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.

A volume-amending method to improve mass conservation of level set approach for incompressible two-phase flows

2008 ◽  
Vol 51 (11) ◽  
pp. 1132-1140 ◽  
Author(s):  
XiangYang Li ◽  
YueFa Wang ◽  
GengZhi Yu ◽  
Chao Yang ◽  
ZaiSha Mao
Keyword(s):  
Level Set ◽  
Mass Conservation ◽  
Two Phase Flows ◽  
Two Phase ◽  
Level Set Approach

Two-phase flow stability analysis using a level set approach

2017 ◽  
Author(s):  
Mamta Raju Jotkar ◽  
Daniel Rodriguez ◽  
Bruno Marins Soares
Keyword(s):  
Stability Analysis ◽  
Level Set ◽  
Two Phase Flow ◽  
Flow Stability ◽  
Phase Flow ◽  
Two Phase ◽  
Level Set Approach

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.

scholarly journals Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Yunfeng Dai ◽  
Zhifang Zhou ◽  
Jin Lin ◽  
Jiangbo Han
Keyword(s):  
Crude Oil ◽  
Level Set Method ◽  
Level Set ◽  
Two Phase Flow ◽  
Volume Fraction ◽  
Contact Angles ◽  
Immiscible Fluids ◽  
Water Volume ◽  
Phase Flow ◽  
Two Phase

To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water) flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.

scholarly journals The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Puyang Gao
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Level Set ◽  
Newtonian Fluid ◽  
Mass Conservation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Correction Technique

In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

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.

A Level Set Approach to 3D Mold Filling of Newtonian Fluids

2003 ◽  
Author(s):  
Thomas A. Baer ◽  
David R. Noble ◽  
Rekha R. Rao ◽  
Anne M. Grillet
Keyword(s):  
Level Set ◽  
Complex Geometry ◽  
Mass Conservation ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Three Dimension ◽  
Interfacial Boundary ◽  
Simulation And Experiment ◽  
Level Set Approach ◽  
Filling Problem

Filling operations, in which a viscous fluid displaces a gas in a complex geometry, occur with surprising frequency in many manufacturing processes. Difficulties in generating accurate models of these processes involve accurately capturing the interfacial boundary as it undergoes large motions and deformations, preventing dispersion and mass-loss during the computation, and robustly accounting for the effects of surface tension and wetting phenomena. This paper presents a numerical capturing algorithm using level set theory and finite element approximation. Important aspects of this work are addressing issues of mass-conservation and the presence of wetting effects. We have applied our methodology to a three-dimension model of a complicated filling problem. The simulated results are compared to experimental flow visualization data taken for filling of UCON oil in the identical geometry. Comparison of simulation and experiment indicates that the simulation conserved mass adequately and the simulated interface shape was in approximate agreement with experiment. Differences seen were largely attributed to inaccuracies in the wetting line model.

Sign in / Sign up

Export Citation Format

Share Document