Vertical Circular Pipe Research Articles

Development of a friction factor correlation applicable to both wet and dry foam flow in circular vertical pipes

BackgroundFoam flow, distinguished by its low density and extensive specific surface area, is employed for the cleaning of plant systems. However, its dual nature as a gas-liquid mixture and a non-Newtonian fluid complicates the prediction of the frictional pressure drop. MethodsThis study constructed a laboratory-scale experimental setup to illustrate the upward flow behavior of aqueous foam in a vertical circular pipe, capturing the foam flow using a high-speed camera. Utilizing the collected data and images, a model was developed for the friction factor to predict the frictional pressure drop of the foam flow, under the assumption that the foam flow is a non-Newtonian, quasi-homogeneous, steady, and fully developed laminar flow. Significant findingsWet foam, characterized by small, uniformly distributed spherical bubbles, is observed at lower foam quality levels. In contrast, dry foam, marked by a larger mean bubble diameter, non-uniform bubble distributions, and slugs, is observed at higher foam quality levels. A notable inflection point in the frictional pressure drop is observed during the transition from wet to dry foam within a vertical pipe. The foam regime and frictional pressure drop characteristics of the foam flow show limited sensitivity to surfactant concentration within the experimental range. A correlation for friction factors, applicable to both wet and dry foam flows in vertical circular pipes, was developed based on the Reynolds number, exhibiting a prediction error of 23.6 %.

Direct numerical simulation of flow and heat transfer of supercritical water with different heat fluxes

The flow and heat transfer characteristics of supercritical water (SCW) are important considerations in the thermal-hydraulic design of the Supercritical Water-Cooled Reactor (SCWR). In the present study, the direct numerical simulation (DNS), developed with OpenFOAM, was utilized to investigate the effect of heat flux on the flow and heat transfer of SCW in a vertical circular pipe. The investigation involves detailed analyses of the wall temperature, velocity distribution, and turbulent statistics at various heat fluxes. It was found that buoyancy first impairs heat transfer, and then recovers heat transfer. This is attributed to the variation of buoyancy production and turbulence production, which are resulted from the buoyancy direct effect and indirect effect, respectively. As the heat flux increases, the recovery occurs earlier with higher magnitude. The vortex structures based on Q-criterion clearly illustrate the same process as well. Several heat-transfer correlations were assessed based on the DNS results. It indicates that Dittus and Boelter correlation (1930) cannot accurately predict the heat-transfer characteristics of SCW, while Chen and Fang correlation (2014) exhibits a higher level of predictive accuracy for Nusselt number. In addition, several turbulence models were evaluated against the DNS data. The results show significant deviations in predicting the heat transfer of SCW. The large discrepancy may be due to the inappropriate model coefficients, the failed predication of turbulence kinetic energy, as well as the constant turbulent Prandtl number commonly applied.

Heat transfer and thermal conductivity of magneto micropolar fluid with thermal non-equilibrium condition passing through the vertical porous medium

This paper investigates the incompressible mixed convection flow of electrically conductive micropolar fluid with a thermal non-equilibrium condition that passes through the vertical circular (pipe) porous medium. The extension of the non-Darcy–Brinkman–Forchheimer model is considered to formulate the governing non-linear system of differential equations for the problem. Furthermore, the rigorous impact of different parameters such as thermal conductivity ratio , inter-phase heat transfer coefficient , Darcy number , Grashof number , Eringen micro-polar parameter , Hartmann number , solid-heat generation , and fluid heat generation parameter on velocity profile , micro-rotational (angular velocity) , temperature of solid and fluid has been investigated by using the computational strength of artificial intelligence based Elman neural networks (ENN) and Levenberg–Marquardt algorithm (LMA). We have compared the solutions calculated by the designed ENN-LM algorithm with the Cuckoo Search Algorithm (CSA), Chebyshev spectral collocation method (CSCM), particle swarm optimization (PSO) algorithm, and Runge–Kutta method. The convergence rate and stability of the ENN-LM technique show that it can be applied to solving complex models involving partial and fractional differential equations.

