Entrainment phenomenon in gas–liquid two-phase flow: A review

The gas–liquid separation equipments are aimed to be designed for maximum efficiency of phase separation. In order to maximize their capacity the flow rates are required to be optimized for the capital cost of equipment. This leads to the situation where the gas phase leaves the separation interface with high velocities and carry liquid phase along with it in the form of droplets reducing the equipment efficiency. This is known as entrainment or carryover. Depending on the nature of the separation interface i.e., turbulence intensity, bubble dynamics, the size and velocity distribution of liquid fragments, droplets at the separation interface varies. This is the main source of empiricism involved in the analysis of such equipments. The mechanics of motion of the dispersed liquid phase in bulk of gas is relatively well studied. In the present paper the various experimental, analytical and numerical investigations carried out to address the issues of entrainment/carryover are carefully analyzed. Further, a critical review has been presented for bringing out a coherent theme and a current status of the subject under reference.     

Current–voltage characteristics of a flat probe in a rarified plasma flow

Mathematical and numerical models of a collision-free plasma flow about the flat probe are developed. The current–voltage characteristics of flat probes located along and transverse across the flow, as well as the distributions of the current density over the probe width, are obtained. The numerical simulation results might be applied in probe diagnostics of plasma flows.     

Numerical simulation of hydrodynamic characteristics in a gas–solid fluidized bed

The fluidization of quartz particles as bed materials in the fluidized bed has significant influences on the combustion and gasification of refused derived fuels. Three-dimensional (3-D) simulations and analyses are performed for Geldart B particles using the computational fluid dynamics (CFD) method based on the kinetic theory of granular flows (KTGF) to investigate the hydrodynamic behavior. The drag models of Syamlal–O’Brien, Gidaspow, and Wen and Yu are selected to analyze the applicability of the kinetic model. The pressure drop, velocity distribution and solid volume fraction are studied numerically when the gas inlet velocity is changed. The results show that the increase of superficial gas velocity would lead to heterogeneous expansion of solid volume fraction and velocity distributions in both the dense phase zone and free board with a similar distribution pattern. The near wall particles form a dense phase structure with the solid volume fraction being greater than 0.3.     

Construction of algorithm for calculation of the flow rate of a gas–liquid mixture in a horizontal pipeline for the microprocessor of an information measurement system

Features of an algorithm for calculation of the flow rate of the liquid phase of a gas–liquid mixture with the use of a variable pressure-drop flow meter with constricting devices are considered. Corresponding dependences for use in calculating the concentration of liquid in a mixture and a correction factor based on the readings of the flow meter for use in determining the flow rate of a single-phase flow are obtained.     

Vapor–liquid critical flow through a layer of spherical particles

Vapor–liquid flow in a cylindrical channel through fillings of spherical particles is studied experimentally. Data on the critical flow of a vapor–water mixture with various vapor contents through densely packed layers of spherical particles from stainless steel with diameters of 2 and 4 mm for a filling column height of 250 and 355 mm are obtained. Experimental data demonstrate the influence of pressure, the vapor content of the mixture at the input, and the geometric parameters of the filling on the critical mass velocity. The linear dependence of the critical mass velocity on the geometric factor \(\sqrt {d/H} \). The possibility of generalizing the experimental results based on the gas dynamic model for the flow of a homogeneous medium is considered.     

Numerical simulation of flow behavior of liquid and particles in liquid–solid risers with multi scale interfacial drag method

Formation of particle clusters in liquid–solid circulating fluidized beds significantly affects macroscopic hydrodynamic behavior of the system. A multi scale interfacial drag coefficient (MSD) is proposed to determine effects of particle clusters on the mesoscale structure, by taking momentum and energy balance of dense phase, dilute phase and interphase into account. Based on the transportation and suspension energy-minimization method, the multi scale interfacial drag coefficient model used in this work is combined with the Euler–Euler two fluid model to simulate the heterogeneous behaviors of liquid–solid circulating fluidized bed. It was found that the reduction in drag coefficient is at least an important factor for the simulation of clusters formation, and the core-annulus flow is observed in the riser. The liquid–solid flow regime was significantly affected by the down-flow of particles in the form of clusters near the walls of the riser. The calculated concentration of particles inside the riser compared reasonably well with the available experimental data obtained by Razzak et al.     

