Experimental investigation of the swirling flow and the helical vortices
induced by a twisted tape inside a circular pipe
Radu Cazan and Cyrus K. Aidun
Citation: Phys. Fluids 21, 037102 (2009); doi: 10.1063/1.3085699
View online: http://dx.doi.org/10.1063/1.3085699
View Table of Contents: http://pof.aip.org/resource/1/PHFLE6/v21/i3
Published by the AIP Publishing LLC.
Additional information on Phys. Fluids
Journal Homepage: http://pof.aip.org/
Journal Information: http://pof.aip.org/about/about_the_journal
Top downloads: http://pof.aip.org/features/most_downloaded
Information for Authors: http://pof.aip.org/authors
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
PHYSICS OF FLUIDS 21, 037102 共2009兲
Experimental investigation of the swirling flow and the helical vortices
induced by a twisted tape inside a circular pipe
Radu Cazan and Cyrus K. Aiduna兲
G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology,
Atlanta, Georgia 30332, USA
共Received 16 December 2007; accepted 12 December 2008; published online 17 March 2009兲
The present paper describes the experimental investigation of the turbulent swirling flow induced by
a twisted tape 共or fin兲 into a 1 in. diameter pipe. The investigation shows the existence of two
corotating helical vortices superimposed over the main swirling flow. The close proximity of the two
corotating vortices creates a local reversing flow at the pipe centerline. The flow is investigated
using LDV measurements and high speed camera visualization with fine air bubble seeding. Three
swirlers with 45, 60, and 90 mm pitch are investigated. Through a reconstruction technique, the
tangential flow field induced by a twisted tape swirler with 60 mm pitch at Re= 7.7⫻ 104 is
described by superposition of 385 measurements. Images and movies recorded with regular and high
speed cameras clearly show that the helical vortices are very stable and that they rotate around their
own axis, confirming the measurements. After extracting the characteristic tangential velocity
profiles of the main vortex and of the two secondary vortices, it was observed that the maximum
tangential velocity of all three vortices is almost the same, approximately half of the bulk velocity.
The pitch of the helical vortices was found to be 4/3 of the pitch of the twisted tape for all three
swirlers investigated, independent of Reynolds number. We hypothesize that the helical vortices are
generated by vortices originating inside the twisted tape swirler. The main rotational flow
accelerates the corotating vortices and decelerates the counter-rotating vortices. As a result, the
counter-rotating vortices disappear while the corotating vortices reach the same maximum tangential
velocity as the main flow. Thus the tangential velocity near the wall is approximately doubled by the
presence of the secondary vortices. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3085699兴
I. INTRODUCTION
Swirl flows have numerous applications across multiple
industries where enhanced mixing is required. Swirl flow
promoters are employed to enhance the heat transfer in heat
exchangers, to homogenize mixtures in casting and in the
chemical industry, and also in combustion to break the fuel
droplets and stabilize flames. There are numerous swirl generation systems but most common are vanes, eccentric fluid
injection, and twisted tape inserts.
The present study tries to elucidate the flow characteristics of swirling flows induced by short twisted tape inserts in
circular pipes. While investigating several swirl inducing devices, an unexpected counter-rotating flow was encountered
in the LDV measurements near the pipe centerline, downstream of a twisted tape swirl promoter.1,2 A similar behavior
has been reported in turbulent swirling jets attributed to the
influence of the cross flow Reynolds stress.3–5 However, the
swirling jets are generated by rotating pipes and the counterrotating flow does not exhibit the spatial periodicity reported
in pipes with twisted tape inserts.1
The main characteristics of the twisted tapes are presented in Fig. 1. The defining parameters are the 180° pitch
H, the pipe diameter d, and the tape thickness ␦. The relevant
a兲
Author to whom correspondence should be addressed. Electronic mail:
cyrus.aidun@me.gatech.edu.
1070-6631/2009/21共3兲/037102/9/$25.00
nondimensional parameters are the Reynolds number
Re= dUb / ␯ and the twist ratio y = H / d where Ub is the bulk
velocity and ␯ is the kinematic viscosity of water. Low values of the ratio y correspond to strong twist and high swirl
numbers.
Twisted tape swirlers have long been investigated, both
numerically and experimentally, in connection with heat
transfer applications for which they have been recognized as
a simple and cheap mean to produce significant heat transfer
enhancement.6 Unfortunately most studies investigated only
the variations of the heat transfer and friction coefficient,
without any attempts to elucidate the mechanisms behind
these changes. A comprehensive list of publications regarding twisted tape inserts is summarized in the recent review
article of Dewan et al.7
Early investigations of the flow field in pipes with full
length twisted tape inserts were performed with probes inserted directly into the flow8–10 which limited the accuracy of
the results. Kreith and Sonju8 investigated the decaying swirl
downstream of a twisted tape using a rotating blade inside
the pipe, thus measuring an average angular velocity which
does not capture the structure of the secondary flow.
