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Title: Are continuum predictions of clustering chaotic?

Abstract

Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ 1≈1/τ, we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a direct consequence of the fundamental kinematic instability, but requires a secondary (inherently multidimensional) instability. Granular matter is a collection of discrete, interacting solid particles which, like classic (molecular) matter, can be generally classified into one of three states:1 (i) under static conditions granular heaps or piles can sustain gravity-induced stress and behave like a solid; (ii) dense granular flows characterized by enduring and multi-particle contacts behave similarly to a fluid; and (iii) rapid granular flows characterized by instantaneous contacts described as a granular gas. However, it is worth noting thatmore » all three granular states are only superficially similar to their molecular counterparts due to the dissipative nature of particle-particle contacts (inelasticity, friction, etc.). In industrial operations, rapid (collision-dominated) granular flows are often encountered in devices in which the particles are fluidized by a gas; such gas-solid flows are the focus of this work. Rapid gas-solid flows are prone to an instability termed clustering in which particles tend to form spatially inhomogeneous patterns of high and low concentrations. Continuum or two-fluid models (TFM) have long been known to be able to predict the qualitative nature of the clustering instability and more recent quantitative assessments have also shown promising results. However, it is yet unknown whether or not such predictions are chaotic. We take a first step in answering this question by simulating fluidization in an unbounded domain and calculating a positive largest Lyapunov exponent (LLE), thereby indicating that continuum predictions of clustering are in fact chaotic. Further, we show that chaotic behavior may be reduced to periodic behavior by constraining the dimensionality of the system.« less

Authors:
ORCiD logo [1];  [1]
  1. Univ. of Colorado, Boulder, CO (United States). Dept. of Chemical and Biological Engineering
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Org.:
USDOE Office of Fossil Energy (FE)
OSTI Identifier:
1465353
Alternate Identifier(s):
OSTI ID: 1349369
Grant/Contract Number:  
FE0026298
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Chaos: An Interdisciplinary Journal of Nonlinear Science
Additional Journal Information:
Journal Volume: 27; Journal Issue: 3; Journal ID: ISSN 1054-1500
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Fullmer, William D., and Hrenya, Christine M.. Are continuum predictions of clustering chaotic?. United States: N. p., 2017. Web. doi:10.1063/1.4977513.
Fullmer, William D., & Hrenya, Christine M.. Are continuum predictions of clustering chaotic?. United States. doi:10.1063/1.4977513.
Fullmer, William D., and Hrenya, Christine M.. Wed . "Are continuum predictions of clustering chaotic?". United States. doi:10.1063/1.4977513. https://www.osti.gov/servlets/purl/1465353.
@article{osti_1465353,
title = {Are continuum predictions of clustering chaotic?},
author = {Fullmer, William D. and Hrenya, Christine M.},
abstractNote = {Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ1≈1/τ, we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a direct consequence of the fundamental kinematic instability, but requires a secondary (inherently multidimensional) instability. Granular matter is a collection of discrete, interacting solid particles which, like classic (molecular) matter, can be generally classified into one of three states:1 (i) under static conditions granular heaps or piles can sustain gravity-induced stress and behave like a solid; (ii) dense granular flows characterized by enduring and multi-particle contacts behave similarly to a fluid; and (iii) rapid granular flows characterized by instantaneous contacts described as a granular gas. However, it is worth noting that all three granular states are only superficially similar to their molecular counterparts due to the dissipative nature of particle-particle contacts (inelasticity, friction, etc.). In industrial operations, rapid (collision-dominated) granular flows are often encountered in devices in which the particles are fluidized by a gas; such gas-solid flows are the focus of this work. Rapid gas-solid flows are prone to an instability termed clustering in which particles tend to form spatially inhomogeneous patterns of high and low concentrations. Continuum or two-fluid models (TFM) have long been known to be able to predict the qualitative nature of the clustering instability and more recent quantitative assessments have also shown promising results. However, it is yet unknown whether or not such predictions are chaotic. We take a first step in answering this question by simulating fluidization in an unbounded domain and calculating a positive largest Lyapunov exponent (LLE), thereby indicating that continuum predictions of clustering are in fact chaotic. Further, we show that chaotic behavior may be reduced to periodic behavior by constraining the dimensionality of the system.},
doi = {10.1063/1.4977513},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
number = 3,
volume = 27,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}

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