Interfacial Balance Equations for Diffusion Evaporation and Exact Solution for Weightless Drop

Introducing of additional terms into the balance equations to specify the conditions at the interface allows to study physical phenomena in the diffusion evaporation (condensation) of the liquid into the neutral gas. We have taken into account the vapour dynamic effects on evaporating liquid, as well as the waste of energy on deformation of the boundary, changing of the interfacial temperature (the interface has an internal energy and therefore heat capacity), to overcome the surface tension etc. This paper presents the balance conditions at the interface with the diffusion evaporation of the liquid into the neutral gas, for the case when the vapour is considered as an impurity in the gas phase. The analysis of the dimensionless criteria is carried out. The areas of parameters for which the effect of some physical factors take a place have been defined. The exact solution of the diffusion evaporation for a spherical drop at zero gravity conditions has been constructed. The explicit expression for the interfacial temperature and evaporation rate were derived. Solution for evaporation rate coincides with the solution obtained by Maxwell (1890).     

Modeling of Gas Cooling and Condensation in a Piston Expansion Machine

A model of gas cooling and condensation in a piston expansion machine has been developed with allowance made for formation of nuclei of the liquid phase and growth of droplets as well as for real thermophysical properties. Internal heat release related to phase transition is taken into account in the adiabatic equation. The processes of cooling and liquefaction of methane in the piston expander are calculated for specific conditions.     

Performance analysis of no-vent fill process for liquid hydrogen tank in terrestrial and on-orbit environments

Two finite difference computer models, aiming at the process predictions of no-vent fill in normal gravity and microgravity environments respectively, are developed to investigate the filling performance in a liquid hydrogen (LH₂) tank. In the normal gravity case model, the tank/fluid system is divided into five control volume including ullage, bulk liquid, gas–liquid interface, ullage-adjacent wall, and liquid-adjacent wall. In the microgravity case model, vapor–liquid thermal equilibrium state is maintained throughout the process, and only two nodes representing fluid and wall regions are applied. To capture the liquid–wall heat transfer accurately, a series of heat transfer mechanisms are considered and modeled successively, including film boiling, transition boiling, nucleate boiling and liquid natural convection. The two models are validated by comparing their prediction with experimental data, which shows good agreement. Then the two models are used to investigate the performance of no-vent fill in different conditions and several conclusions are obtained. It shows that in the normal gravity environment the no-vent fill experiences a continuous pressure rise during the whole process and the maximum pressure occurs at the end of the operation, while the maximum pressure of the microgravity case occurs at the beginning stage of the process. Moreover, it seems that increasing inlet mass flux has an apparent influence on the pressure evolution of no-vent fill process in normal gravity but a little influence in microgravity. The larger initial wall temperature brings about more significant liquid evaporation during the filling operation, and then causes higher pressure evolution, no matter the filling process occurs under normal gravity or microgravity conditions. Reducing inlet liquid temperature can improve the filling performance in normal gravity, but cannot significantly reduce the maximum pressure in microgravity. The presented work benefits the understanding of the no-vent fill performance and may guide the design of on-orbit no-vent fill system.     

Coupled heat and mass transfer during nonisothermal absorption by falling droplet with internal circulation

We considered mass and heat transfer during nonisothermal absorption of a gas by a falling droplet with internal circulation. Gas phase is assumed to be free of inert admixtures and mass transfer is liquid phase controlled. Mass flux is directed from a gaseous phase to a droplet, and the interfacial shear stress causes a fluid flow inside the droplet. Droplet deformation under the influence of interface shear stress is neglected. Absorbate accumulation and temperature increase in the bulk of liquid phase are taken into account. The problem is solved in the approximations of a thin concentration and temperature boundary layers in the liquid phase. The thermodynamic parameters of the system are assumed constant. The system of transient partial parabolic differential equations of convective diffusion and energy balance with time-dependent boundary conditions is solved by combining the similarity transformation method with Duhamel's theorem, and the solution is obtained in a form of Volterra integral equation of the second kind which is solved numerically. Theoretical results are compared with available experimental data for water vapor absorption by falling droplets of aqueous solution of LiBr.     

