The interaction between the fluid and particles is the key to obtain accurate flow and heat transfer rules. For a reactive particle, the Stefan flow will affect the mass, momentum, and energy transfer between the particle and the fluid. The Stefan flow on the coal particle surface cannot be neglected in supercritical water gasification technology. In this paper, the influence of different Stefan flow intensities on the drag coefficient (Cd) and the Nusselt number (Nu) of supercritical water (SCW) cross flowing around a fixed spherical particle with Re in the range of 10–200 is studied; at the same time, the velocity and temperature boundary layers and the flow field around the particle are analyzed. For the influence of the dramatic change of the thermophysical properties of SCW near the pseudo-critical point, simple analysis of the drag coefficient and heat transfer of the particle with Stefan flow is conducted. The results show that with the increase in Stefan flow intensity, Cd and Nu decrease and the thickness of velocity and temperature boundary layers increases. A model of the particle with Stefan flow is constructed, and the Cd and Nu correlation formulas of the particle with Stefan flow are obtained.
References
1.
V. V.
Kalinchak
, “Influence of Stefan flow and convection on the kinetics of chemical reactions and heat and mass exchange of carbon particles with gases
,” J. Eng. Phys. Thermophys.
74
(2
), 323
–330
(2001
).2.
J.
Yu
, K.
Zhou
, and W.
Ou
, “Effects of Stefan flow and CO oxidation on char particle combustion in O2/CO2 atmosphere
,” Fuel
106
, 576
–585
(2013
).3.
J.
Yu
, W.
Ou
, and K.
Zhou
, “Mass transfer coefficients considering boundary layer reaction in oxy-fuel combustion of coal char
,” Fuel
124
, 173
–182
(2014
).4.
Z.
Zhou
, G.
Wang
, B.
Chen
, L.
Guo
, and Y.
Wang
, “Evaluation of evaporation models for single moving droplet with a high evaporation rate
,” Powder Technol.
240
, 95
–102
(2013
).5.
M.
Watanabe
and J.
Yahagi
, “Effects of nonuniform outflow and buoyancy on drag coefficient acting on a spherical particle
,” J. Flow Control, Meas. Visualization
05
(04
), 99
–110
(2017
).6.
K. A.
Cliffe
and D. A.
Lever
, “Isothermal flow past a blowing sphere
,” Int. J. Numer. Methods Fluids
5
, 709
(1985
).7.
R.
Kurose
, H.
Makino
, S.
Komori
, M.
Nakamura
, F.
Akamatsu
, and M.
Katsuki
, “Effects of outflow from the surface of a sphere on drag, shear lift, and scalar diffusion
,” Phys. Fluids
15
(8
), 2338
–2351
(2003
).8.
T. R.
Jayawickrama
, N. E. L.
Haugen
, M. U.
Babler
, M. A.
Chishty
, and K.
Umeki
, “The effect of Stefan flow on the drag coefficient of spherical particles in a gas flow
,” Int. J. Multiphase Flow
117
, 130
–137
(2019
).9.
P.
Chuchottaworn
, A.
Fujinami
, and K.
Asano
, “Numerical analysis of the effect of mass injection or suction on drag coefficients of a sphere
,” J. Chem. Eng. Jpn.
16
(1
), 18
–24
(1983
).10.
R. S.
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
(1999
).11.
J. J.
Murphy
and C. R.
Shaddix
, “Combustion kinetics of coal chars in oxygen-enriched environments
,” Combust. Flame
144
(4
), 710
–729
(2006
).12.
M.
Kestel
, “Numerical modeling of moving carbonaceous particle conversion in hot environments
,” Ph.D. thesis, TU Bergakademie
, 2016
.13.
F. J.
Higuera
, “Combustion of a coal char particle in a stream of dry gas
,” Combust. Flame
152
(1
), 230
–244
(2008
).14.
S.
Farazi
, M.
Sadr
, S.
Kang
, M.
Schiemann
, N.
Vorobiev
, V.
Scherer
, and H.
Pitsch
, “Resolved simulations of single char particle combustion in a laminar flow field
,” Fuel
201
, 15
–28
(2017
).15.
K.
Luo
, C.
Mao
, J.
Fan
, Z.
Zhuang
, and N. E. L.
Haugen
, “Fully resolved simulations of single char particle combustion using a ghost‐cell immersed boundary method
,” AlChE J.
64
(7
), 2851
–2863
(2018
).16.
H.
Zhang
, K.
Luo
, N. E. L.
Haugen
, C.
Mao
, and J.
Fan
, “Drag force for a burning particle
,” Combust. Flame
217
, 188
–199
(2020
).17.
Z.
Wang
, H.
Wang
, K.
Luo
, and J.
Fan
, “Direct numerical simulation of particle-laden turbulent boundary layers without and with combustion
,” Phys. Fluids
32
(10
), 105108
(2020
).18.
H.
Jin
, C.
Fan
, W.
Wei
, D.
Zhang
, J.
Sun
, and C.
Cao
, “Evolution of pore structure and produced gases of Zhundong coal particle during gasification in supercritical water
,” J. Supercrit. Fluids
136
, 102
(2018
).19.
