We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh–Bénard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 108 and the Prandtl number (Pr) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number (St) less than 10−3, and they tend to cluster into bands for 10−3St ≲ 10−2. At even larger St, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle’s trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle’s density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.

1.
A.
Guha
, “
Transport and deposition of particles in turbulent and laminar flow
,”
Annu. Rev. Fluid Mech.
40
,
311
341
(
2008
).
2.
F.
Toschi
and
E.
Bodenschatz
, “
Lagrangian properties of particles in turbulence
,”
Annu. Rev. Fluid Mech.
41
,
375
404
(
2009
).
3.
S.
Tenneti
and
S.
Subramaniam
, “
Particle-resolved direct numerical simulation for gas-solid flow model development
,”
Annu. Rev. Fluid Mech.
46
,
199
230
(
2014
).
4.
V.
Mathai
,
D.
Lohse
, and
C.
Sun
, “
Bubbly and buoyant particle–laden turbulent flows
,”
Annu. Rev. Condens. Matter Phys.
11
,
529
559
(
2020
).
5.
J. H.
Seinfeld
and
S. N.
Pandis
,
Atmospheric Chemistry and Physics: From Air Pollution to Climate Change
(
John Wiley & Sons
,
2016
).
6.
D.
Norbäck
,
C.
Lu
,
Y.
Zhang
,
B.
Li
,
Z.
Zhao
,
C.
Huang
,
X.
Zhang
,
H.
Qian
,
Y.
Sun
,
J.
Wang
 et al., “
Sources of indoor particulate matter (PM) and outdoor air pollution in China in relation to asthma, wheeze, rhinitis and eczema among pre-school children: Synergistic effects between antibiotics use and PM10 and second hand smoke
,”
Environ. Int.
125
,
252
260
(
2019
).
7.
L.
Bourouiba
,
E.
Dehandschoewercker
, and
J. W. M.
Bush
, “
Violent expiratory events: On coughing and sneezing
,”
J. Fluid Mech.
745
,
537
563
(
2014
).
8.
R.
Mittal
,
R.
Ni
, and
J.-H.
Seo
, “
The flow physics of COVID-19
,”
J. Fluid Mech.
894
,
F2
(
2020
).
9.
T.
Dbouk
and
D.
Drikakis
, “
On coughing and airborne droplet transmission to humans
,”
Phys. Fluids
32
,
053310
(
2020
).
10.
S.
Chaudhuri
,
S.
Basu
,
P.
Kabi
,
V. R.
Unni
, and
A.
Saha
, “
Modeling the role of respiratory droplets in Covid-19 type pandemics
,”
Phys. Fluids
32
,
063309
(
2020
).
11.
S.
Balachandar
and
J. K.
Eaton
, “
Turbulent dispersed multiphase flow
,”
Annu. Rev. Fluid Mech.
42
,
111
133
(
2010
).
12.
M. A.
van der Hoef
,
M.
van Sint Annaland
,
N. G.
Deen
, and
J. A. M.
Kuipers
, “
Numerical simulation of dense gas-solid fluidized beds: A multiscale modeling strategy
,”
Annu. Rev. Fluid Mech.
40
,
47
70
(
2008
).
13.
M.
Maxey
, “
Simulation methods for particulate flows and concentrated suspensions
,”
Annu. Rev. Fluid Mech.
49
,
171
193
(
2017
).
14.
L.-P.
Wang
and
M. R.
Maxey
, “
Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence
,”
J. Fluid Mech.
256
,
27
68
(
1993
).
15.
T.
Bosse
,
L.
Kleiser
, and
E.
Meiburg
, “
Small particles in homogeneous turbulence: Settling velocity enhancement by two-way coupling
,”
Phys. Fluids
18
,
027102
(
2006
).
16.
E.
Calzavarini
,
M.
Kerscher
,
D.
Lohse
, and
F.
