Investigation of turbulent puffs in pipe flow with
time-resolved stereoscopic PIV
C.W.H. van Doorne, B. Hof, F.T.M. Nieuwstadt, J. Westerweel, B. Wieneke∗
Delft University of Technology
Laboratory for Aero & Hydrodynamics
Leeghwaterstraat 21, 2628 CA Delft, The Netherlands
∗
La Vision GmbH, Anna-VandenHoeck-Ring 19, D-37081 Göttingen, Germany
Abstract
(a)
(b)
(c)
(a)
(d)
(b)
(c)
(d)
Time-resolved stereoscopic particle image velocimetry (SPIV) was used to study the 3D
flow field and the flow structure of a turbulent spot, or puff, at low Re in a pipe. The
high sampling frequency of the SPIV system (500 Hz) makes it possible to obtain timeresolved velocity measurements over the entire circular cross-section of the pipe. When time
is converted into a spatial coordinate with help of the bulk velocity, i.e. assuming frozen
turbulence, the result is the first quasi-instantaneous 3-D velocity measurement of a turbulent
puff. The 3-D plots of the iso-contours of the streamwise vorticity, and various cuts of the 3-D
vector fields show the complex structure of the flow in the turbulent puff. At the trailing edge
of the puff, where the laminar flow undergoes transition to turbulence, pairs of counter rotating
streamwise vortices result in large mushroom-like structures as seen in flow visualizations.
Integration of the velocity fields over the cross-section of the pipe further shows that very
large spikes occur in the energy of the radial and azimuthal velocity components. These
spikes appear to be related to the presence of hairpin vortices.
3D visualization of the iso-contours of streamwise vorticity (± 3.5 s−1 ) in the puff. The bottom
figure shows the flow in the lower half of the pipe (y < 0) and the structures close to the wall
appear on top (viewing in the positive y-direction).
1
1
Introduction
A particularity of pipe flow is that in the range of 1900 . Re . 2800, laminar flow and turbulent
regions, named ‘flashes’ or ‘puffs’, co-exist, even for very large initial flow perturbations. This was
already observed by Osborne Reynolds [1], but has remained unexplained until today. In some
early investigations on puffs [2][3][4] the downstream velocity and the growth rate of puffs was
determined. Furthermore, the occurrence of splitting and merging of different puffs was observed
as a function of the Re number. The downstream velocity of puffs is found to be slightly smaller
than the bulk velocity. This implies that at the upstream end of a puff there is a net flow of
laminar fluid entering the turbulent region, and therefore a continuous transition from laminar
to turbulent flow occurs at this location. At the downstream end of a puff, the opposite process
takes place, i.e. turbulent fluid from the puff relaminarizes and leaves the puff.
A puff can perhaps be considered as a natural minimal flow unit for turbulence in a pipe, i.e.
the smallest volume in which a chaotic flow can be sustained given the Reynolds number. The
region in which the turbulence is sustained is very small (about three pipe diameters long) and
entirely restricted to the transition region at the upstream end of the puff. This shows that for
a puff the self-sustaining process (SSP) and the transition process are in fact one and the same.
It may be anticipated that the flow dynamics of a puff are also relevant at larger Re. A study
of a turbulent puff seems therefore a good starting point for the study of the transition and the
SSP of turbulence (in a pipe). Only little information is available on the flow structure in puffs,
and that the literature does not give a very consistent picture. Against this background, the main
objective of the measurements described in this paper is to provide more information about the
instantaneous 3D structure of the flow in a puff.
A first attempt of using PIV to resolve the spatial flow structure of transitional flow in a
pipe was by Westerweel & Draad [5], who generated a turbulent slug by injection of a small
amount of fluid into a fully developed laminar flow at Re=5800. PIV was applied to measure the
instantaneous flow field in a plane parallel to the mean flow direction. The consecutive vector
fields were compiled into a single data set that represents a (quasi-) instantaneous cross-section
of the entire turbulent slug. The observed vortical motions may be associated with hairpin-like
structures, but from their 2C-2D PIV measurements it was very difficult to draw conclusions about
the 3D structure of the flow.
