Turbulent Structure in a Drag-reducing Channel Flow with Surfactant Additives
Investigated by PIV System
by
*P.W. Li, **Y. Kawaguchi, **T. Segawa and **A. Yabe
*Dept. Mech. Eng., Kyoto Univ., Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501 Japan
**Mechanical Engineering Laboratory, AIST MITI, 1-2 Namiki Tsukuba, 305-8564 Japan
ABSTRACT
The turbulent frictional drag of water can be reduced dramatically by adding small amounts of drag-reducing
materials, such as polymers or surfactants. The amount of percentage drag reduction easily reaches 80%. In this work,
a double pulse PIV system was used to clarify the spatial velocity distribution of surfactant solution flow in a twodimensional channel of height 40mm, width 500mm and length 6m. A type of cationic surfactant CTAC
(C16 H33 N(CH3 )3 Cl) mixed with counter-ion material NaSal (HOC6 H4 COONa) was used as a drag-reducing additives
to water at a mass concentration of 40ppm. Instantaneous velocity distribution taken by PIV was examined to clarify
the effect of surfactant additives as well as Reynolds number dependency of drag reducing flow.
The following conclusions were drawn from the present study.
1. Figure 1 shows the velocity field with and without surfactant additives. Each figure shows the x-y plane along the
centerline of the channel. As seen in Fig. 1a, the mean velocity distribution taken in drag-reducing flow differs from
turbulent one in water flow without additives. Investigation of instantaneous velocity distribution shows that random
vortex motion disappears. An intermittent change of flow such as turbulent slug was not observed in present study.
2. Figure 1b shows the structure of penetration of low speed fluid into high-speed region, which is one of the
important events of turbulence energy production and turbulent mixing. Although this structure is commonly observed
in water flow, it was not found in drag-reducing flow under the same Reynolds number (see Fig.1a). The strong
vorticity fluctuation near the wall also disappears in drag-reducing flow.
3. As the Reynolds number increases and enters into "post DR region" where Reynolds number exceeds critical value,
the drag-reducing flow starts to become unstable and the PIV picture shows an appearance of turbulent motion near
the wall.
Frame 001  09 De c1 999  F: CT AC 99. 10. 192 1. 45xyV ect orxy00 004. vec
Frame 001  09 De c1 999  F: wa ter99 .1 0.1 914. 55 xyVe cto rxy 0000 1.v ec
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Fig. 1a. Instantaneous velocity distribution in
drag-reducing flow (CTAC 40ppm) at Re=21000
Fig. 1b. Instantaneous velocity distribution in water
flow (CTAC 0ppm) at Re=21000
The figure covers the full channel height. The upper and lower limit of the figure shows the top and bottom surfaces of
the channel respectively. The main flow direction is from right to left. The contours are colored according to the
instantaneous velocity
1
1. INTRODUCTION
Since the discovery of Tom's effect (Mysels, 1949, Toms, 1948), the reduction of turbulent friction between a solid
surface and fluid by adding drag-reducing materials has received increasing attention for saving the pumping power in
fluid transportation. Polymers were initially used as drag-reducing additives for turbulent water flow to reduce the
frictional drag by up to 80%. However, polymer solutions are strongly affected by mechanical degradation, which may
result in shorter lifetime of drag reduction effectiveness. Surfactants were found in the last two decades also to reduce
the frictional drag by 70% to 80% but to be less affected by mechanical degradation (Ohlendorf et al. 1986,
Bewersdorff et al., 1988). Therefore, surfactants are now being considered as practical drag-reducing additives.
One successful application of drag reduction by adding polymers was in the Trans-Alaska Pipeline, where the target
discharge of one million barrels per day was obtained without having to construct additional pumping stations (Burger
et al., 1982). A more recent application of the drag-reducing additives is to reduce the pumping power in district
heating and cooling systems where cationic surfactants are used in closed circuits (Gyr and Bewersdorff, 1995,
Gasljevic and Matthys, 1997, Pollert et al., 1994). Although the environmental contamination arising from the minor
toxic effect of surfactants may restrict their practical application in industry, for a closed circuit the effect on the
environment can be minimized to an acceptable level.
