Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 15.3.1 - An attempt to image single-phase and two-phase flow velocity profiles by using nuclear magnetic resonance
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 Material Information
Title: 15.3.1 - An attempt to image single-phase and two-phase flow velocity profiles by using nuclear magnetic resonance Experimental Methods for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Lemonnier, H.
Jullien, P.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: two-phase flow instrumentation
void fraction
liquid velocity
nuclear magnetic resonance
NMR
MRI
 Notes
Abstract: In this paper we report preliminary results showing that it seems possible to accurately determine the mean velocity and velocity fluctuation rms distributions in single- and two-phase flows by using nuclear magnetic resonance. At low velocity, 10 cm/s, in single-phase flow, the viscous layer is resolved up to y+ = 5 and the 4 first moments of turbulence seems correctly determined. This study shows it is possible to go a step beyond the area-averaged characterization already presented by Lemonnier (2010) and Lemonnier & Jullien (2010). First single-phase data is reported and carefully compared to existing data and DNS. Next selected two-phase flow conditions in bubbly flow regime are reported and compared to the data of Liu (1989). Some comments on other similar studies are given and theory for analyzing the data is provided. Research prospects are also briefly outlined.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Resource Identifier: 1531-Lemonnier-ICMF2010.pdf

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7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010



An attempt to image single-phase and two-phase flow velocity profiles
by using nuclear magnetic resonance

Hervet Lemonnier, Pierre Jullien
DTN/SE2T/LITA, CEA/Grenoble, 38054 Grenoble Cedex 9, France
herve.1emonnier~,cea.fr, pierre~jullien~,cea.fr

Keywords: Two-phase flow instrumentation, void fraction, liquid velocity, nuclear magnetic resonance, NMR, MRI.

Abstract

In this paper we report preliminary, results showing that it seems possible to accurately determine the mean velocity
and velocity fluctuation rms distributions in single- and two-phase flows by using nuclear magnetic resonance. At low
velocity, 10 cm/s, in single-phase flow, the viscous layer is resolved up to y+ = 5 and the 4 first moments of turbulence
seems correctly determined. This study shows it is possible to go a step beyond the area-averaged characterization
already presented by Lemonnier (2010) and Lemonnier & Jullien (2010). First single-phase data is reported and carefully
compared to existing data and DNS. Next selected two-phase flow conditions in bubbly flow regime are reported and
compared to the data of Liu (1989). Some comments on other similar studies are given and theory for analyzing the data
is provided. Research prospects are also briefly outlined.


Introduction

Nuclear magnetic velocimetry has now become a mature
technique for characterizing single-phase turbulent flows.
Recently Elkins et al. (2009) have measured by using
this technique the 3D velocity field including the veloc-
ity fluctuations in the flow downstream a backward facing
step. Dimensions of the investigated zone were significant
(5.1 x 5.1 x 30 cm) and the data compares favorably with
that obtained by using PIV on the same set-up. In addition
velocity levels, 1,4 m/s and Re 48 000 based on the step
height were also significant.
The main interest of MRV is assuredly it is totally non
intrusive and that when developed for single phase-flow
it can also be applied to two-phase flow with almost no
significant change. This is a definite advantage that classi-
cal hot film (HFA) or hot wire anemometer (HWA) do not
share. It is known that the HWA signal processing in bub-
bly flow is cumbersome and prone to many artefacts. In
addition, when recirculations or other flow regimes than
bubbly occur, HWA can no longer be used: an alternate
method is desirable to assess the turbulence characteriza-
tion also in these cases.
Recently Sankey et al. (2009) have produced void
fraction and liquid velocity profiles in horizontal bubbly
flow. Data is not really local but as will be discussed later
is line-averaged and comparison with HWA is therefore
not direct. This particular point will be discussed here.
The motivation of this study is to better understand and
characterize turbulent mixing in two-phase flow. The main
focus is convective boiling and tracking the mechanisms
for critical heat flux occurrence in high pressure water
flow. It is though some progress on this very old problem


would come from multidimensional modeling and there-
fore appropriate modeling of turbulent momentum and
heat flux are required together with interfacial exchanges
in the bulk. In addition wall phenomena is difficult to in-
vestigate and is necessary, to complete the modeling.
It is the purpose of this paper to show that MRV can
be used to characterize non intrusively single-phase and
two-phase turbulent flows and provides a new tool for in-
vestigating turbulent structure and mixing phenomena that
can also be used to benchmark HWA in two-phase flows.
Lemonnier & Jullien (2010) provide data showing that liq-
uid velocity fluctuations and turbulent diffusion can be
characterized in an "area-averaged way" and that obtained
values agree with existing data obtained by other meth-
ods or models. The purpose of this paper is to show that
the distribution of these quantities within a pipe are also
available by using MRV and compares favorably with the
knowledge of these flow as documented by other meth-
ods. Though the data is preliminary, it is believed that it is
of sufficient quality to be considered as an encouragement
for further developments.

