In the chemical engineering area, impinging flow plays a significant role in process intensification and energy consumption reduction. Thoroughly revealing the formation and evolution of vortices within the reactor has emerged as a crucial scientific issue. This paper systematically studies the steady-state flow at low Re (1 ≤ Re ≤ 200, where Re is the Reynolds number) in a cross-shaped reactor by particle image velocimetry technology. The evolution, distribution, and intensity characteristics of vortices in the reactor chamber are focused on. We show that at 55 ≤ Re ≤ 120, the distribution of vorticity and shear rate in the chamber show unimodal and bimodal patterns, respectively, and the center of the chamber is a local area with high vorticity and low shear. In contrast, for 120 < Re ≤ 200, the distribution of vorticity turns into a bimodal pattern, and the shear rate develops into a trimodal pattern. The center of the chamber constitutes a local area characterized by low vorticity and high shear. Additionally, based on the modified monopole vortex model, the distributions of vorticity and velocity of vortices in the steady engulfment flow are accurately depicted.

1.
H.
Qin
,
C.
Zhang
,
Q.
Xu
,
X.
Dang
,
W.
Li
,
K.
Lei
,
L.
Zhou
, and
J.
Zhang
, “
Geometrical improvement of inline high shear mixers to intensify micromixing performance
,”
Chem. Eng. J.
319
,
307
320
(
2017
).
2.
V.
Hessel
,
H.
Löwe
, and
F.
Schönfeld
, “
Micromixers—A review on passive and active mixing principles
,”
Chem. Eng. Sci.
60
(
8–9
),
2479
2501
(
2005
).
3.
K.
Eum
,
K. C.
Jayachandrababu
,
F.
Rashidi
,
K.
Zhang
,
J.
Leisen
,
S.
Graham
,
R. P.
Lively
,
R. R.
Chance
,
D. S.
Sholl
,
C. W.
Jones
, and
S.
Nair
, “
Highly tunable molecular sieving and adsorption properties of mixed-linker zeolitic imidazolate frameworks
,”
J. Am. Chem. Soc.
137
(
12
),
4191
4197
(
2015
).
4.
C.-Y.
Lee
and
L.-M.
Fu
, “
Recent advances and applications of micromixers
,”
Sens. Actuators, B
259
,
677
702
(
2018
).
5.
L.
Li
,
J.
Liu
, and
Z.
Pan
, “
Enhancement of heat transfer and mixing with two side-by-side freely rotatable cylinders in microchannel
,”
Int. J. Heat Mass Transfer
189
,
122717
(
2022
).
6.
D.
Tsaoulidis
, “
Intensified extraction of uranium(VI) in impinging-jets contactors
,”
Chem. Eng. J.
342
,
251
259
(
2018
).
7.
Z.
Dong
,
S.
Zhao
,
Y.
Zhang
,
C.
Yao
,
Q.
Yuan
, and
G.
Chen
, “
Mixing and residence time distribution in ultrasonic microreactors
,”
AlChE. J.
63
(
4
),
1404
(
2017
).
8.
S.
Kawasaki
,
Y.
Xiuyi
,
K.
Sue
,
Y.
Hakuta
,
A.
Suzuki
, and
K.
Arai
, “
Continuous supercritical hydrothermal synthesis of controlled size and highly crystalline anatase TiO2 nanoparticles
,”
J. Supercrit. Fluids
50
,
276
282
(
2009
).
9.
C. K.
Chung
, “
Design and experiments of a short-mixing-length baffled microreactor and its application to microfluidic synthesis of nanoparticles
,”
Chem. Eng. J.
168
,
790
798
(
2011
).
10.
K.
Kechagidis
,
B.
Owen
,
L.
Guillou
,
H.
Tse
,
D.
Di Carlo
, and
T.
Krüger
, “
Numerical investigation of the dynamics of a rigid spherical particle in a vortical cross-slot flow at moderate inertia
,”
Microsyst. Nanoeng.
9
(
1
),
100
(
2023
).
11.
L.
Xue
,
G.
Liu
,
Y.
Wang
,
Z.
Hao
, and
H.
Bie
, “
An investigation of flow regimes and mixing in a novel arrow-shaped jet reactor
,”
Chem. Eng. Sci.
292
,
120002
(
2024
).
12.
J.-W.
Zhang
,
W.-F.
Li
,
X.-L.
Xu
,
M.
El Hassan
,
H.-F.
Liu
, and
F.-C.
Wang
, “
Effect of geometry on engulfment flow regime in T-jet reactors
,”
Chem. Eng. J.
387
,
124148
(
2020
).
13.
J.
Zhang
,
T.
Yao
,
W.
Li
,
M.
El Hassan
,
X.
Xu
,
H.
Liu
, and
F.