The authors are continuing experimental studies on drag reduction phenomena in order to optimize district
heating/cooling systems (Kawaguchi et al. 1996a, 1996b, 1997a, 1997b, Li et al, 2000). Kawaguchi et al. (1996a)
carried out an investigation to see how the turbulent characteristics in a two-dimensional channel are modified by
surfactant additives by using a two-component LDV system, and discussed the effect of surfactant concentration and
Reynolds number. They found that the two components of turbulent intensity were suppressed but have a finite value.
Surprisingly, Reynolds shear stress disappears in fully drag-reducing flow as a result of the de-correlation of the two
components of velocity fluctuation.
As the surfactant solution flow exhibits a complicated dynamical and thermal response, hot-film or other intrusive
methods are unsuitable for measuring flow characteristics. Although the LDV allows us to make accurate
measurements, measurements is limited to only one point at a time. Therefore, little information on the spatial
structure such as length scale of turbulence is revealed by LDV. In contrast, PIV gives spatial information
instantaneously. For this reason, PIV was employed to investigate the structure of drag-reducing flow in this paper.
2. EXPERIMENTAL APPARATUS AND PROCEDURE
2.1 Water Channel
The present experiments were carried out in a closed loop fluid flow facility, which is shown in Figures 2a and 2b. As
shown in Fig. 2, the system consists of reservoir tank (2.0 m3 ), a pump, a settling chamber equipped with a nozzle, a
two-dimensional channel, a diffuser and an electro-magnetic flow meter. The test section is 40mm high (H), 500mm
wide (W) and 6m long (inside measurements). Most of the test section was made of transparent acrylic resin having
thickness of 20mm. The surfactant aqueous solution is circulated by the pump and supplied to the settling chamber.
The chamber is equipped with a perforated pipe, stainless steel mesh and 1/12.5 contraction nozzle. At the entrance of
test section, a honeycomb of 150mm length having 10mm by 10mm rectangular openings was used to remove large
eddies. The PIV measurement position (L) is 3000mm (=75H) downstream from the inlet of the test section. For
measurements of pressure drop, a high-precision differential pressure meter was used. The reading provided by the
flow meter and the flow rate calculated from the velocity profile measured by LDV coincided within 3%.
2.2 PIV system
The PIV measurement system consists of a double pulse laser, laser sheet optics, PIV camera, timing circuit, PC and
software. The double pulse laser, (New wave Research Co. Ltd., MiniLase – II/20Hz) is a combination of a pair of NdYAG lasers the each having an output of 25mJ/pulse and repetition rate 20Hz. By changing the combination of
cylindrical lens, the laser sheet thickness can be modified in the range of 0.14mm to 0.6mm and spread angle in the
2
6m
?
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H
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? Window for PIV
? Pressure tap
? Pressure transducer
? Filter
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? Diffuser
? Flow meter
? Tank( 2m3)
Disturber
? Cooling Coil
Heater
? Thermometer
Thermostat ? Pump
Valve
?
?
?
?
?
?
?
?
?
Fig. 2a. Schematic diagram of two dimensional water channel
Fig. 2b. Picture of the channel
Inner height: H=40mm, width: W=500mm. All the measurements
Seen from contraction. Major parts are
were made at x=3000mm.
made of transparent acrylic resin.
range of 4.3 deg to 13.3 deg. The timing circuit (TSI Model 610032) communicates with the CCD camera and
computer, and generates pulses to control the double pulse laser. The time duration of laser pulses was adjusted to give
reasonable vector images. The interline CCD camera (PIVCAM 10-30, TSI Model 630046) used has a resolution of
1008 by 1018 pixels and can transfer images to the computer at the rate of 30 frames per second. A personal computer
(Pentium II, 400MHz) equipped with image grabber board (TSI Model 600067) was used to control the whole system,
picture frame acquisition and data processing using TSI's Insight ver. 2.01 software. As the generation of error vector
caused by imperfect condition of the optical system or software was unavoidable, a special Fortran program was
written for eliminating the error vectors and performing statistical calculation based on the acquired vector
distribution.