Numerical Investigation on Turbulence and Bubbles Distribution in Bubbly Flow Under Normal Gravity and Microgravity Conditions

Two-phase flows of gas and liquid are increasingly paid much attention to space application due to excellent properties of heat and mass transfer, so it is very meaningful to develop studies on them in microgravity. In this paper, gas-phase distribution and turbulence characteristics of bubbly flow in normal gravity and microgravity were investigated in detail by using Euler–Lagrange two-way model. The liquid-phase velocity field was solved by using direct numerical simulations (DNS) in Euler frame of reference, and the bubble motion was tracked by using Newtonian motion equations that took into account interphase interaction forces including drag force, shear lift force, wall lift force, virtual mass force and inertia force, etc. in Lagrange frame of reference. The coupling between gas–liquid phases was made with regarding interphase forces as a momentum source term in the momentum equation of the liquid phase. Under the normal gravity condition, a great number of bubbles accumulate near the walls under the influence of the shear lift force, and addition of bubbles reduces turbulence of the liquid phase. Different from the normal gravity condition, in microgravity, an overwhelming majority of bubbles migrate towards the centre of the channel driven by the pressure gradient force, and bubbles have little effect on the turbulence of the liquid phase.     

液氢空间贮存过程膜态沸腾数值模拟

为实现液氢在空间中安全高效应用,针对微重力条件下液氢膜态沸腾现象,建立了加热细丝浸没在过冷液氢池中的数值计算模型.采用VOF方法捕捉相界面,相变模型选取Lee模型,利用文献中的实验数据验证了模型的准确性.从气泡运动行为和换热特性两方面开展研究,结果发现液体过冷度和重力水平是影响换热机理的两个重要因素.在高重力水平、低液...     

Diffusion-limited evaporation of thin polar liquid films

The stability of evaporating very thin films of a polar liquid is investigated. The microscopic interaction with the substrate and capillarity are taken into account in a lubrication equation. The stability of a flat interface is studied when evaporation is limited by the diffusion of the vapour in the gas phase. The evaporation rate is computed and evaporation is shown to be stabilizing. A stability phase diagram is obtained. A weakly nonlinear analysis leads to a film-thickness amplitude equation that is non local in space. Physical consequences of the results are eventually discussed.     

Experimental study and modelling of the crystallization of a water droplet

Modelling the crystallisation of a water droplet into a cold humid airflow is the first step in modelling the behaviour of water droplets sprayed out of a snow gun. This modelling, which is based on an experimental study, deals with the behaviour of the droplet which is transformed successively from the supercooled liquid phase to the liquid–solid phase and then the solid phase. These three transformations are brought about by various exchanges: heat transfer with conduction and convection as well as mass transfer with evaporation and sublimation. The supercooling phenomenon is naturally observed during experiments and taken into account in the modelling.     

Analysis of a convective fluid flow with a concurrent gas flow with allowance for evaporation

The paper presents a theoretical analysis of a convective fluid flow with a concurrent gas flow accompanied by evaporation at the interface. The analysis of two-layer flows is based on a mathematical model taking into account evaporation at a thermocapillary boundary and effects of thermal diffusion and diffusion heat conduction in the gas–vapor layer. New exact solutions describing steady two-layer flows in a channel with the interface remaining undeformed and examples of velocity and temperature profiles for the HFE-7100 (liquid)–nitrogen (gas) system are presented. The influence of longitudinal temperature gradients along the channel boundaries, the gas flow rate, and the height of the fluid layer on the flow regime and evaporation rate is studied. A comparison of the calculated data with experimental results is performed.     