L.
Guo
and H.
Jin
, “Boiling coal in water: Hydrogen production and power generation system with zero net CO2 emission based on coal and supercritical water gasification
,” Int. J. Hydrogen Energy
38
(29
), 12953
–12967
(2013
).20.
H.
Jin
, C.
Fan
, L.
Guo
, S.
Liu
, C.
Cao
, and R.
Wang
, “Experimental study on hydrogen production by lignite gasification in supercritical water fluidized bed reactor using external recycle of liquid residual
,” Energy Convers. Manage.
145
, 214
–219
(2017
).21.
Y.
Zhang
, L.
Li
, P.
Xu
, B.
Liu
, Y.
Shuai
, and B.
Li
, “Hydrogen production through biomass gasification in supercritical water: A review from exergy aspect
,” Int. J. Hydrogen Energy
44
(30
), 15727
–15736
(2019
).22.
H.
Jin
, H.
Wang
, Z.
Wu
, Z.
Ge
, and Y.
Chen
, “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
).23.
H.
Jin
, H.
Wang
, Z.
Wu
, Z.
Ren
, and Z.
Ou
, “Numerical investigation on drag coefficient and flow characteristics of two biomass spherical particles in supercritical water
,” Renewable Energy
138
, 11
–17
(2019
).24.
Z.
Wu
, H.
Jin
, and L.
Guo
, “Investigation on the drag coefficient of supercritical water flow past sphere-particle at low Reynolds numbers
,” Therm. Sci.
21
(suppl. 1
), 217
–223
(2017
).25.
Z.-Q.
Wu
, H.
Jin
, Y.-F.
Ren
, and L.-J.
Guo
, “Investigation on drag coefficient of supercirtical water cross-flow past cylinder biomass particel at low Reynolds numbers
,” Therm. Sci.
22
, 383
–389
(2018
).26.
D. L.
Albernaz
, M.
Do-Quang
, J. C.
Hermanson
, and G.
Amberg
, “Thermodynamics of a real fluid near the critical point in numerical simulations of isotropic turbulence
,” Phys. Fluids
28
(12
), 125105
(2016
).27.
L.
Wei
, Y.
Lu
, and J.
Wei
, “Numerical study on the mixed convection heat transfer between a sphere particle and high pressure water in pseudocritical zone
,” Adv. Mech. Eng.
5
, 527182
(2013
).28.
L.
Wei
, Y.
Lu
, and J.
Wei
, “Numerical study on laminar free convection heat transfer between sphere particle and high pressure water in pseudo-critical zone
,” Therm. Sci.
18
(4
), 1293
–1303
(2014
).29.
H.
Zhang
, B.
Xiong
, X.
An
, C.
Ke
, and G.
Wei
, “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
).30.
H.
Zhang
, B.
Xiong
, X.
An
, C.
Ke
, and G.
Wei
, “Prediction on drag force and heat transfer of spheroids in supercritical water: A PR-DNS study
,” Powder Technol.
342
, 99
–107
(2019
).31.
Z.
Wu
, Y.
Ren
, G.
Ou
, and H.
Jin
, “Influence of special water properties variation on the heat transfer of supercritical water flow around a sphere
,” Chem. Eng. Sci.
222
, 115698
(2020
).32.
C.
Fan
and H.
Jin
, “A numerical study on gasification of a single char particle in supercritical water for hydrogen production
,” Fuel
268
, 117399
(2020
).33.
K.
Wittig
, P.
Nikrityuk
, and A.
Richter
, “Drag coefficient and Nusselt number for porous particles under laminar flow conditions
,” Int. J. Heat Mass Transfer
112
, 1005
–1016
(2017
).34.
P.
Bagchi
, M. Y.
Ha
, and S.
Balachandar
, “Direct numerical simulation of flow and heat transfer from a sphere in a uniform cross-flow
,” J. Fluids Eng.
123
(2
), 347
–358
(2001
).35.
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
).36.
A.
Haider
and O.
Levenspiel
, “Drag coefficient and terminal velocity of spherical and nonspherical particles
,” Powder Technol.
58
, 63
–70
(1989
).37.
A.
Richter
and P. A.
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
).38.
R.
Clift
, J. R.
Grace
, and M. E.
Weber
, Bubbles, Drops, and Particles
(Academic Press
, New York
, 1978
).39.
W.
Ranz
and W.
Marshall
, “Evaporation from drops: Part 1
,” Chem. Eng. Prog.
48
(3
), 141
–146
(1952
).40.
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
,” AlChE J.
18
(2
), 361
–371
(1972
).41.
Y.
Rimon
and S. I.
Cheng
, “Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers
,” Phys. Fluids
12
(5
), 949
–959
(1969
).42.
Z.
Wu
, G.
Ou
, Y.
Ren
, and H.
Jin
, “Numerical investigation on the drag characteristics of supercritical water flow past a sphere
,” Sci. China: Technol. Sci.
63
(8
), 1509
–1519
(2020
).© 2021 Author(s).
2021
Author(s)
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