Seymour’s measurements9 showed for the first time the existence of a secondary flow with a double vortex structure for
Reynolds numbers as high as 3 ⫻ 105.
These findings were later confirmed by numerical
simulations,11,12 but the simulations were restricted to low
21, 037102-1
© 2009 American Institute of Physics
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-2
Phys. Fluids 21, 037102 共2009兲
R. Cazan and C. K. Aidun
FIG. 1. Twisted tape parameters.
flow velocities. The simulations provided an insight into the
inception and growth of the secondary vortices along the
twisted tape.
Other investigators13–15 used both numerical simulations
and smoke flow visualizations in swirling air flows to study
the secondary motion. Both the simulations and the images
showed two counter-rotating vortices in each of the two
semicircular cross sections, supporting the idea that the twist
of the semicircular channels induces centrifugal effects similar to Dean vortices.16 These counter-rotating vortices are not
symmetric as in U-bend pipes17,18 but resemble the Dean
vortices in helical pipes19,20 where one of the vortices becomes dominant due to torsion effects.
Some researchers21,22 pointed out that more efficient heat
transfer can be achieved using multiple short twisted tapes.
These devices produce less friction related power losses
compared to full length twisted tapes and they can be optimized using different distances between tapes and tapes with
different pitches.7
The present study improves the understanding of the
flow downstream short twisted tapes, thus enabling the development of more efficient mixers and cooling devices. This
study also illustrates the flow field produced by the interaction of two secondary helical vortices with the main vortex
in the swirling flow produced by a short twisted tape. The
results should be useful for anyone interested in swirling
flows, helical vortices, and multiple vortex interaction.
II. EXPERIMENTAL SETUP
The experimental setup is designed to allow the investigation of the swirling flow induced by a twisted tape in a
circular pipe 共Fig. 2兲. It consists of a closed circuit where
water from the tanks is pumped by a 0.5 HP centrifugal
pump with a frequency controlled motor. The inner diameter
of the testing pipe is 1 in. 共d = 25.4 mm兲 and the pipe is
made of 1.5 mm thick glass which provides optical access.
As pointed out by Seymour9 who investigated 1, 2, and 3 in.
diameter pipes, the tube diameter does not influence the general characteristics of the secondary flow structure, so only a
1 in. diameter pipe is considered in this study. The pump
allows tests at Reynolds numbers in the range of 104 – 105.
The flow circuit has a calming section right before the
twisted tape. The calming section is designed to reduce the
turbulence level23 and consists of a coarse screen, a honeycomb, two fine screens, and a nozzle. The hexagonal cells of
the honeycomb have a flat side to flat side dimension of 6.35
mm and wall thickness of 0.25 mm. The coarse screen and
the two fine screens have square cells with cell sizes of 9.6,
2, and 1 mm. A nozzle with a 9:1 area contraction ratio is
installed 25 mm downstream of the second fine screen. The
system to straighten the flow is similar to the one used by
Seymour.9
The honeycomb and the 9:1 contraction significantly
suppress the velocity fluctuations for all Re investigated. Figure 3 shows the flow characteristics in the absence of the
swirler at two axial locations z = 40 mm and z = 300 mm,
downstream of the contraction end for Re= 7.7⫻ 104 共bulk
velocity Ub = 3.03 m / s兲. At the first location z = 40 mm, the
average axial velocity Vz has a flat profile of approximately
101% of Ub while the velocity fluctuations represent approximately 1% of the bulk velocity throughout the pipe except very close to the walls where viscous effects reduce the
average velocity while increasing turbulence intensity to approximately 18%. The average axial velocity profile is similar for all Re investigated while the normalized root mean
square 共rms兲 fluctuations of the axial velocity, vz⬘ / Ub, near
the centerline represent approximately 1 ⫾ 0.5% of the bulk
velocity. The flow development along the axis is slow and at
the next location, close to the end of the test section millimeters兲, the viscous effects increase the centerline average
axial velocity to 110% of Ub while the decrease in the axial
velocity is accompanied by an increase in fluctuations. The
flow exits from the nozzle into the pipe containing the
twisted tape that generates swirling flow.
FIG. 2. Setup schematic.
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-3
Experimental investigation of the swirling flow
FIG. 3. 共Color online兲 Average axial velocity Vz 共top兲 and normalized rms
fluctuations of the axial velocity vz⬘ / Ub 共bottom兲 for Re= 7.7⫻ 104 in the
absence of the swirler at two axial locations, z = 40 mm and z = 300 mm
downstream of the contraction end.
