This study developed a data-driven model for the prediction of fluid–particle dynamics by coupling a flow surrogate model based on the deep convolutional neural network (CNN) and a Lagrangian particle tracking model based on the discrete phase model. The applicability of the model for the prediction of the single-fiber filtration efficiency (SFFE) for elliptical- and trilobal-shaped fibers was investigated. The ground-truth training data for the CNN flow surrogate model were obtained from a validated computational fluid dynamics (CFD) model for laminar incompressible flow. Details of fluid–particle dynamics parameters, including fluid and particle velocity vectors and contribution of Brownian and hydrodynamic forces, were examined to qualitatively and quantitatively evaluate the developed data-driven model. The CNN model with the U-net architecture provided highly accurate per-pixel predictions of velocity vectors and static pressure around the fibers with a speedup of more than three orders of magnitude compared with CFD simulations. Although SFFE was accurately predicted by the data-driven model, the uncertainties in the velocity predictions by the CNN flow surrogate model in low-velocity regions near the fibers resulted in deviations in the particle dynamics predictions. These flow uncertainties contributed to the random motion of particles due to Brownian diffusion and increased the probability of particles being captured by the fiber. The findings provide guidelines for the development of data science-based models for multiphysics fluid mechanics problems encountered in fibrous systems.

1.
Ansys
,
I.
,
ANSYS Fluent User's Guide, Release 19.0
(
ANSYS, Inc
.,
Canonsburg
,
2018
).
2.
Ashwin
,
N. R.
,
Cao
,
Z.
,
Muralidhar
,
N.
,
Tafti
,
D.
, and
Karpatne
,
A.
, “
Deep learning methods for predicting fluid forces in dense particle suspensions
,”
Powder Technol.
401
,
117303
(
2022
).
3.
Bai
,
H.
,
Qian
,
X.
,
Fan
,
J.
,
Shi
,
Y.
,
Duo
,
Y.
,
Guo
,
C.
, and
Wang
,
X.
, “
Theoretical model of single fiber efficiency and the effect of microstructure on fibrous filtration performance: A review
,”
Ind. Eng. Chem. Res.
60
(
1
),
3
36
(
2020
).
4.
Bang
,
J.
and
Yoon
,
W.
, “
Stochastic analysis of a collection process of submicron particles on a single fiber accounting for the changes in flow field due to particle collection
,”
J. Mech. Sci. Technol.
28
(
9
),
3719
3732
(
2014
).
5.
Boussinesq
,
J.
, Thōrie Analytique de La Chaleur Mise En Harmonie Avec La Thermodynamique et Avec La Thōrie M c ¯anique de La Lumi_re: Refroidissement et C ¯hauffement Par Rayonnement, Conductibilit ¯des Tiges, Lames et Masses Cristallines, Courants de Convection, Thōrie M c ¯ (
Gauthier-Villars
,
1903
), Vol.
2
.
6.
Brunton
,
S. L.
, “
Applying machine learning to study fluid mechanics
,”
Acta Mech. Sin.
37
,
1718
1726
(
2021
).
7.
Brunton
,
S. L.
,
Noack
,
B. R.
, and
Koumoutsakos
,
P.
, “
Machine learning for fluid mechanics
,”
Annu. Rev. Fluid Mech.
52
,
477
508
(
2020
).
8.
Caglar
,
B.
,
Broggi
,
G.
,
Ali
,
M. A.
,
Orgéas
,
L.
, and
Michaud
,
V.
, “
Deep learning accelerated prediction of the permeability of fibrous microstructures
,”
Composites, Part A
158
,
106973
(
2022
).
9.
Chen
,
X.
,
Wang
,
L. G.
,
Meng
,
F.
, and
Luo
,
Z.-H.
, “
Physics-informed deep learning for modelling particle aggregation and breakage processes
,”
Chem. Eng. J.
426
,
131220
(
2021
).
10.
