The effect of volatility on the thermophoretic motion of a high-viscosity sphere in a binary gaseous mixture with regard for thermodiffusion and Stefan effects

The effect of the evaporation coefficient of a large aerosol particle on the velocity of its thermophoretic motion in a binary gaseous mixture is studied. The thermodiffusion of the mixture components and Stefan phenomena are taken into consideration. The results of this study are more general than those obtained previously. The conventional theories of thermophoresis, as applied to a volatile high-viscosity liquid drop, are extended for the cases of weak and moderately intense diffusive evaporation.     

Relationship between the diffusiophoresis rate, evaporation coefficient, and size of a large volatile drop

A new theory of diffusiophoresis of large volatile spherical aerosol drops that is an extension of investigations [1–8] is developed. The influence of the radius of the drop, the surface tension coefficient varying over the surface of the drop, the evaporation coefficient α of the liquid, and the flows inside the drop on the diffusiophoresis rate are taken into account. Expressions obtained allow for direct determination of the velocity of large individual aerosol drops in a binary gas mixture nonuniform in component concentration. It is shown that both the magnitude and the direction of the diffusiophoresis velocity depend on α and the size of the drop. It is assumed that the size of the drop varies but remains considerably greater than the mean free path of gas molecules.     

On the thermophoretic motion of a heated spherical drop in a viscous liquid

Expressions for the force and velocity of the thermophoretic motion of a spherical drop in a viscous liquid are derived for arbitrary temperature differences between the surface of the drop and regions away from it. The temperature dependence of the viscosity is taken into account in the form of an exponential-power series.     

翅片管气化器管内相变传热流动数值模拟

采用Fluent多相流混合物模型,通过用户自定义程序(UDF)实现了液氮相变模拟,模拟了不同进口流速对翅片管气化器管内流体换热量、压力降、含气率及汽化体积的影响,并分析了各参数随进口流速改变而变化的原因。由数值模拟可知,翅片管内流体进出口焓差、含气率及单位质量汽化体积随进口流速的增加而减少,而压力降和总换热量随进口流速的增加而增大,其中压力降增大的主要原因是由加速压降引起。     

Hydrodynamic interaction of two identical evaporating drops taking into account quadratic corrections in the Knudsen number

The effect of quadratic (in the Knudsen number) corrections to the motion of two interacting drops of the same size and of the same liquid due to their evaporation is estimated on the basis of an original modification of the approximate hydrodynamic reflection method and its generalization to thermal and diffusion fields. It is shown that the dependence of the velocity of thermophoretic motion of the drops on their spacing is virtually independent on the physicochemical characteristics of the liquid except for the evaporation heat. The conditions under which the corrections in the Knudsen number noticeably affect this dependence are determined.     

Large Eddy Simulation of a swirl stabilized spray flame

Large Eddy Simulations (LES) of kerosene spray combustion in an axial-swirl combustor have been carried out focusing on the effect of the evaporating droplets on the flame temperature and species concentrations. The LES-PDF methodology is used for both dispersed (liquid) and gas phases. The liquid phase is described using a Lagrangian formulation whilst an Eulerian approach is employed for the gas phase. The predictive capability of LES with sub-grid scale models for spray dispersion and evaporation is assessed placing emphasis on the effect of the unresolved velocity and temperature fields on the droplet evaporation rate. The results of the fully coupled LES formulation exhibit good agreement between the measured and simulated mean velocity fields. The global behaviour of the spray combustion, such as droplet dispersion and evaporation, are captured reasonably well in the simulations. It was found that the large velocity fluctuations observed in the shear layer strongly affect the evaporation rate and thus the temperature distributions. The present work also demonstrated the feasibility of LES to study complex flow features which are typical of gas-turbine combustion chambers.     