This paper describes advanced state-of-the-art time-resolved stereoscopic PIV measurements,
which yield quantitative measurements of the 3-D flow field of a puff. This system is an updated
version of the SPIV system described by Van Doorne et al. [6], which was used for the transition
measurements with periodic suction and blowing. The improved sampling speed of this new
system, with a maximum of 500 Hz, allowed a completely time resolved measurement of the
velocity over the entire circular cross-section of the pipe. The light sheet in the experiments
was oriented perpendicular the main flow direction, and therefore all flow structures are advected
settling
chamber
pump
disturbance
generator
mirror
laser
D=4cm
laser sheet
x
z
350 D
150 D
y
650 D = 26 m
return pipe
Figure 1: Schematic of the pipe flow facility.
2
500 Hz
cameras
−15
5
−10
in−plane velocity (mm/s)
−5
0
5
10
15
u
x
u
0.25
0
20
axial velocity (mm/s)
40
60
80
uz
4
probability density (1/px)
probability density (1/px)
y
3
2
1
0
−1.5
0.2
0.15
0.1
0.05
−1
−0.5
0
0.5
particle displacement (px)
1
0
1.5
(a) in-plane components
0
1
2
3
4
5
6
7
particle displacement (px)
8
(b) axial component
Figure 2: Probability density function of the in-plane velocity components (a) and axial component
(b) determined from the entire measurement sequence, which includes laminar and turbulent flow
regions.
through the measurement plane. When the time is converted into space with the bulk velocity,
with help of the Taylor transformation for frozen turbulence, a quasi-3D flow field is obtained,
which provides a very good picture of the instantaneous 3D flow structure in a puff.
2
Measurements
The puffs were created by injection of a jet with a mass flux of 50% of the total pipe mass flux
and for a short duration (1 D/Ub ) through a 1 mm hole into fully developed laminar pipe flow.
The SPIV measurements were made at a distance of 150 pipe diameters further downstream.
The analysis here concentrates on a single measurement at Re = 2000. It was verified that the
main results and conclusions are generally valid and can in principle be obtained from any other
measurement of a puff.
For the quantitative measurement of the velocity field in a puff we have made use of a stateof-the-art high-speed stereoscopic PIV system. This system is in principle identical to the SPIV
system described by Van Doorne et al. [6][7], except that the cameras and the laser have been
replaced by much faster components. The specifications of the high-speed SPIV system are described in a paper by Van Doorne et al. [8][9]. The measurements were taken in a water pipe flow
facility with a total length of 26 m and an inner diameter of 40 mm. A schematic of the pipe flow
facility is shown in Figure 1. An overview of the experimental parameters is given in Table 1.
The pulsed dual-cavity DPPS Nd:YLF laser (New Wave Pegasus-PIV-30W) has maximum
energy of 10 mJ per pulse at a repetition rate of 1000 Hz. The laser beam diameter is approximately
1.5 mm and the wavelength of the light is 527 nm. The CMOS cameras (LaVision High-Speed-Star2) have a resolution of 1280×1024 pixels with 8 bit dynamic range. The maximum image frame
rate (at the same resolution) is 500 Hz and can be reduced to 250, 125 and 60 Hz, respectively.
It was possible to record 1 000 frames, which corresponds to a measurement time of 2 seconds at
the maximum frame rate. Because this was too short to capture the entire flow field of a puff,
the frame rate was reduced to 125 Hz, which enabled an 8-second measurement time. In order to
limit the maximum particle displacement to about 8 px, the time delay between two subsequent
exposures was set to 4 ms, which reduced the actual measurement frequency to 62.5 Hz.