Choi
,
C. K.
,
Margraves
,
C. H.
, and
Kihm
,
K. D.
, “
Examination of near-wall hindered Brownian diffusion of nanoparticles: Experimental comparison to theories by Brenner (1961) and Goldman et al. (1967)
,”
Phys. Fluids
19
(
10
),
103305
(
2007
).
11.
Deo
,
I. K.
and
Jaiman
,
R.
, “
Predicting waves in fluids with deep neural network
,”
Phys. Fluids
34
(
6
),
067108
(
2022
).
12.
Frost
,
J.
,
Introduction to Statistics: An Intuitive Guide for Analyzing Data and Unlocking Discoveries
(
Jim Publishing
,
2020
).
13.
Fuzzi
,
S.
,
Baltensperger
,
U.
,
Carslaw
,
K.
,
Decesari
,
S.
,
Denier van der Gon
,
H.
,
Facchini
,
M. C.
,
Fowler
,
D.
,
Koren
,
I.
,
Langford
,
B.
, and
Lohmann
,
U.
, “
Particulate matter, air quality and climate: Lessons learned and future needs
,”
Atmos. Chem. Phys.
15
(
14
),
8217
8299
(
2015
).
14.
Gan
,
J.
,
Liu
,
P.
, and
Chakrabarty
,
R. K.
, “
Deep learning enabled Lagrangian particle trajectory simulation
,”
J. Aerosol Sci.
139
,
105468
(
2020
).
15.
Gervais
,
P.-C.
,
Bourrous
,
S.
,
Dany
,
F.
,
Bouilloux
,
L.
, and
Ricciardi
,
L.
, “
Simulations of filter media performances from microtomography-based computational domain. Experimental and analytical comparison
,”
Comput. Fluids
116
,
118
128
(
2015
).
16.
Goodfellow
,
I.
,
Bengio
,
Y.
, and
Courville
,
A.
,
Deep Learning
(
MIT Press
,
2016
).
17.
Guo
,
J.
,
Zhou
,
Q.
, and
Wong
,
R. C.-K.
, “
Effects of volume fraction and particle shape on the rheological properties of oblate spheroid suspensions
,”
Phys. Fluids
33
(
8
),
081703
(
2021
).
18.
Guo
,
X.
,
Li
,
W.
, and
Iorio
,
F.
, “
Convolutional neural networks for steady flow approximation
,” in
Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
(
Association for Computing Machinery
,
New York, NY
,
2016
), pp.
481
–4
90
.
19.
Hosseini
,
S. A.
and
Tafreshi
,
H. V.
, “
Modeling particle filtration in disordered 2-D domains: A comparison with cell models
,”
Sep. Purif. Technol.
74
(
2
),
160
169
(
2010
).
20.
Hosseini
,
S. A.
and
Tafreshi
,
H. V.
, “
On the importance of fibers' cross-sectional shape for air filters operating in the slip flow regime
,”
Powder Technol.
212
(
3
),
425
431
(
2011
).
21.
Hou
,
L.
,
Zhou
,
A.
,
He
,
X.
,
Li
,
W.
,
Fu
,
Y.
, and
Zhang
,
J.
, “
CFD simulation of the filtration performance of fibrous filter considering fiber electric potential field
,”
Trans. Tianjin Univ.
25
(
5
),
437
450
(
2019
).
22.
Huang
,
H.
,
Wang
,
K.
, and
Zhao
,
H.
, “
Numerical study of pressure drop and diffusional collection efficiency of several typical noncircular fibers in filtration
,”
Powder Technol.
292
,
232
241
(
2016
).
23.
Huang
,
Y.-D.
,
Xu
,
X.
,
Liu
,
Z.-Y.
,
Deng
,
J.-T.
, and
Kim
,
C.-N.
, “
Impacts of shape and height of building roof on airflow and pollutant dispersion inside an isolated street Canyon
,”
Environ. Forensics
17
(
4
),
361
379
(
2016
).
