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.

A Direct Numerical Simulation of the Unsteady Development of a Deformable Rising Bubble in a Quiescent Liquid

2008 ◽  
Author(s):  
Alpana Agarwal ◽  
C. F. Tai ◽  
J. N. Chung
Keyword(s):  
Weber Number ◽  
Bubble Dynamics ◽  
Stokes Equations ◽  
Control Volume ◽  
Density Ratio ◽  
Simulation Method ◽  
Liquid Pool ◽  
Accurate Information ◽  
Two Phase ◽  
Wide Range

An accurate finite-volume based numerical method for the simulation of an isothermal two-phase flow, consisting of a deformable bubble rising in a quiescent, unbounded liquid, is presented. This direct simulation method is built on a sharp interface concept and developed on an Eulerian, Cartesian fixed grid with a cut-cell scheme and marker points to track the moving interface. The unsteady Navier-Stokes equations in both liquid and gas phases are solved separately. The mass continuity and momentum flux conditions are explicitly matched at the true phase boundary to determine the interface shape and movement of the bubble. The highlights of this method are that it utilizes a combined Eulerian-Lagrangian approach, and is capable of treating the interface as a sharp discontinuity. A fixed underlying grid is used to represent the control volume. The interface, however, is denoted by a separate set of marker particles which move along with the interface. A quadratic curve fitting algorithm with marker points is used to yield smooth and accurate information of the interface curvatures. This numerical scheme can handle a wide range of density and viscosity ratios. The bubble is assumed to be spherical and at rest initially, but deforms as it rises through the liquid pool due to buoyancy. Additionally, the flow is assumed to be axisymmetric and incompressible. The bubble deformation and dynamic motion are characterized by the Reynolds number, the Weber number, the density ratio and the viscosity ratio. The effects of these parameters on the translational bubble dynamics and shape are given and the physical mechanisms are explained and discussed. Results for the shape, velocity profile and various forces acting on the bubble are presented here as a function of time until the bubble reaches terminal velocity. The range of Reynolds numbers investigated is 1 < Re < 100, and that of Weber number is 1 < We < 10.

Application of Mixing Length Theory to Wavy Turbulent Liquid—Gas Interface

1981 ◽  
Vol 103 (3) ◽  
pp. 492-500 ◽  
Author(s):  
S. Levy ◽  
J. M. Healzer
Keyword(s):  
Liquid Film ◽  
Transition Layer ◽  
Volume Fraction ◽  
Density Ratio ◽  
Constant Density ◽  
Mixing Length ◽  
Two Phase ◽  
Liquid Entrainment ◽  
Wide Range ◽  
Mixing Length Theory

A fully developed and adiabatic two-phase annular model with liquid entrainment is derived for flow in a pipe with negligible gravity effects. The model is based upon application of the single phase mixing length theory to a wavy liquid-gas interface. The model subdivides the flow cross section into three regions: a liquid film, a gas core of constant density, and a transition wavy layer between them. The combination of a constant velocity and a density varying exponentially with distance from the wall is employed in the transition layer. This approach plus appropriate logarithmic velocity distributions in the liquid film and gas core make it possible to specify the two-phase pressure drop, volume fraction, wave velocity, and thickness of the liquid film and transition layer. The liquid entrainment is obtained in terms of the exponent of the density profile in the transition layer, and interface stability considerations are used to express this entrainment parameter semiempirically in terms of an apparent Weber number and density ratio. Comparisons of the model are made with air-water and steam-water test data, and the results generally are satisfactory over a wide range of conditions and for all the important characteristics of this flow pattern.

scholarly journals Foam Quality of Foams Formed on Capillaries and Porous Media Systems

2021 ◽  
Vol 5 (1) ◽  
pp. 10
Author(s):  
Victor Starov ◽  
Anna Trybala ◽  
Phillip Johnson ◽  
Mauro Vaccaro
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Volume Fraction ◽  
Foam Height ◽  
Liquid Volume ◽  
Foam Formation ◽  
Liquid Volume Fraction ◽  
Wide Range ◽  
Soft Porous Media

Foams are of great importance as a result of their expansive presence in everyday life—they are used in the food, cosmetic, and process industries, and in detergency, oil recovery, and firefighting. There is a little understanding of foam formation using soft porous media in terms of the quality of foam and foam formation. Interaction of foams with porous media has recently been investigated in a study by Arjmandi-Tash et al., where three different regimes of foam drainage in contact with porous media were observed. In this study, the amount of foam generated using porous media with surfactant solutions is investigated. The aim is to understand the quality of foam produced using porous media. The effect of capillary sizes and arrangement of porous in porous media has on the quality of foam is investigated. This is then followed by the use of soft porous media for foam formation to understand how the foam is generated on the surface of the porous media and the effect that different conditions (such as concentration) have on the quality of the foam. The quality of foam is a blanket term for bubble size, liquid volume fraction, and stability of the foam. The liquid volume fraction is calculated using a homemade dynamic foam analyser, which is used to obtain the distribution of liquid volume fraction along with the foam height. Soft porous media does not influence substantially the rate of decay of foam produced, however, it decreases the average diameter of the bubbles, whilst increasing the range of bubble sizes due to the wide range of pore sizes present in the soft porous media. The foam analyser showed the expected behaviour that, as the foam decays and becomes drier, the liquid volume fraction of the foam falls, and therefore the conductivity of foam also decreases, indicating the usefulness of the home-made device for future investigations.

