Modeling of bubble coalescence and break-up considering turbulent suppression phenomena in bubbly two-phase flow

New mechanistic bubble coalescence and break-up models considering turbulent suppression phenomena, which can possibly occur in the high liquid velocity condition of turbulent bubbly two-phase flow, are presented. The energy exchange mechanism between a turbulent eddy and interfacial structure was taken into account in the efficiency terms. Numerical simulations of turbulent bubbly flow were conducted in a CFD code to evaluate the newly developed models, in comparison with other advanced models coupled with a bubble-induced turbulent effect for one-group interfacial area transport equation. Local measurements of the bubble characteristics on the bubble size evolution along a vertical pipe flow were performed at KAERI-VAWL test facility using the five-sensor conductivity probe method to provide database for models validation. Results from the calculation clearly show the improvements of the newly developed models.     

Size-dependent coalescence kernel in fertilizer granulation-A comparative study

Granulation is a key process in several industries like pharmaceutical, food, fertilizer, agrochemicals, etc. Population balance modeling has been used extensively for modeling agglomeration in many systems such as crystallization, aerosols, pelletisation, etc. The key parameter is the coalescence kernel, β（ij） which dictates the overall rate of coalescence as well as the effect of granule size on coalescence rate. Adetayo, Litster, Pratsinis, and Ennis （1995） studied fertilizer granulation with a broad size distribution and modeled it with a two-stage kernel. A constant kernel can be applied to those granules which coalesce successfully. The coalescence model gives conditions for two types of coalescence, Type I and II. A twostage kernel, which is necessary to model granule size distribution over a wide size distribution, is applied in the present fluidized bed spray granulation process. The first stage is size-independent and non-inertial regime, and is followed by a size-dependent stage in which collisions between particles are non-random, i.e. inertial regime. The present work is focused on the second stage kernel where the feed particles of volume i and j collide and form final granule ij instead of i ＋j （Adetayo et al., 1995） which gives a wider particle size distribution of granules than proposed earlier.     

Numerical study on coalescence of two pre-existing coplanar flaws in rock

Crack propagation and coalescence processes are the fundamental mechanisms leading to progressive failure processes in rock masses, in which parallel non-persistent rock joints are commonly involved. The coalescence behavior of the latter, which are represented as pre-existing coplanar flaws (cracks), is numerically investigated in the present study. By using AUTODYN as the numerical tool, the present study systematically simulates the coalescence of two pre-existing coplanar flaws in rock under compression. The cumulative damage failure criterion is adopted in the numerical models to simulate the cumulative damage process in the crack initiation and propagation. The crack types (shear or tensile) are identified by analyzing the mechanics information associated with the crack initiation and propagation processes. The simulation results, which are generally in a good accordance with physical experimental results, indicate that the ligament length and the flaw inclination angle have a great influence on the coalescence pattern. The coalescence pattern is relatively simple for the flaw arrangements with a short ligament length, which becomes more complicated for those with a long ligament length. The coalescence trajectory is composed of shear cracks only when the flaw inclination angle is small (such as β ? 30°). When the pre-existing flaws are steep (such as β ? 75°), the coalescence trajectory is composed of tensile cracks as well as shear cracks. When the inclination angle is close to the failure angle of the corresponding intact rock material, and the ligament length is not long (such as L ? 2a), the direct shear coalescence is the more favorable coalescence pattern. In the special case that the two pre-existing flaws are vertical, the model will have a direct tensile coalescence pattern when the ligament length is short (L ? a), while the coalescence between the two inner flaw tips is not easy to achieve if the ligament length is long (L ? 2a).     

The formation of a liquid bridge during the coalescence of drops

This paper examines a mathematical model for the coalescence of two viscous liquid volumes in an inviscid gas or in a vacuum which removes the pressure singularity at the instant of impact inherent in the classical formulation of the continuum model. The very early stages of coalescence are examined in order to study the formation of the liquid bridge in two cases: (i) for two infinitely long, coalescing liquid cylinders; and (ii) for two coalescing spheres. Numerical solutions are computed for the velocity and pressure fields in the flow in both cases, and they confirm the removal of the pressure singularity. Also, the free-surface position at small times is determined.     