24.
Ishigami
,
T.
,
Fuse
,
H.
,
Asao
,
S.
,
Saeki
,
D.
,
Ohmukai
,
Y.
,
Kamio
,
E.
, and
Matsuyama
,
H.
, “
Permeation of dispersed particles through a pore and transmembrane pressure behavior in dead-end constant-flux microfiltration by two-dimensional direct numerical simulation
,”
Ind. Eng. Chem. Res.
52
(
12
),
4650
4659
(
2013
).
25.
Ishigami
,
T.
,
Karasudani
,
T.
,
Onitake
,
S.
,
Shirzadi
,
M.
,
Fukasawa
,
T.
,
Fukui
,
K.
, and
Mino
,
Y.
, “
Effect of liquid volume fraction and shear rate on rheological properties and microstructure formation in ternary particle/oil/water dispersion systems under shear flow: Two-dimensional direct numerical simulation
,”
Soft Matter
18
,
4338
4350
(
2022
).
26.
Jamshidi
,
R.
,
Angeli
,
P.
, and
Mazzei
,
L.
, “
On the closure problem of the effective stress in the Eulerian-Eulerian and mixture modeling approaches for the simulation of liquid-particle suspensions
,”
Phys. Fluids
31
(
1
),
013302
(
2019
).
27.
Jin
,
X.
,
Yang
,
L.
,
Du
,
X.
, and
Yang
,
Y.
, “
Modeling filtration performance of elliptical fibers with random distributions
,”
Adv. Powder Technol.
28
(
4
),
1193
1201
(
2017
).
28.
Johnson
,
M. E.
,
Moore
,
L. M.
, and
Ylvisaker
,
D.
, “
Minimax and maximin distance designs
,”
J. Stat. Plann. Inference
26
(
2
),
131
148
(
1990
).
29.
Kanaoka
,
C.
, “
Fine particle filtration technology using fiber as dust collection medium
,”
KONA Powder Part. J.
36
,
88
113
(
2019
).
30.
Karadimos
,
A.
and
Ocone
,
R.
, “
The effect of the flow field recalculation on fibrous filter loading: A numerical simulation
,”
Powder Technol.
137
(
3
),
109
119
(
2003
).
31.
Katre
,
P.
,
Banerjee
,
S.
,
Balusamy
,
S.
, and
Sahu
,
K. C.
, “
Fluid dynamics of respiratory droplets in the context of COVID-19: Airborne and surfaceborne transmissions
,”
Phys. Fluids
33
(
8
),
081302
(
2021
).
32.
Kawashima
,
K.
,
Shirzadi
,
M.
,
Fukasawa
,
T.
,
Fukui
,
K.
,
Tsuru
,
T.
, and
Ishigami
,
T.
, “
Numerical modeling for particulate flow through realistic microporous structure of microfiltration membrane: Direct numerical simulation coordinated with focused ion beam scanning electron microscopy
,”
Powder Technol.
410
,
117872
(
2022
).
33.
Kiran
,
I. R.
,
Soumitri
,
M. S.
, and
Kishalay
,
M.
, “
Deep learning based dynamic behavior modelling and prediction of particulate matter in air
,”
Chem. Eng. J.
426
,
131221
(
2021
).
34.
Kong
,
Y.
,
Ma
,
X.
, and
Wen
,
C.
, “
A new method of deep convolutional neural network image classification based on knowledge transfer in small label sample environment
,”
Sensors
22
(
3
),
898
(
2022
).
35.
Lee
,
K. W.
and
Liu
,
B. Y. H.
, “
Theoretical study of aerosol filtration by fibrous filters
,”
Aerosol Sci. Technol.
1
(
2
),
147
161
(
1982
).
36.
Li
,
A.
and
Ahmadi
,
G.
, “
Dispersion and deposition of spherical particles from point sources in a turbulent channel flow
,”
Aerosol Sci. Technol.
