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In order to accurately obtain the liquid holdup of the inclined tube gas-liquid two-phase flow at high flow rate, air and water were used as experimental media, the gas volume was set to 180 ~ 2 000 m³/h, and the liquid volume was set to 2 ~ 20 m³/h. The experiment of the inclined tube high-gas-liquid two-phase flow at normal pressure was carried out in a test tube with an inner diameter of 60 mm and a length of 9. 5 m. The main flow patterns in the experimental range are slug flow and annular flow. The experimental flow patterns are drawn into the existing flow patterns, and the Mukherjee-Brill, Kaya and Chokshi flow patterns are found to be suitable for the identification of experimental flow patterns by comparing various flow patterns. The experimental data are further used to test the common liquid holdup prediction model and it is found that the Mukherjee-Brill model is relatively accurate, but the error is close to 20%, which is still large. In view of this, the literature and experimental data of different parameters such as pressure, temperature, pipe diameter and inclination angle under high gas-liquid flow rate at home and abroad are collected to analyze and summarize the influencing factors of liquid holdup. Liquid viscosity, pipe diameter, gas phase velocity, liquid phase velocity, pressure and inclination angle are selected as the comparison sequence and liquid holdup as the reference sequence. The gray correlation degree analysis method determined that the diameter of pipe had a great influence on liquid holdup, so the Mukherjee-Brill liquid holdup model is optimized, and a new liquid holdup calculation model is established considering the influence factors of pipe diameter. The new model is verified by the data of 14 different pipe diameters, including 25. 2 ~ 95. 3 mm, at high gas-liquid flow rates in the literature experiment and this experiment. The average absolute percentage error of the new model is 6. 85%, which is at least 4. 96% less than that of the existing five liquid holdup models. [ABSTRACT FROM AUTHOR]

Pipeline transport is proven to be an efficient method for conveying fluids over long distances, offering benefits such as continuous transport, significant volume capacity, lower energy costs, and substantial environmental advantages. Damage to pipelines could have detrimental effects on the economy, the environment, and pose health and safety risks for the population. The safety issues associated with pipes garner considerable attention in both scientific research and industry. The focus of the current study is on the dynamic stability of a straight fluid-conveying pipe with an elastic support. The investigation is based on the Euler-beam model and involves the use of Laplace and Fourier transformations. The paper draws attention to the stability of inclined pipes, as they haven’t received much attention.

Coarse particle-laden flows in inclined pipes are commonly encountered in a wide range of industrial processes. A fully coupled CFD-DEM model considering various fluid-particle interphase forces and turbulence-particle interactions is used to simulate coarse particles transported in inclined pipes. The energy dissipation is calculated from both the macro and micro perspectives. The effects of pipe's inclination angle, particle concentration, conveying speed and particle diameter on the hydraulic transport characteristics and the energy dissipations are analyzed. The results showed that, with the increase in inclination angle, the deposited particles were gradually dispersed. Pressure drop and energy dissipation displayed a peak at 60°. Both the parameters increased with the increases in particle concentration and conveying speed in 60° inclined pipe. The energy dissipation was mainly due to the turbulent dissipation, wall friction, mean velocity field and particles' gravity. The results further showed that the modulations in the fluid due to particle distribution could significantly change the energy dissipation caused by the fluctuating velocity, thus resulting in the maximum pressure drop and energy dissipation at 60°. The particle-fluid energy dissipation increased almost linearly with the increase in conveying speed, while it varied nonlinearly with the increase in inclination angle and particle parameters. [ABSTRACT FROM AUTHOR]

【Objective】 This paper aims to study the optimal layout of inclined pipes in sedimentation basins in attempts to improve sediment removal efficiency in the Yellow River. 【Method】 Three different layouts of inclined pipes were compared: a single layer (Fs), and two double-layer layouts (Fv1, Fv2), in a gravity-operated sedimentation basin. Sediment distribution of three typical particle sizes in the upstream (Su), middle stream (Sm), and downstream (Sd) was measured. Sediment tests were conducted under a low (Qq) and a high (Qs) flow rate to compare the impact of pipe inclination on sedimentation in the three layouts. 【Result】 The large granular sediment settled prior to entering the inclined pipes, while the fine particle sediment (

The primary focus of this research is to create a precise, yet straightforward drift-flux model tailored for water-gas flow in variously angled pipes. This model is pivotal in estimating the volumetric flow rate of each phase in two-phase pipe flow scenarios. The proposed correlation is developed using twenty-two different (4367 data points) sources with a wide range of input data with different flow patterns. The drift-flux model created in this study underwent validation through the use of experimental data previously documented in the literature. Results indicate this model's stability and practicality, achieving 94.7 % accuracy within a margin of error of ±20 % for the chosen datasets. Furthermore, when compared against several drift-flux models, this newly proposed model consistently outperformed them across a liquid holdup range of 0.01–1. A comparative analysis with the state-of-the-art Unified Model underscores the accuracy of the proposed drift-flux model, highlighting its performance across diverse inclination angles and flow regimes. The proposed model demonstrates excellent predictive accuracy, particularly in vertical flow scenarios. Extending the scope of the study, further research could focus on the application of the developed drift-flux model to other fluid combinations and flow conditions, as well as its integration with mechanistic modeling and computational fluid dynamics simulations to provide more comprehensive insights into the behavior of two-phase flow in pipes with different inclination angles, enhancing the model predictive ability and operational range.

