An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow.However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semiempirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.     

An improved three-dimensional model for interface pressure calculations in free-surface flows

A three-dimensional method for the calculation of interface pressure in the computational modeling of free surfaces and interfaces is developed. The methodology is based on the calculation of the pressure force at the interfacial cell faces and is mainly designed for volume of fluid (VOF) interface capturing approach. The pressure forces at the interfacial cell faces are calculated according to the pressure imposed by each fluid on the portion of the cell face that is occupied by that fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. The present method, referred to as pressure calculation based on the interface location (PCIL), is applied to both static and dynamic cases. First, a three-dimensional motionless drop of liquid in an initially stagnant fluid with no gravity force is simulated as the static case and then two different small air bubbles in water are simulated as dynamic cases. A two-fluid, piecewise linear interface calculation VOF method is used for numerical simulation of the interfacial flow. For the static case, both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used for surface tension calculations. A wide range of Ohnesorge numbers and density and viscosity ratios of the two fluids are tested. It is shown that the presence of spurious currents (artificial velocities present in case of considerable capillary forces) is mainly due to the inaccurate calculation of pressure forces in the interfacial computational cells. The PCIL model reduces the spurious currents up to more than two orders of magnitude for the cases tested.

Also for the dynamic bubble rise case, it is shown that using the numerical solver employed here, without PCIL, the magnitude of spurious currents is so high that it is not possible to simulate this type of surface tension dominated flows, while using PCIL, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.     

Stratified gas-liquid flow in downwardly inclined pipes

Measurements of liquid hold-up and pressure drop are reported for stratified flow in a slightly inclined (0.65° and 2.1°), 5 cm pipeline. Velocity profiles in the gas phase have been determined for a limited number of flow conditions. Semi-empirical correlations are proposed for the transition to slug flow, the interfacial friction factor and the liquid hold-up.     

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.     

The rivulet flow pattern during oil–water horizontal flow through a 12 mm pipe

The present study reports the hydrodynamics of the rivulet pattern during oil–water flow through a 12 mm horizontal acrylic pipe. The interfacial distribution has been observed visually and characterized from signals obtained from an optical probe as well as by isokinetic sampling. The probability density function (PDF) and fast Fourier transform (FFT) of the signals have provided an understanding of the flow configuration. The experiments have revealed that although rivulet flow is a typical separated flow pattern, it has different characteristics as compared to the stratified and annular flow patterns. The holdup and pressure drop under such conditions have been compared with the drift flux model for horizontal flow as well as the two-fluid model as proposed by Brauner and Maron [9] for liquid–liquid flows.     

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.     

Effect of drag-reducing polymers on pseudo-slugs––interfacial drag and transition to slug flow

Drag-reducing polymers were added to air and water flowing in a stratified configuration in a horizontal 2.54 cm pipe. The interface was covered with large amplitude roll waves, that have been called pseudo-slugs, over a range of flow conditions. The damping of small wavelength waves causes a large decrease in the interfacial stress and, therefore, an increase in the liquid holdup. At superficial gas velocities greater than 4 m/s the transition to slug flow is delayed in that it occurs at larger liquid holdups. This observation is interpreted by assuming that turbulence in slugs is damped. This increases the shedding rate of a slug and, therefore, its stability. The pressure drop can increase or decrease when polymers are added. The increase in holdup is accompanied by an increase in gas velocity, which causes an increase in the pressure drop. The decrease in the interfacial stress has the opposite effect.     

An Experimental Study of Mobilization and Creeping Flow of Oil Slugs in a Water-Filled Capillary

An experimental investigation was carried out on mobilization and very slow flow of oil slugs in a capillary tube. The pressure drop of the slug flow was measured at every stage of mobilizing and moving the oil slugs as a function of capillary number in the range of 4 × 10⁻⁷–6 × 10⁻⁶. The pressure drop across the oil slug experienced three stages: build-up, hold-up, and steady stages. During the build-up stage, the convex rear end of the slug was becoming concave into the oil slug and the convex front end of the slug moved ahead to form a new portion of the slug. At the hold-up stage, both the concave rear end and the front end continued to advance, and the initial contact line of the oil slug with the tube wall through a very thin water film was being shortened. At this stage, the pressure drop reached a maximum value and remained nearly constant. At the steady stage, after the oil slug was completely mobilized out of the original contact region, the differential pressure had a step-drop first, and then the oil slug flowed at a lower differential pressure depending on the flow rate. Numerous slug flow tests of this study showed that the hold-up pressure drop was always higher than the steady stage pressure drop. Results also showed that the measured extra pressure drop was significantly high compared to the pressure drop calculated from Poiseuille equation, which is still commonly used in network modeling of multiphase flow in porous media.     

