THESIS
2023
1 online resource (xxi, 155 pages) : illustrations (chiefly color)
Abstract
Developing a unified numerical scheme capable of accurately modeling flow physics
across all flow regimes is a formidable and complex task. In the context of gas-particle
systems, the gas phase is always in the hydrodynamic regime, whereas
the solid particle flow exhibits multi-scale characteristics, from the hydrodynamic
wave interaction in the continuum flow regime to the particle’s free transport in
the collisionless regime, and it varies based on the particle phase’s Knudsen
number (Kn). In this thesis, the multi-scale framework based on the gas-kinetic
scheme (GKS) and unified gas-kinetic wave-particle method (UGKWP) is developed
for the dilute and dense gas-particle system. Specifically, the GKS-UGKWP
seamlessly transitions between an Eulerian-Eulerian method in the
regime of inte...[
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Developing a unified numerical scheme capable of accurately modeling flow physics
across all flow regimes is a formidable and complex task. In the context of gas-particle
systems, the gas phase is always in the hydrodynamic regime, whereas
the solid particle flow exhibits multi-scale characteristics, from the hydrodynamic
wave interaction in the continuum flow regime to the particle’s free transport in
the collisionless regime, and it varies based on the particle phase’s Knudsen
number (Kn). In this thesis, the multi-scale framework based on the gas-kinetic
scheme (GKS) and unified gas-kinetic wave-particle method (UGKWP) is developed
for the dilute and dense gas-particle system. Specifically, the GKS-UGKWP
seamlessly transitions between an Eulerian-Eulerian method in the
regime of intense particle collisions and an Eulerian-Lagrangian formulation in
the collisionless regime. The UGKWP can effectively capture particle non-equilibrium
transport during the intermediate transition regime, achieving a
smooth shift between the Eulerian and Lagrangian limiting formulations, which
is accomplished by weighting the mass distributions with respect to the local
cell’s Kn number, employing exponential functions of the form e
−1/Kn for wave
and (1 − e
−1/Kn) for discrete particles. The GKS-UGKWP successfully captures
phenomena such as non-equilibrium particle trajectory crossings, bubble formation,
particle clustering, and characteristic heterogeneous flow structures in fluidized
beds. The statistical results obtained from the simulations agree well with experimental data. Furthermore, the GKS-UGKWP method is extended to poly-disperse
gas-particle systems using the multi-fluid strategy. Consequently, even
in multi-disperse systems with significant variations in physical properties (e.g.,
particle diameter, material density, etc.), each particle phase can adopt an optimal
strategy for wave and particle decomposition, balancing physical accuracy
and numerical efficiency. In addition, considering radiative transport systems,
the transport of photons also exhibits multi-scale behavior, with the flow regime
determined by the opacity of the background material. In this thesis, a multi-scale
method based on UGKWP is developed for frequency-dependent radiation
transport equations, and it can recover the photon’s free transport and thermal
diffusion process in the limiting optically thin and thick regimes, respectively.
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