During the operation of the water transportation pipelines in the upstream of the Yellow River, varying degrees of sand deposition often occur under a low flow rate. Taking into account the effect of different pipe inclinations, pipe diameters, and inlet sand content, the Eulerian–Eulerian two-phase model was applied in the numerical simulation of sediment-laden flow in a V-inclined pipe. The results indicate that there is a significant difference between a V-inclined pipe and horizontal pipe affected by gravity. Compared with the downward inclined pipe, sand deposition is evident in the upward inclined pipe. The high-velocity region moves upward and the asymmetry of the cross-sectional velocity increases. As the pipe diameter increases, the interaction between sand and the wall as well as the degree of turbulence decrease, so that the distribution of sand volume concentration across the cross section will be more uniform. Under different inlet sand content, the lowest point of the pipe experiences the most sand deposition, with sand volume concentration and velocity distribution across the cross-sections becoming uneven as inlet sand content increases. The location of the maximum liquid velocity varies from section to section. When the inlet sand content increases from 0.42% to 5%, the liquid velocity of the pipe cross-section no longer satisfies the rule of high velocity for middle and low velocity near the wall. [ABSTRACT FROM AUTHOR]

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Copyright of Tunnel Construction / Suidao Jianshe (Zhong-Yingwen Ban) is the property of Tunnel Construction Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Hydraulic transport in pipelines is the most promising conveying method for large ore particles in deepsea mining. The dynamic performances of particles during transportation in vertical, inclined and horizontal pipelines are significant for the design of hydraulic transport systems. In the present study, we focus on the statistical characteristics and flow regimes of the mixture composed of ore particles and seawater in the pipelines. Numerical simulations are conducted by using Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM). The influences of inclination angle and particle diameter are evaluated through two sets of numerical tests. The regulation of the inclined transport is totally different from that of the vertical transport, whereas the dynamics of the mixtures in inclined and horizontal pipes are similar. A number of particles accumulate on the pipe wall even with a small inclination angle. Large hydraulic gradient and local concentration would occur when the inclination angle of the pipe is in the range of 30°–60°. With the decrease of particle diameter, the particle flow becomes uniform, reflected by the almost uniform particle distribution in the vertical pipe and the clear interface between the suspended load and the bed-load in the inclined pipe. However, small particles will introduce larger local concentrations and hydraulic gradients in the inclined pipe, which is not conducive to particle transport. [ABSTRACT FROM AUTHOR]

Two‐phase flow is a common phenomenon in the energy industry, where flow patterns significantly affect heat transfer and pressure drop in different systems. However, there is no unique or comparable flow map because of its dependency on dimensional parameters. Therefore, an analysis using dimensionless numbers makes the results comprehensive. To do so, a series of liquid–liquid flow experiments (1296 experiments) were conducted in a transparent pipe at the different velocities of the phases. The flow patterns were captured using a high‐speed camera. The experiments were performed at eight different inclinations within the range of −20 to +20 degrees. Six flow patterns are observed at different inclinations; stratified flow with mixing at the interface (STMI), dispersion of water in oil (Dw/o), dispersion of oil in water (Do/w), dual continuous (DC), slug, and wavy stratified (WST), where the first five flow patterns are presented in the upward flow and the two last flow patterns disappear in some of the downward flow. The pattern of boundaries for each flow pattern in the upward flow shows dependency on inclination, while in the downward flow condition, a rather general format can be applied to most of the patterns. The analysis illustrates that gravity and buoyancy forces are the dominating forces in the system compared to other forces, such as viscous, inertia, and interfacial tension, which are due to the inclination of the pipe. [ABSTRACT FROM AUTHOR]

Pipeline transportation of liquid CO2 can not only prevent coal mine fires, but also effectively store greenhouse gase CO2 in underground, which is in line with the current global economic development model. Due to the temperature difference of the mine environment and the inclination of the roadway, heat exchange and large pressure drop will inevitably occur in the pipeline. In order to avoid the phase change of liquid CO2 during transportation, it is necessary to consider factors such as ambient temperature, wind speed, insulation cotton, pipeline inclination, and terrain elevation to ensure safe, cost-effective transportation. Based on the commercial simulation software ASPEN HYSYS V8.4, this paper simulates the process of liquid CO2 transportation. The results show that the inclination of the pipeline has a great influence on the CO2 transportation process among environmental factors and is conducive to liquid CO2 transportation.

An experimental investigation on the mixed convection heat transfer of air flowing in circular conduits of a solar collector is conducted. The test rig consists of three different copper pipes with a length of 70 cm. The pipes are heated at constant heat flux. The effect of the pipe inclination angle (θ = 0°, 60°, and 90°), length-to-diameter ratio (L/D = 13.8, 18.4, and 36.7), and heat rate (Q = 5, 11, 19.6, 30, 40.5, and 57.8 W) is studied in the present study. The influences of Richardson number (Ri), inclination angle, and length-to-diameter ratio on the average Nusselt number are examined as well. The results show that the Nusselt number (Nu) is improved by 41.5% as the inclination angle is changed from 0° to 90° at L/D = 13.8. Further, as the length-to-diameter ratio was reduced from 36.7 to 13.8 at 90°, up to 54.9% enhancement in heat transfer is found. Also, it is seen that by increasing the heat rate from 5 W to 57.8 W at 90° and L/D = 13.8, the exchange in heat is improved by 44%. Three empirical correlations were proposed for each studied pipe inclination angle. A good agreement was found between the measured Nu and the calculated Nu from the proposed correlations. [ABSTRACT FROM AUTHOR]

This work is devoted to an experimental study of the effect of coalescence on the average diameter and velocity of gas bubbles in an inclined pipe. The measurements were carried out for agas flow rate of 3.3 and 5 mL/min at pipe inclination angles of 30–60°. The study of gas bubble diameters was performed using a shadow photography method. The values of the average diameter and velocity of the bubbles were obtained depending on the angle of inclination of the pipe. A map of regime parameters was constructed at which gas bubbles form a stable structure—a chain of bubbles with an equal diameter. [ABSTRACT FROM AUTHOR]

This paper investigates the force features of inclined pipes under the action of waves and flows through both test and numerical simulation. Firstly, the wave and flow loads on inclined pipes were examined through tests in circulating water flumes. Next, the unsteady Reynolds-averaged Navier-Stokes (RANS) equations were adopted to numerically simulate the test conditions. Multiple factors were taken into consideration: immersion depth, inclination, flow rate, wave height, and cycle. The results show that, the wave and flow loads on the pipes both increase with wave height and flow rate. When the inclination β = 0°, the flow force is most rapid, conversely, it is most slow when the inclination β = 30°. Furthermore, when the pipe was immersed by 75%, the change of inclination directly affected the ratio of vertical force to horizontal force. For the pipes with different inclinations, the wave load increases basically at the same rate with the rising wave height. With the widening of the inclination, the wave and flow loads on the pipes become less sensitive to immersion depth, and the maximum loads remain near the free water surface.

