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Flow Measurement and Instrumentation 19 (2008) 131137
Flow Measurementand Instrumentation
www.elsevier.com/locate/flowmeasinst
Ultrasonic visualization of thermal convective motion in a liquidgallium layer
Yuji Tasakaa,, Yasushi Takeda a, Takatoshi Yanagisawab
a Graduate School of Engineering, Hokkaido University, Kita-13, Nishi-8, Sapporo 060-8628, JapanbJapan Agency for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan
Received 17 November 2006; received in revised form 12 January 2007; accepted 21 June 2007
Abstract
For low Prandtl number fluids including liquid metals, optical methods cannot be utilized to visualize convective motion, and in this paper the
velocity profile in a liquid gallium layer was measured using ultrasonic velocity profiling, UVP. The applicability of the measurement system was
confirmed with the rotating flow of liquid gallium and in the natural convection appearing in a glycerol solution layer. The vessel for the liquid
gallium layer was optimized for the acoustic properties of liquid gallium. The measured velocity profile shows a cell like convective motion. The
spatio-temporal behavior of large-scale convective motion in turbulent convection was observed as a temporal variation of the velocity profile with
two kinds of periodic fluctuations of the convection cell.c 2007 Elsevier Ltd. All rights reserved.
Keywords: Ultrasonic wave; Thermal convection; Liquid metal; Low Prandtl number; Visualization
1. Introduction
Thermal convection induced by a vertical temperature
gradient in a shallow fluid layer, RayleighBenard convection,
is a basic problem in fluid dynamics, thermal engineering, and
geophysics, but it has not been studied for low Prandtl number
(Pr) fluids. A phase diagram constructed by Krishnamurti [1]
suggests that the convection of low Pr fluids easily changes
from a two-dimensional steady state to a turbulent state
via a three-dimensional state and a time dependent state.
From theoretical considerations, Busse [2] suggested that
RayleighBenard convection is time-dependent at low Rayleigh
numbers, and temperature measurements of the convection ofmercury support this. Rossby [3] reported that the convection of
mercury shows periodic variations in the Nusselt number even
in the transition state of the phase diagram. Yamanaka et al. [4]
showed that the variation is induced by periodic fluctuations
Corresponding address: Division of Energy and Environmental Systems,Graduate School of Engineering, Hokkaido University, Kita-13, Nishi-8Sapporo 060-8628, Japan. Tel.: +81 11 706 6373; fax: +81 11 706 7889.
E-mail address: tasaka@eng.hokudai.ac.jp(Y. Tasaka).
in temperature in the fluid layer in an experimental study
using liquid gallium. This kind of periodic phenomenon
could be related to large-scale convective motion in the fluid
layer. However, these studies do not clarify the type of
convective motion because the studies only made temperature
measurements at a single point. Almost all studies of low Pr
convection relied on such temperature measurements because
optical visualization cannot be used to observe the convective
motion of opaque fluids such as liquid metals. This study
attempted to visualize the convective motion of low Pr fluid by
measuring the velocity profile in the fluid layer using ultrasonic
velocity profiling (UVP).
Initially, UVP was developed for medical purposes, and ithas become a powerful tool in experimental fluid dynamics [5,
6] and fluid engineering because it can measure instantaneous
velocity profiles, and can be applied to fluid flow of opaque
liquids including liquid metal [710]. Results with UVP are
superior to optical methods of velocity measurement such as
PIV (Particle Image Velocimetry). Thanks to the transmission
properties of ultrasonic waves UVP has been applied in
industry, for instance in flow metering in large pipes [11] where
the container wall is opaque, and also in quality control in food
processing [12,13] where fluids are generally opaque. Further,
0955-5986/$ - see front matter c 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.flowmeasinst.2007.06.003
http://www.elsevier.com/locate/flowmeasinstmailto:tasaka@eng.hokudai.ac.jphttp://dx.doi.org/10.1016/j.flowmeasinst.2007.06.003http://dx.doi.org/10.1016/j.flowmeasinst.2007.06.003mailto:tasaka@eng.hokudai.ac.jphttp://www.elsevier.com/locate/flowmeasinst -
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132 Y. Tasaka et al. / Flow Measurement and Instrumentation 19 (2008) 131137
advances with this technique using ultrasonic waves have been
developed in recent years to extend the range of measurable
values [14,15].