16
(
4
),
209
226
(
1992
).
37.
Li
,
H.
,
Ku
,
X.
, and
Lin
,
J.
, “
Eulerian–Lagrangian simulation of inertial migration of particles in circular Couette flow
,”
Phys. Fluids
32
(
7
),
073308
(
2020
).
38.
Lino
,
M.
,
Fotiadis
,
S.
,
Bharath
,
A. A.
, and
Cantwell
,
C. D.
, “
Multi-scale rotation-equivariant graph neural networks for unsteady Eulerian fluid dynamics
,”
Phys. Fluids
34
(
8
),
087110
(
2022
).
39.
Liu
,
B.
,
Tang
,
J.
,
Huang
,
H.
, and
Lu
,
X.-Y.
, “
Deep learning methods for super-resolution reconstruction of turbulent flows
,”
Phys. Fluids
32
(
2
),
025105
(
2020
).
40.
Loshchilov
,
I.
and
Hutter
,
F.
, “
Decoupled weight decay regularization
,” arXiv:1711.05101 (
2017
).
41.
Lu
,
L.
,
Pecha
,
M. B.
,
Wiggins
,
G. M.
,
Xu
,
Y.
,
Gao
,
X.
,
Hughes
,
B.
,
Shahnam
,
M.
,
Rogers
,
W. A.
,
Carpenter
,
D.
, and
Parks
,
J. E.
, “
Multiscale CFD simulation of biomass fast pyrolysis with a machine learning derived intra-particle model and detailed pyrolysis kinetics
,”
Chem. Eng. J.
431
,
133853
(
2022
).
42.
Manigrasso
,
M.
,
Protano
,
C.
,
Martellucci
,
S.
,
Mattei
,
V.
,
Vitali
,
M.
, and
Avino
,
P.
, “
Evaluation of the submicron particles distribution between mountain and urban site: Contribution of the transportation for defining environmental and human health issues
,”
Int. J. Environ. Res. Public Health
16
(
8
),
1339
(
2019
).
43.
Marcato
,
A.
,
Boccardo
,
G.
, and
Marchisio
,
D.
, “
A computational workflow to study particle transport and filtration in porous media: Coupling CFD and deep learning
,”
Chem. Eng. J.
417
,
128936
(
2021
).
44.
Morawska
,
L.
and
Milton
,
D. K.
, “
It is time to address airborne transmission of coronavirus disease 2019 (COVID-19)
,”
Clin. Infect. Dis.
71
(
9
),
2311
2313
(
2020
).
45.
Motamedi
,
H.
,
Shirzadi
,
M.
,
Tominaga
,
Y.
, and
Mirzaei
,
P. A.
, “
CFD modeling of airborne pathogen transmission of COVID-19 in confined spaces under different ventilation strategies
,”
Sustainable Cities Soc.
76
,
103397
(
2022
).
46.
Müller
,
T.
,
Meyer
,
J.
, and
Kasper
,
G.
, “
Low Reynolds number drag and particle collision efficiency of a cylindrical fiber within a parallel array
,”
J. Aerosol Sci.
77
,
50
66
(
2014
).
47.
Ounis
,
H.
,
Ahmadi
,
G.
, and
McLaughlin
,
J. B.
, “
Brownian diffusion of submicrometer particles in the viscous sublayer
,”
J. Colloid Interface Sci.
143
(
1
),
266
277
(
1991
).
48.
Ouyang
,
B.
,
Zhu
,
L.-T.
, and
Luo
,
Z.-H.
, “
Machine learning for full spatiotemporal acceleration of gas-particle flow simulations
,”
Powder Technol.
408
,
117701
(
2022
).
49.
Ouyang
,
B.
,
Zhu
,
L.-T.
,
Su
,
Y.-H.
, and
Luo
,
Z.-H.
, “
A hybrid mesoscale closure combining CFD and deep learning for coarse-grid prediction of gas-particle flow dynamics
,”
Chem. Eng. Sci.
