5th IAHR Symposium on River, Coastal and Estuarine Morphodynamics (RCEM 2007)

NEW IMAGING TECHNIQUE FOR MEASURING FLUID
AND SOLID VELOCITIES IN SAND-LADEN FLOWSOVER DUNES IN AN OPEN CHANNEL
Kotaro CHICHIBU1, Yasunori WATANABE2 and Yasuyuki SHIMIZU3
1Dept. of Hydraulic Research, Hokkaido University
Dr. Eng., Associate Professor, Dept. of Coastal & Offshore Engineering, Hokkaido University
3
Dr. Eng., Professor, Dept. of Hydraulic Research, Hokkaido University
2Abstract
This paper presents quantitative energy and momentum exchanges between fluid and suspended sands
via fluid-sand interactions in open channel flows over sandy dunes through comparisons of the sand-laden
flow over movable bed and the single phase flows over the fixed bed, on the basis of double camera PIV
measurements with an optical selection technique that is capable of measuring simultaneous velocities forthe both water and sand phases at the same locations. Since a boundary shear layer formed behind thedunes is constrained to be developed over a movable bed, the turbulent energy on the separated shear
layer is much lower than that in a fixed bed experiment. While the drag acting on the sands significantly
decelerates the water flow above the shear layer at the inception of sand suspension, in a settling phase,the drag accelerate the water downward. Additional turbulent energy is induced during sand settlement
process, which is over five times higher than the fixed bed case. This additional turbulence may disturb
the bed surface and enhance re-suspension of the disturbed sands. This recursive energy and momentum
exchanges between the sand and water flows via the suspension, diffusion, settlement and re-suspension
processes have important roles to characterize the sand-laden flows over the movable sandy dunes.
Key Words : dune, PIV, interaction, fixed bed, optical selection technique, turbulent energy

1. INTRODUCTION
Turbulence induced in a shear layer near a river sand-bed disturbs a movable sand layer to pick up sandsand carry them to downstream, typically resulting in a formation of sand-laden turbulent flows. The presenceof suspended sands produces additional turbulence around them and often affects the carrying flows due tothe sand-induced turbulence as well as drag force directory received from the carried sands. The energy
exchange between fluid and solid particles, and also energy transfer from the carrying flow to turbulence
may depend on relative length scales of turbulence and a particle (Gore and Crow, 1989). These effects
induced by the suspended sands may appear to change the suspension process and deformation process of a
local bed shape.
In an open channel flows with movable sandy dunes, initial sand suspensions change local flow field
involving separations of a shear layer developing behind a dune crest. Since the sand suspension is alsoenhanced there due to high vertical shear within a separated vortex, details of fluid-solid interactions inturbulent flows involving separated vortices needs to be understood for estimating net flux of sediments.
However, there has been few research on the dynamic interaction between water and suspended sands and its
effect to water flow field since it was very difficult to experimentally measure local velocities of individual
sand particles behind dunes.
Particle imaging velocimetry (PIV) has been commonly used for measuring spatial distributions ofparticle velocities, and many applications to open channel flows have been done (e.g. Anugragh et al,2006). In this study, PIV was also employed for estimating simultaneous velocity distributions for both waterand sand phases over a movable bed involving dunes on the basis of an optical selection technique. Effects ofthe presence of suspended sands to turbulence and mean flows were quantitatively estimated throughcomparisons with measurements for a single water phase over a fixed bed.
This paper organized as follows. In section 2, experimental set-up and our PIV technique are explained.
The measurement results are discussed in section 3, and they are concluded in section 4.

