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.

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.

Study on Entrainment From High-Viscosity Falling Liquid Film of Counter-Current Two-Phase Flow in a Vertical Pipe

2004 ◽  
Author(s):  
Yasuo Koizumi ◽  
Ryou Enari ◽  
Hiroyasu Ohtake
Keyword(s):  
Reynolds Number ◽  
Liquid Film ◽  
Silicon Film ◽  
Water System ◽  
Water Film ◽  
Two Phase ◽  
Silicon Oil ◽  
Falling Liquid Film ◽  
Wide Range ◽  
Counter Current

Behavior of a falling liquid film of highly viscous fluid in the counter-current flow condition was examined. In experiments, water and silicon oils of 500, 1000 and 3000 cSt were used as the liquid phase and air was adopted as the gas phase. A test section vertically oriented was a circular pipe of 30 mm in inner diameter and 5.4 m in length. Flooding velocities of the air-water system were well correlated with traditional correlations such as the Wallis correlation and the Kamei correlation. However, the flooding velocities of silicon films were greatly lower than the expected. When the effect of the viscosity was incorporated into the Wallis correlation, it predicted the experimental results well. The flooding in the air-silicon system was initiated by sudden growth of a wave on the film as in the air-water system although the film Reynolds number of the falling silicon film was considerably low; 0.02 ∼ 4. A considerable amount of droplets were detected a long time before the initiation of flooding in the air–silicon oil experiments as well as in the air–water experiments. The correlations tested for the onset condition of entrainment gave much higher gas velocities than the measured. Predicted velocities were rather close to the flooding velocities. The falling film thickness was predicted well by applying the universal velocity profile to the film flow over a wide range of a film Reynolds number; ranging from a water film to a 3000 cSt silicon oil film.

Prediction of Two-Phase Pressure Drop and Density Distribution From Mixing Length Theory

1963 ◽  
Vol 85 (2) ◽  
pp. 137-150 ◽  
Author(s):  
S. Levy
Keyword(s):  
Single Phase ◽  
Continuous Medium ◽  
Phase System ◽  
Mixing Length ◽  
Test Results ◽  
Two Phase ◽  
Pressure Drops ◽  
Mixing Length Theory ◽  
Phase Pressure ◽  
Good Agreement

Single-phase turbulent mixing length methods are used to predict two-phase flow. Two-phase density and velocity distributions and two-phase pressure drops are derived by treating the two-phase system as a continuous medium where the turbulent exchanges of momentum and density are equal. Good agreement is obtained between test results and analytical predictions.

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.

A Sharp Interface Direct Forcing Immersed Boundary Approach for Fully Resolved Simulations of Particulate Flows

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Jianming Yang ◽  
Frederick Stern
Keyword(s):  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Density Ratio ◽  
Sharp Interface ◽  
Immersed Boundary ◽  
Particulate Flows ◽  
Order Accuracy ◽  
Wide Range ◽  
Direct Forcing ◽  
Coarse Grids

In recent years, the immersed boundary method has been well received as an effective approach for the fully resolved simulations of particulate flows. Most immersed boundary approaches for numerical studies of particulate flows in the literature were based on various discrete delta functions for information transfer between the Lagrangian elements of an immersed object and the underlying Eulerian grid. These approaches have some inherent limitations that restrict their wider applications. In this paper, a sharp interface direct forcing immersed boundary approach based on the method proposed by Yang and Stern (Yang and Stern, 2012, “A Simple and Efficient Direct Forcing Immersed Boundary Framework for Fluid-Structure Interactions,” J. Comput. Phys., 231(15), pp. 5029–5061) is given for the fully resolved simulations of particulate flows. This method uses a discrete forcing approach and maintains a sharp profile of the fluid-solid interface. It is not limited to low Reynolds number flows and the immersed boundary discretization can be arbitrary or totally eliminated for particles with analytical shapes. In addition, it is not required to calculate the solid volume fraction in low density ratio problems. A strong coupling scheme is employed for the fluid-solid interaction without including the fluid solver in the predictor-corrector iterative loop. The overall algorithm is highly efficient and very attractive for simulating particulate flows with a wide range of density ratios on relatively coarse grids. Several cases are examined and the results are compared with reference data to demonstrate the simplicity and robustness of our method in particulate flow simulations. These cases include settling and buoyant particles and the interaction of two settling particles showing the kissing-drafting-tumbling phenomenon. Systematic verification studies show that our method is of second-order accuracy on very coarse grids and approaches fourth-order accuracy on finer grids.

scholarly journals CFD for Subcooled Flow Boiling: Parametric Variations

2013 ◽  
Vol 2013 ◽  
pp. 1-22 ◽  
Author(s):  
Roland Rzehak ◽  
Eckhard Krepper
Keyword(s):  
Heat Flux ◽  
Power Systems ◽  
Nuclear Power ◽  
Volume Fraction ◽  
Flow Boiling ◽  
Working Fluid ◽  
Model Parameters ◽  
Two Phase ◽  
Radial Profiles ◽  
Wide Range

We investigate the present capabilities of CFD for wall boiling. The computational model used combines the Euler/Euler two-phase flow description with heat flux partitioning. Very similar modeling was previously applied to boiling water under high pressure conditions relevant to nuclear power systems. Similar conditions in terms of the relevant nondimensional numbers have been realized in the DEBORA tests using dichlorodifluoromethane (R12) as the working fluid. This facilitated measurements of radial profiles for gas volume fraction, gas velocity, liquid temperature, and bubble size. Robust predictive capabilities of the modeling require that it is validated for a wide range of parameters. It is known that a careful calibration of correlations used in the wall boiling model is necessary to obtain agreement with the measured data. We here consider tests under a variety of conditions concerning liquid subcooling, flow rate, and heat flux. It is investigated to which extent a set of calibrated model parameters suffices to cover at least a certain parameter range.

