https://aiche.onlinelibrary.wiley.com/doi/10.1002/aic.16690
How to Generate Valid Local Quantities of Particle-fluid Flows
for Establishing Constitutive Relations
Qinfu Hou,1* Zongyan Zhou,1 Jennifer
S. Curtis2 and Aibing Yu1,3*
1ARC Research
Hub for Computational Particle Technology, Department of Chemical Engineering,
Monash University, Clayton, VIC 3800, Australia
2College of
Engineering, University of California at Davis, One Shields Ave, Davis, CA
95616, USA
3Centre for Simulation and Modelling of Particulate Systems,
Southeast University - Monash University Joint Research Institute, Suzhou
215123, PR China
Abstract
There are continuum and
discrete approaches to describe granular flows. A continuum approach relies on local average quantities which can be derived
through an averaging method based on a discrete approach. But the selection of
averaging domain and the validity of local quantities for constitutive
relations are not well established, particularly for transient particle-fluid
flows. Here, it is demonstrated that converged local quantities can be achieved
on an averaging domain with proper spatial and temporal sizes. Furthermore, the
relation between solid pressure and solid volume fraction is established, agreeing
qualitatively to all the existing monotonic ones in the literature. But it is quantitatively
different, showing a bifurcation at a high solid volume fraction, which is essentially
linked to the variation of short and enduring contacts among particles with flow
state and solid volume fraction. This bifurcation must be properly recognized
in developing constitutive relations for granular materials.
Keywords: particle-fluid flow, fluidized beds, averaging
method, constitutive relation, solid pressure
[The relations between solid pressure Ps and solid volume fraction εs in fluidized and moving beds. Scattered circle and triangular symbols are from the averaging method with Lt = 180 and Lp = 3. ]
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