Vertical Upward Flow Research Articles

Development of flow regime maps for lead lithium eutectic–helium flows

Abstract Institute for Plasma Research (IPR), Gandhinagar (India) is currently involved in the design and development of its Lead-Lithium Ceramic Breeder (LLCB) module for testing in the International Thermo-nuclear Experimental Reactor (ITER). In order to fulfill the ITER safety requirements, some postulated events need to be analyzed. Among them, the internal loss of coolant accident is being studied using RELAP/SCDAPSIM/MOD4.0 code. To this aim, RELAP/SCDAPSIM/MOD4.0 capabilities of modeling lead lithium eutectic (LLE) and helium flows are being extended nowadays by a collaboration of three institutions, namely IPR, Innovative System Software (ISS) and UPC-BarcelonaTech. The current study is part of this effort and is focused on the adjustments of existing RELAP/SCAPSIM/MOD4.0 flow regime maps in order to deal with the LLE-helium pair. Due to the lack of experimental data, the current study is based on a numerical assessment of LLE-helium flows. The volume of fluid method implemented in OpenFOAM toolkit has been chosen to characterize the flow regime at different mixture velocities and helium fractions. The paper includes a description of the followed methodology and its validation. Results of the systematic simulations of both horizontal and vertical upward flows are shown and the proposed flow diagrams presented. It is worthwhile to mention that the numerically obtained flow regime maps must be validated by an experimental campaign. However, the current approach allows the use of RELAP/SCDAPSIM/MOD4.0 code to properly initiate the study of breeding blanket off-normal events postulated for Lead-Lithium Ceramic Breeder, Helium Cooled Lithium-Lead and Dual Coolant Lithium-Lead designs.

Visualization Study of the Relationship between the Orientation of Tube and the Flow Regimes Near the Expansion Valve

<div class="section abstract"><div class="htmlview paragraph">Several types of noise exist in automobiles. The flow-induced noise in the expansion device can be very disturbing since the expansion device is located near the occupants. In many studies, the flow-induced noise is found to be mitigated when the orientation of the tube is changed. However, no study explores the reason why flow-induced noise changes when the orientation of the tube is changed. The flow-induced noise varies along with the flow regimes near the expansion devices. In this paper, an experimental based research is used to study how the tube orientation changes the flow regimes under the same operating conditions. A pumped R134a system with transparent tubes (1/4-inch ID) is used to visualize the flow regimes near the manual expansion valve. The transparent tube is a continuous connection of horizontal tubes, 45° inclined tubes, and vertical tubes. It is interesting to find that the flow regimes can be very different at the same mass flux, the same quality, and the same pressure when the tube orientation is changed. When the horizontal flow is stratified-wavy flow, the downward vertical flow will either be annular flow or wavy, which depends on the mass flow rate in the system. The upward vertical flow will either be churn flow or plug flow. The 45° inclined downward flow can be wavy flow, while the 45° inclined upward flow can be either intermittent flow or wavy flow. The noise variation for different tubes with the same conditions is also explored in this paper. The results show that the flow regimes, the mass flux, and the vapor mass fraction jointly affect the level of annoyance of flow-induced noise. The vapor mass fraction influences the loudness of the noise, while the flow regimes influence the sharpness of the noise. The higher mass flux makes the flow more turbulent and therefore increases the total annoyance of noise. In the paper, the vertical upward tube installation is found to be the best.</div></div>

Flow boiling CHF experiment with sudden expansion tubes

Abstract Deformed cladding in nuclear power plants can partially block the path of coolant flow and thus alter the heat transfer characteristics between the cladding surface and coolant. In this research, critical heat flux(CHF) in a sudden expansion flow path, was experimentally investigated. Flow boiling CHF experiments were carried out under atmospheric pressure with deionized water for vertical upward flow, with four expansion ratio cases investigated with mass flux ranging from 50 to 250 kg/m2 s. CHF was detected at two different locations. In experiments with either a low expansion ratio(e 1.5) and high mass flux(> 150 kg/m2 s), CHF was detected at the sudden expansion point. Quality at the sudden expansion point was almost zero, which implies that nucleated bubbles under the effect of sudden expansion flow induced CHF at the sudden expansion point. The reason for this transition of CHF location was suggested that local bubble stagnation induced by a balance between drag and buoyancy forces on the bubbles resulted in local flooding in the downward flow.

Influence of Liquid Viscosity and Geometry on Vertical Gas/Liquid Two-Phase Annular-Duct Flow

Summary Two-phase flow in large annular ducts is very common in industrial applications. Nevertheless, many two-phase-flow phenomena in such a geometry have not been fully understood. This article addresses an investigation on the effects of duct geometry and liquid viscosity on vertical upward annular-duct two-phase flows. Compressed air and tap water or mineral oil were the working fluids. Three oil viscosity ranges were tested, from 30 to 400 mPa·s. A 10.0-m-long inclinable experimental setup was designed and built for the experiments conducted in two equivalent geometries. The first is made of a 95-mm-inner-diameter circular pipe (called the reference pipe), and the second is a concentric annular duct with 95-mm hydraulic diameter, the same diameter as the reference pipe. The radial geometries were similar to those observed in oil wells. Flow patterns, total pressure drop, and in-situ volumetric fractions were obtained. According to the results, the standard hydraulic diameter might not be appropriate for the modeling of vertical gas/liquid flow in large annular ducts.

High-Viscosity Liquid/Gas Flow Pattern Transitions in Upward Vertical Pipe Flow

Summary High-viscosity liquid two-phase upward vertical flow in wells and risers presents a new challenge for predicting pressure gradient and liquid holdup due to the poor understanding and prediction of flow pattern. The objective of this study is to investigate the effect of liquid viscosity on two-phase flow pattern in vertical pipe flow. Further objective is to develop new/improve existing mechanistic flow-pattern transition models for high-viscosity liquid two-phase-flow vertical pipes. High-viscosity liquid flow pattern two-phase flow data were collected from open literature, against which existing flow-pattern transition models were evaluated to identify discrepancies and potential improvements. The evaluation revealed that existing flow transition models do not capture the effect of liquid viscosity, resulting in poor prediction. Therefore, two bubble flow (BL)/dispersed bubble flow (DB) pattern transitions are proposed in this study for two different ranges of liquid viscosity. The first proposed transition model modifies Brodkey's critical bubble diameter (Brodkey 1967) by including liquid viscosity, which is applicable for liquid viscosity up to 100 mPa·s. The second model, which is applicable for liquid viscosities above 100 mPa·s, proposes a new critical bubble diameter on the basis of Galileo's dimensionless number. Furthermore, the existing bubbly/intermittent flow (INT) transition model on the basis of a critical gas void fraction of 0.25 (Taitel et al. 1980) is modified to account for liquid viscosity. For the INT/annular flow (AN) transition, the Wallis transition model (Wallis 1969) was evaluated and found to be able to predict the high-viscosity liquid flow pattern data more accurately than the existing models. A validation study of the proposed transition models against the entire high-viscosity liquid experimental data set revealed a significant improvement with an average error of 22.6%. Specifically, the model over-performed existing models in BL/INT and INT/AN pattern transitions.

Application of the image analysis on the investigation of disturbance waves in vertical upward annular two-phase flow

Annular two-phase flow commonly exists in industries process, and the disturbance wave at the gas-liquid interface plays an essential role in the mass, momentum and energy exchange. Although extensive experimental and analytical approaches to properties of disturbance waves have been implemented, most of the empirical correlations constructed to predict the wave properties have defects in prediction, especially under the high-pressure conditions. In the present paper, an image analysis method by acquiring the spatiotemporal distribution of the liquid film is employed to investigate the wave properties in a 20 mm I.D. tube in the upward annular regime. Because the interfacial waves should first penetrate through the gas boundary layer before full development, the effect of the gas boundary layer cannot be ignored and is undoubtedly enhanced when pressure increases. Accordingly, new empirical correlations for wave velocity and frequency are proposed by introducing the excess liquid Reynolds number. Compared with the experimental data from the literature, the proposed equations agree well with the experimental data within the averaged relative deviation of ±35%, especially under high-pressure conditions.

Numerical calculation and multi-factor analysis of slurry diffusion in an inclined geological fracture

Slurry grouting plays an important role in water plugging for hydrogeological engineering and there are multiple factors that restrict the slurry flow. This study investigates the restriction mechanisms, based on a single inclined rough fracture, employing a space stepwise method (SSM) using multi-direction sectors (MDS) for calculating the diffusion of variable-viscosity slurry under constant flow. The specifically developed numerical algorithm is validated by experimental results. The spatio-temporal effects of major factors on the flow, and the rock hydraulic properties, were analyzed for cement-based slurry. The results show that the slurry flow calculated by MDS-SSM exhibits strong fitting with experimental results. The diffusion pattern no longer exhibits a circular plane, but rather a double semi-elliptical distribution. The fracture direction angle, especially for the upward vertical flow, must be considered in the case of a larger dip angle. The main controlling factor of the pressure field is the higher slurry viscosity in regions far from the injection hole, and the influence of dip angle is significantly greater closer to the hole. Roughness has an influence on the fracture hydraulic properties, and the required grouting pressure increases with an increase in roughness. The fracture aperture, viscosity coefficient, and diffusion radius are three key factors with strong sensitivity affecting the forecasting accuracy of grouting parameters. The role of the fracture dip angle can be neglected only in narrow fractures and long-distance diffusion with higher-viscosity slurry or larger pressure. The key threshold value can be obtained with a fitting formula under given conditions.

Vertical upward and downward churn flow: Similarities and differences

Investigation of downward two-phase flows received less attention compared to the vertical upward flows. Downward flows are found in many industries and facilities including; oil/gas production, nuclear industry and petroleum refinery/production facilities such as evaporators, chemical reactors and distillation towers. A thorough understanding of the flow dynamic characteristics occur in such transportation lines, process plants and units is very crucial in terms of design, operation, production and safety.In the current work, air-water two-phase churn flow in a 34 mm I.D. pipe was investigated for two configurations of vertical upward (51 cases) and downward (48 cases). Several conductance probes and pressure transducers were used to measure cross-sectional averaged void fraction time series, and pressure drop along the pipe, respectively.The main objectives of the work were to investigate the similarities and dissimilarities between vertically upward and downward churn flow and specifically understand how gravity could affect the behavior of liquid structures present within the flow. To quantify this, different parameters such as Probability Density Function, distribution coefficient in the drift-flux model, structural velocity, slippage number, dimensionless pressure gradient etc. were used.It was noticed that in both configurations, dimensionless pressure gradient and slippage number demonstrated a strong correlation with the mixture Froude number. There were, however, discrepancies in Probability Density Functions (PDFs) and structural velocities of flow in the two orientations.

Mass measurement based calibration of a capacitive sensor to measure void fraction for R134a in smooth tubes

This paper presents a new capacitive sensor built and used to measure void fraction of both horizontal and vertical upward flow in the low mass flux range in circular tubes with an inner diameter of 7 mm. Three sensors with different axial lengths (D, 2D/3, and D/2) are built and evaluated to examine the possibility of utilizing shorter sensors in applications with space limitations. Results show all three sensors have the capability to measure void fraction. Due to the nonlinear relation between capacitive signals and void fraction, a calibration procedure based on mass measurement (quick-closing valve technique, QCV) is proposed. After the calibration procedure, most void fraction data measured by the sensor falls into the ±15% deviations of the experimental results by QCV for horizontal flow and ±10% for vertical upward flow. Sensors with the same design can be utilized directly to measure void fraction for the similar test conditions in the future studies.

Experimental investigations of kerosene-water two-phase flow in vertical pipe

Oil and water two-phase flow studies are important to the oil industries. This paper aims to determine the flow patterns, holdup, pressure losses, phase inversion, drift flux parameters and mixture properties in vertical upward kerosene and water flow. The experiment was conducted in a 26 mm i.d duct with phase velocities spanning from 0.1 to 1.0 m/s. The averaged holdup was measured using quick close valves in a 1.16 m long test section. The same test section was used to measure the pressure drop. A local impedance probe and high-speed films were used to determine the flow patterns. Six different flow patterns was identified: dispersed bubbly (DB), core annular (CA), bubbly (B), churn turbulent (CT), and elongated water drop (EWD). The kerosene holdup was highest for EWD, spanning from 0.8 to 0.9, followed by CT and CA, which spans from 0.35 to 0.75. The kerosene holdup for bubbly spans from 0.12 to 0.6, being the highest range for all patterns. The phase inversion occurs when the kerosene input fraction is βK = 0.35. There is no evidence of slippage between the dispersed and continuous phases. The drift velocity is due to the misalignment of the dispersed fraction and the mixture velocity profile and the distribution parameter is C0 = 1.10. The pressure loss showed a good agreement with Blasius correlation. The exception is for the bubbly and churn turbulent. The density was determined using the homogeneous model and five different mixture viscosity models were investigated. The pressure loss deviation using (Mukhaimer et al., 2015) mixture viscosity spans from 5 to 25%. The drift-flux correlation increase the predictive capability of the oil fractions in oil pipelines, which contribute to the operational security. In addition, a better pressure drop losses estimative provide in this study helps to a better oil pipeline design.

Experimental Investigation of the Vertical Upward Single- and Two-Phase Flow Pressure Drops Through Gate and Ball Valves

Abstract This paper presents an experimental investigation of the pressure drop (DP) through valves in vertical upward flows. Experiments were carried out using a 1¼″ (DN 32) ball and gate valve. Five opening areas have been investigated from fully open to the nearly fully closed valve, using air with a superficial velocity of 0–3.5 m/s and water 0.05–0.91 m/s. These ranges cover single-phase and the bubbly, slug and churn two-phase flow regimes. It was found that for the single-phase flow experiments, the valve coefficient increases with the valve opening and is the same, in both valves, for the openings smaller than 40%. The single-phase pressure drop increases with the liquid flowrate and decreases with the opening area. The two-phase flow pressure drop was found considerably increased by reducing the opening area for both valves. It reaches its maximum values at 20% opening for the ball valve and 19% opening for the gate valve. It was also inferred that at fully opening condition, the two-phase flow multiplier, for both valves, has been found close to unity for most of the tested flow conditions. For 40 and 20% valve openings the two-phase multiplier decreases in the power-law with liquid holdup for the studied flow conditions. Models proposed originally for evaluating the pressure drop through an orifice in single-phase and two-phase flows were also applied and assessed in the present experimental data.

Wave characteristics of vertical upward adiabatic annular flow in pipes

Annular flow exists in many engineering applications, such as refrigerators, oil extraction, nuclear reactors and so on, due to its high heat and mass transfer efficiencies. Annular flow is characterized by liquid film on the wall and gas core at the center of the flow duct. The interface between the gas and liquid is composed of many different waves that play important role in mass, momentum and energy transfers between gas and liquid phases. Here three important parameters regarding wave characteristics, namely, wave velocity, base film thickness and wave height have been studied. For wave velocity, correlation has been proposed by two methods which are derived from liquid interfacial velocity and interfacial shear stress, respectively. For correlations of base film thickness and wave height, they are proposed in similar forms as that of average film thickness previously developed by the authors. These newly proposed correlations are functions of gas and liquid Weber numbers, and are simpler and more straightforward to use as compared to the existing ones. The newly proposed wave velocity, base film thickness and wave height correlations, respectively, have mean absolute percentage errors of 9.56%, 14.6% and 12.1% compared to current databases. They have shown an improved prediction accuracy compared to the other correlations in the literature.

Quantitative Analysis of Water Vapor Transport during Mei-Yu Front Rainstorm Period over the Tibetan Plateau and Yangtze-Huai River Basin

There are continuous precipitation systems moving eastward from the Tibetan Plateau to the middle and lower reaches of the Yangtze-Huai River during the Mei-yu period. We selected 20 typical Mei-yu front precipitation cases from 2010 to 2015 based on observational and reanalysis data and studied the characteristics of their environmental fields. We quantitatively analyzed the transport and sources of water vapor in the rainstorms using the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT_4.9) model. All 20 Mei-yu front precipitation cases occurred in a wide region from the Tibetan Plateau to the Yangtze-Huai River. The South Asian high and upper level jet stream both had strong intensities during the Mei-yu front rainstorm periods. Heavy rainfall mainly occurred in the divergence zone to the right of the high-level jet and in the convergence zone of the low-level jet, where strong vertical upward flows provided the dynamic conditions required for heavy rainfall. The water vapor mainly originated from the Indian Ocean, Bay of Bengal, and South China Sea. 52% of the air masses over the western Tibetan Plateau originated from Central Asia, which were rich in water vapor. The water vapor contribution at the initial position was only 41.5% due to the dry, cold air mass over Eurasia, but increased to 47.6% at the final position. Over the eastern Tibetan Plateau to the Sichuan Basin region, 40% of the air parcels came from the Indian Ocean, which was the main channel for water vapor transport. For the middle and lower reaches of the Yangtze River, 37% of the air parcels originated from the warm and humid Indian Ocean. The water vapor contribution at the initial position was 38.6%, but increased to 40.2% after long-distance transportation.

Single-phase mixed convective heat transfer and pressure drop in the laminar and transitional flow regimes in smooth inclined tubes heated at a constant heat flux

Heat transfer and pressure drop experiments were conducted in the laminar and transitional flow regimes at different inclination Grashof numbers that generated different levels of buoyancy. A wide range of Grashof numbers were covered by varying both the inclination angle and heat flux. The experiments were conducted on an experimental set-up on which flow could occur through a smooth tube positioned at different inclination angles, from vertical downward (−90°) flow to vertical upward (+90°) flow. The test section had an internal diameter of 5.1 mm, length of 4.6 m and a square-edged inlet was used. The experiments were conducted at different inclination angles between Reynolds numbers of 1000 and 6000 at heat fluxes of 4–8 kW/m2. The test fluid was water and the Prandtl numbers varied from 3 to 7. It was found that an increase in the inclination angle from horizontal flow (0°) to vertical (±90°) flow, decreased the buoyancy effects which led to decreased laminar heat transfer coefficients and friction factors for both upward and downward flows. The onset of buoyancy effects was significant near the vertical inclinations and caused a rapid increase in the laminar heat transfer coefficients and friction factors when the inclination angles moved from vertical to horizontal orientations. An inclined tube Grashof number which is a function of inclination angle was defined and used to express the laminar Nusselt numbers as a forced convection part plus an enhancement component owing to mixed convection. The laminar friction factors were expressed as a function of forced convection/isothermal part multiplied by the mixed convection part. Furthermore, it was found that the critical Reynolds numbers at which transition started increased as the inclination angles increased from horizontal to vertical, while the end of transition were inclination angle independent. This caused the width of the transitional flow regime to decrease, as well as the transition gradients to increase, with increasing inclination angle at different heat fluxes. It was also found that the flow directions (upward and downward) had a negligible effect on the heat transfer coefficients and friction factors in the entire transition and quasi-turbulent regions.

Flow-pattern-based experimental analysis of convective boiling heat transfer in a rectangular channel filled with open-cell metallic random porous media

This paper reports a visualization study on the flow boiling of R245fa in a rectangular channel filled with an open-cell random porous structure made of copper. The boiling heat transfer of the two-phase vertical upward flow inside the channel was measured while the refrigerant was asymmetrically heated by a hot-water-source channel. An experiment was conducted with a constant saturation pressure of 5.9 bar, inlet vapor quality of 0.05–0.99, channel heights of 3 and 5 mm, and mass flux of 133–300 kg/m2 s. The results are compared with those of a plain channel in the same operating conditions. The two-phase flow characteristics are discussed along with the trend of the boiling heat transfer coefficient and mean vapor quality according to the flow patterns obtained with and without the metallic porous media. A non-dimensional analysis was also conducted for comparison.

Hydrodynamics of Intermediate-Scale Taylor Flow under Gravities of Space Colonies

This paper investigates the effect of gravitational strength on hydrodynamics of intermediate-scale Taylor bubble in vertical upward slug flow. Air and water were used as the working fluids and two different sets of superficial velocities (JL = 0.05, JG = 0.15 m/s; and JL = JG = 0.15 m/s) were carefully selected to create laminar slug (Taylor bubble) flows. In order to effectively study the gravitational influence with a reasonable computational cost, an intermediate-scale tube diameter (D = 12 mm) was selected. The governing equations were discretized in a three-dimensional computational domain and numerically solved based on the volume of fluid-continuum surface force (VOF-CSF) method using OpenFOAM. The computational fluid dynamics (CFD) model was validated under normal gravity with existing top performing correlations in literature. To address the space colonization environments, the gravity strength considered in the CFD simulations include 10−4go (microgravity), 0.17go (Moon), 0.38go (Mars), go (=9.81 m/s2, Earth), and 2go (hyper). The simulation results show that by increasing gravity, Taylor bubbles of the slug flow are shrunk both in length and diameter leading to a reduced void fraction. The flow field around Taylor bubbles was found to be significantly affected by gravitational strength. A strong falling-film flow around a Taylor bubble was observed at the hyper-gravity, while no falling-film flow existed at microgravity. The falling-film flow caused a local reversal of wall shear stress, and thus a positive frictional pressure gradient that was intensified by increasing gravitational strength. However, the total pressure gradient including a hydrostatic pressure always were negative despite the positive frictional pressure gradient. The rising velocity of the Taylor bubble exhibited an interesting behavior showing a minimum around normal gravity.

Prediction of flow distribution of vertical upward co-current adiabatic annular flow in 8 × 8 rod bundle

Annular flow in rod bundle occurs frequently in boiling water reactor (BWR) under normal operation and in pressurized water reactor (PWR) under accident conditions. When annular flow occurs, rod film thickness is one of the most important parameters for safety concern. In order to calculate rod film thickness distribution inside rod bundle, both gas and liquid velocity distribution inside rod bundle is necessary. Also, flow distribution inside rod bundle is of importance for calculation of interfacial shear stress and other parameters in each sub-channel. However, entrained droplets in gas core can sharpen the gas velocity profile while existing rods can flatten the gas velocity profile, making it different from that of single phase flow. The liquid velocity distribution inside rod bundle is hard to obtain from experiment because of the complex structure of its geometry. Due to these reasons, this paper deducts gas and liquid velocity profiles from existing adiabatic rod film thickness data. Even the gas velocity profiles for different flow conditions are different, there exists a gas velocity profile that can be applied to all current flow conditions with minimum uncertainties. Based on that gas velocity profile, liquid velocity profile can be calculated. From these flow velocity profiles, film thickness on each rod and interfacial shear stress in each sub-channel can be calculated.

Detecting the Flow Pattern Transition in the Gas-Liquid Two-Phase Flow Using Multivariate Multi-Scale Entropy Analysis

Abstract Due to the complex flow structure and non-uniform phase distribution in the vertical upward gas-liquid two-phase flow, an eight-electrode rotating electric field conductance sensor is used to obtain multi-channel conductance signals. The flow patterns of the vertical upward gas-liquid two-phase flow are classified according to the images obtained from a high-speed camera. Then, we employ the multivariate weighted multi-scale permutation entropy (MWMPE) to detect the instability of flow pattern transition in the gas-liquid two-phase flow. Afterwards, we compare the results of the MWMPE with those of the single-channel weighted multi-scale permutation entropy (SCWMPE) and multivariate multi-scale sample entropy (MMSE). The comparison results indicate that, compared with the SCWMPE and MMSE, the MWMPE has superior performance in terms of the high-resolution presentation of flow instability in the gas-liquid two-phase flow. Finally, we extract the mean value of the MWMPE in whole scales and the entropy rate of the MWMPE in the small scales. The results indicate that the normalized mean value and normalized entropy rate of MWMPE are very sensitive to the transitions of flow patterns, thus allowing the detection of the instability of flow pattern transition.

Water–air flow in straight pipes and across 90∘ sharp-angled mitre elbows

Water–air flow in horizontal and vertical straight pipes and through 90∘ sharp-angled mitre elbows is investigated by visualizing the flow patterns by means of a high-precision camera and by measuring the pressure drop. The flow is studied in pipes with three diameters for about six hundred conditions of water–air flows, characterized by superficial velocities in the ranges of jL* = 0.3–1 m/s for water and jG* = 0.15–34 m/s for air. The portion of the pipe upstream of the elbow is always positioned horizontally, while the portion of the pipe downstream of the sharp bend is oriented horizontally or vertically with the flow moving upward. Plug, slug, slug-annular, and annular flows are visualized in horizontal straight pipes, while slug, churn, and annular regimes are recorded in vertical straight pipes downstream of the sharp bend. These patterns are well predicted by the Mandhane map (Mandhane et al., 1974) for horizontally oriented straight pipes and by the Hewitt–Roberts map (Hewitt and Roberts, 1969) for vertically oriented straight pipes. The changes of the flow patterns as the fluids pass through the mitre elbows are discussed. A multiple membrane flow structure is observed in the vertical upward flow at much higher Reynolds numbers based on the water superficial velocity than in the vertical downward case previously reported in the literature. A dimensional analysis is employed to obtain the non-dimensional parameters that describe the flows through the straight pipes and across the elbows. It is proved that a rigorous way to present the flow regimes and the pressure-drop coefficients of the water–air flow for a given geometry is the space of the Reynolds numbers based on the superficial velocities of air and water for fixed Froude number because the flow is incompressible and isothermal. By expressing the maps in scaled form, the prediction of the flow patterns along the straight portions of the pipe improves. The flow patterns through the elbows are expressed in terms of rescaled Mandhane maps, which, for the first time, simultaneously represent the flow patterns both upstream and downstream of the elbows. New pattern-based empirical correlations are obtained for the scaled pressure drops for the water–air flows through the horizontal and vertical pipes and through the elbows. The correlations are based on the flow patterns and do not rely on widely used prediction models, thereby predicting the pressure drop more accurately than the models presently available in the literature.

Gravitational instabilities in binary granular materials

The motion and mixing of granular media are observed in several contexts in nature, often displaying striking similarities to liquids. Granular dynamics occur in geological phenomena and also enable technologies ranging from pharmaceuticals production to carbon capture. Here, we report the discovery of a family of gravitational instabilities in granular particle mixtures subject to vertical vibration and upward gas flow, including a Rayleigh-Taylor (RT)-like instability in which lighter grains rise through heavier grains in the form of "fingers" and "granular bubbles." We demonstrate that this RT-like instability arises due to a competition between upward drag force increased locally by gas channeling and downward contact forces, and thus the physical mechanism is entirely different from that found in liquids. This gas channeling mechanism also generates other gravitational instabilities: the rise of a granular bubble which leaves a trail of particles behind it and the cascading branching of a descending granular droplet. These instabilities suggest opportunities for patterning within granular mixtures.