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.     

On the use of the stratified momentum balance for the deduction of shear stress in horizontal gas–liquid pipe flow

The use of the stratified flow momentum balance for the deduction of interfacial and liquid wall shear stresses from experimental measurements is examined. A systematic error analysis is applied to the governing equations using the principle of maximum uncertainty. A series of air–water experiments were conducted in 50 and 80 mm diameter pipes, in which gas pressure drop, liquid height and gas wall shear stress were measured. A framework for the correlation of the deduced shear stresses is proposed from the experimental measurements. The uncertainty analysis is used to show that the definition of mean liquid height does not significantly influence the overall results. The development of empirical equations based on such methods may lead to total uncertainties of up to 40%, irrespective of accuracy of the experimental data or the appropriateness of the correlating technique. Comparisons with state-of-the-art correlations for the liquid wall and interfacial friction factor data showed even larger discrepancies between measurement and prediction.     

On the use of the stratified momentum balance for the deduction of shear stress in horizontal gas–liquid pipe flow

The use of the stratified flow momentum balance for the deduction of interfacial and liquid wall shear stresses from experimental measurements is examined. A systematic error analysis is applied to the governing equations using the principle of maximum uncertainty. A series of air–water experiments were conducted in 50 and 80 mm diameter pipes, in which gas pressure drop, liquid height and gas wall shear stress were measured. A framework for the correlation of the deduced shear stresses is proposed from the experimental measurements. The uncertainty analysis is used to show that the definition of mean liquid height does not significantly influence the overall results. The development of empirical equations based on such methods may lead to total uncertainties of up to 40%, irrespective of accuracy of the experimental data or the appropriateness of the correlating technique. Comparisons with state-of-the-art correlations for the liquid wall and interfacial friction factor data showed even larger discrepancies between measurement and prediction.     

Modeling study of three-phase low liquid loading flow in horizontal pipes

A theoretical study is conducted to model the flow characteristics of three-phase stratified wavy flow in horizontal pipelines with a focus on the low liquid loading condition, which is commonly observed in wet gas pipelines. The model predictions are compared to the experimental data of Karami et al. (2016a, b). These experiments were conducted with water or 51 wt% of MEG in the aqueous phase, and inlet aqueous phase fraction values from 0 to100%.Modeling of three-phase flow can be described as a combination of two-phase gas-liquid flow modeling, and a liquid phase oil-water mixing modeling. A mechanistic model is proposed to predict flow characteristics of three-phase stratified wavy flow in pipeline. For the gas-liquid interactions, Watson's (1989) combined momentum balance equation derivation was applied. However, the calculation procedure was reversed, and the wave celerity was assumed as an input, while interfacial friction factor was one of the model's outputs. The liquid-liquid interactions were modeled using a simple energy balance equation and shift in liquid phase center of gravity calculations. The liquid phases can be separated, partially mixed, or fully mixed. The bottom aqueous film velocity was calculated using the law of the wall formulation, and was used to calculate the flowing aqueous phase fraction.The model predictions of different flow characteristics for two and/or three-phase flows were compared with available experimental data. The pressure gradient, wave amplitude, and aqueous phase fraction predictions were in good agreement with the experimental data. However, the liquid holdup predictions were slightly under-predicted by the model. Overall, an acceptable agreement was observed for all cases.Most of the common multiphase stratified flow models are developed with the assumption of steady-state conditions and with constant interfacial friction factor value. This study proposes a novel method to model stratified flow. The predictions are in acceptable agreement with experimental data conducted under stratified wavy flow pattern conditions.     

Equal quality distribution of gas–liquid two-phase flow by partial separation method

This paper proposes a new method for equal quality distribution of gas–liquid two-phase flow by partial separate-phase distribution with a dual-header distributor. The upper and liquid (lower) headers are interconnected with five vertical downward arms. A gas–liquid two-phase mixture enters the distributor from the upper header where most of the liquid of the mixture is removed through the downward arms into the liquid header. Hence, firstly, the remaining gas-rich fluid can be uniformly distributed into the outlet branches, and then secondly, the liquid collected in the liquid header can be uniformly re-distributed into the individual outlet branches. Because both distribution processes are conducted in the condition of single or near single-phase flow, mal-distribution of the two-phase flow is essentially eliminated, and a satisfactory equal quality distribution of gas–liquid two-phase flow is reached. Experiments were conducted in an air–water two-phase flow test loop. The inner diameter of the inlet pipe was 60 mm, the superficial velocity ranges of gas and liquid were 3–32 m/s and 0.02–0.17 m/s respectively, and the quality ranged from 0.02 to 0.44. The flow pattern in the inlet pipe included stratified flow, wavy stratified, slug flow, and annular flow. The experimental results showed that this new method could significantly improve the distribution performance of the two-phase flow. The maximum quality deviation between each outlet branch and the inlet pipe is less than ±1% under the conditions of stratified, wavy stratified and slug flows in the upper header, and less than ±5% in annular flow.     