Wang
, “
Trapping region of impinging jets in a cross‐shaped channel
,”
AlChE. J.
66
(
2
),
e16822
(
2020
).
14.
S.
Tomasi Masoni
,
A.
Mariotti
,
M.
Antognoli
,
C.
Galletti
,
R.
Mauri
,
M. V.
Salvetti
, and
E.
Brunazzi
, “
Prediction of the reaction yield in a X-micromixer given the mixing degree and the kinetic constant
,”
Phys. Rev. Fluids
9
(
2
),
024202
(
2024
).
15.
S.
Tomasi Masoni
,
A.
Mariotti
,
M.
Antognoli
,
C.
Galletti
,
R.
Mauri
,
M. V.
Salvetti
, and
E.
Brunazzi
, “
Reaction performance in T-, X- and arrow-shaped microdevices
,”
Chem. Eng. Res. Des.
193
,
259
267
(
2023
).
16.
S. J.
Haward
,
R. J.
Poole
,
M. A.
Alves
,
P. J.
Oliveira
,
N.
Goldenfeld
, and
A. Q.
Shen
, “
Tricritical spiral vortex instability in cross-slot flow
,”
Phys. Rev. E
93
(
3
),
031101
(
2016
).
17.
P. G.
Correa
,
J. R.
Mac Intyre
,
J. M.
Gomba
,
M. A.
Cachile
,
J. P.
Hulin
, and
H.
Auradou
, “
Three-dimensional flow structures in X-shaped junctions: Effect of the Reynolds number and crossing angle
,”
Phys. Fluids
31
(
4
),
043606
(
2019
).
18.
W.
Zhang
,
L.
Guan
,
Z.
Shi
,
W.
Li
,
H.
Liu
, and
F.
Wang
, “
Investigation of unsteady engulfment flows in a cross-shaped mixer by particle image velocimetry
,”
Chem. Eng. Sci.
284
,
119540
(
2024
).
19.
S.
Tomasi Masoni
,
M.
Antognoli
,
A.
Mariotti
,
R.
Mauri
,
M. V.
Salvetti
,
C.
Galletti
, and
E.
Brunazzi
, “
Flow regimes, mixing and reaction yield of a mixture in an X-microreactor
,”
Chem. Eng. J.
437
,
135113
(
2022
).
20.
W.
Zhang
,
Z.
Shi
,
X.
Xu
,
W.
Li
,
H.
Liu
, and
F.
Wang
, “
Oscillation induced by vortex ring shedding in a cross-shaped channel
,”
Chem. Eng. Sci.
242
,
116756
(
2021
).
21.
R. J.
Santos
,
E.
Erkoç
,
M. M.
Dias
,
A. M.
Teixeira
, and
J. C. B.
Lopes
, “
Hydrodynamics of the mixing chamber in RIM: PIV flow‐field characterization
,”
AlChE. J.
54
(
5
),
1153
1163
(
2008
).
22.
N.
Ait Mouheb
,
D.
Malsch
,
A.
Montillet
,
C.
Solliec
, and
T.
Henkel
, “
Numerical and experimental investigations of mixing in T-shaped and cross-shaped micromixers
,”
Chem. Eng. Sci.
68
(
1
),
278
289
(
2012
).
23.
N.
Burshtein
,
K.
Zografos
,
A. Q.
Shen
,
R. J.
Poole
, and
S. J.
Haward
, “
Periodic fluctuations of streamwise vortices in inertia-dominated intersecting flows
,”
Phys. Fluids
33
(
1
),
014106
(
2021
).
24.
J.-W.
Zhang
,
W.-F.
Li
,
X.-L.
Xu
,
H.-F.
Liu
, and
F.-C.
Wang
, “
Experimental investigation of three-dimensional flow regimes in a cross-shaped reactor
,”
Phys. Fluids
31
(
3
),
034105
(
2019
).
25.
K. K.
Chen
,
C. W.
Rowley
, and
H. A.
Stone
, “
Vortex breakdown, linear global instability and sensitivity of pipe bifurcation flows
,”
J. Fluid Mech.
815
,
257
294
(
2017
).
26.
R. R.
Trieling
,
M.
Beckers
, and
G. J. F.
Van Heijst
, “
Dynamics of monopolar vortices in a strain flow
,”
J. Fluid Mech.
345
,
165
201
(
1997
).
27.
H.
Wang
,
X.
Duan
,
X.
Feng
,
Z.-S.
Mao
, and
C.
Yang
, “
Effect of impeller type and scale-up on spatial distribution of shear rate in a stirred tank
,”
Chin. J. Chem. Eng.
42
,
351
363
(
2022
).
28.