The twisted tapes tested have lengths of 45, 60, and 90
mm and a twist of 180° 共the pitch is equal to the length兲 with
corresponding pitch to diameter ratios 1.77, 2.36, and 3.54,
respectively. The swirlers were manufactured by stereolithography 共Vistatek Inc.兲 using “Somos Watershed 11120”
resin. In our experimental setup, the twisted tape and the
pipe form a single part, so the width of the tape is equal to
the inner diameter of the pipe 共Fig. 4兲 with no gap in between. This design eliminates uncertainties due to any secondary effects of the tape/wall clearance which occur for
common twisted tape inserts. The twisted tape has a profiled
edge to limit flow separation at the leading edge of the
swirler. The tape thickness is 3 mm at the leading edge and
1.5 mm at the trailing edge.
The flow is investigated using LDV measurements and
direct visualization of injected fine air bubbles. The air
bubble generator was built using a spinal needle with a 1.25
mm outer diameter, 0.9 mm inner diameter, and with four
equally spaced holes of 0.45 mm orientated upstream 共Fig.
5兲. A thin long plug is used to prevent water infiltration into
the air circuit when the air injection is stopped. The needle
was inserted into a polycarbonate flange with a 25.4 mm
diameter flow section. The device is installed right upstream
of the swirler. The air mass flow is supplied by a compressed
air line controlled by a ball valve.
The bubble motion is recorded using a black and white
“Phantom V5” high speed camera capable of 4200 frames/s
FIG. 4. 共Color online兲 Twisted tape swirler: Pitch H = 60 mm, diameter
d = 25.4 mm, pitch to diameter ratio y = 2.36.
Phys. Fluids 21, 037102 共2009兲
for frame size of 1024⫻ 256 pixels. The camera was
fitted with a Elicar V-HQ Macro lens with focal length
f = 90 mm while the lighting is provided by two “Lowe”
light sources of 500 and 750 W. In addition to the high speed
camera some images were also recorded with a regular camera 共Sony DSC-H5兲.
Flow velocities are measured using a two-component
LDV system 共TSI Inc.兲 in backscattering mode with an
argon-ion laser 共Coherent Innova 70兲. The laser has a maximum power of 3.4 W. Green light of 514.5 nm was used for
axial velocity measurements while blue light of 488 nm was
used for the tangential velocity measurements. One of the
blue light beams had a phase shift of 1 MHz to distinguish
between positive and negative velocities. The head of the
laser can be translated in all three directions using a traverse
system with three electric motors controlled by a computer.
The spatial resolution of the traverse is 10−2 mm. Velocity
statistics were calculated from batches of 5000 samples collected at each measurement point.
The high curvature of the pipe walls required special
measures to compensate for light refraction. Following previous investigations of the lensing effect of curved glass
walls,24 a rectangular glass enclosure 共340⫻ 40⫻ 50 mm3兲
with 3 mm thick walls was attached to the glass pipe, while
the space between the straight walls and the pipe was filled
with glycerin which has a refraction index close to the refraction index of glass.
The velocities were measured only along the horizontal
diameter where the vertical component of the velocity measured with the laser is equal to the tangential velocity. This
strategy also minimized the effects of light distortion on the
measurements. The level of light distortion induced by the
curved glass walls and medium changes 共air/glass/water兲 is
still significant even with the presence of the rectangular
container filled with glycerin. While the laser head moves 15
mm toward the pipe, the measuring volume created at the
intersection of the light beams actually sweeps 24 mm across
the horizontal diameter inside the pipe. Consequently, the
actual locations of the measurements are determined from
the positions of the laser head after calculating corrections
which account for the angle changes of the light due to refraction at the interfaces between different mediums.24
FIG. 5. 共Color online兲 Air bubbles injector.
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-4
Phys. Fluids 21, 037102 共2009兲
R. Cazan and C. K. Aidun
reaches a maximum for r = ⫾ 5 mm and slowly decays toward the edge of the pipe. When the product r · V␪ is positive,
the flow rotates in the direction of the tape while when the
product is negative the flow rotates against the direction of
the tape.
Aidun and Parsheh1 proposed using the normalized angular velocity at the pipe centerline ␻n to characterize the
periodicity of the flow induced by the twisted tapes, where
␻n =
R␻0
.
Ub
共1兲
R is the pipe radius, ␻0 = lim␻ = ⳵V␪ / ⳵r 兩r=0 is the centerline
r→0
FIG. 6. 共Color online兲 Variation of the average tangential velocity V␪ along
the pipe axis from z = 150 mm to z = 230 mm for the flow induced by a
twisted tape with H = 60 mm pitch at Re= 7.7⫻ 104.
The flow was seeded with 3 ␮m diameter titanium dioxide 共TiO2兲 particles with density of 4.2 g / cm3 and refraction index of 2.6. Initial measurements for the 90 mm swirler
were performed using 0.3 ␮m alumina particles 共Al2O3兲
with density of 3.84 g / cm3 and refraction index 1.67, but
the increase in the diameter and refraction index greatly improved the signal to noise ratio without any loss of
sensitivity.25 As a result, the measurements with TiO2
particles were collected much faster and they showed no
scattering.