• Solids velocity in FB standpipe was accurately measured by tracing a magnetic tracer. • Adverse effects caused by narrow orifice can be addressed via correcting velocity distribution. • The inclined pipe can affect solids mass flow and mitigate the adverse effects caused by narrow orifice. • Solids waving and pulsing behaviors were detected by the magnetic tracer-tracking method. In the present study, the application of a magnetic tracer-tracking method in measuring solids circulation in a fluidized bed standpipe is investigated, due to its advantages of little intervention and cost efficiency, especially in pressurized systems. The method only needs to inject one small magnetic tracer to follow the main solid flow in the standpipe, therefore predicting particles' real-time velocities. The measurement accuracy was thoroughly tested via comparing to conventional descending and accumulation methods. Main tracer properties, including tracer shape, density, and magnet core, were considered. Solids flow patterns in the standpipe were also regulated by changing orifice sizes and adding an inclined pipe, for the purpose of investigating the measurement accuracy in various conditions. The adverse effect of a narrow orifice on measurement was addressed via constructing a model that includes sand particles' non-uniform velocity distribution across the standpipe cross-section. To interpret behaviors of tracers varied in size and density, a mathematical model was constructed to describe forces exerted on the tracer in the solids bed. The behaviors of the tracer immersed into the solids bed were also examined, providing an insight to that in a standpipe with continuous solids circulation. The solids bed density was also regulated by varying the mixture of olivine sand and carbonaceous particles at different proportions. The magnetic tracer-tracking method has been successfully validated, demonstrating good measurement accuracy of solids discharge flow rates in the standpipe, particularly avoiding cumbersome calibration. Moreover, the method can also determine sand waving and oscillated discharge behaviors, which might be related to solids' stick–slip phenomena and is unlikely to be accurately determined using conventional descending and accumulation methods. [ABSTRACT FROM AUTHOR]

This paper aimed to determine new data on terminal velocities and drag coefficients of single spheres moving inside a vertical and inclined glass pipe filled with water using the Particle Image Shadowgraph technique in the range of Reynolds numbers from 1420 to 12,740. The inclination angle α of the pipe varied from 0° to 30° relative to the vertical position. In the experiment, smooth steel spheres with diameters ranging from 3 to 9.5 mm were used, and the pipe had a fixed inner diameter of 40 mm. For verification, the experimental results of the drag coefficients were compared with known data from other authors for a free-settling sphere and a sphere rolling down a pipe wall or plane. Finally, the paper presents a new regression model describing the relationship between the sphere drag coefficient and Reynolds number when the cosine of the pipe inclination angle is varied. [Display omitted] • Particle Image Shadowgraph technique was used in the experimental study. • The velocity was measured at various pipe angles and sphere diameters. • Drag coefficients of the spheres were calculated. • Experimental drag coefficients were compared with known data. • Presented a correlation relating drag coefficient, Reynolds number, and pipe angle. [ABSTRACT FROM AUTHOR]

The investigation of the vibration of pipes containing flowing fluid is very essential to obtain an understanding of their dynamic behavior and prevent their catastrophic failure due to fatigue. Pipelines are subjected to environmental static and dynamic loading including self-weight, restoring, and Carioles forces. This research aims to investigate the vibrations of pipeline structures for examining their structural integrity under these conditions. A linear Euler-Bernoulli beam model is used to analyze the dynamic response of flexible, inclined, and fixed ends pipe conveying fluid made of polypropylene random-copolymer. Closed-form expression for dynamic response is presented by using combining of finite Fourier sine and Laplace transforms method. The influences of the inclination angle, thermal load, and aspect ratio (ratio of outside diameter to the length of pipe) on the dynamical behavior of the pipe–fluid system are studied. The obtained results attest to the importance of considering combining effects of the inclination angle, thermal load, and aspect ratio in analyzing and designing pipe conveying fluid. It is observed that the dynamic deflection can be significantly increased by increasing temperature, aspect ratio, and fluid velocity, while it reduced by increasing the inclination angle with the horizontal axis in the range of (0-90).

This paper investigates the force features of inclined pipes under the action of waves and flows through both test and numerical simulation. Firstly, the wave and flow loads on inclined pipes were examined through tests in circulating water flumes. Next, the unsteady Reynolds-averaged Navier-Stokes (RANS) equations were adopted to numerically simulate the test conditions. Multiple factors were taken into consideration: immersion depth, inclination, flow rate, wave height, and cycle. The results show that, the wave and flow loads on the pipes both increase with wave height and flow rate. When the inclination β = 0°, the flow force is most rapid, conversely, it is most slow when the inclination β = 30°. Furthermore, when the pipe was immersed by 75%, the change of inclination directly affected the ratio of vertical force to horizontal force. For the pipes with different inclinations, the wave load increases basically at the same rate with the rising wave height. With the widening of the inclination, the wave and flow loads on the pipes become less sensitive to immersion depth, and the maximum loads remain near the free water surface. [ABSTRACT FROM AUTHOR]