Effect of curvature on transient natural convection in a vertical circular pipe

Natural convection adjacent to a curved vertical wall is widely present. Unfortunately, the effect of curvature on the transient thermal boundary layer (TBL) adjacent to the concave vertical wall has been neglected. In this study, dynamical evolution and thermal process of transient natural convection in a vertical circular pipe are discussed using scaling analysis, a boundary flow regime for the thin TBL without merging and a duct flow regime for the TBL with merging at the axis of the pipe are distinguished. The scaling laws quantifying the dependence of thickness, velocity and flow rate of the TBL of the fluid with the fixed Prandtl number in the vertical pipe on the Rayleigh number (RaT and Raq) and the ratio of height to radius of the pipe (A) are first reported for the isothermal and isoflux conditions. The curvature effect becomes stronger with the increase of the thickness of the TBL. Under the duct flow regime, the non-dimensional flow rate is scaled with $Ra_T^{1/2}{A^{ - 1}}$ for the isothermal condition and with $Ra_q^{1/2}{A^{ - 3/2}}$ for the isoflux condition. The scaling laws of the thickness, velocity and the flow rate of the TBL in the vertical pipe are validated based on the numerical results from direct numerical simulation (DNS) with good precision. The scaling coefficient is also presented under different regimes and conditions, which can serve as a design guide to determine natural convection in the vertical circular pipe.

Computational case study on upward two-phase flow in vertical circular pipe based on CFD approach: Multidimensional flow instabilities investigation

In this paper, a numeric scheme made up of the three-dimensional (3-D) Two-Fluid Model (TFM) and the Rensselaer Polytechnic Institute (RPI) wall boiling model for two-phase flow instabilities simulation was validated by comparing its results with the flow boiling and instability experimental data. Then two-phase flow instabilities in a vertical circular channel were studied based on the validated numeric scheme. The flow instability was analyzed by both the Lumped Parameter Approach (LPA) and the Distributed Parameter Approach (DPA). The average parameter oscillation characteristics and local distributions were analyzed. The transient responses of the local conditions during the flow instability were discussed. Besides, the stability of the vertical circular tube channel flow boiling system was studied with the stable map based on the subcooling number (Nsub) versus the phase change number (Npch). This study provides a new feasible scheme for the simulation of flow instability which also actualizes an improved understanding of multidimensional flow and heat transfer characteristics in the flow instabilities phenomenon.

Void Fraction and Interfacial Friction in Vertical Circular Pipes with the Square Top End under Flooding Conditions

The objective of this study was to reduce the uncertainties of correlations for flow characteristics in vertical pipes under flooding at the top end. The void fraction α, pressure gradient dP/dz, and countercurrent flow limitation (CCFL) were previously measured with diameter D = 40 mm and working fluid of air and water. The wall friction and interfacial friction factors (fw and fi) were obtained based on the annular flow model, and CCFL and fw were evaluated in detail. Hence, attention was turned to detailed evaluations of α and fi. Liquid film thickness δ and interfacial friction factor fi for smooth film (SF) due to flooding at the top end were obtained using the previously derived fw correlation and existing dP/dz data with D = 20 to 50.8 mm and pressure P = 0.1 to 4.1 MPa, and empirical correlations for δ and fi were derived. The δ term was well expressed by a function of the liquid Reynolds number ReL, and the uncertainty of the δ correlation was ±0.0062 for α = 0.87 to 0.98. fi was expressed by a function of δ/L (where L is the Laplace length) or the Kutateladze parameter KG*, the dimensionless diameter D* (=D/L), and the density ratio of the gas and liquid phases ρG/ρL. The applicability of the derived correlations to conditions of D = 300 mm and P = 7 MPa was evaluated, and the fi correlation was modified based on fi values computed with the δ correlation. The drift-flux parameters for SF were also considered.

Flow Characteristics in a Vertical Circular Pipe under Flooding in Its Inside

Flow Characteristics in a Vertical Circular Pipe under Flooding in Its Inside

Flow Characteristics of Air-Water Two-Phase Flows in a Serpentine Tube

Experiments on air-water two-phase flows in a serpentine tube consisting of vertical U-bends and circular straight pipes were carried out to discuss the flow characteristics based on the high-speed video images of the flows at various gas and liquid superficial velocities. The pipe diameter, D, and the bend radius of curvature, R, were 20 mm, i.e. the bend ratio, R/D, was unity, and the length of the straight pipe was 1500 mm. The void fraction in each section was measured by using a quick-closing valve method. As a result, the following conclusions were obtained: (1) the top and bottom U-bends cause coalescence of large bubbles and liquid slug formation, respectively, which results in enhancement of flow pattern transition between the slug and annular flows, (2) the void fraction in the downward flow is larger than that in the upward flow due to acceleration of the liquid phase and the buoyancy acting on bubbles in the downward flow, and (3) void correlations based on the drift-flux model for fully-developed flows are applicable to the void fractions in the straight pipe sections under the present experimental conditions.

Condensation heat transfer for downward flows of superheated steam-air mixture in a circular pipe

We measured the radial and axial temperature distributions of a saturated steam-air mixture in a vertical circular pipe (diameter, 49.5 mm; cooling height, 610 mm) in our previous study. Those of a superheated steam-air mixture in the same experimental setup were measured in this study. The condensation heat flux qc and heat transfer coefficient hc for the superheated mixture were evaluated, and they were compared with those for the saturated mixture. There was no large difference in qc between the saturated and superheated mixtures. The heat transfer coefficient hc (which was evaluated for the saturation temperature) for the superheated mixture agreed with that for the saturated mixture. hc computed with the diffusion layer model for saturated temperature agreed well with the hc measured for the superheated mixture.

Flow characteristics in vertical circular pipes with the square top end under flooding conditions

Previously, we evaluated flow characteristics in a vertical pipe of diameter D = 20 mm under flooding conditions. Now, we have measured the void fraction α, pressure gradient dP/dz and countercurrent flow limitation (CCFL) characteristics in a vertical pipe of D = 40 mm with the square (i.e. sharp-edged without curvature) top end, and air and water to evaluate the film thickness δ, the wall friction factor fw and the interfacial friction factor fi. The comparison of flow characteristics between pipes of D = 20 and 40 mm showed that the CCFL characteristics and the transition from the smooth film (SF) to the rough film (RF) due to flooding near the bottom end were different. On the other hand, δ and fw for SF were expressed by the same correlation for D = 20 and 40 mm. We discussed the CCFL characteristics and fw in detail for SF; these items are important for assessment of α and fi from the dP/dz data in the absence of α data.

Upward two-phase flow patterns in vertical circular pipe under rolling condition

The experiments on the air-water two-phase flow patterns in a 24 mm diameter vertical circular pipe under both static and rolling conditions were conducted. The superficial velocities were in the range of 0.05–4.07 m/s and 0.02–20.55 m/s for water and air, respectively. Five typical flow pattern morphologies resulting from a rolling motion were observed: dispersed bubbles; bubbles; slug; churn; and annular flow. Flow pattern transitions were identified by analysis of visual images and a bubble chord-length probability distribution function (PDF). The static experimental data was used to validate existing flow pattern transition models that were then modified to fit rolling conditions by considering the additional forces caused by rolling motion. These models also agreed well with the experimental data. Investigation of the influence of the rolling motion on flow pattern transition showed that, as the rolling amplitude increases, the formation of dispersed bubble flow requires a higher superficial liquid velocity. It was also found that, the greater the rolling amplitude, the larger region of churn. The rolling period, however, has little impact on flow pattern transitions.

Liquid-phase turbulence measurements in air-water two-phase flows using particle image velocimetry

Liquid-phase turbulence plays a vital role in determining various gas-liquid two-phase flow parameters, such as void fraction distribution, bubble morphology, bubble-bubble interactions, and interfacial area concentration. In this study, a two-phase flow database including both the gas- and liquid-phases measurements was developed focusing on three bubbly flow conditions in an air-water two-phase flow loop with a vertical one-inch diameter circular pipe test section. A particle image velocimetry (PIV) system integrating an optical phase separation method, i.e., the planar laser-induced fluorescence (PLIF) technique using fluorescent particles and optical filtration, was applied to measure the liquid-phase turbulence information, including the time-averaged velocity, Reynolds stress, and turbulent kinetic energy for the liquid phase. The PIV measurements were taken at three ports along the test section at 14.5, 51.5, and 88.5 pipe inner diameters downstream of a bubble injector. In addition, a double-sensor conductivity probe was used to measure radial distributions of the local time-averaged void fraction and gas velocity. The measured liquid-phase turbulence was used to benchmark Sato's turbulence model considering the bubble-induced shear stress for the three tested bubbly flows. The benchmark results showed good agreement between the PIV measurements and model predictions. In the two bubbly flows tested that have low void fractions being less than 3%, the effect of the bubble-induced turbulence was found not significant. However, the bubble-induced shear stress becomes important with the increase of the void fraction.

Interfacial Friction Factors in Vertical Circular Pipes under Flooding Conditions at the Bottom End

Interfacial Friction Factors in Vertical Circular Pipes under Flooding Conditions at the Bottom End

Estimation of shear rate change in vertically oscillating non-Newtonian fluids: Predictions on particle settling

This study investigates the effect of oscillatory motion on velocity and shear rate change within different non-Newtonian, slightly viscoelastic fluids oscillated in a vertical U-shaped circular pipe. An estimation to quantify the influence on particle settling in an oscillatory environment is also presented. Flow visualization using particle image velocimetry (PIV) technique was deployed to compare the two-dimensional velocity field in the vertical plane of the U-tube axis and the resulting shear rate change in three different non-Newtonian fluids. The experiments were performed in a 1.2 m high, 50 mm diameter transparent test section, at room temperature (21 ± 0.5 °C) and atmospheric pressure.A piston was driven at harmonic motion via a gas buffer, to provide the driving force for the test fluids at four different low frequencies ranging from 0.1 – 0.75 Hz and at three different piston oscillation amplitude ratios of A = a/D = 0.3, 0.4 and 0.5, where a is the displacement amplitude of the piston and D is the pipe diameter. Oscillatory Reynolds number (Reδ) based on Stokes layer thickness was used as the criteria for determining the specific flow regime. 36 different experimental cases were tested within the range of 2 < Reδ < 34, and all the experimental cases exhibited the laminar flow regime.The study reveals that the axial velocity amplitude along the pipe centerline increases with the increasing frequency and with increasing oscillation amplitude irrespective of the non-Newtonian fluid type. The thickness of the shear region decreases with the increase of frequency. The change of shear rate is maximum near the wall region of the pipe and that is achieved at the maximum position of the phase cycle, where the axial velocity also possesses its highest magnitude. The most viscous and the least elastic fluid have reported a maximum reduction of viscosity as an effect of the oscillatory motion and the viscosity reduction becomes insignificant when the non-Newtonian fluids become less viscous.

Comparison of oscillatory flow conditions in Newtonian and non-Newtonian fluids using PIV and high-speed image analysis

Oscillatory flow in pipelines is common in many industrial applications, including oil well drilling. An experimental investigation of oscillatory flow inside a vertical U-shaped circular pipe is presented in this paper to mimic the practical scenario takes place within a vertical oil well. Flow visualization was deployed to compare the velocity distributions in Newtonian (deionized water) and non-Newtonian fluid (a mixture of three water-based polymeric liquids). The experiments were performed in a 1.2 m high, 50 mm diameter transparent test section, at room temperature (21 °C) and atmospheric pressure.Particle image velocimetry (PIV) technique was used to obtain non-invasive instantaneous flow velocity profiles. Based on local velocities, the streamwise (axial) velocity component within the pipe across its diameter was determined and the cross-sectional average velocity together with the normalized axial velocity were also calculated. In addition, high-speed motion pictures were used to determine the displacement of the air-liquid interface at the top of the U-tube limb. This enabled comparison of the flow field with the overall volumetric oscillating flow. A piston was driven at harmonic motion via a gas buffer, to provide the driving force for the test fluids at four different low frequencies ranging from 0.1 to 0.75 Hz. Oscillatory Reynolds number (Reδ) based on Stokes layer thickness was used as the criteria for determining the specific flow regime. According to the literature, the critical value for the oscillating Reynolds number was considered to be 500, and with this as reference all the experimental cases were within the laminar regime. Eight different experimental cases were tested within the ranges of (4 <Reδ < 116) and Womersley number (3 <Wo < 55).At higher frequencies, the viscous effects for the Newtonian fluid are confined to the Stokes layer and the central core of the velocity profile is plug-type. At the same time, higher frequencies resulted with increased velocity amplitudes. The viscous resistance of the non-Newtonian fluid and the presence of shear layer contribute to an uneven velocity profile across the pipe cross-section. Cross-sectional average velocity provides a more complete picture of the kinematic structure of oscillating flow and its dynamic distribution across the cross-section. Non-Newtonian fluid tends to achieve higher normalized axial velocities compared to that for Newtonian fluid, which is more or less equals to unity.The study was partly motivated by challenges associated with operational procedures during drilling and maintenance of petroleum wells. Furthermore, this study is also part of a comprehensive study aimed at investigating the influence of low frequency oscillations on particle settling in non-Newtonian drilling fluids.

Liquid Film Thickness in Vertical Circular Pipes Under Flooding Conditions at the Top End

In our previous study, we measured the void fraction α, pressure gradient dP/dz, and countercurrent flow limitation in a vertical circular pipe (diameter D = 20 mm) under flooding conditions at the square top end and working fluids of air and water to obtain the wall friction factor fw and the interfacial friction factor fi based on the annular flow model. The thickness of the falling liquid film δ obtained from the measured α was relatively well expressed by the correlation for the free-falling film, and the obtained fw was well expressed by the Fanning friction factor f for a circular pipe. Measurements of α in vertical pipes under flooding conditions are few. In this study, therefore, we evaluated α and δ from the measured dP/dz under flooding at the square top end reported by Bharathan et al. with D = 50.8 mm and air-water and by Ilyukhin et al. with D = 20 mm and working fluids of steam and water at pressures of P = 0.6 to 4.1 MPa. As a result, we found that δ obtained from the measured dP/dz and the correlation of fw = f were well correlated in terms of the liquid Reynolds number ReL. The obtained δ was well expressed by the Nusselt’s correlation for the free-falling film in the region of laminar flows, but the obtained δ was larger than the Feind’s correlation for the free-falling film in the region of turbulent flows due to the interfacial friction. We also discussed effects of the diameter and fluid properties on the interfacial friction factor fi.

Pressure drop for gas-liquid two-phase annular flow across grid spacer with mixing vane in vertical circular pipe

This study investigates the effects of mixing vane (MV) attached to a grid spacer on pressure drop for air-water annular flows in a vertical circular pipe of 16 mm I.D. In order to know the effects of MV, grid spacers with or without MV were installed in the test pipe. Three types of grid spacers with MV which has four MVs inclined 20, 30 degree from the vertical flow axis (4-MV20, 4-MV30) and two MVs inclined 30 degree (2-MV30) were used. In addition, two liquid injection methods (wall and center jet injections) are adopted to control liquid droplet entrainment faction in gas core. In the experiment, pressure drop along the channel upstream and downstream from the spacer was measured with a pressure transducer. In the analysis, the correlation of the pressure drop across the spacer is newly developed based on the present data.

Evaluation of gas-lift effect by bubbles rising in a vertical circular pipe

Evaluation of gas-lift effect by bubbles rising in a vertical circular pipe

混合翼付きグリッドスペーサが垂直円管内気液環状二相流の液膜厚さに及ぼす影響

混合翼付きグリッドスペーサが垂直円管内気液環状二相流の液膜厚さに及ぼす影響

垂直円管内の混合翼付きグリッドスペーサーを通過する気液二相環状流の圧力損失

This study investigates the effects of mixing vane (MV) attached to a grid spacer on pressure drop for air-water annular flows in a vertical circular pipe of 16 mm I.D. In order to know the effects of MV, grid spacers with or without MV were installed in the test pipe. Three types of grid spacers with MV which has four MVs inclined 20, 30 degree from the vertical flow axis (4-MV20, 4-MV30) and two MVs inclined 30 degree (2-MV30) were used. In addition, two liquid injection methods (wall and center jet injections) are adopted to control liquid droplet entrainment faction in gas core. In the experiment, pressure drop along the channel upstream and downstream from the spacer was measured with a pressure transducer. In the analysis, a correlation of the pressure drop across the spacer is newly developed based on the present data.