The laser was also used to create a cross section sheet of
light after passing a green light beam through a divergent
cylindrical lens with a focal length f = −40 mm. The air
bubble streams reflect and scatter the laser light, marking the
positions of the centers of the secondary vortices as two
bright white spots on the green circular cross section.
III. RESULTS AND COMMENTS
Tangential velocities were measured in the swirling flow
induced by twisted tape inserts with 45, 60, and 90 mm pitch
at different Re from 25 000 to 100 000. The measurements
were collected along the horizontal diameter of the pipe at 5
mm intervals along the pipe axis. Each measurement set contains 25 radial positions spaced 1 mm apart. The range of
optical accessible locations along the pipe axis is from 25 to
350 mm 共1d to 14d兲 starting from the end of the twisted tape.
Figure 6 shows a sample of these measurements collected
between 150 and 230 mm for the 60 mm swirler at
Re= 7.7⫻ 104 共bulk velocity Ub = 3.03 m / s兲.
As reported previously,1 the profiles of the tangential
velocity V␪ between 170 and 180 mm show a point of inflection which eventually leads to asymmetric counter-rotating
flow near the centerline between 185 and 205 mm but which
returns to the initial typical “S” profile of a simple vortex at
230 mm. This pattern repeats periodically along the pipe axis
for all the three swirlers investigated. Positive values of the
tangential velocity are marked “+” on the plots and negative
values of the tangential velocity are marked “⫺” on the
plots.
The first profile in Fig. 6 is typical for swirling motions.
The tangential velocity increases linearly in a core region,
angular velocity, V␪ is the average tangential velocity, and
Ub = ␯ Re/ 共2R兲 is the bulk velocity.
Figure 7 shows the variation of the normalized angular
velocity at the centerline ␻n along the pipe axis for the three
swirlers investigated. The negative values of ␻n represent
counter-rotating flow while the positive values show rotation
in the direction of the tape.
All three profiles clearly show a periodic sinusoidal
variation with the period 1/3 larger than the corresponding
swirler pitch 共H␻ = 共4 / 3兲 ⫻ H兲. The pitch of the profiles is
independent of Reynolds number, as it can be seen in Fig. 8
for the 90 mm swirler. The angular momentum of the secondary vortices increases with Re. Seymour’s study which
shows the presence of counter-rotating vortices inside the
twisted tape confirms their existence at Re= 3.1⫻ 105.
The air bubble injection device described in Sec. II was
installed to visualize the secondary flow. The air bubbles
trace stable helical trajectories for the entire time of the experiments. The air bubble trajectories do not change with Re,
consistent with the LDV measurements. The LDV measurements were done in the absence of the air bubbles, thus
avoiding any interference.
The pitch of the air bubble streams and the pitch of the
measured normalized angular velocity ␻n are identical as
shown in Fig. 9. This similarity suggests that the sinusoidal
variation of ␻n is generated by two helical vortices originating inside the twisted tape swirler. The centers of the vortices
create low pressure regions which concentrate the air
bubbles. Similar air bubble visualizations were reported in an
investigation of the swirling flow induced in a rectangular
chamber by tangential injection.26 One of the helical structures described there was a double helix similar to the vortex
system showed in Fig. 9 but the structure created using two
plane slopes at the chamber’s bottom was very unstable.
The impact of the swirl decay is very limited over the
short axial length of the pipe in our investigation as both the
measurements 共Figs. 6 and 7兲 and the visualizations 共Fig. 9兲
confirm. This is in agreement with the study preformed by
Kreith and Sonju8 which showed that the swirl behind a
twisted tape decays by about 20% over the first 10 diameters
with slower decay at higher Re and independent of the tape
pitch. The focus of this study is within few diameters downstream of the twisted tape.
Given the helical nature of the flow and its stability,
successive cross sectional flow fields are almost identical
with considering the angular shift. We take advantage of the
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-5
Experimental investigation of the swirling flow
Phys. Fluids 21, 037102 共2009兲
FIG. 7. Variation of the normalized angular velocity ␻n along the pipe axis for flows induced by twisted tapes with H = 45, 60, and 90 mm pitch at
Re= 7.7⫻ 104.
slow decay over the helical vortex pitch along a span of 80
mm 共⬃3 diameters兲 at Re= 7.7⫻ 104 共Fig. 6兲 and the periodicity of the flow 共Fig. 9兲 to recover an approximation of the
flow field from measurements along the center axis at several
axial locations. The measurements collected across the horizontal diameter at successive axial locations can be considered as measurements at different angles of the same cross
sectional flow field. The flow resulting from the combination
of all the measurements from Fig. 6 with appropriate angular
phase shift is shown in Fig. 10.