2. EXPERIMENTS
Dark room(1) Experimental set-up

Experiments were conducted in an open
YAG Lasergate
channel of 10 m in length, 0.15 m in width and0.3m in height with an uniform channel slope ofLaser sheet
1:0.002 (see Fig. 1). Sands of which the mean
diameter is 0.34 mm were used to form a sandI = 0.002
layer of 50 mm thickness on a channel bottom.
During experiments, the sands were consecutively
width : 0.15 m
camerasupplied to maintain a constant layer thickness.
4m
Fluorescent neutral buoyant particles (diameter:0.45 mm) were used as tracers of water flow.
Fix part
Movable bed (sand)Fix part
Movements of the tracers and suspended sands
0.5 m
7.5 m
2m
were recorded by two high-speed video cameras
Fig.
1
Experimental
set-upset in a dark room at the middle of the channel.
Two cases of measurements were carried out for finding effects of the suspended sands over the movablesandy bed to turbulent and carrying mean flows. First, the simultaneous measurement of the tracers and sandparticles over the movable bed (details of the measurement will be explained in the next subsection) wasdone (MB experiment). After this measurement, water in the channel was immediately drained, and the sandsurface was covered with cement to create the fixed bed whose shape is identical with the previous sand bed.
In the later experiment (FB experiment), only neutral buoyant tracers in an open-channel flow with the samedischarge (6.84 l/s) as the former MB experiment were recorded at the same measurement location. The
water depths for the former and later measurements were 112 mm and 104 mm, respectively. The formed
dunes have roughly 17 mm of wave height and 240 mm of wavelength.
(2) Image acquisition and preprocessing

At the measurement location, a YAG laser (wavelength of 532 nm) sheet illuminated a stream- wisecross-section including the square field of view (FOV) of 100 × 100 mm over dunes. Two synchronizedhigh-speed digital video cameras (resolution: 1 K×1 K pixels, frame rate: 500 fps) were mounted at one sideof the channel to record the same FOV (see Fig. 2). The recorded images were sent to PC via an image2

grabber connected with the cameras, and they
were converted into 8-bit gray-scale bitmap.
In order to separately record each of theneutral buoyant tracer and suspended sand bydifferent cameras, an optical selection technique
was introduced. Since the laser beam is directoryreflected on a surface of the sand particle, only thereflected lights from the sand can be recorded by
one camera equipped an optical band-pass filter(band-pass: 527-537 nm). The fluorescent tracer
used in the experiment is excited by the laser toemit fluorescent light of which the peakwavelength is about 570 nm. Therefore, using an
optical high-pass filter (pass 550 nm or longer),the reflected light from the sands is prevented to berecorded, and only the fluorescent light from thetracers can be captured.
In a calibration procedure, a grid board wasrecorded by two cameras for obtaining calibration
coefficients between image and real coordinates.
The captured images were transformed to the real
coordinates using linear projection based on thecoefficients (see Fig. 3). Image noise was reducedby performing a Gaussian digital filter.

YAG Laser
Acrylic plate
Reflection light fromsuspended sands

Mean water
depth

Fluorescent lightfrom tracers

Laser sheet

wave height of thedune (= 17 mm)sandtracer
FOV
wavelength of the dune (= 240 mm)

Sand layer(= 50 mm)

Bottom of flume

Fig. 2 Measurement location

Camera 1

Camera 2

Calibration grid board(3) PIV

Camera 1

Camera 2

PIV (Particle Image Velocimetry) is effective
for measuring a plane distribution of local flow. In
Transformed image in real space
this study, the standard PIV algorithm (so-calledFig. 3 Calibration procedure and image transformation.
cross-correlation method) was used. The
cross-correlation of image intensities in interrogation area and search area for two consecutive frames isN

R fg (∆x, ∆y ) =N∑∑ [ { f ( x , y ) − f }{ g ( x + ∆x, y + ∆y) − g } ]ii =1 j =1Njm

NiNjm

N

∑∑ { f ( x , y ) − f } ∑∑ { g ( x + ∆x, y + ∆y) − g }i =1 j =12ijm

2ii =1 j =1j(1)mwhere f and g are the image intensities in the interrogation and search areas, fm and gm are the mean image
intensities over the both areas, respectively.
The window sizes of the interrogation and search areas were 55 × 55 pixels (5 × 5 mm) and 110 × 110
pixels (10 × 10mm), respectively. An overlapping rate of the window was 50 %. The maximum correlation
Rmax was estimated at sub-pixel accuracy via second-order interpolation. For the window location where Rmax
> 0.7, the velocity is determined byu = ∆xm / ∆t(2)where Δxm is the displacement to give Rmax. In cases that Rmax < 0.7 and number of particles in thewindow are very small, the velocity is interpolated using the so-called square inverse distance method.
uij

u＊ =

∑l
ij

2ij

1

∑l
ij

(3)

