Numerical Jet Atomization: Part II — Modeling Information and Comparison With DNS Results

2006 ◽  
Author(s):  
P. A. Beau ◽  
T. Me´nard ◽  
R. Lebas ◽  
A. Berlemont ◽  
S. Tanguy ◽  
...  
Keyword(s):  
Level Set ◽  
Volume Fraction ◽  
Computing Time ◽  
Mass Conservation ◽  
Liquid Volume ◽  
Liquid Density ◽  
Wide Range ◽  
The Mean ◽  
Break Up ◽  
Primary Break

The main objective of our work is to develop direct numerical simulation tools for the primary break up of a jet. Results can help to determine closure relation in the ELSA model [1] which is based on a single-phase Eulerian model and on the transport equation for the mean liquid/gas interface density in turbulent flows. DNS simulations are carried out to obtain statistical information in the dense zone of the spray where nearly no experimental data are available. The numerical method should describe the interface motion precisely, handle jump conditions at the interface without artificial smoothing, and respect mass conservation. We develop a 3D code [2], where interface tracking is ensured by Level Set method, Ghost Fluid Method [3] is used to capture accurately sharp discontinuities, and coupling between Level Set and VOF methods is used for mass conservation [4]. Turbulent inflow boundary conditions are generated through correlated random velocities with a prescribed length scale. Specific care has been devoted to improve computing time with MPI parallelization. The numerical methods have been applied to investigate physical processes that are involved in the primary break up of an atomizing jet. The chosen configuration is close as possible of Diesel injection (Diameter D = 0.1 mm, Velocity = 100m/s, Liquid density = 696kg/m3, Gas density = 25kg/m3). Typical results will be presented. From the injector nozzle, the turbulence initiates some perturbations on the liquid surface, that are enhanced by the mean shear between the liquid jet and the surrounding air. The interface becomes very wrinkled and some break-up is initiated. The induced liquid parcels show a wide range of shapes. Statistics are carried out and results will be provided for liquid volume fraction, liquid/gas interface density, and turbulent correlations.

Interface Tracking With a Coupled Level Set /VOF/Ghost Fluid Method: Application to Jet Atomization

2007 ◽  
Author(s):  
T. Me´nard ◽  
A. Berlemont
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Level Set Methods ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Ghost Fluid Method ◽  
Level Set Function ◽  
Wide Range ◽  
Break Up

We are here concerned by the primary break-up of a jet: a lot of topological changes occur and the Level Set Method thus appears well designed for our purpose. To describe the interface discontinuities, we use the Ghost Fluid Method (GFM) and a projection method is used to solve incompressible Navier-Stokes equations that are coupled to a transport equation for the level set function. The main drawback of level set methods is that numerical computations in the re-distancing algorithm can generate mass loss in under-resolved regions. To improve mass conservation extension of the method can be developed, namely a coupling between VOF and Level Set. In order to illustrate the abilities of the Level Set/VOF/Ghost Fluid method for interface tracking, we present a 3D simulation of the primary atomization zone of a turbulent liquid jet. The turbulence initiates some perturbations on the liquid surface, that are enhanced by the mean shear and break-up occurs. The generated liquid parcels show a wide range of shapes. Particular behaviors such ligament detachments, droplet formations and break up are described.

Numerical Jet Atomization: Part I — DNS Simulation of Primary Break Up

2006 ◽  
Author(s):  
T. Me´nard ◽  
P. A. Beau ◽  
S. Tanguy ◽  
F. X. Demoulin ◽  
A. Berlemont
Keyword(s):  
Turbulent Flows ◽  
Level Set ◽  
Incompressible Flows ◽  
Fluid Motion ◽  
Mass Conservation ◽  
Ghost Fluid Method ◽  
Closure Relation ◽  
First Results ◽  
Break Up ◽  
Primary Break

DNS simulations are carried out to obtain information in the dense zone of a spray where nearly no experimental data are available. Interface tracking is ensured by Level Set method, Ghost Fluid Method (GFM) is used to capture accurately sharp discontinuities for pressure, density and viscosity. Coupling between Level Set and VOF method is used for mass conservation. Fluid motion is predicted with a projection method for incompressible flows. The numerical methods are described and validations are presented. First results are then presented for 3D simulation of the primary break-up of a liquid jet with the Level Set-VOF-Ghost Fluid method and the results can help to determine closure relation in the ELSA model [Part II of the paper] which is based on a single-phase Eulerian model and on the transport equation for the mean liquid/gas interface density in turbulent flows.