-3
(x10 )
y
Double Pulse
YAG Laser
Water
CTAC 40ppm
8
Flow
z
x
6
L
H
4
W
z
CCD Camera
2
4
0
(x10 )
0
2
4
6
8
Re
Fig.3. Schematic view of PIV arrangement
CCD Camera detects instantaneous velocity distribution in
x-y plane including full height of the channel (40 x 40mm)
3
Fig. 4. Friction factor versus Re
Rec: Critical Reynolds number. I: complete DR flow
II: Post DR flow
The arrangement of the water channel and PIV system are shown in Fig. 3. Cartesian coordinate are also shown in the
diagram. According to the common usage, x, y and z coordinates is aligned to the streamwise, normal to the bottom
wall and spanwise directions respectively. At the location of the measurements, the channel is equipped with two
circular glass windows having aperture of 150mm on the top and bottom walls of the channel. Another two glass
windows, each with a rectangular opening of 200mm in the x-direction by 60mm in the y-direction, are installed on
both sides of the channel. PIV image in the x-y plane are taken through the rectangular window from the z-direction.
To allow this, a laser sheet aligned in the x-y plane is emitted from the top of the channel through the circular window.
Most of the picture frames (40mm by 34mm) were taken to cover full height of the channel. In most of the
experiments, a series of 48 frames at the rate of 30 frames per second was taken. This means velocity field was
recorded in 15 Hz.
Fine particle of aluminum oxide were used for scattering particles, with nominal particle diameter of 5µm. The
concentration was carefully controlled to show clear PIV pictures.
2.3 Surfactant solution
The surfactant solution used in this study was cetyltrimethyl ammonium chloride (CTAC), which has the chemical
formula of C16 H33 N(CH3 )3 Cl , dissolved in tap water. CTAC is a cationic surfactant that is known to be very effective
for drag reduction when accompanied with suitable counter ions. Cationic surfactants are less affected by calcium or
sodium ions naturally found in tap water. This is the reason why cationic surfactants combined with a counter ion such
as sodium salicylate (NaSal, HOC6 H4 COONa) are frequently used in the basic studies or application to district heating
and cooling systems.
For the surfactant drag-reducing additives, the rod-like micelle structure is thought to be the key to give complicated
rheological fluid properties including viscoelasticity. NaSal acts to reduce ion radius of CTAC to deform micellar
shape from globular to rod like. In this experiment, same weight concentration of NaSal is always included in the
CTAC solution. For the sake of simplicity, the solution of surfactant is designated by the surfactant concentration.
Prior to the channel experiment, viscosity of the solution was measured by a rheometer with double wall Couette
geometry (Rheometric Scientific F.E. Ltd., ARES 100FRTN1). At concentrations of 30ppm and 100ppm, the shear
viscosity of the solution at a shear rate of 200 s-1 in 25 deg C was 0.82 and 0.97 mPas respectively, and showed no
stress thinning in the range of 10 s -1 to 300 s -1.
3. RESULTS AND DISCUSSION
3.1 effect of surfactant additives on friction factor and local mean velocity
The friction factor experimentally determined for water with and without surfactant additives is presented in Fig. 4.
Friction factors were obtained from static pressure distribution measurements along the channel. The Reynolds
number was estimated from bulk mean velocity Ub , channel height H and solvent kinematic viscosity ν0 . The friction
factor for water varies smoothly and obeys Dean's (1978) experimental formula for channel flow of Newtonian fluid.
In contrast, the friction factor of the surfactant solution changes in a complicated way. It is observed that friction factor
rises at Re=51000. This critical Reynolds number separates two regimes. These regimes were previously called
"complete DR flow" and "post DR flow " by Kawaguchi et al. (1997b). The largest percentage drag reduction in this
experiment was around 60%.
Mean velocity profile was determined based on the instantaneous velocity distribution taken by PIV. In each frame k,
we can obtain two components of velocity U and V at grid points xi and yj . As location of grid point in each frame is
fixed, we can define local mean velocity as the ensemble average through xi and frame number k as follows.
