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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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International Journal of Multiphase Flow
Article in Press, Corrected Proof- Note to users
enceDirect - International Journal of Multiphase Flow : A numericall... http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4...
3 24/2/2009 20:08