248
,
117268
(
2022
).
50.
Poursamad
,
A.
,
Zoka
,
H. M.
, and
Shirzadi
,
M.
, “
Three-dimensional aerodynamic design optimization of multistage turbine blades in a heavy-duty gas turbine
,” in
Proceedings of the International Gas Turbine Congress (IGTC)
,
Tokyo
(
2019
).
51.
Qu
,
S.
,
Zhang
,
W.
, and
You
,
C.
, “
Modeling of dynamic characteristic of particle in transient gas–solid flow via a machine learning approach
,”
Powder Technol.
412
,
117939
(
2022
).
52.
Regan
,
B. D.
and
Raynor
,
P. C.
, “
Single-fiber diffusion efficiency for elliptical fibers
,”
Aerosol Sci. Technol.
43
(
6
),
533
543
(
2009
).
53.
Ribeiro
,
M. D.
,
Rehman
,
A.
,
Ahmed
,
S.
, and
Dengel
,
A.
, “
DeepCFD: Efficient steady-state laminar flow approximation with deep convolutional neural networks
,” arXiv:2004.08826 (
2020
).
54.
Roache
,
P. J.
, “
Quantification of uncertainty in computational fluid dynamics
,”
Annu. Rev. Fluid Mech.
29
(
1
),
123
160
(
1997
).
55.
Ronneberger
,
O.
,
Fischer
,
P.
, and
Brox
,
T.
, “
U-Net: Convolutional networks for biomedical image segmentation
,” in
Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention
(
Springer
,
2015
), pp.
234
241
.
56.
Rozy
,
M. I. F.
,
Ueda
,
M.
,
Fukasawa
,
T.
,
Ishigami
,
T.
, and
Fukui
,
K.
, “
Direct numerical simulation and experimental validation of flow resistivity of nonwoven fabric filter
,”
AIChE J.
66
(
2
),
e16832
(
2020
).
57.
Rozy
,
M. I. F.
,
Maemoto
,
Y.
,
Ueda
,
M.
,
Fukasawa
,
T.
,
Ishigami
,
T.
,
Fukui
,
K.
,
Sakai
,
M.
,
Mino
,
Y.
, and
Gotoh
,
K.
, “
Direct numerical simulation of permeation of particles through a realistic fibrous filter obtained from x-ray computed tomography images utilizing signed distance function
,”
Powder Technol.
385
,
131
143
(
2021
).
58.
Saarikoski
,
S.
,
Reyes
,
F.
,
Vázquez
,
Y.
,
Tagle
,
M.
,
Timonen
,
H.
,
Aurela
,
M.
,
Carbone
,
S.
,
Worsnop
,
D. R.
,
Hillamo
,
R.
, and
Oyola
,
P.
, “
Characterization of submicron aerosol chemical composition and sources in the coastal area of central Chile
,”
Atmos. Environ.
199
,
391
401
(
2019
).
59.
Shirzadi
,
M.
and
Tominaga
,
Y.
, “
Multi-fidelity shape optimization methodology for pedestrian-level wind environment
,”
Build. Environ.
204
,
108076
(
2021
).
60.
Stechkina
,
I. B.
,
Kirsch
,
A. A.
, and
Fuchs
,
N. A.
, “
Studies on fibrous aerosol filters. IV. Calculation of aerosol deposition in model filters in the range of maximum penetration
,”
Ann. Occup. Hyg.
12
(
1
),
1
8
(
1969
).
61.
Tao
,
R.
,
Yang
,
M.-M.
, and
Li
,
S.-Q.
, “
Filtration of micro-particles within multi-fiber arrays by adhesive DEM-CFD simulation
,”
J. Zhejiang Univ. -Sci. A
19
(
1
),
34
44
(
2018
).
62.
Tominaga
,
Y.
,
Shirzadi
,
M.
,
Inoue
,
S.-I.
