Parametric study of a model for determining the liquid flow-rates from the pressure drop and water hold-up in oil–water flows

A flow-pattern-dependent model, traditionally used for calculation of pressure drop and water hold-up, is accustomed for calculation of the liquid production rates in oil–water horizontal flow, based on the known pressure drop and water hold-up. The area-averaged steady-state one-dimensional two-fluid model is used for stratified flow, while the homogeneous model is employed for dispersed flow. The prediction errors appear to be larger when the production rates are calculated instead of pressure drop and water hold-up. The difference in the calculation accuracies between the direct and inverse calculation is most probably caused by the different uncertainties in the measured values of the input variables and a high sensitivity of the calculated phase flow-rates on even small change of the water hold-up for certain flow regimes. In order to locate the source of error in the standard two-fluid model formulation, several parametric studies are performed. In the first parametric study, we investigate under which conditions the momentum equations are satisfied when the measured pressure drop and water hold-up are imposed. The second and third parametric studies address the influence of the interfacial waves and drop entrainment on the model accuracy, respectively. These studies show that both interfacial waves and drop entrainment can be responsible for the augmentation of the wall-shear stress in oil–water flow. In addition, consideration of the interfacial waves offers an explanation for some important phenomena of the oil–water flow, such as the wall-shear stress reduction.     

Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

Weakly nonlinear stability analysis of a falling film with countercurrent gas–liquid flow has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear and nonlinear stability solutions for the film flow system. The results show that both supercritical stability and subcritical instability are possible for a film flow system when the gas flows in the countercurrent direction. The stability characteristics of the film flow system are strongly influenced by the effects of interfacial shear stress when the gas flows in the countercurrent direction. The effect of countercurrent gas flow in a falling film is to stabilize the film flow system.     

Closure relations effects on the prediction of the stratified two-phase flow stability via the two-fluid model

The possibility of predicting the exact long wave linear stability boundary via the two-fluid (TF) model for horizontal and inclined stratified two-phase flow is examined. The application of the TF model requires the introduction of empirical closure relations for the velocity profile shape factors and for the wave induced wall and interfacial shear stresses. The latter are recognized as the problematic closure laws. In order to explore the closure relations effects and to suggest the necessary modifications that can improve the stability predictions of the TF model, the results are compared with the exact long wave solution of the Orr–Sommerfeld equations for the two-plate geometry. It is demonstrated that with the shape factors corrections and the inclusion of wave induced stresses effects, the TF model is able to fully reproduce the exact long wave neutral stability curves. The wave induced shear stresses in phase with the wave slope, which give rise to the so called “sheltering force”, were found to have a remarkable destabilizing effect in many cases of horizontal and inclined flows. In such cases, the sheltering effects must be included in the TF model, otherwise the region of smooth stratified flow would be significantly over predicted. Based on the results of the exact analysis, a simple closure relation for the sheltering term in the TF model is provided.     

Pure steam condensation model with laminar film in a vertical tube

A new physical model for calculating the liquid film thickness and condensation heat transfer coefficient in a vertical condenser tube is proposed by considering the effects of gravity, liquid viscosity, and vapor flow in the core region of the flow. To estimate the velocity profile in the liquid film, the liquid film was assumed to be in Couette flow forced by the interfacial velocity at the liquid–vapor interface. For simplifying the calculation procedures, the interfacial velocity was estimated by introducing an empirical power-law velocity profile. The resulting film thickness and heat transfer coefficient from the model were compared with the experimental data and the results obtained from the other condensation models. The results demonstrated that the proposed model described the liquid film thinning effect by the vapor shear flow and predicted the condensation heat transfer coefficient from experiments reasonably well.     

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.     

Planar laser-induced fluorescence (PLIF) measurements of liquid film thickness in annular flow. Part II: Analysis and comparison to models

Film thickness distributions in upward vertical air–water annular flow have been determined using planar laser-induced fluorescence (PLIF). Film thickness data are frequently used to estimate interfacial shear and pressure loss. This film roughness concept has been used in a number of models for annular flow of varying complexity. The PLIF data are presently applied to the single-zone interfacial shear correlation of Wallis; the more detailed model of Owen and Hewitt; and the two-zone (base film and waves) model of Hurlburt, Fore, and Bauer. For the present data, these models all under-predict the importance of increasing liquid flow on pressure loss and interfacial shear. Since high liquid flow rates in annular flow induce disturbance wave and entrainment activity, further modeling in these areas is advised.     

