Flow In Annular Pipe Research Articles

Turbulent bifurcations in intermittent shear flows: From puffs to oblique stripes

Localised turbulent structures such as puffs or oblique stripes are building blocks of the intermittency regimes in subcritical wall-bounded shear flows. These turbulent structures are investigated in incompressible pressure-driven annular pipe flow using direct numerical simulations in long domains. For low enough radius ratio $\eta$, these coherent structures have a dynamics comparable to that of puffs in cylindrical pipe flow. For $\eta$ larger than 0.5, they take the shape of helical stripes inclined with respect to the axial direction. The transition from puffs to stripes is analysed statistically by focusing on the axisymmetry properties of the associated large-scale flows. It is shown that the transition is gradual : as the azimuthal confinement relaxes, allowing for an azimuthal large-scale component, oblique stripes emerge as predicted in the planar limit. The generality of this transition mechanism is discussed in the context of subcritical shear flows.

Convective heat transfer of turbulent decaying swirled flows in concentric annular pipes

The heat transfer characteristics of turbulent decaying swirled flows in concentric annular pipes is investigated numerically by means of CFD simulations using the OpenFOAM package. The simulations are performed for different Reynolds numbers and swirl angles at the duct inlet. By including cases with large temperature differences between the fluid and the wall, also the effects of radial temperature gradients on the velocity distribution are accounted for. A novel correlation, holding locally, is proposed and is presented in a form similar to the classical Sieder-Tate correlation, including an additional term to address the influence of the swirled flow. In a similar fashion, a correlation for the friction factor is given in the form of the Petukhov formula, yet with an additional swirl-related term. Also a formula assessing the swirl decay rate is presented. This allows global correlations to be extracted by solving the local ones over the pipe length in a system and integrating.

Turbulent heat transfer to separation nanofluid flow in annular concentric pipe

Turbulent heat transfer to separation nanofluid flow in annular concentric pipe were studied numerically and experimentally. In the numerical study, finite volume method with standard k-ε turbulence model in three dimensional domains was selected. Three different types of water based (Al2O3, CuO, TiO2) nanofluids were employed in this simulation. The adopted boundary conditions were, expansion ratio (ER = 1.25, 1.67, and 2), Reynolds number ranging from 20,000 to 50,000, water based nanofluids used Al2O3, CuO, TiO2 with volume fractions varied between 0 and 2% at different heat fluxes, varied from 4000 W/m2 to 16,000 W/m2. For experimental study, Al2O3 water based nanofluid was used to validate the numerical results. The results show that the volume fraction of nanofluid and Reynolds number significantly affect the surface heat transfer coefficient; an increase in surface heat transfer coefficient was noted when both volume fraction of nanofluids and Reynolds number were increased for all the cases. The improvement of heat transfer was about 36.6% for pure water at the expansion ratio of 2 compared to heat transfer obtained in a straight pipe. Augmentation of heat transfer could be achieved by using nanofluid at expansion ratio 2 where the total improvements were about 45.2% (TiO2), 47.3%(CuO), and 49%(Al2O3). Also the increment in the pressure drop was about 42% for pure water at expansion ratio 2 compared with straight pipe whereas by using nanofluid they were 62.6% (TiO2), 65.4% (CuO) and 57.6% (Al2O3). Good agreements were observed between numerical and experimental results all the way.

Interfacial friction in upward annular gas–liquid two-phase flow in pipes

Accurate prediction of interfacial friction between the gas and liquid in annular two-phase flow in pipes is essential for the proper modelling of pressure drop and heat transfer coefficient in pipeline systems. Many empirical relationships have been obtained over the last half century. However, they are restricted to limited superficial liquid and gas velocity ranges, essentially apply to atmospheric pressures, and the relationships are only relevant for pipes with inner diameters between 10 and 50mm. In this study, we carried out experiments in a large diameter flow loop of 101.6mm internal diameter with the superficial gas and liquid ranges of 11–29m/s and 0.1–1.0m/s respectively. An examination of published interfacial friction factor correlations was carried out using a diverse database which was collected from the open literature for vertical annular flow. The database includes measurements in pipes of 16–127mm inner diameter for the liquid film thickness, interfacial shear stress, and pressure gradient for air-water, air-water/glycerol, and argon-water flows. Eleven studies are represented with experimental pressures of up to 6bar. Significant discrepancies were found between many of the published correlations and the large pipe data, primarily in the thick film region at low interfacial shear stress. A correlation for the interfacial friction factor was hence derived using the extensive database. The correlation includes dimensionless numbers for the effect of the diameter across pipe scales to be better represented and better fit the wide range of experimental conditions, fluid properties, and operating pressures.

