Turbulent bubbly flow in tube under gravity and microgravity conditions

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To cite this version : Colin, Catherine and Kamp, Arjan and Fabre,

Jean. Turbulent bubbly flow in tube under gravity and microgravity

conditions. (2012) In: 6th Japanese-European Two-Phase Flow Group

Meeting, 23 September 2012 - 27 September 2012 (Kumamoto, Japan). (Unpublished)

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Université

de Toulouse

Turbulent bubbly flow in tube

under gravity and microgravity conditions

Catherine Colin, Jean Fabre &Arjan Kamp

Institute ofFluid Mechanics, University of Toulouse

Study supported by the French and European Space Agencies (CNES and ESA)

Motivations:

-+simple goemetry addressing the main issues on bubble dynamics in turbulent flow

Sorne previous experimental studies

In vertical upward flow

Numerous studies in pipes of 30mm to 60mm diameter tubes

Serizawa et al. (1975, 1992), Herringe & Davis, (1976); Van der Welle, (1985); Liu & Bankoff, (1993); Liu, ( 1998); Wang et al., ( 1987); Zun et al. ( 1991); Grossetête, ( 1995), Hosokawa et al. (2006)

•Strong evolution of the void fraction along the pipe, effect of hubble coalescence • Different shapes for the void fraction profiles (wall-peaking or void coring)

depending on the inlet conditions (flow rates, hubble size) and pipe geometry •Difficult to compare the experiments

In downward flow

•Sorne studies in 57mm and 38mm diameter tubes Wang ( 1985); Nakoryakov et al. ( 1994) ; Hibiki et al. (2004) • Void coring observed in general

•Weak effect of coalescence

Neutrally buoyant particles or hubble flow in microgravity condition

Lahey & Bonetto ( 1994)- Kamp ( 1996); Takamasa et al. (2003), Hazaku et al. (2012)

• Rather flat profile of void fraction profiles

Objectives

Our objective is:

r---___,j>

to highlight the role of the

gravity

(slip velocity) upon the

hubble radial distribution

in a tube, the

mean liquid

velocity and turbulence

r---___,j>

through experiments on bubbly flows with the same

experimental facility in constrated gravity conditions:

- in vertical

upward

, downward flows in laboratory

-in

microgravity

conditions (without hubble slip velocity)

r---___,j>

explain sorne results through simple analytical models

Present analysis focused on bubbles with size comparable to the turbulent

length scales

dB ~

l

t

and large range of

U

Ld

u

*

Outline

• Introduction

• Experimental set-up and measurement techniques

• Main results on:

-

vertical upward flow

-

downward flow

-

microgravity flow

• Wall friction and logarithmic law

• Turbulence in bubbly flows

• Void fraction distribution

• Conclusion and perspectives

c 0 0.4 0.3

u

e

u. 0.2 ""C ~ 0.1 0

Vertical upward flow: void fraction distribution

0 jl=1 m/s - D=38mm - jG=0.027m/s - jG=0.112m/s jG=0.23m/s 0.5 r/R

Liu et Bankhoff, IJHMT (1993)

1

. .. };

Serizawa & Kataoka, (1988)

Shape of the void fraction profile depends on the air and liquid flow rates

l

Vertical upward flow: mean velocity and turbulence

1.6 1.4

c=

~

~---..._~

----~ 1.----~

r

1

_

~

. . .

..;;

;::

~

~ 1 JL=1 m/s - D=38mm -0.8 ...J :::J 0.6 0.4 0.2 0 0 -jG=Om/s - jG=0.027m/s - jG=0.23m/s 0.5 r/R Liu et Bankhoff(1993) 1 0.2 0.15

-~ E - 0.1 ~ :::l 0.05 0 0 1 0.005 0.004

-

N 0.003 en

-

N 0.002 E

-

_>

_0.001 :::::J 0 0 0.5 1 r/R

Flattening of the mean velocity profiles, modification of the turbulence level, sometime increased but also decreased (Serizawa et al., 197 5)

0.2

d

0.1

o

.

