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of granular material or particles as described through the classical [[Discrete element method]] (DEM)
▲of granular material or particles as described through the classical [[Discrete element method]] (DEM)
▲(Cundall <ref>{{cite journal
| first1=P. A.
| last1=Cundall
Line 15 ⟶ 11:
| volume=29
| pages=47–65
}}</ref> and Allen <ref>{{cite book
| first1=M. P.
| last1=Allen
| authorlink1=M. P. Allen
| first2=D. J.
| last2=Tildesley
| authorlink2=D. J. Tildesley
| title=Computer Simulation of Liquids
| publisher=Claredon Press Oxford
| year=1990}}</ref>) by additional properties such as the [[thermodynamic]] state, [[stress]]/[[strain]] or [[electro-magnetic]] field for
each particle. Contrary to [[continuum mechanics]] concept the '''Extended Discrete Element Method (XDEM)''' aims at resolving the
particulate phase with its various processes attached to the particles.
While the Discrete Element Method predicts position and orientation in space and time for each particles,
the '''Extended Discrete Element Method (XDEM)''' additionally estimates properties such as internal [[temperature]] and/or [[species]] distribution or
mechanical impact with structures.
Line 35 ⟶ 31:
==History==
Molecular Dynamics developed in the late 1950s by <ref>{{cite journal
| first1=B. J.
| last1=Alder
| first2=T. E.
| last2=Wainwright
| title=Studies in Molecular Dynamics. I. General Method
| journal=J. Chem. Phys.
| year=1959
| volume=31
| pages=459}}</ref> and early 1960s by Rahman <ref>{{cite journal
| first1=A.
| last1=Rahman
Line 51 ⟶ 47:
| year=1964
| volume=136
}}</ref> may be regarded as a
first step pointing in the direction of the '''Extended Discrete Element Method (XDEM)''', although
the forces due to collisions between particles were replaced by energy potentials e.g.~[[Lennard-Jones]] potentials
of [[molecules]] and [[atoms]] as long range forces to determine interaction.
Similarly, the fluid dynamic interaction of particles suspended in a flow were investigated. The [[drag]] forces
exerted on the particles by the relative velocity by them and the flow were treated as additional forces
acting on the particles. Therefore, these [[multiphase flow]] phenomena including a solid e.g.~particulate
and a gaseous or fluid phase resolve the particulate phase by discrete
methods, while gas or liquid flow is described by continuous methods, and therefore, is
labelled the Combined Continuum and Discrete Model (CCDM) as applied by <ref>{{cite journal
| first1=T.
| last1=Kawaguchi
Line 72 ⟶ 68:
| year=1993
| volume=77
}}</ref>, Hoomans <ref>{{cite journal
| first1=B. P. B.
| last1=Hoomans
Line 85 ⟶ 81:
| year=1996
| volume=51
}}</ref>, Xu <ref>{{cite journal
| first1=B. H.
| last1=Xu
Line 96 ⟶ 92:
| volume=52
| pages=2785
}}</ref> and Xu <ref>{{cite journal
| first1=B. H.
| last1=Xu
Line 108 ⟶ 104:
| pages=2646–2647
}}</ref>. Due to a discrete description
of the solid phase, [[constitutive]] relations are omitted, and therefore, leads to
a better understanding of the fundamentals. This was also concluded by Zhu et al. <ref>{{cite journal
| first1=H. P.
| last1=Zhu
Line 123 ⟶ 119:
| volume=62
| pages=3378-3396
}}</ref> and Zhu et al.<ref>{{cite journal
| first1=H. P.
| last1=Zhu
Line 137 ⟶ 133:
| volume=63
| pages=5728–5770
}}</ref> during
a review on particulate flows modelled with the CCDM approach. It has seen a mayor development in
last two decades and describes motion of the solid phase by the [[Discrete Element
Method]] (DEM) on an individual particle scale and the remaining phases
are treated by the [[Navier-Stokes]] equations. Thus, the method is recognized as
an effective tool to investigate into the interaction between a particulate and
fluid phase as reviewed by Yu and Xu <ref>{{cite journal
| first1=B. H.
