A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Movement Properties of Pipe Flow Along Granite Slope of Three Gorges Area of Yangtze River in China

It is well known that, in most cases, soil water doesn't move in the form of laminar flow as described by Darcy law. Only when Reynolds number ( Re ) is no more than 10, does water movement follow Darcy law. A soil profile with 2 9 m long and 2 13 2 60 m deep was excavated on a lower slope located at Zigui County, Hubei Province, China. Field observation found that soil pipes were mainly distributed in the transient layer between horizon B with higher degree of granite weathering and horizon C with lower degree of granite weathering. At the foot of the slope, about 5 7 soil pipes per meter were observed along the vertical direction of the slope. The observed results, obtained by continuous observation of soil pipes and pipe flow processes at granite slope for many rainfall events, indicate that the relationship between velocity of pipe flow and hydraulic gradient along the pipe is parabolic rather than linear. Based on the investigated data of soil, landform, and land use etc., combined with observed data of pipe flow derived from many rainfall events, a pipe flow model was developed. For velocity V p, discharge Q p of pipe flow and radius r of soil pipe, great similarity was found between simulated and observed values. Particularly, the simulated length of soil pipes reflects the great difference among soil pipes as a result of its different position in the soil profile. The length values of 4 soil pipes were estimated to be 98 1%, 27 6%, 11 0% and 3 0% of the longest distance of the catchment, respectively. As a special case of water movement, soil pipe flow follows Darcy Weisbach law. Discharge of pipe flow is much greater than infiltration discharge in common. Only when the depth of groundwater is more than the diameter of soil pipe and water layer submerges soil pipes during rainfall, may pipe flow occur. Under these circumstances, discharge of pipe flow is directly proportional to the depth of groundwater.

Research on the orientation distribution of fibers immersed in a pipe flow

The computed orientation distribution of fibers immersed in laminar pipe flows showed that the longitudinal distributions are wide for small Reynolds numbers and become narrower with increasing Re . For low Re number, the axial orientation distributions are broad with almost no preferred orientations. For high Re number, the axial distribution becomes narrow, with sharp maxima. The mean values of the longitudinal orientation depend strongly on the Re number. The computed results are in qualitative agreement with relevant experimental results.

Characteristics of turbulent flow distribution in branch piping system

Flow distribution in branch piping system is affected by flow characteristics and different geometric variations. Most of the flow distribution studies are performed with one-dimensional analysis to yield overall information only. However, detailed analysis is required to find effects of design parameters on the flow distribution. For this aspect, three-dimensional turbulent flow analysis was performed to assess turbulence model performance and effects of upstream pressure and branch pipe geometry. Three different turbulence models of standard k-e model, realizable k-e model and standard k-co yield similar results, indicating small effects of turbulence models on flow characteristics analysis. Geometric variations include area ratio of main and branch pipes, branch pipe diameter, and connection shape of main and branch pipes. Among these parameters, area ratio and branch diameter and shape show strong effect on flow distribution due to high friction and minor loss. Uniform flow distribution is one of common requirements in the branch piping system and this can be achieved with rather high total loss design.

Numerical Simulation of Turbulent Swirling Pipe Flow with an Internal Conical Bluff Body

Turbulent swirling flow inside a short pipe interacting with a conical bluff body was simulated using the commercial CFD code Fluent.The geometry used is a simplified version of a novel liquid/gas separator used in multiphase flow metering.Three turbulence models,belonging to the Reynolds averaged Navier-Stokes(RANS)equations framework,are used.These are,RNG k-ε,SST k-ωand the full Reynolds stress model(RSM)in their steady and unsteady versions.Steady and unsteady RSM simulations show similar behavior.Compared to other turbulence models,they yield the best predictions of the mean velocity profiles though they exhibit some discrepancies in the core region.The influence of the Reynolds number on velocity profiles,swirl decay,and wall pressure on the bluff body are also presented.For Reynolds numbers generating a Rankine-like velocity profile,the width and magnitude of flow reversal zone decreases along the pipe axis disappearing downstream for lower Reynolds numbers.The tangential velocity peaks increase with increasing Reynolds number.The swirl decay rate follows an exponential form in accordance with the existing literature.These flow features would affect the performance of the real separator and,thus,the multiphase flow meter,noticeably.

