Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 7.1.1 - The Turbulent Shear Stress in the Developing Region of Bubbly Jets
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 Material Information
Title: 7.1.1 - The Turbulent Shear Stress in the Developing Region of Bubbly Jets Bubbly Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Milenković, R.
Yadigaroglu, G.
Sigg, B.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: bubbly jet
turbulent properties
PIV
 Notes
Abstract: In experimental work on bubbly jets and plumes, most data found in the literature relate to the far field of the flow, where nearly asymptotic conditions prevail (e.g., Iguchi et al. 1995, Iguchi et al. 1997). By contrast , the objective of this work was to experimentally analyze the developing region of bubbly jets (Milenković 2005). The first objective was to systematically estimate experimentally the effect of the void-fraction on the main flow properties such as: mean liquid velocity, standard deviation of the liquid velocity, variance of the liquid velocity, kinetic energy and turbulent stress. The experiments were carried out at different Jet Reynolds numbers (i.e., superficial liquid jet velocity) and void fractions, keeping the bubble diameter as constant as possible by means of a specially designed injector. The second objective of the work was to provide a data basis for comparison with calculations using turbulence codes or models for bubbly flows. In this context, it was interesting to learn for instance whether the classical algebraic Reynolds stress expressions that are based on turbulence models such as the mixing-length model of Prandtl, the k − L model as well as the two-equation models like k − ε are applicable under the flow conditions investigated. These models were applied to own experimental results, first in relation to single-phase jets and then to bubbly jets. The findings of these investigations are that the Reynolds stress models are adequate for the developing region of single-phase jets, whereas for bubbly jets, the Reynolds stress models work well in the jet region, but in the transitional region, where buoyancy begins to dominate, wrong predictions of the turbulent shear stress are obtained. The simultaneous bubble and liquid velocity measurements were conducted with the Particle Image Velocimetry (PIV) technique, whereas the void fraction results were obtained with Double Optical Sensors (DOS).
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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Volume ID: VID00171
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 711-Milenkovic-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010





The Turbulent Shear Stress in the Developing Region of Bubbly Jets


R.Z. Milenkovic*, G. Yadigaroglut and B. Sigg

Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
ETH Zurich, WEN B-13, Weinbergstrasse 94, CH-8006 Zurich, and
ASCOMP GmbH, Technoparkstrasse 2, CH-8005 Zurich, Switzerland

formerly, Nuclear Engineering Laboratory, ETH Zurich, Switzerland

rade.milenkovic#.psi.ch and vadi(@ethz.ch

Keywords: bubbly jet, turbulent properties, PIV

Abstract


In experimental work on bubbly jets and plumes, most data found in the literature relate to the far field of the flow,
where nearly asymptotic conditions prevail (e.g., Iguchi et al. 1995, Iguchi et al. 1997). By contrast the objective of
this work was to experimentally analyze the developing region of bubbly jets (Milenkovic 2005).
The first objective was to systematically estimate experimentally the effect of the void-fraction on the main flow
properties such as: mean liquid velocity, standard deviation of the liquid velocity, variance of the liquid velocity, kinetic
energy and turbulent stress. The experiments were carried out at different Jet Reynolds numbers (i.e., superficial liquid
jet velocity) and void fractions, keeping the bubble diameter as constant as possible by means of a specially designed
injector.
The second objective of the work was to provide a data basis for comparison with calculations using turbulence codes
or models for bubbly flows.
In this context, it was interesting to learn for instance whether the classical algebraic Reynolds stress expressions that
are based on turbulence models such as the mixing-length model of Prandtl, the k L model as well as the two-equation
models like k e are applicable under the flow conditions investigated. These models were applied to own
experimental results, first in relation to single-phase jets and then to bubbly jets. The findings of these investigations are
that the Reynolds stress models are adequate for the developing region of single-phase jets, whereas for bubbly jets,
the Reynolds stress models work well in the jet region, but in the transitional region, where buoyancy begins to
dominate, wrong predictions of the turbulent shear stress are obtained.


The simultaneous bubble and liquid velocity measurements were conducted with the Particle Image Velocimetry (PIV)
technique, whereas the void fraction results were obtained with Double Optical Sensors (DOS).









Paper No


1. Introduction


To improve physical insight and to support numerical
analyses of bubbly flows, a number of basic experiments
have been carried out. In the field of free shear flows,
research has been performed on bubbly jets and plane
bubbly mixing layers. (Sun and Faeth, 1986, Stanley an
Nikitopoulos, 1996, Stewart and Crow, 1993, Rightly and
Lachers, 2000, Roig et al., 1998)

In these tests, effects of bubble size and concentration on
turbulence, velocity and void distributions, shear-layer
spreading rates, mixing, characteristic length scales and
velocity correlations have been studied. Basically, these
measurements mainly provided results for statistical
properties and the spatial distribution of local stochastic
variables.


Especially in regard of turbulence modulation and
interactions between bubbles and large- eddy structures,
there are still some unsolved problems and open questions.
One of them, which occupies almost all two-phase flow
researchers, is how shear-induced and bubble-induced
turbulence interact.

