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.

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.

Parallelized numerical modeling of the interaction of a solid object with immiscible incompressible two-phase fluid flow

2017 ◽  
Vol 34 (3) ◽  
pp. 709-724 ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
R. Nikbakhti ◽  
Amirreza Ghasemi ◽  
Faraz Hedayati ◽  
Amir Malvandi
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
High Density ◽  
Immersed Boundary ◽  
Immersed Boundary Methods ◽  
Solid Object ◽  
Computational Tool ◽  
Two Phase ◽  
Content Type

Purpose A numerical method is developed to capture the interaction of solid object with two-phase flow with high density ratios. The current computational tool would be the first step of accurate modeling of wave energy converters in which the immense energy of the ocean can be extracted at low cost. Design/methodology/approach The full two-dimensional Navier–Stokes equations are discretized on a regular structured grid, and the two-step projection method along with multi-processing (OpenMP) is used to efficiently solve the flow equations. The level set and the immersed boundary methods are used to capture the free surface of a fluid and a solid object, respectively. The full two-dimensional Navier–Stokes equations are solved on a regular structured grid to resolve the flow field. Level set and immersed boundary methods are used to capture the free surface of liquid and solid object, respectively. A proper contact angle between the solid object and the fluid is used to enhance the accuracy of the advection of the mass and momentum of the fluids in three-phase cells. Findings The computational tool is verified based on numerical and experimental data with two scenarios: a cylinder falling into a rectangular domain due to gravity and a dam breaking in the presence of a fixed obstacle. In the former validation simulation, the accuracy of the immersed boundary method is verified. However, the accuracy of the level set method while the computational tool can model the high-density ratio is confirmed in the dam-breaking simulation. The results obtained from the current method are in good agreement with experimental data and other numerical studies. Practical/implications The computational tool is capable of being parallelized to reduce the computational cost; therefore, an OpenMP is used to solve the flow equations. Its application is seen in the following: wind energy conversion, interaction of solid object such as wind turbine with water waves, etc. Originality/value A high efficient CFD approach method is introduced to capture the interaction of solid object with a two-phase flow where they have high-density ratio. The current method has the ability to efficiently be parallelized.

Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts

1992 ◽  
Vol 114 (4) ◽  
pp. 936-943 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Published Data ◽  
Circular Duct ◽  
Uniform Wall Temperature ◽  
Wide Range

This paper numerically investigates the effects of buoyancy on fully developed laminar flow in a curved duct with an elliptic cross section. The flow of Newtonian fluids is assumed steady in terms of Boussinesq approximation. The curved elliptic duct is subjected to thermal boundary conditions of axially uniform heat flux and peripherally uniform wall temperature. The numerically generated boundary-fitted coordinate system is applied to discretize the solution domain of the elliptic duct, and the Navier-Stokes equations and the energy equation, including the curvature ratio, are solved by use of the control volume-based finite difference method. The solution covers a wide range of curvature ratios, and Dean and Grashof numbers. The results presented are displayed graphically and in tabular form to illustrate the buoyancy effect. It is further shown that buoyancy acts to increase both the Nusselt number and the friction factor and changes the distribution of the velocity and the temperature. The results for the curved circular duct with and without buoyancy are compared with the data available in the open literature for all cases. Also compared with the published data are the results of laminar flow in a curved elliptic duct, and very good agreement is obtained.

NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

2007 ◽  
Vol 18 (04) ◽  
pp. 536-545 ◽  
Author(s):  
NAOKI TAKADA ◽  
AKIO TOMIYAMA
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Phase Field Modeling ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Field Modeling ◽  
High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

NUMERICAL SIMULATION OF RAYLEIGH–TAYLOR INSTABILITY BASED ON AN IMPROVED PARTICLE LEVEL SET METHOD

2014 ◽  
Vol 11 (04) ◽  
pp. 1350094 ◽  
Author(s):  
HUI TIAN ◽  
GUOJUN LI ◽  
XIONGWEN ZHANG
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Density Ratio ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Wide Range ◽  
Particle Level ◽  
Rayleigh Taylor Instability ◽  
Particle Level Set Method

An improved particle correction procedure for particle level set method is proposed and applied to the simulation of Rayleigh–Taylor instability (RTI) of the incompressible two-phase immiscible fluids. In the proposed method, an improved particle correction method is developed to deal with all the relative positions between escaped particles and cell corners, which can reduce the disturbance arising in the distance function correction process due to the non-normal direction movement of escaped particles. The improved method is validated through accurately capturing the moving interface of the Zalesak's disk. Furthermore, coupled with the projection method for solving the Navier–Stokes equations, the time-dependent evolution of the RTI interface over a wide range of Reynolds numbers, Atwood numbers and Weber numbers are numerically investigated. A good agreement between the present results and the existing analytical solutions is obtained and the accuracy of the proposed method is further verified. Moreover, the effects of control parameters including viscosity, density ratio, and surface tension coefficient on the evolution of RTI are analyzed in detail, and a critical Weber number for the development of RTI is found.

An Improved Three-Dimensional Level Set Method for Gas-Liquid Two-Phase Flows

2004 ◽  
Vol 126 (4) ◽  
pp. 578-585 ◽  
Author(s):  
Hiroyuki Takahira ◽  
Tomonori Horiuchi ◽  
Sanjoy Banerjee
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Interpolation Method ◽  
Density Ratio ◽  
Three Dimensional ◽  
Mass Conservation ◽  
Staggered Grid ◽  
Two Phase ◽  
Level Set Function

For the present study, we developed a three-dimensional numerical method based on the level set method that is applicable to two-phase systems with high-density ratio. The present solver for the Navier-Stokes equations was based on the projection method with a non-staggered grid. We improved the treatment of the convection terms and the interpolation method that was used to obtain the intermediate volume flux defined on the cell faces. We also improved the solver for the pressure Poisson equations and the reinitialization procedure of the level set function. It was shown that the present solver worked very well even for a density ratio of the two fluids of 1:1000. We simulated the coalescence of two rising bubbles under gravity, and a gas bubble bursting at a free surface to evaluate mass conservation for the present method. It was also shown that the volume conservation (i.e., mass conservation) of bubbles was very good even after bubble coalescence.

Bubble Dynamics From Artificial Nucleation Sites During Subcooled Pool Boiling

2009 ◽  
Author(s):  
Xipeng Lin ◽  
David M. Christopher ◽  
Yanshen Li ◽  
Hui Li
Keyword(s):  
High Speed ◽  
Bubble Dynamics ◽  
Stokes Equations ◽  
Liquid Pool ◽  
Numerical Results ◽  
Bottom Surface ◽  
Heating Rates ◽  
Bubble Generation ◽  
Vof Model ◽  
Nucleation Sites

The bubble dynamics of ethanol vapor bubbles growing, coalescing and condensing in a subcooled ethanol liquid pool were investigated experimentally and numerically for a range of subcoolings and heating rates. The bubbles were generated from an artificial pair of nucleation sites made of microscale tubes mounted flush with the bottom surface of the liquid pool with the vapor supplied by a vapor generator. Observations of the bubble generation with a high speed camera show the various coalescence modes with no coalescence at low heating rates and high subcoolings and horizontal and/or vertical coalescence depending on the heating rate and subcooling. At very low subcoolings, the bubbles grew quite large with various types of coalescence. The numerical results using solutions of the Navier-Stokes equations with the VOF model and using a simplified one dimensional model also describe the bubble dynamics and the conditions for coalescence. The numerical results suggest that the condensation rate at the interface is probably much higher than predicted by the model due to significant convection in the liquid pool or due to significant disturbance of the interface by the vapor jet entering the bubble.

scholarly journals Simulation and Experimental Research on a Gas Liquid Separator with Rotary Impeller

