In this study, we examine the development length requirements for laminar Couette–Poiseuille flows in a two-dimensional (2D) channel as well as in the three-dimensional (3D) case of flow through a square duct, using a combination of numerical and experimental approaches. The parameter space investigated covers wall to bulk velocity ratios, r, spanning from 0 (purely pressure-driven flow) to 2 (purely wall driven-flow; 4 in the case of a square duct) and a wide range of Reynolds numbers (Re). The results indicate an increase in the development length (L) with r. Consistent with the findings of Durst et al. (2005, “The Development Lengths of Laminar Pipe and Channel Flows,” ASME J. Fluids Eng., 127(6), pp. 1154–1160), L was observed to be of the order of the channel height in the limit as Re0, irrespective of the condition at the inlet. This, however, changes at high Reynolds numbers, with L increasing linearly with Re. In all the cases considered, a uniform velocity profile at the inlet was found to result in longer entry lengths than in a flow developing from a parabolic inlet profile. We show that this inlet effect becomes less important as the limit of purely wall-driven flow is approached. Finally, we develop correlations for predicting L in these flows and, for the first time, also present laser Doppler velocimetry (LDV) measurements of the developing as well as fully-developed velocity profiles, and observe good agreement between experiment, analytical solution, and numerical simulation results in the 3D case.

References

References
1.
Shah
,
R. K.
, and
London
,
A. L.
,
1978
,
Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data
,
Academic Press
, New York.
2.
McComas
,
S.
,
1967
, “
Hydrodynamic Entrance Lengths for Ducts of Arbitrary Cross Section
,”
ASME J. Basic Eng.
,
89
(
4
), pp.
847
850
.
3.
Durst
,
F.
,
Ray
,
S.
,
Ünsal
,
B.
, and
Bayoumi
,
O. A.
,
2005
, “
The Development Lengths of Laminar Pipe and Channel Flows
,”
ASME J. Fluids Eng.
,
127
(
6
), pp.
1154
1160
.
4.
Poole
,
R. J.
,
2010
, “
Development-Length Requirements for Fully Developed Laminar Flow in Concentric Annuli
,”
ASME J. Fluids Eng.
,
132
(
6
), p.
064501
.
5.
Poole
,
R. J.
, and
Chhabra
,
R. P.
,
2010
, “
Development Length Requirements for Fully Developed Laminar Pipe Flow of Yield Stress Fluids
,”
ASME J. Fluids Eng.
,
132
(
3
), p.
034501
.
6.
Poole
,
R. J.
, and
Ridley
,
B. S.
,
2007
, “
Development-Length Requirements for Fully Developed Laminar Pipe Flow of Inelastic Non-Newtonian Liquids
,”
ASME J. Fluids Eng.
,
129
(
10
), pp.
1281
1287
.
7.
Joshi
,
Y.
, and
Vinoth
,
B. R.
,
2018
, “
Entry Lengths of Laminar Pipe and Channel Flows
,”
ASME J. Fluids Eng.
,
140
(
6
), p.
061203
.
8.
Yunus
,
A. C.
, and
Cimbala
,
J. M.
,
2006
,
Fluid Mechanics Fundamentals and Applications
,
McGraw-Hill
, New York.
9.
Tatsumi
,
T.
, and
Yoshimura
,
T.
,
1990
, “
Stability of the Laminar Flow in a Rectangular Duct
,”
J. Fluid Mech.
,
212
(
1
), pp.
437
449
.
10.
Kountouriotis
,
Z.
,
Philippou
,
M.
, and
Georgiou
,
G. C.
,
2016
, “
Development Lengths in Newtonian Poiseuille Flows With Wall Slip
,”
Appl. Maths. Comp.
,
291
, pp.
98
114
.
11.
Philippou
,
M.
,
Kountouriotis
,
Z.
, and
Georgiou
,
G. C.
,
2016
, “
Viscoplastic Flow Development in Tubes and Channels With Wall Slip
,”
J. Non-Newtonian Fluid Mech.
,
234
, pp.
69
81
.
12.
Ferrás
,
L. L.
,
Afonso
,
A. M.
,
Alves
,
M. A.
,
Nóbrega
,
J. M.
, and
Pinho
,
F. T.
,
2012
, “
Development Length in Planar Channel Flows of Newtonian Fluids Under the Influence of Wall Slip
,”
ASME J. Fluids Eng.
,
134
(
10
), p.
104503
.
13.
