Abstract

Two methods are used to study the process of particle deposition in a turbulent pipe flow. The Monte Carlo method tracks 10,000 particles in the turbulent pipe flow to reproduce the deposition process of the particles. The deposition velocity of the particles is determined by calculating the proportion of particles passing through the test section. The simplified deposition model uses an equivalent Markov motion instead of the radial movement of the particle in the turbulent core. The probability that a particle leaves the turbulent core depends on the radial particle position and the probability density distribution of the random vortex. The probability that a particle penetrates the boundary layer can be solved by integrating the probability density distribution of radial particle velocity. The deposition velocity of particles can be obtained by calculating the probability of an individual particle leaving the turbulent core and penetrating the boundary layer. Five experimental data series from the literature are applied to examine the predictive abilities of the two methods. The results demonstrate that the Monte Carlo method can be properly used to track the particle deposition process in the diffusion–impaction and inertia-moderated regimes. The simplified model is suitable for high-inertia particles.

References

1.
Brennen
,
C. E.
,
2005
,
Fundamentals of Multiphase Flow
,
Cambridge University Press
,
Cambridge
, UK.
2.
Wood
,
N. B.
,
1981
, “
The Mass Transfer of Particles and Acid Vapour to Cooled Surfaces
,”
J. Inst. Energy
,
54
, pp.
76
93
.
3.
Young
,
J. B.
, and
Leeming
,
A. D.
,
1997
, “
A Theory of Particle Deposition in Turbulent Pipe Flow
,”
J. Fluid Mech.
,
340
, pp.
129
159
.10.1017/S0022112097005284
4.
Nerisson
,
P.
,
Simonin
,
O.
,
Ricciardi
,
L.
,
Douce
,
A.
, and
Fazileabasse
,
J.
,
2011
, “
Improved CFD Transport and Boundary Conditions Models for Low-Inertia Particles
,”
Comput. Fluids
,
40
(
1
), pp.
79
91
.10.1016/j.compfluid.2010.08.013
5.
Pallares
,
J.
, and
Grau
,
F. X.
,
2012
, “
Particle Dispersion in a Turbulent Natural Convection Channel Flow
,”
J. Aerosol Sci.
,
43
(
1
), pp.
45
56
.10.1016/j.jaerosci.2011.09.002
6.
Cleaver
,
J. W.
, and
Yates
,
B.
,
1975
, “
A Sub Layer Model for the Deposition of Particles From a Turbulent Flow
,”
Chem. Eng. Sci.
,
30
(
8
), pp.
982
992
.10.1016/0009-2509(75)80065-0
7.
Shaw
,
D. A.
, and
Hanratty
,
T. J.
,
1977
, “
Turbulent Mass Transfer Rates to a Wall for Large Schmidt Numbers
,”
AIChe J.
,
23
(
1
), pp.
28
37
.10.1002/aic.690230106
8.
Davies
,
J. T.
,
1983
, “
A New Theory of Aerosol Deposition From Turbulent Fluids
,”
Chem. Eng. Sci.
,
38
(
1
), pp.
135
139
.10.1016/0009-2509(83)80143-2
9.
Papavergos
,
P. G.
, and
Hedley
,
A. B.
,
1984
, “
Particle Deposition Behaviour From Turbulent Flows
,”
Chem. Eng. Res. Des.
,
63
(
5
), pp.
275
295
.
10.
Kneen
,
T.
, and
Strauss
,
W.
,
1969
, “
Deposition of Dust From Turbulent Gas Streams
,”
Atmos. Environ.
,
3
(
1
), pp.
55
67
.10.1016/0004-6981(69)90115-2
11.
Liu
,
B. Y. H.
, and
Agarwal
,
J. K.
,
1974
, “
Experimental Observation of Aerosol Deposition in Turbulent Flow
,”
J. Aerosol Sci.
,
5
(
2
), pp.
145
155
.10.1016/0021-8502(74)90046-9
12.
Fan
,
F. G.
, and
Ahmadi
,
G.
,
1993
, “
A Sublayer Model for Turbulent Deposition of Particles in Vertical Ducts With Smooth and Rough Surfaces
,”
J. Aerosol Sci.
,
24
(
1
), pp.
45
64
.10.1016/0021-8502(93)90084-M
13.
Muyshondt
,
A.
,
Anand
,
N. K.
, and
McFarland
,
A. R.
,
1996
, “
Turbulent Deposition of Aerosol Particles in Large Transport Tubes
,”
Aerosol Sci. Technol.
,
24
(
2
), pp.
107
116
.10.1080/02786829608965356
14.