Unsteady fluid flow in a slightly curved annular pipe: The impact of the annulus on the flow physics

The motivation of the present study is threefold. Mainly, the etiological explanation of the Womersley number based on physical reasoning. Next, the extension of a previous work [Messaris, Hadjinicolaou, and Karahalios, “Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution,” Phys. Fluids 28, 081901 (2016)] to the annular pipe flow. Finally, the discussion of the effect of the additional stresses generated by a catheter in an artery and exerted on the arterial wall during an in vivo catheterization. As it is known, the square of the Womersley number may be interpreted as an oscillatory Reynolds number which equals to the ratio of the inertial to the viscous forces. The adoption of a modified Womersley number in terms of the annular gap width seems therefore more appropriate to the description of the annular flow than an ordinary Womersley number defined in terms of the pipe radius. On this ground, the non-dimensional equations of motion are approximately solved by two analytical methods: a matched asymptotic expansions method and a single. In the first method, which is valid for very large values of the Womersley number, the flow region consists of the main core and the two boundary layers formed at the inner and outer boundaries. In the second, the fluid is considered as one region and the Womersley number can vary from finite values, such that they fit to the blood flow in the aorta and the main arteries, to infinity. The single solution predicts increasing circumferential and decreasing axial stresses with increasing catheter radius at a prescribed value of the Womersley parameter in agreement with analogous results from other theoretical and numerical solutions. It also predicts the formation of pinches on the secondary flow streamlines and a third boundary layer, additional to those formed at the boundary walls. Finally, we show that the insertion of a catheter in an artery may trigger possible disastrous side effects. It may cause unexpected damage to a predisposed but still dormant location of the arterial wall due to high additional radial pressure that induces an excessive distension of the artery.

A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Film Thickness, Interfacial Shear Stress, and Droplet Size Distribution

The movement and distribution of each phase in annular flow can be considered as random events at a microscopic level. Hence, a probability analysis is appropriate to estimate the morphological features and mechanical characteristics of annular flow from a macroscopic scale. In the present work, three characteristic parameters including the film thickness, interfacial shear stress, and characteristic droplet size are predicted by a probability model as the statistical results of abundant samples. The film thickness can be directly calculated as one of the solutions to the basic equations of annular flow. The interfacial shear stress is estimated as a combination of the frictional and dragging components. The droplet size distribution is obtained using a method of undetermined coefficients. These characteristic parameters are well verified by comparing with the experimental data available in the literature. It is demonstrated that the probability model can accurately calculate the film thickness and maximum droplet size, but the predictions of the interfacial shear stress and mean droplet size are relatively coarse. Furthermore, the effects on the film thickness and Sauter mean diameter of other parameters are discussed in detail. Finally, some important phenomena observed in experiments are interpreted by the probability model.

The effect of the diameter on air-water annular and churn flow in vertical pipes with and without surfactants

In this work, we present results of flow visualisation, pressure gradient measurements, and liquid holdup measurements for air-water flow without and with surfactants in vertical pipes with diameters of 34 mm, 50 mm, and 80 mm. The surfactants cause the formation of foam. This foam has a larger volume and a smaller density than the liquid. The larger volume results in a larger pressure gradient at large gas flow rates. At small gas flow rates, the lower density of the foam causes the transition between the regular annular flow regime and the irregular churn flow regime to shift to lower gas flow rates. As a result foam reduces the pressure gradient and the liquid holdup at small gas flow rates. Surfactants reduce the pressure gradient more effectively for thinner liquid films at the wall; therefore, they are more effective for small pipe diameters and small liquid flow rates.

