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.

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