Nonequilibrium characteristics and spatiotemporal long-range correlations in dense gas-solid suspensions

Highlights

• CFD-DEM simulations of dense gas-solid suspensions were performed.

• Nonequilibrium characteristics were quantified.

• Spatiotemporal long-range correlations of gas-solid flow were analyzed.

• Characteristic correlation length scales linearly with the size of simulation domain.

Abstract

The nonequilibrium properties and strong spatiotemporal long-range correlations in gas-solid suspensions were analyzed systematically by discrete particle simulation in periodic domains. The effective interphase slip velocity is significantly larger than the particle terminal velocity, the particle velocity distribution function is non-Maxwellian with a high-energy tail and the solid concentration distribution function is far from the discrete Poisson distribution, all of which manifest strong deviation from the equilibrium or homogeneous state in gas-solid flow. The solid concentration, gas and solid velocities are spatiotemporally correlated and show a clear scale-dependence. More importantly, all characteristic correlation lengths scale linearly with the size of simulation domain, although the correlation length of solid concentration is much smaller than those of gas and solid velocities. On the other hand, the characteristic correlation times at first increase with increasing domain size and then seem to approach to asymptotic values. Those results indicate that the heterogeneity and spatiotemporal long-range correlations should be considered properly in continuum theory of heterogeneous gas-solid flow.

Introduction

Gas-fluidized beds have been a topic of extensive research as they are widely encountered in industries, such as fossil fuel combustion and pharmaceutical process. Due to the critical role played by mesoscale structures that take the form of bubbles and particle clusters (Ge et al., 2019), a great deal of numerical simulations (Sundaresan, Ozel, Kolehmainen, 2018, Wang, 2020) and experiments (Harris, Davidson, Thorpe, 2002, Cahyadi, Anantharaman, Yang, Karri, Findlay, Cocco, Jia, 2017) have been performed to elucidate the effects of mesoscale structures on the hydrodynamics and transport properties. The formation and dynamic evolution of mesoscale structures resulted in the fact that the gas-solid system as a whole is far from equilibrium and operated in a nonlinear and nonequilibrium state (Li, Qian, Wen, 1996, Li, Kwauk, 2003), which can be for example quantified by the particle velocity distribution function. Extensive theoretical (Wang, Zhao, Li, 2016, Zhao, Wang, 2018, Zhao, Wang, 2019), numerical (Ichiki, Hayakawa, 1995, Wang, Wang, 2018) and experimental (Vaidheeswaran et al., 2017, Wang, Chen, Wang, 2018) studies have concluded that the particle velocity distribution function in dense gas-solid flow is either a non-Maxwellian distribution with a high-energy tail or a bimodal distribution, indicating that the system is far from equilibrium state.

The existence of coherent structures in gas-solid systems has been widely acknowledged (Van Den Akker, 1998, Van Den Akker, 2015), which suggests the existence of long-range correlations in the studied system. The coherent structures and/or the long-range correlation in dilute system has been extensively studied (Eaton, Fessler, 1994, Balachandar, Eaton, 2010, Monchaux, Bourgoin, Cartellier, 2012). For example, Février et al. (2005) investigated velocity correlation in dilute gas-solid suspensions and developed a statistical approach to separate the contribution of spatially correlated continuous field from the instantaneous particle velocity. Capecelatro and co-workers (Capecelatro, Desjardins, Fox, 2014, Capecelatro, Desjardins, Fox, 2015, Capecelatro, Desjardins, Fox, 2015) carried out a systematical study on the spatiotemporal correlation in dilute gas-solid flow with a domain-averaged solid concentration of 0.01 that is defined as the volume of all particles divided by the volume of simulation domain, where particles are assumed to experience single-particle Stokes drag only, without considering the possible effect of locally high solid concentration due to the formation of particle clustering structures. The long-range spatiotemporal correlation of both velocity and concentration were observed at all scales and it was found that the use of periodic boundary condition (PBC) in simulation had less influence in larger domain. On the other side, to the best of our knowledge the nature of long-range correlation in dense gas-solid flow remains unexplored.

In this study, discrete particle simulation (or unresolved CFD-DEM simulation) of dense gas-solid suspensions containing Geldart A and B particles was performed systematically, the nonequilibrium characteristics including the effective interphase slip velocity, the particle velocity distribution function and the solid concentration distribution function were then analyzed; The spatial and temporal correlation function of gas and solid velocity and solid concentration were also studied, which offers insight into the spatiotemporal long-range correlations in dense gas-solid flows; Finally, the article was finished with conclusion, with an appendix of validating the used discrete particle method via comparing to the particle-resolved direct numerical simulation results.