Air-assisted atomization of liquid jets in varying levels of turbulence

2014 ◽  
Vol 764 ◽  
pp. 95-132 ◽  
Author(s):  
A. Kourmatzis ◽  
A. R. Masri
Keyword(s):  
Turbulence Intensity ◽  
Weber Number ◽  
Intensity Level ◽  
Flow Conditions ◽  
Mean Flow ◽  
Potential Core ◽  
Droplet Sizes ◽  
The Mean ◽  
Break Up ◽  
Primary Break

AbstractAir-assisted primary atomization is investigated in a configuration where liquid is injected in a turbulent gaseous jet flow both within as well as outside of the potential core. Cases are studied where the injection point is moved within the flow to maintain a range of constant gaseous mean velocities but changing local fluctuating velocity root-mean-square (r.m.s.) levels. Over a range of mean conditions, this allows for a systematic understanding of both the effects of gas-phase turbulence and mean shear on primary break-up independently. Extensive data is obtained and analysed from laser Doppler anemometry/phase Doppler anemometry, high-speed microscopic backlit imaging and advanced image processing. It is found that the ratio of the turbulent Weber number $\mathit{We}^{\prime }$ to the mean Weber number $\mathit{We}$ is a relevant parameter as is the turbulence intensity. The primary break-up length is found to be heavily influenced not only by the mean velocity, but also by the turbulence level and the mass fuel to air ratio. Above a particular threshold intensity level the break-up time changes in proportion to the change in the integral time scale of the flow. In addition, it is found that regardless of diameter and turbulent flow conditions at the liquid jet, the final size of ligaments converges to a value which is of the order of the measured primary instability wavelength (${\it\lambda}_{1}$). In contrast, cases of different turbulence intensity show the mean of droplet sizes diverging as the spray is advected downstream and this is because droplets are generated from ligaments, the latter of which are subjected both to Rayleigh–Taylor instabilities and turbulent fluctuations. This contribution, for the first time, examines the theoretical applicability of the Rayleigh–Taylor instability in flows where the turbulence is substantial with respect to the mean flow. It is shown that for high turbulence intensities a full theoretical reconstruction of the measured final droplet size distribution is possible from a probability density function of model Rayleigh–Taylor wavelengths (${\it\lambda}_{RT}$). In agreement with the literature (Varga et al. J. Fluid Mech., vol. 497, 2003, pp. 405–434), mean droplet sizes are found to be equal to a mean theoretical Rayleigh–Taylor wavelength normalized by a particular constant value. This, however, is only true for local turbulence intensities less than ${\sim}25\,\%$, or for ratios of the turbulent Weber number to mean Weber number ($\mathit{We}^{\prime }/\mathit{We}$) of less than ${\sim}6\,\%$. Above this, the normalization value is no longer constant, but increases with $\mathit{We}^{\prime }/\mathit{We}$. Finally, the instability wavelengths can be used as part of an approximation that estimates the total number of objects formed after break-up, where the object number is found to be dictated by a balance of both mean flow conditions and local turbulence.

scholarly journals Cytoplasmic Protein Mobility in Osmotically Stressed Escherichia coli

2008 ◽  
Vol 191 (1) ◽  
pp. 231-237 ◽  
Author(s):  
Michael C. Konopka ◽  
Kem A. Sochacki ◽  
Benjamin P. Bratton ◽  
Irina A. Shkel ◽  
M. Thomas Record ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Cellular Response ◽  
Fluorescent Protein ◽  
Volume Fraction ◽  
E Coli ◽  
Surprising Effect ◽  
Wide Range ◽  
Underlying Causes ◽  
The Mean ◽  
Green Fluorescent