The applicability of the measurement system using UVP to
the problem investigated here was established with the rotating
flow of liquid gallium and thermal convection of a glycerol
solution. We measured instantaneous velocity profiles in arectangular vessel filled with liquid gallium (Pr of around 0.03)
heated from below and cooled from above. Comparisons of
temporally averaged velocity profiles measured at higher or
lower positions in the vessel showed that the convective motion
is similar to two-dimensional cells at extremely low Rayleigh
numbers but that the angular velocity of rotation is not uniform
like in two-dimensional cells. A spatio-temporal velocity map
is used to represent the two different temporal behaviors of
the cell motion; one is a meandering motion maintaining the
size of the cell and the other is a repetition of expansions and
contraction of the cell.
2. Experimental
2.1. Measurement technique
Ultrasonic velocity profiling (UVP) utilizes the Doppler
shift frequency and ultrasonic (US) echography to determine
an instantaneous velocity profile. Fig. 1 shows (a) the basic
configuration of the experimental setup, (b) the appearance of
the US signals, and (c) a measured velocity profile in the UVP
measurement. The US waves emitted from a US transducer
propagates in the fluid and a part of the waves is reflected by the
particles of the fluid. If there is a sufficient number of particles
reflecting waves in the fluid, the US echo returns from a wide
range of directions on the line of propagation of the US waves.
Assuming that particles move with the fluid, an echo contains
Doppler shift frequency, fD, velocity information of the fluid
flow. Therefore, the instantaneous velocity at a position in the
direction of propagation is determined by
u(, t) = c fD/2 f0, (1)
where c and f0 are the speed of sound in the fluid and the basic
frequency of the emitted US waves. The suffix in the equation,
, shows that the measured velocity is a velocity component of
the direction. The position on the axis is determined by the
time of flight of the US waves as
= c/2. (2)
Repeated wave bursts and reception of the US echos are
required to determine the instantaneous Doppler shift frequency
fD(t) accurately. The frequency of repetition of waves, fprf,
determines the maximum length where it is possible to measure
a velocity profile, , as
= c/(2 fprf). (3)
Further details of the UVP principles are described in Ref. [16].
Fig. 1. Schematicoutline of theUVP measurements; (a) thebasicconfiguration
of the experimental setup, (b) the appearance of the US signals, and (c) a
measured velocity profile in the UVP measurement.
Table 1
Physical properties of liquid gallium [17]
Symbol Unit Value
Density kg/m3 6.095
Bulk modulus K1 1.26 104
Thermal diffusivity m2/s 1.18 105
Kinematic viscosity m2/s 3.22 107
Prandtl number Pr 0.025
2.2. Liquid gallium
Liquid gallium was used as the low Pr fluid in this study.
An advantage of using liquid gallium as the working fluid is its
safety. It also has a higher vapor pressure than mercury and doesnot react with water like sodium. Table 1 shows the physical
properties of liquid gallium given by Brito et al. [17].
The UVP (ultrasonic velocity profiling) measurements
require the suspension of US (ultrasonic) wave reflecting
particles in the fluid. Here, a fine powder of ZrB2 was
used; particles are 50 m in diameter and have a density of
6.17 kg/m3. This kind of powder has also been used in other
work of UVP measurements in liquid gallium and has provided
good results [18]. Because of the large surface tension of liquid
gallium, mixing the ZrB2 particles into the liquid gallium is
more difficult than mixing them into water. To reduce the
surface tension coefficient, to enable mixing of the particles,
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Y. Tasaka et al. / Flow Measurement and Instrumentation 19 (2008) 131137 133
Fig. 2. Temperature dependence of the speed of sound in liquid gallium
determined by the time of flight method.