Penetration behaviour of individual hydrophilic particle at a gas–liquid interface

The penetration behaviour of a hydrophilic particle impacting on a gas–liquid interface was studied both experimentally and mathematically. The aim of this study was to determine the critical impact velocity below which a falling hydrophilic particle would remain on a horizontal liquid surface. A model to predict the critical velocity has been developed based on energy balance of both the particle and liquid volume in the vicinity of the impact zone. The model also includes the effect of hydrophobicitiy (contact angle) of the particle as well as the change in potential energy of the impacted liquid. Experiments were performed using spherical glass beads of diameter 0.97–1.66 mm, and using liquids with varying density (1000–1182 kg/m³), viscosity (1.002–4.796 mPa s) and surface tension (50.31–87.42 mN/m). High speed video camera was used to obtain the particle impact velocity, cavity profile and velocity of the three-phase contact line (TPCL) at the critical conditions. The TPCL line velocity and cavity profile were used as inputs for the model. The fitted advancing contact angle was employed in the model. It was found that the model was in good agreement with the experimental observations, and the fitted advancing contact angle agreed with the combined molecular-hydrodynamic model well.     

Numerical study of solid–liquid two-phase flow and erosion in ball valves with different openings

In the coal chemical industry, petrochemical industry, and other industries, ball valve is a common and important valve due to its reliable structure. The conveying medium has particles that affect the valve surface under the drive of water flow, thereby making the ball valve face the risk of erosion and damage. In this study, the CFD-DEM method was adopted to study the influence of different openings and particle diameters on the two-phase flow and erosion characteristics inside the ball valve. The two-phase flow and particle distribution of the ball valve were analyzed, and the main erosion wall surfaces were determined. The erosion distribution of these walls was obtained. The variation rule of particle number with erosion rate was analyzed, which shows that particle number played a dominant role in erosion degree. Result also showed that in the case of small opening, the erosion decreased with the increase in particle diameter.     

Cavitation flow instability of subcooled liquid nitrogen in converging–diverging nozzles

The cavitation flow instability of subcooled liquid nitrogen in two types of converging–diverging (C–D) circular nozzles with throat diameters of 1.5 and 2.0 mm was experimentally investigated. Flow observations were also performed to clarify the instability phenomenon and the differences in cavitation behavior between the two nozzles. The cavitation mode changed from continuous mode to intermittent mode as the temperature of the subcooled liquid nitrogen decreased. This change occurred in both C–D nozzles when the temperature of the liquid reached approximately 76 K. Occurrence of the intermittent mode accompanying very large pressure-oscillations was considered to be caused by a drastic reduction of the speed of sound in the single-component, vapor–liquid flow because the speed of sound restricted the throat velocity in the C–D nozzle during cavitation. Oscillation pressure values in intermittent mode were much larger than those in continuous mode, peaking between 74 and 76 K. The magnitude of the oscillation pressure in intermittent mode could be evaluated from the difference between the throat static-pressure immediately prior to the occurrence of cavitation and that during cavitation.     

Application of gas chromatography mass spectrometry with preliminary dispersive liquid–liquid microextraction for the determination of low contents of rocket kerosene in water

A procedure for sensitive determination of rocket kerosene in water is described; it includes the dispersive liquid–liquid microextraction of analytes followed by their separation and determination by gas chromatography mass spectrometry in the mode of chromatogram registration against selected ions (m/z: 67, 81, 85, 95, 136, 137, 174, 183, and 193). The effect of the nature and volume of disperser and extraction solvents, salt additives, and the extraction duration on the efficiency of extraction of analytes is studied. The detectable concentration range is 0.005–0.05 mg/L. The detection limits (S/N = 3) of kerosene RG-1 and T-1 are 0.0015 and 0.0022 mg/L, respectively. The repeatability of the measurement results for the above range varies from 16 to 9% (n = 3); the intermediate precision varies from 20 to 12% (n = 5).     