Nanoparticle Migration in a Fully Developed Turbulent Pipe Flow Considering the Particle Coagulation

Numerical simulations of nanoparticle migration in a fully developed turbulent pipe flow are performed.The evolution of particle number concentration,total particle mass,polydispersity,particle diameter and geometric standard deviation is obtained by using a moment method to approximate the particle general dynamic equation.The effects of Schmidt number and Damkhler number on the evolution of the particle parameters are analyzed.The results show that nanoparticles move to the pipe center.The particle number concentration and total particle mass are distributed non-uniformly along the radial direction.In an initially monodisperse particle field,the particle clusters with various sizes will be produced because of coagulation.As time progresses,the particle cluster diameter grows from an initial value at different rates depending on the radial position.The largest particle clusters are found in the pipe center.The particle cluster number concentration and total particle mass decrease with the increase of Schmidt number in the region near the pipe center,and the particles with lower Schmidt number are of many dif-ferent sizes,i.e.more polydispersity.The particle cluster diameter and geometric standard deviation increase with the increase of Damkhler number at the same radial position.The migration properties for nano-sized particles are different from that for micro-sized particles.

RESEARCH ON THE MOTION OF PARTICLES IN THE TURBULENT PIPE FLOW OF FIBER SUSPENSIONS

The motion of fibers in turbulent pipe flow was simulated by 3-D integral method based on the slender body theory and simplified model of turbulence.The orientation distribution of fibers in the computational area for different Re numbers was computed.The results which were consistent with the experimental ones show that the fluctuation velocity of turbulence cause fibers to orient randomly.The orientation distributions become broader as the Re number increases.Then the fluctuation velocity and angular velocity of fibers were obtained.Both are affected by the fluctuation velocity of turbulence.The fluctuation velocity intensity of fiber is stronger at longitudinal than at lateral,while it was opposite for the fluctuation angular velocity intensity of fibers.Finally,the spatial distribution of fiber was given.It is obvious that the fiber dispersion is strenghened with the increase of Re numbers.

MAGNETOHYDRODYNAMIC PIPE FLOW IN DUCTS WITH PARTIAL CIRCULAR RING CROSS SECTION AND ANNULAR CROSS SECTION

In this paper we use the Green function method to solve the problem of steady one dimensional flow of an incompressible viscous, electrically conducting fluid through a pipe with partial circular ring cross sec- tion and one with annular cross section, in the presence of an applied transverse uniform magnetic field, We ob- tain analytic solutions and carry out some numerical calculations of the velocity distribution and induced magnet- ic field.

Measurement of Fluid Flow in Pipe and Porous Media by High-Resolution Magnetic Resonance Imaging

The objective of this study is to understand the process of fluid flow in pipe and porous media with different pore structures. High-resolution Magnetic Resonance Imaging （MRI） technique was used to visualize the pore structure and measure fluid flow. The porous media was formed by packed bed of glass beads. Flow measurement was carried out by a modified spin echo sequence. The results show that the velocity distribution in pipe is annular and the linear relation between MRI velocity and actual velocity is found in pipe flow measurement. The flow distribution in porous media is rather heterogeneous, and it is consistent with heterogeneous pore structure. The flow through pores with the high volume flow rate is determined largely by geometrical effects such as pore size and cross-sectional area.

K-ε-T MODEL OF DENSE LIQUID-SOLID TWO-PHASE TURBULENT FLOW AND ITS APPLICATION TO THE PIPE FLOW

To predict the characteristics of dense liquid-solid two-phase flow, K-Ε-T model is established, in which the turbulent flow of fluid phase was described with fluid turbulent kinetic energy Kf and its dissipation rate Εf, and the particles random motion was described with particle turbulent energy Kp and its dissipation rate Εp and pseudothermal temperature Tp. The governing equations were also derived. With K-Ε-T model, numerical study of dense liquid-solid two-phase turbulent up-flow in a pipe is performed. The calculated results are in good agreement with experimental data of Alajbegovic et al. (1994), and some flow features are captured.

THEORETICAL ANALYSIS OF USING AIRFLOW TO PURGE RESIDUAL WATER IN AN INCLINED PIPE

A refined theoretical analysis for using the spiral airflow and axial airflow to purge residual water in an inclined pipe was presented. The computations reveal that, in most cases, the spiral flow can purge the residual water in the inclined pipe indeed while the axial flow may induce back flow of the water, just as predicted in the experiments presented by Horii and Zhao et al. In addition, the effects of various initial conditions on water purging were studied in detail for both the spiral and axial flow cases.

ANALYTIC SOLUTIONS OF INCOMPRESSIBLE LAMINAR FLOW IN THE INLET REGION OF A PIPE

The laminar analytic solutions of velocities and pressure in the central zone of the inlet region of pipe flow are given under the condition of uniform inflow, based on the Navier-Stokes equations of incompressible viscous flow.

Optimal transient growth in turbulent pipe flow

The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.

AN ANALYTIC SOLUTION OF DENSE TWO-PHASE FLOW IN A VERTICAL PIPELINE

According to a mathematical model for dense two-phase flows presented in the previous pape[1],a dense two-phase flow in a vertical pipeline is analytically solved, and the analytic expressions of velocity of each continuous phase and dispersed phase are respectively derived. The results show that when the drag force between twophasesdepends linearly on their relative velocity, the relative velocity profile in the pipeline coincides with Darcy's law except for the thin layer region near the pipeline wall, and that the theoretical assumptions in the dense two-phase flow theory mentioned are reasonable.

On the helical pipe flow with a pressure-dependent viscosity

We address the flow of incompressible fluid with a pressure-dependent viscosity through a pipe with helical shape. The viscosity-pressure relation is defined by the Barus law. The thickness of the pipe and the helix step are assumed to be of the same order and considered as the small parameter. After transforming the starting problem, we compute the asymptotic solution using curvilinear coordinates and standard perturbation technique. The solution is provided in the explicit form clearly showing the influence of viscosity-pressure dependence and pipe＇s geometry on the effective flow.

OPTICAL TELEPHONE CORD PASSING THROUGH LONG PIPE WITH SPIRAL FLOW

A new effective technique, useful in telecommunications industry for passing an optical telephone cord attached to a connector through pipeline,has been developed using the spiral flow. Using this technique, the cord could be passed through a straight pipeline 150 meters long and a roll of vinyl tube 50 meters long. However, under the same condition, the cord could not pass through when using the turbulent flow. To obtain a high speed stable spiral flow, a nozzle with an annular slit connected to a conical cylinder was used. A pressurized fluid with no tangential flow was supplied through this slit and the fluid, passing through the conical cylinder, was deformed into spiral flow with the steeper axial velocity distribution compared to that of turbulence pipe flow due to Coanda effect and instability. As a result, the cord was attracted to the axis area of the pipe, which effectively increased the ability for the work of cord passing. This high ability for cord passing is attributed mainly to the reduction of the friction made between the cord and the pipe wall, caused by the deformation to spiral flow.

GENERAL SECOND ORDER FLUID FLOW IN A PIPE

It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study second fluid flow in a paper. First, we derivethe analytical solution which the derivate order is half and then with the analyticalsolution we verify the reliability of Laplace numerical inversion based on Crumpalgouithm for the problem, and finally we analyze the characteristics of second orderfluid flow in a pipe by using Crump method. The results indicate that the more obviousthe viscoelastic properties of fluid is, the more sensitive the dependence of velocity andstress on fractional derivative order is.

Unsteady Rotative Flow of Non-Newtonian Fluid in an Annular Pipe

This paper .Studies power law no-Newtonian fluid rotative flow. in an annularpipe. The governing equation is nonlinear one, we linearized the governing equationby assuming that partial factor is at state. With Laplace transform we obtain ananalytical solution of the problem In the paper several groups of curves are given.these curves reflect the temporal change law and. spatial distribution of fluid velocity.In addition.we study the effection of power law index on the flow field the resultindicates that when the power law index n < l. the flow velocity is highly sensitive tothe index. and this fact is importanl in related engineering decisions.

Improved Dissipation Rate Equation for Swirling and Rotating Pipe Flows

The nature of turbulent swirling and rotating flow in a straight pipe is investigated using a family of near-wall two-equation models. Specifically, the viability of three different near-wall two-equation models is assessed. These models are asymptotically consistent near the wall. The first two models, one with isotropic and another with anisotropic eddy viscosity invoked, solved a dissipation rate equation with no explicit correction made to account for swirl and flow rotation. The third model assumes an isotropic eddy viscosity but solves an improved dissipation rate equation that has explicit corrections made to account for swirl and flow rotation. Calculations of turbulent flows in the swirl number range 0.25 - 1.3 with and without a central recirculation region reveal that, with the exception of the third model, neither one of the other two models can replicate the mean field at the swirl numbers tested. Furthermore, taking stress anisotropy into account also fails to model swirl effect correctly. Significant improvements can be realized from the third model, which is based on an improved dissipation rate equation and the assumption of isotropic eddy viscosity. The predicted mean flow and turbulence statistics correlate well with measurements at low swirl. At high swirl, the two-equation model with an improved dissipation rate equation can still be used to model swirling and rotating pipe flows with a central recirculation region. However, its simulation of flows without a central recirculation region is not as satisfactory.

A HYBRID FEM ALGORTHM FOR FLUID FLOW IN A VISCO-ELASTIC PIPE

A variational principle of hybrid FEM is proposed to solve the flow in a visco-elaslic pipe. As an example, the influence of an axisymmetrical stenosis on an artery vibrating flow with a single frequency is calculated.