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.

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

2003 ◽  
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.

Capturing the Pinch-Off of Liquid Jets by the Level Set Method

2003 ◽  
Vol 125 (5) ◽  
pp. 922-927 ◽  
Author(s):  
Y. Pan ◽  
K. Suga
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Density Ratio ◽  
Three Dimensional ◽  
Liquid Jets ◽  
Surface Phenomena ◽  
Two Phase ◽  
Dynamic Simulations ◽  
Fine Grid ◽  
Radial Profiles

Full three-dimensional dynamic simulations of forced liquid jets flowing into and pinching off in ambient of another liquid were performed by using the level set method for tracking the interface between the immiscible materials. The simulations were performed for jets with viscosity ratios between the inner and outer fluids of 0.17 and 1.7. The jets were forced at Strouhal number of 4.0. The Reynolds, Froud, and Bond numbers based on the conditions at the nozzle exit were 34–35, 0.2, and 6.1, for both cases. The numerical results are compared with the data from the experiment made by Longmire et al. (2001). The comparisons were made for (1) flow images of one complete pinch-off cycle and (2) the axial and radial profiles of the instantaneous velocities around the region of jet disintegration. The feasibility and accuracy of using the level set method in multiphase problems involving interface breakup/coalescence is explored and accessed by simulating such relatively low speed, low density-ratio two-phase flows. Although the level set method is quite promising, due to the surface tension model, it requires very fine grid resolution (the Weber number based on the grid spacing is smaller than 10−2) even for capturing the laminar surface phenomena.

Simulation of Two-Phase Flow Using Conservative Level-Set Method Without Re-Initialization Process

2010 ◽  
Author(s):  
Rabie El Otmani ◽  
M’hamed Boutaous ◽  
Hamda Benhadid
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Two Phase Flow ◽  
Mass Conservation ◽  
Correction Method ◽  
Phase Flow ◽  
Two Phase ◽  
Classical Level ◽  
Level Set Function ◽  
Penalty Factor

Multiphase flows are generated in several industrial domains. The numerical simulation of such flows need to have an exact tracking of the different phase interfaces. The level set method is one of the simplest methods used to study the moving front of the flow. But it is known that this method generates a non mass conservation, and do not respect the uniformity of the signed distance function. Several corrections are usually proposed to solve these problems when using the Level set method. In this paper, a novel two steps correction method is proposed in order to guarantee the flow mass conservation and the exact shape of the flow front. The first step concerns the correction of the mass loss. It consists to add in the transport equation, a penalty or constraint term, built to force the velocity field to satisfy the mass balance or to preserve the conservative property. This term is multiplied to an adjustable penalty factor (β). The second step consists to impose that the isocontours of the level set function (φ) always respect the same distance. With this way, the costly reinitialization procedure is eliminated. The performance of the method is demonstrated and validated using several cases involving two-phase flow. The numerical experiments show that the accuracy and performances of our method is drastically improved compared to other methods. The approach will then applied to track an air-liquid interface in a case of an air bubble moving in a constant volume of liquid. In this case, the classical level set method reveals to be not conservative. A solution is then proposed in order to introduce a correction. To do, Navier-Stokes, continuity and energy equations are coupled to describe the flow and its thermal behavior. A finite element method is used to solve the equations. The solution is also verified by solving the dam-break problem, and bubble rising in water. Good agreements with referenced solutions are demonstrated for all tow investigated problems.

A Level Set Method for Simulation of Coalescence of Droplets

2005 ◽  
Author(s):  
A. Salih ◽  
S. Ghosh Moulic
Keyword(s):  
Surface Tension ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Surface Tension Force ◽  
Tension Force ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Level Set Function ◽  
Set Function

In the present paper, we discuss a numerical method based on the level set algorithm to simulate two-phase fluid flow systems. Surface tension force at the fluid interface is implemented through the CSF model of Brackbill et al. [1]. The incompressible Navier-Stokes equations were solved on a staggered grid using an explicit projection method. A fifth-order WENO [2] scheme was used for advancing the level set function. We improved the implementation of WENO scheme by staggering the level set function. The Navier-Stokes part of the code was validated by computing the standard lid-driven cavity flow and the free surface part of the code was validated by advecting the interface in a prescribed velocity field. The Young-Laplace law for a static drop has been verified to validate the implementation of surface tension force. We simulated the coalescence of two drops under zero-gravity condition and evaluated the mass conservation property of the level set method.

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.

scholarly journals Computing three-dimensional two-phase flows with a mass-conserving level set method

2008 ◽  
Vol 11 (4-6) ◽  
pp. 221-235 ◽  
Author(s):  
S. P. van der Pijl ◽  
A. Segal ◽  
C. Vuik ◽  
P. Wesseling
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Three Dimensional ◽  
Two Phase Flows ◽  
Two Phase

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.

Numerical Simulation of Breaking Waves Using a Level Set Method

2002 ◽  
Author(s):  
Pablo Go´mez ◽  
Julio Herna´ndez ◽  
Joaqui´n Lo´pez ◽  
Fe´lix Faura
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Stokes Equations ◽  
Numerical Study ◽  
Operating Conditions ◽  
Breaking Wave ◽  
Level Set Function ◽  
Set Function ◽  
The Impact

A numerical study of the initial stages of wave breaking processes in shallow water is presented. The waves considered are assumed to be generated by moving a piston in a two-dimensional channel, and may appear, for example, in the injection chamber of a high-pressure die casting machine under operating conditions far from the optimal. A numerical model based on a finite-difference discretization of the Navier-Stokes equations in a Cartesian grid and a second-order approximate projection method has been developed and used to carry out the simulations. The evolution of the free surface is described using a level set method, with a reinitialization procedure of the level set function which uses a local grid refinement near the free surface. The ability of different algorithms to improve mass conservation in the reinitialization step of the level set function has been tested in a time-reversed single vortex flow. The results for the breaking wave profiles show the flow characteristics after the impact of the first plunging jet onto the wave’s forward face and during the subsequent splash-up.

Numerical Simulation of Filling Process in Vertical Centrifugal Casting Based on Projection-Level Set Method

2011 ◽  
Vol 314-316 ◽  
pp. 364-368 ◽  
Author(s):  
Jun Zhang ◽  
Jian Xin Zhou ◽  
Ming Yuan Zhang ◽  
Sheng Yong Pang ◽  
Dun Ming Liao ◽  
...  
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Centrifugal Casting ◽  
Three Dimensional ◽  
Thin Wall ◽  
Filling Process ◽  
Two Phase ◽  
Numerical Result ◽  
Complex Part ◽  
Mould Filling

A three-dimensional incompressible two phase flow model of vertical centrifugal casting is proposed to simulate the fluid flow of mould filling process accurately and effectively. The Projection method is adopted to solve the govern equation of the flow field, and the Level Set method is used to capture the free surface. The mold filling of a complex part with thin-wall is simulated. The numerical result shows that the Projection-Level Set method could simulate centrifugal casting effectively. The present study has a guiding significance to the production of vertical centrifugal casting.

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