Experimental study on the separation performance of a novel gas–liquid separator

A novel two-stage dynamic separator called high-gravity cyclone separator (HGCS) has been designed for gas–liquid separation. It is mainly composed of a cyclone chamber and rotary drum. In this study, its performance, including the separation efficiency and pressure drop, is experimentally investigated, and the effects of the operating conditions and drum parameters are evaluated. For droplets with a mean diameter of 7 μm, the results indicate that the optimal gas inlet velocity and high-gravity factor are 12 m/s and 59.4, respectively, and the separation efficiency reaches 98 %. The effect of liquid concentration is sensitive to the high-gravity factor. At a liquid concentration of 57 g/m³, the maximum efficiency will be 98.75 % when increasing the high-gravity factor to 85.6. Furthermore, a smaller radial height is preferable when the gas inlet velocity is greater than 12 m/s, and a better separation efficiency can be obtained by increasing the drum length to 190 mm. However, when the length is 235 mm, the efficiency will be poor because of the Kelvin–Helmholtz and Rayleigh–Taylor instabilities. Compared with the predominant roles of gas inlet velocity, drum length and radial height in pressure drop, the effects of liquid concentration and high-gravity factor are small.     

Kinetic and electrical phenomena in gas–liquid systems

Disperse systems consisting of a liquid and gas bubbles located in it are considered. Two possible versions of evolution of bubbles under the conditions studied are assessed. In simple liquids, contact between two bubbles causes them to merge, as the separating film breaks. In the case of complex organic liquids, amphiphilic film is formed on the surface of bubbles, and the lifetime of bubbles in contact increases with their size. Under an external electric field, chains of bubbles are formed, lined up along the electric field potential lines. The presence of bubbles in liquid greatly lowers the breakdown threshold, as the critical parameters of the breakdown field in liquids are two to three orders of magnitude higher than those in gases at atmospheric pressure. Various breakdown mechanisms in liquids are discussed from the viewpoint of formation of the gas phase during the passage of an electric current through a liquid medium. The character of propagating a streamer in separate bubbles is studied with their random distribution in liquid and in the case of formation of some structures of bubbles; the critical parameters of disperse systems, that can lead to their electrical breakdown, are presented. Along with the general concepts of electrical breakdown in dispersed systems, experimental studies of these processes are considered, and the nature of electrical breakdown in liquid dielectrics, including transformer oil, is discussed.     

Study of hydrodynamic characteristics of particles in liquid–solid fluidized bed with modified drag model based on EMMS

Flow behavior of solid phases is simulated by means of Eulerian–Eulerian in a liquid–solid fluidized bed with modified drag model based on energy-minimization multi-scale (EMMS) method. The modified EMMS drag coefficient is characterized by the treatment of the particle-rich dense phase and the liquid-rich dilute phase as the two interpenetrating continua. It was shown that the modified EMMS drag coefficient can predict reasonably the solid concentration profiles in a liquid–solid fluidized bed. The distributions of solid velocity, granular temperature and granular pressure are predicted. The phenomenon of back-mixing near the wall is found in the liquid–solids fluidized beds.     

Multiscale modeling of nonequilibrium gas–liquid mixture flows in phase transition regions

This paper presents multiscale modeling substantiated with experimental aspects of state, filtration, and motion of the gas–liquid mixtures involving phase transition regions in concentrated volumes applicable to porous media and pipe flows. Based on physics, it is confirmed analytically that actual levels of underpressure in gas–liquids systems are considerably above traditional understanding of saturation pressure at which gas emission from the liquid and its dissolution in the liquid in a form of embryos can occur. It is demonstrated that these processes are not equilibrium processes, and they can also occur on nanoscales and microscales. Thermo-hydrodynamic analyses and experimental investigation of the gas–liquid systems in areas of phase transition presented here have resulted in useful equations governing such flows in filtration in the porous media and in straight pipes.     

