Understanding the hydrodynamic properties of fluid flow in a curving pipe and channel is important for controlling the flow behavior in technologies and biomechanics. The nature of the resulting flow in a bent pipe is extremely complicated because of the presence of a cross-stream secondary flow. In an attempt to disentangle this complexity, we investigate the fluid dynamics in a bent channel via the direct numerical simulation of the Navier-Stokes equation in two spatial dimensions. We exploit the absence of secondary flow from our model and systematically investigate the flow structure along the channel as a function of both the bend angle and Reynolds number of the laminar-to-turbulent regime. We numerically suggest a scaling relation between the shape of the separation bubble and the flow conductance, and construct an integrated phase diagram.
REFERENCES
1.
P.
Helmholtz
, “XLIII. On discontinuous movements of fluids
,” London Edinburgh Dublin Philos. Mag. J. Sci.
36
, 337
(1868
).2.
D.
McConalogue
and R.
Srivastava
, “Motion of a fluid in a curved tube
,” Proc. R. Soc. London, Ser. A
307
, 37
(1968
).3.
W.
Lyne
, “Unsteady viscous flow in a curved pipe
,” J. Fluid Mech.
45
, 13
(1971
).4.
J.
Humphrey
, A.
Taylor
, and J.
Whitelaw
, “Laminar flow in a square duct of strong curvature
,” J. Fluid Mech.
83
, 509
(1977
).5.
J.
Humphrey
, J.
Whitelaw
, and G.
Yee
, “Turbulent flow in a square duct with strong curvature
,” J. Fluid Mech.
103
, 443
(1981
).6.
A.
Taylor
, J.
Whitelaw
, and M.
Yianneskis
, “Curved ducts with strong secondary motion: Velocity measurements of developing laminar and turbulent flow
,” J. Fluid Eng.
104
, 350
(1982
).7.
M.
Enayet
, M.
Gibson
, A.
Taylor
, and M.
Yianneskis
, “Laser-Doppler measurements of laminar and turbulent flow in a pipe bend
,” Int. J. Heat Fluid Flow
3
, 213
(1982
).8.
M.
Enayet
, M.
Gibson
, and M.
Yianneskis
, “Measurements of turbulent developing flow in a moderately curved square duct
,” Int. J. Heat Fluid Flow
3
, 221
(1982
).9.
D. Y.
Pui
, F.
Romay-Novas
, and B. Y.
Liu
, “Experimental study of particle deposition in bends of circular cross section
,” Aerosol Sci. Technol.
7
, 301
(1987
).10.
K.
Sudo
, M.
Sumida
, and H.
Hibara
, “Experimental investigation on turbulent flow in a square-sectioned 90-degree bend
,” Exp. Fluids
30
, 246
(2001
).11.
R.
Hayes
, K.
Nandakumar
, and H.
Nasr-El-Din
, “Steady laminar flow in a 90 degree planar branch
,” Comput. Fluids
17
, 537
(1989
).12.
J.
Bramley
and S.
Dennis
, “The numerical solution of two-dimensional flow in a branching channel
,” Comput. Fluids
12
, 339
(1984
).13.
J.
Bramley
and D.
Sloan
, “Numerical solution for two-dimensional flow in a branching channel using boundary-fitted coordinates
,” Comput. Fluids
15
, 297
(1987
).14.
H.
Huang
and B. R.
Seymour
, “Finite difference solutions of incompressible flow problems with corner singularities
,” J. Sci. Comput.
15
, 265
(2000
).15.
K.
Fotea
, P.
Prinos
, and A.
Goulas
, Numerical Methods in Laminar and Turbulent Flow
(Pineridge Press
, 1991
), Vol. 1
, pp. 381
–392
.16.
S.
Maharudrayya
, S.
Jayanti
, and A.
Deshpande
, “Pressure losses in laminar flow through serpentine channels in fuel cell stacks
,” J. Power Sources
138
, 1
(2004
).17.
J.
Wang
, “Pressure drop and flow distribution in parallel-channel configurations of fuel cells: U-type arrangement
,” Int. J. Hydrogen Energy
33
, 6339
(2008
).18.
M.
Bowers
and I.
Mudawar
, “High flux boiling in low flow rate, low pressure drop mini-channel and micro-channel heat sinks
,” Int. J. Heat Mass Transfer
37
, 321
(1994
).19.
A.
Goullet
, I.
Glasgow
, and N.