Usually, the velocity fluctuations of the continuous phase,
influenced by the presence of a dispersed phase
(turbulence modulation), are decomposed into two
separate parts, i.e. shear-induced turbulence and bubble-
induced turbulence (Lopez de Bertodano et al., 1994),
(Lance and Bataille, 1991), although the two phenomena
may be difficult to distinguish if they interact. The first
part is assumed to be independent of the relative motion of
bubbles and liquid, and the second part has been addressed
by considering the following contributions (Kitagawa et
al., 2001):

- velocity changes caused by the displacement of the liquid
moving around individual bubbles (often simulated by
potential flow), leading to strong velocity fluctuations and
giving to this part the highest importance;
- velocity changes induced by bubble wakes;
- velocity changes produced by vortex shedding behind
bubbles;
- velocity changes induced by unsteady deformation of
bubbles;
- velocity changes generated by the discrete distribution of
buoyancy forces in the flow field, which drag lumps of
fluid along with the bubbles, especially in case of high
fluid viscosity. These changes can occur even if there is no
relative velocity between bubbles and surrounding liquid.

Various decomposition methods, which have been


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



implemented into turbulent flow simulations, are based on
the use of turbulence models. As in DNS (Direct
Numerical Simulation) the ranges of temporal and spatial
scales of the variables in the Navier-Stokes equations
have to be cut off and since some parameters in turbulence
models used in current RANS (Reynolds Averaged Navier
Stokes) or LES (Large Eddy Simulation) computational
methods must be tuned, experimental investigations are
required for validating these methods and models.


Experimental conditions that can form a good basis for
validating existing models as well as new ideas and
theories and that provide clear conditions for observing
and simulating complex two-phase phenomena are
naturally-developing and triggered bubbly jet flows with
controllable inlet parameters, such as liquid-phase flow
rate, bubble size and void fraction. They represent an
excellent scientific basis, that should be better explored by
advanced measurement and analysis techniques as well as
simulating tools in the future.

Among the few experimental studies performed with
bubbly jet flows most of them were carried out in the far
downstream domain of steady-state flows. Even though
some of the studies were performed in the bubbly plume
zone where buoyancy dominates the flow, the authors refer
to them as bubbly jets (Sun and Faeth, 1986).

In contrast to those investigations, the first objective of
this work was to experimentally analyze the developing
region of bubbly jets (Milenkovi6 2005). The second
objective was to systematically estimate experimentally
the effect of the void-fraction on the main flow properties.


2. Experiment

The experiments described in the following have been
carried out in single-phase, liquid and bubbly jet flows
generated by a special injector (Milenkovic and Fehlmann,
2005). Ajet is injected into a water volume contained in a
large Plexiglas tank to minimize wall effects (Fig. 1).
Single-phase liquid jet flows, consisting of only liquid
flow, as well as bubbly jet flows, formed by injecting gas
bubbles into the vertical water jet, can be produced. The
injector contains 39 uniformly spaced tubes in which the
bubbles are produced. (Only one shown in Fig. 1). The
bubbly jets contain bubbles of variable well-controlled
size and volume fraction. Flows with constant inlet flow
rate of liquid and gas are here referred to as naturally-
developing jets. The basic adjustable parameters are
nozzle diameter, liquid and gas flow rate.

An illustration of shear layer and coherent vortex
structures in a naturally-developing single-phase jet in
comparison with vortex structures for the case of a









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


triggered bubbly jet is presented in Fig. 2. Jets that were
periodically excited with controlled frequency and
amplitude are here referred to as triggered jets. The
periodic modulation of the jet shear layer was done by a
coaxial water layer. More details about the experimental
setup, acquisition techniques, design of the experimental
installation and the results can be found in Milenkovic,
2005, Milenkovic et al. 2005, Milenkovic et al. 2007a and
Milenkovic et al. 2007b.


EF E,
ft E

t t


it t^ t


Fig. 1. Experiment. Schematic of bubbly jet production.
The injector shown at the bottom at a much
larger scale has 39 injection capillaries (only one is
shown).


Fig. 2. LIF photo of naturally-developing single-phase jet
(left) and periodically excited bubbly jet (right). Flow
conditions for the tests correspond to case TF2V1 (Table
3). Excitation frequency (triggered jet) is 3 Hz.


Experiments in single-phase jet flows (for instance
presented in Rodi, 1982) have been mostly conducted in
the fully-developed regions using mainly experimental
techniques such as LDA (Laser Doppler Anemometry),
HFA (Hot Film Anemometry) and HWA (Hot Wire
Anemometry). In the near field of axially-symmetric jets,
there is a lack of data. Here, the main reason for
performing experiments in single-phase jet flows was,
however, to obtain reference data that could be compared
with results for bubbly jets obtained with the same liquid
flow rates. In this way the effects of parameters such as
void fraction and Jet Reynolds number can be studied.

The experiments discussed here have been performed in
order to investigate the basic properties of free turbulent
bubbly shear flows using a vertical bubbly jet with
variable flow parameters such as the Jet Reynolds number
and the void fraction. As shown in Section 3, the Jet
Richardson number and the densitometric Froude number
depend on these flow quantities and therefore they
characterize the degree of jet-like or plume-like behavior.
In order to estimate the effect of the void-fraction on the
main flow properties such as mean liquid velocity,
standard deviation of the liquid velocity, variance of the
liquid velocity, kinetic energy and turbulent stress,
experiments have been carried out at constant Jet Reynolds
number (i.e. superficial liquid jet velocity), while the void
fraction was varied. Also, the turbulent properties at
constant void fraction but variable Jet Reynolds number
were compared. Furthermore, an attempt was made to
keep the bubble diameter constant, as well as possible,
while varying the void fraction. This task was very
difficult to achieve, because a variation of the gas flow rate
affects not only the void fraction but also the bubble size.
Thus, in order to keep the bubble diameter constant at high
gas flow rates, the liquid flow rate inside the tubes had to
be increased.