2ij

where u* denotes the interpolated velocity, uij is the reliable estimated velocity at distance l from the grid
to be interpolated.
Accuracies of our PIV has been confirmed by using PIV standard images (PIV standardization andpopularization project, visualization society of Japan); the relative standard deviation of the velocities was4.97 % and correlation coefficient of the velocities was 0.97.

3

(4) Turbulent statistics

Turbulence properties were statistically estimated on the basis of time-averaged velocity over 10 seconds(5000 video frames). It should be noted that 10 s is much longer than the time-scales of sand-induced
turbulence and a primary vortex separated from the dune crest, and it is much shorter than the time-scale ofpropagation of the dunes. Therefore, it is an appropriate reference time-scale to be able to assume
quasi-steady state.
The instantaneous velocity can be written asu = U + u'(4)where U is the time-averaged velocity and u’ is the fluctuation component. Subscript ‘f’ and ‘s’ denotes
fluid and sand. The turbulence energy can be defined by
kf =

2
1 '2
(u f + v 'f )2

ks =1 '2 '2(us + vs )2(5)and Reynolds stress isu 'f v 'f , u s' vs'(6)

The relative velocity between water and sand phases (ur = us - uf) as a factor to determine drag force wasalso investigated.

ur = us − u f(7)
̲3. RESULT̲̲̲̲yg ̲ ̲,, ,,1-50cm/sec(1) FIXED BED (FB) EXPERIMENT
234cm
cm

Fig. 4 shows the velocity vector of the mean waterflow passing over the fixed dune crest. A typical
separation of a boundary shear layer appears just behindthe crest, and the shear layer extends to downstream. Aweak backward flow appears near the back slope of thedune, and a large-scale rotational flow is formed in alower potion of the shear layer. High turbulent energy isfound to be intensified along the separated shear layer
since strong shear produces turbulence (see Fig. 5). The
turbulent energy is also found to be diffused vertically.
There are high gradients of Reynolds stress near theseparation point and also around the shear layer,suggesting vertical momentum transfers are significant
in these regions (see Fig. 6).

5678
1

2

34

5

678

9cm

cm
Fig. 4 Time-averaged velocities of water flow in FB case.
180

2250

320026034020

4150
5100

6750cmcm

4cm
cm

100

FILE-F:¥07̲02̲07¥fix̲C002S0010̲2¥velocityturbulence̲1̲5997,UV300

FILE-F:¥07̲02̲07¥fix̲C002S0010̲2¥velocityturbulence̲1̲5997,INTENSITY

105-206-40-607-8088123456789cm

cm

0cm 2 / s 2

Fig. 5 Turbulence energy of water flow in FB case.

12345678cm

cm
Fig. 6 Reynolds stress of water flow in FB case49-100cm 2 / s 2

(2) MOVABLE BED (MB) EXPERIMENT

While the shear boundary layer is significantly developed on a non-slip bottom surface where highvelocity gradients occur in FB case, the velocity gradients near the movable bed are constrained to be mild
since a thin upper layer of the sandy bed is drifted with the water flow (see Fig. 7). The resulting shear
boundary layer is weak and the separation occurs at a lower portion of the back slope of the dune, resulting
in weaker turbulent energy on the shear layer (see Fig. 8). On the other hand, the turbulent energy is found to
be intensified and distributed in wide area of the downstream of the dune, which is a different feature with
FB case in which no significant turbulent energy appears over the dune trough (see also Fig. 5). It has been
confirmed that the settlement of the suspended sands is significant in this region, which suggests theintensified turbulence is due to additional turbulence produced during the settling process of suspended
FILE-E:¥07̲01̲27̲tr¥velocityturbulence̲1̲2499,INTENSITY
sands. FILE̲E:¥07̲01̲27̲tr¥velocityaverage̲1̲2499,V[ 4,5],U[ 44,3]
30011-50cm/sec

250
23344cm
cm

cm
cm

25200

150

5100

66750

78123456781923456

78cm

cm
cm

cm

Fig. 8 Time-averaged velocities of water flow in MB case.

