Modeling and direct numerical simulation of particle-laden turbulent flows

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Xu, Ying
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Shankar Subramaniam Glenn R. Luecke Theodore C. Heindel
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Mechanical Engineering

The objective of this study is to improve Eulerian-Eulerian models of particle-laden turbulent flow, especially the interphase TKE transfer term and the dissipation rate in Eulerian-Eulerian models. We begin by understanding the behavior of two existing models---one proposed by Simonin (1996b), and the other by Ahmadi (1989)---in the limiting case of statistically homogeneous particle-laden turbulent flow. The decay of particle-phase and fluid-phase turbulent kinetic energy (TKE) is compared with point-particle direct numerical simulation data. Even this simple flow poses a significant challenge to current models, which have difficulty in reproducing important physical phenomena such as the variation of turbulent kinetic energy decay with increasing particle Stokes number. The model for the interphase TKE transfer timescale is identified as one source of this difficulty. A new model for the interphase transfer timescale is proposed that accounts for the interaction of particles with a range of fluid turbulence scales. A new multiphase turbulence model---the Equilibration of Energy Model (EEM)---is proposed, which incorporates this multiscale interphase transfer timescale. The model for Reynolds stress in both fluid and particle phases is derived in this work. The new EEM model is validated in decaying homogeneous particle-laden turbulence, and in particle-laden homogeneous shear flow. The particle and fluid TKE evolution predicted by the EEM model correctly reproduce the trends with important non-dimensional parameters, such as particle Stokes number.;The interphase transfer of turbulent kinetic energy (TKE) is an important term that affects the evolution of TKE in fluid and particle phases in particle-laden turbulent flow. In this work, we show that the interphase TKE transfer terms must obey a mathematical constraint, which in the limiting case of statistically homogeneous flow with zero mean velocity in both phases, requires these terms be equal and opposite. In the single-point statistical approach called the two-fluid theory, the interphase TKE transfer terms are unclosed and need to be modeled. Multiphase turbulence models that satisfy this constraint of conservative interphase TKE transfer admit a term-by-term comparison with true direct numerical simulations (DNS) that enforce the exact velocity boundary condition on each particle's surface. Analysis of three models reveals that not all models satisfy the requirement of conservative interphase TKE transfer. DNS that invoke the point-particle assumption also do not obey this principle of conservative interphase TKE transfer, and this precludes comparison of model predictions of TKE budgets in each phase with point-particle DNS. This study motivates the development of multiphase turbulence models based on the insights revealed by this analysis, leading to a meaningful comparison of TKE budgets with true DNS.;The immersed boundary method has the ability to simulate the irregular shape objects on the uniform Cartesian grids. In this work, the true DNS using the immersed boundary method is developed, and the drag force coefficient obtained from DNS is verified with laminar flow past a stationary sphere and a single sphere in the homogeneous turbulence. However the memory requirement of the immersed boundary method is found to be quite high and the parallelization of the immersed boundary method is necessary. The idea of the domain decomposition is used to parallelize the numerical solver for the immersed boundary method in this work, and the performance is studied for the resolution of 512 x 256 x 256.;The parallel immersed boundary method is used to study the effects of particle clusters on fluid phase turbulence. This study is inspired by the experiments of Moran and Glicksman Moran and Glicksman (2003a), where the fluid phase fluctuations are found to be enhanced at the high particle concentration, where particle clusters usually form in the CFB. In the DNS study, we use two types of random particle configurations and study the fluid phase TKE in the fixed bed of spheres. The uniform random particle configuration is denoted as MHC and the one with clusters is denoted as GCG in this study. The DNS study shows that the fluid phase TKE is enhanced with GCG along the streamwise direction in the fixed bed. For both MHC and GCG, the fluid phase Reynolds stress is found to be anisotropic. The 2D energy spectra studies show that the energy of GCG at lower wavenumber kappa < 10 is higher than that of MHC. The cutoff wavenumber corresponds to the cluster size estimated using the radius of gyration. After examining the dissipation, and interphase TKE transfer term in the transport equation for Reynolds stress, it is noted that the dissipation is reduced in the second half of the fixed bed for GCG. (Abstract shortened by UMI.)

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Tue Jan 01 00:00:00 UTC 2008