a gas stream is presented. Different from the most previous studies in which the external acceleration is usually assumed to be radial, the present study considers a unidirectional acceleration acting on a spherical droplet with arbitrary initial disturbances and therefore can provide insights into the influence of R–T instability on the atomization of spherical droplets. A general recursion relation coupling different spherical modes is derived and two physically prevalent limiting cases are discussed. In the limiting case of inviscid droplet, the critical Bond numbers to excite the instability and the growth rates for a given Bond number are obtained by solving two eigenvalue problems. In the limiting case of large droplet acceleration, different spherical modes are asymptotically decoupled and an explicit dispersion relation is derived. For given Bond number and Ohnesorge numbers, the critical size of stable droplet, the most-unstable mode and its corresponding growth rate are determined theoretically.     

The simulation of micro droplet behavior of molten lead-free solder in inkjet printing process and its experimental validation

Micro droplets of molten lead-free solder were ejected at 230 °C using a piezoelectric inkjet printing process. The effect of the micro droplet formation of molten lead-free solder was investigated on the pulse time of the waveform. In this study, a numerical system for simulating the shape evolution of micro droplet of molten lead-free solder in the inkjet printing process was developed based on a solution algorithm (SOLA) scheme for the solution of velocity and pressure fields. It is coupled with the volume-of-fluid (VOF) and piecewise-linear interface construction (PLIC) techniques for the transport of mass and construction of the interface. For the treatment of surface tension effects, a CSF (continuum surface force) model is employed. The simulation results were validated with experimental observations. The numerical result was used to understand the mechanisms of the extrusion of the liquid column, the contraction of the liquid thread, and the pinch-off of the liquid thread at the nozzle exit.     

液滴碰撞和聚合模型研究

建立了描述液滴碰撞和聚合过程的数学模型,设计了一种高效的计算液滴碰撞对搜索算法,并在已有研究成果的基础上对液滴碰撞的结果做了进一步的发展．借助平滑粒子流体动力学方法两种实现方式各自的优点,将液滴间的相互作用局限在其周围一定数目的液滴之间,并采用积分核函数定义了液滴间碰撞的概率,通过数值模拟探讨了模型的特性．结果表明,所建模型对所采用的计算网格没有明显的依赖性,具有较高的计算精度和计算效率,不但能很好地维持系统动量的守恒性,而且对液滴初始尺寸分布没有明显的依赖性．     

Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

Numerical Computation of Heat and Mass Transfer in Fluidized Beds with Liquid Injection

The goal of this work is the simulation of concentration and temperature distributions insides fluidized bed with a uniform liquid distribution. Further, a physically based 2D model is developed for the heat and mass transfer processes in fluidized beds with a spray nozzle. The model is a coupled and semi-linear system of convection-reaction-diffusion equations. We considered the numerical solution of these semi-linear partial differential equations with discrete boundary conditions using linear finite elements on an adaptive triangular grid in space and implicit methods in time. We present calculations using, semi implicit and implicit methods in time, and different solvers for solving the linear systems. The complex correlations of mass and liquid flow rates, mass transfer, heat transfer, drying, and transient two dimensional air humidity, air temperature, degree of wetness, liquid film temperature and particle temperature were simulated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotor dynamics behavior of turbo-expander involving droplet impact

ABSTRACT

This paper dedicates on the rotor dynamics behaviour research on the turbo-expander rotor system involving droplet impact. A stochastic model based on Beta distribution and Bernoulli distribution of droplet generation is established and the formulations of droplet impact forces are deduced, which is applied on the rotor dynamics equations of the tilting pad bearing supported turbo-expander considering the temperature gradient for a further analysis. A time domain research is carried out and a conclusion that continuously droplet impact will perturb the steady vibration of the turbo-expander rotor system is obtained. Monte Carlo method is implemented for a statistics dynamics research and the results suggests that in the design of expander impellers, in order to decrease the uncertainty brought by droplet impact, the number of channels should be as few as possible, the droplet impact should be controlled to occur uniformly, and the collision, entrainment of the primary droplets and the stripping of the liquid film on the blade should be strictly restrained.     

Drop formation from a wettable nozzle

The process of drop formation from a nozzle can be seen in many natural systems and engineering applications. However, previous research focuses on the pinch-off mechanism of drops from a non-wettable nozzle. Here we investigate the formation of a liquid droplet from a wettable nozzle. In the experiments, drops forming from a wettable nozzle initially climb the outer walls of the nozzle due to surface tension. Then, when the weight of the drops gradually increases, they eventually fall due to gravity. By changing the parameters such as the nozzle size and fluid flow rate, we have observed different behaviors of the droplets. Such oscillatory behavior is characterized by an equation that consists of capillary force, viscous drag, and gravity. Two asymptotic solutions in the initial and later stages of drop formation are obtained and show good agreement with the experimental observations.     

A probabilistic model of thermal explosion in polydisperse fuel spray

This work is concerned with an analysis of polydisperse spray droplets distribution on the thermal explosion processes. In many engineering applications it is usual to relate to the practical polydisperse spray as a monodisperse spray. The Sauter Mean Diameter (SMD) and its variations are frequently used for this purpose [13]. The SMD and its modifications depend only on “integral” characterization of polydisperse sprays and can be the same for very different types of polydisperse spray distributions.The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF) that corresponds to the initial distribution of fuel droplets size. This approximation of polydisperse spray is more accurate than the traditional ‘parcel’ approximation and permits an analytical treatment of the simplified model. Since the system of the governing equations represents a multi-scale problem, the method of invariant (integral) manifolds is applied.An explicit expression of the critical condition for thermal explosion limit is derived analytically. Numerical simulations demonstrate an essential dependence of these thermal explosion conditions on the PDF type and represent a natural generalization of the thermal explosion conditions of the classical Semenov theory.     

