Unsteady state diffusion of vapour in a closed tube

Results of one-dimensional calculations for unsteady state diffusion of a vapour in a closed tube are compared to calculations (a) for unsteady state diffusion of a vapour in an open tube, and (b) for heat conduction in a finite slab and an infinite slab. In the cases of (b) the effect of the convective term in the transport equation is absent.The total pressure is calculated and differences in the two cases are explained.An experiment is described in which the pressure increase in a closed tube due to the diffusion of water vapour in dry air is measured as a function of time. The experimental results agree quite well with the theoretical predictions. The results of this investigation may be used for the experimental determination of the diffusion coefficient of a vapour in a gas and in pressure measurements in systems with an evaporating liquid.Nomenclature a thermal diffusivity - D diffusion coefficient - w mean particle velocity - g particle flux in the laboratory system - g* particle flux in a system moving with the mean particle velocity w - L length of the tube - n number density of molecules - n _vs saturation number density of vapour molecules - p pressure - p _vs saturation pressure of the vapour - t time - z distance from the liquid surface - N total quantity of evaporated liquid     

An equation set for non-equilibrium two phase flow,and an analysis of some aspects of choking,acoustic propagation,and losses in low pressure wet steam

An equation set for multidimensional, time variant, inviscid flow of a condensing vapour is presented. The equations include the effects of relative motion between the primary gas phase and the suspended liquid droplets. They have been formulated with steam turbine applications in mind but are also relevant to problems of gas-particle and liquid bubble flow.It is shown that the critical velocity in one dimensional choking of low pressure wet steam is identical with the “frozen” speed of acoustic propagation, and the variation of choking mass flow with respect to equilibrium based calculations is described. Results obtained with two different models of droplet growth are compared, and simple formulae for calculating limiting values of choking flow are given. A generalised loss coefficient including the effects of thermodynamic and kinematic non-equilibrium is introduced.     

Influence of gas injection on phase inversion in an oil–water flow through a vertical tube

An experimental study has been made of the influence of gas injection on the phase inversion between oil and water flowing through a vertical tube. Particular attention was paid to the influence on the critical concentration of oil and water where phase inversion occurs and on the pressure drop increase over the tube during phase inversion. By using different types of gas injectors also the influence of the bubble size of the injected gas on the phase inversion was studied. It was found that gas injection does not significantly change the critical concentration, but the influence on the pressure drop is considerable. For mixture velocities larger than 1 m/s, the pressure drop over the tube increases with decreasing bubble size and at inversion can become even larger than the pressure drop during the flow of oil and water without gas injection.     

Numerical investigation of periodic cavitation shedding in a Venturi

Unsteady partial cavitation is mainly formed by an attached cavity which presents periodic oscillations. Under certain conditions, instabilities are characterized by the formation of vapour clouds convected downstream the cavity and collapsing in higher pressure region. Two main mechanisms have been identified for the break-off cycles. The development of a liquid re-entrant jet is the most common type of instabilities, but more recently, the role of pressure waves created by the cloud collapses has been highlighted. This paper presents one-fluid compressible simulations of a self-sustained oscillating cavitation pocket developing along a Venturi geometry. The mass transfer between phases is driven by a void ratio transport equation model. The importance of traveling pressure waves in the physical mechanism is put in evidence. Moreover, the importance of considering a non-equilibrium state for the vapour phase is exhibited.     

Reservoir storage and containment of greenhouse gases, II: Vapour-entry pressures

This paper investigates the role of a nonzero vapour entry pressure on reservoir storage and containment of the greenhouse gas carbon dioxide. Two effects are observed: vapour storage under confining layers, and enhanced lateral spreading of gas under confining layers. Lateral flow of gas under both impermeable and permeable confining layers is solved analytically using Buckley-Leverett assumptions. A full numerical analysis of gas and water transport is also presented, using results from the simulator TOUGH. We consider the injection of CO₂ from a thermal power plant at a rate of 100 kg/s for 10 years, at a depth of 3000 metres. Inclusion of a nonzero vapour entry pressure shows that containment of this gas for at least 5000 years can be expected. The CO₂ is stored predominantly in a high density vapour phase (about 600 kg/m³) under lower permeability confining layers, and also is dissolved in liquid at about 40 kg/m³.     