| last1=Xu
Line 153 ⟶ 149:
| volume=78
| pages=111–121
}}</ref>, Feng and Yu <ref>{{cite journal
| first1=Y. Q.
| last1=Feng
Line 167 ⟶ 163:
| volume=43
| pages=8378–8390
}}</ref> and Deen et al. <ref>{{cite journal
| first1=N. G.
| last1=Deen
Line 181 ⟶ 177:
| volume=62
| pages=28–44
}}</ref>. Based on the CCDM methodology the characteristics of spouted and fluidised beds are
predicted by Gryczka et al. <ref>{{cite journal
| first1=O.
| last1=Gryczka
Line 202 ⟶ 198:
}}</ref>.
The theoretical foundation for the
'''Extended Discrete Element Method (XDEM)''' was developed in 1999 by Peters <ref>{{cite journal
| first1=B.
| last1=Peters
Line 211 ⟶ 207:
| volume=116
| pages=297-301
}}</ref>, who described incineration of a wooden moving bed on a forward acting grate <ref>{{cite journal
| first1=B.
| last1=Peters
Line 219 ⟶ 215:
| volume=131
| pages=132–146
}}</ref>. The concept was later also employed by Sismsek et al. <ref>{{cite journal
| first1=E.
| last1=Simsek
Line 235 ⟶ 231:
| volume=193
| pages=266–273
}}</ref> to predict the furnace process of a grate
firing system. Applications to the complex processes of a blast furnace have been attempted by <ref>{{cite journal
| first1=Shungo
| last1=Natsui
Line 256 ⟶ 252:
| volume=50
| pages=207–214
}}</ref>. Numerical simulation of fluid injection into a gaseous environment nowadays is adopted by a large number of CFD-codes
codes such as Star-CD of [[CD-adapco]], [[Ansys]] and [[AVL]]-Fire. Droplets of a spray are treated by a zero-dimensional approach
to account for heat and mass transfer to the fluid phase.
Line 264 ⟶ 260:
==Methodology==
Numerous challenges in engineering
exist and evolve, that include a continuous and discrete phase
simultaneously, and therefore, cannot be solved accurately by continuous or
discrete approaches, only. Therefore, the '''Extended Discrete Element Method (XDEM)'''
provides a platform, that couples discrete
and continuous phases for a large number of engineering applications.
Although research and development
of numerical methods in each domains of discrete and continuous solvers
is still progressing, respective software tools have reached a high degree of
maturity. In order to couple discrete and continuous approaches, two major
concepts are available:
*'''Monolithic concept''': The equations describing multi-physics phenomena are solved simultaneously by a single solver producing a complete solution.
*'''Partitioned or staggered concept''': The equations describing multi-physics phenomena are solved sequentially by appropriately tailored and distinct solvers with passing the results of one analysis as a load to the next.
The former concept requires a solver that includes a combination of all
physical problems involved, and therefore, requires a large implementation
effort. However, there exist scenarios for which it is difficult to arrange
the coefficients of combined [[differential equations]] in one [[matrix]].
A partitioned concept as a coupling between a number of solvers
representing individual domains of physics offers distinctive
advantages over a monolithic concept.
[[File:Staggered methodology for software coupling.png|thumb|Staggered methodology for discrete/continuous applications.]]
Line 297 ⟶ 293:
Furthermore, a more modular software development is retained that allows by
far more specific solver techniques adequate to the
problems addressed. However, partitioned simulations impose stable and accurate
coupling algorithms that convince by their pervasive character.
Within the staggered concept of the '''Extended Discrete Element Method (XDEM)'''
continuous fields are described by the solution the respective continuous
(conservation) equations. Properties of individual particles such as temperature
are also resolved by solving respective conservation equations that yields both
a spatial and temporal internal distribution of relevant variables.
Mayor conservation principles with their equations and variables
to be solved for and that are employed to an individual particle within the
'''Extended Discrete Element Method (XDEM)''' are listed in the
following table.