ABSTRACT Facile diffusion of globular proteins within a cytoplasm that is dense with biopolymers is essential to normal cellular biochemical activity and growth. Remarkably, Escherichia coli grows in minimal medium over a wide range of external osmolalities (0.03 to 1.8 osmol). The mean cytoplasmic biopolymer volume fraction (〈φ〉) for such adapted cells ranges from 0.16 at 0.10 osmol to 0.36 at 1.45 osmol. For cells grown at 0.28 osmol, a similar 〈φ〉 range is obtained by plasmolysis (sudden osmotic upshift) using NaCl or sucrose as the external osmolyte, after which the only available cellular response is passive loss of cytoplasmic water. Here we measure the effective axial diffusion coefficient of green fluorescent protein (D GFP) in the cytoplasm of E. coli cells as a function of 〈φ〉 for both plasmolyzed and adapted cells. For plasmolyzed cells, the median D GFP ( \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(D_{GFP}^{m}\) \end{document} ) decreases by a factor of 70 as 〈φ〉 increases from 0.16 to 0.33. In sharp contrast, for adapted cells, \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(D_{GFP}^{m}\) \end{document} decreases only by a factor of 2.1 as 〈φ〉 increases from 0.16 to 0.36. Clearly, GFP diffusion is not determined by 〈φ〉 alone. By comparison with quantitative models, we show that the data cannot be explained by crowding theory. We suggest possible underlying causes of this surprising effect and further experiments that will help choose among competing hypotheses. Recovery of the ability of proteins to diffuse in the cytoplasm after plasmolysis may well be a key determinant of the time scale of the recovery of growth.

New Physically Based Approach of Mass Conservation Correction in Level Set Formulation for Incompressible Two-Phase Flows

2005 ◽  
Vol 127 (3) ◽  
pp. 554-563 ◽  
Author(s):  
Snehamoy Majumder ◽  
Suman Chakraborty
Keyword(s):  
Level Set ◽  
Volume Fraction ◽  
Mass Conservation ◽  
Heaviside Function ◽  
Two Phase ◽  
Physically Based ◽  
Static Fluid ◽  
Volume Fraction Function ◽  
Conservation Model ◽  
Level Set Approach

A novel physically based mass conservation model is developed in the framework of a level set method, as an alternative to the Heaviside function based formulation classically employed in the literature. In the proposed “volume fraction based level set approach,” expressions for volume fraction function for each interfacial computational cell are developed, and are subsequently correlated with the corresponding level set functions. The volume fraction function, derived from a physical basis, is found to be mathematically analogous to the Heaviside function, except for a one-dimensional case. The results obtained are compared with the benchmark experimental and numerical results reported in the literature. Finally, transient evolution of a circular bubble in a developing shear flow and rising bubbles in a static fluid, are critically examined. The Cox angle and the deformation parameter characterizing the bubble evolution are critically examined. An excellent satisfaction of the mass conservation requirements is observed in all case studies undertaken.

DNS Study of Collision and Coalescence Over a Wide Range of Volume Fraction

2010 ◽  
Author(s):  
G. Luret ◽  
T. Me´nard ◽  
J. Re´veillon ◽  
A. Berlemont ◽  
F. X. Demoulin
Keyword(s):  
Kinetic Energy ◽  
Weber Number ◽  
Volume Fraction ◽  
Density Ratio ◽  
Liquid Volume ◽  
Kinetic Energy Density ◽  
Two Phase ◽  
Liquid Volume Fraction ◽  
Gas Phases ◽  
Wide Range

Among the different processes that play a role during the atomization process, collisions are addressed in this work. Collisions can be very important in dense two-phase flows. Recently, the Eulerian Lagrangian Spray Atomization (ELSA) model has been developed. It represents the atomization by taking into account the dense zone of the spray. Thus in this context, collisions modeling are of the utmost importance. In this model results of collisions are controlled by the value of an equilibrium Weber number, We*. It is defined as the ratio between the kinetic energy to the surface energy. Such a value of We* has been studied in the past using Lagrangian collision models with various complexity. These models are based on analysis of collisions between droplets that have surface at rest. This ideal situation can be obtained only if droplet agitation created during a collision has enough time to vanish before the next collision. For a spray, this requirement is not always fulfill depending for instance on the mean liquid volume fraction. If there is not enough time, collisions will occur between agitated droplets changing the issue of the collision with respect to the ideal case. To study this effect, a DNS simulation with a stationary turbulence levels has been conducted for different liquid volume fractions in a cubic box with periodic condition in all directions. For liquid volume fraction close to zero the spray is diluted and collisions between spherical droplets can be identified. For a volume fraction close to one, collisions between bubbles are found. For a middle value of the volume fraction no discrete phase can be observed, instead a strong interaction between both liquid and gas phases is taking place. In all this case the equilibrium value of the Weber number We* can be determined. First propositions to determine We* as a function of the kinetic energy, density ratio, surface tension coefficient and the volume fraction will be proposed.