RANS Based Computational Fluid Dynamics Simulation of Fully Developed Turbulent Newtonian Flow in Concentric Annuli

A computational fluid dynamics (CFD) simulation is performed via ansys–CFX for a fully developed turbulent flow in concentric annuli with two radius ratios (R1/R2 = 0.4 and 0.5) at three Reynolds numbers (Re = 8900, 26,600, and 38,700) in terms of the hydraulic diameter D and the bulk velocity Ub. Near-wall turbulence structures close to the inner and outer walls are characterized by analyzing the first-order and second-order statistics. Effects of transverse curvature and the Reynolds number on development of the turbulence structures are emphasized. This study demonstrates the ability to predict the asymmetric features of turbulent flows in annular pipes by using the Reynolds-Averaged Navier–Stokes (RANS) model. Estimation of viscous dissipation in the flow using a RANS model is compared with direct numerical simulation (DNS) results for the first time.

Double-diffusive instability in core–annular pipe flow

The instability in a pressure-driven core–annular flow of two miscible fluids having the same densities, but different viscosities, in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen–Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmetric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect.

Numerical simulation of heat transfer and separation Al2O3/nanofluid flow in concentric annular pipe

Predictions are reported for turbulent three-dimensional heat transfer and flow separation of Al2O3/nanofluid in concentric annular cylinders with sudden expansion, in which the outer cylinder of a downstream section is heated at a uniform heat flux whereas the outer cylinder of the upstream section and the whole inner cylinder are adiabatic. The conservation equations are solved using the finite volume method. The numerical simulations are carried out by standard k-ε turbulence model. Results presented in this paper are for a constant heat flux range of 4000≤q≤16,000W/m2, four nanoparticle volumes (ɸ=0.5%, 1%, 1.5%, and 2%), and three expansion ratios (ER=1.25, 1.67, and 2). The Reynolds number is in the range of 20,000≤Re≤50,000. Results reveal that the volume fraction of Al2O3 and Reynolds number significantly affect the surface heat transfer coefficient: an increase in surface heat transfer coefficient was noted when both volume fraction of Al2O3 and Reynolds number were increased for all cases. It is found that the peak of the heat transfer coefficient occurs after the sudden expansion moved far from the step height with the increase of sudden expansion dimensions due to separation flow in case of both pure water and nanofluid. The size of the recirculation zone increases as the Reynolds number and expansion ratio increase. Increasing the nanoparticle of Al2O3/nanofluid tends to enhance the heat transfer coefficient due to nanoparticle heat transport in the base fluid which raises the convection heat transfer.

Interfacial shear in adiabatic downward gas/liquid co-current annular flow in pipes

Interfacial friction is one of the key variables for predicting annular two-phase flow behaviours in vertical pipes. In order to develop an improved correlation for interfacial friction factor in downward co-current annular flow, the pressure gradient, film thickness and film velocity data were generated from experiments carried out on Cranfield University’s Serpent Rig, an air/water two-phase vertical flow loop of 101.6mm internal diameter. The air and water superficial velocity ranges used are 1.42–28.87 and 0.1–1.0m/s respectively. These correspond to Reynolds number values of 8400–187,000 and 11,000–113,000 respectively. The correlation takes into account the effect of pipe diameter by using the interfacial shear data together with dimensionless liquid film thicknesses related to different pipe sizes ranging from 10 to 101.6mm, including those from published sources by numerous investigators. It is shown that the predictions of this new correlation outperform those from previously reported studies.

Validation and Visualization of Decaying Vortex Flow in an Annulus

Swirling jets produced using inlet swirlers are often used to increase the heat or mass diffusion rates in heat exchangers or reactors, separation of smoke and dust suspended in the air in ventilation ducts etc. The aim of this work is to validate a CFD model through streak-line comparison and to define the fully laminar and turbulent regime for decaying vortex flow produced using a set of axial swirlers in an annular pipe. Flow visualization was conducted using fluorescent dye to visualize on eddy formation along the pipe. Decaying vortex flow was produced using static axial swirlers fitted at the inlet of the annular pipe. In this study, three different swirl angles were investigated: 30°, 45° and 60°. In addition, the Reynolds number (Re) was varied from 10 to 1800. Results shows that the flow regimes for decaying vortex flow in annuli can be defined with reference to axial annular pipe flow.