As shown in Table 1 the experiments were conducted with
two different void fractions of about 1.8 and 3.6%, and
essentially three different Jet Reynolds numbers of 17661,
30275 and 42890. The two selected void fractions belong
to the domains of weakly dilute and dense bubbly flows
(Lance and Bataille, 1991), respectively, which are of
special interest because feedback and bubble-bubble
interactions play a significant role.

For the chosen range of void fractions between 1 and 4%,
a preliminary examination showed no effect of bubble size
(in the range between 2 and 4 mm) on turbulent properties
of the liquid phase, and therefore no further effort was
made to use the available experimental techniques for this
purpose.

The test matrices presented in Table 1 and 2 cover flow
regimes that were investigated for naturally-developing


Paper No









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


single-phase jets (without and with internal liquid flow
inside the injection tubes) and those in Table 3 for bubbly
jets (FiVj, i=1,2,3 and j=1,2 for different liquid and gas
flow rates). Inlet parameters have been varied in order to
change the Jet Reynolds number and the void fraction. The
following identification letters and numbers in the test
matrix indicate different jet flow conditions:
* The letter F is associated with the total liquid flow rate in
the nozzle;
* The letter V means void fraction" and characterizes the
chosen void fraction of the bubbly
jet flow;
* The abbreviation SP means "Single-phase Jet";
* SPIWF means "Single-phase Jet with Internal Water
(Liquid) Flow in the Tubes";
* BJ means "Bubbly Jet".

Parameters that characterize flow conditions in the injector
are:
- Q., liquid flow rate inside the tubes;
- Qe, external liquid flow rate;
o, gas flow rate;
- Qe, total liquid flow rate at the exit of the jet;
- Eh, is the homogeneous void fraction;
- E2, is the approximate average void fraction at the
nozzle exit:
V let
E2 Eh* jet
V,, + V,
where VT is the terminal bubble velocity and V,,e
is the superficial liquid velocity at the jet exit;

Table. 1. Test matrix for experimental investigation of
single-phase ets without internal flow
Test Name TSPF1 TSPF2 TSPF3 TSPF4
Q,,[Ll mn] 0 0 0 0
Qe,[L/mln 70 120 170 220
Q,,,[L/mm 70 120 170 220

ReJet 17661 30275 42890 55055
Vje[m/s] 0.18 0.32 0.45 0.58


Table 3. Test matrix for experimental investigation of
bubbly jets
TestName TF1V1 TF1V2 TF2V1 TF2V2 TF3V1 TF3V2
Q,,,[L/mln] 20 20 20 20 20 20
QL[L/min] 50 50 100 100 150 150
[ Imin] 3 6 3.85 7.6 4.7 9.25
Q,,,[Ll/mn] 70 70 120 120 170 170
Rejet 17661 17661 30275 30275 42890 42890


Frjet
Eh[%
Eh %]


0.04 0.04 0.11 0.11 0.23 0.23

4.49 8.6 3.4 6.49 2.94 5.63


E2%] 1.86 3.56 1.86 3.56 1.86 3.56
Rio 0.7 0.96 0.41 0.56 0.29 0.4

Fro 1.97 1.03 6.24 3.24 12.33 6.41


Y .RI
D
S-1.12
D


0.78 1.07 0.46 0.63 0.32 0.45


Detailed information on experimental techniques
employed during this study can be found in Milenkovic,
2005, Milenkovic et al, 2007a and Milenkovic et al. 2008.




3. Relevant non-dimensional parameters and
characteristic regions

The bubbly jet formed in the bubble injector is directed
upward and injected into stagnant water. The flow can be
classified as a turbulent two-phase jet, which means that
both an initial momentum and a buoyancy flux are present
at the nozzle exit. These quantities can be systematically
varied in order to achieve more plume-like or jet-like flow
conditions. Obviously, the bubbly jet, by its nature, has
also an initial volume flux.


In any kind of bubbly jet flow, the momentum flux
Table. 2. Test matrix for experimental investigation of increases downstream because of buoyancy and the bubbly
single-phase jets with internal flow jet ultimately behaves like a bubbly plume. This means
that a transition region that separates the region of inertia-
Test Name TSPIWF1 TSPIWF2 TSPIWF3 dominated flow from the region where buoyancy
QL,[L/min] 20 20 20 dominates, i.e. the jet-like and plume-like regions in jet
flow, occurs within a certain vertical range downstream of
Qe[L/min] 50 100 150 the jet exit. The boundaries of the range can be defined by
Q,,,[Llmln] 70 120 170 means of a Richardson number, initially introduced by
Morton (Rodi, 1982). This dimensionless number has been
Resj, 17661 30275 42890 widely used in case of turbulent single-phase buoyant jets,
VLn[m/s] 0.94 0.94 0.94 and it can be applied to turbulent bubbly jets.