U (y j ) =
1
KI
K
I
∑∑U (x , y , k )
i
(1)
j
k =1 i =1
4
Water
1.5
1
CTAC 40ppm
Re=6.2x10
3
Re=1.0x10
4
Re=2.1x10
4
Re=4.2x10
4
Re=6.2x10
4
0.5
0
0
5
10 15 20 25
30 35 40
y(mm)
Fig. 5. Mean velocity profiles at various Reynolds numbers measured by PIV
( lines: water, symbols: surfactant 40mmp)
In the typical case, grid number I and J in a frame was 30, frame number was 48 and local mean velocity was
calculated based on 1440 data of instantaneous velocity measured at yj .
The obtained mean velocity profiles with surfactant for various Reynolds numbers are shown by symbols in Fig. 5.
Lines show the velocity profiles for water at each Reynolds number. As commonly known, the velocity profiles for
water is roughly correlated by 1/n power law. In this Reynolds number range, mean velocity near the centerline of the
channel becomes flat and velocity gradient near the wall is large. In contrast with this, velocity profile for surfactant
solution shown steeper peak near the centerline and the mean velocity gradient near the wall of surfactant solution is
lower than that of water flow. This finding corresponds to the result by LDV (Kawaguchi et al. 1996a) that the
velocity profile of drag-reducing flow approaches to but does not coincide to laminar-like velocity profile.
3.2 Effect of surfactant additives to instantaneous velocity distribution
At the beginning, instantaneous velocity distribution for water flow at Re=21000 is discussed. Figure 6 shows a vector
(Fig. 6a) and contour (Fig. 6b) expression of spatial velocity distribution taken by PIV. In these figures, main flow
direction is left to right and frame covers height of the channel. In Fig. 6a, bulk mean velocity Ub was subtracted from
all the vectors to see the vortex motion moving with Ub . This expression can be thought to give picture taken by a
camera moving with the flow. So, the wall looks to move downstream direction at the speed of Ub .
Figure 6a shows a velocity field composed of irregular direction as well as irregular magnitude of the velocity vectors.
Generally, velocity vectors head to right at the core region where y falls within 10mm to 30mm. In contrast with this,
vectors locating closer than 5mm from the wall head to left. Between these regions, rotational eddy motion is clearly
seen. The center location, size and magnitude are not uniform and the figure shows similar pattern of motion
visualized by tracer in turbulent flow. Figure 6b shows contour map based on the magnitude of velocity. Random
pattern of complicated ridge, valley and peaks can be seen in the middle of the channel. This means large velocity
fluctuation in time and space occupies this field. In the region closer than 3mm from the wall, contour lines are closely
distributed. This comes from large velocity gradient near the wall commonly seen in turbulent wall flow.
Figure 1b gives basically the same information with Fig. 6. One interesting finding from the colored contour is
existence of acceleration or deceleration fronts near the wall. The acceleration front start from the location (x,
y)=(15mm, 1mm) and reaches to (5mm, 7mm), The front inclines downward and has angle of about 30 deg from
5
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Fig. 6. Instantaneous velocity distribution in water (CTAC 0ppm), Re=21000
Fig. 6a (Left): Velocity vector. Bulk mean velocity Ub was subtracted from all the velocity
Fig. 6b (Right): Contour according to velocity magnitude.
F ra me 0 0 1  2 9 Ma r2 0 00  F :Li_ P eiwe nc tac 99 _ 10 _ 19 21 . 4 5x yVe cto rxy 00 0 00 . ve c
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Fig. 7. Instantaneous velocity distribution in surfactant solution (CTAC40ppm), Re=21000
Fig. 7a (Left): Velocity vector. Bulk mean velocity Ub was subtracted from all the velocity
Fig. 7b (Right): Contour according to velocity magnitude.