Former theories on MRV in axi-symmetric single-
phase flows

MRV is a purely Lagrangian method. The fluid is tagged
by using is ability to be magnetized provided it is im-
n ersed in a magnetic field for a sufficient time. For water
magnetization results from the spin of protons. Magneti-
zation is significant when the field is applied for typical
one second. Practically speaking, the fluid is magnetized
when traversing a 0.12 T. 2 meter long electromagnet. The
measuring section is located in the last quarter of this elec-









tromagnet were the field is particularly constant and uni-
form. (to one ppm). When magnetization exists it rotates
around the field direction at a constant frequency (5 MHz)
and its value can be measured by using a saddle shaped
coil into which the varying magnetization induces a volt-
age by induction.
Magnetization orientation and phase can be modified
by using auxiliary coils and the phase of the magnetiza-
tion can be "encoded" with the fluid position and velocity
within a so-called measuring volume sized by the detec-
tion coil. In the Spinflow experiment this volume is ap-
proximately a cylindrical volume based on the pipe diam-
eter (49 mm) and with a height of 60 mm approximately.
Within this volume the detection sensitivity is by design
rather uniform and the measured signal can be considered
as a true volume integral of the local magnetization con-
tribution.
A complete theory of the measurement is beyond the
scope of this paper and will be detailed elsewhere since it
is the basis of the correct understanding of the MRV sig-
nals. The sequence of events utlized here is similar to that
utilized by other authors such as Sankey et al. (2009). It
consists in non selective ( RF pulse, followed by a ve-
locity encoding step consisting of two gradient pulses of
strength g duration 6 and separation a. In order to immu-
nize the signal from the main static field fluctuations, a RF
j7 pulse is interspersed with the two gradient pulses to pro-
duce a spin echo. Data is being acquired when applying
a constant gradient field producing a so called gradient-
recalled-echo.
For some selected values of the duration 6 and sepa-
ration of the gradient pulses a which determines the sen-
sitivity of the velocity measurement, the sequence is re-
peated for different values of the gradient strength, g and
data is acquired in a time window centered on the echo.
The data, S(g, t), is therefore a two-dimension complex
variable of the gradient strength and time. It is the pur-
pose of the next paragraphs to describe holy this signal is
related to the velocity distribution within the measuring
volume. In that which follows, the velocity encoding step
is applied with a gradient field in the main flow direction
Z and the reading gradient is applied transversally in the X
direction. The remaining T direction lies in the pipe cross
section and is orthogonal to both X and Z. As a result
the velocity component that is detected is in the pipe axis
and main flow direction while the direction of space in-
vestigated is the transverse directionX. By selecting other
gradients directions other components of the velocity or
direction in space can be simply explored.
By applying successively the events of the sequence
described above, the local magnetization value is given
by.
in = mo exp(ig gRXt) exp(iyg gAv) (1)
where mo is the magnetization strength per unit volume,
v is the averaged Lagrangian velocity on time a, X is


7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


the position in the traverse direction, t is time, gR is the
reading gradient strength and y is the gyromagnetic con-
stant of protons. By using appropriate scales, this expres-
sion can be made non dimensional by introducing the ve-
locity scale 1/vmax = ygmax6 based on the maximum
gradient strength value used in the sequence, gmax, and
with v = uvmax. For the first exponential term in (1),
the non dimensional transverse coordinate is introduced
E = X/R where R is the pipe radius and the following
non-dimensional time y = ygRRt is also introduced. With
this change of variable, the local magnetization reads,

HI = mo exp(i~v) exp(ixu) (2)

If one assumes, the sensitivity distribution within the mea-
suring volume is flat, which is a design criterion for the RF
coil, then the detection coil provides the volume integral
of in within the measuring volume. Next the acquired data
is statistically averaged. One of the reasons for averag-
ing is the increase of the SNR ratio that results while the
other one, more physical, is that turbulence is a stochastic
phenomenon and that information on its moments requires
statistically converged data. Hopefully, and this is one of
the major advantages of NMR, statistical averaging and
volume integration commute and for the sake of a simple
description of the signal processing, it is equivalent to first
average the local signal,

Hi = Uo exp~iiv) Jp(u) exp(ixuldu (3)

where the bar denotes the statistical averaging and p(u) is
the probability distribution of the non-dimensional veloc-
ity at the considered location in the measuring volume and
second, volume-average the result. The signal is therefore
given by further integrating on the measuring volume of
height H and diameter 2R,