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work, co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 mm in diameter. Each tube includes two 10 m long pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly flow, stratified flow, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high-speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood–Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/non-Newtonian liquid.     

Interfacial level gradient effects in horizontal newtonian liquid-gas stratified flow—i

The analysis of reported Newtonian liquid-gas stratified flow data for horizontal circular ducts indicated that an interfacial level gradient (ILG) and therefore non-uniform flow tended to exist over a wide range of test conditions. Significant ILG can be present if high-viscosity liquids and low gas velocities' are used to produce stratified flow. ILG can reduce the liquid holdup and can possibly expand the stratified flow regime by delaying the transition to wavy stratified and/or intermittent flow. Use of the Lockhart-Martinelli parameters Φ²_L and Φ²_G is invalid in stratified flow if ILG is present because of unequal axial pressure gradients in the gas and liquid phases. During uniform stratified flow, especially in the laminar liquid-turbulent gas ftow regime, the combined one-dimensional mechanical energy equations can be used in dimensionless form to accurately predict the liquid holdup and pressure drop. In future stratified flow experiments, the axial pressuregradient in both phases should be measured.     

Dynamics of a liquid film sheared by a co-flowing turbulent gas

Consider the dynamics of a thin laminar liquid film flowing over an inclined wall in the presence of a co-flowing turbulent gas. The solution to the full two-phase flow problem poses substantial technical difficulties. However, by making appropriate assumptions, the solution process can be simplified and can provide valuable insights. The assumptions allow us to solve the gas and liquid problems independently. Solving for the gas flow reduces to finding perturbations to pressure and tangential stresses at the interface, influencing the liquid problem through the boundary conditions. We analyze the effect of gas flow on the liquid problem by developing an integral-boundary-layer model, which is valid up to moderate liquid Reynolds numbers. We seek solitary-wave solutions of this model under the influence of gas flow via a pseudo-arclength continuation method. Our computations demonstrate that as a general trend, the wave speed increases with increasing the gas shear and the liquid flow rate. Further insight into the problem is provided via time-dependent computations of the integral-boundary-layer model.     

Heat transfer and interfacial drag in countercurrent steam-water stratified flow

Local condensation heat transfer coefficients and interfacial shear stresses have been measured for countercurrent stratified flow of steam and subcooled water in rectangular channels over a wide range of inclination angles (4–87°) at two aspect ratios. Dimensionless correlations for the interfacial friction factor have been developed that show that it is a function of the liquid Reynolds number only. Empirical correlations of the heat transfer coefficient, based upon the bulk flow properties, have also been set up for the whole body of data encompassing the different inclination angles and aspect ratios. These indicate that the Froude number as a dimensionless gas velocity is a better correlating parameter than the gas Reynolds number. As an alternative approach, a simple dimensionless relationship for the beat transfer coefficient was obtained by analogy between heat and momentum transfer through the interface. Finally, a turbulence-centered model has been modified by using measured interfacial parameters for the turbulent velocity and length scales, resulting in good agreement with the data.     

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…     

Local characteristics of upward gas-liquid flows

The results of two-phase flow structure measurements in an upward gas-liquid flow in a 86.4 mm i.d. tube by the electrochemical and conductivity techniques are presented. Measurements were made in bubble and slug flow regimes at liquid flow rates ranging from 0.2 to 2 m/s.The flow instability and ambiguity in a bubble regime at low velocities is shown to exist. Great discrepancy between measured wall shear stress values and those predicted by the Lockhart-Martinelli model are due to the nonuniform distribution of gas over the tube cross section. Measurements of intensity of wall shear stress and liquid velocity fluctuations in a two-phase flow are presented.     

The stratified flow of gas and non-newtonian liquid in horizontal pipes

Predictions of pressure drop and holdup are presented for the stratified flow of gas and non-Newtonian liquid obeying the Ostwald-de Waele power law model. The model of Taitel & Dukler (1976) for gas/Newtonian liquid flow is extended to liquids possessing either shear-thinning or shear-thickening laminar flow behaviour and computed results are given for flow behaviour indices in the range $\text{0.1 ≤ n ≤ 2}$. In particular, conditions are defined for drag reduction of the liquid flow by the presence of the gas. It is concluded that drag reduction occurs over the largest ranges of liquid and gas flow rates at the lowest $\text{n}$ values, provided that liquid flow remains laminar, but that maximum drag reduction may be expected for shear-thickening liquids with $\text{n}$ values of 2 or greater. Ratios of the liquid flow rate in the presence of gas to that for liquid flow alone under a constant pressure gradient are also presented. These ratios frequently exceed unity and are greatest for highly shear-thinning liquids.Although the Taitel & Dukler approach is consistent with experiments on gas/Newtonian liquid flow, and, in addition, appears to be valid for immiscible Newtonian liquid-liquid systems, provided that the viscosity ratio of the two phases is at least five, experiments are required to confirm its applicability for gas/non-Newtonian systems.     

