Two-fluid modeling in analyzing the interfacial stability of liquid film flows

The area-averaged two-fluid model formulation of a separated two-phase flow system is used to investigate interfacial stability of liquid film flows. The analysis takes into account the effects of phase change at the interface as well as the dynamic effects of the adjacent vapor flow on the interfacial stability. Wave formation and instability criteria are established in terms of the generalized fluid and flow parameters. The criteria are applied to investigate the stability of laminar liquid film flow with interfacial shear and phase change. The influence of various dimensionless parameters characterizing film thickness, gravity, phase change and interfacial shear are studied with respect to the neutral stability, temporal growth factor and the wave propagation velocity. The results of the present study indicate that the interfacial stability analysis developed within the frame of the two-fluid model formulation proves to be quite accurate as judged by comparing its results with the available experimental data and with the results of much longer and more complex analytical investigations which are valid only for the liquid film free of interfacial shear.     

An investigation on near wall transport characteristics in an adiabatic upward gas–liquid two-phase slug flow

The near-wall transport characteristics, inclusive of mass transfer coefficient and wall shear stress, which have a great effect on gas–liquid two-phase flow induced internal corrosion of low alloy pipelines in vertical upward oil and gas mixing transport, have been both mechanistically and experimentally investigated in this paper. Based on the analyses on the hydrodynamic characteristics of an upward slug unit, the mass transfer in the near wall can be divided into four zones, Taylor bubble nose zone, falling liquid film zone, Taylor bubble wake zone and the remaining liquid slug zone; the wall shear stress can be divided into two zones, the positive wall shear stress zone associated with the falling liquid film and the negative wall shear stress zone associated with the liquid slug. Based on the conventional mass transfer and wall shear stress characteristics formulas of single phase liquid full-pipe turbulent flow, corrected normalized mass transfer coefficient formula and wall shear stress formula are proposed. The calculated results are in good agreement with the experimental data. The shear stress and the mass transfer coefficient in the near wall zone are increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity. The mass transfer coefficients in the falling liquid film zone and the wake zone of leading Taylor bubble are lager than those in the Taylor bubble nose zone and the remaining liquid slug zone, and the wall shear stress associated falling liquid film is larger than that associated the liquid slug. The mass transfer coefficient is within 10⁻³ m/s, and the wall shear stress below 10³ Pa. It can be concluded that the alternate wall shear stress due to upward gas–liquid slug flow is considered to be the major cause of the corrosion production film fatigue cracking.     

非球形固体颗粒对弯管内壁的磨损机制

为研究弯管内固体颗粒在液相夹带条件下的运动特性及颗粒对弯管内壁的磨损,采用计算流体动力学与离散元耦合的方法,建立数值模型,考虑固液两相之间的作用,对弯管内的固液两相流动进行数值模拟;通过软件的应用程序编程接口嵌入自编译磨损模型;借助试验结果,验证数值模型的有效性. 结果表明,所建立的数值模拟方案可以准确地模拟颗粒在管内的运动特征并能够预测弯管内壁的磨损位置以及磨损程度. 弯管内的二次流对颗粒运动有重要影响,弯管外侧壁面中心线附近的磨损较严重,磨损的形式以小角度划擦切削为主. 弯管磨损主要与颗粒对壁面的碰撞速度、碰撞角度及碰撞频率有关. 运动中的颗粒与壁面发生多次碰撞,碰撞角度逐渐减小. 随着颗粒球形度的增大,在相同碰撞条件下引起的磨损量变小,但是会降低颗粒的随流性. 颗粒形状影响颗粒在流场中的运动速度以及颗粒与壁面的碰撞. 随着颗粒球形度增大,严重磨损区域向弯管进口方向移动,壁面平均磨损量先减小后增大;当输送颗粒的球形度为0.91时,壁面磨损量最小.      

