The bluff body simulations over canonical forms like circular and square cylinders are very well studied and the correlations for bulk parameters like mean drag coefficient and Strouhal numbers for the same are reported widely. In the case of elliptic cylinder, the literature is very sparse, especially for moderate Reynolds number (Re). Hence, in this work, a detailed study about fluid flow characteristics over an elliptic cylinder placed in a free stream is performed. Simulations are carried out for different Re ranging from 50 to 500 with axis ratio (AR) varied between 0.1 to 1.0 in steps of 0.1. Immersed boundary method is used for the solid boundary condition implementation which avoids the grid generation for each AR and a single Cartesian grid is used for all the simulations. The effect of AR for various Reynolds numbers is also focused on using the in-house code. The influence of AR is phenomenal for all the Re and the values of wake length, drag coefficient, and Strouhal number decrease with decreasing AR for a particular Re. The critical ARs, for vortex shedding and wake formation, are identified for various Re. Detailed correlations for wake length, critical ARs for vortex shedding and wake formation, mean drag coefficient and Strouhal number, in terms of AR, are reported in this work.

## References

References
1.
Tritton
,
D. J.
,
1959
, “
Experiments on the Flow Past a Circular Cylinder at Low Reynolds Numbers
,”
J. Fluid Mech.
,
6
, pp.
547
567
.10.1017/S0022112059000829
2.
Zdravkovich
,
M. M.
,
1997
,
Flow Around Circular Cylinders, Vol. 1: Fundamentals
,
Oxford University Press
,
New York
.
3.
Williamson
,
C. H. K.
,
1996
, “
Vortex Dynamics in the Cylinder Wake
,”
Ann. Rev. Fluid Mech.
,
28
, pp.
477
539
.10.1146/annurev.fl.28.010196.002401
4.
Okajima
,
A.
,
1982
, “
Strouhal Numbers of Rectangular Cylinders
,”
J. Fluid Mech.
,
123
, pp.
379
398
.10.1017/S0022112082003115
5.
Sharma
,
A.
, and
Eswaran
,
V.
,
2004
, “
Heat and Fluid Flow Across a Square Cylinder in the Two-Dimensional Laminar Flow Regime
,”
Numer. Heat Transfer, Part A
,
45
, pp.
247
269
.10.1080/10407780490278562
6.
Williamson
,
C. H. K.
, and
Brown
,
G. L.
,
1998
, “
A Series in $1/Re$ to Represent the Strouhal–Reynolds Number Relationship of the Cylinder Wake
,”
J. Fluids Struct.
,
12
(
8
), pp.
1073
1085
.10.1006/jfls.1998.0184
7.
Henderson
,
R. D.
,
1995
, “
Details of the Drag Curve Near the Onset of Vortex Shedding
,”
Phys. Fluids
,
7
(
9
), pp.
2102
2104
.10.1063/1.868459
8.
Lugst
,
H. J.
, and
Haussling
,
H. J.
,
1974
, “
Laminar Flow Past an Abruptly Accelerated Elliptic Cylinder at 45 deg Incidence
,”
J. Fluid Mech.
,
65
, pp.
711
734
.10.1017/S0022112074001613
9.
Tandea
,
S.
,
1977
, “
,”
Prog. Aerosp. Sci.
,
17
, pp.
287
348
.10.1016/0376-0421(76)90011-7
10.
Patel
,
K. A.
,
1981
, “
Flow Around the Impulsively Started Elliptic Cylinder at Various Angles of Attack
,”
Comput. Fluids
,
9
, pp.
167
175
.10.1016/0045-7930(81)90014-1
11.
Ota
,
T.
, and
Nishiyama
,
H.
,
1986
, “
Flow Around Two Elliptic Cylinders in Tandem Arrangement
,”
ASME J. Fluids Eng.
,
108
, pp.
98
103
.10.1115/1.3242551
12.
Ota
,
T.
,
Nishiyama
,
H.
, and
Taoka
,
Y.
,
1987
, “
Flow Around an Elliptic Cylinder in the Critical Reynolds Number Regime
,”
ASME J. Fluids Eng.
,
109
, pp.
149
155
.10.1115/1.3242635
13.
Jackson
,
C. P.
,
1987
, “
A Finite Element Study of the Onset of Vortex Shedding in Flow Past Variously Shaped Bodies
,”
J. Fluid Mech.
,
182
, pp.
23
45
.10.1017/S0022112087002234
14.
Park
,
J. K.
,
Park
,
S. O.
, and
Hyun
,
J. M.
,
1989
, “
Flow Regimes of Unsteady Laminar Flow Past a Slender Elliptic Cylinder at Incidence
,”
Int. J. Heat Fluid Flow
,
10
, pp.
311
317
.10.1016/0142-727X(89)90019-2
15.
,
H.
,
1994
, “
Oscillating Viscous Flow Over an Inclined Elliptic Cylinder
,”
Ocean Eng.
,
21
, pp.
401
426
.10.1016/0029-8018(94)90012-4
16.
D'Alessio
,
S. J. D.
, and
Kocabiyik
,
S.
,
2001
, “
Numerical Simulation of the Flow Induced by a Transversely Oscillating Inclined Elliptic Cylinder
,”
J. Fluids Struct.
,
15
, pp.
691
715
.10.1006/jfls.2000.0372
17.
Kocabiyik
,
S.
, and
D'Alessio
,
S. J. D.
,
2004
, “
Numerical Study of Flow Around an Inclined Elliptic Cylinder Oscillating in Line With an Incident Uniform Flow
,”
Eru. J. Mech. B/Fluids
,
23
, pp.