The number of diameters used for reconstruction of the
flow field depends on the periodicity of the angular velocity
variation. For the 60 mm long swirler, the variation of the
angular velocity at the centerline exhibits an 80 mm period.
The measurements were collected every 5 mm along the pipe
so the cross sectional flow field reconstruction includes
n = 80/ 5 = 16 measurement sets. The angle between the
measurements was determined assuming equal spacing
共␪ = 180° / 16= 11.25°兲. Each measurement set contains 25
radial positions spaced 1 mm apart. As the centerline measurement is repeated in all 16 measurement sets, the cross
sectional flow field is characterized by 16⫻ 25− 15= 385 independent measurements.
The arrows in Fig. 10 show the location of the measurements and the relative magnitude and orientation of the tangential velocity in the cross sectional field. The arrows are
not complete velocity vectors as they lack the radial velocity
component. The radial velocity components must have the
same order of magnitude as the tangential velocities of the
secondary vortices to satisfy mass conservation in the regions showing low tangential velocities near the edges of the
secondary vortices. To display the arrows, the velocities were
projected on the vertical and horizontal axis using the corresponding angle for each measurement diameter 共0° for the
first one, 11.25° for the second, 22.50° for the third, etc.兲.
The cumulative plot in Fig. 10 shows a three vortex
structure with two secondary vortices superimposed over the
main swirling flow created by the twist of the tape. The two
FIG. 8. 共Color online兲 Variation of the normalized angular velocity ␻n with Reynolds number for the swirler with pitch H = 90 mm.
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-6
R. Cazan and C. K. Aidun
FIG. 9. 共Color online兲 Side and top views of the air bubble streams showing
their helical nature and the corresponding centerline angular velocities calculated from LDV measurements 共tape pitch H = 60 mm, Re= 7.7⫻ 104兲.
secondary vortices have the diameter equal to the pipe radius. They rotate in the same direction as the main flow and
have a skewed shape due to its presence.
Despite the fact that the swirler is symmetric and the two
helical vortices have the same pitch, the angle formed by
their centers and the center of the main vortex 共which is also
the center of the pipe兲 is 155° instead of 180° angle. The 25°
phase shift between the two helical vortices with 80 mm
pitch suggests that the weaker vortex starts its helical path
downstream of the other vortex. If we consider that the helical vortices twist 180° over an axial distance of 80 mm,
then a helical vortex rotates 25° over an axial distance of
⌬z = 80/ 180° ⫻ 25° = 11.11 mm 共one of the vortices reaches
stable state at about 11 mm downstream of the other one兲.
The measurements are confirmed by air bubble visualization 共Figs. 11 and 12兲. Air bubbles collect at the center of
the secondary vortices forming helical streams. A thin laser
sheet reveals the location of the centers of the secondary
vortices in the pipe cross sectional plane 共Fig. 11 enhanced
online兲.
The movie available for the online version of this paper
shows the laser sheet moving along the pipe axis, highlight-
FIG. 10. 共Color online兲 Reconstructed average tangential velocity field of
the swirling flow induced by a twisted tape with pitch H = 60 mm at
Re= 7.7⫻ 104.
Phys. Fluids 21, 037102 共2009兲
FIG. 11. 共Color online兲 Air bubble visualization of the helical vortices at
Re= 7.7⫻ 104 共the flow is from right to left兲. The laser sheet shows the
location of the centers of the secondary vortices in the pipe cross section
共enhanced online兲. 关URL: http://dx.doi.org/10.1063/1.3085699.1兴
ing the stability of the helical vortices and confirming that
their centers are located about a quarter of a diameter away
from the pipe edge, consistent with the measurements. The
secondary vortices are stationary with slight vibration as they
respond to random turbulent fluctuations. The minimum
pressure location in the flow field is not at the pipe centerline, as in regular swirling flows, but at the center of the
secondary vortices, as proved by the air bubble streams. The
existence of the 155° angle between the secondary vortices is
confirmed by the slight asymmetry of the air bubble streams
visible in Fig. 11.
A high speed camera recording shows the rotation of
individual air bubbles around the secondary vortices 200
times slower than the actual motion 共Fig. 12 enhanced online兲. The stray bubbles rotating under the influence of the
main vortex are entrapped as they approach the secondary
vortices. Once the bubbles are entrapped in a secondary vortex, they spiral around the center of the secondary vortex.
Within about 3 diameters along the pipe axis, most bubbles
are entrapped near the center of the secondary vortices.
Downstream the bubbles size increases, restricting good visualization close to the entrance of the straight pipe.