3
mean axial velocity (mm/s)
50
40
47.6
30
47.4
magnified view
20
47.2
10
47
0
0
0
2
4
4
time (s)
8
6
8
Figure 3: Mean axial velocity averaged over the pipe cross-section as a function of time.
3
Results
A detailed discussion of the measurement accuracy of the SPIV system in laminar and turbulent
flow is given Van Doorne et al. [6][7][9]. The probability density functions (PDF) of the three
velocity components, evaluated from the entire measurement sequence of the puff, are shown in
Figure 2. The asymmetry between ux and uy and the minor peak-locking in uz are comparable
to those observed before [7].
The development of a puff (growth, decay, splitting, propagation velocity, etc.) is very sensitive
to the exact value of Re. It is therefore important that the flow rate remains constant during the
experiment. This is verified by Figure 3, which shows the average streamwise velocity measured
with the SPIV over the cross-section of the pipe (the bulk velocity Ub ) as function of time. The
time averaged bulk velocity is 47.3 mm/s and the root mean square (RMS) of the bulk velocity
is 0.085 mm/s, which is 0.18% of the mean bulk velocity. A small trend in the graph shows that
there has been a very small change in the flow rate (of the order of 0.4% of the total flow rate),
which attributed to fluctuations in the pump. It can further be concluded that the measurement
uncertainty of the flow rate is somewhat smaller than 0.18%.
The axial velocity at the centerline of the pipe is plotted in Figure 4. Upstream from the puff the
laminar flow has a parabolic velocity profile, and therefore the axial velocity is maximal (2Ub ) for
t > 7(s). If the graph is read backward in time, i.e. in the downstream direction, a first sharp spike
is observed at t=5.3 s (z ∗ =0). This point (z2 ), where the velocity drops very suddenly for the first
time, is normally defined as the trailing edge (TE) of the puff, and it is therefore used as the origin
of the non-dimensional downstream distance z ∗ (= (t2 − t)Ub /D). A little farther downstream, at
z3 , a second spike is observed. And the sharp decrease of the velocity at z4 is followed by a series of
smaller fluctuations. Around z7 the flow starts to become laminar again. Immediately downstream
from this point of relaminarization, the velocity profile still resembles that of a turbulent flow, and
therefore the centerline velocity is still relatively low. Farther downstream the parabolic velocity
profile is restored by the gradual growth of the viscous shear layers from the wall, hence the
slow increase of the centerline velocity in the downstream direction, which continues for z ∗ > 6.
Note further that the rapid velocity fluctuations around z5 are represented by approximately 10
measurement points, which shows that the SPIV measurements are indeed time resolved. An
indication of the noise level can be obtained from the measurement for t > 7 s. The flow is
laminar and the uncorrelated small velocity fluctuations are due to the PIV interrogation noise,
which is of the order of 1 mm/s or 0.1 px.
The spikes in the neighborhood of the TE and the overall shape of the centerline velocity
of the puff are observed in all our measurements and can also be found in the measurements of
e.g. Wygnanski & Champagne [10] and Darbyshire & Mullin [11]. In boundary-layer transition,
4
1
z
uz / Ub
7
2
z
6
5
4
3
2
6
z
7
8
95
1
1.9
90
1.8
85
1.7
80
1.6
75
1.5
70
1.4
centerline velocity (mm/s)
0
2
time (s)
3
4
5
z z
z z
65
1.3
6
4
2
0
−2
60
z*
Figure 4: Axial velocity on the center line of the pipe.
and also for transition in pipe flow triggered by periodic blowing and suction [12], similar spikes
have been observed, and it has been shown that these were related to (a series) of hairpin-like
vortices in the flow. The observation of such a series of hairpin vortices strongly suggests that
the spikes in the axial velocity of the puff, as observed in Figure 4, can also be explained by the
development strong hairpin vortices in the flow.
