This work is devoted to the numerical investigation of heat and fluid flow past a sphere with a centric, cylindrical bore. Such spherical rings are of interest in many technological processes. In chemical reactors, for example, spherical rings are used as a catalyst with an increased reacting surface. Motivated by this fact, we considered spherical rings with different bores and different orientations in flow regimes corresponding to Reynolds numbers from 10 up to 300. The results show a significant influence of the bore diameter on the symmetry and hence the steadiness of the flow field. The Nusselt number can be increased, which leads to a moderate rise in the drag coefficient. Thereby, the effect of the borehole depends on the Reynolds number, the bore diameter, and the angle of attack. For that reason, drag forces and total heat transfers do not simply follow the heat exchanging surface area. Based on the presented results, new correlations are given for both the drag coefficient and the Nusselt number; correlations which incorporate the bore geometry and the bore orientation in the flow field.

References

References
1.
Kramers
,
H.
, 1946, “
Heat Transfer From Spheres to Flowing Media
,”
Physica
,
XII
, pp.
61
80
.
2.
Ranz
,
W. E.
, and
Marshall
,
W. R.
, 1952, “
Evaporation From Drops
,”
Chem. Eng. Process.
,
48
, pp.
173
180
.
3.
Yuge
,
T.
, 1960, “
Experiments on Heat Transfer From Spheres Including Combined Natural and Forced Convection
,”
ASME J. Heat Transfer
,
82
, pp.
214
220
.
4.
Brown
,
W. S.
,
Pitts
,
C. C.
, and
Leppert
,
G.
, 1962, “
Forced Convection Heat Transfer From a Uniformly Heated Sphere
,”
ASME J. Heat Transfer
,
84
, pp.
133
172
.
5.
Brian
,
P. L. T.
, and
Hales
,
H. B.
, 1969, “
Effects of Transpiration and Changing Diameter on Heat and Mass Transfer to Spheres
,”
AIChE J.
,
15
, pp.
419
425
.
6.
Friedlander
,
S. K.
, 1957, “
Mass and Heat Transfer to Single Spheres and Cylinders at Low Reynolds Numbers
,”
AIChE J.
,
3
, pp.
43
48
.
7.
Sayegh
,
N. N.
, and
Gauvin
,
W. H.
, 1979, “
Numerical Analysis of Variable Property Heat Transfer to a Single Sphere in High Temperature Surroundings
,”
AIChE J.
,
25
, pp.
522
534
.
8.
Oliver
,
D. L. R.
, and
Chung
,
J. N.
, 1990, “
Unsteady Conjugate Heat Transfer From a Translating Fluid Sphere at Moderate Reynolds Numbers
,”
Int. J. Heat Mass Transfer
,
33
, pp.
401
408
.
9.
Michaelides
,
E. E.
, and
Feng
,
Z.
, 1994, “
Heat Transfer From a Rigid Sphere in a Nonuniform Flow and Temperature Field
,”
Int. J. Heat Mass Transfer
,
14
, pp.
2069
2076
.
10.
Bagchi
,
P.
,
Ha
,
M. Y.
, and
Balachandar
,
S.
, 2001, “
Direct Numerical Simulation of Flow and Heat Transfer From a Sphere in a Uniform Cross-Flow
,”
ASME J. Fluids Eng.
,
123
, pp.
347
358
.
11.
Richter
,
A.
, and
Nikrityuk
,
P. A.
, 2012, “
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
, pp.
1343
1354
.
12.
Nijemeisland
,
M.
, and
Dixon
,
A. G.
, 2001, “
Comparison of CFD Simulations to Experiment for Convective Heat Transfer in a Gas-Solid Fixed Bed
,”
Chem. Eng. J.
,
82
, pp.
231
246
.
13.
Suekane
,
T.
,
Yokouchi
,
Y.
, and
Hirai
,
S.
, 2003, “
Inertial Flow Structures in a Simple-Packed Bed of Spheres
,”
AIChE J.
,
49
, pp.
10
17
.
14.
Gunjal
,
P. R.
,
Ranade
,
V. V.
, and
Chaudhari
,
R. V.
, 2005, “
Computational Study of a Single-Phase Flow in Packed Beds of Spheres
,”
AIChE J.
,
51
, pp.
365
378
.
15.
Jafari
,
A.
,
Zamankhan
,
P.
,
Mousavi
,
S. M.
, and
Pietarinen
,
K.
, 2008, “
Modeling and CFD Simulation of Flow Behavior and Dispersivity Through Randomly Packed Bed Reactors
,”
Chem. Eng. J.
,
144
, pp.
476
482
.
16.
Kopanidis
,
A.
,
Theodorakakos
,
A.
,
Gavaises
,
M.
, and
Bouris
,
D.
