Even after several decades of experimental and numerical testing, our present-day knowledge of the axisymmetric turbulent boundary layer (TBL) along long thin circular cylinders still lacks a clear picture of many fundamental characteristics. The main issues causing this reside in the experimental testing complexities and the numerical simplifications. An important characteristic that is crucial for routine scaling is the boundary layer length scales, but the downstream growth of these scales (boundary layer, displacement, and momentum thicknesses) is largely unknown from the leading to trailing edges. Herein, we combine pertinent datasets with many complementary numerical computations (large-eddy simulations) to address this shortfall. We are particularly interested in expressing the length scales in terms of the radius-based and axial-based Reynolds numbers (Rea and Rex). Although the composite dataset gave an averaged shape factor H = 1.09 that is substantially lower than the planar value (H = 1.27), the shape factor distribution along the cylinder axis actually begins at the flat plate value then decays logarithmically to near unity. The integral length scales displayed power-law evolutions with variable exponents until high Rea (Rea > 35,000) where both scales then mimic streamwise consistency. Beneath this threshold, their streamwise growth is much slower than the flat plate (especially at low-Rea). The boundary layer thickness grew according to an empirical expression that is dependent on both Rea and Rex where its streamwise growth can far exceed the planar turbulent flow. These unique characteristics rank the thin cylinder axisymmetric TBL as a separate canonical flow, which was well documented by the previous investigations.

References

References
1.
Richmond
,
R. I.
,
1957
, “
Experimental Investigation of Thick Axially Symmetric Boundary Layers on Cylinders at Subsonic and Hypersonic Speeds
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
2.
Yu
,
Y. S.
,
1958
, “
Effects Of Transverse Curvature on Turbulent Boundary Layer Characteristics
,”
J. Ship Res.
,
3
, pp.
33
41
.
3.
Willmarth
,
W. W.
, and
Yang
,
C. S.
,
1970
, “
Wall Pressure Fluctuations Beneath Turbulent Boundary Layers on a Flat Plate and a Cylinder
,”
J. Fluid Mech.
,
41
, pp.
47
80
.10.1017/S0022112070000526
4.
Rao
,
G. N. V.
and
Keshavan
,
N. R.
,
1972
, “
Axisymmetric Turbulent Boundary Layers in Zero Pressure-Gradient Flows
,”
ASME J. Appl. Mech.
,
94
, pp.
25
32
.10.1115/1.3422623
5.
Afzal
,
N.
, and
Singh
,
K. P.
,
1976
, “
Measurements in an Axisymmetric Turbulent Boundary Layer Along a Circular Cylinder
,”
Aero. Q.
,
27
, pp.
217
228
.
6.
Willmarth
,
W. W.
,
Winkel
,
R. E.
,
Sharma
,
L. K.
, and
Bogar
,
T. J.
,
1976
, “
Axially Symmetric Turbulent Boundary Layers on Cylinders; Mean Velocities Profiles and Wall Pressure Fluctuations
,”
J. Fluid Mech.
,
76
(
1
), pp.
35
64
.10.1017/S002211207600311X
7.
Luxton
,
R. E.
,
Bull
,
M. K.
, and
Rajagopalan
,
S.
,
1984
, “
The Thick Turbulent Boundary Layer on a Long Fine Cylinder in Axial Flow
,”
J. Aero.
,
88
, pp.
186
199
.
8.
Lueptow
,
M. R.
,
Leehey
,
P.
, and
Stellinger
,
T.
,
1985
, “
The Thick Turbulent Boundary Layer on a Cylinder: Mean and Fluctuating Velocities
,”
Phys. Fluids
,
28
(
12
), pp.
3495
3505
.10.1063/1.865417
9.
Neves
,
J. C.
,
Moin
,
P.
, and
Moser
,
R. D.
,
1994
, “
Effects of Convex Transverse Curvature on Wall-Bounded Turbulence. Part 1. The Velocity and Vorticity
,”
J. Fluid Mech.
,
272
, pp.
349
383
.10.1017/S0022112094004490
10.
Woods
,
M.
,
2002
, “
Computation of Axial and Near-Axial Flow Over a Long Circular Cylinder
,” Ph.D. thesis, School of Mechanical Engineering, University of Adelaide, Adelaide, Australia.
11.
Tutty
,
O. R.
,
2008
, “
Flow Along a Long Thin Cylinder
,”
J. Fluid Mech.
,
602
, pp.
1
37
.10.1017/S0022112008000542
12.