Experimental Investigation of Liquid Entrainment in Gas in Horizontal Pipes

2009 ◽  
Author(s):  
I. Mantilla ◽  
L. Gomez ◽  
R. Mohan ◽  
O. Shoham ◽  
G. Kouba ◽  
...  
Keyword(s):  
Film Thickness ◽  
Liquid Film ◽  
Solution Viscosity ◽  
Gas Velocity ◽  
Flow Loop ◽  
Horizontal Pipes ◽  
Wave Characteristics ◽  
Liquid Entrainment ◽  
Wide Range ◽  
Superficial Gas Velocity

The objective of this project is to investigate experimentally the phenomena of liquid entrainment in gas in horizontal pipes. This report contains the results of an experimental study on wave characterization. Entrainment in annular flow in horizontal pipes has been studied experimentally. It has been found out that wave characteristics and entrainment fraction are strongly interrelated and must be utilized together in any related analysis. Two experimental facilities, 2-inch and 6-inch diameter, have been designed, constructed and utilized for entrainment measurements in stratified and annular horizontal flow. For the 2-inch flow loop, the range of superficial liquids velocities are 0.35 cm/s to 10 cm/s, and from 2 m/s to 80 m/s for the superficial gas velocities. For the 6-inch flow loop, the ranges of the superficial liquid velocities and superficial gas velocities are from 0.35 cm/s to 10 cm/s and from 2 m/s to 20 m/s, respectively. Appropriate instrumentation for entrainment (adjustable liquid film extractor) and liquid film characteristics (conductance probes and multi-channel conductivity meter) measurements have been developed and implemented. The effects of fluid properties on entrainment and wave characteristics have been studied by utilizing air-water-Butanol solution (surface tension effects) and air-water-Glycerin solution (viscosity effects). Simultaneous measurements have been carried out for both wave characteristics and entrainment for a wide range of flow conditions. Closure relationships have been developed based on the data for wave celerity, frequency, amplitude and spacing. The entrainment fraction has been normalized with the maximum entrainment fraction and correlated with the ratio of the superficial gas velocity to the superficial gas velocity at the onset. The wave amplitude (Δhw) normalized by the film thickness (hL) tends to values of Δhw / hL = 0.2 to 0.3 for high gas rates. The wave spacing (Lw) for air-water normalized by the mean film thickness (hL) exhibits a clear linear behavior with gas velocity, almost independent of the liquid velocity.

A Cost-Effective Modeling Approach for Simulating Phase Change and Flow Boiling in Microchannels

2015 ◽  
Author(s):  
Zhenhai Pan ◽  
Justin A. Weibel ◽  
Suresh V. Garimella
Keyword(s):  
Heat Transfer ◽  
Liquid Film ◽  
Phase Change ◽  
Volume Fraction ◽  
Flow Boiling ◽  
Thin Liquid Film ◽  
Cost Effective ◽  
Source Terms ◽  
Time Step ◽  
Two Phase

High-fidelity simulation of flow boiling in microchannels remains a challenging problem, but the increasing interest in applications of microscale two-phase transport highlight its importance. In this paper, a volume of fluid (VOF)-based flow boiling model is proposed with computational expense-saving features that enable cost-effective simulation of two-phase flow and heat transfer in realistic geometries. The vapor and liquid phases are distinguished using a color function which represents the local volume fraction of the tracked phase. Mass conservation is satisfied by solving the transport equations for both phases with a finite-volume approach. In order to predict phase change at the liquid-vapor interface, evaporative heat and mass source terms are calculated using a novel, saturated-interface-volume phase change model that fixes the interface at the saturation temperature at each time step to achieve stability. Numerical oscillation of the evaporation source terms is thus eliminated and a non-iterative time advancement scheme can be adopted to reduce computational cost. The reference frame is set to move with the vapor slug to artificially increase the local velocity magnitude in the thin liquid film region in the relative frame, which reduces the influence of numerical errors resulting from calculation of the surface tension force, and thus suppresses the development of spurious currents. This allows use of non-uniform meshes that can efficiently resolve high-aspect-ratio geometries and flow features and significantly reduces the overall numerical expense. The proposed model is used to simulate the growth of a vapor bubble in a heated 2D axisymmetric microchannel. The bubble motion, bubble growth rate, liquid film thickness, and local heat transfer coefficient along the wall are compared against previous numerical studies.

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