A two-fluid model for reactive dilute solid–liquid mixtures with phase changes

Based on the Eulerian spatial averaging theory and the Müller–Liu entropy principle, a two-fluid model for reactive dilute solid–liquid mixtures is presented. Initially, some averaging theorems and properties of average quantities are discussed and, then, averaged balance equations including interfacial source terms are postulated. Moreover, constitutive equations are proposed for a reactive dilute solid–liquid mixture, where the formation of the solid phase is due to a precipitation chemical reaction that involves ions dissolved in the liquid phase. To this end, principles of constitutive theory are used to propose linearized constitutive equations that account for diffusion, heat conduction, viscous and drag effects, and interfacial deformations. A particularity of the model is that the mass interfacial source term is regarded as an independent constitutive variable. The obtained results show that the inclusion of the mass interfacial source term into the set of independent constitutive variables permits to easily describe the phase changes associated with precipitation chemical reactions.     

界面剪切力作用下波状液膜流的水动力稳定性

液膜流的水动力稳定性作为保障其高效传热传质性能的重要因素之一,受多种因素的制约和影响. 当气液界面处存在因气流流动而产生剪切力作用时,剪切力将通过改变界面处的边界条件,从而影响液膜流动的稳定性. 基于边界层理论,采用积分法建立了剪切力作用下降液膜表面波演化方程,分析了界面剪切力对水动力稳定性的影响. 研究表明,正向剪切力为不稳定性因素,反向剪切力在较小雷诺数时为不稳定因素,在大雷诺数时为稳定性因素;正向剪切力使临界波数和临界波速增大,反向剪切力使其减小;剪切力对临界波速的影响在不同雷诺数下也有所不同.      

Experimental study on axial development of liquid film in vertical upward annular two-phase flow

Accurate measurements of the interfacial wave structure of upward annular two-phase flow in a vertical pipe were performed using a laser focus displacement meter (LFD). The purpose of this study was to clarify the effectiveness of the LFD for obtaining detailed information on the interfacial displacement of a liquid film in annular two-phase flow and to investigate the effect of axial distance from the air–water inlet on the phenomena. Adiabatic upward annular air–water flow experiments were conducted using a 3 m long, 11 mm ID pipe. Measurements of interfacial waves were conducted at 21 axial locations, spaced 110 mm apart in the pipe. The axial distances from the inlet (z) normalized by the pipe diameter (D) varied over z/D = 50–250. Data were collected for predetermined gas and liquid flow conditions and for Reynolds numbers ranging from Re_G = 31,800 to 98,300 for the gas phase and Re_L = 1050 to 9430 for the liquid phase. Using the LFD, we obtained such local properties as the minimum thickness, maximum thickness, and passing frequency of the waves. The maximum film thickness and passing frequency of disturbance waves decreased gradually, with some oscillations, as flow developed. The flow development, i.e., decreasing film thickness and passing frequency, persisted until the end of the pipe, which means that the flow might never reach the fully developed state. The minimum film thickness decreased with flow development and with increasing gas flow rate. These results are discussed, taking into account the buffer layer calculated from Karman’s three-layer model. A correlation is proposed between the minimum film thickness obtained in relation to the interfacial shear stress and the Reynolds number of the liquid.     

STABILITY OF ULTRATHIN LIQUID FILM EVOLUTION WITH SURFACTANT

针对固体基底上厚度小于100 nm的含活性剂超薄液膜演化过程, 基于润滑理论推导出包含分离压影响的液膜厚度和活性剂浓度的演化方程, 采用正则模态法导出了描述液膜线性稳定性的特征方程, 分析了多个特征参数对线性稳定性的影响, 数值模拟了液膜厚度和活性剂浓度演化历程, 对比了模拟所得非线性结果与线性分析预测结果的一致性.结果表明:范德华力具有促进扰动增长的作用, 较强的玻恩斥力促使扰动衰减, 使液膜趋于稳定;较小的毛细力数易使液膜凹陷处发生二次失稳, 并最终导致去润湿现象发生;液膜厚度和溶于液膜内部的活性剂浓度初值越大, 液膜稳定性越强, 液膜表面活性剂浓度影响则相反;增大吸附系数不利于液膜稳定性.     

Measurements of velocity,temperature and velocity fluctuation distributions in falling liquid films

The velocity, temperature and velocity fluctuation distributions within falling spindle oil films in an inclined rectangular channel were measured using hot-wire techniques and thin thermocouples. The interfacial shear was caused by cocurrent air flow.The results indicate that the liquid films are as a whole much more laminar-like than turbulent in a range of Reynolds numbers (4γ/μ) up to the experimental limit of 6000. Mixing motion occurs in the vicinity of the interface; however, the flow near the wall surface exhibits no sign of such eddy motions, as predicted by the wall law for single phase turbulent flow. Although velocity fluctuation is observed within films with interfacial shear, mean velocity profiles are approximately the same as those obtained by the laminar film prediction.     

Long waves between a subsonic gas flow-film interface flowing down an inclined plate

The present work deals with temporal stability properties of a falling liquid film down an inclined plane in the presence of a parallel subsonic gas flow. The waves are described by evolution equation previously derived as a generalization of the model for the Newtonian liquid. We confirm linear stability results of the basic flow using the Orr–Sommerfeld analysis to that obtained by long wave approximation analysis. The non-linear stability criteria of the model are discussed analytically and stability branches are obtained. Finally, the solitary wave solutions at the liquid–gas interface are discussed, using specially envelope transform and direct ansatz approach to Ginzburg–Landau equation. The influence of different parameters governing the flow on the stability behavior of the system is discussed in detail.     

A two-phase, two-component model for vertical upward gas-liquid annular flow

In this paper, a new two-fluid two-component computational fluid dynamics (CFD) model is developed to simulate vertical upward two-phase annular flow. The two-phase VOF scheme is utilized to model the roll wave flow, and the gas core is described by a two-component phase consisting of liquid droplets and gas phase. The entrainment and deposition processes are taken into account by source terms of the governing equations. Unlike the previous models, the newly developed model includes the effect of liquid roll waves directly determined from the CFD code, which is able to provide more detailed and, the most important, more self-standing information for both the gas core flow and the film flow as well as their interactions. Predicted results are compared with experimental data, and a good agreement is achieved.     

A study on the numerical stability of the two-fluid model near ill-posedness

The two-fluid model is widely used in studying gas–liquid flow inside pipelines because it can qualitatively predict the flow field at low computational cost. However, the two-fluid model becomes ill-posed when the slip velocity exceeds a critical value, and computations can be quite unstable before the flow reaches the ill-posed condition. In this work, computational stability of various convection schemes together with the Euler implicit method for the time derivatives in conjunction with the two-fluid model is analyzed. A pressure correction algorithm for the two-fluid model is carefully implemented to minimize its effect on numerical stability. von Neumann stability analysis shows that the central difference scheme is more accurate and more stable than the 1st-order upwind, 2nd-order upwind, and QUICK schemes. The 2nd-order upwind scheme is much more susceptible to instability than the 1st-order upwind scheme and is inaccurate for short waves. Excellent agreement is obtained between the predicted and computed growth rates of harmonic disturbances. The instability associated with the two-fluid model discretized system of equations is related to but quantitatively different from the instability associated with ill-posedness of the two-fluid model. When the computation becomes unstable due to the ill-posedness, the machine roundoff errors from a selected range of short wavelengths, which scale with the grid size, are amplified rapidly to render the computation of any targeted long wavelength variation useless. For the viscous two-fluid model with wall friction and interfacial drag, a small-amplitude long wavelength disturbance grows due to viscous Kelvin–Helmholtz instability without triggering the grid scale short waves when the system remains well posed. Under such a condition, central difference is found to be the most accurate discretization scheme among those investigated.     

Flow pattern transition,pressure gradient,hold-up predictions in gas/non-Newtonian power-law fluid stratified flow

This work focuses on gas/non-Newtonian power-law fluid stratified pipe flow. Two different theoretical approaches to obtain pressure gradient and hold-up predictions are presented: the steady fully developed two-fluid model and the pre-integrated model. The theoretical predictions are compared with experimental data available for horizontal and for slightly downward inclined air/shear thinning fluid stratified flow taken from literature. The predictions of the pre-integrated model are validated showing a good agreement when compared with experimental data. The criteria for the transition from the stratified flow pattern are applied to gas/non-Newtonian stratified flow. The neutral stability analysis (smooth/wavy stratified flow) and the well-posedness (existence region of stratified flow) of governing equations are carry out. The predicted transition boundaries are obtained using the steady fully developed two-fluid model and the pre-integrated model, where the shape factors and their derivatives are accounted for. A comparison between the predicted boundaries and experimental flow pattern maps is presented and shows a good agreement. A comment on the shear stress modeling by the pre-integrated model is provided.     

垂直上升气液环状流流动参数的数值计算

提出了一个新的气核-液膜耦合模型来求解垂直上升气液环状流在充分发展段的流动参数.本模型考虑了液膜、气核以及它们之间的相互影响和作用.模型中基本的气核区域和液膜区域的质量和动量方程由Fluent6.3.26进行求解,而液滴方程以及相界面上的夹带和沉积作用通过用户自定义接口函数UDF(User Defined Functi...     

Finite-amplitude stability analysis of liquid films down a vertical wall with and without interfacial phase change

The generalized kinematic equation for film thickness, taking into account the effect of phase change at the interface, is used to investigate the nonlinear stability of film flow down a vertical wall. The analysis shows that supercritical stability and subcritical instability are both possible for the film flow system. Applications of the result to isothermal, condensate and evaporate film flow show that mass transfer into (away from) the liquid phase will stabilize (destabilize) the film flow. Finally, we find that supercritical filtered waves are always linearly stable with regard to side-band disturbance.     

切应力协同下受热过冷层流液膜的破断特性

针对界面切应力协同下受热过冷层流液膜流动的破断过程, 建立了不同气液流向下的临界液膜厚度和最小润湿量的理论模型, 分析了不同驱动力作用下, 接触角、流体温度、界面切应力和壁面热流密度对液膜破断特性的影响. 研究表明: 临界液膜厚度和最小润湿量均随壁面热流密度的增加而增大; 重力驱动下的接触角影响在不同热流密度下有所不同, 流体温度在不同驱动力下对最小润湿量的影响截然相反; 同向切应力驱动下临界液膜厚度和最小润湿量随切应力增加而减小; 在重力和切应力协同驱动下, 同向切应力对最小润湿量的影响与重力和切应力所起作用的相对大小有关, 反向切应力使得临界液膜厚度和最小润湿量有所增大.      

Co-current stratified gas–liquid downflow—Influence of the liquid flow field on interfacial structure

The transition from smooth to wavy stratified flow is studied for various pipe inclination angles with the aim to contribute to the realistic modeling and simulation of long distance two-phase pipe flow. The influence of the liquid flow field on interfacial structure is studied through local axial velocity measurements in the liquid phase in conjunction with other liquid layer characterization experiments. Observations based on fast-video recordings, are used to identify the main patterns of wave evolution. Liquid layer thickness time records are acquired using a parallel wire conductance technique from which mean layer thickness, RMS and power spectra of the fluctuations, as well as wave celerities are calculated. Laser Doppler Anemometry (LDA) is employed to investigate the flow structure in the thin liquid layer both with and without interfacial shear induced by a co-current gas flow. The results reveal the influence of the liquid flow field development on the interfacial structure. In particular, the new data of axial velocity profiles and liquid layer characteristics suggest that the onset of the interfacial waves is strongly affected by the liquid flow structure, possibly by the laminar to turbulent transition within the layer.     

Variation of velocity profile of jet and its effect on interfacial stability

IntroductionSincenineteencentury ,thestabilityofgas_liquidtwo_phasejethasattractedalotofpeoplefortheoreticalstudybecauseofitswideapplicationsinindustry .Thestabilitybehavioriscloselyrelatedtotheshapeofbasicvelocityprofile,andthevelocityprofilesmeasuredfromexperimentsarenotaccurateenough ,itisworthwhiletostudythevelocitymodelinthenumericalsimulation .Insimplermodels,top_hatprofile[1,2 ]issuggestedasbasicflowfortheinviscidandincompressibleliquidandgas.Tocompareitwithrealisticflow ,Suetal.[3]ass…