Peculiarities of Acoustic Wave Reflection from a Boundary or Layer of a Two-Phase Medium

A mathematical model is presented for determining the oblique incidence of an acoustic wave at both a boundary and layer of a gas–drop mixture or a bubbly liquid of finite thickness. The basic wave reflection and transmission patterns are established for the incidence of a low-frequency acoustic wave at an interface between a pure gas and a gas–drop mixture, as well as between a pure and bubbly liquid. A range of varying volume fractions for a drop is determined, for which the zero value of the reflection coefficient is possible for low frequencies at oblique incidence. It is shown that the reflection coefficient will never be zero at angles of incidence above 24.5° from a gas–drop mixture at a pure gas boundary; however, when a wave is incident from a pure gas at a gas–drop mixture boundary, a zero reflection coefficient is possible for nonzero angles of incidence and the volume fraction of inclusions. The results of calculating reflection of an acoustic wave from a two-phase layer of a medium with a finite thickness are presented. It is established that the minimum reflection coefficient is possible depending on the perturbation frequency for a certain range of angles of incidence for the boundary or the layer of the gas–drop mixture, which is governed mainly by difference in densities between it and the pure gas.     

On the theory of thermodiffusiophoresis of a moderately coarse two-layer volatile aerosol particle

A hydrodynamic method with slip is used to construct a theory of uniform thermodiffusiophoretic transfer of a volatile high-viscosity two-layer particle under conditions in which one component of a moderately rarefied binary gas mixture undergoes phase transition on the particle’s surface. The solid spherical core and high-viscosity sheath of the particle are concentric to each other. The theory suggests that, when moving, a two-layer volatile aerosol particle may be considered as a homogeneous particle with an effective thermal conductivity. The effect of the evaporation rate, interfacial temperature steps, and presence of the core on the rate of thermodiffusiophoresis is considered. Thermal diffusion terms, Stefan effects, and the heat evolution due to the convective transfer of the evaporating mass are taken into account. Under the same initial assumptions, formulas derived in this work are of wider practical significance than those following from the conventional approaches.     

自由流区近壁蒸发及未蒸发颗粒的热泳分析

本文给出了自由分子流区作用在壁面附近蒸发及未蒸发颗粒上的热泳力的分析结果.分析中气体分子在壁面和颗粒表面处均假定为部分镜反射和部分漫反射.分析表明,作用在近壁颗粒上的热泳力不仅依赖于气体中的温度梯度,还和气体的压力以及壁面与气体温度比有关.颗粒表面的温度和镜反射分数对作用于未蒸发颗粒的热泳力没有影响,但明显影响作用于蒸发颗粒的热泳力.研究表明,近壁效应及蒸发对颗粒热泳的附加影响是不容忽视的.     

Toward a theory of evaporation processes in liquid-solid systems

A theoretical analysis is presented of isothermal evaporation of a volatile component from a solid covered by a liquid layer. Binary compounds are considered, with the covering liquid produced by thermal decomposition of the solid material. It is shown that the relaxation time of the volatile concentration profile is much shorter than the characteristic time of motion of the melting interface; i.e., the instantaneous profile of volatile concentration at any time is a linear function of the spatial coordinate. A new nonlinear Stefan-type problem of evaporation in a solid-liquid-vacuum system is formulated that involves two moving phase transition interfaces: an evaporating interface and a melting interface. Exact analytical solutions to the problem are found. It is shown that the melting interface moves faster than the evaporating interface; i.e., the thickness of the liquid layer increases with time, its growth rate increasing with evaporation rate coefficient. It is demonstrated that the concentration profile evolves self-similarly in the course of time. An increase in evaporation rate coefficient leads to a steepening of the concentration gradient across the liquid layer, changing the volatile concentration at the evaporating interface, and the evaporative flux changes accordingly.     

