A laminar, incompressible, viscous pipe flow with a controllable swirl induced by wall rotation has been studied both numerically and experimentally up to an axial Reynolds number (Re) of 30. The pipe consists of two smoothly joined sections that can be rotated independently about the same axis. The circumstances of flow entering a stationary pipe from a rotating pipe (so-called decaying swirl) and flow entering a rotating pipe from a stationary pipe (growing swirl) have been investigated. Flow visualisations show that at a certain swirl ratio the flow undergoes a reversal and vortex breakdown occurs. The variation of this critical swirl ratio with Reynolds number is explored and good agreement is found between the experimental and numerical methods. At high Re the critical swirl ratio tends to a constant value, whereas at low Re the product of the Reynolds number and the square of the swirl ratio tends to a constant value in good agreement with an existing analytical solution. For decaying swirl the vortex breakdown manifests itself on the pipe axis, whereas for growing swirl a toroidal zone of recirculation occurs near the pipe wall. The recirculating flow zones formed at critical conditions are found to increase radially and axially in extent with increasing Reynolds number and swirl ratio.

1.
D.
Peckham
and
S.
Atkinson
, “
Preliminary results of low speed wind tunnel tests on a gothic wing of aspect ration 1.0
,” Aeronautical Research Council Technical Report, C.P. No 508, T.N. Aero 2504,
1957
.
2.
S.
Leibovich
, “
The structure of vortex breakdown
,”
Ann. Rev. Fluid Mech.
10
,
221
246
(
1978
).
3.
M. P.
Escudier
, “
Vortex breakdown: Observations and explanations
,”
Prog. Aerospace Sci.
25
,
189
229
(
1988
).
4.
O.
Lucca-Negro
and
T.
O’Doherty
, “
Vortex breakdown: A review
,”
Prog. Energy Combust. Sci.
27
,
431
481
(
2001
).
5.
M.
Samimy
,
K.
Breuer
,
L.
Leal
, and
P.
Steen
,
A Gllery of Fluid Motion
(
Cambridge University Press
,
2003
).
6.
M. P.
Escudier
, “
Observations of the flow produced in a cylindrical container by a rotating endwall
,”
Exp. Fluids
2
,
189
196
(
1984
).
7.
J. M.
Lopez
and
A. D.
Perry
, “
Axisymmetric vortex breakdown. Part 3. Onset of periodic flow and chaotic advection
,”
J. Fluid Mech.
234
,
449
471
(
1992
).
8.
M. R.
Visbal
, “
Computed unsteady structure of spiral vortex breakdown on delta wings
,” AIAA Paper 96-2074,
1996
.
9.
M. P.
Escudier
and
N.
Zehnder
, “
Vortex-flow regimes
,”
J. Fluid Mech.
115
,
105
121
(
1982
).
10.
J.
Faler
and
S.
Leibovich
, “
Disrupted states of vortex flow and vortex breakdown
,”
Phys. Fluids
20
,
1385
(
1977
).
11.
M. P.
Escudier
, “
Vortex breakdown and the criterion for its occurrence
,” in
Intense Atmostpheric Vortices
, edited by
L.
Bengtsson
and
M.
Lighthill
(
Springer
,
1982
), pp.
247
258
.
12.
Z.
Lavan
,
H.
Nielsen
, and
A. A.
Fejer
, “
Separation and flow reversal in swirling flows in circular ducts
,”
Phys. Fluids
12
,
1747
1757
(
1969
).
13.
D.
Macdonald
, “
The zeros of
$j_1^2 ( \zeta ) - j_0 ( \zeta )j_2 ( \zeta ) = 0$
j12(ζ)j0(ζ)j2(ζ)=0
with an application to swirling flow in a tube
,”
SIAM J. Appl. Math.
51
,
40
48
(
1991
).
14.
Z.
Rusak
and
C.
Meder
, “
Near critical swirling flow in a slightly contracting pipe
,”
AIAA J.
42
,
2284
2293
(
2004
).
15.
C.
Crane
and
D.
Burley
, “
Numerical studies of laminar flow in ducts and pipes
,”
J. Comput. Appl. Math.
2
,
95
111
(
1976
).
16.
D.
Silvester
,
R.
Thatcher
, and
J.
Duthie
, “
The specification and numerical solution of a benchmark swirling laminar flow problem
,”
Comput. Fluids
12
,
281
292
(
1984
).
17.
M. P.
Escudier
,
I. W.
Gouldson
,
A. S.
Pereira
,
F. T.
Pinho
, and
R. J.
Poole
, “
On the reproducibility of the rheology of shear-thinning liquids
,”
J. Non-Newtonian Fluid Mech.
97
,
99
124
(
2001
).
18.
F.
Durst
,
S.
Ray
,
B.
Ünsal
, and
O.
Bayoumi
, “
The development lengths of laminar pipe and channel flows
,”
J. Fluids Eng.
127
,
1154
1160
(
2005
).
19.
M. P.
Escudier
,
J.
OLeary
, and
R. J.
Poole
, “
Flow produced in a conical container by a rotating endwall
,”
Int. J. Heat Fluid Flow
28
,
1418
1428
(
2007
).
20.
J.
Van Doormaal
and
G.
Raithby
, “
Enhancements of the simple method for predicting incompressible fluid flows
,”
Numer. Heat Transfer
7
,
147
163
(
1984
).
21.
J. H.
Ferziger
and
M.
Perić
,
Computational Methods for Fluid Dynamics
, Corr. 2nd print ed. (
Springer
,
Berlin
,
1997
).
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