The cross-sectional averages of the kinetic energy of the in-plane velocity (Exy = hu2x + u2y i),
and the axial velocity (Ez = hu2z i) are shown in Figure 5a and in Figure 5b. The wavy pattern in
Ez and the sequence of distinct peaks in Exy further seem to indicate a quasi-periodic organization
of flow in a puff. A peak in Exy coincides approximately with a sharp decrease (in the downstream
direction) of the axial velocity (figure 4), and also with a minimum in Ez . The turbulent energy
of the in-plane velocity (Exy ) is of course extracted from the energy of the mean flow (Ez ). The
strong in-plane motions related to the maximum in Exy will advect slow moving fluid from the
wall to the center of the pipe and thus induce the sharp decrease of the centerline velocity. The
hairpin-vortex model seems consistent with these observations.
In Figure 6 a sequence of flow fields is displayed which gives a much more direct view on
the structure of the flow. The streamwise vortices, the streaks and the shear regions have been
visualized by the axial vorticity, the axial velocity and the in-plane vorticity respectively. The first
flow field (z ∗ = −3.4) is measured upstream from the puff, where the laminar flow has a nearly
parabolic velocity profile. A first weak disturbance is observed, which consists of a low speed
streak at the wall (1) and a region of increased shearing (2) on top of the streak.
A little farther downstream (z ∗ = −1.1), six low speed streaks and the related shear regions
have formed periodically around the circumference of the pipe. At this point, the disturbance
of the laminar flow is restricted to the wall region and the central part of the flow has remained
unaffected. The graph of the axial vorticity reveals the presence of several streamwise vortices, and
some of the weak vortices have been marked by a circle (3). It seems that the low speed regions
are not necessarily formed by a pair of counter rotating vortices (3), but can also be formed by a
single strong vortex (4). Quite remarkable is that the strongest wall normal velocity fluctuations
are directed toward the wall (5, 6) and thus form regions with a high velocity close the wall. Only
a little farther downstream, at z1 , Ez reaches a first local minimum (Figure 5b).
5
z
7
0.025
6
z
5
z
4
=0
.7
=0 4
.0
=−
0.
82
=4
.4
9
=3
.7
1
=2
.7
=2 8
.1
4
z
z
3
z
2
z
z
0.18
1
0.14
mean kinetic energy
2
< ux +uy > / Ub
2
2
0.015
0.01
6
z
5
z
z
4
3
z
2
z
1
<u2> / U2 − 1.15
z
b
<u2+u2> / U2
x y
b
0.16
0.02
z
7
0.12
0.1
0.08
0.06
0.04
0.005
0.02
0
6
5
4
3
2
1
0
−1
−2
0
−3
6
5
4
3
2
1
0
−1
−2
−3
z*
z*
(a) in-plane velocity
(b) axial velocity
Figure 5: Kinetic energy of the in-plane (a) and axial velocity (b). A constant (1.15) has been
subtracted from the kinetic energy of the axial velocity to be able plot the two lines on a single
scale.
Around z ∗ = −0.53, Exy reaches a local maximum (Figure 5a), which seems related to the
combined action of several strong vortices which have a symmetric configuration with respect to
the indicated line (7). The development of the disturbance is most obvious in the left half of the
pipe, but also in the right half of the pipe the streaks have become more pronounced and the shear
layers have moved somewhat further toward the center of the pipe. The centerline velocity is still
not affected at this point (Figure 4).
The vector fields at the TE of the puff (z2 ; z ∗ = 0) show a strong ejection of low speed fluid into
the central region of the pipe (10), which explains the sudden decrease of the centerline velocity
(spike) in Figure 4. This event is clearly related to the large hairpin-like vortex indicated by (9).
The two counter rotating vortices which form the legs of the hairpin are strongly inclined with
respect to the wall, which results in the rather elongated iso-contours of the streamwise vorticity.
The tip of the hairpin vortex (i.e. the connection of the two legs) is characterized by a large
in-plane vorticity, and it is clearly visible in the corresponding image (11). A second pair of very
strong counter rotating vortices (8) is also seen to pump a considerable amount of fluid from
the wall, which might have deflected the direction of the hairpin vortex number (9). Upstream
from the TE at z ∗ = −0.15, the vector fields show strong motions parallel to the wall, and the
iso-contours of the streamwise vorticity form rather elongated regions close to the wall.