Each figure covers the full channel height. The upper and lower limit of the figure shows the top and bottom surfaces
of the channel respectively. The main flow direction is from left to right.
the wall. Note that the mean flow direction in Fig. 1 is right to left. Another acceleration front appears at the location
6
between (35mm, 3mm) and (23mm, 7mm). Deceleration front is not clear but can be seen between (27mm, 2mm) to
(20mm, 7mm). These acceleration or deceleration fronts are characteristic feature of the near wall turbulence. The
turbulent structure accompanied with rapid acceleration or deceleration was investigated by VITA method applied to
hot wire record (Blackwelder and Kaplan, 1976, Johansson and Alfredsson, 1982). A study on spatial structure
relating to turbulence control was also made based on the hot wire array probe (Kawaguchi et al., 1983).
Figure 7 shows velocity field obtained in surfactant solution flow. Reynolds number was 21000 and equal to the case
for Fig. 6. Fig. 7a and 7b shows a vector and contour expression of spatial velocity distribution respectively. Bulk
mean velocity Ub was subtracted from the vectors and show in Fig. 7a to see the vortex motion moving with Ub .
Tilting angle of mean flow and each velocity vector are not always zero but much smaller than that in Fig. 6a. Weakly
accelerated region can be seen in Fig. 7a at (x, y)=(7mm, 25mm) and (30mm, 25mm) but vortex motion cannot be
clearly detected from this figure. Kawaguchi et al., (1996a) found that the dye streak in water is diffused by eddies
having variety of sizes. In contrast with this, dye streak in drag-reducing flow is much stable and slowly curved and it
suggests diminish of random motion of eddies. The present result given by PIV corresponds to the previous flow
visualization study.
Figure 7b also shows complicated ridge and valley pattern in the core region where y=10mm and 30mm. In the region
close to the wall within 10mm, the contour lines run approximately parallel to the wall and its space is wider than the
case in water flow in Fig. 6b. This comes from thickened shear layer and smaller velocity gradient near the wall. The
reason and mechanism of drag reduction by additives are still under discussion because of the lack of experimental
and analytical information. In addition to this, turbulence production is essentially a recurring process. We can observe
the weak turbulence intensity in drag reducing flow and this suggests low production rate. Production rate of
turbulence sometimes expressed as Reynolds shear stress multiplied by mean velocity gradient. These two terms can
have small values in weakened turbulence intensity. Therefore, we encounter difficulties to isolate the reason for lower
production rate from simple observation.
According to Kawaguchi et al. (1996a), in fully drag reducing flow, both of turbulent intensities in two components u'
and v' are suppressed but have finite value. The suppression ratio of y-directional components is much larger than the
ratio of x-directional components. An astonishing fact is that Reynolds shear stress disappears in whole range of the
channel. Therefore, correlation factor of two velocity components Ruv is completely zero in spite of the presence of u'
and v'. Kawaguchi et al. (1997b) also found that coherent structure detected by quadrant analysis shows no
distinguished contribution from sweep or ejection. In other words, contribution from wallward and outward interaction
are comparable to sweep and ejection.
In Newtonian fluid flow such as water, two components of velocity fluctuation usually have negative correlation in
shear layer. The idea of mixing length hypothesis is widely accepted to give a good approximation in such case. The
idea contains random movement of fluid particles, and mixing after certain time period. De-correlation of turbulence
components in drag-reducing shear flow suggests some of the idea in mixing length theory is unsuitable. The free
movements of fluid particles are inhibited in drag reducing state. Some inhibition force is required but shear viscosity
cannot stand because of large Reynolds number.
The investigations are still going but force coming from extensional viscosity can be one of the candidates. Trouton
ratio is defined as the ratio of the extensional viscosity and shear viscosity. All the low molecular weight fluid has
Trouton ratio of 3 but some polymeric liquid have much larger values such as 10000. Although all the drag-reducing
fluid have complicated Rheological properties, large Trouton ratio is commonly found in drag-reducing fluid
including dilute surfactant solution used in the present study. If we suppose the high extensional viscosity, stretching
motion of vortex will be inhibited and production rate will be suppressed. At the same time, movement of the fluid
must overcome the strong stretching resistance and discrepancy from the mixing length hypothesis becomes large.