Paper No


V,,e[mls] 0.18


0.32 0.45









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


The Richardson number (Ri) and the densitometric Froude
number (Fr), that is also used to characterize buoyant jets,
are defined at the jet exit as follows (Rodi, 1982 ):

Qo .
Rio =

(1)


V

Fr = (1 -)
B -D
(2)
where Qo is the initial water-volume flux, Bo the
initial buoyancy flux, Mo the initial momentum flux,
D the size of the nozzle and E the void fraction.
The Richardson number and the densitometric Froude
number characterize the degree of jet-like or plume-like
behaviour of the initial flow, since they represent the
relative importance of inertial and buoyancy forces at the
inlet.
The initial buoyancy flux Bo is defined as:
/Ap
Bo=g Qo

(3)
According to Rodi, 1982 and Gebhart, 1988, the density
deficiency should be scaled with the density Pef of the
source fluid. For the bubbly jet considered here as a
mixture of air and water P,rePBJ-(1 E)-pE+(F)-G ,
where Psp is the mixture density. In other references
(Papanicolaou and List, 1988 and Sun and Faeth, 1986),
the scaling density is the density of the ambient fluid,
which is in our case the water density PL

Here, the second definition is preferred because the
quantities Q, M and B must also be formulated as integrals
over the radial r coordinate at any downstream position,
where the mixture density is a function of r. Because of
the small values of E, the difference between the two
approaches is not important; indeed:
Apo p p, p-[(1-E)-p,+Ep, ] E(p p,)
PL PL PL PL
(4)
as PG zp_ p p, p [(1 -)-p,+fp,] E(p- p,)
PsJ PBJ (1 E)'P +EP o (1 E)'p


2 V
M =(-)-D2.
4 (1-E)


Bo =(4).D2.E g.Vj,


The Richardson and the densitometric Froude number can
then be written as:

Rio=() -D-Vltg' E (l-E)j '
4 j


V
Fro=- je
E(1 -E).g D
Then


Rio=(-) *Fro '(1 -E
4


The Richardson number is
number Frjt=V je(g-D)
Frt
Fr0 (-)
o (1 E)


also related to the Jet Froude
because:


and thus:


Ri =( ) -Fr e '' )-E)
4 e


Since the two quantities are closely related and the
Richardson number can also be directly defined at any
downstream level, only the Richardson number will be
used in the following.
For the distinction between jet, transition and plume
region, the length scale ratio IM is used (Rodi, 1982):

B'o 4
1= 0 =(T) -Rio -D(1-F) (14)
Bo
Papanicolaou and List, 1988 present criteria for the limits
of the regions for buoyant single-phase jets; no such
criteria were found for turbulent bubbly jets but possibly
the same criteria apply:

0< --Ri< 1, jet (inertial) region (15)
D


1 < -Rio <5, transition region
D


for << 1.
The fluxes are given as

Qo=(4).D- V ,,


5<-D -Ri D
Thus, for Rio <0.2, the buoyancy forces begin to
(6) influence the jet only downstream of the developing region


Paper No









Paper No


ylD>5. However, with Rio>l, the transition
from jet to plume already starts at ylD<1. At such
values of Rio, buoyancy has a strong influence on the
development of the large vortices.
In order to provide an estimate of the local degree of
plume-like or jet-like behaviour for the flow, the local
Richardson number is used Papanicolaou and List, 1988:


Ri(y) Q(y)-B(y))
Ri(y)y)= (18)

where M(y), B(y) and Q(y) are experimental
results for momentum, buoyancy and volume flux of the
mean distance y from the jet origin.
In Papanicolaou and List, 1988, it is shown that in the
three regions defined in Equations (15) to (17), Ri(y)
and M (y) depend very differently on y, for instance,
Ri(y) varies linearly with y/1, up to
y/1= 1.5 and Ri(y) is constant for
yv/1>1.5.
Evaluated values of these parameters for tested flow
conditions can be found in Tables 1, 2 and 3.

4. Results and discussions

Since very complex phenomena take place during bubble
and jet formation in the injector (Milenkovic and
Fehlmann, 2005), it is necessary to discuss the effects of
the different flows which mix in the injector. First, the
flow conditions in the injector as well as in the zone close
to the jet exit must be analyzed before the additional
effects of bubbles on liquid turbulent properties can be
discussed.

The liquid volume flow at the nozzle exit QLo, i.e. the
superficial averaged liquid velocity at the nozzle exit
Ve,, was kept constant for different internal flow rates
QL,, (compare test conditions presented in Tables 3
with 1 and 2). Since the injection tubes are positioned
below the nozzle exit, both single phase and two-phase
flow properties are influenced by mixing phenomena
which already take place in the zone of flow establishment
and the boundary layer forming in the injector nozzle.
Thus, the small jets generated at the tube exits raise the
turbulence level in the jet.

In case of two-phase flow, additional turbulence is
produced by the bubbles. Since bubbles are formed by
injecting gas into the liquid flow inside the tubes it is
difficult to separate pseudo turbulence induced by the
bubbles from turbulence produced by the liquid jets from
the tubes, because these phenomena interact. Therefore, in
order to quantitatively estimate the effect of the void
fraction on turbulent properties, it is necessary to first


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



perform experiments with single-phase jets produced with
and without internal liquid flow inside the tubes. It is also
important to compare these data with results of turbulence
calculations in the near jet region. Additional information
regarding enhancement of turbulence due to the presence
of bubbles in case of inertia-dominated bubbly jet flow
can be obtained from CFD calculations. The experimental
results on single-phase and bubbly jets can be useful for
validating codes and especially the models for pseudo
turbulence in the inertial region of the bubbly jet.