固体颗粒对沟槽湍流边界层影响的实验研究

本文采用粒子图像测速技术(particles image velocimetry, PIV)研究固体颗粒对放置在平板湍流边界层中的平壁和沟槽壁面减阻效果的影响. 实验对清水和加入粒径为155 μm聚苯乙烯颗粒的流法向二维速度场信息进行采集, 对不同工况下的平均速度剖面、雷诺应力和湍流度等统计量进行对比, 分析流体在边界层中的行为. 运用空间局部平均结构函数提取了不同工况湍流边界层喷射?扫掠行为的空间拓扑结构并进行比较. 结果发现, 在不同的壁面条件下, 粒子加入后的对数律区中无量纲速度均略大于清水组, 雷诺切应力有所降低, 湍流度有所减弱. 对于不同流场速度下的沟槽而言, 颗粒的加入均降低了壁面附近的阻力, 而颗粒单独作用于光滑壁面的减阻效果并不明显. 加入粒子后的相干结构数目有所增加, 法向脉动速度下降. 沟槽壁面附近的相干结构数目有所增加, 法向脉动速度在自由来流速度较大时有所上升, 在速度较小时有所下降. 这表明不同减阻状况下的沟槽均能将大涡破碎成更多的涡, 并且粒子的加入强化了这种破碎作用.      

Experimental study on hydrodynamic characteristics of upward gas–liquid slug flow

To clarify the impacts of the hydrodynamic boundary layer and the diffusion boundary layer in the near wall zone on gas–liquid two-phase flow induced corrosion in pipelines, the hydrodynamic characteristics of fully developed gas–liquid slug flow in an upward tube are investigated with limiting diffusion current probes, conductivity probes and digital high-speed video system. The Taylor bubble and the falling liquid film characteristics are studied, the effects of various factors are examined, and the experimental results are compared with the data and models available in literature. The length of Taylor bubble, the local void fraction of the slug unit and the liquid slug, the shear stress and mass transfer coefficient in the near wall zone, are all increased with the increase of superficial gas velocity and decreased with the increase of superficial liquid velocity, whereas the length of liquid slug and the liquid slug frequency are changed contrarily. The alternate wall shear stress due to upward gas–liquid slug flow is considered to be one of the major causes for the corrosion production film fatigue cracking. A normalized formula for mass transfer coefficient is obtained based on the experimental data.     

Experimental study of the flow regimes resulting from the impact of an intermittent gasoline spray

The present paper reports a complete set of measurements made with a two-component phase Doppler anemometer of the two-phase flow generated at the impact of a transient gasoline spray onto a flat surface. The spray is generated by a pintle injector and the fuel used was gasoline. The measurements of droplet size–velocity were processed to provide time fluxes of number, mass, normal momentum, and energy of the poly-dispersion of droplets ejected at impact, and analyzed based on predictive tools available in the literature. The results show that splash is the dominant mechanism by which secondary droplets are ejected from the surface, either in the stagnation region or in the core region of the spray. In the stagnation region, a large fraction of each incident droplet adheres to the surface and the axial incident momentum contributes with a larger parcel than tangential momentum. As a result, the normal velocity of ejected droplets is much smaller than that of the original incident droplets, while tangential velocity is enhanced. The region near the stagnation point is immediately flooded upon impact of the leading front of the spray, forming a liquid film that is forced to move radially outwards as droplets continue to impinge during the steady period. Spray/wall interaction in the core region thus occurs in the presence of a moving thin liquid film, which enhances transfer of tangential momentum. As a result, film spreading and dynamics as a result of impingement forces are crucial to accurate model spray/wall interaction. The outer region of the spray is dominated by the vortical structure induced by shear forces, which entrains small responsive secondary droplets to re-impinge. Furthermore, prediction of the outcome of spray impact requires a precise knowledge of the two-phase flow in the presence of the target.     