0

Vertical

downward flow: void fraction profiles

\ '1 • l.Om/s 6. - Il= 0.018 D -Il 0.039 db • O. n1m 0 - Il= 0.084 da=0.8mm Do

oo

0 0 0

80

0 0 0 D OJ 0

_oD

0 5 10 15 20 25 y( mm)

jL=lm/s-

D=42mm

(j

Kashinshy & Randin, /JMF 1999

\ ₁ -= 1.0 m/!'1 dB=l.Smm d = I.Smm 0 0 0 0 0 0 00 0 0 0 D 0 0 OJ y( mm) 25

Vertical downward flow:

Mean velocity profiles

-

V₁ = 1 Omjs

-;::j _{;:::3 Vt = I.Om} "'"- d = O.Rn1m

-:J

~ d.,.::. J.Smm X - P= o b:. • ~ = O.OIR 0 - rl = 0 ow O. 0-~ · 00 4 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

y

j

R

yjR

Vertical downward flow:

Streamwise turbulent intensity

x- = 0 ~ . = . 2 0- p = 0.0 2 0 - 13= .11 1 =O. 7 rn/ 0~

1

= 1. 0 /. d = 1. mm

Enhancement or reduction of turbulence lev el compared

to single-phase flow, depending on air and water flow rates and

bubble size

ICl-3 <ia.>=O. mis

Microgravity Flows

0.15 C) lnL Co 0.10 Kl Coœ ts Il

Very few studies

8

Lahey et Bonetto (1994) () ln N eutrally buoyant partiel es

ln "";"' o.to Kl Coll!

"

c _Il .... ~ -:::~ "-J ~

Hazaku, Takamasa, Hibiki,

fr-::> IJMF 2012

~

~ _o.to

Bubbly flow in lg and

OG-::1

b

~ 1:::1 _{measurements on the gas}

0.05 Il

E

phase only

0

Both void peaking and void

C> cl1!

Kl l _{coring profiles}

0.10

~ in microgravity in 9mm tube

0.05 Il _{(large bubbles and entrance}

VI

O. effect memory)

0 0 O.

Ra i al P ition.r/ R [ -]

Outline

• Experimental set-up and measurement techniques

• Main results on:

-

vertical upward flow

-

downward flow

-

microgravity flow

• Wall friction and logarithmic law

• Turbulence in bubbly flows

• Void fraction distribution

• Conclusion and perspectives

local measurement

section

rotating separator

The two-phase flow

loop EDlA

Air and water in a tube of 40 mm:

pressure transducer control valve sanie nozzles and orifices air outlet

water reservoir air bottle 200 b

motor cryostat

Metrology:

Pressure transducers Validyne

centrifugai pump

Conductive 0-ring probes (global void fraction)

Local measurements in bubbly flows

in a 40 mm diameter pipe

Dual optical fibre probe

for:

-measurements of

local void fraction

,

hubble velocities

- determination of the

hubble diameters distribution

using a

backward transformation of the measured chard length distributions

(Kamp, 1996).

Hot film anemometry

for:

-measurement of the

axial mean and RMS velocity

of the liquid

Specifie data processing for phase discrimination

In microgravity conditions several parabolas required for each

measurement point ( statistical convergence).

20s 20s 20s

Parabolic fiights

11000 rn Caravelle, KC135,Airbus A300 «ZERO G »

1 ftight = 30 to 40 parabolas

Micro gravity period T = 20 s with Jz

<

0.03 g

Measurement period T- L/U ~ 10 to 15 s

L=pipe length, U flow velocity

Several parabolas required for statistical

8000 rn convergence of local measurements

...

2rnn.

Flow parameters

/

Ul

upward

Run

glgo

}L le <a>m

dP!dx

_u*

d

Re

(mis) (mis)

(Palm

1

(mis)

mm

Sl 0.27 0 0 -29 0.017 10800 Re=lOOOO S3 0.77 0 0 -160 0.040 30800 S4 1 0 0 -281 0.053 40000 Ul -1 0.27 0.023 0.033 268 0.039 3.3 11720 Vertical up-flow U3 -1 0.77 0.046 0.038 141 0.053 3.5 32640 U4 -1 1 0.023 0.018 -125 0.056 3.4 40920 Vertical dawn-flow D3 1 0.77 0.053 0.095 1148 0.064 4.2 32920 D4 1 1 0.024 0.031 585 0.059 3.1 40960 Ml 0 0.27 0.030 0.100 -35 0.019 1.8 12000 Microgravity flow M3 0 0.78 0.046 0.054 -222 0.047 2.0 33040 M4 0 1 0.028 0.032 -270 0.052 1.2 41120