4.1. Effects of void and Jet Reynolds number on
mean and turbulent properties of the liquid
The measurements were conducted by the PIV and DOS
technique in the bubbly jet region as well as in the
transition region. The velocity profiles presented in the
following sections are normalized by the superficial
vertical liquid velocity at the jet exit V,,, in order to
visualize the effect of the void fraction and of the Jet
Reynolds number on the properties of the liquid phase.

In Fig. 3, the normalized mean velocity profiles and
normalized standard deviation of the vertical liquid
velocity are compared at y/D = 1.12, in the jet region, for
three Jet Reynolds numbers. For each Jet Reynolds
number data are presented for a single-phase jet (with and
without) inertial liquid water flow in the tubes and for the
two void fractions given in Table 3. The increase of the
momentum flow and the turbulent fluctuations caused by
bubble-induced buoyancy enhances entrainment of the
surrounding fluid.
In Fig. 4 the same comparison is shown for the transition
region at y/D = 3.9.










7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


02
*// 1

o /
_____ 00-----------------
o 12 14 1 oo 02 o4 oB 08 10 12 14 16


0SlngephasejetwlthlWF(TSPMF3)
3V2) 03



''.:. .^.^^^
B-- o ------------


Fig. 3. Profiles of the normalized mean velocity of the
liquid and of the normalized standard deviation of the
vertical liquid velocity at y/D = 1.12.


00 02 04 '6 08 10 12 14

yZ=1 12 -S ngIe phae et (TSPF
S lngle phase jetwIth IWF (TSPM
-*Bubbljet(TF2?l)
--Bubblyjet(TF Y2)
4


SSnglephaseetwh WF(TSP/WF1
-*Bubblyjet(TFmV)





L..--_. . .


A
' / A


S -Bubbly"et (T 3V2)
I*-"X U \y1 I





Fig. 5. Profiles of the normalized mean velocity of the
liquid (left) and of the normalized standard deviation of
the vertical liquid velocity (right) at y/D = 3.9 for two
different void fractions. The data of Crow for single-phase
jets are also included.

In order to distinguish inertia- and buoyancy-dominated
regions of the jet, it is necessary to determine the local Jet
Richardson number defined in Chapter 3. Therefore, the
total momentum and buoyancy flow must be calculated
from the profiles presented in the previous section. The
total turbulent momentum flow can be obtained by
integration of the profiles of the mean vertical velocity of
the liquid and of the standard deviation of the vertical
liquid velocity. In general, the mean total momentum flow
of a jet can be decomposed into the momentum of the
mean and turbulent components
Mo,=M+m (19)
where, for axisymmetric flow:

M= V2(y,r)[l -E(y,r)]-2-rr.rdr
o (20)

and

m=f v2 y,r)[-E(y,r)]2-rr-rdr (21)

In (19) and (20), V represents the long-term time
average of the space-filtered vertical velocity of the liquid
obtained by PIV and v2 is the variance of the liquid
velocity. Index L for liquid phase is dropped.

In order to determine the effect of the bubbles on jet
characteristics, it is necessary to compare results for
single-phase jets with and without internal liquid flow
inside the tubes with results of bubbly jets formed by using
the same internal liquid flow inside the tubes.


Fig. 4. Profiles of the normalized kinetic energy of the
liquid and of the normalized stress term of the liquid at y/
D= 1.12.


Paper No


/ 1 Snglephasejetw (TSPF f)
YID- =1 12 Slnglephasejet(T SPAf )
20 A-h -^ --Bubblyjet(F V2)
18 i k ubbyj^tTI^2)



, ,, '


o. .. . .. .









Paper No


Single-phase jets

For single-phase jets, the following relations hold for the
tests with and without internal liquid flow at the nozzle
exit (y = 0):
R R
f VSP-2--rdr= f VSP.-2--rdr
0 0
R-2 R -2 (22)
f v y-2-2-r dr f v 2P -2- T-r dr
o o


Bubbly jets

For bubbly jets, when both gas and liquid are injected
through the capillaries and tubes, respectively, the total
momentum flow at elevation y is
--23
M (y) f[VF (y,r)+ 2,(y,r)]-[1 E(y,r)]-2-.r-rdr (23)
o
The buoyancy flow is
B(y)=f g-VL(y,r)-E(y,r)-'2-T-rdr (24)
0

The integration results for the mean momentum flow of
the jet M the turbulent component of the momentum
flow m of the jet, as well as the local Richardson number

Ri(y) and the nondimensional coordinate L.Ri ,
D
which characterize jet-like and plume-like behavior of the
bubbly jet, are presented in Tables (4), (5), (6) and (7).