during the mixing, the liquid gallium was kept at a high
temperature, around 500 C, for 30 min in a furnace.As expressed in Eqs. (1) and (2), the speed of sound in
a medium is directly related to the measurement accuracy of
both velocity and position with the UVP. Further, the mean
temperature of the system depends on the Rayleigh number
in the system in this study. Only the speed of sound in liquid
gallium at 30 C, close to the melting point of the gallium
(29.8 C), has been reported [17,19]. The speed of sound
at several temperatures from 30 to 50 C was measured by
the time of flight method and the temperature dependence
of the speed of sound was determined. Fig. 2 shows that
there is a gradual decrease in the speed of sound c with
respect to temperature. By a least square estimate, the following
relationship is obtained
c(T) = 0.616T+ 2891.9. (4)
Testing liquid gallium was well deoxidized by 10% hydrochlo-
ric acidethanol solution before the measurement, and hence
there is little influence of gallium oxide on the relational
expression.We performed trial measurements of liquid gallium flow
in a simple configuration to confirm the usefulness of the
UVP system for measurements with liquid gallium. Fig. 3 is a
photograph of the experimental apparatus with a supplemental
illustration; the liquid gallium is contained in a 87 mm
inner diameter glass beaker, covered with a 10% hydrochloric
acidethanol solution to prevent oxidation. A magnetic stirrer, a
0.2 T magnet, is beneath the beaker and the liquid gallium layer
is driven by the Lorentz force induced by the rotating magnetic
field of the magnetic stirrer. It was expected that the flow inside
the beaker becomes like a Rankine vortex, which consists of
a rigid vortex and a free vortex. This system was originally
developed for deoxidization of liquid gallium.Ultrasonic (US) waves, with a 4 MHz basic frequency and
a 5 mm effective diameter, is emitted from the US transducer
outside of the beaker. The velocity profile of the liquid gallium
layer along the line of propagation of the US waves, the axis,
is obtained by the UVP on a UVP monitor model Duo (Met-
Flow S. A. [20]). The signal filter in this system is optimized
by Met-Flow for measurements of slow flows. Fig. 4 shows
an instantaneous velocity profile, where the horizontal and
Fig. 3. Photograph of the experimental apparatus for the trial measurements
and supplemental illustration; a rotating magnet is beneath the bottom of the
vessel to induce moves in the liquid gallium in the vessel.
Fig. 4. Instantaneous velocity profile in the liquid gallium layer measured by
UVP, where represents the distance from the ultrasonic transducer and u is
the velocity component to the axis.
the vertical axes are the distance from the transducer and the
velocity. The velocity is largest at the center and decreases
toward the wall of the vessel. The measurement axis is located
at a small distance from the center line of the beaker, and the
profile is consistent with expectations. The estimated rotating
speed near the center is 1 rps at the surface of the liquid gallium
layer. Assuming that the flow near the center confirms to rigid
body rotation, the maximum velocity on the measured line is 90
to 100 mm/
s, and would suggest that the measured velocity isquantitatively accurate.
2.3. Experimental setup
To determine the convective motion in a liquid gallium layer,
a rectangular vessel was constructed. The vessel for the liquid
gallium consists of three parts, the glass side walls, top and
bottom copper plates, 25 mm thick, with grooves for flowing
water to control the temperature. Fig. 5 shows a schematic
outline of the vessel, where the top and the bottom figures
show horizontal and vertical cross sections of the vessel. It
is 50 mm high (L), 200 mm wide (=4L) and 50 mm deep
(=L) with this shape, fluid layer flows would be restricted to a
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134 Y. Tasaka et al. / Flow Measurement and Instrumentation 19 (2008) 131137
(a) Horizontal cross section. (b) Side view and vertical cross section.
Fig. 5. Schematic outline of the experimental apparatus holding the liquid gallium, units in mm.
Table 2
Acoustic properties of liquid gallium and Pyrex glass, where the reflection coefficient of liquid gallium is defined as Rg = (ZgZ)/(Zg+Z), with Zg the acoustic
impedance of liquid gallium
Symbol Unit Liquid gallium Pyrex glass Plexiglas
Acoustic impedance Z 106 kg/(m2 s) 17.4 13.1 3.2
Sound speed c m/s 2860 5640 2730(longitudinal wave)
Reflection coefficient Rg 0.14 0.69
(for liquid gallium)
convective flow pattern. It was expected that a cell like pattern
would appear with an axis of rotation parallel to the y axis.
The side walls of the vessel are made of Pyrex glass which
can be wetted with liquid gallium. The acoustic impedance of
Pyrex glass is very close to that of liquid gallium as shown
in Table 2, and hence the ultrasonic (US) waves pass through
the side wall, rather than the other parts of the vessel (the
reflection coefficient for US waves passing through the Pyrex
grass to the liquid gallium, Rg, is one fifth lower than that for
Plexiglas, as shown in the table). The top and the bottom plates
are made of copper and are held in place with 15 mm thick
acrylic plates. There is a circular 12 mm diameter channel at
the top of the copper plates. The temperature of the flowing
water in the channels was controlled by thermostatic baths. The
water flows kept the surface temperatures of the top and the
bottom plates constant. The cooling temperature T1 (top plate)
was kept a higher temperature than the melting temperature of
gallium (29.8 C), at 32 C, and the Rayleigh numbers were
varied in the R = 200800Rc range by changing the heating
temperature T2. The Rayleigh number R is defined as
R =g(T2 T1)L
3
, (5)
where g, , , and are the gravity acceleration, bulk modulus,
thermal diffusivity, and kinematic viscosity of liquid gallium
respectively; Rc is the critical Rayleigh number of Rayleigh
Benard convection in a shallow fluid layer, Rc = 1707.7 [21].
