7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30June 4, 2010
An attempt to image singlephase and twophase 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: Twophase 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 twophase flows by using nuclear magnetic resonance. At low
velocity, 10 cm/s, in singlephase 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 areaaveraged characterization
already presented by Lemonnier (2010) and Lemonnier & Jullien (2010). First singlephase data is reported and carefully
compared to existing data and DNS. Next selected twophase 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 singlephase 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 setup. 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 phaseflow
it can also be applied to twophase 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 lineaveraged 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 twophase 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 singlephase and
twophase turbulent flows and provides a new tool for in
vestigating turbulent structure and mixing phenomena that
can also be used to benchmark HWA in twophase flows.
Lemonnier & Jullien (2010) provide data showing that liq
uid velocity fluctuations and turbulent diffusion can be
characterized in an "areaaveraged 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 axisymmetric 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 socalled 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
recalledecho.
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 twodimension 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 30June 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
nondimensional 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 nondimensional veloc
ity at the considered location in the measuring volume and
second, volumeaverage 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)
JH/2 JR 
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 II2nu, 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 30June 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 axisymmetric flows
In the former theories of the signal, the axisymmetric 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 singlephase 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: Areaaveraged probability distribution of veloc
ity, II(u) at JL 10.5 cm/s in singlephase flow. For the
flow conditions see table 1.
The flow conditions for the singlephase 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 areaaveraged information on the
flow such as the areaaveraged 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 30June 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
1DVe102V002
040j
08
u, nd vel
1DVel02V002
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, nd gmad
Figure 1: Signal at echo, S(x, 0) at JL = 10.5 cm/s in
singlephase 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
1DVel02V00
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 areaaveraged 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, nd vel
7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30June 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 setup 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 30June 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 singlephase 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 singlephase 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
1DVel02V002
o r
a
Time sample number
5o 100
Figure 8: Real and imaginary parts of S(0,n).
20 15 10 5 0
va*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
ya*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 30June 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; y3/2
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 30June 4, 2010
10 5Gc, e u 28n
25 20 15 10 5 0 5 10 15 20 25
1DVel02V002 X (mm)
Figure 14: Chord averaged values of the velocity and
timespace 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 106 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 singlephase 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,
Twophase flow data
e Liu (1989) measured liquid velocity and fluctuation rms
orov in twophase bubbly flow. Before assessing further the
measurement procedure, it has been though worthwhile to
present some results in twophase flow with the process
ing algOrithm as it is now. The theory is almost unchanged
(25) with respect to singlephase 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 spacetime 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 30June 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 e1021 002 p
un 1318tnt
0 02 04 06 08
101 e1021 002 p
(b) Density
(b) Density
Figure 15: Comparison between the MRV measurements
and singlephase data by Liu (1989, p. 239), JL = 0.376
m/s.
By inverting the HankelFourier transform as in (14),
one has,
s(u, P') = R (PIp(u, p') (30)
RL2
where RL2 = L~ 2 is the areaaveraged liquid frac
tion. This fundamental result shows that in twophase flow
the velocity distribution can be obtained as easily as in
singlephase 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 twophase 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 twophase flows, as the data processing procedure
7th International Conference on Multiphase flows,
ICMF2010, Tampa, FL USA, May 30June 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 twophase 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 areaaveraged 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 quasiGaussian
(flatness around 3.5) with some bump in the higher veloc
ities in twophase flow with a positive (~ .5) skewness all
throughout the pipe section, in contrast to the singlephase
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, nd vel
101 e1021 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 singlephase 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 twophase 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 HankelFourier 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 e1021 002
04 06 on s 1 12
p
(c) Density
Figure 17: Comparison between the MRV measurements
and twophase 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 30June 4, 2010
Liu, T. TJ. 1989. Experimental .,,I rary,te.. of turbu
lence structure in twophase 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. NASATM110436. 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, 126135.
the past the origin of many artefacts in the PFGSE data
processing for obtaining areaaveraged quantities. It is
hoped it will provide some hints and a cure for utilizing
MRV accurately in twophase flows.
Some singlephase 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
spacedistribution 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 twophase 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
crosscheck 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
largeeddy 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, 175209.
Elkins, C. J., Alley, M. T., Saetran, L., & Eaton, J. K.
2009. Threedimensional magnetic resonance velocime
try measurements of turbulent quantities in complex flows.
Exp. Fluids, 46, 285296.
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 twophase 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 timeaveraged NMR imaging: measurement of
velocity profiles and turbulent intensity. M . eo
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