Terrestrial and microgravity applications of self-rewetting fluids

Dilute aqueous solutions of high-carbon alcohols (number of C≥4) show an increase in the surface tension with increasing temperature in a particular temperature region. Liquid/vapor phase change in these aqueous solutions induces a very strong liquid flow in the vicinity of the interface due to both thermocapillary flow and the Marangoni flow caused by the preferential evaporation of alcohol-rich composition. Since such a spontaneous local liquid flow directs toward dry patch or hotter area, the expression of “self-rewetting” has been employed for these liquids. The present author focused his attention to this particular surface tension behavior, and has been studying both terrestrial and microgravity applications utilizing self-rewetting fluids as a working fluid in heat transfer devices. This article briefly introduces some of the recent research subjects related to self-rewetting fluids conducted by the present author and co-workers. First, the improvement in the thermal performance of wicked heat pipes with using self-rewetting fluids is emphasized based on detailed experimental evaluations. The experimental results on ultra-light weight wickless heat pipes, fabricated with 25µm thick polyimide film, in low gravity condition are then given.     

The Effect of Gravity and Shear Stress on a Liquid Film Driven in a Horizontal Minichannel at Local Heating

The present study is focused on the investigation of gravity effect on thermocapillary deformations in a film flowing under action of co-current gas flow, which creates the tangential force on the gas–liquid interface. The influence of local heating intensity on the heater at a substrate is also investigated. Effects of surface tension, temperature dependent viscosity and thermocapillarity are taken into account. Investigations have shown that gravity has a significant effect on the film deformations and pattern. Decreasing of gravity level leads to a flow destabilization. 3D liquid film pattern noticeably changes in spanwise direction. Increasing of heat flux leads to increasing of liquid film deformations. Dependence of film thinning on heat flux is strongly nonlinear. The most dangerous deformations (regions of minimum film thickness with possible disruption of liquid) take place behind the downstream edge of the heater at any gravity conditions.     

Colloidal Material Box: In-situ Observations of Colloidal Self-Assembly and Liquid Crystal Phase Transitions in Microgravity

To study the self-assembly behavior of colloidal spheres in the solid/liquid interface and elucidate the mechanism of liquid crystal phase transition under microgravity, a Colloidal Material Box (CMB) was designed which consists of three modules: (i) colloidal evaporation experimental module, made up of a sample management unit, an injection management unit and an optical observation unit; (ii) liquid crystal phase transition experimental module, including a sample management unit and an optical observation unit; (iii) electronic control module. The following two experimental plans will be performed inside the CMB aboard the SJ-10 satellite in space. (i) Self-assembly of colloidal spheres (with and without Au shell) induced by droplet evaporation, allowing observation of the dynamic process of the colloidal spheres within the droplet and the change of the droplet outer profile during evaporation; (ii) Phase behavior of Mg₂Al LDHs suspensions in microgravity. The experimental results will be the first experimental observations of depositing ordered colloidal crystals and their self-assembly behavior under microgravity, and will illustrate the influence of gravity on liquid crystal phase transition.     

Evaporation of additive droplets in a pulse MHD generator

Theoretical investigation into evaporation of additive droplets in the combustion chamber of a pulse MHD generator were undertaken. Flow in the chamber is considered as stationary and one-dimensional; mixing in a direction perpendicular to flow is believed to be ideal, and mixing is lacking in the flow direction. It is suggested that droplets are monodisperse, spherical, and motionless relative to the gas medium. The droplet evaporation can be taken as occurring in the diffusion mode. The specific heat c _p and heat conductivity coefficient are taken to be constant and independent of temperature and the concentration of components. The Lewis number is believed to be the unit value; and the Soret and Dufour effects, negligible. A formula for calculation of the droplet evaporation rate with allowance made for chemical reactions occurring in liquid and gas media is obtained.     

