J. Chim. Phys. (1999) 96,951-957
O EDP Sciences, Les Ulii
Influence of gravity upon the bubble distribution
in a turbulent pipe flow: Comparison between
numerical simulations and experimental data
D. Legendre, C. colin*, J. Fabre and J. Magnaudet
lnstitut de Mecanique des Fluides de Toulouse, UMR 5502 du CNRS, INPAJPS,
avenue du Professeur Camille Soula, 31400 Toulouse, France
Correspondenceand reprints.
&SUM&
La prtdiction de la distribution radiale des bulles dans un 6coulement gaz-liquide
en tube est cruciale pour le dimensionnement des syst2mes thermohydrauliques.
Actuellement aucun mod2le n'est capable de prtdire la distribution spatiale des
phases de manikre satisfaisante et particuliSrement dans des conditions de
microgravitk. Cette distribution dkpendant fortement de la gravitt, des exptriences
(avec la boucle EDIA) et des simulations num6riques (avec le code JADIM) ont 6tt
rtalis6es conjointement dans des conditions de gravitt normale et en microgravitt.
Elles consistent i effectuer un suivi un lagrangien de bulles isoltes dans un
tcoulement turbulent cisaillt en tube.
Mots-cKs : bulle, turbulence, micropesanteur, S.G.E., suivi lagrangien
ABSTRACT
The prediction of the radial distribution of the bubbles in a turbulent
flow is
crucial for the design of the thermohydraulic loops. Up to now, no satisfactory
model does exist, especially in microgravity conditions. The bubble distribution
strongly depends on gravity. Therefore experiments (with the two-phase flow loop
EDIA) and numerical simulations (with the code JADIM) are performed under
normal gravity conditions and in microgravity. They consist of a lagrangien
tracking of single bubbles in a turbulent shear flow in pipe.
Key words: bubble, turbulence, microgravity, L.E.S., lagrangian tracking
D. Legendre et al.
952
INTRODUCTION
The radial distribution of the bubbles in a gas-liquid turbulent bubbly pipe flow is
strongly gravity dependent. Its prediction remains difficult because of the coupled
effects of the bubble drift velocity (due to gravity), the turbulence of the liquid
phase, the dynamics of the bubbles and the vicinity of a wall. The distribution of the
phases controls the momentum, heat and mass transfer at the pipe wall. Then a good
prediction of the phases distribution is crucial for the design of thennohydraulic
loops for power supply systems, for example.
In order to analyse the role of the gravity and the turbulence of the liquid phase
upon the bubble distribution, experiments are performed on earth and also in
microgravity conditions. The experimental results are compared to those of
numerical simulations.
EXPERIMENTS
Experimental set-up
Experiments with air-water flow in a pipe of 40 mm diameter and 4 m long are
camed out with the two-phase flow loop EDIA (Colin et al., [l]). For bubbly flow
conditions, the superficial velocity of liquid j, ranges between 0.3 and 1 m/s and the
superficial velocity of gas j, between 0.02 and 0.1 mls. Water is axially injected in
the tube and the air bubbles are injected through 24 hypodermic needles of 0.34mm
diameter: At 2.8 m from the bubble injection, the tube is equipped with local
probes, which can be moved radially:
- a single hot film probe for the measurements of the longitudinal velocity of
the liquid phase,
-
a double optical probe for the measurements of void fraction, bubble
diameter and velocity.
High-speed video pictures of the flow can also be taken to determine the bubble size
after image processing. Experiments are performed in the laboratory in vertical
upward and downward flow and under microgravity conditions during parabolic
flights aboard the "Caravelle" or "Airbus A300 Zero-G aircrafts.
Bubble distribution in a turbulent shear flow
953
Experimental results
Data have been obtained for several experimental conditions. The radial
distributions of the void fraction a,the axial mean velocities of the liquid U, and
gas U, and the r.m.s. velocities of the phases have been measured (Kamp, [2]). The
main result is the strong influence of gravity upon the void fraction distributions.
On earth, the classical peak of void fraction near the wall in upward flow and the
void coring effect in downward flow are observed. In microgravity conditions, the
radial distribution of the bubbles is rather flat with a maximum near the pipe centre
(figure 1). The radial distribution of the bubbles is attributed to different effects:
the lift force due to the drift velocity of the bubbles and the vorticity of the liquid
flow, the action of the turbulence of the liquid phase and the bubble dynamics.
From the sign of the mean drift velocity U, - U,, positive in upward flow, negative
in downward flow (figure 2), it follows that the lift force (last term of the r.h.s. of
equation [l]) pushes the bubbles towards the pipe wall in upward flow and towards
the pipe centre in downward flow.
Figure 1: Voidfraction distriburior~
6 vertical upwardflow, A downwardflow
0
Figure 2: Radial distributions of U,, UG
micrograviryflow
U,: opetl symbols, U,r closed symbols
The role of the turbulence of the liquid phase on the radial bubble distribution is
more difficult to analyse. In microgravity conditions, the lift force vanishes and the
action of the turbulence of the 1iquid.phaseupon the bubbles distribution can clearly
954
D. Legendre et al.
be highlighted. There is actually no model able to predict the void fraction
distribution in microgravity.