基于气液相界面捕捉的统一气体动理学格式

气液相界面运动的研究无论是在科学还是工程领域都是非常重要的. 其中, 非平衡流动的计算尤其受到关注. 基于此, 我们构造了捕捉气液相界面的统一气体动理学格式. 由于统一气体动理学格式将自由输运和粒子碰撞耦合起来更新宏观物理量和微观分布函数, 故而可以求解非平衡流动. 具体思路是, 通过将范德瓦尔斯状态方程所表达的非理想气体效应引入统一气体动理学格式之中来捕捉气液相界面, 两相的分离与共存通过范德瓦尔斯状态方程描述. 由于流体在椭圆区域是不稳定的, 因此气液相界面可以通过蒸发和凝结过程自动捕捉. 如此, 一个锋锐的相界面便可以通过数值耗散和相变而得到. 利用该方法得到麦克斯韦等面积律(Maxwell construction)对应的数值解, 并与其相应的理论解相比较, 二者符合良好. 而后, 通过对范德瓦尔斯状态方程所描述的液滴表面张力进行数值计算, 验证了Laplace定理. 此外, 通过模拟两个液滴的碰撞融合过程, 进一步证明了该格式的有效性. 但是, 由于范德瓦尔斯状态方程的特性, 其所构造的格式仅适用于液/气两相密度比小于5的情况.      

垂直上升管内油—气—水三相弹状流压力降的研究

给出一种垂直上升油－气－水三相弹状流压力降的计算模型。该模型考虑弹状流中Ｔａｙｌｏｒ气泡周围下降液膜的变化历程。通过油－气－水弹状流的实验研究发现，该模型的数值模拟结果与低压工况下的实验值符合得较好。本模型是计算垂直油－气－水三相弹状流中液相的连续相为水相时的压力降的有效方法。     

Experimental and Numerical Investigation on Cavitating Flows in Diesel Injection Systems

The present study is concerned with the phase change during rapid depressurization of fluids: the role of vapor bubbles nucleation and growth and the effect on the system fluid dynamics were modeled and experimental measurements were made. Following a control-volume approach, averaged equations governing the motion of a one-dimensional, homogeneous, no-slip two-phase flow were used considering both thermal equilibrium (equal temperature) and non-equilibrium (non-equal temperature) between the liquid and vapor phases. In the non-equilibrium model, the heat transfer from the liquid to the vapor and the corresponding mass transfer velocity were modeled. Model results were compared with experimental data for a loss-of-coolant accident in nuclear power plants: the comparison of numerical vs. experimental data showed the role of nucleation velocity during the earliest phase of rapid depressurization. The experimental study of two-phase flow in a diesel engine injection system has been carried out using a rotative pump which is operated by using a purpose-developed test-bench; pressure measurements inside the system pipes were performed using pressure transducers; moreover, an ultrasonic technique was employed to study phase change phenomena. Several measurements were performed comparing the results obtained by different experimental techniques with the model outputs.Sommario.presente studio riguarda il fenomeno della cavitazione durante la depressurizzazione di fluidi. E'stata considerata la velocità di formazione e nucleazione delle bolle di vapore e le equazioni di conservazione sono state integrate con solutori al 1°e 2°ordine di tipo ENO. Sono stati utilizzati dati sperimentali ottenuti durante incidenti per perdita di refrigerante in centrali nucleari; per quanto riguarda gli apparati di iniezione, gli autori hanno sviluppato due differenti tecniche sperimentali, basate rispettivamente sulla pressione e sulla riflessione degli ultrasuoni. Il confronto dei risultati numerici con quelli sperimentali è stato soddisfacente.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I