,
Wakui
,
T.
, and
Machida
,
T.
, “
Computational fluid dynamics simulations of snow accumulation on infrared detection sensors using discrete phase model
,”
Cold Reg. Sci. Technol.
180
,
103167
(
2020
).
63.
Tritton
,
D. J.
, “
Experiments on the flow past a circular cylinder at low Reynolds numbers
,”
J. Fluid Mech.
6
(
4
),
547
567
(
1959
).
64.
van der Hoef
,
M. A.
,
van Sint Annaland
,
M.
,
Deen
,
N. G.
, and
Kuipers
,
J. A. M.
, “
Numerical simulation of dense gas-solid fluidized beds: A multiscale modeling strategy
,”
Annu. Rev. Fluid Mech.
40
,
47
70
(
2008
).
65.
Vejerano
,
E. P.
and
Marr
,
L. C.
, “
Physico-chemical characteristics of evaporating respiratory fluid droplets
,”
J. R. Soc. Interface
15
(
139
),
20170939
(
2018
).
66.
Wang
,
H.
,
Zhao
,
H.
,
Guo
,
Z.
, and
Zheng
,
C.
, “
Numerical simulation of particle capture process of fibrous filters using lattice Boltzmann two-phase flow model
,”
Powder Technol.
227
,
111
122
(
2012
).
67.
Wang
,
K.
and
Zhao
,
H.
, “
The influence of fiber geometry and orientation angle on filtration performance
,”
Aerosol Sci. Technol.
49
(
2
),
75
85
(
2015
).
68.
Wang
,
Z.
,
Li
,
X.
,
Liu
,
L.
,
Wu
,
X.
,
Hao
,
P.
,
Zhang
,
X.
, and
He
,
F.
, “
Deep-learning-based super-resolution reconstruction of high-speed imaging in fluids
,”
Phys. Fluids
34
(
3
),
037107
(
2022
).
69.
World Health Organization,
Ambient Air Pollution: A Global Assessment of Exposure and Burden of Disease
(
World Health Organization
,
2016
).
70.
Wu
,
H.
,
Zhang
,
H.
,
Hu
,
G.
, and
Qiao
,
R.
, “
Deep learning-based reconstruction of the structure of heterogeneous composites from their temperature fields
,”
AIP Adv.
10
(
4
),
045037
(
2020
).
71.
Wu
,
Q.
,
Zhao
,
Y.
,
Shi
,
Y.
, and
Chen
,
S.
, “
Large-eddy simulation of particle-laden isotropic turbulence using machine-learned subgrid-scale model
,”
Phys. Fluids
34
(
6
),
065129
(
2022
).
72.
Yasuda
,
T.
,
Ookawara
,
S.
,
Yoshikawa
,
S.
, and
Matsumoto
,
H.
, “
Machine learning and data-driven characterization framework for porous materials: Permeability prediction and channeling defect detection
,”
Chem. Eng. J.
420
,
130069
(
2021
).
73.
Yeh
,
H.-C.
and
Liu
,
B. Y. H.
, “
Aerosol filtration by fibrous filters. I. Theoretical
,”
J. Aerosol Sci.
5
(
2
),
191
204
(
1974
).
74.
Zhang
,
L.
,
Diao
,
Y.
,
Chu
,
M.
,
Zhou
,
F.
,
Li
,
Z.
, and
Shen
,
H.
, “
Study on external magnetic field improving the capture of Fe-based fine particles by magnetic fibers with different arrangement structures
,”
Part. Sci. Technol.
40
(
6
),
675
685
(
2022
).
75.
Zhang
,
Y.
,
Lu
,
X.-B.
, and
Zhang
,
X.-H.
, “
An optimized Eulerian–Lagrangian method for two-phase flow with coarse particles: Implementation in open-source field operation and manipulation, verification, and validation
,”
Phys. Fluids
33
(
11
),
113307
(
2021
).

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