Abstract

Two-dimensional flow over bluff bodies is studied in the unsteady laminar flow regime using numerical simulations. In previous investigations, lift and drag forces have been studied over different cross-sectional shapes like circles, squares, and ellipses. We aim to extend the previous research by studying the variation of hydrodynamic forces as the shape of the body changes from a circular cylinder to a more streamlined or a bluffer body. The different body shapes are created by modifying the downstream circular arc of a circular cylinder into an ellipse, hence elongating or compressing the rear part of the body. The precise geometry of the body is quantified by defining a shape factor. Two distinct ranges of shape factors with fundamentally different behavior of lift and drag are identified. The geometry constituting the limit is where the rear part ellipse has a semi-minor axis of half the radius of the original circle, independent of the Reynolds number. On the other hand, the vortex shedding frequency decreases linearly over the whole range of shape factors. Furthermore, the variation of the forces and frequency with Reynolds number, and how the relations vary with the shape factor are reported.

References

References
1.
Zdravkovich
,
M.
, and
Bearman
,
P.
,
1998
,
Flow around Circular Cylinders: Fundamentals
, Vol.
1
,
American Society of Mechanical Engineers
,
New York
.
2.
Schlichting
,
H.
,
1979
,
Boundary Layer Theory
, 7th ed.,
McGraw-Hill
,
New York
.
3.
Green
,
S. I.
,
1995
,
Fluid Vortices: Fluid Mechanics and Its Applications
, Vol.
30
,
Springer
,
Dordrecht, The Netherlands
.
4.
Perry
,
A.
,
Chong
,
M.
, and
Lim
,
T.
,
1982
, “
The Vortex-Shedding Process behind Two-Dimensional Bluff Bodies
,”
J. Fluid Mech.
,
116
, pp.
77
90
.10.1017/S0022112082000378
5.
Roshko
,
A.
,
1954
, “
On the Development of Turbulent Wakes from Vortex Streets
,” California Institute of Technology, Pasadena, CA, Report No. NACA 1191.
6.
Bloor
,
M. S.
,
1964
, “
The Transition to Turbulence in the Wake of a Circular Cylinder
,”
J. Fluid Mech.
,
19
(
2
), pp.
290
304
.10.1017/S0022112064000726
7.
Williamson
,
C.
,
1996
, “
Vortex Dynamics in the Cylinder Wake
,”
Annu. Rev. Fluid Mech.
,
28
(
1
), pp.
477
539
.10.1146/annurev.fl.28.010196.002401
8.
Rajani
,
B.
,
Kandasamy
,
A.
, and
Majumdar
,
S.
,
2009
, “
Numerical Simulation of Laminar Flow past a Circular Cylinder
,”
Appl. Math. Model.
,
33
(
3
), pp.
1228
1247
.10.1016/j.apm.2008.01.017
9.
Mansy
,
H.
,
Yang
,
P.-M.
, and
Williams
,
D. R.
,
1994
, “
Quantitative Measurements of Three-Dimensional Structures in the Wake of a Circular Cylinder
,”
J. Fluid Mech.
,
270
, pp.
277
296
.10.1017/S0022112094004271
10.
Braza
,
M.
,
Chassaing
,
P.
, and
Minh
,
H. H.
,
1986
, “
Numerical Study and Physical Analysis of the Pressure and Velocity Fields in the near Wake of a Circular Cylinder
,”
J. Fluid Mech.
,
165
(
1
), p.
79
.10.1017/S0022112086003014
11.
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
(
3
), pp.
479
499
.10.1016/j.jfluidstructs.2006.09.004
12.
Tritton
,
D.
,
1959
, “
Experiments on the Flow past a Circular Cylinder at Low Reynolds Numbers
,”
J. Fluid Mech.
,
6
(
4
), pp.
547
567
.10.1017/S0022112059000829
13.
Dennis
,
S.
, and
Chang
,
G.-Z.
,
1970
, “
Numerical Solutions for Steady Flow past a Circular Cylinder at Reynolds Numbers up to 100