*H/2 *R -l2X
S(x, y)= dZ ~ d R2X dfin (4)
J-H/2 J-R -
By performing the integration, and further assuming
the flow is fully developed, one has,


Six, Y) 2nloR2H IIJ\ru, (),E

exp(i~v) exp(ixu)dudE (5)

By inverse Fourier transforming the signal with re-
spect to u and E,
(., ( 1 2 x S(xy

2x7 ,S(0, 0)
exp( -i~v) exp( -ixu)dxdy, (6)

the following result is obtained,

f(u, E) =2 II-2nu, E) (7)









where II is the chord average of p.

1
nl,! 2 -0 pp(,Ed


4~ p(u, E)~ $ 1,

(8)


7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


equation one get the probability distribution of the veloc-
ity,

s~~u, pX )=xpixu)Jo /P' )dxdp'


where 17 = T/R and the bracketed notation denotes the
chordal average. By taking the two first moments of II,
one has-







(10)

where a denotes the local mean value of the velocity and it'
is its fluctuation. It can be further shown that the centered
variance of II is given by,

Mn2 ML = (u 1117;)2~ r 17 11,2~ 17 (11)

where clearly the space distribution of the mean velocity
contributes as the mean value on the chord of the fluctu-
ation rms. Since these quantities depend on E they have
been sometimes confused with the true mean velocity and
fluctuation centered variance. This procedure based on the
double inverse Fourier transform of the data is the basis of
the analysis of Sankey et al. (2009) and the earlier work
by Li et al. (1994).

Another model for MRV in axi-symmetric flows

In the former theories of the signal, the axi-symmetric na-
ture of the flow could not be taken into account. If instead
of performing the space integration (4) in cartesian coor-
dinates, it is done by choosing polar coordinates,


Sx, y) = dZ rdr dOdil (12)

further assuming the flow is fully developed and axi-
symmetrical (p does not depend on Z nor on 9 the polar
angle in the OXT plane), the following result is obtained,


S(x, y) =27rmoR2H ilpdy ^p~u, p)
exp(ixu)Jolpv)du (13)

where Jo is the Bessel function of first kind and zeroth
order. This equation shows that the signal is the Hankel
transform with respect to time y and the Fourier transform
with respect to the velocity u of the velocity probability
distribution p. By taking the inverse transforms of the this


Then,


2(u, p') = p(u, p')


The mean velocity and velocity centered variance can
be deduced from the knowledge of p and taking its two
first moments,


Ap) = up(u, p)dit


l(p) = .Ilr_ u pdi


from which the velocity fluctuation rms can be deduced as
usual by,


U2 = 2 -~2


In addition, since p is known higher order moments
can be calculated and statistical quantities such as the
skewness and flatness factors can also be evaluated.

Validation of the single-phase measurements

Eggels et al. (1994) have used DNS to compute pipe flow
at a relatively low Reb 5300 that can be reach in the
Spinflow experiment with JL 10.8 cm/s at 200C. The
simulation has been thoroughly compared to existing data
obtained by HFA and PIV. The calculations were checked
several times by other authors and are considered as suffi-
ciently accurate to be considered in the AGARD data base
(AGARD n.d.).
Worth is to comment the procedure detailed by Eggels
et al. (1994) to get statistically converged information
from the DNS calculations. The local variables are space
integrated on 9 and Z on a length of 2.5 times the radius.
Next the results is statistically averaged on 40 time sam-
ples taken in the 2 last time units of the calculation. The
time scale of their simulation is D/u,, where it, is the
friction velocity. Equation (12) shows the NMR signal is
obtained in the same way. The length of integration in
Z is roughly one diameter and it was found that 64 aver-
ages was enough to get statistically converged data. The
similarity between the experiment and the DNS findings
confirms the detailed discussion on the turbulent structure
size and their strong correlation as detailed by Eggels et al.
(1994).








































































Figure 2: Area-averaged probability distribution of veloc-
ity, II(u) at JL 10.5 cm/s in single-phase flow. For the
flow conditions see table 1.



The flow conditions for the single-phase validation are
given in Table 1. The other sequence parameters will
be given and discussed in the next section. It is worth
mentioning that the signal at echo S(x, 0) is identical to
that produced by the PFGSE sequence utilized by Lemon-
nier (2010) and provides area-averaged information on the
flow such as the area-averaged liquid velocity JL and by an
approximate procedure detailed by Lemonnier & Jullien
(2010) the friction velocity u,. The figure 1 shows the sig-
nal at echo. It is remarkably similar to that shown by these


Run JL u, Uc 6 a ng
(cm/s) (cm/s) (cm/s) (ms) (ms)


Ill****1
II....