Liquid gallium oxidizes easily, and the air in the vessel was
removed using a vacuum pump through two 10 mm diameter
holes drilled in the top plate with a buffer tank for liquid gallium
which was poured into the vessel with pressurized argon gas
through the 10 mm diameter hole (Fig. 6). Gallium pouring in
to the vessel was well deoxidized. The US wave transducer was
Fig. 6. Schematic outline of a filling process of liquid gallium to the vessel: (1)
air in the vessel was removed using a vacuum pump through two holes drilled
in the top plate and a buffer tank (2) liquid gallium (Ga) was poured into the
vessel with pressurized by argon gas (Ar).
placed at one end of the vessel and US wave bursts emitted
by the transducer propagated in the gallium layer parallel to
the x direction. Silicon oil was used as a coupler between thetransducer and the Pyrex glass plate to prevent existing air layer
in the very thin gap. The US wave bursts were at a 4 MHz basic
frequency and a 5 mm effective diameter, resulting in a spatial
resolution of the measured velocity profile in the liquid gallium
layer, , of around 1.4 mm.
3. Results and discussions
3.1. Flow patterns
Liquid gallium is opaque and it is difficult to make direct
comparisons between a measured velocity profile and the actual
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Y. Tasaka et al. / Flow Measurement and Instrumentation 19 (2008) 131137 135
Fig. 7. (a) Temporally averaged velocity profile of the convective motion in
glycerol solution, and (b) Sketch of observed convective motion in glycerol
solution. ux
represents the x axis velocity component of the convective motion.
convective pattern. To establish whether the profile and the
pattern are similar, UVP measurements and observations of the
convective motion were performed in a transparent glycerol
solution.
Fig. 7 shows the results of the measurements for a 28 wt%
glycerol solution (Pr 18). The fluid layer is 200 mm wide,
30 mm deep, and 20 mm high. The side walls are Plexiglas,
and the top and the bottom plates are aluminum and copper
respectively. Flowing, temperature controlled water maintained
a constant temperature at the top and bottom boundary of
the fluid layer. The Rayleigh number, determined from the
temperature difference between the top and bottom boundaries,
is around 800Rc. 80 m nylon powder was used as tracer
particle and its density is quite similar to the solution. Fig. 7(a)
shows a temporally averaged velocity profile obtained from
1024 instantaneous profiles, where ux represents the velocity
component on the x axis. Fig. 7(b) shows the location of the
transducer and illustrates the observed convection pattern. As
shown in the figure, the formed convection pattern is a quasi-
two-dimensional cell, with axis of rotation perpendicular to the
measurement direction. The convective motion is unsteady and
the size of the cells change temporally; however, the width of
cells do not become larger than the height of the fluid layer. The
measured velocities vary in the measured direction and attainalternately positive and negative values. In comparison with
the observed convection pattern, the variations between positive
and negative values correspond to the motion in individual cells.
At a set Rayleigh number, the convective motion is dominated
by separated thermal boundary layers at the top and the bottom
boundaries, and hence the rotation of a cell may be seen to be
similar to a rigid vortex. A velocity profile would show a flat
distribution without boundaries between cells when the rigid
vortex is measured by the UVP along a line. The obtained
velocity, however, includes both flat and sinusoidal profiles;
suggesting that some movement in some of the cells differs
from that of a rigid vortex.
Fig. 8. Temporally averaged velocity profile of the convective motion in liquid
gallium layer determined at (a) a low and (b) a high position. ux represents the
x axis velocity component of the convective motion.
Fig. 8 shows temporally averaged velocity profiles measured
at a high and a low position in the fluid layer of liquid gallium,
the horizontal axis x represents the distance from the ultrasonic
(US) transducer. The sampling period of the profile is 80 ms and
1024 profiles were used in the averaging, the spatial resolution
on the x axis is 1.44 mm. The Rayleigh number is 770Rc where
convective motion is turbulent. The profiles are not smooth
but somewhat broken. As mentioned in the next section, we
consider that it may be due to rather imperfection of seeding
than turbulent motion.Low in the fluid layer (Fig. 8(a)), the velocity profile has two
pairs of variations in the velocity between positive and negative
values in the fluid layer. The measured velocity is from 10
to 10 mm/s. At the higher position (Fig. 8(b)), the velocity
oscillates and the measured velocity profile is approximately
symmetrical to that measured at the lower position. The range
of velocities at the higher position is similar to that determined
at the lower position. A comparison with the results in the
glycerol solution (Fig. 7) suggests that there are two pairs of
cells with axis of rotation parallel to the y axis. The motion of
the cells is quite different for a rigid vortex because the velocitydoes not show a flat profile but has mainly a sinusoidal profile.
