Liquid Volume Fraction Research Articles

The Liquid Maldistribution Analysis of the Trickle Bed Reactor with the CFD Method

The liquid phase maldistribution factor has been investigated in trickle bed reactor, and the results are compared with the previous measurement data from literature by using the Electrical Resistance Tomography. The simulation results are in agreement with the experimental results to some degree. The flow rates and particle sizes have been simulated with the method of multiphase flow. There are two different particles with average diameters of 3.4 mm and 5.3 mm. The flow rate has been studied ranging from 100 ml/min to 1100 ml/min. It has been found that the changes of the particles and liquid flow rates have a significant impact on the distribution of the liquid volume fraction. The internal liquid holdup is more serious, and the wall-flow phenomenon is more obvious in a bigger flow rate. The prediction of the liquid volume fraction distribution is a key research technique. Regression predictions have also been researched on the section near outlet, which can predict the internal flow state of the trickle bed under the condition of high temperature and high pressure. The average liquid volume fraction is linear with flow rates. The maldistribution factor is the index correlation with the flow rates. The results and main conclusions can be used to predict the distributions and get the properties in a trickle bed reactor.

Spatio-temporal identification of plume dynamics by 3D computed tomography using engine combustion network spray G injector and various fuels

Understanding of plume direction and mixture quality in a combustion chamber is crucial to improve engine performance. While a variety of diagnostics using laser and x-ray facilities have been applied to identify plume direction, most applications require sophisticated experimental setup as well as troubleshooting for light attenuation or scattering issues. In this study, we acquire temporally and spatially resolved liquid volume fraction by three-dimensional tomographic reconstruction of ensemble-averaged extinction images to produce unique information on plume movement and growth in the midst of a multi-plume spray. Measurements were carried out in a constant-flow spray vessel coupled with high-speed Mie-scattering, diffused back-illumination extinction, and schlieren imaging. Four different fuels, a single component iso-octane, a multi-component surrogate with di-isobutylene, a multi-component fuel with olefinic molecular structure, and a 70% standardized gasoline 30% ethanol (e30) blend were injected using Engine Combustion Network (ECN) Spray G injector under ECN G2 (50 kPa absolute), G3 (100 kPa absolute), and G3HT (G3 with 393 K ambient temperature) conditions. Planar slices, available from the tomographically reconstructed extinction data, confirmed greater plume-to-plume interaction for the flash-boiling G2 iso-octane condition with an approximately 6° smaller plume direction angle relative to the injector axis, compared to the nozzle drill angle. The olefinic and e30 fuels, which have broader distillation curves, exhibited stronger plume growth and eventual complete spray plume collapse and longer time for evaporation. Using the 3D dataset, we show that factors that increase plume growth also create more interaction between plumes to ultimately reduce the plume direction angle.

Gravimetric Constraints on the Hydrothermal System of the Campi Flegrei Caldera

AbstractThe Campi Flegrei caldera (Italy) has been undergoing unrest over the past five decades including episodes of rapid ground deformation, seismicity, and variations in gas emissions. Hydrothermal fluids and gases are released most vigorously in the central sector of the caldera at the fumarolic fields of Solfatara volcano and Pisciarelli. We conducted a high‐precision gravity survey coupled with inverse modeling to image the shallow (<2‐km depth) structure of the hydrothermal feeder system. Results indicate the presence of three low density bodies beneath Pozzuoli, Astroni volcano and the Solfatara/Pisciarelli fumarolic fields. The first two are inferred to be sealed hydrothermal systems trapped beneath impermeable cap rock, while the latter depicts a plume‐like geothermal feeder system reaching the surface via a combination of Solfatara's maar‐diatreme structure and the intersection of NW‐SE and NE‐SW trending regional faults. The density contrasts of the reservoirs from background values are best explained by a multiphase mixture of caldera fill containing a secondary and interconnected void volume fraction of between 0.2 and 0.3 that hosts a vapor volume fraction ψv of between 0.38 and 1 and a liquid volume fraction ψl fraction of between 0 and 0.62. This work highlights the control of volcano‐tectonic structures on fluid movement in the shallow crust of hydrothermally active volcanic systems undergoing sustained or periodic unrest.