Toschi
, “
Dimensionality and morphology of particle and bubble clusters in turbulent flow
,”
J. Fluid Mech.
607
,
13
24
(
2008
).
17.
Q.
Zhang
,
H.
Liu
,
Z.
Ma
, and
Z.
Xiao
, “
Preferential concentration of heavy particles in compressible isotropic turbulence
,”
Phys. Fluids
28
,
055104
(
2016
).
18.
G.
Ahlers
,
S.
Grossmann
, and
D.
Lohse
, “
Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection
,”
Rev. Mod. Phys.
81
,
503
(
2009
).
19.
D.
Lohse
and
K.-Q.
Xia
, “
Small-scale properties of turbulent Rayleigh-Bénard convection
,”
Annu. Rev. Fluid Mech.
42
,
335
364
(
2010
).
20.
F.
Chillà
and
J.
Schumacher
, “
New perspectives in turbulent Rayleigh-Bénard convection
,”
Eur. Phys. J. E
35
,
58
(
2012
).
21.
K.-Q.
Xia
, “
Current trends and future directions in turbulent thermal convection
,”
Theor. Appl. Mech. Lett.
3
,
052001
(
2013
).
22.
A.
Mazzino
, “
Two-dimensional turbulent convection
,”
Phys. Fluids
29
,
111102
(
2017
).
23.
B.-F.
Wang
,
Q.
Zhou
, and
C.
Sun
, “
Vibration-induced boundary-layer destabilization achieves massive heat-transport enhancement
,”
Sci. Adv.
6
,
eaaz8239
(
2020
).
24.
M. K.
Verma
,
Physics of Buoyant Flows: From Instabilities to Turbulence
(
World Scientific
,
2018
).
25.
T.
Hiroaki
and
M.
Hiroshi
, “
Turbulent natural convection in a horizontal water layer heated from below
,”
Int. J. Heat Mass Transfer
23
,
1273
1281
(
1980
).
26.
R.
Krishnamurti
and
L. N.
Howard
, “
Large-scale flow generation in turbulent convection
,”
Proc. Natl. Acad. Sci. U. S. A.
78
,
1981
1985
(
1981
).
27.
Q.
Zhou
,
C.
Sun
, and
K.-Q.
Xia
, “
Morphological evolution of thermal plumes in turbulent Rayleigh-Bénard convection
,”
Phys. Rev. Lett.
98
,
074501
(
2007
).
28.
H.-D.
Xi
,
S.
Lam
, and
K.-Q.
Xia
, “
From laminar plumes to organized flows: The onset of large-scale circulation in turbulent thermal convection
,”
J. Fluid Mech.
503
,
47
56
(
2004
).
29.
R.
Puragliesi
,
A.
Dehbi
,
E.
Leriche
,
A.
Soldati
, and
M. O.
Deville
, “
DNS of buoyancy-driven flows and Lagrangian particle tracking in a square cavity at high Rayleigh numbers
,”
Int. J. Heat Fluid Flow
32
,
915
931
(
2011
).
30.
M.
Lappa
, “
On the transport, segregation, and dispersion of heavy and light particles interacting with rising thermal plumes
,”
Phys. Fluids
30
,
033302
(
2018
).
31.
H. J.
Park
,
K.
O’Keefe
, and
D. H.
Richter
, “
Rayleigh-Bénard turbulence modified by two-way coupled inertial, nonisothermal particles
,”
Phys. Rev. Fluids
3
,
034307
(
2018
).
32.
S.
Chen
and
G. D.
Doolen
, “
Lattice Boltzmann method for fluid flows
,”
Annu. Rev. Fluid Mech.
30
,
329
364
(
1998
).
33.
C. K.
Aidun
and
J. R.
Clausen
, “
Lattice-Boltzmann method for complex flows
,”
Annu. Rev. Fluid Mech.
42
,
439
472
(
2010
).
34.
A.
Xu
,
W.
Shyy
, and
T.