Experimental investigation of the interaction between a plane wall jet and a parallel offset jet

The dual-jet flow generated by a plane wall jet and a parallel offset jet at an offset ratio of d/w = 1.0 has been investigated using Particle Image Velocimetry (PIV). The particle images are captured, processed, and subsequently used to characterize the flow in terms of the 2D velocity and vorticity distributions. Statistical characteristics of the flow are obtained through ensemble averaging of 360 instantaneous velocity fields. Also presented is a time series of instantaneous flow fields to illustrate the dynamic interaction between the two jets. Results reveal that the near field of the flow is characterized by a periodic large-scale Karman-like vortex shedding similar to what would be expected in the wake of a bluff body. The existence of the Karman-like vortices results in periodic interactions between the two jets; in addition, these vortices produce noticeable impact on the jet outer layers, i.e., the free shear layer of the offset jet and the wall boundary layer of the wall jet. A schematic of vortex/shear layer interaction is proposed to illustrate the flow pattern.     

Experimental study of the gas flow in an air-blasted liquid sheet

An experimental study has been performed to improve the understanding of the initial air–liquid interaction in the near field of an air-blasted breaking water sheet. For the first time, planar laser-induced fluorescence (PLIF) has been used to visualize the air-flow field, seeding the air streams with acetone vapor. Mie scattering from the liquid sheet, together with the acetone fluorescence signal has enabled simultaneous determination of the instantaneous water sheet location and the air-flow structures. The two-phase flow visualization has revealed detachment of the air boundary layer over the air–water interface behind the zones of strong curvature. The pressure field induced by these vortices has been identified as a cause of the enhanced sheet flapping and the instability growth. Received: 30 October 2000/Accepted: 29 March 2001     

A comparative study of flame-wall interaction and flame-cooling air interaction

This paper presents a three-dimensional (3D) direct numerical simulation (DNS) study of flame-wall interaction (FWI) and flame-cooling air interaction (FCAI). A preheated, methane/air mixture enters a channel with constant temperature walls, where the top wall is effusion cooled. An imposed vertical hot sheet near the inlet creates two flame branches interacting with the top and bottom walls. The flame is observed to be leaner in the region where it interacts with the effusion cooling jets. In this region, the flame is longer and features reduced CO mass fraction. The fluctuations in the heat release rate (HRR) and CO mass fraction are also relatively small near the top wall. Near the bottom wall, finger-like flame structures are formed due to the interaction of turbulent vortices with the flame surface. These flame structures initially move away from the wall as they propagate further downstream before eventually collapsing at the wall. This leads to the creation of regions of high wall heat flux and CO. While analysis of the CO thermochemical state shows a complex picture near the bottom wall, two-dimensional (2D) manifolds can be identified near the top wall. Therefore, a framework to estimate CO mass fraction due to FCAI based on 1D freely-propagating flame solutions is proposed showing a good agreement with the DNS results.     

Film boiling on a hot body moving in a fluid

We investigate the transient film boiling in the vicinity of a stagnation point on the frontal surface of a very hot blunt body which moves with a constant velocity in an incompressible viscous fluid in the presence of a vapor layer near the body surface. Within the unsteady two-phase boundary layer approximation, the equations of motion of the liquid and vapor phases are formulatedwith account of the conservation of mass, momentum, and energy on the a priori unknown phase interface. In the vicinity of the stagnation point on the body surface, the solution of the boundary layer equations is sought in the form of series in the longitudinal coordinate. For the leading terms of the series, a parabolic system of partial differential equations is obtained, which is solved numerically. The similarity parameters controlling the film boiling process are determined. On the basis of parametric numerical calculations, the dynamics of the vapor layer are investigated for the case of a plane hot body moving in water with the room pressure and temperature. In the space of governing parameters, the limits of the existence of steady and unsteady film boiling regimes are found.     