Microstructural Evolution of Semi-Solid AZ61 Magnesium Alloy during Reheating Process

2006 ◽  
Vol 116-117 ◽  
pp. 275-278 ◽  
Author(s):  
Hong Yan ◽  
Fa Yun Zhang
Keyword(s):  
Magnesium Alloy ◽  
Microstructural Evolution ◽  
Volume Fraction ◽  
Isothermal Holding ◽  
Liquid Volume ◽  
Liquid Volume Fraction ◽  
The Mean ◽  
Semi Solid ◽  
Reheating Process ◽  
Holding Temperature

The microstructural evolution of AZ61 semi-solid magnesium alloy during semi-solid remelting process was studied in this paper. The semi-solid billet was fabricated by strain-induced melt activation (SIMA) method. The results showed that the initial semi-solid grains melt mainly through coalescence. With the prolongation of isothermal holding time, the grains grew up and spheroidized, in which the mean diameter of grain and liquid volume fraction increased. In the meantime, the higher the holding temperature, the faster the grain grew and spheroidized. The suitable reheating temperature of AZ61 semi-solid magnesium alloy was 592. The samples were susceptible to serious deformation beyond 597.

Robust Conservative Level Set Method for 3D Mixed-Element Meshes — Application to LES of Primary Liquid-Sheet Breakup

2014 ◽  
Vol 16 (2) ◽  
pp. 403-439 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Experimental Data ◽  
Level Set ◽  
Multiphase Flows ◽  
Volume Fraction ◽  
Computational Cost ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Liquid Volume ◽  
Mixed Element ◽  
Conservative Level Set

AbstractIn this article we detail the methodology developed to construct an efficient interface description technique — the robust conservative level set (RCLS) — to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy. The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries. In addition, special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method. This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm. The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases. Finally, the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas. This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh. The numerical results have been validated qualitatively against theoretical predictions and experimental data. In particular, the expected breakup regime was observed in the simulation results. Finally, the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data. This constitutes a first step towards a quantitative validation.

Equilibrium structure and diffusion in concentrated hydrodynamically interacting suspensions confined by a spherical cavity

2017 ◽  
Vol 836 ◽  
pp. 413-450 ◽  
Author(s):  
Christian Aponte-Rivera ◽  
Yu Su ◽  
Roseanna N. Zia
Keyword(s):  
Spherical Cavity ◽  
Volume Fraction ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Cavity Size ◽  
Cavity Radius ◽  
Particle Volume ◽  
Wide Range ◽  
Long Time ◽  
The Mean

The short- and long-time equilibrium transport properties of a hydrodynamically interacting suspension confined by a spherical cavity are studied via Stokesian dynamics simulations for a wide range of particle-to-cavity size ratios and particle concentrations. Many-body hydrodynamic and lubrication interactions between particles and with the cavity are accounted for utilizing recently developed mobility and resistance tensors for spherically confined suspensions (Aponte-Rivera & Zia, Phys. Rev. Fluids, vol. 1(2), 2016, 023301). Study of particle volume fractions in the range $0.05\leqslant \unicode[STIX]{x1D719}\leqslant 0.40$ reveals that confinement exerts a qualitative influence on particle diffusion. First, the mean-square displacement over all time scales depends on the position in the cavity. Additionally, at short times, the diffusivity is anisotropic, with diffusion along the cavity radius slower than diffusion tangential to the cavity wall, due to the anisotropy of hydrodynamic coupling and to confinement-induced spatial heterogeneity in particle concentration. The mean-square displacement is anisotropic at intermediate times as well and, surprisingly, exhibits superdiffusive and subdiffusive behaviours for motion along and perpendicular to the cavity radius respectively, depending on the suspension volume fraction and the particle-to-cavity size ratio. No long-time self-diffusive regime exists; instead, the mean-square displacement reaches a long-time plateau, a result of entropic restriction to a finite volume. In this long-time limit, the higher the volume fraction is, the longer the particles take to reach the long-time plateau, as cooperative rearrangements are required as the cavity becomes crowded. The ordered dynamical heterogeneity seen here promotes self-organization of particles based on their size and self-mobility, which may be of particular relevance in biophysical systems.

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