| 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 bench mark 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. |