The Effect of the Evaporation Coefficient and Temperature Jumps on the Thermophoresis of a Particle in a Binary Gas Mixture in View of Thermodiffusion and Stefan Effects

A theory of uniform thermophoretic motion of a solitary spherical volatile particle in an unbounded incompressible binary mixture of gases with a phase transition of one of the components on the surface of the condensed phase is constructed on the basis of hydrodynamic method under slip conditions. Analysis is performed of the direct relative effect of the evaporation coefficient and boundary temperature jumps on the distribution of the velocity, temperature, and concentration of the volatile component and on the rate of thermophoresis of a moderately large highly viscous sphere. The thermodiffusion terms, Stefan effects, and the heat flux associated with convective transfer of evaporating mass are taken into account. A generalization is performed by taking into account the internal circulation of the matter of a large liquid one-component droplet and the thermocapillary phenomena. The inferences made in this paper disagree with those of the traditional theories in the cases of thermophoresis of a solitary aerosol particle under conditions of weak and moderately strong diffusion evaporation. Analysis has revealed that, in the case of weak evaporation of a large particle, the difference between the results increases as the binary gas mixture is saturated with vapors of the volatile component. Apparently, the calculation formulas for the rate of thermophoretic transfer have a wider range of validity than those previously obtained, all other things being equal.     

Retardation of a Heat Front in a Porous Medium Containing an Evaporating Liquid

We have investigated heat transfer in a layer of silica gel impregnated with a liquid (water, aqueous solutions of calcium and magnesium chlorides, formic acid, and carbon tetrachloride). The layer was arranged on a substrate impenetrable for vapor and it was heated from above by a concentrated light flux. It has been found that the evaporation of the liquid contained in the pores of silica gel substantially slows down the propagation of the heat front into the layer so that the effective thermal conductivity of the layer can be reduced to 0.01 W/(m·K); this value is approximately 4–20 times smaller than the values typical of the majority of standard heat-insulating materials. The time of the front lag depends on the layer thickness, density of the incident heat flux, amount of liquid in the pores, and evaporation heat of the liquid. The observed trends in the motion of the front have been described by a simple one-dimensional model that takes into account phase transition (liquid evaporation) in the interior of the porous matrix.     

Two-phase Flow in Fuel Cells in Short-term Microgravity Condition

A visual observation of liquid–gas two-phase flow in anode channels of a direct methanol proton exchange membrane fuel cells in microgravity has been carried out in a drop tower. The anode flow bed consisted of 2 manifolds and 11 parallel straight channels. The length, width and depth of single channel with rectangular cross section was 48.0 mm, 2.5 mm and 2.0 mm, respectively. The experimental results indicated that the size of bubbles in microgravity condition is bigger than that in normal gravity. The longer the time, the bigger the bubbles. The velocity of bubbles rising is slower than that in normal gravity because buoyancy lift is very weak in microgravity. The flow pattern in anode channels could change from bubbly flow in normal gravity to slug flow in microgravity. The gas slugs blocked supply of reactants from channels to anode catalyst layer through gas diffusion layer. When the weakened mass transfer causes concentration polarization, the output performance of fuel cells declines.     

微重力环境低温流体无排气加注过程数值研究

针对加注系统受注贮箱,采用CFD方法就液氮贮箱无排气加注过程开展数值仿真,对比了不同重力水平下的无排气加注性能,分析了加注口结构、壁面初始温度、加注流体温度和加注流量等因素对微重力无排气加注性能的影响规律。所构建的二维轴对称模型将流体区与固壁区一起作为求解区域并划分网格,并通过植入用户自定义程序(UDF)计算加注口液体闪蒸过程及气液之间的热质交换。经过实验数据验证,该模型能够合理展示箱内温度场分布和相分布情况,并获得贮箱压力等参数变化信息。数值计算结果表明:(1)加注条件相同时,微重力工况较常重力工况体现出更好的无排气加注性能。(2)微重力条件下,无排气加注性能几乎不受加注口结构的影响,壁面初始温度和加注流体温度越高,贮箱压力越高,加注流量仅对加注时间有显著影响。     

Evaporation kinetics of volatile liquids and release kinetics of water from a smectite clay: Comparison between experiments and finite element calculations