Another aspect of drag reduction is inhomogeneous turbulence suppression, which means y-directional components v'
are much suppressed than x-
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0 .0 26 56 88
35
F ram e00 1 29M ar 2000 F: Li _Peiw enctac99_ 10_1921. 45xyVecto rxy00002. vec
0
0
10
20
30
40
X mm
Fig. 8. Series of instantaneous velocity distributions taken under the same condition, CTAC 40ppm, Re=21000
The figure covers the full channel height. The upper and lower limits of the figure shows the top and bottom surfaces
of the channel. The main flow direction is from left to right. the contours are colored according to the instantaneous
velocity.
8
directional one, u'. It can be also explained by large extensional viscosity. Due to the redistribution process, the excess
energy in one directional components, such as u' is shared to another components v' and w'. As eddy-stretching motion
is included in this process, when the extensional motion is resisted, given energy to x-directional component does not
redistributed to y or x-directional components. This may explain the observation that v' is much suppressed than u' in
drag-reducing flow. This inhomogeneous suppression comes from the inhibition of energy transfer from u' to v' by
large resistance of eddy stretching.
As above qualitative explanation contains hypothetical idea, further investigations and effort to quantitative estimation
are necessary in the future. One of the projects would be accurate characterization of the drag reducing solution by
sensitive Rheometer. The other one may be direct simulation of non-Newtonian fluid turbulence containing reasonable
constitutive equation.
The mean velocity profile falls between those of laminar and turbulent velocity profiles in Newtonian fluid flow.
Recently, Saeki et al. (2000) made PTV measurements in drag-reducing flow in a pipe and found some transitional
characteristics where laminar flow and turbulent slug pass the pipe alternatively. The idea is attractive because the
some kind of surfactant solution is known to have much longer relaxation time. The authors also tried to detect the
intermittent characteristics of the flow by PIV images. The 48 frames of velocity distribution were recorded and
compared each other. 12 examples of the frame are shown in Figure 8. As seen in the figure, drag-reducing velocity
profile and weak turbulence intensity are observed in all figures. There are no clear evidence of intermittent nature of
laminar and turbulent slug in our PIV images at Re=21000. One of the differences may be the surfactant concentration
in the solution. Saeki at al. used 800ppm of Ethoquad O/12 and 480ppm of NaSal. These concentrations are 10 to 20
times larger than present work, which uses 40ppm of CTAC and NaSal. In addition to large Trouton ratio,
concentrated surfactant solutions have complicated rheological properties such as non-Newtonian shear viscosity, nonzero normal stress and large storage modulus. It is possible that these stress cause different way to modify turbulence
in the flow. Further discussion and investigation may be also necessary on this subject.
F ra me 0 01  2 9 Ma r 20 0 0  F :Li_ P eiwen wa ter9 9_ 1 0_ 19 1 4. 5 5x yVe ctorx y0 00 0 0. v ec
F ra me 0 01  2 9 Ma r 20 0 0  F :Li_ P eiwen cta c9 9 _1 0_ 1 92 1. 4 5x yVe cto rxy 00 00 0 .v ec
40
Vo rticity
35
30
Y mm
25
4 0. 92 36
2 9. 15 35
1 7. 38 34
5 .6 13 25
-6 .1 56 88
-1 7. 92 7
-2 9. 69 71
-4 1. 46 73
30
25
20
15
10
10
5
5
0
10
20
30
0
40
X mm
1 8 .57 5 6
1 2 .85 8 8
7 .1 41 9 6
1 .4 25 1 3
-4 .2 91 7
-1 0 .00 8 5
-1 5 .72 5 4
-2 1 .44 2 2
20
15
0
Vo rticity
29
25
21
17
13
9
5
1
35
Y mm
29
25
21
17
13
9
5
1
0
10
20
30
40
X mm
Fig. 9a. Vorticity fluctuation distribution in water
Fig. 9a. Vorticity fluctuation distribution in drag-reducing
flow (CTAC 0ppm) at Re=21000, -41.5s-1< ωz '<40.9 s-1
flow (CTAC 40ppm) at Re=21000, -21.4 s-1< ωz '<18.5 s-1
Contour lines in each figure are drawn at the class of 8 levels between minimum and maximum value in each frame.