G 3 51 G/cm,B 6 deg Run 1288 tnt


7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


Re[p(u,p)]


1275 10.26 0,671 13.64 1.5
1288 10.50 0,660 13.98 3


25 64
12.5 128


Table 1: Flow conditions for the selected data in single-
phase for comparison with calculation by Eggels et al.
(1994).


05
04 -


02-
S01-
S0


-0 2
-0 3-
-0 4-
G 3 51 G/cm, 6
-0 5
-1 -08 -06
1DVe102-V002


040j
08


u, n-d vel


1DVel02-V002


G 3 51 G/cm,B 6 deg


Run 1288 tnt


Figure 3: Local density probability of velocity as a func-
tion of the radius p = r/R as given by (14). For the flow
COnditions see table 1.


-04 -02 0 02 04 06 08
x, n-d gmad


Figure 1: Signal at echo, S(x, 0) at JL = 10.5 cm/s in
single-phase flow. For the flow conditions see table 1.


Velocity (cm/s)
-40 -20 0


20 40


200
2


0 03

0025

002

0 015

0 01


0 0


-0 005

1DVel02-V00


02 04 06 08


Figure 4: Comparison between the measurements of the
mean velocity on the Spinflow experiment and the DNS
calculations by Eggels et al. (1994). For the flow condi-
tions see table 1.



authors by using PFGSE. They showed that the Fourier
transform of this particular signal is the area-averaged dis-
tribution of velocity probability the first moment of which
is JL. The Figure 2 shows the result of this transformation.
It was shown that the plateau level at low velocity was in-
versely proportional to the friction velocity squared. The
corresponding values are shown in Table 1. By assuming
Blasius law for friction a value of 0,717 cm/s is obtained
which agrees fairly well with this determination.
The figure 3 shows the probability distribution ob-
tained as the inverse Hankel and Fourier transform of the
signal. A part from a base line artefact at u = 0 the results
is smooth and well behaved. By taking a slice of this sur-
face at a constant p value, p(u, p) is obtained from which
the 4 first moments are calculated.
Figure 4 shows the mean velocity computed as the first
moment of p. It is agreement with the DNS calculation of


-150 -100 -50 0 50 100 150
u/umax, n-d vel






7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


35
3




15


05


02 04 06 08


02 04 06 08


Figure 5: Comparison between the measurements of the
velocity fluctuation rms on the Spinflow experiment and
the DNS calculations by Eggels et al. (1994). Blasius
law CF 0.079Re 0.2 has been assumed for the friction
velocity. For the flow conditions see table 1.


Eggels. Two deviations are observed:

The profile seems "shrinked" by 2% approximately,

the velocity profile close to the wall does not tend
toward zero as it should.

The think we know the reasons for these discrepancies (if
not yet the cure) as it will be shown in the next section. It
is remarkable that the viscous laver is accurately resolved
up to U/U Uc .2 which is twice closer to the wall that the
PIV and LDA data shown by Eggels. This corresponds to
y+ 5 here.
The Figure 5 shows the comparison of the axial ve-
locity rms as computed from the centered variance of p.
Agreement is correct. The increasing trend with p is well
reproduced, the viscous layer is also well resolved though
the peak seems slightly overestimated. The hydrodynamic
of our particular set-up has not yet been carefully validated
and it is assumed here the flow is fully developed with no
further justification. However, the measurement are per-
formed roughly 3.5 meter (Z/D 71) from the last honey
comb and gas injection section. 1.3 meter (Z/D 26) up-
stream of the measuring section, a slight sudden enlarge-
ment (44 to 49 mm) is present and the flow might not be
fully developed at that the measuring station, the Reynolds
number being relatively moderate. A reason for the over-
shoot of the fluctuation profile and its oscillatory nature
will be given in the next section.
The figure 6 shows the skewness factor as determined
from the third centered moment of p and appropriately
normalized by the fluctuation rms. Again it is remark-
able to observe that the numerical trends are well repro-
duced. The plateau in the core flow at -.5 is well described
whereas close to the center some return symmetry seems
to be observed. This trend was also observed in the core


Figure 6: Comparison between the measurements of
skewness factor on the Spinflow experiment and the DNS
calculations by Eggels et al. (1994). For the flow condi-
tions see table 1.