Numerical calculations of the evaporation kinetics of bulk volatile liquids and of water from smectite clay granules are compared with experimental results. The weight loss of the volatiles is analyzed by thermogravimetry and differential calorimetry. Under the thermodynamic conditions of the experiments, finite element calculations are in good agreement with the experimental data, and an approximate semi-analytical model is developed in order to explain the dependence of the rate of evaporation on the temperature, the chemical species and the carrier gas flow rate. The initial rate of evaporation of water from the clay granule is close to that for bulk water. Its decrease with time is determined mainly by changes in the gas/condensed phase partition given by the equilibrium desorption isotherm, with little limitations due to internal diffusion effects for the present experimental conditions. Its temperature dependence could also be approximately described by an Arrhenius-type equation derived from the semi-analytical model. Further analysis of the experimental measurements reveals steps in the heat of vaporization of water as a function of water concentration, that could be related to the equilibrium desorption isotherm.     

Effect of Oxygen Enrichment in Propane Laminar Diffusion Flames under Microgravity and Earth Gravity Conditions

Diffusion flames are the most common type of flame which we see in our daily life such as candle flame and match-stick flame. Also, they are the most used flames in practical combustion system such as industrial burner (coal fired, gas fired or oil fired), diesel engines, gas turbines, and solid fuel rockets. In the present study, steady-state global chemistry calculations for 24 different flames were performed using an axisymmetric computational fluid dynamics code (UNICORN). Computation involved simulations of inverse and normal diffusion flames of propane in earth and microgravity condition with varying oxidizer compositions (21, 30, 50, 100 % O₂, by mole, in N₂). 2 cases were compared with the experimental result for validating the computational model. These flames were stabilized on a 5.5 mm diameter burner with 10 mm of burner length. The effect of oxygen enrichment and variation in gravity (earth gravity and microgravity) on shape and size of diffusion flames, flame temperature, flame velocity have been studied from the computational result obtained. Oxygen enrichment resulted in significant increase in flame temperature for both types of diffusion flames. Also, oxygen enrichment and gravity variation have significant effect on the flame configuration of normal diffusion flames in comparison with inverse diffusion flames. Microgravity normal diffusion flames are spherical in shape and much wider in comparison to earth gravity normal diffusion flames. In inverse diffusion flames, microgravity flames were wider than earth gravity flames. However, microgravity inverse flames were not spherical in shape.     

Theoretical prediction of piloted ignition of polymeric fuels in microgravity at low velocity flows

A numerical model developed for the prediction of the piloted ignition delay of solid polymeric materials exposed to an external radiant heat flux is used to predict the ignition delay and critical heat flux for ignition of solid fuels in microgravity at low velocity flows. The model considers the coupled thermochemical processes that take place in the condensed phase, including oxidative and thermal pyrolysis, phase change, radiation absorption, and heat and mass transfer in a multi-phase and multi-composition medium. Ignition is considered to occur when a critical pyrolysate mass flow rate is reached at the sample surface. Microgravity experimental surface temperature and ignition delay data previously obtained in a KC-135 aircraft are used to infer, in conjunction with the theoretical analysis, the critical mass flow rate for ignition. This value is then used to predict the ignition delay as a function of the external radiant heat flux, and the critical heat flux for ignition. Calculations are made for Polymethylmethacrylate (PMMA) and a Polypropylene/Fiberglass composite at airflows of 0.09 and 0.15 m/s under microgravity conditions and at 1.0, 1.75 and 2.5 m/s under normal gravity. The experiments and theoretical predictions show that the ignition delay and critical heat flux for ignition decrease as the forced airflow velocity decreases. It is predicted that at the tested lower velocities, the critical heat flux for ignition is close to half the value measured in normal gravity. The results have important implications since they indicate that materials could ignite easier under the conditions expected in spacecraft, and consequently stricter design specifications may be needed for fire safety.