J. S.
Ayala
,
H. L.
De Moura
,
R. D. L.
Amaral
,
F. D. A.
Oliveira Júnior
,
J. R.
Nunhez
, and
G. J.
De Castilho
, “
Two-dimensional shear rate field and flow structures of a pseudoplastic fluid in a stirred tank using particle image velocimetry
,”
Chem. Eng. Sci.
248
,
117198
(
2022
).
29.
P.
Chakraborty
,
S.
Balachandar
, and
R. J.
Adrian
, “
On the relationships between local vortex identification schemes
,”
J. Fluid Mech.
535
,
189
214
(
2005
).
30.
K. K.
Chen
,
C. W.
Rowley
, and
H. A.
Stone
, “
Vortex dynamics in a pipe T-junction: Recirculation and sensitivity
,”
Phys. Fluids
27
(
3
),
034107
(
2015
).
31.
A.
Fani
,
S.
Camarri
, and
M. V.
Salvetti
, “
Investigation of the steady engulfment regime in a three-dimensional T-mixer
,”
Phys. Fluids
25
(
6
),
064102
(
2013
).
32.
J.-Z.
Wu
,
H.-Y.
Ma
, and
M.-D.
Zhou
,
Vorticity and Vortex Dynamics
(
Springer
,
Berlin, Heidelberg
,
2006
).
33.
T.
Leweke
,
S.
Le Dizès
, and
C. H. K.
Williamson
, “
Dynamics and instabilities of vortex pairs
,”
Annu. Rev. Fluid Mech.
48
(
1
),
507
541
(
2016
).
34.
P.
Liu
,
Y.
Zhao
,
Q.
Qu
, and
T.
Hu
, “
Physical properties of vortex and applicability of different vortex identification methods
,”
J. Hydrodyn.
32
(
5
),
984
996
(
2020
).
35.
T.
Gerz
,
F.
Holzäpfel
, and
D.
Darracq
, “
Commercial aircraft wake vortices
,”
Prog. Aerosp. Sci.
38
(
3
),
181
208
(
2002
).
36.
C.
Eloy
and
S.
Le Dizès
, “
Three-dimensional instability of Burgers and Lamb–Oseen vortices in a strain field
,”
J. Fluid Mech.
378
,
145
166
(
1999
).
37.
A.
Antkowiak
and
P.
Brancher
, “
Transient energy growth for the Lamb–Oseen vortex
,”
Phys. Fluids
16
(
1
),
L1
L4
(
2004
).
38.
S.
Rodriguez
,
F.
Espinoza
,
S.
Steinberg
, and
M.
El-Genk
, “
Towards a unified swirl vortex model
,” in
42nd AIAA Fluid Dynamics Conference and Exhibit
(
AIAA
,
2012
), p.
3354
.
39.
J. B.
Flór
and
G. J. F.
Van Heijst
, “
Stable and unstable monopolar vortices in a stratified fluid
,”
J. Fluid Mech.
311
(
1
),
257
(
1996
).
40.
R. C.
Kloosterziel
and
G. J. F.
van Heijst
, “
An experimental study of unstable barotropic vortices in a rotating fluid
,”
J. Fluid Mech.
223
,
1
24
(
1991
).
41.
O.
Lucca-Negro
and
T.
O'Doherty
, “
Vortex breakdown: A review
,”
Prog. Energy Combust. Sci.
27
(
4
),
431
481
(
2001
).
42.
D.
Jarman
,
D.
Butler
,
G.
Tabor
, and
R.
Andoh
, “
Modelling of vortex flow controls at high drainage flow rates
,”
Proc. Inst. Civ. Eng.: Eng. Comput. Mech.
168
,
17
34
(
2015
).
43.
V. T.
Wood
and
L. W.
White
, “
A new parametric model of vortex tangential-wind profiles: Development, testing, and verification
,”
J. Atmos. Sci.
68
,
990
1006
(
2011
).
44.
W.
Zhou
,
K.
Jiang
,
T.
Zhang
,
C.
Liu
,
H.
Li
,
Z.
Zhang
, and
Y.
Tang
, “
Dynamic of centrifugal step emulsification and prediction of droplet diameter
,”
Phys. Fluids
34
(
12
),
122009
(
2022
).
45.
Y.
Ji
,
E.
Missi
,
J.
Bellettre
,
T.
Burghelea
,
A.
Montillet
, and
P.
Massoli
, “
Dynamics of a Newtonian droplet in the turbulent flow of a shear thinning fluid in a microchannel
,”
Phys. Rev. Fluids
8
(
4
),
043301
(
2023
).
46.
D.
Kumar
,
A.
Shenoy
,
S.
Li
, and
C. M.
Schroeder
, “
Orientation control and nonlinear trajectory tracking of colloidal particles using microfluidics
,”
Phys. Rev. Fluids
4
(
11
),
114203
(
2019
).
You do not currently have access to this content.