The second large spike in the centerline velocity (at z3 ) coincides approximately with the
enormous peak in Exy and the large minimum in Ez . This extremely violent event is also related
to a very strong hairpin vortex in the flow. This is most easily recognized from the vector fields
for z ∗ = 0.83 (Figure 6, part 2), which show the very large low speed region (16), the legs (14)
and the tip (17) of the hairpin vortex. The maximum in Exy occurs only slightly farther upstream
at z ∗ = 0.74 (∆z = 0.1D =4 mm). The enormous cross flow observed at this point (13) extends
over the entire cross-section of the pipe and is directed away from the hairpin vortex, which
suggests that the relatively fast fluid at this point is deflected by the low momentum region of the
hairpin vortex slightly ahead (16). Note further the striking symmetry of the streamwise vorticity
distribution with respect to the indicated line (12).
After the violent event at z3 , there follows a rapid decay of the turbulent energy Exy in the
downstream direction (Figure 5a), which indicates that the turbulent fluctuations decay and the
flow returns to the laminar state. However, two rather marked local maxima in Exy can still be
observed at z4 and z5 , and the first is also accompanied by a strong decrease of the centerline
velocity and Ez . So far, this type of event appeared to be related to strong hairpin-like vortices
6
in the flow. These local maxima might therefore be anticipated to correspond to two decaying
hairpin vortices, where the first one has still maintained some of its activity. This, however,
does not become entirely obvious from the vector fields displayed in Figure 6. At z ∗ = 2.1 (z4 )
strong in-plane motions are directed away from the center of the pipe, which indicates a strong
deceleration of the axial velocity. This is in line with the observations at z3 and seems to indicate
the existence of a similar flow structure. But, slightly downstream from the energy peak at z3 ,
where the legs, the tip and the low momentum region between the legs of the hairpin vortex could
clearly be visualized, it is quite impossible to find any good indications of a hairpin vortex at
the same downstream distance from z4 , i.e. at z ∗ = 2.2. For the local maximum of Exy at z5 ,
the vorticity distribution and the region of low axial velocity seem to give some more support
for the idea that the decaying turbulent structures still resemble the typical hairpin vortices (18).
Slightly farther downstream, in the vector fields for z ∗ = 2.8, we observe again two regions of very
strong in-plane motions, which are directed in opposite directions, away from the symmetry line
indicated by number (21). These motions seem related to the two counter rotating vortices (19
and 20) on either side of the line of symmetry, which may also correspond to a decaying hairpin
vortex.
The last remaining disturbances, visualized for z6 , are some weak streamwise vortices in the
central region of the pipe. At a distance of 6.3D downstream from the TE (z ∗ = 6.3) the flow is
completely relaminarized, but the axial velocity profile is still not completely axisymmetric, and
the centerline velocity is much smaller that for the parabolic velocity profile. Farther downstream,
the parabolic velocity profile will be restored by the gradual growth of the viscous boundary layers
from the wall.
In the discussion of the cross-sections of the SPIV measurements, we have concentrated on
the overall organization of the flow, and it seems that large hairpin vortices play a crucial role.
However, the flow contains many other (small scale) motions that were not explicitly mentioned,
although they largely determine the chaotic appearance of the flow and render the analysis very
difficult. This is nicely illustrated by the 3D view of the iso-contours of the streamwise vorticity
in Figure 7(a). The complicated structure of the numerous streamwise vortices makes it indeed
very difficult to point out the pairs of counter rotating vortices which form the hairpin vortices
discussed before. Instead, it seems that a substantial part of the vortices does not occur in pairs
at all, but exist rather individually. Figure 7(b) shows only a part of the vortices, in the lower
half of the pipe (y < 0). Some of the structures, indicated by the letters a-d, seem to follow each
other quasi-periodically in the downstream direction. However, this periodicity does not coincide
with the sequence of peaks in Exy , Ez and in the centerline velocity (indicated by z1 –z7 ), which
stresses once more the complex structure of the flow.
