In industrial applications, the phenomenon of scCO2 (supercritical carbon dioxide) flowing over particles is quite common. Considering that the scCO2 is chemically inactive but has high solubility, the pure Stefan flow will present without the related diffusion of a chemical reaction component and reaction heat, during the process of a spherical particle in the solid phase dissolved in a system of scCO2. To this, particle resolve-direct numerical simulation without considering the role of gravity and buoyancy is employed in this paper to investigate the high-temperature scCO2 flowing over a low-temperature stationary sphere with the uniformly, normally, and outward distributed Stefan flow on its surface, with the above cases conducted in the process of small variations on physical properties of scCO2. We present a series of variables in the flow field and temperature field near the sphere surface to study the effects of Stefan flow on them compared with cases without Stefan flow. Related distribution details of the velocity boundary layer and the temperature boundary layer near the sphere surface under conditions with or without the Stefan flow are also presented and analyzed. Different from other similar studies, our study also pays more attention to variables of the local fluid field as well as temperature field near the surface of the spherical particle. The results show that the presence of Stefan flow will reduce flow resistance of the freestream but inhibits heat transfer performance. Simpler correlations in form compared with previous well-established correlations are presented and are used to describe the operating conditions proposed herein.
References
1.
D.
Kim
, H.
Choi
, and H.
Choi
, “Characteristics of laminar flow past a sphere in uniform shear
,” Phys. Fluids
17
(10
), 103602
(2005
).2.
B.
Gruncell
, N.
Sandham
, and G.
McHale
, “Simulations of laminar flow past a superhydrophobic sphere with drag reduction and separation delay
,” Phys. Fluids
25
(4
), 043601
(2013
).3.
Q.
Lin
, D.
Boyer
, and H.
Fernando
, “Turbulent wakes of linearly stratified flow past a sphere
,” Phys. Fluids A: Fluid Dyn.
4
(8
), 1687
–1696
(1992
).4.
M.
Kotouč
, G.
Bouchet
, and J.
Dušek
, “Drag and flow reversal in mixed convection past a heated sphere
,” Phys. Fluids
21
(5
), 054104
(2009
).5.
Y.
Liu
and X.
Yu
, “General formulation of drag force on assemblage of spherical particles in fluids: A critical review and a new empirical formula
,” Phys. Fluids
34
(6
), 063307
(2022
).6.
A.
Chavda
, P.
Mehta
, and A.
Harichandan
, “Numerical analysis of multiphase flow in chemical looping reforming process for hydrogen production and CO2 capture
,” Experim. Comput. Multiphase Flow
4
(4
), 360
–376
(2022
).7.
K.
Luo
, Z.
Wang
, D.
Li
et al., “Fully resolved simulations of turbulence modulation by high-inertia particles in an isotropic turbulent flow
,” Phys. Fluids
29
(11
), 113301
(2017
).8.
A.
Haji
and M.
Naebe
, “Cleaner dyeing of textiles using plasma treatment and natural dyes: A review
,” J. Cleaner Prod.
265
, 121866
(2020
).9.
Z.
Zhou
, G.
Wang
, L.
Guo
et al., “Evaluation of evaporation models for single moving droplet with a high evaporation rate
,” Powder Technol.
240
, 95
–102
(2013
).10.
J.
Huang
, L.
Tao
, Q.
Wang
et al., “Transport properties of CO2 in different reactivity coke solution loss reaction based on Stefan flow theory
,” ACS Omega
5
(41
), 26817
–26828
(2020
).11.
X.
Ku
, J.
Lin
, and T.
Chen
, “CFD simulation of the steam gasification of millimeter-sized char particle using thermally thick treatment
,” Combust. Flame
213
, 63
–86
(2020
).12.
F.
Shang
, Z.
Ge
, C.
Zhou
et al., “Numerical study on a single char particle gasification considering Stefan flow effects in a hot CO2/O2/H2O atmosphere
,” Fuel
324
, 124804
(2022
).13.
N.
Vorobiev
, A.
Becker
, M.
Schiemann
et al., “Particle shape and Stefan flow effects on the burning rate of torrefied biomass
,” Fuel
210
(1
), 107
–120
(2017
).14.
H.
Zhang
, K.
Luo
, J.
Fan
et al., “Drag force for a burning particle
,” Combust. Flame
217
, 188
–199
(2020
).15.
M. G.
Nugraha
, R.
Andersson
, and B.
Andersson
, “On the Sherwood number correction due to Stefan flow
,” Chem. Eng. Sci.
249
, 117292
(2022
).16.
L.
Liu
, M.
Mi
, S.
Kong
et al., “Evaporation of a sessile water droplet during depressurization
,” Int. J. Therm. Sci.
159
, 106587
(2021
).17.
F.
Prodi
, G.
Santachiara
, F.
Belosi
et al., “Phoretic forces on aerosol particles surrounding an evaporating droplet in microgravity conditions
,” Atmos. Res.
142
, 40
–44
(2014
).18.
Y.
Feng
, Y.
Li
, L.
Cui
et al., “Cold condensing scrubbing method for fine particle reduction from saturated flue gas
,” Proc. Inst. Civ. Eng. Energy
171
, 1193
–1205
(2019
).19.
H.
Jin
, Y.
Wang
, Z.
Wu
et al., “Influence of Stefan flow on the drag coefficient and heat transfer of a spherical particle in a supercritical water cross flow
,” Phys. Fluids
33
(2
), 023313
(2021
).20.
X.
Chen
, S.
Du
, Q.
Zhou
et al., “Effect of Stefan flow on the drag force in flow past random arrays of spheres
,” Chem. Eng. J.
412
, 128691
(2021
).21.
S.
Du
, L.
Zhao
, Q.
Zhou
et al., “Effect of Stefan flow on the drag force of single reactive particle surrounded by a sea of inert particles
,” Chem. Eng. Sci.
253
, 117546
(2022
).22.
K.
Jiang
, J.
Shi
, H.
Jin
et al., “Research progress of industrial application based on two-phase flow system of supercritical carbon dioxide and particles
,” Powder Technol.
407
, 117621
(2022
).23.
L.
Wei
, Y.
Lu
, and J.
Wei
, “Flow separation from a spherical particle in supercritical water
,” Chem. Eng. Res. Des.
92
(11
), 2273
–2282
(2014
).24.
Z.
Wu
, G.
Ou
, H.
Jin
et al., “Numerical investigation on the drag characteristics of supercritical water flow past a sphere
,” Sci. China Technol. Sci.
63
(8
), 1509
–1519
(2020
).25.
Z.
Wu
, Y.
Ren
, H.
Jin
et al., “Influence of special water properties variation on the heat transfer of supercritical waterflow around a sphere
,” Chem. Eng. Sci.
222
, 115698
(2020
).26.
H.
Jin
, H.
Wang
, Z.
Wu
et al., “Numerical investigation of the effect of surface roughness on flow and heat transfer characteristics of single sphere particle in supercritical water
,” Comput. Math. Appl.
81
, 562
–572
(2021
).27.
X.
Li
, Z.
Wu
, H.
Wang
et al., “The effect of particle wake on the heat transfer characteristics between interactive particles in supercritical water
,” Chem. Eng. Sci.
247
, 117030
(2022
).28.
X.
Li
, Z.
Wu
, H.
Wang
et al., “Numerical investigation of heat transfer characteristics between two particles and supercritical water
,” J. Supercrit. Fluids
177
, 105327
(2021
).29.
H.
Zhang
, B.
Xiong
, X.
An
et al., “Prediction on drag force and heat transfer of spheroids in supercritical water: A PR-DNS study
,” Powder Technol.
342
, 99
–107
(2019
).30.
H.
Zhang
, B.
Xiong
, X.
An
et al., “Numerical investigation on the effect of the incident angle on momentum and heat transfer of spheroids in supercritical water
,” Comput. Fluids
179
, 533
–542
(2019
).31.
Y.
Wang
, H.
Jin
, L.
Guo
et al., “Numerical simulation of adiabatic/cooled/heated spherical particles with Stefan flow in supercritical water
,” Phys. Fluids
33
(5
), 053305
(2021
).32.
Y.
Wang
, M.
Zhang
, H.
Jin
et al., “The influence of Stefan flow on the flow and heat-transfer characteristics of spherical-particle pair in supercritical water
,” Int. J. Multiphase Flow
151
, 104045
(2022
).33.