15


a0 2 04 06 on


Figure 7: Comparison between the measurements of flat-
ness factor on the Spinflow experiment and the DNS cal-
culations by Eggels et al. (1994). For the flow conditions
see table 1.


by the PIV data mentioned by Eggels (only in the range
.4 < p < .5) while the DNS results were confirmed by
Loulou et al. (1997) by using a different numerical algo-
rithm. The sharp transition to positive skewness values is
well resolved though again it seems to occur further from
the wall in the experiment than in the calculations. We
think the reason is identical to that for which the mean
velocity profile seems also shifted towards the interior as
will be discussed in the next section.
The figure 7 shows the flatness factor as determined
from the fourth centered moment of p and normalized by
the fluctuation rms. The trends again are surprisingly well
reproduced when considered the error accumulation that
occurs when evaluating high order moments. The transi-
tion form larger to smaller values than 3 (Gaussian behav-
ior) is well captured by the NMR measurements while the






7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010



---1 ****]
~a=0 28218
gg=1 0768 G/cm









G 3 51 G/cm,B 6 deg Run 1288 tnt


excursion to lower values than 3 close to the wall is well
reproduced in location and amplitude. However the tran-
sition to values larger than 3 at the immediate vicinity of
the wall could not be captured.


Some comments on the single-phase validation

By using a numerical simulation of the NMR measure-
ment, it is possible to interpret some of the discrepancies
observed between the NMR measurements and the DNS
calculations. Namely,

The oscillatory nature of the fluctuation rms profile
and the non vanishing velocity at the wall.

The apparent shift of the profiles away from the
wall.

As indicated earlier, some sequence parameters such as
the gradient strength magnitudes have not been given.
Their design value are known but their effective value in a
given sequence depend also on the frequency response of
the power amplifiers feeding the coils and the field images
produced in the metallic parts of the electromagnet by the
fast varying gradient pulses (though the gradient coils are
of the shielded type which should in principal immunize
them against this phenomenon). As a result the gradients
strength is not known accurately and must be calibrated
on the data directly.
The velocity encodmng maximum gradient strength
has been determined from single-phase flow experiments
where the flow rate is known and can be compared to the
mean velocity measured by the PFGSE NMR sequence
(see Lemonnier & Jullien 2010, for the details). A value
ofgmax = 3.51 G/cm has been assumed here after a single-
phase calibration.
There is no direct way to calibrate the transverse gra-
dient strength gR, it can only be performed indirectly. If
one considers the signal in absence of velocity encoding,
S(0, y), by assuming a flat sensitivity profile with the de-
tection coil (referred as the perfect coil configuration here-
after) the expected signal is,


S(0, y) f~y) (19)


When considering now the signal evolution with re-
spect to the sample number instead of y, the following be-
havior is expected,



S(0, n) = f(an), a = ygR TsR (20)

where Ts is the sampling time (4ps in the data discussed
here) and gR 1.07 G/cm is the reading gradient mag-
nitude. By data fitting on S(0, n) a and gR can be deter-
mined accurately for the given wave form utilized in the
sequence. The figure 8 shows that the real signal deviates


0 4


100
1DVel02-V002


o r


a
Time sample number


5o 100


Figure 8: Real and imaginary parts of S(0,n).


-20 -15 -10 -5 0
v-a*Timebin


5 10 15 20


Figure 9: Numerical simulation of S(0, y) for the actual
RF coil and the sequence utilized in this study.


35

30

25

20
a


-20 -15 -10 -5 0
y-a*Time bm


5 10 15 20


Figure 10: Numerical simulation of S(0, y) for a perfect
RF coil and the sequence utilized in this study.


slightly from the expected ideal behavior: it is not cen-
tered, not symmetrical and the first lobes amplitudes are
visibly different from their expected values.




















































Figure 12: Comparison of the measured velocity fluctua-
tion rms and the true velocity rms according to (24)


The figure 11 shows the difference between the real
mean velocity and that actually measured based on the di-
rect integration of (24) on Eggels results. Significant de-
viations occur only at p 1 on a range of order f0.02 as
shown by the data of figure 4.
When the same calculation is performed with the vari-
ance and the centered variance is calculated, the figure 12
shows an oscillatory behavior, an overshoot, a displace-
ment toward the wall of the rms peak together with a
steepening of the descending front to 0. For unknown rea-
sons all the oscillations are not shown in the data of figure
5 but it is believed that the other discrepancies between the
measurement and the reference calculation are explained
by this phenomenon. It will be shown later that this phe-
nomenon spoils significantly the zeroth order moment of
s which is unfortunately related to the mean density distri-
bution.


-

-

.