At the set Rayleigh number, 770Rc, the convection is
turbulent according to the flow regime diagram [1] and hence
the convection displays multi-scale motion. The obtained
velocity profile shows the large-scale motion of the cells, and
it is not possible to accurately determine small-scale motion
using the current UVP system because of the low speeds of the
convective motion.
3.2. Spatio-temporal behavior
The UVP (ultrasonic velocity profiling) can measure an
instantaneous velocity profile, and this makes it possible
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136 Y. Tasaka et al. / Flow Measurement and Instrumentation 19 (2008) 131137
(a) R = 428Rc.
(b) R = 770Rc.
Fig. 9. Spatio-temporal velocity profile. Color represents velocity, and counter clockwise rotation of a cell is represented by yellow and clockwise rotation by green.
to investigate the spatio-temporal variation in large-scale
convective motion. Fig. 9 shows the spatio-temporal velocitydistributions measured at R = 428Rc and 770Rc, where the
horizontal and vertical axes are the time and position measuredlow in the fluid layer, the colors represent velocity values. Black
points in the figures represent data voids caused by a lack ofparticles to reflect the ultrasonic waves and the shape of the
particles. The ZrB2 powder is shaped like powder grains and itsirregular surface scattered the ultrasonic waves. In comparison
with the temporally average velocity profile (Fig. 8), i t ispossible to distinguish two cells in these figures.
At R = 428Rc, there are four convection cells in the
fluid layer (Fig. 9(a)); counter clockwise rotation of a cell isrepresented by yellow and clockwise rotation by green. The
cells sway as expressed by the movement of the boundarybetween yellow and green. Small-scale velocity fluctuations are
superimposed on the large-scale fluctuation, but it is difficultto evaluate the small-scale phenomena because the small-
scale fluctuations are only a few times the velocity resolutionof the measurements, O(1 mm/s), and are indistinguishable
from the noise in the signals. The band enclosed by thebroken red line shows repeated expansion and contraction of
the cell maintaining the position on the x axis as shown inFig. 10(a). This movement is very slow with a period of
approximately 60 s (corresponding to 0.017 Hz of frequency).At the higher Rayleigh number, R = 770Rc, the motion
of the convection cell is different (Fig. 9(b)). There arestill four cells of the same size as with the lower Rayleigh
number, but the cell enclosed by the broken red line movesperiodically on the x axis without changes in size as shown in
Fig. 10(b) different from the convective motion in Fig. 9(a).
Fig. 10. Schematic illustration of motion in a convection cell; (a) repeated
expansion and contraction of the cell maintaining the position on the x axis,
(b) meandering motion with maintaining the size of the cell.
Further, the motion of the neighbouring cell corresponds
to that observed at the lower Rayleigh number. Convective
motion is faster than at the lower Rayleigh number and
the frequency determined by Fourier analysis is 0.059 Hz.
Simultaneous measurements of temperature fluctuations by a
thermistor shows the corresponding frequency. Selection of the
fluctuation pattern shown in Fig. 9 is alternative; it cannot be
determined which fluctuation pattern is chosen at each Rayleigh
number because the selections of the fluctuation pattern and
the number of the cells are strongly dependent on initial
condition and boundary condition, e.g. initial temperature
distribution in liquid gallium, temperature difference between
the boundaries and the gallium, etc. This is typical in many
instability phenomena. It is confirmed that there are three states
of convection with different number of cells; two, three or four.
Generally, it is difficult to control the number of cells.
4. Concluding remarks
Ultrasonic velocity profiling, UVP, was used to investigate
large-scale convective motion of a low Prandtl number fluid.