Characterization of Fluid-Phase Behavior Using an Advanced Microwave Re-Entrant Cavity

To advance the thermodynamic models needed for many industrial processes, accurate measurements of fluid-phase behavior are essential. Therefore, we present a newly designed microwave re-entrant cavity apparatus to deliver improved phase-behavior measurements of pure and multicomponent fluids. The re-entrant geometry has spatially distinct resonant modes, which are used to determine the dielectric permittivity of the liquid and vapor phase and the liquid volume fraction (Λ). The first mode (fvac ≈ 320 MHz) is sensitive to small liquid volumes, the second (1.86 GHz) is sensitive to small vapor volumes, and the third (6.57 GHz) is sensitive to the interface location. At equilibrium, a system of three equations, one for each mode, allows for the dielectric permittivity of each phase and Λ to be determined from the measured resonant frequencies. The cavity’s suitability for solving this inverse problem was explored using finite element analysis and experiments with pure propane and pentane. A primary limitation of the method was the dependence of the mode-shape functions (Gn) on phase permittivities, which become measurable for high-frequency modes. We propose a solution to account for this dependence using finite element simulations that map the Gn surface as a function of Λ and the ratio of phase dielectric permittivities.

Numerical study on mixing flow behavior in gas-liquid ejector

A multiphase mathematic model based on realizable k-e turbulence model for subsonic flow was presented to investigate the mixing flow behaviors between gas and water in the gas-liquid ejector. The simulation was carried out to predict the pumping performance of the ejector by a commercial computational code ANSYS-FLUENT 15.0. General agreements between the predicted results and experimental data validated the present theoretical model. Using the present approach, the pressure, velocity, and turbulence intensity distribution along center-line and contours of gas and liquid volume fraction profiles were predicted. It is found that the mixing process between gas and water in ejector can be divided into three periods, co-axial flow, mixing shock flow, and bubble flow. The prediction results show that the mixing shock is a dominant position in affecting the mixing flow behavior in gas-liquid ejector and the ejector’s performances.

Modelling of foamed emulsion drainage

The drainage of foams created using emulsions has been investigated from both experimental and theoretical point of view. The drainage of emulsion foam is investigated using mixture of sodium dodecyl sulphate and oil, which were prepared using the double syringe method. For the preparation of each emulsion, SDS solution and oil are passed from one syringe into the other through a plastic tube leading to thorough mixing. In the course of drainage both the foam height and the thickness of the free liquid layer accumulated at the bottom of the foam were measured. A theoretical model was developed, taking into account both surface viscosity and non-Newtonian behaviour of the foamed emulsion to describe the time evolution of both the foam height and the thickness of the free liquid layer. The model is based on consideration of drainage of non-Newtonian liquid through the Plateau borders and the mobility of the gas/liquid interface is taken into account. Both experiments and theoretical predictions show no measurable change of the foam height while a free liquid layer starts to accumulate at the bottom boundary of the foam after an initial rapid increase of liquid volume fraction to the maximum value at the bottom of the foam. Theoretical predictions of rate of drainage, free liquid layer formation, foam height and liquid volume fraction for foamed emulsion systems of various oil volume fractions are compared with experimental observations. Comparison of the predicted and the experimentally measured time dependences showed a reasonable agreement.

Microphase Separation of Ionic Liquid-Containing Diblock Copolymers: Effects of Dielectric Inhomogeneity and Asymmetry in the Molecular Volumes and Interactions between the Cation and Anion

We study the phase behavior of a block copolymer and ionic liquid mixture using the Landau theory of Leibler and field-theoretic techniques in polymer physics. Our weak-segregation theory of microphase separation accounts for electrostatic screening, the excluded volume effect, and the dielectric contrast between the species. The results of the phase diagrams for ionic liquid-containing poly(styrene-block-2-vinylpyridine) and poly(ethylene oxide-block-styrene) qualitatively agree with the observed transitions between the ordered microstructures corresponding to lamellae, hexagonally packed cylinders, and body-centered cubic lattices. We show that moderate changes in the model parameters for molecular volumes and nonbonded interactions can qualitatively alter the trend of the phase boundaries. Specifically, our theory highlights the following features: (a) The effect of the dielectric contrast between the constituent blocks may cause a driving force for microphase separation, whereas the effect of electrostatic screening is likely minimal. (b) Reentrance into a lamellar phase, hexagonally packed cylinder phase, or disordered phase may occur when the volume fraction of an ionic liquid is increased. (c) Asymmetry in the molecular volumes and interactions between the cation and anion in an ionic liquid may cause substantial changes in the phase boundaries. The present results also suggest that despite its simplicity, the Born solvation energy of the ions can be used to consider the dissolution of an ionic liquid in block copolymers when the dielectric contrast is large.

