From EMMS Model to EMMS Paradigm

  • Jinghai Li
  • Wei Ge
  • Wei Wang
  • Ning Yang
  • Xinhua Liu
  • Limin Wang
  • Xianfeng He
  • Xiaowei Wang
  • Junwu Wang
  • Mooson Kwauk
Chapter

Abstract

Here, the energy minimization multiscale (EMMS) model is applied to other systems, including gas/liquid, turbulent flow, foam drainage, emulsions, and granular flow, to determine how the compromise between dominant mechanisms defines the stability conditions of meso-scale structures. The general applicability of the EMMS model implies that all meso-scale phenomena may follow a common law. Physically, the compromise between dominant mechanisms results in stability conditions, whereas mathematically, the formulation can be expressed as a multi-objective variational (MOV) problem. Based on this common attribute, the EMMS model is extended to the EMMS paradigm of computation that considers the structural consistency between problem, modeling, software and hardware, and hopefully to ‘meso-science’ in the future.

Keywords

Chemical process Competition Compromise Coordination Coorelation between scales EMMS model EMMS paradigm Emulsions Fluidization Foam drainage GPU computing Granular flow Meso-scale Meso-scale modeling Meso-science Multiphase Multi-phase flow Multiscale Multi-scale Multiscale paradigm Stability condition Structural consistency Supercomputing Turbulent flow Universality Variational criterion Virtual process engineering 

Notation

A

Particulate medium A

B

Particulate medium B

\( C_{\text{d}} \)

Drag coefficient, dimensionless

dcl

Cluster diameter, m

dp

Particle diameter, m

\( E_{\text{j}} \left( {\mathbf{x}} \right) \)

Objective function with respect to dominant mechanism j

\( E_{\text{OH}} \)

Hydrophilic potential in unit volume, m2/s3

\( E_{\text{WT}} \)

Lipophilic potential in unit volume, m2/s3

\( E_{\rm s} \)

Surface energy in unit area, m2/s3

\( E_{{{\upmu}}} \)

Viscous dissipation rate in unit volume, m2/s3

F

Body force, N

Fi

Constraints condition i

f

Inertial force, N

\( G_{\rm s} \)

Solid flow rate, kg/(m2 s)

\( g \)

Gravitational acceleration, m/s2

\( H_{\text{a}} \)

Potential a in unit volume, m2/s3

\( H_{\text{b}} \)

Potential b in unit volume, m2/s3

\( L \)

Characteristic length of flow, m

\( N_{\text{surf}} \)

Surface dissipation rate in unit mass, m2/s3

\( N_{\text{st}} \)

Energy consumption for transporting and suspending particles in unit mass, m2/s3

\( N_{\text{turb}} \)

Liquid dissipation rate in the turbulent in unit mass, m2/s3

\( R \)

Pipe radius, m

\( Re \)

Reynolds number, dimensionless

Rm

Density ratio of two media, dimensionless

Rv

Dimensionless random velocity fluctuation, dimensionless

\( r \)

Radial coordinate, m

Ug

Superficial gas velocity, m/s

Umb

Minimum bubbling velocity, m/s

Umf

Minimum fluidization velocity, m/s

Upf

Superficial solid velocity in the dilute phase, m/s

\( u\left( r \right) \)

Local fluid velocity in the pipe flow, m/s

u′

Temporal velocity fluctuations in the x-direction, m/s

\( \bar{u} \)

Time-averaged velocity in the x-direction, m/s

\( W_{\text{st}} \)

Energy consumption for transporting and suspending particles in unit volume, m2/s3

\( \bar{W}_{\nu} \)

Viscous shear dissipation rate in unit volume, m2/s3

\( \bar{W}_{\text{te}} \)

Turbulent dissipation rate in unit volume, m2/s3

X

State parameter

v′

Temporal velocity fluctuations in the y-direction, m/s

\( \bar{v} \)

Time-averaged velocity in the y-direction, m/s

\( S \)

Surface energy in unit volume, m2/s3

Greek Letters

α

Weighting factor for the inertial effect, dimensionless

\( \varepsilon \)

Local average voidage, dimensionless

\( \phi \)

Liquid fraction, dimensionless

\( \varphi_{\text{r}} \)

Dissipation rate of unit amount of kinetic energy across unit length, m2/s3

\( \gamma \)

Surface tension of surfactant solution, N/m

\( \eta \)

Kolmogorov microscales, m

\( \mu \)

Fluid viscosity, kg/(m s)

\( \nu \)

Kinematic viscosity, m2/s

\( \rho \)

Density, kg/m3

Subscripts

a

Index of particle a

b

Index of particle b

f

Fluid

g

Gas

m

Meso-scale or macro-scale

mb

Minimum bubble

mf

Minimum fluidization

p

Particle

s

Solid or small scale

Abbreviations

ACE

Accuracy, capability and efficiency

CFB

Circulating fluidized bed

CFD

Computational fluid dynamics

CPU

Central processing unit

DNS

Direct numerical simulation

EMMS

Energy-minimization multiscale

FCC

Fluid catalytic cracking

FD

Fluid-dominated

GPU

Graphics processing unit

MaPPM

Macro-scale pseudo-particle modeling

PFC

Particle-fluid compromising

PPM

Pseudo-particle modeling

RAM

Random access memory

SPH

Smoothed particle hydrodynamics

TFM

Two-fluid model

T-S

Tollmien-Schlichting

VPE

Virtual process engineering

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jinghai Li
    • 1
  • Wei Ge
    • 1
  • Wei Wang
    • 1
  • Ning Yang
    • 1
  • Xinhua Liu
    • 1
  • Limin Wang
    • 1
  • Xianfeng He
    • 1
  • Xiaowei Wang
    • 1
  • Junwu Wang
    • 1
  • Mooson Kwauk
    • 1
  1. 1.Institute of Process EngineeringChinese Academy of SciencesBeijingPeople’s Republic of China

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