The velocity fields measured by experiments or determined through simulations are essential in advancing our understanding of the complex atomization process of impinging jets. However, existing methods are expensive and time-consuming. In this study, we apply deep learning to the estimation of the three-dimensional velocity fields produced by the atomization of two impinging jets. Two deep learning models are developed, namely, a liquid volume fraction (LVF) estimation model based on the Swin Transformer architecture and a three-dimensional velocity field estimation model based on four-dimensional convolution (4D-Conv). The dataset for training the models is generated by direct numerical simulations (DNS). To train the LVF model, we utilize two gray images generated by a pinhole camera model, mimicking the acquisition of experimental images. We then introduce a mask generated by binocular vision techniques into the LVF model. The LVF fields estimated with the mask are in better agreement with the reference DNS data. We further utilize the estimated LVF fields to train the 4D-Conv-based model. The mean absolute percentage error compared with the results of a full-flow test is found to be less than 5%. The results indicate that the proposed approach has the potential to accurately reconstruct volume velocity data from two-dimensional images.

1.
C.
Ruan
,
F.
Xing
,
Y.
Huang
,
L.
Xu
, and
X.
Lu
, “
A parametrical study of the break-up and atomization process of two impinging liquid jets
,”
Atomization Sprays
27
,
1025
(
2017
).
2.
E. A.
Ibrahim
and
A. J.
Przekwas
, “
Impinging jets atomization
,”
Phys. Fluids A
3
,
2981
(
1991
).
3.
X.
Chen
and
V.
Yang
, “
Recent advances in physical understanding and quantitative prediction of impinging-jet dynamics and atomization
,”
Chin. J. Aeronaut.
32
,
45
(
2019
).
4.
P.
Wood
,
A.
Hrymak
,
R.
Yeo
,
D.
Johnson
, and
A.
Tyagi
, “
Experimental and computational studies of the fluid mechanics in an opposed jet mixing head
,”
Phys. Fluids A
3
,
1362
(
1991
).
5.
R. J.
Adrian
, “
Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: Speckle velocimetry vs particle image velocimetry
,”
Appl. Opt.
23
,
1690
(
1984
).
6.
A. A.
Adamczyk
and
L.
Rimai
, “
2-dimensional particle tracking velocimetry (PTV): Technique and image processing algorithms
,”
Exp. Fluids
6
,
373
(
1988
).
7.
M.
Raffel
,
C. E.
Willert
,
F.
Scarano
,
C. J.
Kähler
,
S. T.
Wereley
, and
J.
Kompenhans
,
Particle Image Velocimetry: A Practical Guide
(
Springer International Publishing
,
Cham
,
2018
).
8.
C. W. H.
van Doorne
and
J.
Westerweel
, “
Measurement of laminar, transitional and turbulent pipe flow using stereoscopic-PIV
,”
Exp. Fluids
42
,
259
(
2007
).
9.
Y.
Yang
and
B. S.
Kang
, “
Development and validation of digital holographic particle velocity measurement system for rotational flows
,”
Optik
126
,
2223
(
2015
).
10.
C.
Cierpka
and
C. J.
Kähler
, “
Particle imaging techniques for volumetric three-component (3D3C) velocity measurements in microfluidics
,”
J. Visualization
15
(
1
),
1–31
(
2012
).
11.
Y.
Gim
,
D. K.
Jang
,
D. K.
Sohn
,
H.
Kim
, and
H. S.
Ko
, “
Three-dimensional particle tracking velocimetry using shallow neural network for real-time analysis
,”
Exp. Fluids
61
,
26
(
2020
).
12.
H. G.
Maas
,
A.
Gruen
, and
D.
Papantoniou
, “
Particle tracking velocimetry in three-dimensional flows: Part 1. Photogrammetric determination of particle coordinates
,”
Exp. Fluids
15
,
133
(
1993
).
13.
R. D.
Keane
,
R. J.
Adrian
, and
Y.
Zhang
, “
Super-resolution particle imaging velocimetry
,”
Meas. Sci. Technol.
6
,
754
(
1995
).
14.
H.
Wang
,
Y.
Liu
, and
S.
Wang
, “
Dense velocity reconstruction from particle image velocimetry/particle tracking velocimetry using a physics-informed neural network
,”
Phys. Fluids
34
,
017116
(
2022
).
15.
N.
Meng
and
F.
Li
, “
Large eddy simulations of unsteady non-reaction flow characteristics using different geometrical combustor models
,”
Aerosp. Sci. Technol.
126
,
107638
(
2022
).
16.
Y.
Zhao
,
Z.
Xia
,
Y.
Shi
,
Z.
Xiao
, and
S.
Chen
, “
Constrained large-eddy simulation of laminar-turbulent transition in channel flow
,”
Phys. Fluids
26
,
095103
(
2014
).
17.
G.
Zheng
,
W.
Nie
,
S.
Feng
, and
G.
Wu
, “
Numerical simulation of the atomization process of a like-doublet impinging rocket injector
,”
Procedia Eng.
99
,
930
(
2015
).
18.
X.
Chen
,
D.
Ma
, and
V.
Yang
, “
High-fidelity numerical simulations of impinging jet atomization
,” AIAA Paper No. 2012-4328,
2012
.
19.
S. S.
Deshpande
,
L.
Anumolu
, and
M. F.
Trujillo
, “
Evaluating the performance of the two-phase flow solver interfoam
,”
Comput. Sci. Discovery
5
,
014016
(
2012
).
20.
G.
Tryggvason
,
S.
Dabiri
,
B.
Aboulhasanzadeh
, and
J.
Lu
, “
Multiscale considerations in direct numerical simulations of multiphase flows
,”
Phys. Fluids
25
,
031302
(
2013
).
21.
J.
Rabault
,
J.
Kolaas
, and
A.
Jensen
, “
Performing particle image velocimetry using artificial neural networks: A proof-of-concept
,”
Meas. Sci. Technol.
28
,
125301
(
2017
).
22.
D.
Kochkov
,
J. A.
Smith
,
A.
Alieva
,
Q.
Wang
,
M. P.
Brenner
, and
S.
Hoyer
, “
Machine learning accelerated computational fluid dynamics
,”
Proc. Natl. Acad. Sci.
118
,
e2101784118
(
2021
).
23.
X.
Ma
,
C.
Wang
,
B.
Huang
, and
G.
Wang
, “
Application of two-branch deep neural network to predict bubble migration near elastic boundaries
,”
Phys. Fluids
31
,
102003
(
2019
).
24.
Y.
LeCun
,
Y.
Bengio
, and
G.
Hinton
, “
Deep learning
,”
Nature
521
,
436
(
2015
).
25.
A.
Krizhevsky
,
I.
Sutskever
, and
G. E.
Hinton
, “
ImageNet classification with deep convolutional neural networks
,”
Commun. ACM
60
,
84
(
2017
).
26.
C.
Kong
,
J.
Chang
,
Y.
Li
, and
Z.
Wang
, “
A deep learning approach for the velocity field prediction in a scramjet isolator
,”
Phys. Fluids
33
,
026103
(
2021
).
27.
Z.
Deng
,
C.
He
,
Y.
Liu
, and
K. C.
Kim
, “
Super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework
,”
Phys. Fluids
31
,
125111
(
2019
).
28.
M. D.
Ribeiro
,
A.
Rehman
,
S.
Ahmed
, and
A.
Dengel
, “
DeepCFD: Efficient steady-state laminar flow approximation with deep convolutional neural networks
,” arXiv.2004.08826 (
2021
).
29.
R.
Han
,
Y.
Wang
,
Y.
Zhang
, and
G.
Chen
, “
A novel spatial-temporal prediction method for unsteady wake flows based on hybrid deep neural network
,”
Phys. Fluids
31
,
127101
(
2019
).
30.
V.
Sekar
,
Q.
Jiang
,
C.
Shu
, and
B. C.
Khoo
, “
Fast flow field prediction over airfoils using deep learning approach
,”
Phys. Fluids
31
,
057103
(
2019
).
31.
M.
Morimoto
,
K.
Fukami
, and
K.
Fukagata
, “
Experimental velocity data estimation for imperfect particle images using machine learning
,”
Phys. Fluids
33
,
087121
(
2021
).
32.
B.
Liu
,
J.
Tang
,
H.
Huang
, and
X.-Y.
Lu
, “
Deep learning methods for super-resolution reconstruction of turbulent flows
,”
Phys. Fluids
32
,
025105
(
2020
).
33.
H.
Chen
,
M.
Guo
,
Y.
Tian
,
J.
Le
,
H.
Zhang
, and
F.
Zhong
, “
Intelligent reconstruction of the flow field in a supersonic combustor based on deep learning
,”
Phys. Fluids
34
,
035128
(
2022
).
34.
K.
Poulinakis
,
D.
Drikakis
,
I. W.
Kokkinakis
, and
S. M.
Spottswood
, “
Machine-learning methods on noisy and sparse data
,”
Mathematics
11
,
236
(
2023
).
35.
M.
Frank
,
D.
Drikakis
, and
V.
Charissis
, “
Machine-learning methods for computational science and engineering
,”
Computation
8
,
15
(
2020
).
36.
K.
Fukami
,
K.
Fukagata
, and
K.
Taira
, “
Super-resolution reconstruction of turbulent flows with machine learning
,”
J. Fluid Mech.
870
,
106
(
2019
).
37.
X.
Jin
,
P.
Cheng
,
W.-L.
Chen
, and
H.
Li
, “
Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder
,”
Phys. Fluids
30
,
047105
(
2018
).
38.
A.