Microstructure and yielding of capillary force induced gel

We have investigated the rheology and structure of a gel formed from a mixture of non-Brownian particles and two immiscible liquids. The suspension of particles in a liquid undergoes gelation upon the addition of a small content of second, wetting liquid which forms liquid bridges between particles leading to a sample spanning network. The rheology of this gel primarily exhibits a yield stress at low shear rates followed by a linear variation of shear stress at high shear rates. The apparent yield stress extracted from the flow curves increases rapidly with volume fraction of second liquid before saturation, while it exhibits a monotonic increase with increasing particle concentration. Rescaling of the yield stress curves using suitable shift factors results in an empirical expression for the yield stress showing squared dependence on liquid fraction and a rapid increase with particle fraction above a certain value, both combined in a highly nonlinear manner. The microstructural variations with changing secondary liquid content and particle fractions are captured using three dimensional X-ray tomography technique. The microstructure is observed to show increased local compactness with increased liquid content and increased spatial homogeneity with increased particle fractions. The images from X-ray tomography are analysed to obtain the distributions of particle-particle bonds (coordination number) in the system which serve to explain the observed yield stress behavior in a qualitative manner.

Gas–liquid two‐phase flow characteristics of the jet vortex drainage gas production tool based on computational fluid dynamics

AbstractThis study is aimed at the problems of traditional vortex tools in gas wells, including notable pressure losses and short effective distances. An organic combination of jet vortex drainage and gas production tools was designed and installed without additional power equipment. Based on the liquid film force balance model, gas–liquid two‐phase flow and turbulence models of the jet vortex tool were established with UG and Fluent flow simulation software. The gas–liquid mixture was analyzed before and after the jet vortex tool, and the flow trajectory, pressure loss, liquid volume fraction change, and change rate were examined. According to the simulation results, the comprehensive influence of each structural parameter on the effective working distance was optimized, and optimal structural parameters of the jet vortex tool were obtained. The results indicate that the jet vortex tool reduces the critical liquid‐carrying flow rate and pressure loss and increases the axial and initial velocities of the gas and liquid phases, combined with swirl tool distance model, the effective flow distance is increased correspondingly, and the liquid‐carrying capacity of the gas well is improved.

VOFTools 5: An extension to non-convex geometries of calculation tools for volume of fluid methods

VOFTools 5: An extension to non-convex geometries of calculation tools for volume of fluid methods

Numerical simulation of the flow in a vertical vane type tank with micro downward acceleration

Vane type propellant tank is widely used in propellant system of satellite at present for that it can be refuelled in space. The performance of a vertical vane type tank is determined by propellant management device (PMD). The VOF model with commercial code (Fluent) was used to simulate the gas-liquid distribution with micro downward acceleration. Two kinds of volume fractions of liquid were chosen for the simulation. The flow rate of the liquid can reach 1300 ml/s. The potential energy caused by gravity for the initial conditions would be released in three seconds. The liquid in the tank would keep steady state in 28 seconds. These results could provide a reference for high acceleration maneuvers of a satellite.

Volume measurement of atomizing fragments using image slicing

The complete structure of atomizing liquid fragments can be analysed by employing multi-dimensional visualization techniques. These techniques require advanced image processing, where objects from multiple views are matched to extract information. However, in higher Weber number sprays, owing to a population of randomly shaped atomizing fragments, matching objects from different imaging frames is very challenging. This paper presents a novel image processing technique to extract volumetric information without a need for matching. The spray is visualized using high speed long-distance microscopy from two perpendicular angles. The developed in-house script employs the principle of image discretisation, where each image is divided into a number of slices and the individual slice from each camera is matched to compute the liquid volume fraction in each image. The volume of individual objects is calculated based on their planar area and orientation. An error analysis is performed using dozens of three-dimensional virtual models of fragment like shapes with known volume. The paper concludes with an analysis of spray volume measured for a range of real twin-fluid atomized cases. The proposed methodology enables the measurement of volume fragments with reasonable accuracy in atomizing sprays with exit Weber numbers of up to around 100. This is a significant extension from an earlier limit of We ~ 20 [1].