Fig. 7 Turbulent energy of water flow in MB case.

0cm 2 / s 2

1
Dynamic contributions of the suspended sands tothe carrying flow are discussed bellow. Since drag2
acting on a particle may be proportional to square of
the relative velocity, the relative velocity (ur = us - uf)
3
may be regarded as degree and direction to decelerate4
the water flow due to the drag of the suspended sands.
The high horizontal ur occurs in the vicinity of the5separation point while moderate ur is also horizontally
distributed above the separated shear layer (Fig. 9),6which shows the suspended sands horizontally7
decelerate the water flow. In particular, high dragappearing at the separation point may be associated8with the inception of sand suspension. The settling
1
2
3
45
6
7
8
9
sands give downward drag to induce downwardcmcmacceleration of the water flow beneath the shear layer.
Fig. 10 shows the difference in the water velocity Fig. 9 Relative velocity of water and sand phases ( us – uf ).
(umov - ufix) of FB and MB cases. It can be seen that,in MB case, the horizontal water velocity above the shear layer is lower and the velocity bellow the layer ishigher than that in FB case. Despite the same water discharge with FB case was given to MB case, themaximum velocity of the carrying water flow decreases 5.5 % from that of FB case. This may be caused by
the dynamic effects of the suspended sands to decelerate the water flow above the layer and to accelerate
bellow the layer as already mentioned.
In the settling region, the turbulent energy in MB case is found to be significantly intensified over fivetimes higher than that in FB case (see Fig. 11). This additional turbulence induced during the settling process
may disturb the bed surface and enhance re-suspension of the disturbed sands.
This recursive energy and momentum exchanges between the sand and water flows via the suspension,diffusion, settlement and re-suspension processes have important roles to characterize the sand-laden flows
over the movable sandy dunes.

cm
cm-10cm/sec

5

FILE-comturbulence,COMPARISON OF INTENSITY[0,8]1722633544-10cm/sec

cm
cm

cm
cm

18556

6

7

78

432
18

12345cmcm

678

19Fig. 10 Difference in the water velocities for FB and MB cases.

2345

678

90cm
cm

Fig. 11 Rate of turbulent energy between FB and MB case. ( kMB / kFD ).

4. CONCLUSIONSIn this paper, energy and momentum exchanges between fluid and suspended sands via fluid-sandinteractions in open channel flows over sandy dunes is investigated through comparisons of the sand- laden
flow over movable bed and the single phase flows over the fixed bed. Simultaneous velocities for the bothwater and sand phases at the same locations are successfully measured on the basis of double camera PIV
system with an optical selection technique.
Since a boundary shear layer formed behind the dunes is constrained to be developed over a movablebed, the turbulent energy on the separated shear layer is much lower than that in no sand over a fixed bed
experiment.
While the drag acting on the sands significantly decelerates the water flow above the shear layer at theinception of sand suspension, in a settling phase, the drag accelerate the water downward.
Additional turbulent energy is induced during sand settlement process, which is over five times higher
than the fixed bed case. This additional turbulence may disturb the bed surface and enhance re-suspension ofthe disturbed sands.
It is found that this recursive energy and momentum exchanges between the sand and water flows via thesuspension, diffusion, settlement and re-suspension processes have important roles to characterize thesand-laden flows over the movable sandy dunes.

REFERENCES
1) Gore, R. A. & Crowe, C. T. 1989. Effect of particle size on modulating turbulent intensity, Int. J.
Multiphase Flow, Vol.15, pp.279-285.
2) Singh, A., Nir, A. & Semiat, R. 2006. Free-surface flow of concentrated suspensions, Int. J. MultiphaseFlow, Vol.32, pp.775-790.
3) Visualization society of Japan. Standardization and popularization project. Standard images.
(http://www.vsj.or.jp/piv/)

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