In this paper, the entropy generation analysis in dropwise condensation in an inclined pipe is carried out. As the vapor passes through the inclined pipe, the flow of the droplets occurs due to the interfacial shear and gravity. Three distinct zones considered in the numerical study include the saturated vapor flowing in the axial direction, saturated liquid traveling through the bottom of the pipe, and the condensate droplet flowing on the inner side of the pipe wall. With the aim of achieving optimal geometrical conditions of the pipe and flow, the entropy generation was calculated for various cases. The results show that the minimum entropy generation of 0.0754 W·K−1 occurs in a configuration with a diameter of 9.5 mm and an inclination angle of 1°. Finally, the Bejan number, irreversibility distribution ratio, and variation according to the flow conditions were presented. [ABSTRACT FROM AUTHOR]

The inclined pipe is widely used as a downward particle-conveying structure. Bubbles accompanying with the descending particles always induce complex flow pattern and pipe vibration, which would shorten the service life of equipment. In this paper, the gas-solid interaction and fluid-vibration coupling were experimentally studied by analyzing dynamic pressure and displacement of an inclined pipe. The results showed that, with increased mass flow rate, there was a progressive gas-solid flow behavior in the inclined pipe due to the water-pouring phenomenon. With the generation and upward channeling flow of bubbles, the downward particle flow showed an unstable motion, causing pressure fluctuations and severe vibration of the pipe system. Downward behavior of particles in the inclined pipe were eventually divided into three flow patterns: (1) creeping stratified flow, (2) gas channeling flow, and (3) dense phase fluidization flow. This work can provide theoretical basis for the design and operation of inclined pipe. [Display omitted] • A water-pouring phenomenon affects the gas-solid flow behavior in the inclined pipe. • Particle downward flow in the inclined pipe is divided into three flow patterns. • Valve bubbles upwardly flow into the pipe introducing particles' regular flow. • Channeling bubbles cause pressure fluctuations and severe vibration of the pipe. • A dense phase fluidization flow occur as the particle flow rate close to the maximum. [ABSTRACT FROM AUTHOR]

A new method is proposed for coating the inner surface of pipes in a confined space in which a sloping position of the pipe is expected during the process. Mathematical modeling of non-pressure fluid flow in an inclined pipe was carried out. The method implies controlled outflow of the material being applied and simultaneous rotation of the pipe being worked. The thickness of the coating depends on the velocity of the material flow along the inner surface of the pipe. The dependence of the fluid velocity on the radius of the pipe being worked and the level height in the filling column is calculated. The results of calculating the analytical dependence in the Mathcad application are presented. Dependence diagrams of material flow are presented for various design parameters that make it possible to determine the operating practices in the process of applying the coating. Uniform coating is obtained due to constant velocity of the material flow along the full length of the pipe. The obtained graphs were analyzed and the direction of further research connected with the influence of rotational velocity and fluid viscosity was determined. The use of the proposed method makes it possible to increase labor productivity and improve the quality of protective coating.

An experimental investigation of single Taylor bubbles rising in stagnant and downward flowing non-Newtonian fluids was carried out in an 80 ft long inclined pipe (4°, 15°, 30°, 45° from vertical) of 6 in. inner diameter. Water and four concentrations of bentonite–water mixtures were applied as the liquid phase, with Reynolds numbers in the range 118 < Re < 105,227 in countercurrent flow conditions. The velocity and length of Taylor bubbles were determined by differential pressure measurements. The experimental results indicate that for all fluids tested, the bubble velocity increases as the inclination angle increases, and decreases as liquid viscosity increases. The length of Taylor bubbles decreases as the downward flow liquid velocity and viscosity increase. The bubble velocity was found to be independent of the bubble length. A new drift velocity correlation that incorporates inclination angle and apparent viscosity was developed, which is applicable for non-Newtonian fluids with the Eötvös numbers (E0) ranging from 3212 to 3405 and apparent viscosity (μapp) ranging from 0.001 Pa∙s to 129 Pa∙s. The proposed correlation exhibits good performance for predicting drift velocity from both the present study (mean absolute relative difference is 0.0702) and a database of previous investigator’s results (mean absolute relative difference is 0.09614).

Secondary flow significantly changes the flow structure and increases flow resistance. The pipeline motion further contributes to the evolution of secondary flow. This study aims to elucidate the characteristics of two-phase secondary flow in inclined pipelines under additional periodic motion conditions. Based on the CFD technique, three-dimensional oscillating two-phase flow fields were simulated using the VOF model and dynamic mesh method. The focus was on four common flow patterns observed in inclined pipes, namely stratified flow, slug flow, turbulence flow, and transitional flow. The impact mechanisms of swaying, heaving, and coupling motion on the structural evolution, velocity profile, and relative intensity of secondary flow were analyzed. The results indicate that additional periodic motion exhibits a significant dominant behavior on secondary flow when the amplitude exceeds 1.0 D. Heave motion has a more pronounced effect on the secondary flow structure. Additional periodic motion induces periodic evolution of secondary flow structure in stratified flow, with the evolution period aligning with the period of the additional motion. Under additional periodic motion, there is no one-to-one correspondence between secondary flow velocity and axial velocity. Additional motion significantly suppresses the axial velocity of slug flow. Furthermore, additional periodic motion significantly increases the relative intensity of secondary flow, exceeding 10%. When the amplitude is less than 1.5 D , additional motion suppresses the relative intensity of secondary flow in turbulence flow and transitional flow. • Propose a scheme to numerically simulate the three-dimensional oscillating flow field using dynamic mesh combined with UDF. • The reliability of the CFD model was verified using experimental data from the published literature. • The details of secondary flow evolution in inclined pipe under additional periodic motion are revealed. • Analyze the secondary flow behavior of four typical flow patterns under additional periodic motion conditions. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation for dense particulate flows with coarse particles in inclined pipe to identify different flow regimes by means of computational fluid dynamics-discrete element method. The drag, gravitational, pressure gradient and virtual mass forces on particles, as well as the effect of particle–particle collisions are considered. Two flow regimes and their transitions are observed and described. The influence of Stokes number S t , Froude number F r , inclination angle β , etc., on critical flow regimes is analyzed to identify the dependence of flow regimes on these parameters. A new diagram for recognizing regime transition is given. The temporal variations of flow fields are also analyzed to illustrate propagating of kinematic waves. The wave velocity increases with F r , β , and particle concentration increasing. Two dimensionless numbers, collision stress and fluid–particle interaction stress, are defined to explain the regime transition mechanism. The maximum pressure drop occurs at approximately β = 60°. [Display omitted] • An optimized CFD-DEM is used to investigate dense particulate flows in inclined pipe. • The flow regimes and their transitions of dense particulate flows in inclined pipe are analyzed. • A new phase diagram for recognizing different flow regimes is given. • Temporal variations of particle quantities are analyzed to illustrate propagating of kinematic waves. [ABSTRACT FROM AUTHOR]