Table 4. Results of the integration for test TSPF3
TSPF3 M-103[ 4/s21 m-105[m4/s2]
y/D=0.555 1.26 2.1
y/D= 1.12 1.26 2.6

Table 5. Results of the integration for test TSPIWF3
TSPIWF3 .-103 L 4 /2] m-10Lm'[4/s2
y/D=0.555 1.2 2.25
ylD= 1.12 1.3 3.46

Table 6. Results of the integration for test TF3V1
F3V1 yID-Ro M- 103[m4/s2] m10O[m41s Ri(y)
y/D
0.555 0.16 1.23 2.87 0.3
1.12 0.32 1.38 3.3 0.28
3.9 3.9 1.66 23.3 0.29


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



Table 7. Results of the integration for test TF3V2
F3V2 yID-Rio 7 -103[m4/s2] m10O[m4/s Ri(y)
y/D
0.555 0.22 1.64 3.6 0.34
1.12 0.45 1.8 5.3 0.27
3.9 1.56 2.4 22.9 0.33

These results show the following:
The values of m in Table 5 (case TSPIWF3) are higher
than those in Table 4 (case TSPF3) because of the small
jets formed downstream of tubes in the zone of flow
establishment (in the injector nozzle).
* In the transition region of the bubbly jet, m increases
with the void fraction. The enhancement of turbulent
momentum flow is caused by buoyancy.
* In case of turbulent bubbly jets, the nondimensional
elevation at y/D = 1.12 falls into the inertial region,
because --Rio< whereas y/D = 3.9 lies in the
Dv
transition region -Rio>I The results for Ri(y),
however, do not show the linear increase with y/ll
that was presented in Papanicolau and List, 1998 for
buoyant jets in the range yl1M< 1.5
The integral (23) can be compared with the momentum
flow prevailing at the tube exit and with that of the nozzle
exit. The total turbulent momentum flow in the jet nozzle
prevailing at the tube exit level ( M ) is given by:
SQ ,,v ,*Q'+Q e v l1+ v- (25)
QDGVa VQ
where the first part of the equation represents the
momentum flow at the exit of the tubes corrected with the
homogeneous void fraction in the tubes, and the second
part is the contribution by the outer flow. The turbulent

contribution VL is the same as that of the single-

phase case without internal liquid flow.

AM is the difference between Mo,0 and M It is
larger than the turbulent portion at the nozzle exit (m)
because only part of AM is transformed into turbulent
momentum flow, the rest going into pressure increase
(compare m given in Tables (4), (5), (6) and (7) with AM
given in Table (8)).
The calculated values of the momentum for cases
TSPIWF3, TF3V1 and TF3V2 are presented in Table (8).









Paper No


Table 8. Total momentum in the nozzle at the tube exit and
momentum of mean flow at the nozzle exit.
Test Ao,, -103 Af103 AM 104 E2
Name [m4/s2] [m4/s2] [m4/s2] [%]


SPIWF3 1.38 1.26 1.16 0
F3V1 1.45 1.29 1.6 1.86
F3V2 1.52 1.31 2.1 3.56

The analysis presented above is performed in order to
explain how single- and two-phase flow properties for
different flow conditions should be compared in order to
estimate the effects of the bubbles.
Since, in case of bubble production, the liquid slugs
ejected from the tubes have higher velocity than in single-
phase flows with equal internal liquid flow QL, the
momentum flows of bubble-laden fluids in the developing
region of the jet are different from those of the
corresponding single-phase case. On the other side, it is
possible to compare two-phase flow cases with different
void fraction in order to quantify concomitant effects of its
variation, and the single-phase case with internal flow is
just the limiting case with e = 0%. Thus, there is about the
same difference of additional momentum flow produced
by the internal liquid flow between the case e = 1.86% and
e = 3.6% as between single-phase and a = 1.86% (see data
in Table 8).

Based on the experimental results of mean and turbulent
properties of the liquid presented above, the following
conclusions can be drawn:
* Turbulent fluctuations of the single-phase jet with
internal liquid flow are stronger than those of the jet
without flow in the tubes due to the higher turbulence level
at the nozzle exit, which is produced by the liquid jets
from the tubes. This effect is especially pronounced in
case of small Jet Reynolds numbers. For higher Jet
Reynolds numbers, the enhancement of turbulence due to
the effects of the small jets is weaker. The cause of this is
the same internal flow QL,, for all three Jet Reynolds
numbers (see plots of the normalized standard deviation of
the vertical velocity of the liquid presented in Fig. 3).
* The kinetic energy of the liquid in case of the bubbly jets
increases with increasing void fraction in both the inertial
and transition regions (see Fig. 4).
* The joint effects of bubbles and inlet turbulence are more
pronounced in case of low Jet Reynolds number. This can
be concluded by comparing vertical-velocity profiles. In
the inertial region of the jet, the velocity profiles already
have a Gaussian shape. In case of higher Jet Reynolds
number, the profiles are still flat in the inertial region (see
Fig. 3).
* The effect of the bubbles on entrainment is less intense in
the case of higher Jet Reynolds number.
* In the inertial region of the bubbly jet, the shear layer is


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



shifted toward the jet centerline, which means contracting,
i.e. shrinking of the jet due to acceleration.
* The effect of the bubbles on the mixing processes is
much more pronounced in the transition region. The
shrinking of the jet is presented in the scalar map (see Fig.
6).


