Effect of initial disturbance amplitude in gravity affected jet break-up

The initial disturbance amplitude has an effect on stretching jets that is not observed for capillary jet instability where gravitational acceleration is not significant. For inviscid and viscous fluids, gravity diminishes the effect that the initial amplitude has on jet length and its ability to prevent satellite formation. In stretching jets, not only the dimensionless frequency of the disturbance but also its initial amplitude must be known to properly study their satellite forming nature. Indirect methods of relating the applied disturbance energy to an initial velocity perturbation are not simple when the gravity parameter G is changing. When G≠0, the optimum disturbance frequency Ω_opt and the initial disturbance amplitude are related, with Ω_opt∝f(G)×ln(1/ε_v). Results from numerical simulations and experiments are presented here.     

Breakup mode of an axisymmetric liquid jet injected into another immiscible liquid

The breakup of an axisymmetric liquid jet, injected vertically upward from a nozzle into another immiscible liquid, into droplets is studied numerically. The unsteady motion of the interface separating two immiscible fluids is followed by solving the Navier-Stokes equations for incompressible and Newtonian fluids in axisymmetric cylindrical coordinates with a Front-Tracking method. The evolution of the interface and the specific surface area of the droplets are in good agreement with experimental results. Three breakup modes, dripping, jetting with uniform droplets, and jetting with non-uniform droplets, are identified. The different modes are shown on a Weber number—the viscosity ratio map.     

Simulation of break-up behavior of immiscible droplet under shear field by means of continuous-velocity lattice gas cellular automata

Continuous-velocity lattice gas cellular automata method is applied to the simulation of the motion of a single droplet under a three-dimensional shear field. Immiscible binary fluid model with segregation intensity parameter is employed. A simple collision rule is introduced in order to describe the momentum transport from moving boundaries to the fluid. The calculations well simulate two types of the deformation and break-up behaviors, fracture and tipstreaming, of the droplet. The segregation intensity parameter of the fluid particles reasonably controls the surface tension of the droplet. The break-up behavior of the droplet is well correlated with the ratio of the shear strength and the segregation intensity parameter.     

Simulations of microfluidic droplet formation using the two-phase level set method

Microdroplet formation is an emerging area of research due to its wide-ranging applications within microfluidic based lab-on-a-chip devices. Our goal is to understand the dynamics of droplet formation in a microfluidic T-junction in order to optimize the operation of the microfluidic device. Understanding of this process forms the basis of many potential applications: synthesis of new materials, formulation of products in pharmaceutical, cosmetics and food industries. The two-phase level set method, which is ideally suited for tracking the interfaces between two immiscible fluids, has been used to perform numerical simulations of droplet formation in a T-junction. Numerical predictions compare well with experimental observations. The influence of parameters such as flow rate ratio, capillary number, viscosity ratio and the interfacial tension between the two immiscible fluids is known to affect the physical processes of droplet generation. In this study the effects of surface wettability, which can be controlled by altering the contact angle, are investigated systematically. As competitive wetting between liquids in a two-phase flow can give rise to erratic flow patterns, it is often desirable to minimize this phenomenon as it can lead to a disruption of the regular production of uniform droplets. The numerical simulations predicted that wettability effects on droplet length are more prominent when the viscosity ratio λ (the quotient of the viscosity of the dispersed phase with the viscosity of the continuous phase) is O(1), compared to the situation when λ is O(0.1). The droplet size becomes independent of contact angle in the superhydrophobic regime for all capillary numbers. At a given value of interfacial tension, the droplet length is greater when λ is O(1) compared to the case when λ is O(0.1). The increase in droplet length with interfacial tension, σ, is a function of with the coefficients of the regression curves depending on the viscosity ratio.     

Three-dimensional vortex simulation of particle-laden air jet

The effect of particle diameter on the gas-particle two-phase compound round jet is numerically analyzed by the three-dimensional vortex method presented in a prior study. The air jet issues from a round nozzle into the co-flowing air stream, where the Reynolds number based on the air velocity at the nozzle exit is 2×10⁴ and the velocity ratio between the co-flowing stream and the jet at the nozzle exit is 0.27. The flow direction is vertical downward. Spherical glass particles having diameters 60, 80 and are loaded from the nozzle. The mass loading ratio is 0.27. The analysis made clear the air turbulent modulations due to the particles, such as the relaxation of velocity decay, the increment and decrement of momentum diffusion at the developing and developed regions, respectively. It also clarified that the air turbulent modulations become markedly as the particle diameter decreases.     