Z.
Ou
, L.
Guo
, D.
Thévenin
et al., “A directional ghost-cell immersed boundary method for low Mach number reacting flows with interphase heat and mass transfer
,” J. Comput. Phys.
468
, 111447
(2022
).34.
Z.
Ou
, L.
Guo
, H.
Jin
et al., “Interface-resolved direct numerical simulations of interphase momentum, heat, and mass transfer in supercritical water gasification of coal
,” Phys. Fluids
34
(10
), 103319
(2022
).35.
Z.
Ou
, L.
Guo
, H.
Jin
et al., “Fully resolved direct numerical simulation of single coal particle gasification in supercritical water
,” Fuel
329
, 125474
(2022
).36.
K.
Jiang
, W.
Wang
, H.
Jin
et al., “Effect of the variable physical properties on sub- and supercritical CO2 flowing over a stationary spherical particle
,” Phys. Fluids
34
(10
), 103605
(2022
).37.
T.
Jayawickrama
, N.
Haugen
, K.
Umeki
et al., “The effect of Stefan flow on the drag coefficient of spherical particles in a gas flow
,” Int. J. Multiphase Flow
117
, 130
–137
(2019
).38.
T.
Jayawickrama
, N.
Haugen
, M.
Babler
et al., “The effect of Stefan flow on Nusselt number and drag coefficient of spherical particles in non-isothermal gas flow
,” Int. J. Multiphase Flow
140
, 103650
(2021
).39.
M.
Kestel
, “Numerical modeling of moving carbonaceous particle conversion in hot environments
,” Ph.D. thesis (TU Bergakademie
, 2016
).40.
J.
Xie
and G.
Xie
, “Vortex dynamics of supercritical carbon dioxide flow past a heated circular cylinder at low Reynolds numbers
,” Phys. Fluids
34
(1
), 017111
(2022
).41.
F.
Özkan
, A.
Wenka
, E.
Hansjosten
et al., “Numerical investigation of interfacial mass transfer in two phase flows using the VOF method
,” Eng. Appl. Comput. Fluid Mech.
10
(1
), 100
–110
(2016
).42.
E.
Lemmon
, M.
Huber
, and K.
McLinden
, “Reference fluid thermodynamic and transport properties—REFPROP
,” NIST Standard Reference Database 23
, Version 9.0 (BibSonomy
, 2010
).43.
J.
Xie
and G.
Xie
, “Three-dimensional wake transition for CO2 flow at supercritical pressure over single heated cylinder
,” Phys. Fluids
34
(9
), 094106
(2022
).44.
R.
Clift
, J.
Grace
, and M.
Weber
, Bubbles, Drops, and Particles
(Academic Press
, New York
, 1978
).45.
A.
Richter
and P.
Nikrityuk
, “Drag forces and heat transfer coefficients for spherical, cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers
,” Int. J. Heat Mass Transfer
55
(4
), 1343
–1354
(2012
).46.
A.
Haider
and O.
Levenspiel
, “Drag coefficient and terminal velocity of spherical and non-spherical particles
,” Powder Technol.
58
, 63
–70
(1989
).47.
W.
Ranz
and W.
Marshall
, “Evaporation from drops. I
,” Chem. Eng. Prog.
48
(3
), 141
–146
(1952
).48.
S.
Whitaker
, “Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles
,” AIChE J.
18
(2
), 361
–371
(1972
).49.
VDI,
VDI Heat Atlas
(Springer
, Berlin
, 2010
).50.
R.
Miller
and J.
Bellan
, “Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream
,” J. Fluid Mech.
384
, 293
–338
(1999
).51.
J.
Murphy
and C.
Shaddix
, “Effects of Stefan flow on heat transfer from reacting carbon particles
,” Sandia-Report No. 2003-8720J
, 2003
, pp. 1
–24
.52.
T.
Johnson
and V.
Patel
, “Flow past a sphere up to a Reynolds number of 300
,” J. Fluid Mech.
378
, 19
–70
(1999
).53.
S.
Dennis
and J.
Walker
, “Calculation of the steady flow past a sphere at low and moderate Reynolds numbers
,” J. Fluid Mech.
48
(4
), 771
–789
(1971
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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