This paper analyzes a coupled thermo-hydro-mechanical behavior of unsaturated soils based on the theory of mixtures. Unsaturated soil is considered as a mixture composed of soil skeleton, liquid water, vapor, dry air, and dissolved air. In addition to the mass and momentum conservation equations of each component and the energy conservation equation of the mixture, the system is closed using other 37 constitutive （or restriction） equations. As the change in water chemical potential is identical to the change in vapor chemical potential, a thermodynamic restriction relationship for the phase transition between pore water and pore vapor is formulated, in which the impact of the change in gas pressure on the phase transition is taken into account. Six final govern- ing equations are given in incremental form in terms of six primary variables, i.e., three displacement components of soil skeleton, water pressure, gas pressure, and temperature. The processes involved in the coupled model include thermal expansions of soil skeleton and soil particle, Soret effect, phase transition between water and vapor, air dissolution in pore water, and deformation of soil skeleton.     

Effect of density ratio on critical heat flux in closed end vertical tubes

An experimental study was conducted to measure the critical axial heat flux in countercurrent two phase flow of liquid and its vapour in a closed-end vertical tube. The experimental results for four different fluids; carbon-tetrachloride, normal hexane, ethyl alcohol and water, were reduced to give a correlation for evaluation of the flooding critical heat flux. Results of other investigators on vertical heated tubes and vertical thermosyphons were also reduced and compared with the present experimental results. The effect of the density ratio of liquid to its vapour on the critical heat flux was shown. The length to diameter ratio of the test section was shown to have an influence on the flooding critical heat flux and was included in the correlation obtained.     

Modeling of simultaneous heat and mass transfer processes in ammonia–water absorption systems from general correlations

This paper presents a general differential mathematical model to analyze the simultaneous heat and mass transfer processes that occur in different components of an ammonia–water absorption system: absorber, desorber, rectifier, distillation column, condenser and evaporator. Heat and mass transfer equations are considered, taking into account the heat and mass transfer resistances in the liquid and vapour phases. The model considers the different regions: vapour phase, liquid phase and an external heating or cooling medium. A finite difference numerical method has been considered to solve the resulting set of nonlinear differential equations and an iterative algorithm is proposed for its solution. A map of possible solutions of the mass transferred composition z is presented when varying the interface temperature, which enables to establish a robust implementation code. The analysis is focused on the processes presented in ammonia–water absorption systems. The model is applied to analyze the ammonia purification process in an adiabatic packed rectification column and the numerical results show good agreement with experimental data.     

Water Hammer in a Liquid with Gas Bubbles

The problem of water hammer in a pipeline through which a liquid with gas bubbles flows is considered. The influence of the gas phase on the value of the pressure jump is studied     

Gas Injection in a Liquid Saturated Porous Medium. Influence of Gas Pressurization and Liquid Films

We study numerically and experimentally the displacement of a liquid by a gas in a two-dimensional model porous medium. In contrast with previous pore network studies on drainage in porous media, the gas pressurization is fully taken into account. The influence of the gas injection rate on the displacement pattern, breakthrough time and the evolution of the pressure in the gas phase due in part to gas compressibility are investigated. A good agreement is found between the simulations and the experiments as regards the invasion patterns. The agreement is also good on the drainage kinetics when the dynamic liquid films are taken into account.     

Coupled fields in a deformable unsaturated medium

This paper considers several problems involving coupled heat–moisture–air flow indeformable unsaturated media. A set of coupled non-linear governing equations expressed in terms of displacements, capillary pressure, air pressure and temperature are used in the analysis. The mathematical model accounts for fully coupled heat and moisture flow, volume strain effects on water-air-heat flow, stress and temperature dependence of the water retention curve, heat sink due to thermal expansion, phase change between liquid water and vapour water, and compressibility of liquid water. Numerical solutions are obtained by using the finite element method. Comparisons with existing analytical and experimental results for problems involving infiltration, drying–rewetting (hysteresis effects) and heating confirm the general validity of the present mathematical model. Coupled fields in a confined clay cylinder are also examined. It is found that consideration of absorbed liquid flow due to thermal gradients (thermo-osmosis effect) results in increased drying and shrinkage near the heated boundary. The case of a confined clay cylinder under combined heating and infiltration is also studied. Important features of coupled fields are discussed.     