Hydrodynamic properties of a turbulent confined solid-liquid jet evaluated using PIV and CFD

Particle image velocimetry is used to evaluate liquid and solid velocities and turbulence levels in the developing region of a confined solid-liquid jet. The measurements are conducted utilizing the method of matching refractive indices together with digital phase separation. The diameters of the solids are and the maximum mean volume fractions for which measurements can be performed is 1.9%, a number estimated from image analysis. The experimental results are compared with those from numerical simulations using the mixture, dispersed and per-phase realizable k-ε models together with two models for the drag force. The results show that the differences in axial velocity between the two phases are small and the axial RMS velocities generally increases with increasing volume fraction and are larger for the dispersed phase compared to the continuous phase. The numerical simulations capture the flow structure well, but generally, the continuous-phase centreline velocities are underestimated close to the inlet and overestimated further downstream. Regardless of solid loading, the per-phase turbulence model in combination with a drag force modified by a correction factor as to take into account the turbulence of the carrier phase provides the best numerical results.     

An experimental investigation of the convective instability of a jet

This paper is an experimental study of the convective instability of a jet. It is well known that a jet issuing forth from a nozzle is unstable due to surface tension forces that cause it to break downstream into drops. We apply a disturbance of a given frequency at the nozzle tip. This applied frequency determines the wavelength and the growth rate of the growing disturbances and, thereby, the drop size. We measure the wavelength and the growth rate by fitting the entire digitized image of a jet to the functional form suggested by the linear theory. Thus, it makes use of the entire profile instead of the small number of points used in previous studies. Also, in contrast to previous work, we independently measure the jet velocity and the wave speed. At high non-dimensional jet velocity, the experimental results for the growth rates and the wave numbers agree with the linear stability theory of an infinite jet in the absence of gravity. At very low velocity (low Froude number) gravity is important and the agreement is not good.     

A drag correlation of fluid particles rising through stagnant liquids in vertical pipes at intermediate Reynolds numbers

A drag correlation for a fluid particle rising along the axis of a vertical pipe at low and intermediate Reynolds numbers, Re, is proposed by making use of available correlations and a numerical database accumulated by interface tracking simulations. The accuracy of the interface tracking method has been verified through comparisons between measured and predicted velocities of single drops in vertical pipes. Being similar to drag model for solid spheres proposed by Michaelides, the developed drag correlation takes into account inertial and wall effects as their linear combination. The correlation gives good estimation of the drag coefficient for fluid particles rising through stagnant liquids in vertical pipes under the conditions of 0.13?Eo?30, −10.0?log M?2.0, 0.083?Re<200, 0?κ?10.0 and λ?0.6, where Eo is the Eötvös number, M the Morton number, κ the viscosity ratio and λ the ratio of particle diameter to pipe diameter.     

The impact of external electrostatic fields on gas-liquid bubbling dynamics

The effect of an applied electric potential on the dynamics of gas bubble formation from a single nozzle in glycerol was studied experimentally. Dry nitrogen was bubbled into glycerol through a nozzle having an electrified tip while pressure measurements were made upstream of the nozzle. As the applied electric potential was increased from zero, bubble size reduced, bubble shape became more spherical, and bubbling frequency increased. At constant gas flow, bubble-formation exhibited a classic period-doubling route to chaos with increasing potential. We defined an electric Bond number assuming that both the liquid and gas phases are conducting. This is in contrast to previous studies where one phase was considered a perfect conductor and the other one a perfect nonconductor or insulator. Although electric potential and gas flow appear to have similar effects on the period-doubling bifurcation process for this system, the relative impact of electrostatic forces, as measured in terms of electric Bond number for conducting liquid and gas phases, is smaller. However, the relative impact of electrostatic forces for the case of insulating liquid and conducting gas phases is comparable to flow forces. Further data collection is required for different nozzle geometries and liquid column heights in order to verify the relative impacts of electrostatic and flow forces, and would allow us to ascertain if electrostatic potential is a feasible manipulated variable for controlling this system.     