Lattice Boltzmann Study on the Motion of Dual Droplets in Microchannels With Contact Angle Hysteresis北大核心CSCD

接触角滞后表现为流体在非理想固体表面上运动时前进接触角和后退接触角不同,是两相流体在润湿表面上流动的重要现象.该文采用改进的伪势格子Boltzmann(LB)多组分模型,并与几何润湿边界条件相结合,研究了两个液滴在具有接触角滞后性微通道表面上的运动行为,主要研究了通道内特征数、通道表面性质以及液滴初始参数的影响.研究结果表明：毛细数的增大有助于液滴的移动,然而并不利于液滴的排出,且毛细数的增加对上游液滴的影响大于其对下游液滴的影响;另一方面,接触角滞后性窗口越大,液滴运动和形变更迟缓,但形变程度更明显,两液滴更早地发生合并,但更晚地排出管道;液滴间距的增加使液滴的运动行为在不同阶段表现为不同的模式,但都导致通道中残留小液滴,使得液滴排出通道的时间增加.研究结果还表明：上游液滴和下游液滴的相对尺寸差距越大,越不利于液滴排出管道.     

Singularly perturbed homotopy analysis method

In this paper we combined the homotopy analysis method (HAM) and the method of integral manifold (MIM) to investigate the problem of thermal explosion in two-phases polydisperse combustible mixtures of gas with fuel droplets. The size distribution of the fuel droplets is assumed to be continuous in the form of an exponential distribution and is found from the solution of the kinetic equation for the probability density function. The system of the polydisperse fuel spray takes into account the effects of the thermal radiation and convection. By applying the HAM and the MIM, we derived an analytical solution of the system and we compared our results with the numerical solutions.     

Numerical Investigation of Dense Turbulent Sprays with an Eulerian Approach and DQMOM

The spray characteristics of the injected liquid fuel predominantly influence the combustion and emissions in IC-engines and gas turbines. This is predetermined by a dense spray region in which droplet-droplet interaction processes play a significant role. In order to accurately describe and control the dense spray behavior in modern engines, an appropriate numerical modeling tool is needed. This contribution aims at including droplet-droplet interactions into an Eulerian approach coupled to the Direct Quadrature Method of Moments (DQMOM) in order to describe evaporating droplet polydispersity and analyze dense turbulent sprays phenomena. Among the advantages of the Eulerian approach are a lower computational cost through optimal parallel computing and a straightforward liquid-gas phase coupling. To assess the designed tool, numerical results are compared to Phase Doppler Anemometry (PDA) measurements of a hollow-cone water spray. The experiment provides comprehensive validation data that include gas velocities, droplet size distribution, droplet mass fluxes and droplet velocities. Turbulence is captured by two different k-ε based models. Preliminary results show that the designed tool is able to capture the process under study in a satisfactory way. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

压力旋流喷雾理论与喷雾粒度特性的探讨

本文试图以实验观察的压力旋流喷雾工况为依据,提出关于压力旋流喷射雾化机理的模型设想——压力旋流喷射锥膜雾化理论。在一些基本假定条件下,导出压力旋流喷雾粒度特性关系式:(d_z的单位为米)

上述理论与所导出的关系式基本上同实际喷雾工况相符合,依此能对实际的喷雾工况进行较好的解释。本文还对国内电厂使用的一些油喷雾咀的喷雾粒度特性进行理论计算,以同实验数相对照,结果表明理论对实践有一定的价值,可供有关方面参考。     

Droplet solutions in the diblock copolymer problem with skewed monomer composition

A droplet solution characterizes the lamellar phase of a diblock copolymer when the two composing monomers maintain a skewed ratio. We study the threshold case where the free energy of a droplet solution is comparable to the free energy of the constant solution. Using a Lyapunov-Schmidt reduction approach, adapted to calculus of variations, we prove the existence of a free energy local minimizer with a given number of droplets. Also determined are the free energy, the droplet location, and the droplet size. Supported in part by a Direct Grant from CUHK and an earmarked Grant of RGC of Hong Kong.     

Unsteady Cavitation in Injection Nozzles ‐ Dynamic Interaction of Internal Flow and Jet Formation ‐

This actual extension of our previous work demonstrates the strong interaction of cavitation inside injection nozzles with the external jet flow. Due to the high sensitivity of cavitation on the imposed initial and boundary conditions, simulations with restriction to the internal nozzle flow are qualitatively and quantitatively incorrect. Results of this very first simulations indicate the potential of cavitation for enhancement of atomization and spray formation.     

Computation of the Coupled Dynamics of Fibers in a Spray

The PUR-fiber-spray molding technology is a manufacturing process which produces polyurethane-based (PUR) composites by spraying the matrix together with reinforcing fibers in a tool form or on a substrate. Thereby chopped fibers are laterally (sidewise) injected in the polyurethane-air spray cone for wetting before the entire composite is spread on the substrate, where it starts curing. To investigate and compute the fiber orientation and density distribution in the final composites manufactured by this process, a new approach simplifying the multiply coupled interaction of the three phases is presented in this paper. Hereby it is presumed that the final position and orientation of a fiber on a substrate results from its dynamics and coupled interactions with air, PUR-droplets and other fibers within the spray cone. Thus, a model of the process is built, that computes the transient behavior of the air-liquid droplets mixture by the CFD code ANSYS Fluent and its influence on the dynamics of the fibers by an extra code called FIDYST. For this multiphase problem two approaches are presented for the droplet-fiber coupling using a concept called “homogenization” of the liquid phase (droplets in the continuous phase). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)