Analysis of the velocity profiles from Fig. 6 suggests
that the velocity distribution of the main tangential velocity
field is described by the measurements which do not cross
the secondary vortices. The measurements least affected by
the secondary vortices are the ones collected perpendicular to
the line crossing through their centers 共Fig. 10兲. In the case
of the twisted tape with 60 mm pitch presented in Fig. 6
these measurements are the ones collected at the axial location z = 225 mm for which ␻n exhibits a peak in Fig. 7.
In order to reveal the effect of the secondary vortices on
the total tangential velocity field, the background created by
the velocity field of the main vortex was subtracted from all
FIG. 12. High speed close-up of the air bubbles at Re= 7.7⫻ 104
near the straight pipe entrance 共enhanced online兲. 关URL:
http://dx.doi.org/10.1063/1.3085699.2兴
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-7
Experimental investigation of the swirling flow
Phys. Fluids 21, 037102 共2009兲
FIG. 15. 共Color online兲 Average tangential velocity profiles of the three
vortices present in the flow.
FIG. 13. 共Color online兲 The actual tangential velocity profile of the lower
secondary vortex is highlighted in the plot of ⌬V␪ = V␪共z1兲 − V␪共z2兲 where
V␪共z1 = 180 mm兲 are the measurements through the center of the lower vortex and V␪共z2 = 225 mm兲 is the main vortex velocity distribution.
velocity profiles in Fig. 6. The actual velocity distribution of
the secondary vortices can be extracted only from the measurements which cross through their centers. These measurements sets are identified in Fig. 6 as the ones showing maximum counter-rotating flow, respectively, the measurements
at z = 180 mm for the lower vortex 共located on the lower side
of Fig. 10兲 and z = 190 mm for the upper vortex. The background removal process is shown in Fig. 13 for the measurements which cross through the center of the lower vortex.
The total tangential velocity field after subtraction of the
velocity field induced by the main vortex is shown in Fig. 14
as seen looking upstream. Compared to the original field, the
secondary vortices recovered the round shape and their centers shifted approximately 1.5 mm toward exterior. The arrows show the direction of rotation for both secondary vortices and also for the main field.
Figure 15 shows the tangential velocity profiles of all
three vortices present in the flow field ignoring the angle
difference between the two secondary vortices. These velocity profiles are extracted from the measurements which cross
FIG. 14. 共Color online兲 Average tangential velocity contours of the secondary vortices after removing the main vortex background. The circles show
the boundaries of the vortices while the arrows show their rotation.
through the center of the secondary vortices, thus showing
the actual distance between the center of the pipe and the
centers of the vortices and also the actual tangential velocity
magnitudes.
The fact that without the main vortex influence the two
secondary vortices recovered their symmetric shape suggests
that the overall flow field is the result of a simple superposition of the fields induced by the secondary vortices on the
field generated by the main vortex, regardless of Reynolds
numbers or the turbulence level, as hypothesized by Aidun
and Parsheh.1
The maximum velocity induced by the secondary vortices is approximately the same as the maximum velocity induced by the main vortex. As the core region of the secondary vortex is smaller than the core region of the main vortex,
the angular velocity is correspondingly higher. Figure 15 also
shows that the upper vortex is slightly stronger than the
lower vortex.
Figures 16 and 17 show the influence of the secondary
vortices on the axial average velocity Vz and the rms fluctuations of the axial velocity vz⬘ and tangential velocity v␪⬘ for
Re= 7.7⫻ 104. The fluctuations are normalized by the bulk
velocity Ub = 3.03 m / s. While the average axial velocity
profiles and the rms profiles for both axial and tangential
velocities are not as instructive as the average tangential velocity, they still display distinctive features.
Figure 16 shows the changes in the average axial velocity profiles at three axial locations. The axial velocity profiles
FIG. 16. 共Color online兲 Average axial velocity Vz 共top兲 and normalized rms
fluctuations of the axial velocity vz⬘ / Ub 共bottom兲 for Re= 7.7⫻ 104 for a
60 mm pitch twisted tape swirler at three axial locations z = 150 mm,
z = 185 mm and z = 230 mm downstream of the swirler.
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-8
Phys. Fluids 21, 037102 共2009兲
R. Cazan and C. K. Aidun
FIG. 19. Schematic of the secondary vortices inception and evolution 共the
first three images show the evolution inside the twisted tape swirler while
the fourth shows the secondary vortices inside the straight pipe兲.
FIG. 17. 共Color online兲 Average tangential velocity V␪ 共top兲 and normalized rms fluctuations of the tangential velocity v⬘␪ / Ub 共bottom兲 for
Re= 7.7⫻ 104 for a 60 mm pitch twisted tape swirler at three axial locations
z = 150 mm, z = 185 mm, and z = 230 mm downstream of the swirler.
are, in general, not symmetric as the two secondary vortices
are not identical, as explained previously. The increase in the
average tangential velocity due to the superposition of the
main and the secondary vortices 共z = 185 mm兲 significantly
decreases the axial velocity 共⬃1 m / s兲 while the core region
within the 10 cm diameter is less affected.
