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continuum and discrete simulations?
Sofiane Ben ahiaUS DOE, National Energy Technology Laboratory
May 4-6, 2010
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Collaborations
Research was conducted in collaboration with two groups:
Filtered drag models: Y. Igci and S. Sundaresan1 (Princeton University)
EMMS drag model: W. Wang and J . Li2 (Institute of ProcessEn ineerin , Chinese Academ of Sciences)
1 Igci, Y.; Andrews, A.T.; Sundaresan, S.; Pannala, S.; OBrien, T.AIChE J. 2008; 54; 1431-1448.
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2
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Goals, Objectives, and Challenges
Conduct fast and accurate gas-solids f low simulations
us ng coarse gr s.
Implement EMMS and filtered drag models in MFIX
Conduct comparative study of these drag models with
experimental data3
Challenges:
Subgrid models are still being developed
Consideration of other effects (e.g. polydispersity,particle-wall interaction)
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3 Benyahia, S. On the effect of subgrid drag closures. Ind. Eng. Chem. Res. DOI: 10.1021/ie900658k
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Simulation Conditions2
Twogassolids
outlets
0.35m
0.14m
Process temperature 297 K
Process pressure 1.01 x 105 Pa
Air density ~1.2 kg/m3
Air viscosity 1.8 x 10-5 Pas
Gas-phase turbulence length-scale 0.01 m
Solids density 930 kg/m3
.
60cells
10.5m
450cells
Particle diameter 54micron
Single-particle terminal velocity 0.074 m/s
Particle-particle restitution coefficient 0.9
2.78m
artc e-wa resttuton coe c ent 0.7
Specularity coefficient 0.0001
Particle-particle angle of internalpi/6
Two
solids
side
inlets
0.35m
0.14meps_mf =0.4
eps =0.3, Vs:computedParticle-wall angle of friction pi/16
Void fraction at maximum packing 0.4
Void fraction at minimum fluidization 0.6
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as n e
Vg=1.5m/s2 Lu, B.; Wang, W.; Li, J . Chem. Eng. Sci. 2009; 64; 3437-3447.
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Instantaneous values of friction coefficient
1.6
1.2
filtered
EMMS
WenYu
0.8Hd
0
.
0.5 0.6 0.7 0.8 0.9 1
Voidage
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Void fraction contour profiles
Wen-Yu drag Filtered drag EMMS drag Wen-Yu dra Filtereddra EMMS dra
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Instantaneous Time-averaged
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Solids mass flux through outlets40050
Solids massflux (kg/m2s)
Solids massflux (kg/m2s)
EMMS
300
30
40Wen-Yu
10010
20
00
0 10 20 30 40Time (sec)
Drag model Wen-Yu Filtered EMMS Experimental
Solids mass flux(kg/m2s)
205 12.3 16.9 14.3
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Standard deviation(kg/m2s)
25.2 5.64 5.59 -
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Vertical void fraction profiles10 10
6
8
m)
EMMS
FilteredWenYu
experiment6
8
)
EMMS
Filtered
WenYu
experiment
4
Height(
4
Height(
2 2
0
0.7 0.8 0.9 1Voidfraction
0
0.7 0.8 0.9 1Voidfraction
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Numerical data based oncomputed pressure gradient
Numerical data based oncomputed void fraction
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Horizontal profiles at 7 m above inlet
Solidsmassflux2
0.2
EMMS
Filtered
WenYu 0
400
0.1s
400
EMMS
Filtered
WenYu
0
0 0.03 0.06 0.09Width(m)800
0 0.03 0.06 0.09Width(m)
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Future work
Why is the pressure gradient under-8
10
HiFriction(phi=0.01)
pre c e a e o om sec on o
riser? 6
eight(m)
LoFriction(phi=0.0001)
experiment
Increase particle-wall friction inJ ohnson-J ackson BC
2
4
Effect of polydispersity is currentlyinvestigated by considering threeparticle sizes of 30, 60, and 120
0
0.7 0.8 0.9 1Voidfraction
microns
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Are subgrid models needed for discretepart c e s mu at ons
There is no reason why not if fluid flow is not properly
resolved (coarse grids)
The same approach3 used for continuum models can be
applied for discrete models, i.e. does the slip velocity
increase from that of homogeneous state as Euleriangrid is refined?
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3 Agrawal et al. The role of meso-scale structures in rapid gas-solids flows. J. Fluid Mech. 445 (2001) 151.
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-
0 ggggg V
gVxVPVVtV
gg
N
pppg
c
p
pgggggg
ggg T
1
Continuum gas-phase
conservation equations
gVVPPVVt
Vsssgpssgsssss
sss
Continuum solids-phasemomentum equation
sp
sppg
p
p
p
gp PVxV
Pg
td
Vd
Newtons law of motion fordiscrete particles
65.23
g
ppggg
Dp
VxVC
max
max
max
old
ss
ss
s
s
PP
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pt s
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Simulation conditions
Fully periodic domain
Air density 1.3 kg/m3
Air viscosity 1.8 x 10-5 Pas
0.4 m
So s ens ty 1500 g/m
Particle diameter 75 micron
Void fraction at maximum packing 0.4
Eulerian grid density 8x32, 16x64, 32x128, 64x256
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0.1 m
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Snapshots of particle position-velocity (8x32)
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1.0 sec 1.5 sec 2.0 sec 10 sec 20 sec
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Snapshots of particle posit ion-velocity (16x64)
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1.0 sec 1.5 sec 2.0 sec 10 sec 20 sec
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Snapshots of particle position-velocity (32x128)
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1.0 sec 1.5 sec 2.0 sec 10 sec 20 sec
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Snapshots of particle position-velocity (64x256)
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1.0 sec 1.5 sec 2.0 sec 10 sec 20 sec
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Transient Favre-averaged slip velocity
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Slip-velocity for continuum & MP-PIC models
Grid size 8x32 16x64 32x128 64x256
Continuum slipvelocity & St. Dev.
(cm/s)
18.70.16
22.63.9
49.610.8
52.08.7
MP-PIC slipvelocity & St. Dev.
(cm/s)
18.50.005
18.50.005
50.715.1
55.413.8
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Summary
Sub-grid corrections are demonstrated to be
both needed and useful for both continuum
and discrete approaches to gas-solids flow
Our limited quantitative analysis indicates thatthe same subgrid corrections developed for
continuum models may be used with DPM
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