基于滑移速度壁模型的复杂边界湍流大涡模拟

采用滑移速度壁模型实现了浸入边界方法与壁模型相结合的大涡模拟.本文首先分别采用平衡层模型和非平衡壁模型对周期山状流进行数值模拟,以考查在壁模型中考虑切向压力梯度的作用.数值结果表明,流场的压力对本文所采用的壁模型形式并不敏感,但是考虑切向压力梯度可以显著改进壁面摩擦力的计算结果,并且能够准确的预测强压力梯度区以及分离区内的流动平均统计特性.不考虑压力梯度效应的平衡层模型显著低估了壁面摩擦力的分布,同时无法准确预测分离区内的平均速度剖面.非平衡模型的修正项正比于切向压力梯度和壁面法向距离,因此在强压力梯度区或者网格较粗时,计算得到的平均压力和摩擦力分布以及流动的低阶统计量均与参考的实验和计算结果吻合.在此基础上,通过回转体绕流的大涡模拟考查了该方法用于模拟高雷诺数壁湍流的适用性,非平衡壁模型可以准确地捕捉流动的物理结构并较准确地预测其水动力学特性.结果表明,将浸入边界方法与非平衡滑移速度壁模型相结合的大涡模拟,有望成为数值模拟复杂边界高雷诺数壁湍流的工具.      

Numerical simulation of soil–water interaction using smoothed particle hydrodynamics (SPH) method

An application of smoothed particle hydrodynamics (SPH) to simulation of soil–water interaction is presented. In this calculation, water is modeled as a viscous fluid with week compressibility and soil is modeled as an elastic–perfectly plastic material. The Mohr–Coulomb failure criterion is applied to describe the stress states of soil in the plastic flow regime. Dry soil is modeled by one-phase flow while saturated soil is modeled by separate water and soil phases. Interaction between soil and water is taken into account by means of pore water pressure and seepage force. Simulation tests of soil excavation by a water jet are calculated as a challenging example to verify the broad applicability of the SPH method. The excavations are carried out in two different soil models, one is dry soil and the other is fully saturated soil. Numerical results obtained in this paper have shown that the gross discontinuities of soil failure can be simulated without any difficulties. This supports the feasibility and attractiveness of this a new approach in geomechanics applications. Advantages of the method are robustness, conceptual simplicity and relative ease of incorporating new physics.     

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...     

Flooding and upward film flow in tubes—I. Experimental studies

New data are presented on the details of the flooding process and upward film flow including film and entrainment flow rates, film structure, pressure drop, sd well as interfacial and wall shear. These data are used to explore the mechanism of flooding and upward film flow in part II.     

A separated flow model for predicting two-phase pressure drop and evaporative heat transfer for vertical annular flow

A separated flow model has been developed that is applicable to vertical annular two-phase flow in the purely convective heat transfer regime. Conservation of mass, momentum, and energy are used to solve for the liquid film thickness, pressure drop, and heat transfer coefficient. Closure relationships are specified for the interfacial friction factor, liquid film eddy-viscosity, turbulent Prandtl number, and entrainment rate. Although separated flow models have been reported previously, their use has been limited, because they were tested over a limited range of flow and thermal conditions. The unique feature of this model is that it has been tested and calibrated against a vast array of two-phase pressure drop and heat transfer data, which include upflow, downflow, and microgravity flow conditions. The agreements between the measured and predicted pressure drops and heat transfer coefficients are, on average, better or comparable to the most reliable empirical correlations. This separated flow model is demonstrated to be a reliable and practical predictive tool for computing two-phase pressure drop and heat transfer rates. All of the datasets have been obtained from the open literature.     

Single-beam gamma densitometry measurements of oil–water flow in horizontal and slightly inclined pipes

Gamma densitometry is a frequently used non-intrusive method for measuring component volume fractions in multiphase flow systems. The application of a single-beam gamma densitometer to investigate oil–water flow in horizontal and slightly inclined pipes is presented. The experiments are performed in a 15 m long, 56 mm diameter, inclinable stainless steel pipe using Exxsol D60 oil (viscosity 1.64 mPa s, density 790 kg/m³) and water (viscosity 1.0 mPa s, density 996 kg/m³) as test fluids. The test pipe inclination is changed in the range from 5° upward to 5° downward. Experimental measurements are reported at three different mixture velocities, 0.25, 0.50 and 1.00 m/s, and the inlet water cut is varied from 0 to 1. The gamma densitometer is composed of radioactive isotope of Am-241 with the emission energy of 59.5 keV, scintillation detector [NaI(Tl)] and signal processing system. The time averaged cross-sectional distributions of oil and water phases are measured by traversing the gamma densitometer along the vertical pipe diameter. Based on water volume fraction measurements, water hold-up and slip ratio are estimated. The total pressure drop over the test section is measured and frictional pressure drop is estimated based on water hold-up measurements. The measurement uncertainties associated with gamma densitometry are also discussed. The measured water hold-up and slip ratio profiles are strongly dependent on pipe inclination. In general, higher water hold-up values are observed in upwardly inclined pipes compared to the horizontal and downwardly inclined pipes. At low mixture velocities, the slip ratio decreases as the water cut increases. The decrease is more significant as the degree of inclination increases. The frictional pressure drop for upward flow is slightly higher than the horizontal flow. In general, there is a marginal difference in frictional pressure drop values for horizontal and downwardly inclined flows.     