2020 ◽  
Vol 316 ◽  
pp. 03001
Author(s):  
Baihui Wang ◽  
Yingbin Li ◽  
Mingjun Deng ◽  
Baolu Shi ◽  
Wenjin Shang ◽  
...  
Keyword(s):  
Life Support ◽  
Environmental Control ◽  
Simulation Method ◽  
Two Phase ◽  
Design And Optimization ◽  
Manned Spacecraft ◽  
Vof Model ◽  
Wide Range ◽  
Two Parameters ◽  
Liquid Separator

Gas-liquid separation technology under microgravity is the basis for various gas and liquid treatments on a manned spacecraft, which has a wide range of applications in Environmental Control and Life Support System. Dynamic gas-liquid separator is commonly used for the separation of gas-liquid two-phase flow, which has two essential performance parameters called liquid outlet pressure and separating efficiency. Predicting these two parameters accurately under a specific structure has guiding significance for design and application of the dynamic gas-liquid separator. In this study, CFD simulations were conducted using the Volume of Fluid (VOF) model at steady state conditions. In addition, experiments were designed to verify the accuracy of numerical results. Finally, the performance of the separator under microgravity was predicted. It is showed that the simulation method can be utilized to determine the transport performance of dynamic gas-liquid separator, which has significant value in design and optimization.

scholarly journals Numerical Investigation of Water Entry of Half Hydrophilic and Half Hydrophobic Spheres

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Sun Zhao ◽  
Cao Wei ◽  
Wang Cong
Keyword(s):  
Stokes Equations ◽  
Density Ratio ◽  
Surface Force ◽  
Simulation Method ◽  
Numerical Approach ◽  
Water Entry ◽  
Numerical Results ◽  
Navier Stokes ◽  
Force Coefficient ◽  
Navier Stokes Equations

A numerical simulation to investigate the water entry of half-half sphere which is hydrophobic on one hemisphere and hydrophilic on the other is performed. Particular attention is given to the simulation method based on solving the Navier-Stokes equations coupled with VOF (volume of fluid) method and CSF (continuum surface force) method. Numerical results predicted experimental results, validating the suitability of the numerical approach to simulate the water entry problem of sphere under different wetting conditions. Numerical results show that the water entry of the half-half sphere creates an asymmetric cavity and “cardioid” splash, causing the sphere to travel laterally from the hydrophobic side to the hydrophilic side. Further investigations show that the density ratio and mismatch of asymmetric in wetting condition affect the trajectory, velocity, and acceleration of the half-half sphere during water entry. In addition, the total hydrodynamic force coefficient is investigated as a result of the forces acting on the sphere during water entry dictated by the cavity formation.

scholarly journals An Assessment of Suitability of a SIMPLE VOF/PLIC-CSF Multiphase Flow Model for Rising Bubble Dynamics

2012 ◽  
Vol 4 (1) ◽  
pp. 65-83 ◽  
Author(s):  
S. Senthil Kumar ◽  
Y. M. C. Delauré
Keyword(s):  
Bubble Dynamics ◽  
Stokes Equations ◽  
Piecewise Linear ◽  
Navier Stokes ◽  
Simple Type ◽  
Two Phase ◽  
Simple Method ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Fluid Properties

A Volume of Fluid (VOF) – Youngs' model for the solution of an incompressible immiscible two-phase flows is presented. The solver computes the flow field by solving the family of Navier Stokes equations on a fixed (Eulerian) Staggered Cartesian grid using the Finite Volume formulation of Semi-Implicit Pressure Linked Equation (SIMPLE) method and tracks the position of interface between two fluids with different fluid properties by Piecewise Linear Interface Construction (PLIC) Method. The suitability of the SIMPLE type implementation is assessed by investigating the dynamics of free rising bubbles for different fluid properties and flow parameters. The results obtained with the present numerical method for rising bubbles in viscous liquids are compared with reported numerical and experimental results.

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