Application of SLIPI-Based Techniques for Droplet Size, Concentration, and Liquid Volume Fraction Mapping in Sprays

Structured laser illumination planar imaging (SLIPI)-based techniques have been employed during the past decade for addressing multiple light scattering issues in spray imaging. In this article, SLIPI droplet sizing based on the intensity ratio of laser-induced fluorescence (LIF) over Mie scattering (SLIPI-LIF/Mie) and SLIPI-Scan for extinction-coefficient (µe) mapping are applied simultaneously. In addition, phase Doppler anemometry (PDA) and numerical calculations based on the Lorenz–Mie theory are also employed in order to extract the droplets Sauter mean diameter (SMD), the droplets number density (N), and the liquid volume fraction (LVF) in a steady asymmetric hollow cone water spray. The SLIPI-LIF/Mie ratio is converted to droplets SMD by means of a calibration procedure based on PDA measurements. The droplet SMD for the investigated spray varies from 20 µm to 60 µm, the N values range from 5 to 60 droplets per mm3, and the LVF varies between 0.05 × 10−4 and 5.5 × 10−4 within the probed region of the spray. To generate a series of two-dimensional images at different planes, the spray scanning procedure is operated in a “bread slicing” manner by moving the spray perpendicularly to the light sheet axis. From the resulting series of images, the procedure described here shows the possibility of obtaining three-dimensional reconstructions of each scalar quantity, allowing a more complete characterization of droplet clouds forming the spray region.

A generalized lattice Boltzmann model for solid–liquid phase change with variable density and thermophysical properties

In this paper, we modify the calculations of volume fraction of liquid and temperature, and propose a generalized two-relaxation-time (TRT) lattice Boltzmann model for the solid–liquid phase change problem with variable density and thermophysical properties. Two benchmark problems are used to validate the new model. The results show that this generalized model can handle the differences in both density and thermophysical properties.

Development of limited-view tomography for measurement of Spray G plume direction and liquid volume fraction

The method for direct injection of fuel in the cylinder of an IC engines is important to high-efficiency and low-emission performance. Optical spray diagnostics plays an important role in understanding plume movement and interaction for multi-hole injectors, and providing baseline understanding used for computational optimization of fuel delivery. Traditional planar or line-of-sight diagnostics fail to capture the liquid distribution because of optical thickness concerns. This work proposes a high-speed (67 kHz) extinction imaging technique at various injector rotations coupled to computed tomography (CT) for time-resolved reconstruction of liquid volume fraction in three dimensions. The number of views selected and processing were based on synthetic (modeled) liquid volume fraction data where extinction and CT adequately reconstructed each plume. The exercise showed that for an 8-hole, symmetric-design injector (ECN Spray G), only three different views are enough to reproduce the direction of each plume, and particularly the mean plume direction. Therefore, the number of views was minimized for experiments to save expense. Measurements applying this limited-view technique confirm plume–plume variations also detected with mechanical patternation, while providing better spatial and temporal resolution than achieved previously. Uncertainties due to the limited view within pressurized spray chambers, the droplet size, and optically thick regions are discussed.Graphic abstract

Liquid transport in scale space

When a liquid stream is injected into a gaseous atmosphere, it destabilizes and continuously passes through different states characterized by different morphologies. Throughout this process, the flow dynamics may be different depending on the region of the flow and the scales of the involved liquid structures. Exploring this multi-scale, multi-dimensional phenomenon requires some new theoretical tools, some of which need yet to be elaborated. Here, a new analytical framework is proposed on the basis of two-point statistical equations of the liquid volume fraction. This tool, which originates from single phase turbulence, allows us notably to decompose the fluxes of liquid in flow–position space and scale space. Direct numerical simulations of liquid–gas turbulence decaying in a triply periodic domain are then used to characterize the time and scale evolution of the liquid volume fraction. It is emphasized that two-point statistics of the liquid volume fraction depend explicitly on the geometrical properties of the liquid–gas interface and in particular its surface density. The stretch rate of the liquid–gas interface is further shown to be the equivalent for the liquid volume fraction (a non-diffusive scalar) of the scalar dissipation rate. Finally, a decomposition of the transport of liquid in scale space highlights that non-local interactions between non-adjacent scales play a significant role.