Flows of two immiscible liquids through inclined pipes are often encountered in industrial processes. The interfacial characteristics in inclined pipes are of significance for understanding the mechanism of flow pattern transition and modeling the flow parameters. This paper developed a novel experimental technique to access the interface characteristics of liquid-liquid flows, during which optical and electrical methods were successfully combined by matching the refractive index and conductivity of the flows. A planar laser-induced fluorescence (PLIF) system was set up with a continuous laser and high-speed camera. Organic and aqueous phases were chosen to match refractive indices. The liquid-liquid interface in the middle of the pipe could be clearly visualized by the PLIF system. Meanwhile, two conductance parallel-wire array probes (CPAPs) were designed to reconstruct the liquid-liquid interfaces at upward and downward pipe cross-sections. The performances of the CPAP were validated using the PLIF results and employed to investigate the liquid-liquid interfacial structures. The interfacial shape and its instability were uncovered using the reconstructed interfaces by the CPAPs.

In order to study the heterogeneous flow and its influencing factors in inclined pipeline, through theoretical analysis, the expression of settlement velocity including pipeline dip angle and concentration factor is given. On the basis of the theory of fluid-solid coupling, by studying the relationship between the energy of the solid particles suspended by vortices and the total energy required for the suspension of solid particles, a calculation model for velocity for heterogeneous flow in inclined slurry pipe is proposed. The flow of narrow-graded coal slurry with average particle size of 2.2 mm, 2.7 mm and 3.1 mm and concentration of 3%~18% in horizontal and inclined pipes with pipe diameter of 25 mm, 30 mm and 50 mm was studied by experimental method and 82 sets of heterogeneous flow data of different coal types, volume concentration, pipeline passage and angle were obtained. The results show that the maximum deviation between the measured values flow is not more than 16%. The heterogeneous flow of coal slurry is positively correlated with the volume concentration of coal slurry, the diameter of pipeline and particle size, and negatively correlated with the inclination of pipeline. The comparison between the proposed model and other similar formulas shows that the model can accurately predict the heterogeneous flow of coal slurry in inclined and horizontal pipelines under experimental conditions. [ABSTRACT FROM AUTHOR]

Heat transfer in a partially-filled, rotating inclined pipe with water flowing through it is experimentally investigated. The test section is a 1000 mm long stainless steel pipe with 32.8 mm inner diameter and 1.1 mm wall thickness. The outer wall is painted black to improve its emissivity. The outer wall temperature distribution is captured using a thermal camera. Uniform wall heat flux (1405–10784 W/m 2 ), water volumetric flow rate (100–830 ml/min), rotation rate (10–300 RPM) and pipe inclination angle (3° and 6°) are varied to study their influence on the heat transfer coefficient. Local heat transfer coefficient along the length of the partially filled rotating test section is reported. While heat transfer coefficient increases with the increase in wall heat flux, liquid volume flow rate and rotation rate, it decreases with increase in inclination angle. A generalised correlation to predict the average Nusselt number is developed in terms of four dimensionless numbers, viz., the flow Reynolds number to capture the effect of the axial fluid flow, rotation Reynolds number to account for the effect of pipe rotation, flow Froude number to take care of the effect of pipe inclination and dimensionless heat flux to incorporate the effect of wall heat flux on the heat transfer coefficient. [ABSTRACT FROM AUTHOR]

The paper deals with mathematical and physical modelling of flow of partially-stratified settling slurry in inclined pipes. Experimental results are presented of flows of aqueous slurries of four fractions of sand and gravel in two laboratory loops of different pipe diameters. They show a considerable variation in pressure drop and distribution of solids with the pipe slope. The degree of flow stratification and frictional pressure drop decrease with the increasing angle of inclination in the ascending pipe while the opposite applies in the descending pipe. A predictive mathematical model is presented which is based on a description of a layered structure of partially stratified slurry flow and takes flow inclination into account. The experimentally observed effects of pipe inclination are well reproduced by model predictions. Predicted pressure drops and solids distributions are in a very reasonable agreement with the experimental results and indicate suitability of the model for engineering practise. [ABSTRACT FROM AUTHOR]