279
302
.10.1016/j.euromechflu.2003.09.001
18.
Faruquee
,
Z.
,
Ting
,
D. S.-K.
,
Fartaj
,
A.
,
Barron
,
R. M.
, and
Carriveau
,
R.
,
2007
, “
The Effects of Axis Ratio on Laminar Fluid Flow Around an Elliptical Cylinder
,”
Int. J. Heat Fluid Flow
,
28
, pp.
1178
1189
.10.1016/j.ijheatfluidflow.2006.11.004
19.
Mittal
,
R.
, and
Iaccarino
,
G.
,
2005
, “
Immersed Boundary Methods
,”
Ann. Rev. Fluid Mech.
,
37
, pp.
239
261
.10.1146/annurev.fluid.37.061903.175743
20.
Kim
,
J.
,
Kim
,
D.
, and
Choi
,
H.
,
2001
, “
An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries
,”
J. Comput. Phys.
,
171
, pp.
132
150
.10.1006/jcph.2001.6778
21.
Pacheco
,
J. R.
,
Pacheco-Vega
,
A.
,
Rodic
,
T.
, and
Peck
,
R. E.
,
2005
, “
Numerical Simulation of Heat Transfer and Fluid Flow Problems Using an Immersed-Boundary Finite-Volume Method on Non-Staggered Grids
,”
Numer. Heat Transfer, Part B
,
48
, pp.
1
24
.10.1080/10407790590935975
22.
Su
,
S. W.
,
Lai
,
M. C.
, and
Lin
,
C. A.
,
2007
, “
An Immersed Boundary Technique for Simulating Complex Flows with Rigid Boundary
,”
Comput. Fluids
,
36
, pp.
313
324
.10.1016/j.compfluid.2005.09.004
23.
Brown
,
D. L.
,
Cortez
,
L.
, and
Minion
,
M.
,
2001
, “
Accurate Projection Methods for the Incompressible Navier–Stokes Equations
,”
J. Comput. Phys.
,
168
, pp.
464
499
.10.1006/jcph.2001.6715
24.
Shin
,
S. J.
,
Huang
,
W. X.
, and
Sung
,
H. J.
,
2008
, “
Assessment of Regularized Delta Functions and Feedback Forcing Schemes for an Immersed Boundary Method
,”
Int. J. Numer. Methods Fluids
,
58
, pp.
263
286
.10.1002/fld.1706
25.
Van der Vorst
,
H. A.
,
2000
, “
Iterative Methods for Large Linear Systems
,” Tech. Report, Mathematical Institute, Utrecht University, Utrecht, The Netherlands.
26.
Guy
,
R. D.
, and
Hartenstine
,
D. A.
,
2010
, “
On the Accuracy of Direct Forcing Immersed Boundary Methods with Projection Methods
,”
J. Comput. Phys.
,
229
, pp.
2479
2496
.10.1016/j.jcp.2009.10.027
27.
Sudhakar
,
Y.
, and
,
S.
,
2010
, “
Flight Force Production by Flapping Insect Wings in Inclined Stroke Plane Kinematics
,”
Comput. Fluids
,
39
, pp.
683
695
.10.1016/j.compfluid.2009.11.004
28.
Sudhakar
,
Y.
, and
,
S.
,
2012
, “
Vortex Shedding Characteristics of a Circular Cylinder With an Oscillating Wake Splitter Plate
,”
Comput. Fluids
,
53
, pp.
40
52
.10.1016/j.compfluid.2011.09.003
29.
Raman
,
S. K.
,
Prakash
,
K. A.
, and
,
S.
,
2012
, “
Natural Convection from a Heated Elliptic Cylinder With Different Axis Ration in a Square Enclosure
,”
Numer. Heat Transfer Part A
,
62
, pp.
639
658
.10.1080/10407782.2012.707058
30.
Lange
,
C.
,
Durst
,
F.
, and
Breuer
,
M.
,
1998
, “
Momentum and Heat Transfer from Cylinders in Laminar Crossflow at 10−4 ≤ Re ≤ 200
,”
Int. J. Heat Mass Transfer
,
41
(
22
), pp.
3409
3430
.10.1016/S0017-9310(98)00077-5
31.
Dennis
,
S. C. R.
, and
Chang
,
G.-Z.
,
1970
, “
Numerical Solutions for Steady Flow Past a Circular Cylinder at Reynolds Numbers up to 100
,”
J. Fluid Mech.
,
42
, pp.
471
489
.10.1017/S0022112070001428
32.
Raman
,
S. K.
,
2012
, “
Fluid flow and Heat Transfer Over an Elliptic Cylinder Using Immersed Boundary Method
,” M.S. thesis, Department of Applied Mechanics, Indian Institute of Technology, Madras, India.
33.
Dennis
,
S. C. R.
, and
Dunwoody
,
J.
,
1966
, “
The Steady Flow of a Viscous Fluid Past a Flat Plate
,”
J. Fluid Mech.
,
24
, pp.
577
595
.10.1017/S0022112066000831
34.
Mittal
,
R.
, and
Balachandar
,
S.
,
1996
, “
Direct Numerical Simulation of Flow Past Elliptic Cylinders
,”
J. Comput. Phys.
,
124
, pp.
351
367
.10.1006/jcph.1996.0065
35.
Kim
,
M. S.
, and
Sengupta
,
A.
,
2005
, “
Unsteady Viscous Flow Over Elliptic Cylinder at Various Thickness With Different Reynolds Number
,”
J. Mech. Sci. Technol.
,
19
, pp.
877
486
.10.1007/BF02916136