The main flow direction is from left to right
9
One of the advantages of PIV measurements is that PIV can offer information of vorticity based on the spatial
distribution of velocity. In wall turbulence, velocity gradient has large value near the wall. Therefore, local mean
velocity was subtracted from the instantaneous velocity to eliminated contribution of mean velocity gradient to
vorticity. Vorticity fluctuation ωz' is defined as follows.
ω z ' ( xi , y j ) =
{
}

1  ∂V ( xi , y j )
∂
−
U ( xi , y j ) − U ( y j ) 

2 
∂xi
∂y j

(2)
Figures 9a and 9b show comparison of vorticity fluctuation with and without surfactant additives. Note that contour
lines are drawn to divide the range defined by minimum and maximum values appearing in the frame. These values
are designated under each figure. As shown in Fig. 9a, large positive and negative voticities were observed in the case
of water. This was found near the wall and its spatial scale is small. In comparison with this, surfactant additives
suppress violent vortical motion. Vorticity fluctuation is relatively weak and evenly distributed and its size is large.
3.3 Effect of Reynolds number in drag reducing flow
Kawaguchi et al. (1997b) made measurements of turbulence by LDV in same channel and examined the Reynolds
number dependency of the flow. They separated the Reynolds number range into four regions according to the friction
factor behavior. In the range of large drag reduction, where we are most interested was separated into two regimes into
"complete DR region" and "post DR region" by critical Reynolds number. Large drag reduction rate and low
turbulence intensity characterize complete DR region. Reynolds shear stress was zero and it comes from de-correlation
of two components of velocity fluctuation. Along with the increase of Reynolds number, frictional factor gradually
increases and flow approaches to turbulent flow in Newtonian fluid. One interesting finding by Kawaguchi et al.
(1997b) is that in post DR region, de-correlation of two components of velocity fluctuation, which is a key phenomena
in drag-reduction disappears. In post DR region, the flow is a kind of mixed state of drag reducing state and normal
turbulent state because the frictional drag and turbulence intensity comes midway of two states. But the correlation
coefficient of two components of velocity fluctuation takes comparable value of that in normal turbulent state.
Figures 10 shows the velocity distribution in drag reducing flow at different Reynolds numbers. According to the
classification in Fig. 4, cases for Figs. 10a to 10d belongs complete DR flow and other two belongs to post DR flow. It
can be observed that the flow starts to be unstable at Re=42000. At Re=52000 and 62000, the figures contains typical
motion in turbulent flow of Newtonian fluid. Penetration of low speed fluid into high speed flow, acceleration front
can be seen in Figs. 10e and 10f. According to these figures, flow state in post DR flow can be thought to be a
combination of drag reducing flow in core region and turbulent flow near the wall.
Control of drag reduction, which means temporal termination of drag reduction is also important issue for industrial
use of this technology (Li et al., 2000). The finding of such a combination is interesting from the view of controlling
drag reduction phenomena. The velocity fluctuation observed near the wall has similar characteristics of ordinary
turbulence because the correlation between two velocity components has large negative value (Kawaguchi et al.,
1997b). But at Re=62000, the occurrence of such a motion is still insufficient to recover turbulent transport. The drag
reduction rate is still large and have value of 30% (Fig.4) and mean velocity profile is different from that in water at
this Reynolds number as seen in Fig. 5. Therefore, giving disturbance in near wall region by some obstacle is not a
good method if the core region remains still drag-reducing state. Kawaguchi et al. (1996b) tried to give disturbance by
heater strip on the channel wall. The idea comes from the micellar structure destruction by high temperature at the
heater. Slightly enhanced Reynolds shear stress was observed but heat transfer enhancement or increase of frictional
drag was not achieved. Kawaguchi et al. (1997a) also investigated thermal boundary layer in drag reducing flow and
found double diffusivity layers. This may come from the present observation that flow can be unstable in near wall
region
but
still
covered
by
stable
drag-reducing
flow
in
outer
layer.