- -

-


7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


To find the causes of these differences and to elabo-
rate the necessary corrections, a numerical simulation of
the NMR signal (deserving another discussion elsewhere)
has been performed based on a generally well accepted
theory. The main feature of this model is to account for
the real RF coil geometry and to account for the real sen-
sitivity (almost flat but not exactly) of the coil within the
measuring volume. The figure 10 shows with the same al-
gorithm the perfect coil signal whereas the real coil signal
is shown in Figure 9. Fitting of the ideal behavior on the
results of the simulation shows the width of the main lobe
is overestimated by 2% approximately for the real coil. As
a result, the calibration procedure described above overes-
timates by the same amount gR and therefore underesti-
mates the position (p is the conjugate variable of y in the
Hankel transform) by 2%. It is in our opinion the reason
for the apparent "shrink" of the position in Figures 4 to 7.
The second issue is the oscillatory nature of the fluctu-
ation rms and the non vanishing velocity at the wall. These
effects are easy to understand with the perfect coil model
described by (13). The inverse Hankel transform is nec-
essarily performed on a finite range signal y e [0, ymax].
For the data shown here ymax~ 70. Beyond this value,
it is believed that noise prevails on the signal. Based on
the asymptotic expansion of J1 for large values of its ar-
gument, the magnitude of the signal varies as


on
Measured -
0 15 Residueu

0 1


00


-005

-01



02


0 a 2 04 06 on s 1 1


-7


Figure 11: Comparison of the measured mean velocity
and the true mean velocity according to (24)


-esre
Resea


|S(y)| s; y-3/2
Tr


SAR


For the selected value of yma = 70, this corresponds to
SNR~ 400. The inverse transform, is therefore calculated
by


F~p) =yf0y)Jo(py)dv (22)


instead of having taken, vma -o. As a result,


s(u,. p') = p(u; P)A(P, p')dll (23)

where a behaves as 2ymax/7rsincOymax(p p')) for large
values of yma and tends towards a Dirac delta function
when ymax co. Fory1ma 70 the width of the first a
lobe is approximately f0.04. Property (23) is transferred
to moments of s; since,


M;,(s)=l u/.slu)dit M;,~i(p(, p)a(p, p')dP
(24)

The practical significance of these equations is that the
finite time window of the signal induces an implicit space-
average on the data, the order of magnitude of which is the
first lobe width of a.


a on a 4 on as 1
P






7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010









10 5Gc, e u 28n





-25 -20 -15 -10 -5 0 5 10 15 20 25
1DVel02-V002 X (mm)

Figure 14: Chord averaged values of the velocity and
time-space composite variance calculated from the double
Fourier transform of the signal s.


11 cm/s here instead of 14 cm/s and we think the reasons
for this have been explained in the section on former the-
ory. In addition, the fix proposed by Li et al. (1994) to get
the actual rms profile from this data remains to us unjus-
tified. Clearly, for the fluctuations, the space integration
effect is dominant since the mean value of the fluctuation
rms lies well below 1.5 cm/s and an almost constant value
of 3 cm/s is found with this procedure.


0 0 1 0 2 0 3 0 4 0 5 06 0 7 0 8 0 9
r/R


Figure 13: Distribution of the Kolmogorov scales based
on the isotropic model, D 49 mm, v 10-6 m 2/s,
Rey, = 360, u, = 0.717 cm/s.

Run gmax gR 6
(G/cm) (G/cm) (ms) (ms)


1275 3.51 1.0767
1288 3.51 1.0766


3 12.5


Table 2: Sequence parameters for the single-phase data.


Spectral quality of the measurement


:s are
re ki-
case


This issue has not yet been discussed and some hint
provided by Eggels et al. (1994) who calculated th
netic energy dissipation rate profile, e, for the test
considered here. The units of their e' is u /D, i.e.
e'u /D. By considering the corresponding Kolmog
scales, one has respectively for time and space,


Two-phase flow data


e Liu (1989) measured liquid velocity and fluctuation rms
orov in two-phase bubbly flow. Before assessing further the
measurement procedure, it has been though worthwhile to
present some results in two-phase flow with the process-
ing algOrithm as it is now. The theory is almost unchanged
(25) with respect to single-phase flow. The derivation of the
signal equation is similar except that the local magnetiza-
Ich tion is now,


4 =


D 2/_1
-Re, 2


=DRe, et'


m = moXL exp(igy) exp(ixu)


The figure 13 shows the time scale ranges between 50
ms at the wall to 200 ms at the pipe center whereas; for
completeness the space scale is also shown to range be-
tween 200 and 500 pm from the wall to the center. The
table (2) shows that the velocity encoding time a is below
the smallest time scale in the flow by a factor of 2.