10 20 3D 4D 50 60 7D 8D 90 100 110 12D 13
X E_


0 20 40 50 60 70 90 100110 12'3C
X mm]


Fig. 6. Scalar maps of the standard deviation of the vertical
liquid velocity (m/s) for the single-phase (left) and the
bubbly jet (right): -Ri=1; -=0.5.
* The evaluated results for Ri(y) do not show the expected
linear dependency on y/ll in the inertial region. More
analysis is required for clarification (see data in Tables 6
and 7).
* In general, bubbles affect turbulent properties in the jet
center as well as in the shear layer and significantly
influence entrainment in the transition region of the bubbly
jet (see Figs. 3 and 4).
* The PIV measurements presented provide mainly results
for statistical properties of bubbly jets similar to results
produced by LDA or HWA. Nevertheless, they can be very
useful for validating CMFD codes, especially because they
cover the inertial and transition regions of bubbly jets,
which have not yet been explored in detail.


4.2. The turbulent shear stress in the developing
region of bubbly jets
In turbulent bubbly flows, where liquid and gas represent
the continuous and dispersed phase, respectively, the
modeling methods of single phase flows can be used as
building blocks, taking into account the effect of the void
fraction. Some of the basic concepts such as the mixing-
length model of Prandtl, the k L model and two-equation
models like k e have been tested. In experimental work
on bubbly jets and plumes, most data found in the
literature relate to the far field of the flow, where nearly
asymptotic conditions prevail. One objective of this work
is, however, to experimentally analyze the developing part
of bubbly jets. In this context, it is interesting to learn if
algebraic Reynolds stress expressions that are based on the
turbulence models mentioned above are applicable for the
investigated flow conditions. In the following sections
some of these models are applied to own experimental
results, first in relation to the single-phase jets and then
subsequently to the bubbly jets. In addition, the modelling









Paper No


of pseudoturbulence in the bubbly flows is also discussed.

Single-phase flows

In comparison to the Prandtl hypothesis, an improvement
was introduced by the k L model (see Rodi, 1984). The
eddy viscosity can be expressed by the velocity scale
((k) and a turbulent length scale L, where kL is
the kinetic energy of the turbulent motion and L is here
defined as the scale given by the gradient thickness of the
jet mixing layer:

L=6=
SV (26)
Ox m
The kinetic energy can approximately be calculated by

kL *(i 2+ + 2 -*(i 2+2v2) (27)
2 2


/


1 Mode l(U=U Ub)







Fig. 7. Comparison between the calculated Reynolds stress
term based on the k L model and the measured one by
PIV for single-phase jets at yl D= 1.12.


y/D-= 12 -
100 mm Co




LII I LSi I


Fig. 8. Comparison of experimentally determined
normalized values of measured and calculated stress term
(u-v)L from measured kinetic energy kL and
constant Cp = 0.09.


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



It should be emphasized that the definition of L chosen
here as the representative length scale differs from the
original one presented in Rodi, 1984. This is the reason
why the original constant named C, is replaced with
C,. The results are presented in Fig. 7 for four
different single-phase jet velocities at y/D = 1.12. The
value for the constant C, used to fit the experimental
data obtained by PIV was 0.06.

In the k e model, one of the most popular, the eddy
viscosity is represented by (Rodi, 1984).
k2
v,=C,-k (28)
ED
For shear layers in local equilibrium, where the production
of the kinetic energy is equal to the dissipation,
experiments have shown that

C = jk ) 0.09 (29)

i.e.

---0.3 (30)
kL
Experimentally determined values for the constant
C,, that relates the measured stress term (u-v)L
and the kinetic energy kL in the near field region of the
single-phase jet, are presented in Fig. 8 for four different
jet velocities. Using Equation (30) with C,=0.09,
very good agreement between calculated (presented as
C kL in Fig. 8) and measured stress is achieved for
all cases. The data are scaled with the centerline single-
phase superficial velocity at the nozzle exit VLSP,0. The
stress term obtained by the PIV technique and simplified
models for the turbulent stress that are usually used in
RANS modeling agree very well in the near jet region of
the single-phase jets. Therefore, despite the fact that these
data were obtained by PIV, they can be very useful for
code validation and for comparing with data obtained with
the LDA or HWA techniques.

Bubbly jet

In the inertia-dominated region of the bubbly jet (y/D =
1.12), the above-mentioned k L models were tested for
four flow regimes. Namely, experiments were done for
two different Jet Reynolds numbers, while the void
fraction was also varied in order to examine the bubble
effects on jet turbulence. Since the effect of buoyancy in
this region is relatively small compared to inertial forces, it
is realistic to assume that existing single-phase models
work well, as shown in Milleli, 2002. This is reasonable to
expect, since the liquid-phase turbulence is mainly driven
by shear in the near jet region although it also contains
decaying turbulence produced in the nozzle. In the case of
a bubbly jet with void fraction of about 2%, the situation
will not be dramatically changed. The diagrams presented
in Fig. 9 show a comparison between experimental data


a

npS~i~


STSPF3 k- /V


2


SPF4 k
: ,









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


and predictions of the turbulent shear stress calculated
with the k-L turbulence models. Very good agreement
was found between calculated Reynolds stress term and
measured PIV stress term in the inertial region of bubbly
jets. In the case of the bubbly jet, no data on the jet
development region have been found in the literature.


4
X/RV



0 -

[ / *


oTF3VZ Experiment
^ I. .. ,


Fig. 9. Comparison between measured PIV term and the
calculated Reynolds stress term based on the k-L model in
the inertial region of bubbly jets.