This study reports an experiment to investigate the wetted wall fraction (WWF), which represents the shape of the continuous interface of the air–water stratified and wavy flow regimes, in horizontal and inclined pipes with an inner diameter of 40 mm. Using the experimental data, a semi-empirical model to predict the WWF was developed based on the energy balance for the liquid phase in separated flows. The model used a relationship between the WWF and the center of gravity of the liquid phase with a concave interface that can describe continuous changes to the flow regime from a stratified to an annular. The coefficients of the model were empirically determined based on a wide range of experimental data from the literature obtained in the air and various liquids covering a void fraction of greater than 0.79, a pipe with inner diameter in the range 24–150 mm, density differences varying from 812 to 1052 kg/m 3 , a range of liquid phase viscosity of 0.87–5.66 mPa s, surface tension ranging from 27.9 to 72.7 mN/m, a wide range of inclination angles from −27° for a downward flow to +3° for an upward flow, and gas and liquid Reynolds numbers based on a superficial velocity of up to 219,000 and 7500, respectively. This WWF model was tested using an extensive experimental database of the WWF and void fraction in the stratified and wavy flow regimes, and yielded the best agreement compared with existing models in the literature. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer inside an inclined pipe was visualized. Based on the analogy, mass transfer experiments were conducted instead of heat transfer ones using an electroplating system. The inclination ( θ ), diameter ( D ), and the length ( L ) of the pipe were varied 0° ~ 90°, 0.026 m ~ 0.063 m and 0.1 m ~ 0.3 m, respectively. The Ra D ranged from 2.98 × 10 9 to 4.22 × 10 10 and the Sc was 2094. The circumferential and axial flows interact with each other, which causes the complex internal flows inside the inclined pipe. The different copper plating patterns were appeared depending on the inclination ( θ ), diameter ( D ), and the length ( L ) and their influences on heat transfer inside the pipe were analyzed. [ABSTRACT FROM AUTHOR]

Experiments of air-water-oil three-phase flow pattern is investigated in a 20 mm diameter inclined pipe with a length of 6 m using a high speed digital camera. The superficial velocities are in the range of 0.25–3 m/s, 0.25–2.3 m/s, and 0.08–13 m/s for water, low viscosity oil and air, respectively. For describing flow patterns in three-phase flow, two parameters are considered: Interaction of gas and liquids mixture, and interaction of water and oil phases. The flow patterns for different pipe angles are discussed. Observed flow patterns are stratified-oil/water (or water/oil), wavy-stratified-o/w, bubbly-o/w, slug-o/w, plug-o/w, plug-stratified and annular-o/w. Major flow patterns for upward and downward pipe are slug-o/w and wavy-stratified-o/w, respectively. Also the effects of inclination angle varying from −45° to +45° and different oil cuts on flow patterns have been studied. The results show that by increasing the oil cut for different inclination angles, bubbly region extends and plug region becomes smaller. [ABSTRACT FROM AUTHOR]

In this study, a new and improved electrical conductance sensor is proposed for application not only to a horizontal pipe, but also an inclined one. The conductance sensor was designed to have a dual layer, each consisting of a three-electrode set to obtain two instantaneous conductance signals in turns, so that the area-averaged void fraction and structure velocity could be measured simultaneously. The optimum configuration of the electrodes was determined through numerical analysis, and the calibration curves for stratified and annular flow were obtained through a series of static experiments. The fabricated conductance sensor was applied to a 45 mm inner diameter U-shaped downward inclined pipe with an inclination angle of 3° under adiabatic air-water flow conditions. In the tests, the superficial velocities ranged from 0.1 to 3.0 m/s for water and from 0.1 to 18 m/s for air. The obtained mean void fraction and the structure velocity from the conductance sensor were validated against the measurement by the wire-mesh sensor and the cross-correlation technique for the visualized images, respectively. The results of the flow regime classification and the corresponding time series of the void fraction at a variety of flow velocities were also discussed. [ABSTRACT FROM AUTHOR]

A numerical investigation is carried out to investigate the transitional flow behaviour of nanofluids flow in an inclined pipe using both single and multi-phase models. Two different nanofluids are considered, and these are Al 2 O 3 –water and TiO 2 –water nanofluids. Moreover, SST κ − ω transitional model is implemented to study the nanofluids flow in inclined pipe. Gravitational force is also adopted by considering Boussinesq approximation in the momentum equation. Results reveal that Buoyancy force play a significant role on the degeneration of heat transfer rate with the increase of Reynolds number for different inclination angles. It indicates that mixed convection has opposite effect on the inclined pipe than the forced convection on the horizontal pipe. Moreover, some deformation of the flow and temperature fields near the upstream region is observed with the increase of inclination angle due to Buoyancy force. [ABSTRACT FROM AUTHOR]

In this work, local heat transfer coefficients (HTC) and different flow patterns of oil-water two-phase flow in a horizontal and slightly upward inclined (+4° and +7°) pipe were investigated. The test section was an 11 mm inner diameter (ID) copper pipe with a length to diameter ratio of 164. Water and diesel fuel (2.49 mPa s viscosity and 798 kg/m 3 density) were selected as immiscible liquids and high speed photography technique was used for the flow pattern identification. The superficial Reynolds numbers ranged from 1350 to 13,700 for water and 300–3700 for oil. The experimental results indicated that the oil-water heat transfer is dependent on the inclination angle and flow pattern. As the pipe inclination angle increases averaged HTC values for each flow pattern increases. It was found that the effect of the flow pattern on the oil-water HTCs is higher than the pipe inclination. In addition, an artificial neural network (ANN) model was developed for predicting the HTC of oil-water two-phase flow in the studied different inclination angles of pipe. Superficial oil Reynolds number ( Re so ), superficial water Reynolds number ( Re sw ), inclination angles (IA) and some numbers appropriated for each flow pattern (FPN) were selected as input variables, whereas two-phase HTC ( h TP ) values were selected as output variables. The ANN was trained, validated and tested against the experimental data. The obtained optimal ANN model had good prediction for all of the positions and all flow patterns. Mean absolute percent error (MAPE) of 1.98% and correlation coefficient (R) of 0.993 for testing data set and MAPE of 1.81% and R value of 0.995 for all data sets were achieved. [ABSTRACT FROM AUTHOR]