In order to analyse the role of the gravity and the turbulence of the liquid phase,
basic experiments and numerical simulations are performed on earth and also in
microgravity conditions. Both physical experiments and numerical simulations
consist of the determination of the trajectory of single bubbles in a single-phase
turbulent shear flow. In this basic situation, the single bubbles do not influence the
turbulence of the liquid phase.
NUMERICAL SIMULATIONS
The numerical simulations are performed with the code JADIM, allowing Large
Eddy Simulations of the turbulence (Calmet & Magnaudet, [3]) and a lagrangian
tracking of particles (Climent & Magnaudet, [4]). The local instantaneous
characteristics of a wall turbulent shear flow are obtained by LES with a great
accuracy (close to that obtained with Direct Numerical Simulations) for Reynolds
number up to 40,000. Moreover the analysis by direct numerical simulation of the
forces acting on a spherical single bubble (Legendre, [ 5 ] ) can be used to write an
equation for the bubble dynamics:
U,
and v are the instantaneous velocities of the liquid phase and the bubble, p,, p,
are the densities of gas and liquid,
Ptb
is the bubble volume and d the bubble
diameter, C, is a virtual mass coefficient taken equal to 112. C, and C, are the drag
and lift coefficients calculated by Legendre & Magnaudet [6]. The instantaneous
velocity
U,,
of a turbulent liquid pipe flow is computed by the code JADIM, the
bubble velocity v is calculated from equation [l] and the instantaneous trajectory of
single bubbles is obtained after integration of the velocity v. The probability density
function of the radial repartition of the bubbles can be deduced from a statistical
analysis of the instantaneous trajectories and compared to the experimental data.
Bubble distribution in a turbulent shear flow
The first results of the numerical simulations confurn
955
the tendencies
experimentally observed. Under the action of the lift force bubbles move radially
towards the pipe wall in vertical upward flow (figure 3b), towards the pipe centre
in downward flow (figure 3c). In microgravity, in absence the drift velocity, the lift
force vanishes. The action of the large turbulent eddies is dominant on the bubble
dispersion and the radial bubble distribution is more homogeneous. The bubble
motion is controlled by the instantaneous added mass force (third term of the r.h.s.
of equation [l]), taking into account the temporal variations of the turbulent
Structures.
(Og)
(- lg)
(lg)
Figure 3: Computed trajectories of bubbles of 0.5 mm diameter in a turbulent channel flow (h=2cm,
Re=40,000) in vertical upwardflow (- Ig), downwardflow ( l g ) and micrograviryflow (Og)
In figure 4 the dimensionless radial distribution of bubbles (of 0.5 mm diameter)
obtained by numerical simulations, 2 m downstream the bubble injection, is
compared to the experimental dimensionless radial void fraction distribution
measured by Karnp with the same superticid
velocity (i,=lrn/s), but with
simultaneous injection of several bubbles (j,=0.023 mfs). In this run, since the
956
D. Legendre et a1
turbulence of the liquid phase is close to the turbulence of the single phase flow and
the bubble interactions are weak, the comparison with the numerical simulations of
single bubble trajectories seems to be pertinent. The numerical simulations are in
quite good agreement with the experimental data, with, however, a small underestimation of the void fraction near the wall.
Figure 4: Dimensionless void fraction distribution re experiments, - simulations
< mis the cross-sectionalaveraged void fraction
CONCLUSION AND PERSPECTIVES
In most of the eulerian models, the interfacial momentum transfer (including the
forces acting on the bubbles) is modelised from the mean velocity fields, leading to
some discrepancy with the bubble distribution experimentally observed. The present
paper pointed out the importance of the instantaneous characteristics of the
turbulence upon the bubble dynamics. This aspect should be taken into account in
further developments of predictive models for two-phase flows.
The first comparison of the bubble trajectories numerically computed with
experimental data is promising. These results will be soon compared to
experimental data obtained in the two-phase flow loop EDlA with injection of single
bubbles, in a turbulent liquid flow. Spherical bubbles with diameter smaller than 1
mm are injected one at a time, in a water flow, through an hypodermic needle at the
pipe centre. Two synchronised high-speed video cameras located in two
perpendicular plans take pictures of the bubbles downstream from the bubble
Bubble distribution in a turbulent shear flow
957
injection. After image processing, the three-dimensional trajectory of the bubbles is
rebuilt. The probability density function of the radial bubble distribution can be
obtained in different pipe sections downstream the bubble injection in order to be
compared to the statistical results of the numerical simulations. Experiments are
carried out in laboratory in vertical upward and downward flow. Microgravity
experiments have been performed recently during a parabolic flights campaign
aboard the Airbus A300 "Zero G" aircraft. These f i s t experimental data are
processing.
Acknowledgements: The authors would like to acknowledge the Centre National #Etudes Spatiales
for funding and organisation of the parabolic flights campaigns.
REFERENCES
1 Colin C., Fabre J., Dukler A.E., (1991). In!. J. Multiphaseflow, 17, 533-544.
2
Kamp A., (1996), Doctorat thesis, Institut National Polytechnique Toulouse.
3 Calmet, I., Magnaudet J., (1997), Phys. Fluids 9 (2).
4 Climent E.,Magnaudet J., (1997), C.R. Acad. Sci. Paris, t. 324, SCrie I1 b.
5 Legendre D., (1996), Doctorat thesis, Institut National Polytechnique Toulouse.
6 Legendre D., Magnaudet J., (1998), Journal of Fluid Mech., 368, 81-126.
J. Chim. Phys.