Characterization and CFD-modeling of the hydrodynamics of a prismatic spouted bed apparatus

Recently the importance of spouted bed technology has significantly increased in the context of drying processes as well as granulation, agglomeration or coating processes. However, the understanding of the complex interactions within and between the single phases is still low and needs further improvement. Several research groups apply both continuum as well as discrete element simulations to understand the hydrodynamics of the spouting process. This work focuses on the simulation of the hydrodynamic behavior of a prismatic spouted bed apparatus by applying the Euler/Euler continuum approach in the commercial computational fluid dynamics (CFD) software package FLUENT 6.2. The simulations are validated by experiments. Calculated and experimental (by PIV-measurements) obtained velocity vector maps, as well as measured and calculated gas phase pressure fluctuations over the entire bed are compared. The aim of this work is to improve the understanding of the hydrodynamics of the spouting process.     

Dynamic simulation of a 2D bubble column

The present paper demonstrates how 2D, dynamic simulations of a flat bubble column are feasible, applying state-of-the-art dynamic turbulence models, when an appropriate turbulent dispersion term is applied in the conservation equation for the gas volume fraction. The kω turbulence model yielded a better qualitative prediction of the bubble plume than the kε model, due to the low-Reynolds number treatment of the former model. The simple mixing length turbulence model gave the best prediction of the meandering plume, without any dispersion term. The mixing length model is, however, almost identical to a Large-Eddy simulation when run time-dependent on a fine mesh, and should be applied with care due to the use of a constant turbulence length scale and the inherent 3D nature of turbulence. By refining the mesh to the extreme end, it was shown that an apparently grid independent numerical solution was really grid-dependent, even when dynamic turbulence models were applied. The apparently grid independent solution was computed with an increment in the computational mesh that was of the same size as an equilibrium Kolmogorov length scale.     

Effects of cross-flow velocity, capillary pressure and oil viscosity on oil-in-water drop formation from a capillary

The formation of oil drops from a single capillary with a diameter of 200 μm into a cross-flowing continuous water phase has been studied experimentally with the particle image velocimetry (PIV) technique and numerically with the computational fluid dynamics (CFD) software Fluent. The drop formation time and the volume of the detached drop were used as validation parameters and the results from the two methods corresponded well, with a difference of less than 5% for the drop formation time and 10% for the drop volume. The cross-flow velocity has a major impact on drop size, which decreases as the cross-flow increases. An increase in cross-flow, oil viscosity and capillary pressure displace the position of necking and drop detachment away from the capillary opening, which will have a decreasing effect on the final size of the drop.     

Effects of wall-heating on the linear instability characteristics of pressure-driven two-layer channel flow

The linear stability analysis of a pressure-driven two-layer channel flow of two immiscible, Newtonian and incompressible fluids is considered. The walls of the channel are maintained at different constant temperatures and Nahme's law is applied to model the temperature dependence of the fluid viscosity. A modified Orr–Sommerfeld equation for the disturbance streamfunction coupled to a linearized energy equation is derived and solved using a spectral collocation method. Our results indicate that increasing the dimensionless top wall temperature has a non-monotonic effect on the linear stability characteristics. We also found that increasing the thermal conductivity and density ratios stabilise the flow for the set of parameter values considered; the viscosity ratio has a non-monotonic effect on the maximal growth rate. An energy ‘budget’ analysis shows that the most dangerous mode is of ‘interfacial’ type.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

New method for the determination of precipitation kinetics using a laminar jet reactor

In this paper a new experimental method for determining the kinetics of fast precipitation reactions is introduced. Use is made of a laminar jet reactor, which is also frequently applied to determine the kinetics of homogeneous gas-liquid reactions. The liquid containing one or more of the precipitating reactants passes a gas-filled reactor as a stagnant jet in which no mixing occurs. The remaining reactant needed for precipitation is supplied in gaseous form and causes the precipitation reaction to occur while it is diffusing into the jet. Hydrodynamics as well as transport phenomena are precisely known for this system, whereas agglomeration can be minimized by adjustment of the concentration of the solute supplied by the gas. The kinetics of the different crystallization steps can be determined by analyzing the size distribution of the produced particles. This new method is experimentally demonstrated for the precipitation of CuS using H₂S gas. The obtained data were successfully used to simulate a packed bed absorber in which H₂S is absorbed by a CuSO₄ solution.     