Further downstream, where the effect of the buoyancy
forces starts to dominate the flow, bubbles can
significantly influence the turbulence of the liquid phase
and also affect the spreading in the mixing layer. Results
presented in Fig. 10 show that turbulent shear stresses in
the transitional and, further downstream, in the plume
regions cannot be predicted by using single-phase
Reynolds stress models. These data can however be used
for testing new models. The fact that the calculated shear
stresses are partly higher than the experimental ones
x/R <0.5, E =3.56 indicates that bubble-induced
turbulence modifies the effect of shear flow on the
turbulent stress, and thus, the two sources of turbulence
interact.


The variance of the vertical velocity fluctuations p,
of the liquid that accounts for the pseudo turbulence in the
liquid produced by the bubbles can be expressed for low-
void fractions as (Lance and Bataille, 1991):
--- E.W2 (31)
where W is the relative velocity. In our case, the void
fraction is higher than 1.5%, and therefore the chosen
model may not be applicable. Anyway, the variance of the
residual vertical velocity fluctuation v ,, calculated
as the difference between the measured V and
v,pt obtained from Equation 31 is presented in
Figs.lla and Ilb for two Jet Reynolds numbers and the
highest void fraction cases.
Since shear-induced and bubble-induced turbulence
mingle in the transition and plume regions of bubbly jets,
it is not easily possible to separate their effects. On the
other hand, one can compare the variance of the residual
velocity fluctuations with that of essentially shear-induced
velocity fluctuations of the corresponding single-phase
flow case, which, however, have not been measured at y/D
= 3.9. Nevertheless, it is to be expected that the two
quantities are distinctly different, since the Reynolds stress
models discussed previously did not perform well in the
transition region of bubbly jets.
The presented experimental data can be very useful for:
* Testing the pseudo turbulence model proposed by Lance
(Equation (31)) in case of bubbly flows with higher void
fractions than those investigated by Roig, 1998, who found
good agreement between these two quantities in case of a
bubbly mixing layer with void fraction 1.9%.
* Testing different turbulence models, first in the transition
region of bubbly jets, where inertial forces are still
dominant, and subsequently in the purely buoyancy-
dominated region which can also be called bubbly plume.

Obviously, additional extensive experimental work is
required to develop new techniques that enable
simultaneous measurement of the relative velocity and of
the void fraction. This information can play an important
role in turbulence modeling of bubbly flows.


Fig. 10. Comparison between the measured PIV term and
the calculated Reynolds stress term based on the k-L
model in the transitional region of bubbly jets.


a) b)
Fig. 11. Kinetic energy of the liquid for case TF1V2 (a)
and for case TF3V2 (b).

5. Conclusions
Based on the experimental results presented, the following
conclusions can be drawn:
* Turbulent fluctuations of the single-phase jet with


Paper No


./^:


8-,









Paper No


internal liquid flow in the injector tubes are stronger than
those of the jet without internal flow, due to the higher
turbulence level at the nozzle exit, which is induced by the
liquid jets from the tubes. This effect is especially
pronounced in the case of small Jet Reynolds numbers. For
higher Jet Reynolds numbers, the enhancement of
turbulence is weak, since the liquid velocity inside the
tubes is the same for all three Rej, numbers.
* Due to bubble drift, turbulence intensities of the bubbly
jets are higher than those of the single-phase jets in both,
the inertial and the transition regions.
* The joint effects of bubbles and inlet turbulence are more
pronounced in case of low Reynolds number jets. This can
be concluded by comparing vertical velocity profiles. In
the inertial region of the jet, the velocity profiles already
have Gaussian shape. In case of higher Reynolds jet
number, profiles are still flat in the inertial region;
* In the inertial region of the bubbly jet, the shear layer is
shifted toward the jet centerline, which means contracting
or shrinking of the jet due to its acceleration.
* In the transition region of the bubbly jets, the vertical
velocity profiles have Gaussian shape, the entrainment is
enhanced due to the presence of bubbles, and shear layer
turbulence becomes less important.

Some of the basic concepts such as the k L model and
two-equation models like the k e have been tested in the
developing region of the jet. In experimental work on
bubbly jets and plumes, most data found in the literature
relate to the far field of the flow, where nearly asymptotic
conditions prevail. The models applied to own
experimental results showed that:
- For all single-phase cases, very good agreement was
found between algebraic Reynolds stress expressions that
are based on turbulence models and the stress term
measured by PIV in the near field close to the nozzle exit.
- In the region of the inertia-dominated part of the bubbly
jet (y/D = 1.12), the k L model gave good agreement
with the experimental results, because the effect of
buoyancy in near jet region and liquid-phase turbulence is
mainly driven by shear.

Further downstream, where the effect of the buoyancy
forces starts to dominate the flow, bubbles significantly
influence the turbulence of the liquid phase and also
appear to interact with the shear-induced turbulence in the
mixing layer. No attempt was made to decompose the total
kinetic energy into contributions due to shear-induced
turbulence and pseudo turbulence.



Acknowledgements
The experimental investigations presented here were done
at the Thermal Hydraulics Laboratory, Paul Scherrer
Institute (PSI). The author is grateful to Max Fehlmann for
his valuable assistance and numerous technical


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



contributions to the design and erection of the
experimental installation.
The support of the project by the Swiss National Science
Foundation under contract No. 200020-103630, 21-61698
is gratefully acknowledged.



References


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



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