10
Fr am e 001  29M ar 200 0 F:L i_ Pe i we n c ta c 99_1 0_1921. 50xyVe c t or xy00001. ve c
Fr am e 001 2 9M ar 2000 F :Li _Pe i we nc t ac 99_10_19 22.0 0xyV e c to r xy00001. ve c
40
30
25
25
Y mm
30
25
20
20
20
15
15
15
10
10
10
5
5
5
10
20
30
0
40
X mm
0
0
10
20
30
40
Fig. 10 a. Re=6200
30
Y mm
20
S p ee d
30
30
25
25
20
20
15
15
10
10
10
5
5
5
20
30
40
0
0
10
20
X mm
Fig. 10 d. Re=42000
X mm
Fig. 10e. Re=52000
30
40
1. 3 30 3
1. 1 52 41
0. 9 74 50 9
0. 7 96 61 1
0. 6 18 71 4
0. 4 40 81 6
0. 2 62 91 8
0. 0 85 02
35
15
10
40
S pe ed
1 . 15 35 4
1 . 00 65 7
0 . 85 95 96
0 . 71 26 27
0 . 56 56 57
0 . 41 86 87
0 . 27 17 17
0 . 12 47 47
35
25
30
Fr am e 001 2 9M ar 2000 F :Li _Pe i we nc t ac 99_10_19 21.3 0xyV e c to r xy00001. ve c
40
S p ee d
0. 99 0 36 3
0. 86 3 36 4
0. 73 6 36 5
0. 60 9 36 6
0. 48 2 36 6
0. 35 5 36 7
0. 22 8 36 8
0. 10 1 36 9
20
Fig. 10c. Re=21000
Fr am e 001 2 9M ar 2000 F :Li _Pe i we nc t ac 99_10_19 21.2 0xyV e c to r xy00001. ve c
35
0
10
X mm
Fig. 10b. Re=10000
Fr am e 001 2 9M ar 2000 F :Li _Pe i we nc t ac 99_10_19 21.1 0xyV e c to r xy00001. ve c
0
0
X mm
Y mm
0
S p ee d
0. 5 68 53 2
0. 4 90 87 1
0. 4 13 21
0. 3 35 54 9
0. 2 57 88 8
0. 1 80 22 6
0. 1 02 56 5
0. 0 24 90 39
35
30
0
Y mm
40
S pe ed
0 . 27 55 1
0 . 23 75 6 1
0 . 19 96 1 2
0 . 16 16 6 3
0 . 12 37 1 4
0 . 08 57 6 5
0 . 04 78 1 61
0 . 00 98 6 71 5
35
Y mm
Y mm
40
S pe ed
0 . 16 54 3 3
0 . 14 30 0 9
0 . 12 05 8 6
0 . 09 81 6 23
0 . 07 57 3 87
0 . 05 33 1 51
0 . 03 08 9 15
0 . 00 84 6 78 5
35
Fr am e 001 2 9M ar 2000 F :Li _Pe i we nc t ac 99_10_19 21.4 5xyV e c to r xy00001. ve c
0
0
10
20
30
40
X mm
Fig. 10f. Re=62000
Fig. 10. Reynolds number dependency of drag reducing flow (CTAC 40ppm)
the figures covers the full channel height. the upper and lower limits of the figure shows the top and bottom surfaces of
the channel respectively. The main flow direction is from left to right
4.CONCLUSIONS
The following conclusions ware drawn from the present study.
1. The instantaneous velocity distribution taken in drag-reducing flow differs from turbulent one in water flow without
additives. Investigation of instantaneous velocity distribution shows that random vortex motion disappears. An
intermittent change of flow such as turbulent slug was not observed in present study.
2. The instantaneous velocity distribution taken in water flow exhibits the penetration of low speed fluid into highspeed region, which is one of the important events of turbulence energy production and turbulent mixing. Although
this structure is commonly observed in water flow, it was not found in drag-reducing flow under the same Reynolds
number. The strong vorticity fluctuation near the wall also disappears in drag-reducing flow.
3. As the Reynolds number increases and enters into "post DR region" where Reynolds number exceeds critical value,
the drag-reducing flow starts to become unstable and the PIV picture shows an appearance of turbulent motion near
the wall.
11
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