Comments on earlier work

Sankey et al. (2009) and Li et al. (1994) utilized a double-
Fourier transform based analysis which is believed to pro-
vide profiles of chord averaged values of the velocity and
for the fluctuations a space-time composition of fluctua-
tions as shown by (11). If their processing method is ap-
plied to our data, the Figure 14 shows that the mean ve-
locity profiles differ significantly: maximum velocity is


where XL is the liquid presence function since the gas does
not contain protons and does not contribute to the mea-
surement. By statistically averaging, one has,


n = mo expiigy)/ iiip(u) exp(ixuldui (28)

where alL is the local void fraction and p must be un-
derstood as the liquid velocity probability density distri-
bution. Further integrating in space in polar coordinates
gives,


S.(x, y) 2rmoR2H1 6 pdpi alL p)P 8, P

exp(ixu)Jo(py)du (29)













































v


7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


1++



08 -





0 21" Lmu(1989) -
Urunl31" +
Lmu (1989) -
urunl31" +
0 02 04 06 08 1
r/R


08-






04


0 02 04 06 08


02


(a) Velocity


(a) Velocity


So approx
So


So approx
So


1317tnt


0 G 3 1Gemwn 0 deg
0 02 04 06
101 e102-1 002 p


un 1318tnt


0 02 04 06 08
101 e102-1 002 p


(b) Density


(b) Density


Figure 15: Comparison between the MRV measurements
and single-phase data by Liu (1989, p. 239), JL = 0.376
m/s.



By inverting the Hankel-Fourier transform as in (14),
one has,


s(u, P')- = R (PIp(u, p') (30)
RL2

where RL2 = L~ 2 is the area-averaged liquid frac-
tion. This fundamental result shows that in two-phase flow
the velocity distribution can be obtained as easily as in
single-phase flow and, in addition the liquid fraction pro-
file can also be measured in principle. It is obtained by
taking the the zeroth order moment of (30) and produces
the curve labeled .5b in the figures. In fact at present, this
moment is obtained by an approximate method by restrict-
ing the integration around the main peak of the s The dis-
crepancy between the two methods is not yet understood.
The figure 15 shows the comparison between the


Figure 16: Comparison between the MRV measurements
and two-phase data by Liu (1989, p. 239), JL = 0.376
m/s, JG = 0.027 cm/s.


NMR data and some data obtained by Liu (1989). This
author's test section was 38.1 mm in diameter whereas in
the Spinflow experiment the diameter is 49 mm. The mean
velocity, 38 cm/s approximately, is preserved between the
two experiments and the friction velocity of the two ex-
periments that scales the velocity rms are close (2,3 and
2,2 cm/s respectively). Considering this Re distorsion, the
comparison is quite good. The wall layer is approximately
4 times thinner than in this case compared to the case of
Figure 4 and is not fully resolved. The density distribution
is shown in Figure 15(b) it is reasonably flat as it should
however its mean value should be closer to 1 than it is
shown in the figure. In addition, there is a clear deficit in
the density close to the center. It is believed this is linked
to the uneven sensitivity of the real RF coil.
In two-phase flows, as the data processing procedure






7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


is today, the results are encouraging but remain inaccurate
for the mean liquid velocity and local void fraction. At the
moment this paper is written, the reasons for this loss of
accuracy in the mean velocity are unknown. However, the
magnitude and trend in the velocity rms are correct. The
increase of the velocity rms by the presence of the bub-
bles is well described as well as the change in the profile
towards a quasi uniform profile. In figure 16 the condi-
tions of Liu have been reproduced by assuming the same
superficial velocity for each phase. Mean void fraction re-
ported by this author is 4%. Wall peaking is reported up
;0to 7% at r/R 0.9 in this case and seems also visible in
figure 16(b).
The figure 17 shows two-phase flow data at a much
Run 13191nt
higher mean void fraction RL2 11.7%. The void frac-
tion plateau at 10% reported by Liu seems recovered in
figure 17(c) as well as void fraction wall peaking at 17%
for r/R = .9. This is encouraging whereas the same
-0 45 problem with the mean velocity is clearly visible in fig-
ure 17(b). Surprisinghy the observed discrepancies in the
.* mean velocity does not deteriorate with the increase of the
-0 35 mean void fraction value. The evolution of the velocity
-0 3 rms seems however consistent with the Liu's data.
o 2 Obvioushy the liquid flow rate is not preserved by
Sthe processing method. In principle, the liquid flow rate
-0 2 is included in the data S(x, 0) where the data processing
015 should be identical to the PFGSE sequence utilized to get
-or area-averaged data and where this did not seem to occur
(Lemonnier 2010).
+ 00
-- Higher order statistics are not shown here owing to the
to uncertainty in the mean velocity, however it is worth men-
tioning that the velocity distributions are quasi-Gaussian
(flatness around 3.5) with some bump in the higher veloc-
ities in two-phase flow with a positive (~ .5) skewness all
throughout the pipe section, in contrast to the single-phase
flow data showing that in these particular flow conditions
So appro the liquid agitation resulting from the bubble presence su-
persedes the production by shear, which controls single-
phase flow turbulence.