Zhao
, “
Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries
,”
Acta Mech. Sin.
33
,
555
574
(
2017
).
35.
H.
Huang
,
M.
Sukop
, and
X.
Lu
,
Multiphase Lattice Boltzmann Methods: Theory and Application
(
John Wiley & Sons
,
2015
).
36.
A.
Xu
,
L.
Shi
, and
T. S.
Zhao
, “
Accelerated lattice Boltzmann simulation using GPU and OpenACC with data management
,”
Int. J. Heat Mass Transfer
109
,
577
588
(
2017
).
37.
A.
Xu
,
L.
Shi
, and
T. S.
Zhao
, “
Thermal effects on the sedimentation behavior of elliptical particles
,”
Int. J. Heat Mass Transfer
126
,
753
764
(
2018
).
38.
A.
Xu
,
L.
Shi
, and
H.-D.
Xi
, “
Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number
,”
Int. J. Heat Mass Transfer
140
,
359
370
(
2019
).
39.
A.
Xu
,
L.
Shi
, and
H.-D.
Xi
, “
Statistics of temperature and thermal energy dissipation rate in low-Prandtl number turbulent thermal convection
,”
Phys. Fluids
31
,
125101
(
2019
).
40.
G. A.
Voth
and
A.
Soldati
, “
Anisotropic particles in turbulence
,”
Annu. Rev. Fluid Mech.
49
,
249
276
(
2017
).
41.
E.
Calzavarini
,
L.
Jiang
, and
C.
Sun
, “
Anisotropic particles in two-dimensional convective turbulence
,”
Phys. Fluids
32
,
023305
(
2020
).
42.
R.
Clift
,
J.
Grace
, and
M.
Weber
,
Bubbles, Drops, and Particles
(
Academic Press
,
1978
).
43.
J. P.
Duguid
, “
The size and the duration of air-carriage of respiratory droplets and droplet-nuclei
,”
J. Hyg.
44
,
471
479
(
1946
).
44.
B. I.
Shraiman
and
E. D.
Siggia
, “
Heat transport in high-Rayleigh-number convection
,”
Phys. Rev. A
42
,
3650
(
1990
).
45.
Y.
Zhang
,
Q.
Zhou
, and
C.
Sun
, “
Statistics of kinetic and thermal energy dissipation rates in two-dimensional turbulent Rayleigh–Bénard convection
,”
J. Fluid Mech.
814
,
165
184
(
2017
).
46.
G.
Akiki
,
T. L.
Jackson
, and
S.
Balachandar
, “
Pairwise interaction extended point-particle model for a random array of monodisperse spheres
,”
J. Fluid Mech.
813
,
882
928
(
2017
).
47.
G.
Akiki
,
W. C.
Moore
, and
S.
Balachandar
, “
Pairwise-interaction extended point-particle model for particle-laden flows
,”
J. Comput. Phys.
351
,
329
357
(
2017
).
48.
J.
Schumacher
, “
Lagrangian dispersion and heat transport in convective turbulence
,”
Phys. Rev. Lett.
100
,
134502
(
2008
).
49.
R.
Ni
and
K.-Q.
Xia
, “
Experimental investigation of pair dispersion with small initial separation in convective turbulent flows
,”
Phys. Rev. E
87
,
063006
(
2013
).
50.
C.
Sun
,
H.-D.
Xi
, and
K.-Q.
Xia
, “
Azimuthal symmetry, flow dynamics, and heat transport in turbulent thermal convection in a cylinder with an aspect ratio of 0.5
,”
Phys. Rev. Lett.
95
,
074502
(
2005
).
51.
Q.
Wang
,
S.-N.
Xia
,
B.-F.
Wang
,
D.-J.
Sun
,
Q.
Zhou
, and
Z.-H.
Wan
, “
Flow reversals in two-dimensional thermal convection in tilted cells
,”
J. Fluid Mech.
849
,
355
372
(
2018
).
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