声悬浮条件下环己烷液滴的蒸发凝固

采用单轴式声悬浮方法研究了环己烷液滴的蒸发过程,发现环己烷液滴的蒸发可以使自身温度降至熔点以下并发生凝固.高速摄像实时观测表明,环己烷晶核开始形成于液滴赤道附近,并以枝晶方式长大,平均生长速度为12.5-160.4 mm/s.进一步研究发现,声悬浮条件下平均Sherwood数与平均Nusselt数的比值Sh/Nu是在自然对流条件下的1.3倍,这表明声流边界层有效提高了环己烷液滴的蒸发速率而对传热的促进作用相对较小,因而可以使液滴降至更低温度,进而发生凝固.据此,提出了挥发性液体在声悬浮条件下发生蒸发凝固的必要条件. 关键词： 声悬浮 声流 环己烷 蒸发凝固     

测量气体分子平均速率的一种简易方法

用一种简易的方法测量了常温下气体分子运动的平均速率.根据易挥发性液体的质量随时间逐渐减少的特点和盛放液体的容器加盖前后挥发的气体分子对容器作用力的变化,通过分析天平测量液体质量的改变得到挥发出来的气体分子对容器的作用力,利用变质量物体的动量守恒定理,测量得到了易挥发性气体分子的平均速率,实验结果较好地与理论值符合.     

油气两相流体纵掠水平螺旋扁管管束摩擦压降的实验研究

以汽油-压缩空气为介质,对气液两相流体纵掠螺距为200mm的螺旋扁管管束的摩擦压降进行了实验研究。讨论并分析了质量含气率、混合物质量流速对摩擦压降的影响。提出了两种预测两相摩擦压降的方法:全液相摩擦乘子、L-M关系式。     

Drop splashing on a dry smooth surface

The corona splash due to the impact of a liquid drop on a smooth dry substrate is investigated with high-speed photography. A striking phenomenon is observed: splashing can be completely suppressed by decreasing the pressure of the surrounding gas. The threshold pressure where a splash first occurs is measured as a function of the impact velocity and found to scale with the molecular weight of the gas and the viscosity of the liquid. Both experimental scaling relations support a model in which compressible effects in the gas are responsible for splashing in liquid solid impacts.     

Experimental investigation of liquid drop evaporation on a heated solid surface

Evaporation of a water drop was studied experimentally at a temperature difference between the solid surface and surrounding atmosphere from 30 to 60 °C. The studies were performed on the substrates with micro- and nanocoatings with different wettability. The features of evaporation were studied for the pinned, partially pinned, and depinned three-phase contact line (solid-liquid?gas interface). It is shown that with a decrease in the water drop volume, the specific evaporation rate (mass flow per unit of surface area) increases, particularly at the last stage of evaporation.     

The theory of nonstationary thermophoresis of a solid spherical particle

The theory of nonstationary thermophoresis of a solid spherical particle in a viscous gaseous medium is presented. The theory is constructed on the solutions of fluid-dynamics and thermal problems, each of which is split into stationary and strictly nonstationary parts. The solution of the stationary parts of the problems gives the final formula for determining the stationary component of the thermophoretic velocity of this particle. To determine the nonstationary component of the thermophoretic velocity of the particle, the corresponding formula in the space of Laplace transforms is derived. The limiting value theorems from operational calculus are used for obtaining the dependence of the nonstationary component of the thermophoretic velocity of the spherical particle on the strictly nonstationary temperature gradient for large and small values of time. The factors determining the thermophoretic velocity of the particle under investigation are determined.     

Transient thermal analysis of a cryogenic oxidizer tank in the liquid rocket propulsion system during the prelaunch helium gas pressurization

The transient thermal behavior in the cryogenic oxidizer tank for the liquid propulsion system of the KSLV-I satellite launching space vehicle is theoretically investigated for the pressurization process by gaseous helium injection followed by the readiness check stage. The numerical model is established using the transient mass and energy conservation of oxygen/helium mixtures both in ullage and liquid regions. At the liquid-gas interface, various modes of heat and mass transfer are considered, including the liquid evaporation and the helium absorption. The present study focuses on the effects of the increasing pressurization level on some of important properties that should be considered in the propulsion system design, such as tank pressure, ullage gas temperature, and evaporation of liquid oxygen. Particularly, the tank pressure drop after the pressurization is investigated in the proposed design of propulsion system. Also, the effect of the initial loading of liquid oxygen in the oxidizer tank is studied and discussed. As for the helium absorption into the liquid region, its mass is negligibly small and it should not be the concern in design and operation of the oxidizer tank system.     