4
Discussion and conclusion
In this paper we have investigated the flow structure in a puff with the help of time resolved
SPIV measurements. This resulted in a completely different and complementary view of the flow
structure compared to previous PIV measurements by Westerweel & Draad [5], where the laser
sheet was parallel to the main flow direction. The time resolved measurement of all three velcoity
components over the entire cross-section of the pipe, has been converted into a quasi-instantaneous
3D flow field of the puff. The 3-D plots of the iso-contours of the streamwise vorticity give a good
impression of the complicated structure of the flow. It was found that the large fluctuations of the
centerline velocity (spikes) close to the TE of the puff are related to large hairpin-like vortices in
the flow. It was further found that the spikes in the centerline velocity coincide with large peaks
in the kinetic energy of the in-plane velocity (Exy ) and a sharp decrease of the energy of the axial
velocity (Ez ). This shows clearly that the hairpin vortices extract energy from the mean flow
and produce non-streamwise velocity fluctuations, which results in the turbulent motions. The
conclusions are supported by observations from flow visualizations reported elsewhere [9].
In view of the current observations, which have revealed the important role of the streamwise
7
vortices and a large asymmetry of the flow around the pipe axis, it has to be concluded that the
toroidal (axis-symmetric) vortex model, which was derived from ensemble averaged flow field [10],
is inappropriate to describe the flow dynamics. Instead, there is clearly a large similarity between
the quasi periodic regeneration of hairpin vortices in a puff and the dynamics of hairpin packets
observed in the near wall region of turbulent flow at much larger Re numbers, which can be
described by the vortex model of Smith et al. [13, 14]. Therefore, when the Re number is slowly
increased, the hairpin vortices in the puff should be expected to decrease gradually in size and
the flow will continuously change into fully developed turbulence. This view further suggests that
the intermittency which is so clearly observed for puffs at very low Re numbers, is probably not
much different from the highly intermittent character of the flow in the near wall region in fully
developed turbulent shear flow observed by Den Toonder & Nieuwstadt [15].
References
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12(1):1–169, 1957.
[4] E.R. Lindgren. Propagation velocity of turbulent slugs and streaks in transition pipe flow.
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2002. LADOAN.
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stereoscopic-piv for flow with large out-of-plane motion. In Proceedings of the EUROPIV 2
final workshop on Particle Image Velocimetry, Zaragoza, Spain. Springer Verlag, 2003.
[8] C.W.H. Van Doorne, B. Hof, R.H. Lindken, J. Westerweel, and U. Dierksheide. Time resolved
stereoscopic PIV in pipe flow. visualizing 3d flow structures. In Proc. 5th Int. Symp. On PIV,
Busan, Korea, 2003.
[9] C.W.H. Van Doorne. Stereoscopic PIV on Transition in Pipe Flow. PhD thesis, Delft University of Technology, 2004.
[10] I.J. Wygnanski and F.H. Champagne. On transition in a pipe. part 1. the origin of puffs and
slugs and the flow in a turbulent slug. J. Fluid Mech., 59:281–335, 1973.
[11] A.G. Darbyshire and T. Mullin. Transition to turbulence in constant-mass-flux pipe flow. J.
Fluid Mech., 289:83–114, 1995.
[12] G. Han, A. Tumin, and I. Wgnanski. Laminar-turbulent transition in poiseuille pipe flow
subjected to periodic perturbation emanating from the wall. part 2. late stage of transition.
J. Fluid Mech., 419:1–27, 2000.
8
[13] C.R. Smith. A synthesized model of the near-wall behaviour in turbulent boundary layers.