Aubry
, “Effects of microchannel geometry on pulsed flow mixing
,” Mech. Res. Commun.
33
, 739
(2006
).20.
Y.
Ma
, C.-P.
Sun
, M.
Fields
, Y.
Li
, D. A.
Haake
, B. M.
Churchill
, and C.-M.
Ho
, “An unsteady microfluidic T-form mixer perturbed by hydrodynamic pressure
,” J. Micromech. Microeng.
18
, 045015
(2008
).21.
Y. K.
Suh
and S.
Kang
, “A review on mixing in microfluidics
,” Micromachines
1
, 82
(2010
).22.
B. J.
Jimenez
, “Transition to turbulence in two-dimensional Poiseuille flow
,” J. Fluid Mech.
218
, 265
(1990
).23.
A.
Fortin
, M.
Jardak
, J.
Gervais
, and R.
Pierre
, “Old and new results on the two-dimensional Poiseuille flow
,” J. Comput. Phys.
115
, 455
(1994
).24.
25.
H.
Moffatt
, “Viscous and resistive eddies near a sharp corner
,” J. Fluid Mech.
18
, 1
(1964
).26.
F. H.
Harlow
and J. E.
Welch
, “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface
,” Phys. Fluids
8
, 2182
(1965
).27.
S. A.
Orszag
, “Accurate solution of the Orr–Sommerfeld stability equation
,” J. Fluid Mech.
50
, 689
(1971
).28.
B. F.
Armaly
, F.
Durst
, J.
Pereira
, and B.
Schönung
, “Experimental and theoretical investigation of backward-facing step flow
,” J. Fluid Mech.
127
, 473
(1983
).29.
P. G.
Spazzini
, G.
Iuso
, M.
Onorato
, N.
Zurlo
, and G. M.
Di Cicca
, “Unsteady behavior of back-facing step flow
,” Exp. Fluids
30
, 551
(2001
).30.
F.
Pan
and A.
Acrivos
, “Steady flows in rectangular cavities
,” J. Fluid Mech.
28
, 643
(1967
).31.
M.
Nallasamy
and K. K.
Prasad
, “On cavity flow at high Reynolds numbers
,” J. Fluid Mech.
79
, 391
(1977
).32.
B.
Cantwell
and D.
Coles
, “An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder
,” J. Fluid Mech.
136
, 321
(1983
).33.
A.
Prasad
and C. H.
Williamson
, “The instability of the shear layer separating from a bluff body
,” J. Fluid Mech.
333
, 375
(1997
).34.
A.
Okajima
, “Strouhal numbers of rectangular cylinders
,” J. Fluid Mech.
123
, 379
(1982
).35.
H.-Q.
Zhang
, U.
Fey
, B. R.
Noack
, M.
König
, and H.
Eckelmann
, “On the transition of the cylinder wake
,” Phys. Fluids
7
, 779
(1995
).36.
J.
Delville
, L.
Ukeiley
, L.
Cordier
, J. P.
Bonnet
, and M.
Glauser
, “Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition
,” J. Fluid Mech.
391
, 91
(1999
).37.
Y.
Couder
, J. M.
Chomaz
, and M.
Rabaud
, “On the hydrodynamics of soap films
,” Physica D
37
, 384
(1989
).38.
M. A.
Rutgers
, X. L.
Wu
, and W. B.
Daniel
, “Conducting fluid dynamics experiments with vertically falling soap films
,” Rev. Sci. Instrum.
72
, 3025
(2001
).39.
P.
Vorobieff
and R. E.
Ecke
, “Soap film flows: Statistics of two-dimensional turbulence
,” Phys. Rev. E
60
, 2953
(1999
).40.
T.
Pedley
, R.
Schroter
, and M.
Sudlow
, “Flow and pressure drop in systems of repeatedly branching tubes
,” J. Fluid Mech.
46
, 365
(1971
).41.
Z.
Zhang
and C.
Kleinstreuer
, “Transient airflow structures and particle transport in a sequentially branching lung airway model
,” Phys. Fluids
14
, 862
(2002
).42.
K.
Perktold
and G.
Rappitsch
, “Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model
,” J. Biomech.
28
, 845
(1995
).43.
S.
Zhao
, X.
Xu
, A.
Hughes
, S.
Thom
, A.
Stanton
, B.
Ariff
, and Q.
Long
, “Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation
,” J. Biomech.
33
, 975
(2000
).© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.