Numerical analysis of two-phase flow from a stratified region through a small circular side branch

A numerical analysis using a commercial CFD code, ANSYS CFX, was used to model two-phase flow discharging from a stratified region through a small branch of circular cross-section. The purpose of this study is to assess the capability of the code in predicting the pertinent flow parameters and to generate detailed results that can provide insights into some of the flow phenomena. The inhomogeneous, free surface model was used and the code predictions were evaluated by comparing results with previous correlation equations and experimental data. Results were obtained for the critical heights of the interface at the onsets of gas and liquid entrainment, as well as the mass flow rate and quality during two-phase discharge. Additional results including force balances and pressure contours were also analysed to provide insight into the flow characteristics just before the onsets of liquid and gas entrainment. All results are in good agreement with existing correlation equations and experimental data. CFD modelling is therefore a possible tool for predicting the correct results for discharging two-phase flow for the geometry under consideration; the computation time required to obtain converged results, however, was found to be excessive.     

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...     

Flow pattern,void fraction and pressure drop of refrigerant two-phase flow in a horizontal pipe—II: Analysis of frictional pressure drop

Two-phase flow in horizontal pipe was analyzed with simplified models for annular and stratified flow. The velocity profiles for the liquid and gas phase were described with the Prandtl mixing length. From this analysis, the frictional pressure drop was calculated with the modified Baker map for flow pattern transition. The intermediate region, i.e. wavy flow, was interpolated between annular and stratified flow. Comparison of this analysis with existing experimental data of refrigerants showed good agreement.     

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.     

Two-phase stratified flow splitting at a T-jun

The objective of this study is to investigate, experimentally and theoretically, two-phase splitting under stratified wavy flow conditions at a regular horizontal T -junction with an inclined branch arm.

Experimental data have been acquired with the side arm at horizontal conditions, downward inclination angles of −5, −10, −25, −40 and −60°, and upward inclinations of 1, 5, 10, 20, and 35° from the horizontal. The data reveal that gravity forces have a significant effect on the flow splitting. For downward inclination of the side arm more liquid is diverted into the branch arm, as compared to the case in which the side arm was horizontal. All the liquid was found to be diverted into the branch arm when the branch arm inclination was increased to −60°. For upward inclination angles a significant amount of the inlet gas has to be diverted into the side arm in order to get any liquid to flow into that arm. However, once liquid has started flowing, not much more additional gas has to be diverted into the side arm to get all of the liquid to flow into the branch. At 35° almost all the gas has to be diverted for any liquid flow into the branch.

A mechanistic model has been developed for the prediction of the splitting phenomenon for both the horizontal and the downward orientations of the side arm. The model is based on the momentum equations applied for the separation streamlines of the gas phase and the liquid phase. Very good agreement is observed between the prediction of the model and the data acquired for all the cases.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Two-phase flow split at T junctions: Effect of side arm orientation and downstream geometry

The effect of flow pattern and geometry on the phase split of gas/liquid flows at T junctions has been examined for a horizontal main tube and horizontal and vertically upwards side arms. Important phenomena which control this split in annular and wavy stratified flow have been identified. The capability of current models to predict the split are discussed. In particular, the effect of geometry in the downstream leg of the main pipe was studied. The configurations studied had no effect in annular flow but influenced the amount of liquid taken off at high take off when stratified flow approached the junction.     

Liquid-phase axial mixing in two-phase horizontal pipe flow

The liquid-phase axial dispersion coefficient and volume-averaged fractional phase hold-ups have been measured in two-phase horizontal pipe flow. Radioactive ^99mTc—technetium-99 metastable—(as an aqueous solution of sodium pertechnate) was used as a tracer. The pulse technique with two-point measurement was employed. Superficial gas (air) and liquid (water) velocities were varied in the range 20–2300 and 30–800mm/s, respectively. The flow regimes covered were bubbly, elongated bubbly, stratified, wavy and slug. Experiments were also performed using single-phase pipe flow. The liquid-phase dispersion coefficient has been shown to depend upon the flow regime and the superficial gas and liquid velocities.