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.

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.

Influence of Inertia Terms on High Pressure Gap Flow Applications in Hydraulics

2019 ◽  
Author(s):  
Felix Fischer ◽  
Andreas Rhein ◽  
Katharina Schmitz
Keyword(s):  
High Pressure ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Fluid Phase ◽  
Simulation Models ◽  
Rigid Bodies ◽  
Navier Stokes ◽  
Dependent Manner ◽  
Fluid Inertia ◽  
Navier Stokes Equations

Abstract Hydraulic pumps, which reach pressures up to 3000 bar, are often realized as plunger-piston type pumps. In the case of a common-rail pump for diesel injection systems, the plunger is driven by a cam-tappet construction and the contact during suction stroke is maintained by a helical spring. Many hydraulic piston-based high pressure pumps include gap seals, which are formed by small clearances between the two surfaces of the piston and the bushing. Usually the gap height is in the magnitude of several micrometers. Typical radial gaps are between 0.5 and 1 per mil of the nominal diameter. These gap seals are used to allow and maintain pressure build up in the piston chamber. When the gap is pressurized, a special flow regime is reached. For the description of this particular flow the Reynolds equation, which is a simplification of the Navier-Stokes equations, can be used as done in the state of the art. Furthermore, if the pressure in the gap is high enough — 500 bar and above — fluid-structure interactions must be taken into account. Pressure levels above 1500 or 2000 bar indicate the necessity for solving the energy equation of the fluid phase and the rigid bodies surrounding it. In any case, the fluid properties such as density and viscosity, have to be modelled in a pressure dependent manner. This means, a compressible flow is described in the sealing gap. Viscosity changes in magnitudes while density remains in the same magnitude, but nevertheless changes about 30 %. These facts must be taken into account when solving the Reynolds equation. In this paper the authors work out that the Reynolds equation is not suitable for every piston-bushing gap seal in hydraulic applications. It will be shown that remarkable errors are made, when the inertia terms in the Navier-Stokes equations are neglected, especially in high pressure applications. To work out the influence of the inertia terms in these flows, two simulation models are built up and calculated for the physical problem. One calculates the compressible Reynolds equation neglecting the fluid inertia. The other model, taking the fluid inertia into account, calculates the coupled Navier-Stokes equations on the same geometrical boundaries. Here, the so called SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm is used. The discretization is realized with the Finite Volume Method. Afterwards, the solutions of both models are compared to investigate the influence of the inertia terms on the flow in these specific high pressure applications.

Swirling Laminar Pipe Flow of Suspensions

1973 ◽  
Vol 40 (2) ◽  
pp. 331-336 ◽  
Author(s):  
S. K. Tung ◽  
S. L. Soo
Keyword(s):  
Pipe Flow ◽  
Stokes Equations ◽  
Fluid Phase ◽  
Navier Stokes ◽  
Swirl Ratio ◽  
Particulate Phase ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Flow Reynolds Number ◽  
Laminar Pipe Flow

Vortex pipe flow of suspensions with laminar motion in the fluid phase is treated. The pipe consists of two smoothly joined sections, one stationary and the other rotating with a constant angular velocity. The flow properties of the fluid phase are determined by solving the complete Navier-Stokes equations numerically. The governing parameters are the flow Reynolds number and swirl ratio. Subsequent numerical solution to the momentum equations governing the particulate phase provides for both particle velocity and concentration distributions.

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