Kinetic theory of polydisperse gas–solid flow: Navier–Stokes transport coefficients

Abstract

The particulate phase stress and solid–solid drag force in the multifluid modeling of polydisperse gas–solid flows are usually closed using kinetic theory. This research aims to establish the hydrodynamic equations and constitutive relations of the multifluid model for polydisperse systems via species kinetic theory, in which the non-equipartition of energy and interphase slip velocity between different species are considered. Whereas previous studies have used approximations, such as Taylor series expansions, to simplify the calculation of collision integrals, the present study, for the first time, solves the collision integrals analytically without any approximations to obtain accurate constitutive relations. Explicit expressions for the constitutive laws are obtained, including the particle stress tensor, solid–solid drag force, heat flux, and energy dissipation rate up to the Navier–Stokes order. The present study offers more complete and mathematically rigorous constitutive laws for the multifluid modeling of polydisperse gas–solid flows.

Kinetic Theory of Polydisperse Granular Mixtures: Influence of the Partial Temperatures on Transport Properties—A Review

“…Here, as for molecular mixtures [ 11 , 55 , 99 , 100 , 101 ], we use the conserved number densities , the flow velocity associated with the conserved total momentum, and the granular temperature T associated with the total kinetic energy. On the other hand, due to energy nonequipartition, other authors [ 48 , 49 , 102 , 103 , 104 , 105 , 106 , 107 ] employ the set consisting of the conserved number densities , the species flow velocities associated with the non-conserved species momenta, and the partial (or species) temperatures . However, this choice is potentially confusing since, although more detailed, has no predictive value on the relevant hydrodynamic large space and time scales [ 108 ].…”

“…However, this choice is potentially confusing since, although more detailed, has no predictive value on the relevant hydrodynamic large space and time scales [ 108 ]. In particular, the two-temperature Chapman–Enskog solution considered in these works [ 48 , 49 , 102 , 103 , 104 , 105 , 106 , 107 ] is phenomenological and assumes local Maxwellian distributions even for non-homogeneous situations. Although this approach yields vanishing Navier–Stokes transport coefficients for low-density mixtures, it can be considered as reliable to estimate the collisional transfer contributions to the irreversible fluxes [ 106 , 109 ].…”

Particle Pressures in Gas-Fluidized Beds: A Computational Fluid Dynamics–Discrete Element Method Study

“…A proper description of gas–solid flow, which is key to designing and optimizing the industrial process, is challenging due to its nonequilibrium and heterogeneous properties. , With the rapid development of computer technology, various computational fluid dynamics (CFD) models have been proposed to simulate gas–solid flow, among which the continuum model is preferred when facing industrial scale reactors. , New physical concepts of the solid phase, such as granular pressure, granular viscosity, and granular temperature, arise from the basic hypothesis in continuum theory for gas–solid two-phase flows . Those quantities affect the simulation results significantly in some cases and are usually closed by empirical/semiempirical correlations or kinetic theory of granular flow (KTGF). ,− Although some of these constitutive laws do work well in practice, lower-level information is necessary for a deeper understanding of their physics.…”

Particle–particle drag force in inertial bidisperse gas–particle suspensions

“…Segregation is desired in the classification of particles, but should be avoided in the process where various particle types need to be well mixed, such as olefin polymerization and co-gasification of coal and biomass. In the literature, the multi-fluid model (MFM) (Iddir & Arastoopour 2005;Chao et al 2011;Zhao & Wang 2021), in which the gas and the particles are treated as interpenetrating continuous phases, is one of the most prevalent methods for studying segregation. In MFM, the transport equations of each particle type are established, and the closure relations are obtained by the kinetic theory of granular flow (KTGF) or by experiments.…”

“…In § 3, the simulation method is explained in detail. In § 4, the particle-particle drag relation of Zhao & Wang (2021) is validated against simulation results, and a new methodology is proposed. In § 5, MFM simulations are performed to verify the proposed model.…”