scholarly journals A Lagrangian Approach for the Incompressible Navier-Stokes Equations with Variable Density

2012 ◽  
Vol 65 (10) ◽  
pp. 1458-1480 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha
Keyword(s):  
Stokes Equations ◽  
Variable Density ◽  
Lagrangian Approach ◽  
Navier Stokes ◽  
Navier Stokes Equations

Discussion on Clustering Effects in Vertical Gas-Particle Flows

2000 ◽  
Author(s):  
Eivind Helland ◽  
Rene Occelli ◽  
Lounes Tadrist
Keyword(s):  
Gas Phase ◽  
Stokes Equations ◽  
Lagrangian Approach ◽  
Inelastic Collisions ◽  
Navier Stokes ◽  
Coupling Term ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Drag Forces ◽  
Particle Flows

Abstract Simulations of 2D gas-particle flows in a vertical riser using a mixed Eulerian-Lagrangian approach are addressed. The model for the interstitial gas phase is based on the Navier-Stokes equations for two-phase flow with a coupling term between the gas and solid phases due to drag forces. The motion of particles is treated by a Lagrangian approach and the particles are assumed to interact through binary, instantaneous, non-frontal, inelastic collisions with friction. In this paper different particle clustering effects in the gas-particle flow is investigated.

NUMERICAL ANALYSIS OF A TWO PHASE FLOW MODEL

2012 ◽  
Vol 09 (03) ◽  
pp. 1250036 ◽  
Author(s):  
MOHAMED ABDELWAHED ◽  
MOHAMED AMARA
Keyword(s):  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Discretization ◽  
Variable Density ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Quality Of Water ◽  
Coupling Characteristics

Due to ever increasing water demand, the preservation of water quality is becoming a very important issue. Eutrophication is amongst the particular problems threatening the quality of water. This paper begins with presenting a mathematical model for aeration process in lake used to combat water eutrophication. Two phases are numerically simulated to study the injected air effect on water by using a corrected one phase model described by Navier–Stokes equations with variable density and viscosity representing the mixture. This model is numerically studied by coupling characteristics scheme for time discretization and mixed finite element method for space approximation. An error estimates in space and time for the velocity are obtained. Numerical results are given firstly in support of the mathematical analysis and secondly to simulate a real application case of the studied problem.

scholarly journals Dynamics of a contracting fluid compound filament with a variable density ratio

2021 ◽  
Vol 24 (2) ◽  
pp. first
Author(s):  
Truong V. Vu ◽  
Vinh T. Nguyen ◽  
Phan H. Nguyen ◽  
Nang X. Ho ◽  
Binh D. Pham ◽  
...  
Keyword(s):  
Interfacial Tension ◽  
Stokes Equations ◽  
Weighting Function ◽  
Density Ratio ◽  
Variable Density ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Front Tracking Method ◽  
Fixed Grid ◽  
Eulerian Grid

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

An Eulerian-Lagrangian Approach for the Numerical Simulation and Visualization of Two-Dimensional Fluidized Beds

2002 ◽  
Author(s):  
Ph. Traore´ ◽  
C. Herbreteau ◽  
R. Bouard
Keyword(s):  
Stokes Equations ◽  
Distinct Element ◽  
Fluid Phase ◽  
Lagrangian Approach ◽  
Lagrangian Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Type Method ◽  
Contact Points ◽  
Mechanical Models

This paper deals with an Eulerian-Lagrangian model for dispersed multiphase flow in which all the interactions of any kind are taking into account. The fluid phase and particles interactions are two way coupled while all the collisions between the particles or between the particles and the walls are calculated. The Navier-Stokes equations (fluid phase continuity and momentum equations including exchange from the particle to the fluid is modeled to simulate the effect of the presence of the particles in the fluid phase) are solved on a staggered Eulerian grid by a finite volume discretisation type method. The originality of the Lagrangian approach used here for the particles motion, lies in the way of managing the collisions which are calculated using simple mechanical models such as a spring, dashpot and friction slider at the contact points following the Distinct Element Method DEM [1]. In the Lagrangian stage, motion’s calculation of each discrete particle including collisions effects is generally time consuming. In the context of this paper we shall show how to optimized the contacts tracking algorithm in an efficient way to increase significantly the capability of the DEM.

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