,”
J. Fluid Mech.
,
42
(
3
), pp.
471
489
.10.1017/S0022112070001428
14.
Gautier
,
R.
,
Biau
,
D.
, and
Lamballais
,
E.
,
2013
, “
A Reference Solution of the Flow over a Circular Cylinder at Re = 40
,”
Comput. Fluids
,
75
, pp.
103
111
.10.1016/j.compfluid.2012.12.017
15.
Park
,
J.
,
Kwon
,
K.
, and
Choi
,
H.
,
1998
, “
Numerical Solutions of Flow past a Circular Cylinder at Reynolds Numbers up to 160
,”
KSME Int. J.
,
12
(
6
), pp.
1200
1205
.10.1007/BF02942594
16.
Sohankar
,
A.
,
Norberg
,
C.
, and
Davidson
,
L.
,
1998
, “
Low-Reynolds-Number Flow around a Square Cylinder at Incidence: Study of Blockage, Onset of Vortex Shedding and Outlet Boundary Condition
,”
Int. J. Numer. Methods Fluids
,
26
(
1
), pp.
39
56
.10.1002/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-P
17.
Yoon
,
D.-H.
,
Yang
,
K.-S.
, and
Choi
,
C.-B.
,
2010
, “
Flow past a Square Cylinder with an Angle of Incidence
,”
Phys. Fluids
,
22
(
4
), p.
043603
.10.1063/1.3388857
18.
Mittal
,
R.
, and
Balachandar
,
S.
,
1996
, “
Direct Numerical Simulation of Flow past Elliptic Cylinders
,”
J. Comput. Phys.
,
124
(
2
), pp.
351
367
.10.1006/jcph.1996.0065
19.
Lugt
,
H.
, and
Haussling
,
H.
,
1974
, “
Laminar Flow past an Abruptly Accelerated Elliptic Cylinder at 45 Incidence
,”
J. Fluid Mech.
,
65
(
4
), pp.
711
734
.10.1017/S0022112074001613
20.
Kim
,
M.-S.
, and
Sengupta
,
A.
,
2005
, “
Unsteady Viscous Flow over Elliptic Cylinders at Various Thickness with Different Reynolds Numbers
,”
J. Mech. Sci. Technol.
,
19
(
3
), pp.
877
886
.10.1007/BF02916136
21.
Chandra
,
A.
, and
Chhabra
,
R.
,
2011
, “
Flow over and Forced Convection Heat Transfer in Newtonian Fluids from a Semi-Circular Cylinder
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
225
241
.10.1016/j.ijheatmasstransfer.2010.09.048
22.
Boisaubert
,
N.
,
Coutanceau
,
M.
, and
Ehrmann
,
P.
,
1996
, “
Comparative Early Development of Wake Vortices behind a Short Semicircular-Section Cylinder in Two opposite Arrangements
,”
J. Fluid Mech.
,
327
(
11
), pp.
73
99
.10.1017/S0022112096008464
23.
Farhadi
,
M.
,
Sedighi
,
K.
, and
Fattahi
,
E.
,
2010
, “
Effect of a Splitter Plate on Flow over a Semi-Circular Cylinder
,”
Proc. Inst. Mech. Eng., Part G
,
224
(
3
), pp.
321
330
.10.1243/09544100JAERO594
24.
Bhinder
,
A. P. S.
,
Sarkar
,
S.
, and
Dalal
,
A.
,
2012
, “
Flow over and Forced Convection Heat Transfer around a Semi-Circular Cylinder at Incidence
,”
Int. J. Heat Mass Transfer
,
55
(
19–20
), pp.
5171
5184
.10.1016/j.ijheatmasstransfer.2012.05.018
25.
Chatterjee
,
D.
,
Mondal
,
B.
, and
Halder
,
P.
,
2013
, “
Unsteady Forced Convection Heat Transfer over a Semicircular Cylinder at Low Reynolds Numbers
,”
Numer. Heat Transfer, Part A
,
63
(
6
), pp.
411
429
.10.1080/10407782.2013.742733
26.
Roshko
,
A.
,
1954
, “
On the Drag and Shedding Frequency of Two-Dimensional Bluff Bodies
,” National Advisory Committee for Aeronautics, Washington, DC, Report No.
NACA-TN-3169
.https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930083869.pdf
27.
Williamson
,
C.
,
1989
, “
Oblique and Parallel Modes of Vortex Shedding in the Wake of a Circular Cylinder at Low Reynolds Numbers
,”
J. Fluid Mech.
,
206
, pp.
579
627
.10.1017/S0022112089002429
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