Transition between coalescence and bouncing of droplets on a deep liquid pool

This study focused on the bouncing of sub-millimetric droplets (below 0.7 mm) of three different fluids, distilled water, technical ethanol and 1-propanol on a deep liquid pool of the same fluids. Four different flow regimes including low-energy-collision coalescence, bouncing, high-energy-collision coalescence, and partial coalescence were observed in the experiments. These regimes were plotted in velocity-diameter diagrams, which showed that there was a diameter limit, D ≈ 0.2 mm, above which the low-energy-collision coalescence was inhibited. The contact time, in which the impinging droplets and the liquid surface interacted in the bouncing process, was studied, and the results showed the same characteristic time scale of the contact time as those of Richard et al. (in Nature 417, 2002, 811) and Thoroddsen and Takehara (in Phys. Fluids 12 (6), 2000, 1265–1267). The restitution coefficients for all fluids were investigated, and the water data agreed well with the values reported in the literature (Bach et al., J. Fluid. Mech. 518, 2004, 157–185; Jayaratne and Mason, Proc. R. Soc. Lond. A 280 (1383), 1964, 545–565). Based on stable restitution coefficients, which varied with fluids, the effects from both viscosity and surface tension were discussed. Further, a correlation (K = We · Oh^−0.58) was generalized to characterize the two transitions between coalescence (both high-energy- and low-energy-collision types) and bouncing, and a comparison with the model and data of Huang and Zhang (in Petrol Sci. 5, 2008, 62–66) showed that the generalized model characterized the coalescence-bouncing threshold well for the experimental fluids in the present study and oil with much higher viscosity.     

Experimental study on vibrations of a nonwoven fabric cylindrical filter

Unexpected vibrations on a cylindrical filter made of nonwoven fabrics were clarified experimentally. Two types of filter with length L=1.8 m and 3.7 m, both 45 cm in diameter and 1.08 mm in thickness, were used. This is a new type of aeroelastic vibration phenomenon because the filter is a closed cylindrical vessel. In addition, the flow velocity of inner air was very slow and inner air flowed out slowly from the filter surface. The velocity distribution of air flow from a fan duct as well as the frequency and amplitude of the filter vibration were measured for two types of filter. By setting up a roll core panel at the outlet of the fan duct, we could rectify the outflow and suppressed the vibration of the shorter filter with L=1.8 m. However, this method was not adequate for the longer filter with L=3.7 m, and we could suppress the vibration by shielding the inner surface of the filter at the top region.     

A parameter investigation of shear-induced coalescence in semidilute PIB–PDMS polymer blends: effects of shear rate, shear stress volume fraction, and viscosity

In this work, drop coalescence of polymer blends under shear flow in a parallel flow apparatus was investigated by optical sectioning microscopy. In each experiment, shear rate was set at values low enough to avoid any break-up phenomena. The time evolution of the drop size distribution was determined by motorized sample scanning and iterative acquisition of stacks of images along sample depth. Drop size and location in the acquired images was found by automated image analysis techniques. A systematic experimental campaign to investigate the effects of shear rate (in the range 0.1–0.5 s⁻¹), volume fraction (2.5–10%), and viscosity of the two phases (3–63 Pa s) at different viscosity ratio (0.1–2.3) was carried out. By comparing data from different experiments, it was found that at any strain value, the average drop size decreases monotonically with the shear stress, calculated as the product of shear rate and matrix viscosity. Furthermore, the coalescence rate slowed down with increasing viscosity ratio. Overall, these results provide an extensive set of data, which can be used as a benchmark for modeling shear-induced coalescence in polymer blends.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

Experimental study of microhole growth and coalescence in ductile materials

The growth and coalescence of two microholes in copper foil were studied experimentally byin situ tensile tests under a scanning electronic microscope. Two microholes of 15–35 μm in diameter were arranged in different distances and orientations. It was found that the mechanisms of microhole evolution were represented by slipping band creation, and then crack initiation and propagation along the slipping bands in ligament. The process of microhole growth and coalescence was influenced by the inter-center distance and orientation of microholes. The critical surface of microholes at coalescence is about 2–2.5 times that of the initial one. The variation of both the inter-center distance and orientation depends on the initial angle.     

A unified criterion for the growth and coalescence of microvoids

A yield criterion is developed which unifies void growth and void coalescence theories. Standard void growth theory assumes that plastic flow is diffuse, if not prevalent everywhere within the matrix of the elementary cell considered. On the other hand, void coalescence theory assumes states of post-localized plasticity whereby plastic flow is restricted to intervoid ligaments. The new theory accommodates both scenarios through some appropriate choice of microscopic velocity fields. An important implication for actual evolution problems is a seamless transition from void growth to void coalescence. This is in contrast with previous hybrid approaches whereby abrupt transitions are associated with the presence of unavoidable corners in the effective yield surface. More generally, the new criterion is applicable to describe yielding in porous metal plasticity for both low and high void volume fractions.     

Experimental and numerical investigation of turbulent cross-flow in a staggered tube bundle

This paper presents the results of measurements and numerical predictions of turbulent cross-flow in a staggered tube bundle. The bundle consists of transverse and longitudinal pitch-to-diameter ratios of 3.8 and 2.1, respectively. The experiments were conducted using a particle image velocimetry technique, in a flow of water in a channel at a Reynolds number of 9300 based on the inlet velocity and the tube diameter. A commercial CFD code, ANSYS CFX V10.0, is used to predict the turbulent flow in the bundle. The steady and isothermal Reynolds–Averaged Navier–Stokes (RANS) equations were used to predict the turbulent flow using each of the following four turbulence models: a k-epsilon, a standard k-omega, a k-omega-based shear stress transport, and an epsilon-based second moment closure. The epsilon-based models used a scalable wall function and the omega-based models used a wall treatment that switches automatically between low-Reynolds and standard wall function formulations.

The experimental results revealed extremely high levels of turbulence production by the normal stresses, as well as regions of negative turbulence production. The convective transport by mean flow and turbulent diffusion were observed to be significantly higher than in classical turbulent boundary layers. As a result, turbulence production is generally not in equilibrium with its dissipation rate. In spite of these characteristics, it was observed that the Reynolds normal stresses approximated from the k-based two-equation models were in a closer agreement with experiments than values obtained from the second moment closure. The results show that none of the turbulence models was able to consistently reproduce the mean and turbulent quantities reasonably well. The omega-based models predicted the mean velocities better in the developing region while the epsilon-based models gave better results in the region where the flow is becoming spatially periodic.     

Study on the coalescence mechanism of splitting failure of crack-weakened rock subjected to compressive loads

It is of important significance to study the coalescence mechanism of splitting failure of crack-weakened rock masses under compressive loads. In this paper, a simplified mechanism of crack propagation, in which the crack grows along the direction of maximum principal compressive stress, is proposed. Thus, only mode I is taken into account in the formulation and solution. On the basis of the near crack line analysis method, the elastic–plastic stress field near the crack line is analyzed, and the law that the length of the plastic zone along the crack line is varied with an external loads have been established by the matching condition of the elastic- plastic fields on the boundary, the coalescence stress and the strength properties of rock masses have been determined. The solution is a function of the geometry of the crack array. The results show that the crack coalescence depends on the crack interface friction coefficient, the sliding crack spacing, orientation of the cracks, and the crack half-length. The conclusions are of important significance for rock mass engineering.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

A continuous-discontinuous cellular automaton method for cracks growth and coalescence in brittle material简

A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.     

Experimental and numerical study of flat momentumless wake

Flat momentumless wake behind wing profile has been studied both experimentally and with numerical simulation based on the second order Reynolds stress turbulence model. Some obtained regular trends of momentumless wake decay are mainly consistent with previous experiments by Dmitrenko et al. (Dmitrenko, Yu.M., Kovalev, I.I., Luchko, N.N., Cherepanov, P.Ya., 1987. J. Eng. Phys. 52, 743–751 (in Russian)), Cimbala and Park (Cimbala, J.M., Park, W.J., 1990. J. Fluid Mech. 213, 479–509; Park, W.J., Cimbala, J.M., 1991. J. Fluid Mech. 224, 29–47). Transverse distributions of statistical characteristics and its evolution along the flow axis depend on initial conditions and body shape. It was shown that characteristic turbulence parameters associated with the wake's width, mean velocity deficit, turbulence kinetic energy, and its dissipation rate are not constant as some of the theories predict.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

Experimental study on the wake behind tapered circular cylinders

The flow around tapered cylinders can act as basic models for numerous bluff body flows with a spanwise variation of either the body shape or the inflow conditions. The well-known vortex street is influenced by strong three-dimensional effects from the spanwise variation of the shedding frequency, namely oblique vortex shedding and vortex dislocations. Stereo-PIV was chosen to study these phenomena, since it allows analyzing planes with the full three-component, instantaneous velocity fields and local, time-dependent variations in the same setting. Hence, detailed aspects of the vortex dislocation phenomenon are presented. Single vortex dislocation events are presented through the local variation of the three measured velocity components u, v and w. Longer time-series reveal both period and location of these dislocation events, as well as quantity and sizes of the cells of constant shedding velocity in between them. The influence of the Reynolds number and the cylinder aspect ratio on the vortex cells could be shown. The analysis of the vortex shedding behavior shows good agreement with previously published results. At the same time, the applied PIV technique provides more spatial information than point-based measurements and offers insight into a Reynolds number range that is currently out of reach of Direct Numerical Simulations.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.