Simulation of laminar flow through eccentric annuli using isogeometric variational multiscale method

We present an application of the Residual-based variational multiscale (RBVMS) methodology to the computation of laminar eccentric annular pipe flow with eccentricities of 0.5 and 1. Isogeometric analysis is utilized for higher order approximation of the geometry and solution using Non-uniform rational B-splines (NURBS) functions. The ability of NURBS exactly representing curved circular geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through the eccentric annuli. By using the exact representation of circular boundary, the limiting case of the eccentricity, i.e. the inner circular wall actually touches the outer circular wall, is successfully demonstrated.

Film thickness of vertical upward co-current adiabatic flow in pipes

Average liquid film thickness is important for detailed mechanistic modeling of annular two-phase flow in engineering applications. The existing models and correlations either have large relative errors or narrow application range. Because of this, a new liquid film thickness model has been developed for vertical annular flow in pipes based on three databases. The model includes the pressure, liquid and gas velocities, diameter, and viscosity effects on liquid film thickness. Analysis indicates the film thickness to be a function of Weber numbers for both liquid and gas, and the viscosity number. The model is compared with film thickness data which considers a wide range of liquid and gas superficial velocities, system pressure, fluid properties, as well as several pipe diameters. The trend in the current and available film thickness models at various system conditions are analyzed, highlighting the improvement and widening applicability of the new model. The newly proposed film thickness model results in an average relative error of 14% considering the complete database.

Full 3D Simulations of Two-Phase Core–Annular Flow in Horizontal Pipe Using Level Set Method

Simulating core---annular flow is an important task in the oil industry. Many attempts have been made to simulate vertical upflow or downflow. However, in the case of horizontal pipes, simulation is likely to succeed when the effect of gravity is ignored, because the motion of the fluid is no longer axisymmetric. This gravity-ignoring simulation is acceptable when the density of oil is almost similar to that of water, but in most cases, density-matching does not occur in reality. A few attempts have been made to simulate flow in horizontal pipes (Ooms et al. in Phys Fluids 25:032102, 2013), but these attempts used 2D cross-sectional simulation or 3D simulation of a specific moment. This paper discusses several results for core---annular flow in horizontal pipes with gravity effect, using full 3D simulation. Using a level set method, we express the interface of core---annular flow and compare different cases with different parameters.

A probability model for fully developed annular flow in vertical pipes: Prediction of the droplet entrainment

The phase distributions and mechanical properties of annular flow can be regarded as random states. Hence the probability analysis is an appropriate method to investigate the possibilities of the relevant events and the statistic results of some characteristic parameters. In the present work, a probability model for fully developed annular flow in vertical pipes is proposed to predict the phase distributions and mechanical characteristics. The probability model works in three mechanisms. First, a vortex generation theory on energy transfer from vortexes to droplets is supposed to describe the atomization process. Second, a random walk theory is applied to track the droplet deposition on the liquid film. Third, the atomization and deposition rates are respectively related to the probabilities of droplet generation and elimination by analyzing the interaction between vortexes and droplets. Based on the knowledge of dynamic equilibrium between atomization and deposition processes, a balance equation is established to close the equation set and the representative parameters of annular flow can be solved. The new model is a statistical method and almost links all the parameters involved in annular flow. By comparing the predicted droplet entrainment with experimental data available in the literature, the present model is well verified and demonstrates advantages both in accuracy and in convenience. Furthermore, the effects on the entrainment of many parameters, including the gas flow rate, liquid flow rate, gas density, liquid density, gas viscosity, surface tension and pipe diameter, are discussed in detail.