A spray flamelet/progress variable approach combined with a transported joint PDF model for turbulent spray flames

A spray flamelet/progress variable approach is developed for use in spray combustion with partly pre-vaporised liquid fuel, where a laminar spray flamelet library accounts for evaporation within the laminar flame structures. For this purpose, the standard spray flamelet formulation for pure evaporating liquid fuel and oxidiser is extended by a chemical reaction progress variable in both the turbulent spray flame model and the laminar spray flame structures, in order to account for the effect of pre-vaporised liquid fuel for instance through use of a pilot flame. This new approach is combined with a transported joint probability density function (PDF) method for the simulation of a turbulent piloted ethanol/air spray flame, and the extension requires the formulation of a joint three-variate PDF depending on the gas phase mixture fraction, the chemical reaction progress variable, and gas enthalpy. The molecular mixing is modelled with the extended interaction-by-exchange-with-the-mean (IEM) model, where source terms account for spray evaporation and heat exchange due to evaporation as well as the chemical reaction rate for the chemical reaction progress variable. This is the first formulation using a spray flamelet model considering both evaporation and partly pre-vaporised liquid fuel within the laminar spray flamelets. Results with this new formulation show good agreement with the experimental data provided by A.R. Masri, Sydney, Australia. The analysis of the Lagrangian statistics of the gas temperature and the OH mass fraction indicates that partially premixed combustion prevails near the nozzle exit of the spray, whereas further downstream, the non-premixed flame is promoted towards the inner rich-side of the spray jet since the pilot flame heats up the premixed inner spray zone. In summary, the simulation with the new formulation considering the reaction progress variable shows good performance, greatly improving the standard formulation, and it provides new insight into the local structure of this complex spray flame.     

Influence of the accommodation coefficient on the water drop evaporation process in a radiation field

The process of water drop evaporation in a field of intense laser radiation is examined on the basis of the hydro-thermodynamics equations under the assumption of quasistationarity in the conditions in the surrounding medium and in the radius. The influence of the accommodation coefficient on heating of the drops on the magnitude of the surface jump in water vapor density and on the position of the upper bound of the convective evaporation region is analyzed. It is shown that the surface jump in the vapor does not alter the rate of convective evaporation of the drop in practice, but can result in substantially different time dependences of the radius of a diffusely evaporating drop as compared with those found without it. The solution obtained is compared with the solution of the problem of evaporation in a Stefan approximation.     

Investigations of Droplet‐Plasma Interaction using Multi‐Dimensional Coupled Model

Recently developed multi‐dimensional coupled fluid‐droplet model is used to investigate the behavior of complex interaction between the liquid precursor droplets and atmospheric pressure plasma (APP). The significance of this droplet‐plasma interaction is not well understood under diverse realm of working conditions in two‐phase flow. In this study, we explain the implication of vaporization of liquid droplets in APP which are subsequently responsible to control major characteristics of surface coating depositions. Coalescence of water droplets is more dominant than Hexamethyldisiloxane (HMDSO) droplets because of its sluggish rate of evaporation. A disparity in the performance of evaporation is identified in two independent mediums, such as gas mixture and discharge plasma using HMDSO precursor. The length of evaporation of droplets is amplified by an increment of gas flow rate indicating with a reduction in the gas temperature and electron mean energy. In particular, the spatio‐temporal density distributions of charged particles show a clear pattern in which the typical nitrogen impurity ions are primarily effective as compared to other helium ionic species along the pulse of droplets in APP. Finally, we contrast the behavior of discharge species in the pure helium and He‐N2 gas mixtures revealing the importance of stepwise and Penning ionization processes. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)