Modeling of the break-up of deformable particles in developed turbulent flow

Dynamic behavior of the drops and bubbles in developed turbulent flow depend on turbulent length scale (λ), Morton (Mo), Weber (We) and Reynolds (Re_a) numbers. In the present work, in order to calculate the maximum stable size of drops and bubbles, the A factor of break-up, Ay (Ay=ωa/U), that is the ratio of the break-up rate in developed turbulent flow to the mean velocity of the flow has been introduced and the effect of the pipe roughness on this factor has also been given. Comparison of all the results obtained in this study with those taken from the literature for the range of Mo?7, We?10 and Re_a?100 showed a good agreement.     

A numerical investigation of aerosol dynamics in a wall-less reactor

This paper describes a numerical investigation of aerosol formation during silane decomposition in a wall-less reactor. The wall-less reactor is amenable to numerical investigation because the homogeneous chemical reactions leading to the formation of solid particles are isolated from heterogeneous effects, such as occur at the walls of a laminar flow aerosol reactor. The flow/heat transfer and gas-phase chemical kinetics are simulated utilizing separate one-way coupled models. The aerosol dynamics model is based on a simplified sectional model originally developed by Okuyama et al. This model is modified to allow for the simulation of particle growth via condensation. Simulations have been performed which indicate that particle growth via condensation may be an important process. Additionally, the effects of total reactor pressure, temperature and inlet silane concentration on the dynamics of the aerosol population have been investigated. Conditions which result in the formation of larger and more numerous particles have been identified.     

Nonlinear characterization of oil–gas–water three-phase flow in complex networks

Understanding the dynamics of oil–gas–water three-phase flow has been a challenge in the fields of nonlinear dynamics and fluid mechanics. We systematically carried out oil–gas–water three-phase flow experiments for measuring the time series of flow signals, which is studied in terms of the mapping from time series to complex networks. Two network mapping methods are proposed for the analysis and identification of flow pattern dynamics, i.e. Flow Pattern Complex Network (FPCN) and Fluid Dynamic Complex Network (FDCN). Through detecting the community structure of FPCN based on K-means clustering, distinct flow patterns can be successfully distinguished and identified. A number of FDCN's under different flow conditions are constructed in order to reveal the dynamical characteristics of three-phase flows. The network information entropy of FDCN is sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the three-phase flow. These interesting and significant findings suggest that complex networks can be a potentially powerful tool for uncovering the nonlinear dynamics of oil–gas–water three-phase flows.     

The effect of CO2 dissolved in a diesel fuel on the jet flame characteristics

This paper is concerned with an experimental study of the jet diffusion flame characteristics of fuel containing CO₂. Using diesel fuel containing dissolved CO₂ gas, experiments were performed under atmospheric conditions with a diesel hole-type nozzle of 0.19 mm orifice diameter at constant injection pressure. In this study, four different CO₂ mass fraction in diesel fuel such as 3.13%, 7.18%, 12.33% and 17.82% were used to study the effect of CO₂ concentration on the jet flame characteristics. Jet flame characteristics were measured by direct photography, meanwhile the image colorimetry is used to assess the qualitative features of jet flame temperature. Experimental results show that the CO₂ gas dilution effect and the atomization effect have a great influence on the flame structure and average temperature. When the injection pressure of diesel fuel increased from 4 MPa to 6 MPa, the low temperature flame length increased from 18.4 cm to 21.7 cm and the full temperature flame length decreased from 147.6 cm to 134.7 cm. With the increase of CO₂ gas dissolved in the diesel fuel, the jet flame full length decreased for the jet atomization being improved greatly meanwhile the low temperature flame length increased for the CO₂ gas dilution effect; with the increase of CO₂ gas dissolved in the diesel fuel, the average temperature of flame increases firstly and then falls. Experimental results validate that higher injection pressure will improve jet atomization and then increased the flame average temperature.