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.