Friedlander
,
S. K.
, and
Johnstone
,
H. F.
,
1957
, “
Deposition of Suspended Particles From Turbulent Gas Streams
,”
J. Ind. Eng. Chem.
,
49
(
7
), pp.
1151
1156
.10.1021/ie50571a039
15.
Beal
,
S. K.
,
1970
, “
Deposition of Particles in Turbulent Flow on Channel or Pipe Walls
,”
Nucl. Sci. Eng.
,
40
(
1
), pp.
1
11
.10.13182/NSE70-A18874
16.
Liu
,
B. Y. H.
, and
Ilori
,
T. A.
,
1974
, “
Aerosol Deposition in Turbulent Pipe Flow
,”
Environ. Sci. Technol.
,
8
(
4
), pp.
351
356
.10.1021/es60089a001
17.
Forney
,
L. J.
, and
Spielman
,
L. A.
,
1974
, “
Deposition of Coarse Aerosols From Turbulent Flow
,”
J. Aerosol Sci.
,
5
(
3
), pp.
257
271
.10.1016/0021-8502(74)90061-5
18.
El-Shobokshy
,
M. S.
, and
Ismail
,
I. A.
,
1980
, “
Deposition of Aerosol Particles From Turbulent Flow Onto Rough Pipe Wall
,”
Atmos. Environ.
,
14
(
3
), pp.
297
304
.10.1016/0004-6981(80)90063-3
19.
Caporaloni
,
M.
,
Tampieri
,
F.
,
Trombetti
,
F.
, and
Vittori
,
O.
,
1975
, “
Transfer of Particles in Nonisotropic Air Turbulence
,”
J. Atmos. Sci.
,
32
(
3
), pp.
565
568
.10.1175/1520-0469(1975)032<0565:TOPINA>2.0.CO;2
20.
Guha
,
A.
,
1997
, “
A Unified Eulerian Theory of Turbulent Deposition to Smooth and Rough Surfaces
,”
J. Aerosol Sci.
,
28
(
8
), pp.
1517
1537
.10.1016/S0021-8502(97)00028-1
21.
Derevich
,
I. V.
,
2000
, “
Statistical Modelling of Mass Transfer in Turbulent Two-Phase Dispersed Flow—2: Calculation Results
,”
Int. J. Heat Mass Transfer
,
43
(
19
), pp.
3725
3734
.10.1016/S0017-9310(00)00039-9
22.
Massah
,
M.
,
Khamehchi
,
E.
,
Mousavi-Dehghani
,
S. A.
,
Dabir
,
B.
, and
Tahan
,
H. N.
,
2020
, “
A New Theory for Modeling Transport and Deposition of Solid Particles in Oil and Gas Wells and Pipelines
,”
Int. J. Heat Mass Transfer
,
152
, p.
119568
.10.1016/j.ijheatmasstransfer.2020.119568
23.
Fichman
,
M.
,
Gutfinger
,
C.
, and
Pnueli
,
D.
,
1988
, “
A Model for Turbulent Deposition of Aerosols
,”
J. Aerosol Sci.
,
19
, pp.
813
840
.10.1016/0021-8502(88)90261-3
24.
Hutchinson
,
P.
,
Hewitt
,
G. F.
, and
Dukler
,
A. E.
,
1971
, “
Deposition of Liquid or Solid Dispersions From Turbulent Gas Streams: A Stochastic Model
,”
Chem. Eng. Sci.
,
26
(
3
), pp.
419
439
.10.1016/0009-2509(71)83016-6
25.
Reeks
,
M. W.
, and
Skyrme
,
G.
,
1976
, “
The Dependence of Particle Deposition Velocity on Particle Inertia in Turbulent Pipe Flow
,”
J. Aerosol Sci.
,
7
(
6
), pp.
485
495
.10.1016/0021-8502(76)90054-9
26.
Swailes
,
D. C.
, and
Reeks
,
M. W.
,
1994
, “
Particle Deposition From a Turbulent Flow—I: A Steady-State Model for High Inertia Particles
,”
Phys. Fluids
,
6
(
10
), pp.
3392
3403
.10.1063/1.868397
27.
Kallio
,
G. A.
, and
Reeks
,
M. W.
,
1989
, “
A Numerical Simulation of Particle Deposition in Turbulent Boundary Layers
,”
Int. J. Multiphase Flow
,
15
(
3
), pp.
433
466
.10.1016/0301-9322(89)90012-8
28.
Li
,
A.
, and
Ahmadi
,
G.
,
1993
, “
Deposition of Aerosols on Surfaces in a Turbulent Channel Flow
,”
Int. J. Eng. Sci.
,
31
(
3
), pp.
435
451
.10.1016/0020-7225(93)90017-O
29.