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Y. Tasaka et al. / Flow Measurement and Instrumentation 19 (2008) 131137 137
The applicability of the measurement technique was confirmed
in rotating liquid gallium and in the thermal convection of
a glycerol solution. The vessel for the liquid gallium was
designed to solve problems of wetting and permeability of
ultrasonic waves, and the velocity profile measured at lower
and higher positions in the fluid layer showed convection
cells in the liquid gallium layer. The spatio-temporal velocityfield measured by the UVP expressed different motions of
convection cells, including repeated expansion and contraction
and periodical meandering motion. The large-scale motion has
been discussed with temperature variations at a point in the
fluid layer [3]; however, the spatio-temporal behavior has not
previously been discussed for flow patterns and is shown in this
study for the first time. The measurement system here cannot
detect small-scale motion in the natural convection because of
a lack of data due to an insufficient number of tracer particles,
and the ZrB2 powder used in this study is shaped like powder
grains and not optimum for UVP measurements. It would be
possible to compensate for this by optimizing the shape of the
tracer particles.
Acknowledgement
This work is supported by Grant-Aided Research for Science
of the Japanese Ministry of Education & Science: No.18760116
and No.18204038. The authors express thanks for this support.
References
[1] Krishnamurti R. On the transition to turbulent convection. Part 2. The
transition to time-dependent flow. J Fluid Mech 1970;42:30920.
[2] Clever RM, Busse FH. Transition to time-dependent convection. J Fluid
Mech 1974;65:62545.[3] Rossby HT. A study of Benard convection with and without rotation. J
Fluid Mech 1969;36:30938.
[4] Yamanaka Y, Kakimoto K, Ozoe H, Churchill SW. RayleighBenard
oscillatory natural convection of liquid gallium heated from below. Chem
Eng J 1998;71:2015.
[5] Takeda Y. Quasi-periodic state and transition to turbulence in a rotating
Couette system. J Fluid Mech 1996;389:8199.
[6] Takeda Y, Fischer WE, Sakakibara J. Decomposition of modulated waves
in a rotating Couette System. Science 1994;263:502.
[7] Takeda Y. Measurement of velocity profile of mercury flow by ultrasound
Doppler shift method. Nucl Tech 1987;79:1204.
[8] Brito D, Nataf H-C, Aubert J, Masson J-P. Ultrasonic Doppler
velocimetry in liquid gallium. Exp Fluids 2001;31:65363.[9] Eckert S, Gerbeth G. Velocity measurements in liquid sodium by means
of ultrasound Doppler velocimetry. Exp Fluids 2002;32:5426.
[10] Mashiko T, Tsuji Y, Mizuno T, Sano M. Instantaneous measurement of
velocity fields in developed thermal turbulence in mercury. Phys Rev E
2004;69:036306.
[11] Mori M, Takeda Y, Taishi T, Furuichi N, Aritomi M, Kikura H.
Development of a novel flow metering system using ultrasonic velocity
profile measurement. Exp Fluids 2002;32:15360.
[12] Ouriev B, Windhab E, Braun P, Zeng Y, Birkhofer B. Industrial
application of ultrasound based in-line rheometry: Visualization of steady
shear pipe flow of chocolate suspension in pre-crystallization process. Rev
Sci Instrum 2003;74:52559.
[13] Ouriev B, Windhab E. Transient flow of highly concentrated suspensions
investigated using the ultrasound velocity profiler-pressure difference
method. Meas Sci Technol 2003;14:196372.
[14] Sandrin L, Manneville S, Fink M. Ultrafast two-dimensional ultrasonic
speckle velocimetry: A tool in flow imaging. Appl Phys Lett 2001;78:
11557.
[15] Ozaki Y, Kawaguchi T, Takeda Y, Hishida K, Maeda M. High time
resolution ultrasonic velocity profiler. Exp Thermal Fluid Sci 2004;26:
2538.
[16] Takeda Y. Instantaneous velocity profile measurement by ultrasonic
Doppler method, JSME Int J B38 1995; 816. Invited Paper.
[17] Brito D, Cardin P, Nataf H-C, Marolleau G. Experimental study of a
geostrophic vortex of gallium in a transverse magnetic field. Phys Earth
Planet Int 1995;91:7798.
[18] Aubert J, Brito D, Nataf H-C, Cardin P, Masson J-P. A systematic
experimental study of rapidly rotating spherical convection in water and
liquid gallium. Phys Earth Planet Int 2001;128:5174.[19] Beyer RT, Ring EM. Liquid Metals: Chemistry and Physics. New York:
Marcel Dekker; 1972 [Chapter 9].
[20] Met-Flow SA. Lausanne (Switzerland). Visit http://www.met-flow.ch.
[21] Reid WH, Harris DL. Some further results on the Benard problem. Phys
Fluids 1958;1:10210.
http://www.met-flow.ch/http://www.met-flow.ch/http://www.met-flow.ch/
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