Modeling and Simulation of two-phase flows
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Abstract
The primary objective of this study is to improve the predictive
capabilities of two-phase flow simulations that solve for average
equations, such as Lagrangian-Eulerian (LE) and Eulerian-Eulerian
simulations. The predictive capabilities of LE and EE simulations
depend both on the numerical accuracy and on the accuracy of models
for the fluid--particle and particle-particle interaction terms. In
the first part of this study, a high fidelity ‘true’ DNS approach
based on immersed boundary method (IBM) is developed to propose
accurate models for fluid--particle terms, such as interphase momentum
transfer, and also interphase heat and mass transfer, by solving for
steady flow and scalar transport past homogeneous assemblies of fixed
particles. IBM is shown to be a robust tool for simulating gas--solids
flow and does not suffer from the limitations of lattice Boltzmann
method (LBM): (1) compressibility errors with increasing Reynolds
number; (2) calibration of hydrodynamic radius; (3) non-trivial to
extend to non-isothermal systems. In the Stokes regime, average
Nusselt number from scalar IBM simulations is in reasonable agreement
with the frequency response measurements of Gunn and Desouza (1974) and
free surface model of Pfeffer and Happel (1964), but differs by as much as
300 % from the widely used heat and mass transfer correlation
of Gunn (1978), which is attributed to the unjustified assumption
of negligible axial diffusion in Stokes flow regime made by Gunn. At
higher Reynolds numbers, scalar IBM results are far from Gunn's
correlations but in reasonable agreement with other experimental
data. A correlation is proposed for heat and mass transfer as function
of solid volume fraction and Reynolds for a particular value of
Prandtl/Sherwood number equal to 0.7.
In the second part of this study, the numerical accuracy of LE
simulations is investigated because LE simulations are very frequently
used to verify EE simulations, and as a benchmark in the development
of new simulation techniques for two--phase flows, such as the recent
quadrature method of moments QMOM (Fox, 2008). Accurate
calculation of the interphase transfer terms in LE simulations is
crucial for quantitatively reliable predictions. Through a series of
static test problems that admit an analytical form for the interphase
momentum transfer term, it is shown that accurate estimation of the
mean interphase momentum transfer term using certain interpolation
schemes requires very high numerical resolution in terms of the number
of particles and number of multiple independent
realizations. Traditional LE (TLE) simulations, that use real
particles or computational particles having constant statistical
weight, fail to yield numerically--converged solutions due to high
statistical error in regions with few particles. We propose an
improved LE simulation (ILE) method that remedies the above limitation
of TLE simulations and ensures numerically converged LE simulations.