Vaswani
,
N.
Shazeer
,
N.
Parmar
,
J.
Uszkoreit
,
L.
Jones
,
A. N.
Gomez
,
L.
Kaiser
, and
I.
Polosukhin
, “
Attention is all you need
,” arXiv.1706.03762 (
2017
).
39.
S.
Khan
,
M.
Naseer
,
M.
Hayat
,
S. W.
Zamir
,
F. S.
Khan
, and
M.
Shah
, “
Transformers in vision: A survey
,”
ACM Comput. Surv.
54
,
1–41
(
2022
).
40.
N.
Carion
,
F.
Massa
,
G.
Synnaeve
,
N.
Usunier
,
A.
Kirillov
, and
S.
Zagoruyko
, “
End-to-end object detection with transformers
,” in
ECCV
(
Springer
,
Cham
,
2020
), pp.
213
229
.
41.
M.
Chen
,
A.
Radford
,
R.
Child
,
J.
Wu
,
H.
Jun
,
D.
Luan
, and
I.
Sutskever
, “
Generative pretraining from pixels
,” in
ICML 20
(International Conference on Machine Learning,
2020
), pp.
1691
1703
.
42.
A.
Dosovitskiy
,
L.
Beyer
,
A.
Kolesnikov
,
D.
Weissenborn
,
X.
Zhai
,
T.
Unterthiner
,
M.
Dehghani
,
M.
Minderer
,
G.
Heigold
,
S.
Gelly
,
J.
Uszkoreit
, and
N.
Houlsby
, “
An image is worth 16x16 words: Transformers for image recognition at scale
,” arXiv.2010.11929 (
2021
).
43.
P.
Esser
,
R.
Rombach
, and
B.
Ommer
, “
Taming transformers for high-resolution image synthesis
,” arXiv.2012.09841 (
2021
).
44.
N.
Parmar
,
A.
Vaswani
,
J.
Uszkoreit
,
Ł.
Kaiser
,
N.
Shazeer
,
A.
Ku
, and
D.
Tran
, “
Image transformer
,” arXiv.1802.05751 (
2018
).
45.
Z.
Liu
,
Y.
Lin
,
Y.
Cao
,
H.
Hu
,
Y.
Wei
,
Z.
Zhang
,
S.
Lin
, and
B.
Guo
, “
Swin transformer: Hierarchical vision transformer using shifted windows
,” arXiv.1802.05751 (
2021
).
46.
Y.
Bai
,
J.
Mei
,
A.
Yuille
, and
C.
Xie
, “
Are transformers more robust than CNNs?
,” arXiv.2111.05464 (
2021
).
47.
W. F.
Hendria
,
Q. T.
Phan
,
F.
Adzaka
, and
C.
Jeong
, “
Combining transformer and CNN for object detection in UAV imagery
,”
ICT Express
9
,
258
(
2023
).
48.
X.
Lin
,
J.
Wang
, and
C.
Lin
, “
Research on 3D reconstruction in binocular stereo vision based on feature point matching method
,” in
ICISCAE
(
IEEE
,
2020
), pp.
551
556
.
49.
C.
Zhang
,
Z.
Zhang
,
K.
Wu
,
X.
Xia
, and
X.
Fan
, “
Atomization of misaligned impinging liquid jets
,”
Phys. Fluids
33
,
093311
(
2021
).
50.
P.
Sturm
, “
Pinhole camera model
,” in
Computer Vision: A Reference Guide
(
Springer International Publishing
,
2021
), pp.
983
986
.
51.
J.
Kim
and
C.
Lee
, “
Prediction of turbulent heat transfer using convolutional neural networks
,”
J. Fluid Mech.
882
,
A18
(
2020
).
52.
C.
Atkinson
and
J.
Soria
, “
An efficient simultaneous reconstruction technique for tomographic particle image velocimetry
,”
Exp. Fluids
47
,
553
(
2009
).
53.
T.-Y.
Lin
,
P.
Dollár
,
R.
Girshick
,
K.
He
,
B.
Hariharan
, and
S.
Belongie
, “
Feature pyramid networks for object detection
,” arXiv.1612.03144 (
2017
).
54.
K.
He
,
X.
Zhang
,
S.
Ren
, and
J.
Sun
, “
Deep residual learning for image recognition
,” arXiv.1512.03385 (
2015
).
55.
K.
Cho
,
B.
van Merrienboer
,
C.
Gulcehre
,
D.
Bahdanau
,
F.
Bougares
,
H.
Schwenk
, and
Y.
Bengio
, “
Learning phrase representations using RNN encoder-decoder for statistical machine translation
,” arXiv.1406.1078 (
2014
).
56.
S.
Woo
,
J.
Park
,
J.-Y.
Lee
, and
I. S.
Kweon
, “
CBAM: Convolutional block attention module
,” arXiv.1807.06521 (
2018
).
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