Jordan
,
S. A.
,
2011
, “
Axisymmetric Turbulent Statistics of Long Slender Circular Cylinders
,”
Phys. Fluids
,
23
,
075105
.10.1063/1.3609272
13.
White
,
F. M.
,
1969
, “
The Axisymmetric Turbulent Boundary Layer on an Extremely Long Cylinder
,”
Navy Underwater Sound Laboratory
,
New London, CN
, NUSL Report No. 1058.
14.
Jordan
,
S. A.
,
2012
, “
An Inflow Method for Axisymmetric Turbulent Boundary Layers Along Very Long Slender Cylinders
,”
ASME J. Fluids Eng.
,
134
,
051202
.10.1115/1.4006512
15.
Lund
,
T. S.
,
Wu
,
X.
, and
Squires
,
K. D.
,
1998
, “
Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations
,”
J. Comput. Phys.
,
140
, pp.
233
258
.10.1006/jcph.1998.5882
16.
Cipolla
,
K. M.
, and
Keith
,
W. L.
,
2003
, “
Momentum Thickness Measurements for Thick Axisymmetric Turbulent Boundary Layers
,”
ASME J. Fluids Eng.
,
125
, pp.
569
575
.10.1115/1.1568359
17.
Jordan
,
S. A.
,
1999
, “
A Large-Eddy Simulation Methodology in Generalized Curvilinear Coordinates
,”
J. Comput. Phys.
,
148
, pp.
322
340
.10.1006/jcph.1998.6112
18.
Jordan
,
S. A.
,
2001
, “
Dynamic Subgrid-Scale Modeling for Large-Eddy Simulations in Complex Topologies
,”
ASME J. Fluids Eng.
,
123
, pp.
619
627
.10.1115/1.1374215
19.
Lilly
,
D. K.
,
1992
, “
A Proposed Modification of the Germano Subgrid-Scale Closure Method
,”
Phys. Fluids A
,
4
, pp.
633
635
.10.1063/1.858280
20.
Jordan
,
S. A.
,
2007
, “
The Spatial Resolution Properties of Composite Compact Finite Differencing
,”
J. Comput. Phys.
,
221
, pp.
558
576
.10.1016/j.jcp.2006.06.026
21.
Keating
,
A.
,
Piomelli
,
U.
,
Balaras
,
E.
, and
Kaltenbach
,
H.-J.
,
2004
, “
A-Priori and A-Posteriori Tests of Inflow Conditions for Large-Eddy Simulation
,”
Phys. Fluids
,
16
, pp.
4696
4712
.10.1063/1.1811672
22.
Spalding
,
D. B.
,
1961
, “
A Single Formula for the Law of the Wall
,”
ASME J. Appl. Mech.
,
28
, pp.
455
458
.10.1115/1.3641728
23.
Rao
,
G. N.
V
.
,
1967
, “
The Law of the Wall in a Thick Axi-Symmetric Turbulent Boundary Layer
,”
ASME J. Appl. Mech.
,
89
, pp.
237
338
.10.1115/1.3607642
24.
Jordan
,
S. A.
,
2008
, “
A-Priori Assessments of Numerical Uncertainty in Large Eddy Simulations
,”
ASME J. Fluids Eng.
,
127
, pp.
1171
1182
.10.1115/1.2060735
25.
Berera
,
F. L.
,
2004
, “
An Investigation of the Flow Along and Induced Vibration of Long Cylinders
,” Ph.D. thesis, School of Mechanical Engineering, Adelaide University, Adelaide, Australia.
26.
Snarski
,
S. R.
, and
Lueptow
,
R. M.
,
1995
, “
Wall Pressure and Coherent Structures in a Turbulent Boundary Layer on a Cylinder in Axial Flow
,”
J. Fluid Mech.
,
286
, pp.
137
171
.10.1017/S0022112095000681
27.
De Langre
,
E.
,
Paidoussis
,
M. P.
,
Doare
,
O.
, and
Modarres-Sadeghi
,
Y.
,
2002
, “
Flutter of Long Flexible Cylinders in Axial Flow
,”
J. Fluid Mech.
,
571
, pp.
371
389
.10.1017/S002211200600317X
28.
Chase
,
D. M.
,
1987
, “
Character of the Turbulent Wall Pressure Spectrum at Subconvective Wavenumbers and a Suggested Comprehensive Model
,”
J. Sound Vib.
,
112
(
1
), pp.
125
147
.10.1016/S0022-460X(87)80098-6
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