Numerical solution of gas–solid flow in fluidised bed at sub-atmospheric pressures

Fluidised beds are characterised by excellent thermal and chemical uniformity and have a wide application range including heat and surface treatment, ore roasting and catalyst production. However, compared to other gas-based systems, to fluidise a particulate mass, a significant quantity of gas is required. To conserve gas there is potential to operate the fluid bed under low-pressure conditions. It is also observed that heat transfer remains constant with reduction in pressure. The present work has numerically studied the nature of hydrodynamics in fluidised bed at sub-atmospheric conditions and a new drag law is proposed to account for the increased mean free path of the fluid. A wide range of sub-atmospheric pressures were considered such that slip flow regime, which is characterised with Kn ～ 1, is applicable. An open source code (MFIX) is used to numerically solve the multiphase problem of a jet in the fluidised bed column with an immersed surface at vacuum pressure conditions. Bubbling fluidisation in shallow and deep beds are also solved. The new drag model takes into consideration the effect of slip flow to model drag force on the particles and the results of velocity distributions in the column and around the submerged surface is presented. The results of velocity distributions from the slip flow model are compared with the existing Gidaspow’s model. Significant differences were observed in the simulation results of velocity distributions and flow structure in the fluidised bed under vacuum conditions.     

Modeling of vapor–liquid–liquid equilibria in binary mixtures

Vapor compression and Joule–Thomson (JT) cycles provide cooling power at the boiling temperatures of the refrigerants. Maintaining a fixed pressure in the evaporator allows for a stable cooling temperature at the boiling point of a pure refrigerant. In these coolers enhanced cooling power can be achieved by using mixed refrigerants. However, gas mixtures usually do not change their phase at a constant temperature, therefore, the cooling temperature has to be actively controlled. An exception to this rule holds for binary mixtures that can form a vapor–liquid–liquid equilibrium (VLLE).Phase equilibria in binary mixtures are usually modeled based on experimental results only. In the present study only the vapor pressures of the pure mixture components are required. The calculated results of nitrogen–ethane, nitrogen–ethylene, and nitrogen–propane mixtures are compared with experimental data presented in literature showing deviations of less than 1%.     

A space–time analysis of blood flow in a 3D vessel with multiple aneurysms

In this study, 3D unsteady flow dynamics in an arterial vessel with two asymmetric aneurysms in series have been numerically investigated under pulsatile flow conditions for a full cycle of period T. The non-linear partial differential equations governing the conservation of mass and momentum of viscous incompressible fluid have been numerically analysed by a time accurate cell centered finite volume method in implicit Euler time marching setting. The influence of Reynolds' number (Re), Strouhal's number (St), and degree of dilations (¹ ₁, ² ₁, ¹ ₂, ² ₂) on wall shear stress (WSS), wall pressure (WP) and velocities (u, v, w) have been investigated. While the WSSs increase with either increasing St or increasing Re, WPs are seen to get lowered. During the systolic phase high WPs are seen at the distal end of aneurysms, especially at the distal tip of the larger aneurysm. Decreasing St is seen to delay the flow separation process but the vortex shedding with 3D features is always noticed towards the end of the diastolic phase of the flow cycle.     

Determination of the Joule–Thomson coefficient in problems of measuring the flow rate of natural gas

Existing methods of calculating the Joule–Thomson coefficient for natural gas are analyzed. A procedure for use in calculations of gas flow rate employing the variable pressure drop method is proposed which gives increased measurement accuracy by eliminating the additional error in determining the temperature of the natural gas. Translated from Izmeritel’naya Tekhnika, No. 5, pp. 46–49, May, 2009.     

The effect of internal particle heat conduction on heat transfer analysis of turbulent gas–particle flow in a dilute state

In many cases the conduction mechanism inside a particle can not be ignored (large particles, low thermal conductivity and high porosity) during turbulent gas–particle flows. However, the accurate solution might be difficult to apply. Therefore, we first develop here the ability to conduct accurate solution and then we define the criterion for which the internal conductivity might be ignored. A combination between commercial C.F.D. code and user defined programs was developed to predict numerically the gas–particle velocity and temperature profiles. The selected criterion (defined at the outlet of the pipe’s cross-section), referred to the relation between the computational desirable average temperature difference without ignoring internal heat conductivity and the average particles temperature by ignoring internal heat conductivity, determines whether to consider the heat conduction mechanism in numerical simulations or to ignore it. It was found that the average particles temperature for T _p =  f(r) is lower than the case when T _p =  constant. Also, it was found that the non-dimensional temperature difference criterion is a continuous function of [Bi ×  (d _p/D)] for a specific geometry, various pipe and particle diameters, various particles’ thermal conductivities, constant heat flux and Re number. The numerical code enables to extend the classical criterion for Bi number of solids to various gas–particle systems and different operational conditions.