In this work, the ability of artificial neural networks (ANNs) to predict void fraction of gas–liquid two–phase flow in horizontal and inclined pipes was investigated. For this purpose, an ANN model was designed and trained using a total of 301 experimental data points reported in the literature for inclination angles between –20° and +20°. Pipe inclination angle as well as superficial Reynolds number of gas (Re sg ) and liquid (Re sl ) were chosen as input parameters of different structures of multilayer perceptron (MLP) neural networks, while the corresponding void fraction was selected as their output parameter. A hyperbolic tangent sigmoid and a linear function were employed as transfer functions of hidden and output layers, respectively, and Levenberg–Marquardt back propagation algorithm was used to train the networks. By trial–and–error method, a three–layer network with 10 neurons in the hidden layer was achieved as optimal structure of the ANN which made it possible to predict the void fraction with a high accuracy. Mean absolute percent error (MAPE) of 1.81% and coefficient of determination (R 2 ) of 0.9976 for training data and MAPE of 1.52% and R 2 value of 0.9948 for testing data were obtained. Also for all data, MAPE of 1.95% and R 2 value of 0.9972 were calculated, and 96% data were within ±5% error band. In addition, the accuracy of the proposed ANN model was compared with the predictions from 17 void fraction correlations available in the literature for different flow patterns and horizontal and inclined flows. For all cases, the proposed ANN model gave better performance than all of the studied correlations. The results confirm the very good capability of the ANNs to predict the void fractions of gas–liquid flow in inclined pipes, regardless of flow pattern. Finally, by performing interpolation using the trained network, the void fraction values for some other conditions were predicted. [ABSTRACT FROM AUTHOR]

To characterize the effect of pipe inclination, low viscosity, flow rate and inlet water cut on annular flow pattern, a low viscosity oil-water two-phase annular flow in horizontal and slightly inclined (+1°, +3° and +5°) pipes with diameter of 20 mm has been experimentally investigated. A modified VOF model based on the CFD software package FLUENT was used to predict the in-situ oil fraction and pressure drop. The experimental data indicate that annular flow appears at a medium-high water cut. The slip ratio increases with flow rate increase but decreases with increasing water cut. The changes are more significant as the degree of inclination increases. Pressure drop is strongly dependent on flow rate, as it increases rapidly as inlet flow rate increase. Good agreement between the experimental data and calculated results of slip ratio and pressure drop was obtained. [ABSTRACT FROM AUTHOR]

In this experimental work the effect of inclination on the pressure gradient in two phase oil–water flow is investigated. The experiments were performed in a 6 m long, 20 mm inner diameter and inclinable acrylic pipe using oil (3 mPa s viscosity and 830 kg/m 3 density) and water (1 mPa s viscosity and 990 kg/m 3 density) as test fluids. Pressure gradients between inlet and outlet of flow in pipe were measured for inclination angles of 0°, ±5°, ±15°, ±30° and ±45° with respect to the horizontal plane. The experimental results were compared with Homogeneous and Two-Fluid models. It was observed that in high mixture velocities, where dispersed flow prevails, there is a peak pressure gradient which is related to phase inversion. It was also found that, phase inversion appears at higher inlet water cut values in inclinations of −30° and −45° compared with other inclinations. However the two-fluid model and homogeneous model both over-predicted the pressure drop, but two-fluid model predicted the pressure drop with less average deviation. Several correlations for effective mixture viscosity in a homogeneous model were considered and the results were compared with experimental results. Acceptable agreement was seen between the computed and measured data. The experimental two-phase friction factors were compared with the friction factors for single phase flow of oil and water, at the same velocities as the two phase mixture and it was found that the experimental friction factors were less than the predicted friction factors of single phase flow. [ABSTRACT FROM AUTHOR]

This paper presents the application of artificial neural network (ANN) in prediction of water holdup of oil–water two-phase flow in a vertical and an inclined pipe (90°, 75°, 60°, and 45° from horizontal) without knowing the type of flow pattern. For this purpose, superficial velocity of water and oil and the inclination angles of the pipe were used as input parameters, while water holdup values of two-phase flow were used as output parameters in training and testing of the multi-layer, feed-forward, back-propagation neural networks. Experimental data (468 data points) were taken from literature and used for developing of the ANN model. The obtained results showed that the network predictions have very good agreement with the experimental water holdup data. The accuracy between the neural network predictions and experimental data was achieved with low average absolute percent error (AAPE) and high coefficient of determination ( R 2 ) for both training data (AAPE = 2.34% and R 2 = 0.999) and testing data (AAPE = 2.89% and R 2 = 0.997) sets. In addition, a comparison of the prediction results of the proposed ANN model with Mukherjee et al. (1981) correlation (AAPE = 9.83% and R 2 = 0.961) revealed that the correlation had more deviations. [ABSTRACT FROM AUTHOR]

In this research, the utilization of data-driven approaches to predict the flow pattern of a two-phase flow in a horizontal, inclined, and vertical pipe (−90 to 90°) is investigated. Although multiphase flows have been modeled using artificial neural network models, there is still a long way to draw a road map to optimize these models. To fill this gap, an artificial neural network (ANN) was applied using 8766 experimental samples where 70% of the data was used to train the models, 15% was used for cross-validation, and 15% was used for testing. The generated neural network considers the flow pattern as the output that is predicted using 10 inputs which are flow pressure, liquid surface tension, inclination angle, density, viscosity, and superficial velocity of both gas and liquid streams plus the pipe diameter. Also, superficial liquid and gas Reynold's numbers, mixture Froud number, and Weber number are used to replace the dimensional inputs. It is to be noted that the neural network performance increased when the model is considered a classification problem. The results indicate that using a multi-layer perceptron artificial neural network has high accuracy in predicting the flow regime, demonstrating a high accuracy of 97.3% in predicting the flow pattern. Moreover, the dimensionless-based model's accuracy was demonstrated to be inferior in forecasting the flow regime compared to the dimensional-based model in terms of accuracy. Furthermore, the accuracy of the generated neural network was also validated against Barnea's model which showed an incorrect classification percentage of 1.7%. • Evaluation of neural network to predict two-phase flow patterns in an inclined pipe. • The performance success of the algorithms was investigated. • Dimensional-based neural networks produce higher prediction results. • Due to overlapping, dimensionless-based analysis is less accurate. • For flow pattern prediction, the proposed neural network has an accuracy of 97.3%. [ABSTRACT FROM AUTHOR]