In G.K. Patterson and J.L. Zakin, editors, Proc. 8th Symp. on Turbulence, University of
Missouri (Rolla), 1984.
[14] C.R. Smith, J.D.A. Walker, A.H. Haidari, and U. Sobrun. On the dynamics of near-wall
turbulence. Philos. T. Roy. Soc. A, 336 (1641):131–175, 1991.
[15] J.M.J. den Toonder and F.T.M. Nieuwstadt. Reynolds number effects in a turbulent pipe
flow for low to moderate re. Phys. Fluids, 9(11):3398–3409, 1997.
[16] S.M. Soloff, R.J. Adrian, and Z.C. Liu. Distortion compensation for generalised stereoscopic
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Table 1: Overview of relevant parameters of the high speed SPIV measurements.
Pipe
diameter
40
mm
length
28
m
wall thickness
1.6
mm
material
glass
Flow
fluid
water
temperature
22.5
C◦
−6
kinematic viscosity
0.946×10
m2 /s
bulk velocity (flow meter)
46.4
mm/s
bulk velocity (SPIV)
47.3
mm/s
Reynolds number
2000
Seeding
type
Sphericel
diameter
10
µm
Light sheet
laser type
Nd:YLF
maximum energy
10
mJ/pulls
thickness
1.5
mm
Imaging
camera type
CMOS
viewing angle
±45
degrees
resolution
1280×1024
px
measurement frequency
62.5
Hz
lens focal length
105
mm
f-number
2.8
image magnification
0.35
viewing area
40×45
mm2
exposure delay time
4.0
ms
maximum particle displacement 8
px
PIV interrogation 3C reconstruction method
3D calibration (Soloff et al [16])
interrogation area
32×32
px
interrogation area
1.4×1.4
mm2
resolution with 50% overlap
0.7×0.7
mm2
9
Puff, Re=2000
z*=−3.4
t=8.2 s
10 mm/s
(1)
z*=−1.1
(6)
t=6.2 s
(4)
(2)
10 mm/s
(5)
≈Z1
(3)
z*=−0.53
10 mm/s
t=5.8 s
(7)
−5
−3
−1
1
axial vorticity (1/s)
3
5 0
18
36
54
axial velocity (mm/s)
72
90 0
2.5
5
7.5
10
12.5
inplane vorticity (1/s)
Figure 6: SPIV measurements of a puff at Re=2000, Part 1. See for explanation of the numbers
the text.
10
15
z*=−0.15
t=5.4 s
10 mm/s
z*=0.038
t=5.3 s
10 mm/s
(8)
(11)
(10)
(9)
Z2
z*=0.74
10 mm/s
t=4.7 s
(13)
(12)
Z3
z*=0.83
(14)
t=4.6 s
10 mm/s
(15)
(16)
Figure 6: cont’d (part 2).
11
(17)
z*=2.1
t=3.5 s
10 mm/s
z*=2.2
t=3.4 s
10 mm/s
z*=2.4
t=3.3 s
10 mm/s
Z4
−5
−3
−1
1
axial vorticity (1/s)
3
5 0
18
36
54
72
axial velocity (mm/s)
Figure 6: cont’d (part 3).
12
90 0
2.5
5
7.5
10
inplane vorticity (1/s)
12.5
15
z*=2.7
t=3 s
10 mm/s
t=3 s
10 mm/s
(18)
Z5
z*=2.8
(18)
(19)
(21)
(20)
z*=3.9
t=2 s
10 mm/s
t=0.016 s
10 mm/s
≈Z6
z*=6.3
Figure 6: cont’d (part 4).
13
(d)
(c)
(b)
(a)
(d)
(c)
(b)
(a)
(a)
(b)
Figure 7: 3D visualization of the iso-contours of streamwise vorticity (± 3.5 s−1 ) in the puff.
Sub-figure (b) shows the flow in the lower half of the pipe (y < 0) and the structures close to the
14
wall appear on top (viewing in the positive y-direction).