Line 332 ⟶ 328:
The solution of these equations in principle defines a three-dimensional and
transient field of the relevant variables such as temperature or species.
However, the application of these conservation principles to a large number of
particles usually restricts the resolution to at most one representative
dimension and time due to CPU time consumption. Experimental evidence
at least in reaction engineering supports the assumption
of one-dimensionality as pointed out by Man and Byeong <ref>{{cite journal
| first1=Y. H.
| last1=Man
Line 348 ⟶ 344:
| volume=97
| pages=1–16
}}</ref>,
while the importance
of a transient behaviour is stressed by Lee et al. <ref>{{cite journal
| first1=J. C.
| last1=Lee
Line 362 ⟶ 358:
| volume=105
| pages=591–599
}}</ref>, <ref>{{cite journal
| first1=J. C.
| last1=Lee
Line 381 ⟶ 377:
[[File:Particles impacting on a conveyer belt.png|thumb|Deformation of a conveyor belt due to impacting granular material.]]
Problems that involve both a continuous and a discrete phase
are important in applications as diverse as
pharmaceutical industry e.g.~drug production, agriculture food and processing industry,
mining, construction and agricultural machinery, metals manufacturing, energy production
and systems biology. Some predominant examples are coffee, corn flakes, nuts, coal,
sand, renewable fuels e.g.~biomass for energy production and fertilizer.
Initially,
such studies were limited to simple flow configurations as pointed out by Hoomans <ref>{{cite journal
| first1=B. P. B.
| last1=Hoomans
Line 403 ⟶ 399:
| year=1996
| volume=51
}}</ref>, however, Chu and Yu <ref>{{cite journal
| first1=K. W.
| last1=Chu
Line 413 ⟶ 409:
| volume=179
| pages=104–114
}}</ref> demonstrated that the method could be applied to a
complex flow configuration consisting of a fluidized bed, conveyor belt and
a cyclone. Similarly, Zhou et al. <ref>{{cite journal
| first1=H.
| last1=Zhou
Line 431 ⟶ 427:
}}</ref> applied the CCDM
approach to the complex geometry of fuel-rich/lean burner for pulverised
coal combustion in a plant and Chu et al. <ref>{{cite journal
| first1=K. W.
| last1=Chu
Line 449 ⟶ 445:
| volume=22
| pages=893–909
}}</ref> modelled the complex flow of air, water, coal and magnetite particles of
different sizes in a dense medium [[cyclone]] (DMC).
The CCDM approach has also been applied to fluidised beds as reviewed
by Rowe and Nienow <ref>{{cite journal
| first1=P. N.
| last1=Rowe
Line 463 ⟶ 459:
| volume=15
| pages=141–147
}}</ref> and Feng and Yu <ref>{{cite journal
| first1=Y. Q.
| last1=Feng
Line 477 ⟶ 473:
| volume=43
| pages=8378–8390
}}</ref> and applied by Feng and Yu <ref>{{cite journal
| first1=Y. Q.
| last1=Feng
Line 487 ⟶ 483:
| volume=6
| pages=549–556
}}</ref> to the
chaotic motion of particles of different sizes in a gas fluidized bed.
Kafuia et al. <ref>{{cite journal
| first1=K. D.
| last1=Kafuia
| first2=C.
Line 501 ⟶ 497:
| volume=57
| pages=2395–2410
}}</ref> describe discrete
particle-continuum fluid modelling of gas-solid fluidised beds.
Further applications of the '''Extended Discrete Element Method (XDEM)''' include
thermal conversion of biomass on a backward and forward actingn grate.
Heat transfer in a [[packed bed]] [[reactor]] was laso investigated for
hot air streaming upward through the packed bed to heat the particles, which dependent on
position and size experience different heat transfer rates.
The [[deformation]] of a conveyor belt due to impacting [[granular material]] that is discharged over a chute
represents an application in the field of [[stress]]/[[strain]] analysis.
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