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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]

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]

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]

• 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]

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]

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]

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]

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]

Abstract: The influence of a surfactant additive on the interfacial structure and on the transition from the smooth to the wavy stratified flow regime in inclined pipes is investigated for various gas–liquid flow rates. The effect of a surfactant on the gas–liquid stratified downflow patterns is studied using a dilute aqueous solution of a non-ionic surfactant , which is found to have a dramatic effect on two-phase flow characteristics. A conventional solution having a surface tension similar to that of the surfactant solution is also employed and this verifies that the atypical behavior of the surfactant solution is ascribed to its special chemical structure and not to its low surface tension. Liquid layer thickness time records are acquired using a parallel-wire conductance technique from which the statistics of the layer thickness, as well as wave celerities, are calculated. Laser doppler anemometry (LDA) is employed to investigate the flow structure in the thin liquid layer both with and without interfacial shear induced by a co-current gas flow. A differential pressure transducer is used for pressure drop measurements in the liquid phase. The interpretation of the results verifies that the “delayed” appearance of the interfacial waves should be associated with the turbulence retardation within the liquid layer and it facilitates the clarification of the mechanisms in which the surfactant interacts with the turbulent structures and causes significant drag reduction. [Copyright &y& Elsevier]

Abstract: The transition from smooth to wavy stratified flow is studied for various pipe inclination angles with the aim to contribute to the realistic modeling and simulation of long distance two-phase pipe flow. The influence of the liquid flow field on interfacial structure is studied through local axial velocity measurements in the liquid phase in conjunction with other liquid layer characterization experiments. Observations based on fast-video recordings, are used to identify the main patterns of wave evolution. Liquid layer thickness time records are acquired using a parallel wire conductance technique from which mean layer thickness, RMS and power spectra of the fluctuations, as well as wave celerities are calculated. Laser Doppler Anemometry (LDA) is employed to investigate the flow structure in the thin liquid layer both with and without interfacial shear induced by a co-current gas flow. The results reveal the influence of the liquid flow field development on the interfacial structure. In particular, the new data of axial velocity profiles and liquid layer characteristics suggest that the onset of the interfacial waves is strongly affected by the liquid flow structure, possibly by the laminar to turbulent transition within the layer. [Copyright &y& Elsevier]

Pneumatic conveying of fine powder has merits, such as no dust pollution and wide flexibility of pipeline layout. Thus, pneumatic conveying is widely used in industry. However, there is no information about the relation between the pressure drop for pneumatic conveying of fine powder and the mechanical properties of powder.We explained that the pressure drop of pneumatic conveying of powder in a horizontal pipe could be estimated from the dynamic friction coefficient of the powder in the previous paper. However, the relation between the pressure drop of pneumatic conveying in an inclined pipe and the mechanical properties of the powder is not cleared yet.The effect of mechanical properties and the angle of an inclined pipe on the pressure drop for pneumatic conveying of fine powder was examined and compared with the calculated results by our model. Based on these results, it is cleared that the pressure drop for pneumatic conveying of fine powder can be estimated from the dynamic friction coefficient of the powder and the inclined angle of the pipe. [Copyright &y& Elsevier]

This paper aims to provide design information for flow aid systems in the pneumatic conveying of powders, specifically for the system involving the use of knockers when an inclined pipeline is choked with powder. Acrylic pipes with a length 60 cm and inside diameters ranging from 2.6 to 6.4 cm were filled with powder whose mass was in the range of 30-270 g. The pipe was set at angles 10-50° to the horizontal. The impact stress, 1-4.1 g (where g is the acceleration due to gravity), was exerted on the pipe, and the mass of powder that fell from the lower end of the pipe W (due to the impact) was correlated satisfactorily in terms of a variable related to the shear stress at the pipe wall. Within the experimental range studied, W was found to decrease almost linearly with the compressibility of powders for given experimental conditions. [ABSTRACT FROM AUTHOR]

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 ( E 0 ) ranging from 3212 to 3405 and apparent viscosity ( μ a p p ) 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). [ABSTRACT FROM AUTHOR]

• Studied the behaviour of elongated bubbles in slightly upwardly inclined pipes. • Bubble characteristics; shape, length, fraction and velocity are presented. • Information on the bubble velocity behaviour along the pipe is discussed. • Experimental results comparison with some recently developed drift velocity models. Two phase flow is of great interest in chemical and petroleum industries, and multiphase pipe flow models with closure relationships require experimental data for their development and validation. However, only little experimental information is available for slightly upward inclined pipes. Experimental investigations of single elongated bubble in marginally upwardly inclined pipes less than 10° have therefore been performed. Observations of the bubble drift velocity along the pipe has been highlighted. The drift velocity data presented here can contribute to improve knowledge of pipe inclination and viscosity dependency in drift velocity correlations. The new data on the bubble characteristics - shape, length, fraction and drift velocity may also provide useful information for the development and validation of numerical models. The measured drift velocity data have therefore been compared with some recently developed bubble velocity correlations. [ABSTRACT FROM AUTHOR]

• Focused on the effect of contact angle and liquid velocity on the behavior of liqud film and the development of flooding waves using the VOF method. • An analytical force model is proposed to study the effect of contact angle on the onset of flooding including the shear force. • The histograms of the forces at various contact angles and liquid velocities are investigated for the mechanism of the onset of flooding. • The results of the numerical simulation provide ideas for the data divergence of different flooding correlations. The purpose of the present study is to investigate the characteristics of interfacial waves on flooding phenomena in an inclined pipe. The effects of liquid velocity and contact angle on the waves at the onset of flooding are studied with a two-dimensional computational fluid dynamic model. Flooding in a 30° inclined pipe is observed by using the Volume of Fluid (VOF) method. It is found when the contact angle is equal to 120°, the pipe wall cannot form a uniform liquid film and the gas velocity required on the onset of flooding decreases as the contact angle and liquid velocity increase. For a detailed understanding of the effects of contact angle and liquid velocity, an analytical forces model is proposed on the flooding waves, including gravity F gw , the pressure of the gas core F pc , pressure variations in the liquid film F pl , wall shear force F ws , interfacial shear force F ss and surface tension force F σ. Through the quantitative calculation of all forces, it is found that the amplitude and length of the flooding wave increase with liquid velocity. As the contact angle increases, the crests become sharper. Further, through analyzing the histogram distribution of the forces, the increase of the contact angle will change the mechanism of flooding from carrying droplets to rising waves. It provides a theoretical basis for the development of mechanistic models to predict the onset of flooding in the future. [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. [ABSTRACT FROM AUTHOR]

Flexible risers transporting hydrocarbon liquid–gas flows may be subject to internal dynamic fluctuations of multiphase densities, velocities and pressure changes. Previous studies have mostly focused on single-phase flows in oscillating pipes or multiphase flows in static pipes whereas understanding of multiphase flow effects on oscillating pipes with variable curvatures is still lacking. The present study aims to numerically investigate fundamental planar dynamics of a long flexible catenary riser carrying slug liquid–gas flows and to analyse the mechanical effects of slug flow characteristics including the slug unit length, translational velocity and fluctuation frequencies leading to resonances. A two-dimensional continuum model, describing the coupled horizontal and vertical motions of an inclined flexible/extensible curved riser subject to the space–time varying fluid weights, flow centrifugal momenta and Coriolis effects, is presented. Steady slug flows are considered and modelled by accounting for the mass–momentum balances of liquid–gas phases within an idealized slug unit cell comprising the slug liquid (containing small gas bubbles) and elongated gas bubble (interfacing with the liquid film) parts. A nonlinear hydrodynamic film profile is described, depending on the pipe diameter, inclination, liquid–gas phase properties, superficial velocities and empirical correlations. These enable the approximation of phase fractions, local velocities and pressure variations which are employed as the time-varying, distributed parameters leading to the slug flow-induced vibration (SIV) of catenary riser. Several key SIV features are numerically investigated, highlighting the slug flow-induced transient drifts due to the travelling masses, amplified mean displacements due to the combined slug weights and flow momenta, extensibility or tension changes due to a reconfiguration of pipe equilibrium, oscillation amplitudes and resonant frequencies. Single- and multi-modal patterns of riser dynamic profiles are determined, enabling the evaluation of associated bending/axial stresses. Parametric studies reveal the individual effect of the slug unit length and the translational velocity on SIV response regardless of the slug characteristic frequency being a function of these two parameters. This key observation is practically useful for the identification of critical maximum response. • Planar dynamics of inclined curved flexible riser carrying slug liquid–gas flows are investigated. • Mechanistic slug flow model is applied to identify liquid–gas flow features within a slug unit cell. • Slug flow-induced vibration is subject to fluctuations of phase fractions, velocities and pressure. • Effects of slug unit length, translational velocity and characteristic frequency are investigated. • Transient and steady-state responses highlight fundamental coupling mechanism of mean drift and oscillation components. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the motion of a single Taylor bubble through stagnant Newtonian liquid in an inclined pipe by performing a complete dimensionless treatment followed by an order of magnitude analysis of the terms of equations of motion. The main contribution of this analysis is that Froude, Eötvös and Reynolds numbers are the main physical parameters prompting the dimensionless governing equations for inclination angle up to θ ≤ 70 °. The bubble drift velocity diminishes in inclination angles near the horizontal orientation, and thus the reduced Galilei number is suggested to govern the bubble dynamics. To support the developed logical approach of the problem, the present study employs a CFD study so as to investigate the hydrodynamics of single Taylor bubble drifting through stagnant liquid in an inclined pipe through using the volume-of-fluid (VOF) methodology implemented in the computational fluid dynamics software package, ANSYS Fluent (Release 16.0). The simulation results show good correspondence with the developed dimensionless treatment of the problem. No bubble propagates in a zero axial pressure gradient horizontal pipe, hence, a simplified model is suggested to solve the challenging problem of the three-dimensional Taylor bubble in near horizontal and horizontal pipes, and thus saving computational resources. • A dimensionless analysis followed by the order of magnitude analysis of Navier-Stokes equations of motion is performed. • The main parameters affecting the dynamics of Taylor bubble in inclined pipe are Froude, Eötvös, Reynolds and reduced Galilei numbers. • Eötvös number is the sole dimensionless parameter affecting the dynamics of Taylor bubbles in horizontal pipes. • A simplified 2D model is suggested to solve the challenging problem of 3D Taylor bubble in horizontal pipes. [ABSTRACT FROM AUTHOR]

The impact forces caused by gas–liquid slug flow can lead to the vibration of process system or fatigue failure of pipe fittings. In this study, a piston‐flow‐model coupling with slug model is developed to calculate the impact forces, which can contribute to the structure design and flow assurance. An experiment installation is installed to study the characteristics of slug flow and validate the reliability of the model. The accuracy of this model is above 90% for the superficial velocity of gas below 2 m/s, whereas the average deviation is 29.2% for the cases of superficial velocity of gas above 2 m/s. The modified model addressing the liquid holdup agrees well with the experimental data, of which the average deviation is 6.25%. [ABSTRACT FROM AUTHOR]