scholarly journals A magnetic resonance study of temperature-dependent microstructural evolution and self-diffusion of water in Arctic first-year sea ice

2005 ◽  
Vol 40 ◽  
pp. 179-184 ◽  
Author(s):  
C. Bock ◽  
H. Eicken
Keyword(s):  
Magnetic Resonance ◽  
Sea Ice ◽  
Microstructural Evolution ◽  
Volume Fraction ◽  
Bulk Liquid ◽  
Liquid Volume ◽  
Liquid Volume Fraction ◽  
Cross Sectional ◽  
Pore Connectivity ◽  
Pore Number

AbstractThe microstructural evolution of brine inclusions in granular and columnar sea ice has been investigated through magnetic resonance imaging (MRI) for temperatures between –28 and –3˚C. Thin-section and salinity measurements were completed on core samples obtained from winter sea ice near Barrow, Alaska, USA. Subsamples of granular (2–5cm depth in core) and columnar sea ice (20–23 cm depth) were investigated with morphological spin-echo and diffusion-weighted imaging in a Bruker 4.7T MRI system operating at field gradients of 200 mTm–1 at temperatures of approximately –28, –15, –6 and –3˚C. Average linear pore dimensions range from 0.2 to 1 mm and increase with bulk liquid volume fraction as temperatures rise from –15 to –3˚C. Granular ice pores are significantly larger than columnar ice pores and exhibit a higher degree of connectivity. No evidence is found of strongly non-linear increases in pore connectivity based on the MRI data. This might be explained by shortcomings in resolution, sensitivity and lack of truly three-dimensional data, differences between laboratory and field conditions or the absence of a percolation transition. Pore connectivity increases between –6 and –3˚C. Pore-number densities average at 1.4±1.2mm–2. The pore-number density distribution as a function of cross-sectional area conforms with power-law and lognormal distributions previously identified, although significant variations occur as a function of ice type and temperature. At low temperatures (< –26˚C), pore sizes were estimated from 1H self-diffusivity measurements, with self-diffusivity lower by up to an order of magnitude than in the free liquid. Analysis of diffusional length scales suggests characteristic pore dimensions of <1 μm at < –26˚C.

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.

Leakage, Drag Power and Rotordynamic Force Coefficients of an Air in Oil (Wet) Annular Seal

2017 ◽  
Author(s):  
Luis San Andrés ◽  
Xueliang Lu
Keyword(s):  
Test Data ◽  
Volume Fraction ◽  
Damping Coefficient ◽  
Liquid Volume ◽  
Pure Liquid ◽  
Test Results ◽  
Liquid Volume Fraction ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Annular Seal

Wet gas compression systems and multiphase pumps are enabling technologies for the deep sea oil and gas industry. This extreme environment determines both machine types have to handle mixtures with a gas in liquid volume fraction (GVF) varying over a wide range (0 to 1). The gas (or liquid) content affects the system pumping (or compression) efficiency and reliability, and places a penalty in leakage and rotordynamic performance in secondary flow components, namely seals. In 2015, tests were conducted with a short length smooth surface annular seal (L/D = 0.36, radial clearance = 0.127 mm) operating with an oil in air mixture whose liquid volume fraction (LVF) varied to 4%. The test results with a stationary journal show the dramatic effect of a few droplets of liquid on the production of large damping coefficients. This paper presents further measurements and predictions of leakage, drag power, and rotordynamic force coefficients conducted with the same test seal and a rotating journal. The seal is supplied with a mixture (air in ISO VG 10 oil), varying from a pure liquid to an inlet GVF = 0.9 (mostly gas), a typical range in multiphase pumps. For operation with a supply pressure (Ps) up to 3.5 bar (a), discharge pressure (Pa) = 1 bar (a), and various shaft speed (Ω) to 3.5 krpm (ΩR = 23.3 m/s), the flow is laminar with either a pure oil or a mixture. As the inlet GVF increases to 0.9 the mass flow rate and drag power decrease monotonically by 25% and 85% when compared to the pure liquid case, respectively. For operation with Ps = 2.5 bar (a) and Ω to 3.5 krpm, dynamic load tests with frequency 0 < ω < 110 Hz are conducted to procure rotordynamic force coefficients. A direct stiffness (K), an added mass (M) and a viscous damping coefficient (C) represent well the seal lubricated with a pure oil. For tests with a mixture (GVFmax = 0.9), the seal dynamic complex stiffness Re(H) increases with whirl frequency (ω); that is, Re(H) differs from (K-ω2M). Both the seal cross coupled stiffnesses (KXY and −KYX) and direct damping coefficients (CXX and CYY) decrease by approximately 75% as the inlet GVF increases to 0.9. The finding reveals that the frequency at which the effective damping coefficient (CXXeff = CXX-KXY/ω) changes from negative to positive (i.e., a crossover frequency) drops from 50% of the rotor speed (ω = 1/2 Ω) for a seal with pure oil to a lesser magnitude for operation with a mixture. Predictions for leakage and drag power based on a homogeneous bulk flow model match well the test data for operation with inlet GVF up to 0.9. Predicted force coefficients correlate well with the test data for mixtures with GVF up to 0.6. For a mixture with a larger GVF, the model under predicts the direct damping coefficients by as much as 40%. The tests also reveal the appearance of a self-excited seal motion with a low frequency; its amplitude and broad band frequency (centered at around ∼12 Hz) persist and increase as the gas content in the mixture increase. The test results show that an accurate quantification of wet seals dynamic force response is necessary for the design of robust subsea flow assurance systems.

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