超声速气流中雾化燃料喷射的三维数值研究

首次用双流体模型对雾化燃料在扩张形超燃室中沿九喷嘴顺流喷射的混合问题进行了数值研究。气相用迎风 TVD格式求解三维全 Navier- Stokes方程 ,液相用预估、校正 NND格式求解三维 Euler方程。相间相互作用的常微分方程用预估、校正Runge- Kutta法求解。用三维 Poisson方程生成网格。结果表明 :气相较液相的扩散效果好 ,小直径液滴的扩散效果好。相间速度滑移、改变气相喷射压力和喷射速度对液相扩散的贡献不大 ,但调整喷射角度会明显地增强液相的扩散、混合 ,本文结果未出现阻塞。     

Vapor core turbulence in annular two-phase flow

 This paper reports a new technique to measure vapor turbulence in two-phase flows using hot-film anemometry. Continuous vapor turbulence measurements along with local void fraction, droplet frequency, droplet velocity and droplet diameter were measured in a thin, vertical duct. By first eliminating the portion of the output voltage signal resulting from the interaction of dispersed liquid droplets with the HFA sensor, the discrete voltage samples associated with the vapor phase were separately analyzed. The data revealed that, over the range of liquid droplet sizes and concentrations encountered, the presence of the droplet field acts to enhance vapor turbulence. In addition, there is evidence that vapor turbulence is significantly influenced by the wall-bounded liquid film. The present results are qualitatively consistent with the limited data available in the open literature. Received: 17 August 1998/Accepted: 12 April 1999     

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.     

Flow of a suspension in a flat channel with porous walls

In the flow of a suspension in a channel with porous walls, when the size of particles of a suspended phase is much less than the width of the channel but greatly exceeds the size of the pores (in particular, in the flow of blood in the plasma separator used in an artificial kidney system [1, 2]), phenomena are observed which apparently cannot be satisfactorily explained by means of the well-known solutions of problems on the motion of a Newtonian fluid [3]. For example, the flow rate of the liquid phase of the suspension through the walls depends on the velocity of the main flow and does not depend on the pressure drop on the wall at fairly high values of it [1, 2]. The present study gives below the formulation and an approximate solution, which explains this effect, of the problem of an incompressible two-phase suspension in a long slit with porous walls which are impermeable in relation to the suspended phase and through which the liquid phase is pumped. Certain effects are taken into account which are caused by the high volume concentration of the suspended phase.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 37–43, November–December, 1987.     

An analytic solution of dense two-phase flow in a vertical pipeline

According to a mathematical model for dense two-phase flows presented in theprevious paper,a dense two-phase flow in a vertical pipeline is analytically solved,and theanalytic expressions of velocity of each continuous phase and dispersed phase arerespectively derived The results show that when the drag force between two phases dependslinearly on their relative velocity,the relative velocity profile in the pipeline coincides withDarcy’s law except for the thin layer region near the pipeline wall,and that the theoreticalassumptions in the dense two-phase flow theory mentioned are reasonable.     

Some three-dimensional effects during vortex generation at a straight edge

For vortices generated by an impulsively started flow about a straight sharp edge bounded by side-walls, one might expect the vortex-flow in the mid-plane to remain unaffected by the walls for a time. Experiments in water using rectangular nozzles with generally moderate width-to-height ratios showed that a flow was initiated from the walls into the vortex core and towards the mid-plane. This flow set in at the same time as the main flow began. The fastest mass transport took place near the junction between the edge and the walls. This water moved within the vortex axis with an initially constant velocity approximately a third of that of the main flow, independent of the width, the height and the edge-angle within a surprisingly large range of these parameters. A further feature of the wall-near flow is the appearance and growth of a region of vortex breakdown in the core near the wall. In the mid-plane a flow was initiated directed radially outwards from the centre of the vortex. This flow was also short lived, beginning both before the axis became significantly distorted, as well as before any noticeable axial velocity gradient near the mid-plane existed. This radial motion seems thus to be the most sensitive measure of the flow in the mid-plane becoming three-dimensional. During this time the forces associated with the axial and radial flow may be significant. Despite the abovementioned relatively fast secondary flow, the trajectory of the vortex-centre in the mid-plane seems unaffected.     