, 2011, “
Pore Scale 3D Modelling of Heat and Mass Transfer in the Gas Diffusion Layer and Cathode Channel of a PEM Fuel Cell
,”
Int. J. Therm. Sci.
,
50
, pp.
456
467
.
17.
Sheard
,
G. J.
,
Thompson
,
M. C.
, and
Hourigan
,
K.
, 2003, “
From Spheres to Circular Cylinders: The Stability and Flow Structures of Bluff Ring Wakes
,”
J. Fluid Mech.
,
492
, pp.
147
180
.
18.
Yao
,
Z.
, and
Bowick
,
M. J.
, 2011, “
The Shrinking Instability of Toroidal Liquid Droplets in the Stokes Flow Regime
,”
Eur. Phys. J. E
,
34
, pp.
1
6
.
19.
Deen
,
N.
,
Annaland
,
M. V. S.
, der
Hoef
,
M. V.
, and
Kuipers
,
J.
, 2007, “
Review of Discrete Particle Modeling of Fluidized Beds
,”
Chem. Eng. Sci.
,
62
, pp.
28
44
.
20.
Johnson
,
T. A.
, and
Patel
,
V. C.
, 1999, “
Flow Past a Sphere up to a Reynolds Number of 300
,”
J. Fluid Mech.
,
378
, pp.
19
70
.
21.
ANSYS, Inc., 2011, “
ANSYS-FLUENTTM V 13.0—Commercially Available CFD Software Package Based on the Finite Volume Method
,” Southpointe, 275 Technology Drive, Canonsburg, PA 15317, www.ansys.comwww.ansys.com
22.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Taylor & Francis Inc.
,
London
.
23.
Leonard
,
B. P.
, 1979, “
A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation
,”
Comput. Methods Appl. Mech. Eng.
,
19
, pp.
59
98
.
24.
Posdziech
,
O.
, and
Grundmann
,
R.
, 2007, “
A Systematic Approach to the Numerical Calculation of Fundamental Quantities of the Two-Dimensional Flow Over a Circular Cylinder
,”
J. Fluids Struct.
,
23
, pp.
479
499
.
25.
Ozalp
,
A. A.
, and
Dincer
,
I.
, 2010, “
Laminar Boundary Layer Development Around a Circular Cylinder: Fluid Flow and Heat-Mass Transfer Characteristics
,”
ASME J. Heat Transfer
,
132
,
121703
.
26.
Ferziger
,
J. H.
, and
Peric
,
M.
, 2002,
Computational Methods for Fluid Dynamics
, 3rd ed.,
Springer
,
Berlin
.
27.
Schlichting
,
H.
, and
Gersten
,
K.
, 2003,
Boundary-Layer Theory
,
Springer
,
New York
.
28.
Shirayama
,
S.
, 1992, “
Flow Past a Sphere: Topological Transitions of the Vorticity Field
,”
AIAA J.
,
30
, pp.
349
358
.
29.
Tabata
,
M.
, and
Itakura
,
K.
, 1998, “
A Precise Computation of Drag Coefficients of a Sphere
,”
Int. J. Comput. Fluid Dyn.
,
9
, pp.
303
311
.
30.
Mittal
,
R.
, 1999, “
A Fourier-Chebyshev Spectral Collocation Method for Simulating Flow Past Spheres and Spheroids
,”
Int. J. Numer. Methods Fluids
,
30
, pp.
921
937
.
31.
Clift
,
R.
,
Grace
,
J. R.
, and
Weber
,
M. E.
, 1978,
Bubbles, Drops and Particles
,
Academic
,
New York
.
32.
Haider
,
A.
, and
Levenspiel
,
O.
, 1989, “
Drag Coefficient and Terminal Velocity of Spherical and Nonspherical Particles
,”
Powder Technol.
,
58
, pp.
63
70
.
33.
Yow
,
H. N.
,
Pitt
,
M. J.
, and
Salman
,
A. D.
, 2005, “
Drag Correlations for Particles of Regular Shape
,”
Adv. Powder Technol.
,
16
, pp.
363
372
.
34.
Jeong
,
J.
, and
Hussain
,
F.
, 1995, “
On the Identification of a Vortex
,”
J. Fluid Mech.
,
285
, pp.
69
94
.
35.
StatPoint Technologies, Inc., 2011, “
STATGRAPHICS Centurion XVITM—Commercially Available Software Package for Statistical Analysis
,” Warrenton, VA, www.statlets.comwww.statlets.com
36.
Omori
,
T.
,
Kakirlic
,
S.
,
Tropea
,
C.
, and
Obi
,
S.
, 2008, “
Shearless and Sheared Flow Past a Circular Cylinder: Comparative Analysis by Means of LES
,”
Int. J. Heat Fluid Flow
,
29
, pp.
703
720
.
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