Vertical upward flow:

Void fraction and hubble size

-D-z=D jL =lm/s j0=0.03m/s 0.08 ooooolr-z= 11 D 6 -o-z=70D 5 0.06 d 4 0.04 (mm) 3 a ₂ 0.02 1 0.00 0 0 0.5 1 0 0.5 1 2r/D 2r/D

•Bubbles injected through 32 capillary tubes of 0.3mm diameter at z=O • Maximum of void fraction near the wall

• Axial evolution of the void fraction profiles partly due to bubble coalescence

1.6 1.4

UL 1.2

UG 1

(ml s) _{0 .8}

Vertical upward flow:

mean and RMS velocities of liquid and gas

0.16 u' _L 0.12 u' ₀ 0.08 (mis) 0.04 U4 0.6 o o o o 0 o o o o o o o ₀₀

• • •

•

D D [\] D D~

•••

•••

•

••

o o0 0.4 , •• ~~---::----~ ... ...a.... 0 ~---~~---~ 0.2 Ul 0 ~---~~---~ 0

Liquid: closed symbols Gas: open symbols

0.5 2r/D 1 jL =0 .27rn/s - ja=O .02rn/s 0.12 0.1 0.08 u'L 0.06 u' _{G 0.04} (m/s) 0.02 0 0.5 2r/D • •o • • • oo 0 o

L-

-Ul ••••••• 0 ooooo o 0 oO 0 1

• Flattening of the mean velocity profiles •Bubble drift velocity 20 to 30 cm/s

0 ~---~~---~

•lncrease or decrease of turbulence in two-phase flow •RMS velocities of gas depend on the flow conditions

0 0.5

2r/D

a

Vertical downward flow:

Void fraction and bubble sizes

jL =lm/s- ja=0.02m/s D4 0.16 _{jL =0.77m/s- ja=0.05m/s D3 5} 0.12 d 4 0.08 (mm)

•

D ZID=4 Z/D=70 i A A AA A • • • AA A~

...

~'-D D o:PD 3

t

D .D .D

•o

~ .D D !i!!D ~

•••• a-

•

2 0.04 0.00 0 0.5 2r/D

• Void coring effect

1

•No bubbles in the near wall region •Weak effect ofbubble coalescence

0 0.5

2r/D

•Slow development of the flow in the axial direction

Vertical downward flow

•u

L

ou

G 1.4 UL _1.2

• •

UG (m/s)l.O D4 0.8 li _li li lilililili D3 0.6 0 0.5 1 2r/D

• Flattening of the mean velocity profiles

•Bubble drift velocity- 20 to- 30 cm/s decreases near the wall

0.16 u' _L jL =lm/s- ja=0.02m/s u' _G 0.12 D (m/s) 0.08 Do D D oo 0 o _D oC:::C 0.04 0 0 0.5 2r/D 0.12 u' _L 0.1

• • • •

u' _G

• •

0.08 (mis) li lili li li li lili 0.06 0.04

o.o2

·L =0.77m/s- ja=0.05m/s 1 li

•lncrease or decrease of turbulence in two-phase flow •RMS velocities of gas depend on the flow conditions

0 ~---~~---~

0 0.5

2r/D

Micro-gravity flows

0.04 0.03 a 0.02 0.01 0.00 0 0 ₀ 0 0 0 jL =lm/s- ja=0.02m/s 0.5 2r/D M4 1

• Small bubbles (surfactant) u'

L

• Flat profile of void fraction u' a

• Mean bubble drift velocity near 0 (mis)

• No significant increase of turbulence in bubbly flow

•

~/-M_~2to3

good agreement with the Tchen' s Theory

1.4 g • 1.2 UL

•

g UG (ml s) 1 0.8 0.6 0 0.5 1 2r/D 0.16 D D 0.12 D D D 0.08

•

0.04 0 ~---~---~ 0 0.5 2r/D 1

Influence of gravity on the structure of bubbly flow:

a

Migro gravity

,

1-g upward flow

,

downward flow

0.08 1.6 0.06 _1.4 0.04 UL

u

1.2 G (ml s) 1 0.02 0.8 0.6 ._____ _ _ _ ____.__ _ _ _ ______, 0 0.5 2r/D 1 ₀

Microgravity Bubbly flows similar to single-phase flow In normal gravity, upward flow or downward flow:

2 regions in the flow: wall region and a core region

0.5

2r/D

Void fraction, velocity distribution and turbulence strongy depend on gravity Turbulence can be reduced or enhanced /single-phase flow

Outline

• Experimental set-up and measurement techniques

• Main results on:

- vertical upward flow

- downward flow

- microgravity flow

• Wall friction and logarithmic law

• Turbulence in bubbly flows

• Void fraction distribution

• Conclusion and perspectives

Wall friction

Very few measurements reported in bubbly flows

- determined from pressure drop: requires very good accuracy on void fraction measurements (Liu, IJMF 1997):

~

4

4

2

dx = pLg(l- <a>)+ D 'tw = pLg(l- <a>)+ D pLu*

-direct method as electrochemical method (Nakoryakov et al., 1999)

-indirect methods: log law fitting (validity?) or extrapolation of the turbulent shear stress ( difficult not linear in hubble flow)

Sorne correlations or models

- 'tJ'two =f(Re, <a>) by Herringe et Davis (1978) and Beyerlein et al., (1985) - Including void fraction distribution by Sato et al. ( 1981) or Marié ( 1987)

Wall friction

Wall shear stress is obtained from measurements of pressure drop and mean void fraction Run g }L le <a> _u*o (mls₁ (mis) (mis) Ul -1 0.27 0.023 0.043 0.017 U3 -1 0.77 0.046 0.043 0.043 U4 -1 1 0.023 0.019 0.053 D3 1 0.77 0.053 0.075 0.044 D4 1 1 0.024 0.024 0.053 Ml 0 0.27 0.030 0.055 0.017 M3 0 0.78 0.046 0.041 0.043 M4 0 1 0.028 0.025 0.053 u* d (mis) mm 0.039 3.3 0.053 3.5 0.056 3.4 0.064 4.2 0.059 3.1 0.019 1.8 0.047 2.0 0.052 1.2 Re R' _l* 11720 2.77 32640 1.5 40920 0.59 32920 1.8 40960 0.68 12000 0 33040 0 41120 0 Ratio ofbuoyancy over wall friction

. lgl

<a> D

Rt* =..:...:. _ _ _

Wall friction in bubbly flow

Marié et al. (1997): analysis of the turbulent bubbly boundary layer, estimation of u*

approximated expression : u* ===

1

+

.!..(1-10.6

~

0

)Ri*d u*o

1

< UL > 1

(a -a

)gd "th R. w c Wl l*d = ₂ u*o 0.5 2.2 2.0

Simple expression

1.8 1.4 1.2

~"

•• 0 1 2 •

Closed symbols - Kamp (1996) Open symbols - Nakoryakov

et al. (1994)- d=0.8 to1.5mm

Liquid Mean velocity

24 22 20 UL 18 ~ 16 14 12 • R~=lO,OOO .6. ReL =30 ,000 • ReL =40,000 (11.

Single phase flow Microgravity flows

10 ~~~~~~~~~~~~

10 1000

= L mj

d = 1.

Kashinski & Randin, 1999 Downward flow and

Millimetric bubbles

~1

In agreement with A. Soldati

22 20 18 ;; 16 ~ ~ 14 12

Liquid Mean velocity

0.59 0.68 À ÀÀÀ À ÀÀÀÀ 1.50 À À À À ÀÀÀÀÀ 1.80 Core region _. ReL =30 ,000 • ReL =40 ,000 ~ 4 2 0 00 -2 U3 Ri* 1.0 3.0 10 Up-flows Down-flows Ul • 8 1 ••••• ••••• 2.77 • • 6 .______.____.____.__ ... _ ___._____.__ ... 10 1000 -4

•In gravity-depend flows: departure from the log-law in the inertial region (Ul,

U3, D3)-the constant B<5.5

• Presence of an homogeneous region farther from the wall (flat velocity profile)

ô/D==0.48/Ri*

Outline

• Experimental set-up and measurement techniques

• Main results on:

- vertical upward flow

- downward flow

- microgravity flow

• Wall friction and logarithmic law

• Turbulence in bubbly flows

• Void fraction distribution

• Conclusion and perspectives

Turbulent shear stress

Axial Momentum Bal. Eq. of the mixture

Turbulent shear stress is calculated from the measurements of a

-,

• [dP

]

r pLg

fr

'dr' aUL -pL UL VL = dz + p Lg 2(1 - a) - (1 - a )r 0 ar - !-! L

Tr

Production

rr*

=

-(1- a)u

'v auL __!!__ L L

ar

2u; 1.0 U L v'L 40 _{Wall region} 2 0.8 u* 0.6 0.4 0.2 0.0 0 jL =lrnls jG=O .025m/s l:i

ISJI:i&

c l:i l:i 0.2 0.4 0.6 r::Jl.l:i f ~

,;

~

0.8 1 Upflow, Downflow II* 30 20 Microgravity 10 Single-phase flow 0 0.2 0.4 0.6 0.8 2r/D 2r/D 1

Turbulent kinetic energy of the liquid

1 (

2 2 2)

kL = 2 UL + VL + WL

For very low void fractions

kL is splitted into 2 contributions = kLs +kLB

Shear-induced turbulence (steady axi-symetric flow):

(Lopez de Bertodano et al., 1994, Chahed et al., 2003)

( )- d U L ( b 1 d [ ( )

V~

dkLS

l

-pL 1 - a UL VL dr -pL 1 - a f LS + - dr pL 1 - a - I dr = Ü

(b) r a k

(a) (c)

Production Dissipation Diffusion

Bubble-induced turbulence:

Asymptotiques solutions :

If diffusion is negligible: Prod=Diss

(Lance & Bataille, 1991 Garnier et al., 2001)

Turbulent kinetic energy of the liquid

r

r

Dashed lines kLS = uL vL equilibrium between production and dissipation in the wall region

..Je:

good estimation of the turbulence lev el near the wall, when an inertia region does exist.

U3

D3

Bubble induced turbulence

Ul

r

In the core region, when

kLB>> kLS

(Lance & Bataille, 1991

Garnier et al., 2 001)

Homogeneous core region dominated by hubble induced turbulence,

if

Ri* d/D >

1

Conclusion: Mean velocity and turbulence

•Simple expression to predict the wall friction velocity in bubbly flow u*

•Relevant number to predict the buoyancy effect Ri* or Ri*d

•Logarithmic law still valid in bubbly flow for Ri*=O (Sand M) and Ri*<1.

When Ri*> 1 the inertia region becomes smaller and the additive constant B

decreases.

•The turbulent shear stress can be calculated from the streamwise momentum balance eq.

Two regions exist in the flow:

- a wall region where the log. Law is still valid. Even when Ri*> 1, kL can be estimated from a balance between its production and its dissipation. In this region a maximum value of the void fraction is obtained in upflow and this region is free ofbubble in downward flow

- A core region where the wall is homogeneous and where the bubble induced turbulence dominates when Ri*d> 1. The production of shear induced turb. is negligible .

Bubble slip velocity

ULc== U

G-

UL

_. ReL=lO,OOO • ReL =30 ,000

0.41

.

0.3 • ReL =40 ,000

.

..

.

 •    . . . !---··-~-~~-~.,. î~.·~

-,-.._ ""l

-

!Ë 0.2 ..__, Cj ~...:) 0.1 0.0 • • • Â 0 Up-flow 0.5 2r!D

••

_•

•

•

_• • 1

Bubble slip velocity in the inertia-capillaro regime

(Mende/son) [ ] 1/2 uoo = 2.14~ + 0.505gd pLd 0.4 r

t

Down-flow ~ 0.3

i . . .

~

.

.

. .

·.

..__, 0.2 • • • • • Cj • • • ~...:)

•

0.1

•

Micro gravity

Il. B ll.o <>ll.o 0

0 0.2 0.4 0.6 0.8 1

2r/D

In microgravity, hubble slip velocity of 2mm/s due to Coriolis acceleration

U -- _!_ g d2 • h 1 0 002

oo 18 v Wlt g go = .

Bubble slip velocity decreases near the wall: in agreement with numerical simulations of Adoua (2009)~increase in the drag coefficient for an ellipsoïdal hubble in a shear flow

Outline

• Experimental set-up and measurement techniques

• Main results on:

- vertical upward flow

- downward flow

- microgravity flow

• Wall friction and logarithmic law

• