Liquid Entrainment Rate Research Articles

Modeling and simulation of air-water upward annular flow characteristics in a vertical tube using CFD

Annular flow refers to a special type of two-phase flow pattern in which liquid flows as a thin film at the periphery of a pipe, tube, or conduit, and gas with relatively high velocity flows at the center of the flow section. This gas also includes dispersed liquid droplets. The liquid film flow rate continuously changes inside the tube due to two processes-entrainment and deposition. To determine the liquid holdup, pressure drop, the onset of dryout, and heat transfer characteristics in annular flow, it is important to have proper knowledge of flow characteristics. Especially a better understanding of entrainment fraction is important for the heat transfer and safe operation of two-phase flow systems operating in an annular two-phase flow regime. Therefore, the objective of this work is to develop a computational model for the simulation of the annular two-phase flow regime and assess the various existing models for the entrainment rate. In this work, Computational Fluid Dynamics (CFD) in ANSYS FLUENT has been applied to determine annular flow characteristics such as liquid film thickness, film velocity, entrainment rate, deposition rate, and entrainment fraction for various gas-liquid flow conditions in a vertical upward tube. The gas core with droplets was simulated using the Discrete Phase Model (DPM) which is based on the Eulerian-Lagrangian approach. The Eulerian Wall Film (EWF) model was utilized to simulate liquid film on the tube wall. Three different models of Entrainment rate were implemented and assessed through user-defined functions (UDF) in ANSYS. Finally, entrainment for fully developed flow was determined and compared with the experimental data available in the literature. From the simulations, it was obtained that the Bertodano correlation performed best in predicting entrainment fraction and the results were within the ±30 % limit when compared to experimental data.

Flow rate measurement of gas-liquid annular flow through a combined multimodal ultrasonic and differential pressure sensor

Natural gas is an important strategic reserve resource for the country, also plays an important role in energy transition. During mining and transportation, natural gas has high liquid content and high-pressure characteristics, typically exhibiting gas-liquid annular flow state. Accurate flow metering of each individual phase without separation is significant to academic research and industrial production. Therefore, a combined ultrasonic and differential pressure sensor is presented to acquire flowing information. Based on the limited flowing information (liquid film fraction and gas velocity) measured by dual mode ultrasonic sensor, a two-fluid model is established to solve liquid velocity and droplet entrainment rate for calculating phase flow rates by analyzing the momentum balance between gas and liquid phases. The pressure drop by differential pressure sensor is introduced to make this two-fluid model closed and solvable. Considering the effects of system pressure and pipe diameter on pressure drop, a closed correlation for friction factor at the gas-liquid interface is established. Furthermore, the phase flow rates are calculated by the experimental measurement values obtained by dual mode ultrasonic sensor and the two-fluid model. The relative error of total flow rate is within ±10 % and the mean absolute percentage error is 5.220 %.

Research on entrainment characteristics and Over-Reading model for gas-liquid flow in Venturi

The accurate measurement of gas-liquid flow is becoming increasingly significant in the oil and gas industry. Over-Reading (OR) model is the foundation for the gas-liquid flow measurement using Venturi. In this paper, a new OR model based on the form of Chisholm model for horizontal Venturi has been developed. The relationship between entrainment rate and OR in the throat of Venturi has been considered, which could be linked by the gas-liquid velocity slip. The liquid film thickness and entrainment rate in the throat of Venturi were measured by the conductance probes and cross-correlation method. The laboratory experiments of OR were conducted under the pressures of 0.2–1.4 MPa and at a wider range of Lockhart-Martinelli parameter (XLM:0–1.794). Without piecewise modeling, the relative errors of the new OR model are less than ±5% at the confidence level of 99.1%. The extension of the new OR model has been verified by the published data set of De Leeuw.

A pressure drop model for the annular-mist flow in vertical Venturi

Venturi is one of the most commonly used flowmeters for measuring gas-liquid flow at the natural gas wellhead. A better understanding of the flow mechanism and the causes for pressure drop is necessary for the establishment of the measurement model. In this study, a one-dimensional pressure drop model between the two pressure taps of Venturi has been proposed for vertical annular-mist flow. The relations between the liquid film, entrainment rate, void fraction, and velocity slip have been revealed when the annular flow went through Venturi. We consider the gas acceleration in the throat of Venturi. The proportions of various pressure drops are given. The experimental results show that the relative errors of the pressure drop have a confidence probability of 98.5% within 10%. The predicted results are also in good agreement with the on-site data. It proves that the new pressure drop model has good performance.

Development and performance study of a natural silk fiber facial mask paper

Facial masks are beauty products which composed of a facial mask paper and beauty solution. Silk contains the amino acid structure closest to the human skin, and has the skin-friendly, cosmetic and antibacterial functions, but the common method for making nonwoven facial mask paper is not suitable for silk. In this paper, the silkworm’s spinning path is intervened manually to obtain a smart silk facial mask paper (SMC) of controllable thickness, so that the sericin on the silk fiber is well preserved. In the experiment where the SMC is compared with the nonwoven 384-cuprammonium rayon facial mask paper (CRMC) which is the most widely used in the market, it is found that the ways of forming the two facial mask paper are completely different, and therefore the morphologies under SEM are obviously different. The thickness of the SMC is 0.183 mm and the areal weight of it is 38.0 g/m2. It is very close to the CRMC (0.187 mm, 38.4 g/m2). The porosity of the SMC is 84.0%, which is slightly lower than that of the CRMC (86.3%), but its pores are well distributed. Compared with the CRMC, the smart SMC has higher dry and wet strength, lower elongation, slightly lower air permeability and liquid entrainment rate, and better antibacterial performance.

Validation of RELAP5 MOD3.3 code for entrainment phenomenon against FATE test facility

The fourth stage of Automatic Depressurization System(ADS4) is a crucial part in the passive core cooling system. During LOCA transient or long-term cooling period, entrainment/offtake phenomenon will take place at the ADS4 branch. This phenomenon may affect the depressurization process or boric acid balancing. The RELAP5 mod3.3 is expected to be useful and effective for analyzing the thermal-hydraulic behaviors in design, licensing and safety analysis of nuclear power plant. In this case, accurately evaluating the entrainment/offtake model in RELAP5 is quite important for safety analysis of passive nuclear power plant. A Full scAle Test facility for liquid Entrainment (FATE) is designed and fabricated to give a better understanding of entrainment's scaling effect and quantify the uncertainty of existing models. The geometry of upper plenum, hot leg and ADS4 pipe are all the same with CAP1400. Test data of both onset of liquid entrainment (OLE) and entrainment rate for different gas and liquid flow rate are achieved. Calculation results are compared with the experiment data and existing entrainment models. The differences are discussed and analyzed.

Prediction of the Critical Gas Velocity of Liquid Unloading in a Horizontal Gas Well

Summary Analysis of the experimental data for liquid-entrainment rate, forces exerted on liquid droplet, and secondary flow occurring in the gas core show that the liquid is mainly carried in the form of film in the inclined annular flow. Therefore, it is more reasonable to establish a mathematical model from the bottom-film reversal than from the droplet reversal. In this study, a new analytical model is developed from force balance of the bottom film of the inclined tubing after studying the bottom-film thickness and gas/liquid interfacial friction factor to reveal the liquid-loading mechanism. Furthermore, a new Belfroid-like empirical model is proposed that is based on the calculation results of a wide range of flowing parameters from the new analytical model to predict the liquid-loading status of gas wells. The new empirical model introduces a coefficient Cd,p,uSL,T to consider how the fluid properties under downhole flow condition affect the critical gas velocity. Cd,p,uSL,T in the new empirical model increases with the pipe diameter, liquid velocity, and flowing pressure, and decreases with the flowing temperature. The new analytical model, having an average error of 8.45%, agrees well with the published experimental data, and it also performs well in predicting the pressure gradient at liquid unloading condition. The new empirical model could be applied for the prediction of real field operations and has been validated with an accuracy rate of 95% against data newly collected from 60 horizontal wells. The new work can accurately and easily judge the liquid-loading status, and it also reveals how the fluid properties under downhole flowing condition affect the liquid loading.

Models development of liquid drops entrainment at a T-junction with a large vertical up branch

The liquid entrainment process at the vertical up tee branch is widespread in mass and heat transfer applications. Existing liquid entrainment models mainly apply to T-junctions with small diameter ratios of branch to main line (d/D), which are unable to predict the liquid entrainment under large d/D conditions. The models of liquid entrainment onset and entrainment rate are developed under reasonable assumptions. The entrainment onset model was developed based on the wave theory, force analysis and potential flow theory. The Bond number is innovatively introduced into the model to represent the effect of surface tension acting on the entrainment onset. The model is compared against the relevant experimental data which shows good agreement. In the modeling of the entrainment rate, the key parameters are obtained by nondimensionalizing the conservation equations governing the liquid entrainment process, and the constants in the model are determined by genetic algorithm. The model agrees well with existing experimental data.

Experimental simulation of liquid entrainment in ADS-4 depressurization line in AP1000

The fourth stage Automatic Depressurization System is an important passive safety feature in Westinghouse AP1000 which enables controlled depressurization of reactor coolant system in small break LOCA. However, large amount of coolant can be carried to the containment via the ADS-4 branch entrainment and the upper plenum entrainment during the depressurization process, which poses great threats to core uncovering and melting. The automatic Depressurization and Entrainment TEst Loop (ADETEL) modeled after AP1000 with a scaling ratio of 1:5.6 was constructed to investigate the entrainment and depressurization behavior after the actuation of ADS-4 valves. The entrainment and depressurization features were investigated under different initial pressure, mixture liquid level in the pressure vessel and heating power. The entrainment deposition effect of the reactor internals was also investigated. The test data reveals that large amount of water are entrained through the ADS-4 branch line within a short period of time. The liquid entrainment rate and the reduced rate of the mixture liquid level in the pressure vessel increase with the initial system pressure. It is notable that the core uncovery was experienced when the initial pressure was set to 0.5 MPa in current experimental conditions. The reactor internals have little effect on the entrained mass and the mixture liquid levels in the pressure vessel.

Experimental investigation of liquid entrainment in vertical up tee branch with double-end gas inlets

Tee branches are widely used in nuclear power plants for varying purposes. The tee branch is adopted by the fourth stage Automatic Depressurization System (ADS-4) in Westinghouse AP600/AP1000 to depressurize the primary loop during the small break loss of coolant accident (SBLOCA). However, large amount of coolant will be entrained simultaneously through the ADS-4 branch which poses the threat of core uncovering and melting. Visualization experiments with double-end gas inlets were conducted to investigate the ADS-4 tee branch entrainment phenomena in AP1000. Entrainment process were recorded by high speed camera and analyzed in detail. The onset of liquid entrainment and entrainment rate data were obtained and compared with existing data and correlations, and discrepancies were found in the comparison due to the difference of test section geometric configuration. The gas flow rate has little effect on the branch quality at the same dimensionless gas chamber height in entrainment rate tests. The entrainment frequency was also studied. The test data reveal that the entrainment period decreases rapidly with the increase of entrainment rate in low range of the entrainment rate, and gradually stabilizes in high range of the entrainment rate.

Air Injection in Water with Different Nozzles

Air injection systems have a wide range of environmental engineering applications. In this study, we conducted experiments on air injection in a relatively large water tank to investigate the effect of nozzle type, including single/multiple orifice nozzles and a porous airstone, on the characteristics of the bubbles and the induced flow structure. Measurements of bubble characteristics and flow field surrounding the bubble core were obtained using a double-tip optical probe and particle image velocimetry, respectively. The results revealed that bubble velocity did not change significantly with different nozzles, but bubble size decreased significantly while interfacial area, liquid entrainment rate, and kinetic energy of the mean and turbulent flow increased significantly by using the porous airstone instead of nozzles with large orifices. The results for a nozzle with multiple orifices of small diameter are comparable to those for the airstone, which suggests the suitability of its use for systems susceptible to clogging of the pores. Correlations using adequate length and velocity scales are also proposed to describe both bubble and liquid flow characteristics. Finally, applications of the results for different artificial aeration/mixing systems are presented.

Effect of ejector configuration on hydrodynamic characteristics of gas–liquid ejectors

Ejectors are gas–liquid contactors that are reported to provide higher mass transfer rates than conventional contactors. Detailed experiments were performed and computational fluid dynamics (CFD) modeling studies were undertaken to understand the hydrodynamic characteristics of the ejector geometry. The CFD model provides a basis for quantifying the effects of operating conditions on the ejector performance. CFD studies shows that there is an optimum ratio of nozzle area to throat area (area ratio), at which the liquid entrainment rate is the highest. This can lead to substantial economic benefit in the industrial practice. The liquid entrainment rate correlates with pressure difference between the water surface in the suction chamber and the throat exit for a wide variety of ejector geometries and operating conditions.

Effect of Geometry on Mass Transfer Characteristics of Ejectors

Ejectors are gas-liquid contactors that are reported to provide higher mass transfer rates than conventional contactors. Detailed experiments were performed, and Computational Fluid Dynamics (CFD) modeling studies were undertaken to understand the mass transfer characteristics of the ejector geometry. The mass transfer coefficient and interfacial area were predicted from the volume averaged energy dissipation rate. Studies show that there is an optimum ratio of nozzle area to throat area (area ratio), at which the liquid entrainment rate is the highest. Using optimized geometry can lead to substantial economic benefit in the industrial practice.

Hydrodynamics and mass transfer characteristics of gas–liquid ejectors

In the present work, experimental investigations have been carried out on ejectors employing air as a motive fluid and water as the entrained fluid. A semi-empirical model has been developed to predict the liquid entrainment rate taking into account: (i) the compressible nature of air, (ii) pressure drop for two-phase flow and (iii) losses due to changes in cross sectional area. The effects of gas velocity, liquid level in the suction chamber, nozzle diameter and throat diameter on the liquid entrainment, entrainment ratio (L/G), pressure drop, gas hold-up, mass transfer coefficient and interfacial area have been investigated. The liquid entrainment rate increases with the increased liquid level in the suction chamber and with the increase in gas velocity. The ratio of throat cross sectional area to the nozzle cross sectional area (area ratio) was found to be a critical parameter. These results have been explained on the basis of pressure profiles of ejector (along the centre line of the ejector). The liquid entrainment rate predicted from the semi-empirical model is in good agreement with the experimental values. The mass transfer coefficient and interfacial area increase with increase in gas velocity. Correlations have been proposed to estimate the fractional gas hold-up, mass transfer coefficient and interfacial area in the ejectors.

Hydrodynamic Characteristics of Gas–Liquid Ejectors

In the present work, experimental investigations have been carried out on ejectors employing gas (air) as a motive fluid and liquid (water) as the entrained fluid. A semi-empirical model has been developed to predict the liquid entrainment rate taking into account, (1) the compressible nature of air, (2) pressure drop for two phase flow and (3) losses due to changes in cross sectional area. The effects of gas velocity, liquid level in the suction chamber, nozzle diameter, throat height and throat diameter on the liquid entrainment, entrainment ratio and pressure drop have been investigated. It has been observed that the liquid entrainment rate increases with an increase in the liquid level in the suction chamber. It was also found to increase with an increase in the gas velocity. The ratio of throat cross-sectional area to the nozzle cross-sectional area (area ratio) was found to be a critical parameter. The results have been explained on the basis of pressure profiles. The values of liquid entrainment rate predicted from the semi-empirical model were found to be in good agreement with the experimental measurements.

Liquid entrainment by an expanding core disruptive accident bubble—a Kelvin/Helmholtz phenomenon

Abstract The final stage of a postulated energetic core disruptive accident (CDA) in a liquid metal fast breeder reactor is believed to involve the expansion of a high-pressure core-material bubble against the overlying pool of sodium. Some of the sodium will be entrained by the CDA bubble which may influence the mechanical energy available for damage to the reactor vessel. The following considerations of liquid surface instability indicate that the Kelvin–Helmholtz (K–H) mechanism is primarily responsible for liquid entrainment by the expanding CDA bubble. First, an instability analysis is presented which shows that the K–H mechanism is faster than the Taylor acceleration mechanism of entrainment at the high fluid velocities expected within the interior of the expanding CDA bubble. Secondly, a new model of liquid entrainment by the CDA bubble is introduced which is based on spherical-core-vortex motion and entrainment via the K–H instability along the bubble surface. The model is in agreement with new experimental results presented here on the reduction of nitrogen-gas-simulant CDA bubble work potential. Finally, a one-dimensional air-over-water parallel flow experiment was undertaken which demonstrates that the K–H instability results in sufficiently rapid and fine liquid atomization to account for observed CDA gas-bubble work reductions. An important byproduct of the theoretical and experimental work is that the liquid entrainment rate is well described by the Ricou–Spalding entrainment law.

Drop Entrainment in a Rotary Spraying Apparatus

Drop entrainment is studied in a rotary tray apparatus with spraying and multiple recycling of the liquid in the contact elements. The main contribution to the amount of the entrained liquid is from the fine drops carried away by the flowing gas (vapor) from the cloud of the sprayed liquid. Equations are suggested for calculating the liquid entrainment rate.

The code RENONS for the prediction of nonvolatile species release from liquid surfaces into a gas

In the field of nuclear safety, the release of volatile and nonvolatile species from liquid surfaces into a gas atmosphere is important for aerosol source term considerations. In case of a hypothetical fast breeder reactor accident with tank failure, primary coolant sodium with suspended or solved fuel particles and fission products may be released into the containment. The code package REVOLS/RENONS calculates, based on theoretical mechanistic models, the release of these species from the pool surface into the inert gas atmosphere of the inner containment. Hereby, the module REVOLS calculates the RElease of VOlatile Species (Koch et al., 1991). Whereas the evaporative release of the volatile species is governed by diffusive and convective transport processes, the release of the nonvolatile may be governed by mechanic processes entraining droplets from the wavy surface under conditions of convection in the atmosphere. The modular structured code RENONS (RElease of NONvolatile Species) calculates the liquid entrainment rate of nonvolatile species from pool surfaces by a parallel gas flow. Hence, the influence of the system temperatures, the pool inventory and the geometry as well as the decisive influence of the thermal hydraulic conditions on the entrainment rate can be investigated.

Liquid Entrainment from a Mobile Bed Scrubber

Liquid entrainment rate and drop size distribution were measured in the exhaust gas stream from a mobile bed scrubber. The pilot plant scrubber was 46 cm (18 in.) square and was packed with 3.8 cm (1.5 In.) diameter hollow polyethylene spheres to a static depth of 25 cm (10 in.). Entrainment flow rate depends on both gas and liquid rates. At a liquid/gas ratio of 6.7 l/m3 (50 gal/Mcf) and a superficial gas velocity of 2.6 m/sec (8.5 ft/sec) the entrainment flow rate was 0.0064 l/m3 (0.05 gal/Mcf) and at 3.75 m/sec (12.3 ft/sec) it was 0.031 l/m3 (0.23 gal/Mcf). The mass median drop diameter was about 400 nm at a liquid/gas ratio of 6.7 l/m3. The drop size distribution appears to be bimodal. Dye impregnated paper and cascade impactor techniques were used to measure drop size.

Droplet size resulting from breakup of liquid at gas-liquid interfaces of liquid-submerged subsonic and sonic gas jets

It has been demonstrated both analytically and experimentally (Chawla 1975a; Bell, Boyce & Collier 1972) that, due to existence of the Kelvin-Helmholtz instability at the gas-liquid interfaces of liquid-submerged subsonic and sonic gas jets, liquid at the interface breaks up and becomes entrained in the form of droplets in these gas jets. The study of this phenomenon has numerous industrial applications. For example, in the study of the fuel-failure propagation potential of fission-gas jet impingement in liquid metal cooled fast breeder reactor subassemblies, the liquid entrainment rate and droplet size control the rate of heat transfer in the impingement area of the fission-gas jet (Chawla 1975b). The study of the rate of entrainment and droplet size at the gas-liquid interface of a sonic gas jet submerged in a liquid is also of interest in the field of boiling water reactor safety (Chawla 1975b) and in a number of chemical-engineering processes. An analysis of the rate of liquid entrainment at the gas-liquid interface of a liquid-submerged sonic gas jet has been presented previously (Chawla 1975b). The purpose of the present note is to obtain the droplet sizes due to breakup of the liquid at the interfaces of subsonic and sonic gas jets submerged in a liquid. The existing correlations (e.g. Hinze 1948, 1955) for droplet size do not explicitly include the effect of Mach number or compressibility of gas stream; the present analysis, however, explicitly obtains this dependence for both subsonic and sonic gas jets.