Galvis
,
E.
,
Yarusevych
,
S.
, and
Culham
,
J.
,
2012
, “
Incompressible Laminar Developing Flow in Microchannels
,”
ASME J. Fluids Eng.
,
134
(
1
), p.
014503
.
14.
Ray
,
S.
,
Ünsal
,
B.
, and
Durst
,
F.
,
2012
, “
Development Length of Sinusoidally Pulsating Laminar Pipe Flows in Moderate and High Reynolds Number Regimes
,”
Int. J. Heat Fluid Flow
,
37
, pp.
167
176
.
15.
Muzychka
,
Y.
, and
Yovanovich
,
M.
,
2009
, “
Pressure Drop in Laminar Developing Flow in Noncircular Ducts: A Scaling and Modeling Approach
,”
ASME J. Fluids Eng.
,
131
(
11
), p.
111105
.
16.
Astill
,
K. N.
,
Ganley
,
J. T.
, and
Martin
,
B. W.
,
1968
, “
The Developing Tangential Velocity Profile for Axial Flow in an Annulus With a Rotating Inner Cylinder
,”
Proc. R. Soc. London
,
307
(
1488
), pp.
55
69
.
17.
Holeschovsky
,
U. B.
, and
Cooney
,
C. L.
,
1991
, “
Quantitative Description of Ultrafiltration in a Rotating Filtration Device
,”
AIChE J.
,
37
(
8
), pp.
1219
1226
.
18.
Cohen
,
S.
, and
Marom
,
D. M.
,
1983
, “
Experimental and Theoretical Study of a Rotating Annular Flow Reactor
,”
Chem. Eng. J.
,
27
(
2
), pp.
87
97
.
19.
Davoodi
,
M.
,
Lerouge
,
S.
,
Norouzi
,
M.
, and
Poole
,
R. J.
,
2018
, “
Secondary Flows Due to Finite Aspect Ratio in Inertialess Viscoelastic Taylor-Couette Flow
,”
J. Fluid Mech.
,
857
, pp.
823
850
.
20.
Dennis
,
D. J. C.
,
Seraudie
,
C.
, and
Poole
,
R. J.
,
2014
, “
Controlling Vortex Breakdown in Swirling Pipe Flows: Experiments and Simulations
,”
Phys. Fluids
,
26
(
5
), p.
053602
.
21.
Mettu
,
S.
,
Verma
,
N.
, and
Chhabra
,
R.
,
2006
, “
Momentum and Heat Transfer From an Asymmetrically Confined Circular Cylinder in a Plane Channel
,”
Heat Mass Transfer
,
42
(
11
), pp.
1037
1048
.
22.
Chakraborty
,
J.
,
Verma
,
N.
, and
Chhabra
,
R.
,
2004
, “
Wall Effects in Flow Past a Circular Cylinder in a Plane Channel: A Numerical Study
,”
Chem. Eng. Proc.
,
43
(
12
), pp.
1529
1537
.
23.
Escudier
,
M. P.
,
O'Leary
,
J.
, and
Poole
,
R. J.
,
2007
, “
Flow Produced in a Conical Container by a Rotating Endwall
,”
Int. J. Heat Fluid Flow
,
28
(
6
), pp.
1418
1428
.
24.
Fellouah
,
H.
,
Castelain
,
C.
,
El Moctar
,
A.
, and
Peerhossaini
,
H.
,
2006
, “
A Numerical Study of Dean Instability in Non-Newtonian Fluids
,”
ASME J. Fluids Eng.
,
128
(
1
), pp.
34
41
.
25.
Ferziger
,
J. H.
, and
Peric
,
M.
,
2012
,
Computational Methods for Fluid Dynamics
,
3rd ed.
,
Springer Science & Business Media
,
London
.
26.
White
,
F. M.
,
2006
,
Viscous Fluid Flow
,
3rd ed.
,
McGraw-Hill
,
New York
.
27.
Owolabi
,
B. E.
,
Poole
,
R. J.
, and
Dennis
,
D. J. C.
,
2016
, “
Experiments on Low-Reynolds-Number Turbulent Flow Through a Square Duct
,”
J. Fluid Mech.
,
798
, pp.
398
410
.
28.
Draad
,
A.
, and
Nieuwstadt
,
F.
,
1998
, “
The Earth's Rotation and Laminar Pipe Flow
,”
J. Fluid Mech.
,
361
, pp.
297
308
.
You do not currently have access to this content.