Measurement of the liquid film thickness in micro tube slug flow

Slug flow is one of the representative flow regimes of two-phase flow in micro tubes. It is well known that the thin liquid film formed between the tube wall and the vapor bubble plays an important role in micro tube heat transfer. In the present study, experiments are carried out to clarify the effects of parameters that affect the formation of the thin liquid film in micro tube two-phase flow. Laser focus displacement meter is used to measure the thickness of the thin liquid film. Air, ethanol, water and FC-40 are used as working fluids. Circular tubes with five different diameters, D = 0.3, 0.5, 0.7, 1.0 and 1.3 mm, are used. It is confirmed that the liquid film thickness is determined only by capillary number and the effect of inertia force is negligible at small capillary numbers. However, the effect of inertia force cannot be neglected as capillary number increases. At relatively high capillary numbers, liquid film thickness takes a minimum value against Reynolds number. The effects of bubble length, liquid slug length and gravity on the liquid film thickness are also investigated. Experimental correlation for the initial liquid film thickness based on capillary number, Reynolds number and Weber number is proposed.     

Volume of fluid approach of boiling flows in concentrated solar plants

The Computational Fluid Dynamics (CFD) model proposed in this paper allows the flow patterns that evolve during progressive boiling inside large scale horizontal tubes to be simulated from the initial vapor generation stage to large vapor slugs. The volume of fluid (VOF) model was employed in combination with relatively simple hypothesis. The aim of the present work is to improve the design of receiver tubes at concentrated solar power plants with direct steam generation by simulating the evolution of flow regimes within these tubes. Despite numerous studies conducted in the past years on convective boiling, only a few made use of the VOF model to simulate large flow regime transitions. This work presents a preliminary and relatively qualitative approach to address this problem. Heat and mass transfer at the tube inner wall and at the liquid-gas interface were solved with the additional transport of two scalars. One accounts for the enthalpy field and the other represents the dispersed vapor phase of the liquid. This new phase was created at the wall surface of the liquid phase and rises up to the liquid-vapor interface. Different phenomena linked to the boiling process were taken into account: vapor creation at the wall, its transport, recondensation and the creation of large structures. This model was validated with boiling flow in a bent tube at different mass flow rates and heat fluxes, which allowed us to observe the evolution of two-phase flow patterns. Finally, numerical simulation of direct steam generation inside a concentrated solar plant receiver clearly showed the apparition and evolution of various two-phase flow patterns.     

Numerical Simulation of the Buoyancy-Driven Bouncing of a 2-D Bubble at a Horizontal Wall

The rise of a buoyant bubble and its interaction with a target horizontal wall is simulated with a 2-D numerical code based on the Boundary Element Method (BEM). Developed from a viscous potential flow approximation, the BEM takes into account only the part of the energy dissipation related to the normal viscous stresses. Hence, a simple analytical model based on lubrication approximation is coupled to the BEM in order to compute the drainage of the interstitial liquid film filling the gap between the bubble and the near wall. In this way the bubble–wall interaction is fully computed: the approach stage, the bubble deformation stage and, depending on the values of the Reynolds number and the Weber number, the rebound and the bubble oscillations. From computation of both the bubble interface motion and the liquid velocity field, a physical analysis in terms of energy budget is proposed. Though, in the present study, the bubble under consideration is basically supposed to be a 2-D gaseous cylinder, a comparison between our numerical results and the experiments of Tsao and Koch (1997) enlightens interestingly the physics of bouncing.     

Particle imaging velocimetry of a wet aqueous foam with an underlying liquid film

 We investigate the utility of particle imaging velocimetry (PIV) for performing kinematic measurements in wet aqueous foam with a liquid film beneath it. The flow velocities are measured near the walls of a square cross-section horizontal duct. The flow velocities are useful for validating the rheological models. We show that there is a discrepancy between the velocity profiles in the wet foam and the Bingham plastic model of flow. The velocity measurements reveal a more complex flow pattern, which may be analysed following three different regimes: a plug flow, a shear flow in a vertical plane and a three-dimensional shear flow. The transition between the plug flow and the shear flows may be explained by a shear-induced migration of bubbles. Received: 25 April 2000 / Accepted: 26 February 2001