Uijttewaal
,
W. S. J.
, and
Oliemans
,
R. V. A.
,
1996
, “
Particle Dispersion and Deposition in Direct Numerical and Large Eddy Simulations of Vertical Pipe Flows
,”
Phys. Fluids
,
8
(
10
), pp.
2590
2604
.10.1063/1.869046
30.
Matida
,
E. A.
,
Nishino
,
K.
, and
Torii
,
K.
,
2000
, “
Statistical Simulation of Particle Deposition on the Wall From Turbulent Dispersed Pipe Flow
,”
Int. J. Heat Fluid Flow
,
21
(
4
), pp.
389
402
.10.1016/S0142-727X(00)00004-7
31.
Chibbaro
,
S.
, and
Minier
,
J. P.
,
2008
, “
Langevin PDF Simulation of Particle Deposition in a Turbulent Pipe Flow
,”
J. Aerosol Sci.
,
39
(
7
), pp.
555
571
.10.1016/j.jaerosci.2008.03.002
32.
Guingo
,
M.
, and
Minier
,
J. P.
,
2008
, “
A Stochastic Model of Coherent Structures for Particle Deposition in Turbulent Flows
,”
Phys. Fluids
,
20
(
5
), p.
053303
.10.1063/1.2908934
33.
Jin
,
C.
,
Potts
,
I.
, and
Reeks
,
M. W.
,
2015
, “
A Simple Stochastic Quadrant Model for the Transport and Deposition of Particles in Turbulent Boundary Layers
,”
Phys. Fluids
,
27
(
5
), p.
053305
.10.1063/1.4921490
34.
Marchioli
,
C.
,
Giust
,
A.
,
Salvetti
,
M. V.
, and
Soldati
,
A.
,
2003
, “
Direct Numerical Simulation of Particle Wall Transfer and Deposition in Upward Turbulent Pipe Flow
,”
Int. J. Multiphase Flow
,
29
(
6
), pp.
1017
1038
.10.1016/S0301-9322(03)00036-3
35.
Loyseau
,
X. F.
, and
Verdin
,
P. G.
,
2016
, “
Statistical Model of Transient Particle Dispersion and Deposition in Vertical Pipes
,”
J. Aerosol Sci.
,
101
, pp.
43
64
.10.1016/j.jaerosci.2016.07.013
36.
Batchelor
,
G. K.
,
1953
,
The Theory of Homogeneous Turbulence
,
Cambridge University Press
,
Cambridge, UK
.
37.
Davies
,
J. T.
,
1972
,
Turbulence Phenomena
,
Academic Press
,
New York
.
38.
Kolmogorov
,
A. N.
,
1991
, “
Dissipation of Energy in the Locally Isotropic Turbulence
,”
Proc. Math. Phys. Sci.
,
434
(
1890
), pp.
15
17
.
39.
ANSYS Fluent
,
2017
, “
Fluent 18.1 User's Guide
,” ANSYS, Canonsburg, PA.
40.
White
,
F. M.
,
2011
,
Fluid Mechanics
, 7th ed.,
McGraw-Hill
,
New York
.
41.
Laufer
,
J.
,
1954
, “
The Structure of Turbulent Flow in Fully Developed Pipe Flow
,”
National Advisory Committee for Aeronautics
,
Washington, DC
, Report No. 1174.
42.
Perry
,
R. H.
, and
Chilton
,
C. H.
,
1973
,
Chemical Engineer's Handbook
, 5th ed.,
McGraw-Hill
,
New York
.
43.
Alexander
,
L. G.
, and
Coldren
,
C. L.
,
1951
, “
Droplet Transfer From Suspending Air to Duct Walls
,”
Ind. Eng. Chem.
,
43
(
6
), pp.
1325
1331
.10.1021/ie50498a024
44.
Postma
,
A. K.
, and
Schwendiman
,
L. C.
,
1960
, “
Studies in Micromeritics I. Particle Deposition in Conduits as a Source of Error in Aerosol Sampling
,” Hanford Atomic Products, Richland, Washington, DC, Report No. HW-65308.
45.
Sehmel
,
G. A.
,
1968
, “
Aerosol Deposition From Turbulent Airstreams in Vertical Conduits
,” Pacific Northwest Laboratory, AEC Research and Development, Richland, Washington, DC, Report No. BNWL-578.
46.
Sheldon
,
M. R.
,
2014
,
Introduction to Probability Models
, 11th ed.,
Academic Press
,
New York
.
47.
Baumert
,
H. Z.
,
2013
, “
Universal Equations and Constants of Turbulent Motion
,”
Phys. Scr.
,
2013
(
T155
), p.
014001
.10.1088/0031-8949/2013/T155/014001
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