Experimental study of jet structure and pressurisation upon liquid nitrogen injection into water

The rapid phase change and heat transfer obtained by direct contact heat exchange between a cryogen and water can generate high rates of pressurisation, which is of interest to a number of applications. A visualization study of liquid nitrogen injection into water is conducted in this work, with synchronized pressure and temperature measurement, to obtain insight into this complex phenomenon. High speed imaging reveals a four-stage evolution of liquid nitrogen jet structure upon injection into water, with a thick vapour blanket forming around a liquid nitrogen core and break-up brought on predominantly through impact with the vessel wall. Maximum pressurisation rate occurs in the third stage of injection due to a combination of heat and mass transfer. Pressurisation rates in excess of 350 bar/s are recorded and found to vary proportionally with injection pressure. The scenario of gaseous nitrogen injection is also investigated, and compared with liquid nitrogen injection. A clear advantage of liquid nitrogen injection is elucidated from the point of heat transfer and pressurisation, and implications for use in a cryogenic engine are discussed.     

Driving Potentials of Heat and Mass Transport in Porous Building Materials: A Comparison Between General Linear,Thermodynamic and Micromechanical Derivation Schemes

In systems of coupled transport processes the question of the appropriate driving potentials is a point of discussion. In this article, three different approaches to derive models for transport currents are systematically compared. According to a general linear approach, an arbitrary full set of independent state variables and material properties is sufficient to describe any transport current. This approach is derived here from a symmetry principle. Thermodynamic and micromechanical approaches are more complex and even less general, but they allow additional statements about the transport coefficients and they reduce the number of transport processes. In the thermodynamic approach the additional information stems from the calculation of the entropy production rate; the micromechanical approach involves a microphysical model of the considered porous system. As a practical example, the three derivation schemes are applied to the often-encountered case of non-hysteretic heat and moisture transport in homogeneous building materials. It is shown, how the general state variables of a porous system are reduced to only two. Then from the general linear approach it can be seen, that all equations for the moisture transport current using a main driving potential (e.g. moisture content, vapour pressure, chemical potential) and an independent secondary driving potential (e.g. temperature, liquid pressure) are equivalent, without recurrence to the thermodynamic or micromechanical approach. However, the transport coefficients are arbitrary phenomenological functions depending on the two state variables. Based on a literature survey it is shown, which additional statements can be made in the thermodynamic and in the micromechanical approach. The latter yields the pressure-driven model (vapour and liquid pressure as the two driving potentials). Finally it is shown, what is to be expected, if in more complex systems the number of state variables increases.     

Atomized non-equilibrium two-phase flow in mesochannels: Momentum analysis

Two-phase pressure drop measurements are very difficult to make while the fluid is in non-equilibrium condition, i.e. while phase change is taking place. This is further complicated when an atomized liquid is introduced in the system at much higher velocity than other components such as liquid layer, vapor core, and entrained droplets. The purpose of this paper is to develop a model to predict the two-phase pressure characteristics in a mesochannel under various heat flux and liquid atomization conditions. This model includes the momentum effects of liquid droplets from entrainment and atomization. To verify the model, an in-house experimental setup consisting of a series of converging mesochannels, an atomization facility and a heat source was developed. The two-phase pressure of boiling PF5050 was measured along the wall of a mesochannel. The one-dimensional model shows good agreement with the experimental data. The effects of channel wall angle, droplet velocity and spray mass fraction on two-phase pressure characteristics are predicted. Numerical results show that an optimal spray cooling unit can be designed by optimizing channel wall angle and droplet velocity.