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12 - Coarse-Graining in Multiphase Flows: From Micro to Meso to Macroscale for Euler–Lagrange and Euler–Euler Simulations

from Part II - Challenges

Published online by Cambridge University Press:  31 January 2025

By
S. Balachandar
Edited by
Fernando F. Grinstein ,
Filipe S. Pereira  and
Massimo Germano
Fernando F. Grinstein
Affiliation:
Los Alamos National Laboratory
Filipe S. Pereira
Affiliation:
Los Alamos National Laboratory
Massimo Germano
Affiliation:
Duke University, North Carolina
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Summary

Particle-resolved (PR), Euler–Lagrange (EL), and Euler–Euler (EE) formulations are the three widely used computational approaches in multiphase flow. In PR formulation, the focus is on the flow physics at the microscale and all the details are resolved at the microscale. However, due to computational limitations, the PR approach cannot reach the length and time scales needed to explore the meso and macroscale multiphase phenomenon. In the EL formulation of a dispersed multiphase flow, the continuous phase is averaged (or filtered), and all the microscale details of the flow on the scale of individual particles are coarse-grained. If all the dispersed phase elements (i.e., all the particles, drops, or bubbles) are tracked then there is no averaging of the dispersed phase. In the EE formulation, both the continuous and dispersed phases are averaged/filtered. We will discuss systematic coarse graining to obtain the governing equations of the EL and EE approaches. The coarse-graining process introduces two interesting challenges: (i) the unavoidable closure problem where the Reynolds stress and flux terms must be expressed in terms of filtered meso/macroscale variables, and (ii) the coupling between the continuous and the dispersed phases must be appropriately posed in terms of the filtered variables. Recent innovations on both these fronts are discussed.

Type
Chapter
Information
Coarse Graining Turbulence
Modeling and Data-Driven Approaches and their Applications
 , pp. 355 - 380
Publisher: Cambridge University Press
Print publication year: 2025

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