The flow pattern in two-phase flows is a significant factor which influences many other parameters such as heat transfer and pressure drop in pipelines. In the present work, flow patterns of two-phase oil–water flow is investigated experimentally in a 20 mm diameter pipe with a length of 6 m. A high speed digital camera has been equipped for visualization, flow regime identification and flow recording. In this study acting forces on dispersed phase are discussed theoretically and flow patterns in different pipe inclination angles are investigated in two-phase oil–water flow. The range of inclinations has been varied between −45 and +45°. Flow pattern maps are investigated for every inclination angle of pipe and compared with other available experimental data. Finally, the effect of pipe inclination angle on transition boundaries between flow patterns is investigated comprehensively. Various flow patterns are seen; bubbly, slug, smooth stratified, wavy stratified, churn, annular and dual continuous flow. From the obtained results, it can be inferred that non-stratified flows such as bubbly and slug flows are dominant flow patterns in the upward flows and stratified flows are dominant flow patterns in the downward flows. [ABSTRACT FROM AUTHOR]

A rotating platform was used to create dynamic load, and the mixture air-water two-phase flow and boiling steam-water two-phase flow were obtained in an inclined test pipe. By changing the parameters, such as inclination of the test pipe, rotational speed, inlet temperature, flow rate, and so on, the experiments for two-phase flow in the pipe at inclination of 0°, 45°, and 66° were conducted, respectively. The effects of acceleration and inclination on their flow and heat transfer characteristics were investigated. The two-phase flow patterns in inclined pipes under rotation conditions were caught with a video camera. The images show that the impact mixed flow and churn flow were found in this research. The results show that the acceleration and pipe inclination significantly influence the flow characteristic and heat transfer of the two-phase pipe flow. As the directions of the dynamic load and the gravity are opposite to the flow direction, the greater the dynamic load and inclination, the higher the pressure drop and the heat emission, and the lower the flow rate, the void fraction, and the fluid temperature. Therefore, the dynamic load and gravity will improve the flow resistance, enhance heat emission and reduce the heat gained by the fluid. [ABSTRACT FROM AUTHOR]

Abstract: The turbulent heat transfer in gas-solid flows through an inclined pipe under various inclination angles is studied with constant wall heat flux. The hydrodynamic k − τ and kθ − τθ thermal two phase model is used in a lagrangian/Eulerian four way approach. The numerical results agreed reasonably with available experimental data in vertical and horizontal pipe flows. The effects of inclination angles on the flow patterns are reported. The pressure drop and Nusselt number are enhanced significantly as the inclination increases up to a certain angle. The mass loading ratio has influence on the optimal inclination angle. With increasing loading ratio, the optimal inclination angle of maximum pressure drop shifts to the lower amount. [Copyright &y& Elsevier]

Abstract: The stratified oil–water flow pattern is common in the petroleum industry, especially in offshore directional wells and pipelines. Previous studies have shown that the phenomenon of flow pattern transition in stratified flow can be related to the interfacial wave structure (problem of hydrodynamic instability). The study of the wavy stratified flow pattern requires the characterization of the interfacial wave properties, i.e., average shape, celerity and geometric properties (amplitude and wavelength) as a function of holdup, inclination angle and phases’ relative velocity. However, the data available in the literature on wavy stratified flow is scanty, especially in inclined pipes and when oil is viscous. This paper presents new geometric and kinematic interfacial wave properties as a function of a proposed two-phase Froude number in the wavy-stratified liquid–liquid flow. The experimental work was conducted in a glass test line of 12m and 0.026m i.d., oil (density and viscosity of 828kg/m3 and 0.3Pas at 20°C, respectively) and water as the working fluids at several inclinations from horizontal (−20°, −10°, 0°, 10°, 20°). The results suggest a physical relation between wave shape and the hydrodynamic stability of the stratified liquid–liquid flow pattern. [Copyright &y& Elsevier]

Abstract: The study is motivated by the problem of pipeline corrosion due to water accumulation at low spots. Lab-scale experiments were conducted to identify the critical conditions required for the onset of water displacement by oil flow from a low horizontal section into an upward inclined section of the pipeline. Two test loops with pipe diameters of 27mm and 41mm I.D. with diesel flow were used. Water withdrawal from tapping valves distributed along the up-hill section enabled to follow the water displacement for oil flow rates exceeding the critical value. A model for predicting the water displacement by the oil flow, which is based on the formation of a water plug in the lowest (horizontal) section, is suggested. The predicted amounts of water withdrawn from the tapping valves favorably compare with the experimental results. Considering other competing mechanisms, up-scaling to larger pipe diameters is examined. The analysis indicates that water plug formation appears to be the controlling mechanism for water displacement also in larger pipe diameters encountered in field operations. [Copyright &y& Elsevier]

Abstract: The influence of non-ionic surfactant additives on the interfacial structure during both co-current gas–liquid upflow and downflow in slightly inclined pipes is investigated. Experiments are conducted in a 24mm i.d. pipe for various gas–liquid flow rates and pipe inclination angles (β=±1° and ±3° from the horizontal position). Dilute aqueous solutions of the non-ionic surfactant Triton X-100 are employed, in order to study the effect of the additive on the flow pattern and the liquid layer characteristics (i.e. mean layer thickness, amplitude and frequency of the interfacial waves). In particular, the new data of the liquid layer characteristics indicate how the interfacial structure and the transition between the various flow regimes, during co-current gas–liquid flow in slightly inclined pipes, are affected by the addition of small amounts of the non-ionic surfactant. [Copyright &y& Elsevier]