A conjugate heat transfer model for unconstrained melting of macroencapsulated phase change materials subjected to external convection

A new conjugate heat transfer model for unconstrained melting of macroencapsulated phase change material subjected to external convection is presented. Flow and heat transfer processes are modeled for the phase change material, the capsule wall and the external heat transfer fluid. The solvers for each region operate in a segregated and sequential manner and are coupled by mixed thermal boundary conditions. For the description of the solid body motion in unconstrained melting, the enthalpy-porosity method is modified. The solid body surface is reconstructed from the liquid volume fraction field for every time step by a triangulated isosurface using a marching tetrahedra technique. Based on computation of the forces exerted on the solid, the motion of the solid is determined iteratively in a strong coupling between solid velocity and pressure. The new conjugate heat transfer solver is utilized to simulate the commonly experimentally and numerically investigated scenario of a spherically encapsulated phase change material immersed in a water bath. The coupled flow and heat transfer is investigated for a natural convection dominated mixed convection problem with a Richardson number of 50 · 103 and Stefan numbers of 0.075, 0.1, 0.15, 0.2 and 0.25. Contrary to the commonly made assumption, the resulting capsule wall temperature is transient and highly non-uniform. The differences in melting times range from 50.7 to 67.5% between the consideration of external heat transfer and the assumption of constant uniform wall temperatures.

A Study for Rotordynamic and Leakage Characteristics of a Long-Honeycomb Seal With Two-Phase, Mainly Air Mixtures

Abstract This paper investigates the impact of the oil (silicone oil PSF-5cSt) presence in the air on the leakage and rotordynamic characteristics of a long-honeycomb seal with length-to-diameter ratio L/D = 0.748 and diameter D = 114.656 mm. Tests are carried out with inlet pressure Pi = 70.7 bars, pressure ratio (PR) = 0.35 and 0.25, inlet liquid volume fraction (LVF) = 0%, 3.5%, and 7%, and shaft speed ω = 10, 15, and 20 krpm. During the tests, the seal is centered. Test results show that leakage mass flow rate m˙ increases (as expected) as inlet LVF increases. Increasing inlet LVF makes direct stiffness K increase more rapidly with increasing excitation frequency Ω. Increasing inlet LVF has a negligible effect on K at low Ω values, but increases K at high Ω values. The value of effective damping Ceff at about 0.5ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5ω. Increasing inlet LVF increases the value of Ceff at about 0.5ω, reducing the possibility of subsynchronous vibrations (SSVs) at about 0.5ω. San Andrés's model is used to produce predictions. The model assumes that the test fluid in the seal clearance is an isothermal-homogenous mixture. The model adequately predicts m˙, K, and the value of Ceff at about 0.5ω.

A Study on the Leakage and Rotordynamic Performance of a Long Labyrinth Seal Under Mainly Air Conditions

Abstract This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure Pi = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients Hij are measured. The real parts of Hij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness KΩ and cross-coupled stiffness kΩ. The imaginary parts of Hij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m˙ of the test seal steadily increases as inlet LVF increases. KΩ is negative under all test conditions, and the magnitude of KΩ increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, kΩ is a small negative value. Injecting oil into the air increases kΩ slightly and make the magnitude of kΩ closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on kΩ. C normally increases as inlet LVF increases. The value of the effective damping Ceff = C − kΩ/Ω near 0.5ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5ω. Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of Ceff near 0.5ω. Also, the liquid presence does not change the insensitiveness of m˙, KΩ, kΩ, C, and Ceff to change in ω; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m˙, KΩ, kΩ, C, and Ceff.

A 3D Moment of Fluid method for simulating complex turbulent multiphase flows

This paper presents the moment of fluid method as a liquid/gas interface reconstruction method coupled with a mass momentum conservative approach within the context of numerical simulations of incompressible two-phase flows. This method tracks both liquid volume fraction and phase centroid for reconstructing the interface. The interface reconstruction is performed in a volume (and mass) conservative manner and accuracy of orientation of interface is ensured by minimizing the centroid distance between original and reconstructed interface. With two-phase flows, moment of fluid method is able to reconstruct interface without needing phase volume data from neighboring cells. The performance of this method is analyzed through various transport and deformation tests, and through simple two-phase flows tests that encounter changes in the interface topologies. Exhaustive mesh convergence study for the reconstruction error has been performed through various transport and deformation tests involving simple two-phase flows. It is then applied to simulate atomization of turbulent liquid diesel jet injected into a quiescent environment. The volume conservation error for the moment of fluid method remains small for this complex turbulent case.