The axial and tangential velocity fluctuations in Figs. 16
and 17 both show an increase near the centers of the secondary vortices. This is most likely due to the fluctuation of the
secondary vortices visible by the air bubble visualization 共the
movie accompanying Fig. 11兲. The small amplitude fluctuations seem random as a power spectra analysis of the measurements did not reveal any dominant frequency. Their impact is slightly stronger on tangential velocities which show
maximum fluctuations of approximately 13% while the axial
velocity fluctuations have a maximum of approximately
10%. Near the pipe centerline both the axial and tangential
velocity fluctuations are approximately 8%.
IV. VORTEX INCEPTION AND DEVELOPMENT
Previous studies9,12,15 of swirling flows induced by
twisted tapes inserts suggested that the secondary motion is
based on the centrifugal imbalance caused by the radial velocity distribution coupled with the rotational motion created
by the twist of the tape. These studies showed two counterrotating vortices appearing each side of the twisted tape and
changing their aspect along the pipe. As Reynolds number
increased, the vortices corotating relative to the tape twist
increased in size while the counter-rotating vortices decreased in size.
We did not notice any trace of a counter-rotating vortex
either in air bubble images or in the LDV measurements
inside the straight pipe. A photograph of the swirler under
intense light proves that the vortices change their pitch compared to the twisted tape while still inside the twisted semicircular channels. The air bubble stream drifts away from the
tape toward the center of the channels and it continues
smoothly inside the straight pipe 共Fig. 18兲. The photograph is
not very clear as the swirler was not designed to be optically
accessible.
One possible scenario could be the vortex creation
mechanism shown in Fig. 19. The tape twist induces two
secondary vortices in each half of the pipe: A large but weak
counter-rotating vortex and a smaller and stronger corotating
vortex. Under the influence of the tangential component of
the main flow the corotating vortex is accelerated and expands while the counter-rotating vortex slows down and
shrinks.
As the corotating vortex strengthens and expands its core
slowly moves away from the twisted tape resulting in the
increase of the vortex pitch relative to the twisted tape pitch
共as shown in Fig. 7兲.
Once the twisted tape ends, the corotating secondary
vortices preserve their size, helical trajectory, and pitch inside the straight pipe while the weak counter-rotating vortices disappear.
The same tangential velocity component drives the main
vortex and also accelerates the secondary vortices. As a result all vortices reach approximately the same maximum tangential velocity, fact confirmed by the measurements. Figure
15 shows that for the swirling flow induced by the tape with
60 mm pitch at Re= 7.7⫻ 104 the maximum velocity of all
three vortices is approximately half the magnitude of the
bulk velocity.
The pitch of the secondary vortices H␻ = 共4 / 3兲 ⫻ H must
be characteristic to 180° twisted tapes and it is unlikely to be
the same for longer tapes. We expect longer tapes to force
the secondary vortices to a pitch closer to the twisted tape
pitch.
The reason the two corotating vortices can coexist is the
presence of the main vortex which reduces the tangential
velocity of the two secondary vortices near the pipe centerline, allowing a smooth transition.
V. CONCLUSIONS
FIG. 18. 共Color online兲 The air bubble stream drifts away from the tape
toward the center of the channel 共right兲 and continues smoothly inside the
straight pipe 共left兲 共H = 60 mm, Re= 7.7⫻ 104兲.
The present study reveals some features of the swirling
motion induced by twisted tapes, characteristics which can
be used to design mixers with improved efficiency and calibrate numerical simulations. We hypothesize that vortices are
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions
037102-9
Experimental investigation of the swirling flow
generated inside the twisted tape, with the corotating vortices
surviving with the bulk swirling flow. The corotating pair of
helical vortices are remarkably stable and persistent downstream of the twisted tape inside the pipe.
As hypothesized previously, the periodicity in the measurements are based on the secondary corotating spiral vortices with wavelength corresponding to the pitch of the vortex. This does not mean that the core reverses direction
periodically. We show that the Reynolds number in the range
of 25 000 to 100 000 has no effect on the normalized angular
velocity.
The presence of the two secondary vortices almost
doubles the tangential velocity near the wall which should
have a significant impact on heat transfer and near wall particulate agglomeration. The total tangential field created by
the interaction of the three vortices can be described by superposition of the velocity fields of the secondary vortices on
the velocity field of the main vortex. We identified the characteristic tangential velocity profiles for each vortex for the
swirling flow induced by a twisted tape with 60 mm pitch at
Re= 7.7⫻ 104.
1
C. K. Aidun and M. Parsheh, “Spatially periodic reversing core in a
twisted-fin generated swirling pipe flow,” Phys. Fluids 19, 061704 共2007兲.