1513 二重円管内乱流の亜臨界遷移に関する直接数値シミュレーション

We perform direct numerical simulation (DNS) for annular pipe flow and report localized structures in subcritical transition. Our flow system is the simplest fundamental annular pipe flow which is a flow between two concentric cylinders and is driven by a constant uniform pressure gradient in the axial direction. By changing Reynolds number (Re_τ = uτδ/ν) and radius ratio (η = r_<in>/r_<ou>) systematically, we found several localized intermittent turbulent states. To observe the effect of η, we choose low to high radius ratios, which are 0.1, 0.3, 0.5, and 0.8. At η &ge; 0.5, we confirmed stripe pattern similar to that in the plane Poiseuille flow. In contrast, with a low η of 0.1, localized structures corresponding to equilibrium puffs and splitting puffs arise. The moderate η of 0.3 gives rise to localized turbulence taking a form of finite (like a puff) and helical shape (like a stripe pattern).

The effects of wall roughness on erosion rate in gas–solid turbulent annular pipe flow

In the present study, the effects of wall roughness on erosion rate for gas–solid flows in horizontal annular pipes for different ratios of inner to outer radii and also for different values of solid particle concentration are investigated. The results are compared with earlier studies, and the effect of various parameters is discussed. The impingement angles and impact velocities of solid particles, which are needed for using the comprehensive erosion model, are evaluated using a four-way coupled Eulerian–Lagrangian simulation approach of gas–solid flows. The turbulent gas phase flow is solved using the k–ε model. For the simulation of particle movement, the fluctuations of gas phase velocity are evaluated by the eddy interaction method. The numerical results indicate that the solid particle induced erosion rate at the outer wall of annular pipes is considerably larger in comparison with a simple circular pipe with the same outer radius, and the erosion rate further increases as the radius ratio increases. The results also show that the erosion rates at both inner and outer walls increase as wall roughness increases and are much higher compared with those for smooth walls or walls with a small roughness.

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 2: Liquid holdup and pressure gradient dynamics

In this paper, we study the effect of surfactants on both the liquid holdup and the dynamics of the pressure gradient in annular and churn flow in vertical pipes. This effect is linked to the influence of the surfactants on the morphology of the air–water interface, which is studied in a related paper (van Nimwegen et al., 2014). The experimental results, obtained using a vertical flow loop with a 5cm internal diameter at ambient pressure, show three different effects of the surfactants on the measured quantities, depending on the air and water flow rates. (i) At large air flow rates, in the annular flow regime for air–water flow, the surfactants increase the pressure gradient; this is solely due to the increase of the frictional pressure gradient, caused by the larger interfacial stress between the foamy waves overlaying the foam substrate along the wall and the gas core. (ii) At low air flow rates and low water flow rates, in the churn flow regime for air–water flow, the surfactants decrease significantly both the average pressure gradient and the pressure gradient fluctuations. While the frictional pressure gradient increases, the liquid holdup decreases by more than a factor of two; the foam suppresses the flooding waves, making the flow much more regular, leading to the small pressure gradient fluctuations. Furthermore, there exists an optimum surfactant concentration for decreasing the average pressure gradient and the pressure gradient fluctuations. (iii) At low air and high water flow rates, in the churn flow regime for air–water flow, the average pressure gradient and the pressure gradient fluctuations are both somewhat decreased by the surfactants.

The effect of surfactants on air–water annular and churn flow in vertical pipes. Part 1: Morphology of the air–water interface

In this work, the influence of surfactants on air–water flow was studied by performing experiments in a 12 metre long, 50mm inner diameter, vertical pipe at ambient conditions. High-speed visualisation of the flow shows that the morphology of the air–water interface determines the formation of foam. The foam subsequently alters the flow morphology significantly. In annular flow, the foam suppresses the roll waves, and a foamy crest is formed on the ripple waves. In the churn flow regime, the flooding waves and the downwards motion of the liquid film are suppressed by the foam. The foam is transported in foam waves moving upwards superposed on an almost stagnant foam substrate at the pipe wall. Foam thus effectively reduces the superficial gas velocity at which the transition from annular to churn flow occurs. These experiments make more clear how surfactants can postpone liquid loading in vertical pipes, such as in gas wells.