Partial Realization of the EMMS Paradigm

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


This chapter uses the top-down mode of the EMMS paradigm on CPU clusters to realize structural similarity between problem, model, and software, but not hardware. First we propose a set of structure-dependent conservation equations based on the structure of the problem. A computing scheme is then realized by integrating EMMS drag into the reduced SFM; that is, EMMS-based multi-fluid modeling (EFM). In this process, the structure of both model and software (coding) is consistent with that of the investigated multiscale problem. Simulation with the EFM starts with the global prediction of the macro-scale distribution. Using this as an initial condition greatly reduces the time needed to reach a steady state. Time-dependent, regional evolution is then simulated; its accuracy is guaranteed because of the meso-scale modeling of both drag and mass transfer coefficient. Extensive application of the EMMS paradigm identifies advantages over conventional computational fluid dynamics (CFD) approaches such as higher accuracy and efficiency. Complete realization of the EMMS paradigm with consistent hardware will be discussed in  Chap. 7.


Choking Circulating fluidized bed Computational fluid dynamics EMMS Flow regime transition Mass transfer Meso-scale Mesoscale Multiscale CFD  Multi-scale CFD SFM 



Inert term or acceleration of particles, m/s2


Interface area, m2


Effective drag coefficient for a particle


Standard drag coefficient for a particle


Cluster diameter, m


Particle diameter, m


Molecular diffusion, m2/s


Particle-particle coefficient of restitution


Particle-wall coefficient of restitution


Volume fraction of clusters


Drag, N


Gravity acceleration, m/s2


Radial distribution function


Solids flux, kg/m2 s


Heat transfer coefficient, W/m2 k


Riser height, m


Initial bed height, m


Heterogeneity index


Solid inventory, kg


Mass transfer coefficient between gas and particle, m/s


Mass transfer coefficient between gas and particle, m/s


Ozone decomposition rate, 1/s


Saturation carrying capacity, kg/m2 s

\( \dot{m} \)

Flux of mass exchange per unit area of interface, kg/(m2 s)


Mass-specific energy consumption to suspend and transport particles, W/kg


Mass-specific energy consumption to transport particles, W/kg


Total rate of energy dissipation, W/kg


Number density


Pressure, Pa


Structural solid pressure, Pa


Radial position, m


The radius of the bed, m


Superficial velocity (= g), m/s


Macro-scale superficial gas velocity, m/s


Superficial slip velocity, m/s


True velocity, m/s


Volume, m3


Volume-specific energy consumption to suspend and transport particles, W/m3


Mass fraction of gas species


Axial height, m


Archimedes number (d p 3 g(ρ pρ g)/μ g 2 )


Damköhler number (k r/(k p α p))


Reynolds number (ρ g d p U s/μ g)


Local superficial Reynolds number (ρ g d p U s/μ g)


Global superficial Reynolds number (ρ g d p U g/μ g)


Schmidt number (μ g/ρ g D m)


Sherwood number (kd p/D m)

Greek Letters


Interfacial area per unit volume, m2/m3


Outer surface area per unit volume of particles, m2/m3


Drag coefficient with structure in a control volume, kg/(m3 s)


Effective drag coefficient, kg/(m3 s)


Drag coefficient without structure in a control volume, kg/(m s)


Volume fraction of bubbles


Volume fraction, or voidage


Asymptotic voidage in the top dilute region


Asymptotic voidage in the bottom dense region




Voidage at incipient fluidization


Maximum voidage for particle aggregation


Average solids concentration


Volume fraction of close-packed solids


Viscosity, Pa s


Diffusion stress tensor, Pa


Structural stress tensor, Pa


Stress tensor, Pa


Density, kg/m3


Interphase mass exchange rate, kg/(m3 s)



Component A


Bulk phase




Dense phase


Emulsion phase


Dilute phase


Gas phase


Meso-scale interphase


Phase index






Terminal velocity


Gas in the dense phase


Gas in the dilute phase


Solid in the dense phase


Solid in the dilute phase


Slip in the dense phase


Slip in the dilute phase


Slip at the meso-scale interphase


Minimum fluidization


Imposed pressure across the riser


Averaging over bed height


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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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