2
A. A. Islek, M.S. thesis, Georgia Institute of Technology, 2004.
3
L. Facciolo and P. H. Alfredsson, “The counter-rotating core of a swirling
turbulent jet issued from a rotating pipe flow,” Phys. Fluids 16, L71
共2004兲.
4
L. Facciolo, N. Tillmark, A. Talamelli, and P. H. Alfredsson, “A study of
swirling turbulent pipe and jet flows,” Phys. Fluids 19, 035105 共2007兲.
5
Y. Maciel, L. Facciolo, C. Duwig, L. Fuchs, and P. H. Alfredsson, “Nearfield dynamics of a turbulent round jet with moderate swirl,” Int. J. Heat
Fluid Flow 29, 675 共2008兲.
6
M. M. Abu-Khader, “Further understanding of twisted tape effects as tube
insert for heat transfer enhancement,” Heat Mass Transfer 43, 123
共2006兲.
7
A. Dewan, P. Mahanta, K. S. Raju, and P. Suresh Kumar, Proc. Inst. Mech.
Eng., Part A 218, 509 共2004兲.
8
F. Kreith and O. K. Sonju, “The decay of a turbulent swirl in a pipe,” J.
Fluid Mech. 22, 257 共1965兲.
9
E. V. Seymour, “Fluid flow through tubes containing twisted tapes,” The
Engineer 222, 634 共1966兲.
10
E. Smithberg and F. Landis, “Friction and forced convection heat transfer
Phys. Fluids 21, 037102 共2009兲
characteristics in tubes with twisted tape swirl generators,” ASME J. Heat
Transfer 86, 39 共1964兲.
11
A. W. Date, “Prediction of fully-developed flow in a tube containing a
twisted-tape,” Int. J. Heat Mass Transfer 17, 845 共1974兲.
12
Y. Kazuhisa, H. Hidetoshi, and T. Saburo, “Numerical simulation on heat
transfer enhancement in twisted-tape-inserted tubes,” J. Enhanced Heat
Transfer 11, 379 共2004兲.
13
R. M. Manglik and A. E. Bergles, “Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes: Part I—laminar flows,”
ASME J. Heat Transfer 115, 881 共1993兲.
14
R. M. Manglik and C. Ranganathan, in Experimental Heat Transfer, Fluid
Mechanics and Thermodynamics, edited by M. Giot, F. Mayinger, and G.
P. Celata 共Edizioni ETS, Pisa, 1997兲, p. 1631.
15
K. K. Yerra, R. M. Manglik, and M. A. Jog, “Optimization of heat transfer
enhancement in single-phase tubeside flows with twisted-tape inserts,” Int.
J. Heat Exchangers 8, 117 共2007兲.
16
A. Ujhidy, J. Nemeth, and J. Szepvolgyi, “Fluid flow in tubes with helical
elements,” Chem. Eng. Process. 42, 1 共2003兲.
17
K. C. Cheng, T. Inaba, and M. Akiyama, “Flow visualization studies of
secondary flow patterns and centrifugal instability in curved circular and
semicircular pipes,” Proceedings of the Third International Symposium
Flow Visualization, 1987, p. 531.
18
W. R. Dean, “Note on the motion of fluid in a curved pipe,” Philos. Mag.,
Suppl. 4, 208 共1927兲.
19
H. C. Kao, “Torsion effect on fully developed flow in a helical pipe,” J.
Fluid Mech. 184, 335 共1987兲.
20
P. Tiwari, S. P. Antal, and M. Z. Podowski, “Three-dimensional fluid
mechanics of particulate two-phases flow in U-bend and helical conduits,”
Phys. Fluids 18, 043304 共2006兲.
21
O. H. Klepper, “Heat transfer performance of short twisted tape,” AIChE
J. 35, 1 共1972兲.
22
S. K. Saha, A. Dutta, and S. K. Dahl, “Friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly
spaced twisted-tape elements,” Int. J. Heat Mass Transfer 44, 4211
共2001兲.
23
C. Farell and S. Youssef, “Experiments on turbulence management using
screens and honeycombs,” ASME J. Fluids Eng. 118, 26 共1996兲.
24
J. Glover, P. R. Bullen, and D. J. Cheeseman, “The effects of refraction on
the measurement of velocity of water flow in a circular pipe using a three
beam laser Doppler anemometer,” Proceedings of the Developments in
Measurements and Instrumentation in Engineering, Durham, England,
1985, p. 59.
25
R. Menon and W. T. Lai, “Key considerations in the selection of the seed
particles for LDV measurements,” Fourth International Conference on Laser Anemometry, Cleveland, OH, 1991.
26
S. V. Alekseenko, P. A. Kuibin, V. L. Okulov, and S. I. Shtork, “Helical
vortices in swirl flow,” J. Fluid Mech. 382, 195 共1999兲.
Downloaded 27 Sep 2013 to 146.232.129.75. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions