a numerically convergent lagrangian–eulerian simulation method for dispersed two-phase flows

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International Journal of Multiphase Flow

Article in Press, Corrected Proof- Note to users

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doi:10.1016/j.ijmultiphaseflow.2008.12.004

Copyright 2009 Elsevier Ltd All rights reserved.

A numerically convergent Lagrangian

Eulerian simulation method for dispersed

two-phase flows

R. Garga,

, C. Narayananb,

and S. Subramaniama, ,

aDepartment of Mechanical

Engineering, Center for

Computational Thermo-fluids

Research, Iowa State

University, Ames, IA 50011, USA

bASCOMP GmbH, Technoparkstrasse 1, 8005 Zurich, Switzerland

Received 29 May 2008; revised 20 November 2008; accepted 21

December 2008. Available online 14 January 2009.

Abstract

In LagrangianEulerian (LE) simulations of two-way coupled

particle-laden flows, the dispersed phase is represented either by

real particles or by computational particles. In traditional LE (TLE)

simulations, each computational particle is assigned a constant

statistical weight, which is defined as the expected number of real

particles represented by a computational particle. If the spatial

distribution of particles becomes highly non-uniform due to

particlefluid or particleparticle interactions, then TLE simulations

fail to yield numerically converged solutions due to high statistical

error in regions with few particles. In this work, a particle-laden

lid-driven cavity flow is solved on progressively refined grids todemonstrate the inability of TLE simulations to yield numerically

converged estimates for the mean interphase momentum transfer

term. We propose an improved LE simulation (ILE) method that

remedies the above limitation of TLE simulations. In the ILE method,

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the statistical weights are evolved such that the same physical

problem is simulated, but the number density of computational

particles is maintained near-uniform throughout the simulation,

resulting in statistical error that remains nearly constant with grid

refinement. The evolution of statistical weights is rigorously justified

by deriving the consistency conditions arising from the requirement

that the resulting computational ensemble correspond to a statistical

description of the same physical problem with real particles. The

same particle-laden lid-driven cavity flow is solved on progressively

refined grids to demonstrate the ability of ILE simulation to achieve

numerically converged estimates for the mean interphase momentum

transfer term. The accuracyof the ILE method is quantified using a

test problem that admits an analytical solution for the mean

interphase momentum transfer term. In order to improve the accuracy

of numerical estimates of the mean interphase momentum transfer

term, an improved estimator is proposed to replace the conventional

estimator. The improved estimator results in more accurate estimates

that converge faster than those obtained using the conventional

estimator. The ILE simulation method along with the improved

estimator is recommended for accurate and numerically convergent

LE simulations.

Article Outline

1. Introduction

2. Governing equations

3. Statistical description of dispersed phase: computational particles

3.1. Traditional LE simulation (TLE): equally weighted

particles

3.2. Improved LE simulation (ILE): unequal and evolving

weights

3.2.1. Consistency requirements

3.2.2. Computational particle number density control algorithm4. Numerical estimation of mean interphase momentum transfer term

5. Lid-driven cavity flow problem

6. Test problem

6.1. Computation setup

7. Results

8. Discussion

9. Conclusions

Acknowledgements

References

Corresponding author.

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Article in Press, Corrected Proof- Note to users


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a numerically convergent lagrangian–eulerian simulation method for dispersed two-phase flows

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