Conclusions and prospects


Re[plu,p)]


u, n-d vel


101 e102-1 002


G 3 51 G em,B 6 deg


(a) Probability distribution


**""" ..






Liu(1989) -
Urunl319
Lm18) -
uiun13


04~


0 a 2 04 on as


(b) Velocity


It has been clearly shown that single-phase mean velocity
and velocity rms was possible with an unsuspected accu-
racy in the wall vicinity by using MRV. These results are
very encouraging and further research is still needed to
apply this technology with confidence to two-phase flows.
In addition, earlier studies produced distribution of chord
averaged quantities by using a double Fourier method. It
has been shown that the same data can be made local by
USing an appropriate Hankel-Fourier transform.
A detailed model of the MRV measurement is under
development to understand the discrepancies between the
real equipment and the simplified model utilized for inter-
pretation the MRV signals. This helped understanding in


1319tat


o 2
101 e102-1 002


04 06 on s 1 12
p

(c) Density


Figure 17: Comparison between the MRV measurements
and two-phase data by Liu (1989, p. 239), JL 0.376
m/s, JG 0.067 cm/s.






7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30-June 4, 2010


Liu, T. T-J. 1989. Experimental .,,I rary,te.. of turbu-
lence structure in two-phase bubbly flow. Ph.D. thesis,
Northwestern University, Evanston, IL USA.

Loulou, P., Moser, R. D., Mansour, N. N., & Cantwell,
B. J. 1997. The structure of turbulence in fully developed
pipe flow. Tech. rept. NASA-TM-110436. Nasa, Ames
research Center, CA USA.

Sankey, M., Yang, Z., Gladden, L., Johns, M. L., & Newl-
ing, D. Listerand B. 2009. SPRITE MRI of bubbly flow
in a horizontal pipe. 1. Mag. Res, 199, 126-135.


the past the origin of many artefacts in the PFGSE data
processing for obtaining area-averaged quantities. It is
hoped it will provide some hints and a cure for utilizing
MRV accurately in two-phase flows.
Some single-phase data on the transverse velocity and
fluctuations have already been obtained and seem to agree
with the data by Eggels. We miss today a complete the-
ory for this measurement and even if the magnitude and
space-distribution look correct, it has not been shown here
for this reason. In the same spirit, it is believed that ve-
locity correlation u'v' may also be within reach by usmng
a method similar to that of Li et al. (1994). However, a
model for analyzing correctly the data is not yet available.
This two latter issues together with the correct understand-
ing of the two-phase data processing is our top priority.
We are currently studying the practical implementa-
tion of HWA and optical probe sensors to determine the
velocity and void fraction distribution in the Spinflow ex-
periment. When the equipment is ready, it is planned to
cross-check the MRV and HWA/optical probe data. The
focus is on identifying the flow conditions where HWA
can be utilized safely by using MRV as a benchmark for
HWA. In addition, turbulent diffusion will also be studied
and subsequent modeling should follow.

References

AGARD. A selection of test cases for the validation of
large-eddy simulation of turbulent flows. Tech. rept. AR-
345. AGARD. torroja.dmt.upm.es/ftp/AGARD/.

Eggels, J. G., Unger, F., Weiss, M. H., Westerweel, J.,
Adrian, R. J., Friedrich, R., & Nieuwstadt, F. T. M. 1994.
Fully developed turbulent pipe flow: a comparison be-
tween numerical simulation and experiment. 1. Fluid
Mech., 268, 175-209.

Elkins, C. J., Alley, M. T., Saetran, L., & Eaton, J. K.
2009. Three-dimensional magnetic resonance velocime-
try measurements of turbulent quantities in complex flows.
Exp. Fluids, 46, 285-296.

Lemonnier, H. 2010. Nuclear magnetic resonance a new
tool for the validation of multiphase multidimensional
CFD codes. Nucl. Eng. Design.

Lemonnier, H., & Jullien, P. 2010. On the use of nu-
clear magnetic resonance to characterize two-phase flows.
Sumitted to Nucl. Eng. Des.

Li, T.-Q., Seymour, J. D., Powell, R. L., McCarthy, K L.,
Odberg, L., & McCarthy, M J. 1994. Turbulent pipe flow
studied by time-averaged NMR imaging: measurement of
velocity profiles and turbulent intensity. M . eo
nance imaging, 12(6), 923-934.




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