A model for droplet entrainment in heated annular flow

The ability to accurately predict droplet entrainment in annular two-phase flow is required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. Most annular flow entrainment models in the open literature are formulated in terms of dimensionless groups, which do not directly account for interfacial instabilities. However, many researchers agree that there is a clear presence of interfacial instability phenomena having a direct impact on droplet entrainment. The present study proposes a model for droplet entrainment, based on the underlying physics of droplet entrainment from upward co-current annular film flow that is characteristic to light water reactor safety analysis. The model is developed based on a force balance and stability analysis that can be implemented into a transient three-field (continuous liquid, droplet, and vapor) two-phase heat transfer and fluid flow systems analysis computer code.     

Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes

This experimental study comparatively examined the two-phase flow structures, pressured drops and heat transfer performances for the cocurrent air–water slug flows in the vertical tubes with and without the spiky twisted tape insert. The two-phase flow structures in the plain and swirl tubes were imaged using the computerized high frame-rate videography with the Taylor bubble velocity measured. Superficial liquid Reynolds number (Re_L) and air-to-water mass flow ratio (AW), which were respectively in the ranges of 4000–10000 and 0.003–0.02 were selected as the controlling parameters to specify the flow condition and derive the heat transfer correlations. Tube-wise averaged void fraction and Taylor bubble velocity were well correlated by the modified drift flux models for both plain and swirl tubes at the slug flow condition. A set of selected data obtained from the plain and swirl tubes was comparatively examined to highlight the impacts of the spiky twisted tape on the air–water interfacial structure and the pressure drop and heat transfer performances. Empirical heat transfer correlations that permitted the evaluation of individual and interdependent Re_L and AW impacts on heat transfer in the developed flow regions of the plain and swirl tubes at the slug flow condition were derived.     

Experimental study of non-uniform inlet conditions and three-dimensional effects of vertical air–water two-phase flow in a narrow rectangular duct

To study the three-dimensional interfacial structure development in vertical two-phase flow, air–water upflow experiments were performed in a rectangular duct. Various non-uniform two-phase profiles were created by injecting air from individually controlled spargers at the duct inlet into uniformly injected water flow. A four-sensor conductivity probe was used to measure local void fraction, interfacial area concentration, bubble velocity and Sauter mean diameter at three axial locations to record the development of two-phase parameters. Experimental results showed that the lateral development across the wider dimension of the duct was significant with a non-uniform inlet profile when compared to a uniform inlet profile. It is postulated that lift, wall and turbulent forces are the major contributors to the lateral distribution of the two-phase interfacial structures making this an useful experiment for benchmarking three-dimensional two-fluid models. In examining the interfacial area, the shearing-off of group 1 bubbles (defined as the smaller spherical and distorted bubbles) from the skirt region of group 2 bubbles (defined as the bigger cap and churn bubbles), the coalescence of group 2 bubbles due to wake entrainment, and random collision are the major source and sink mechanisms of interfacial area concentration.     

The prediction of stratified two-phase flow with a two-equation model of turbulence

A two-equation model is applied to a stratified two-phase flow system to predict turbulent transport mechanisms in both phases.In the present analysis, the effects of interfacial waves on the flow field are formulated in terms of boundary conditions for the gas-liquid interface. For the gas phase, the wavy interface has such flow separation effects as a rough surface in a single-phase flow. While for the liquid phase, the waves generate turbulant energy which is transported progressively toward a lower wall region. The analytical results are in good agreement with available data regarding pressure drop, holdup and velocity profiles.     

Mixing characteristics of turbulent water vapour jets measured using an isokinetic sampling probe

 Horizontal turbulent water vapour (steam) jets were discharged into ambient air from a circular convergent nozzle under unchoked/choked and saturated/superheated nozzle exit conditions, resulting in two-phase (liquid and vapour), two-fluid (air and water) condensing free jets. Flow properties and mixing characteristics have been measured with the aid of an isokinetic sampling probe arrangement. Radial and axial profiles of air and steam mass flow rates and mass fractions were measured from which entrainment, centreline decay and half-width spreading rates were calculated and compared with data from the literature. Overall, the mixing characteristics of the condensing jets are very similar to those of non-condensing jets extensively reported in the literature. Received: 30 September 1996 / Accepted: 19 May 1997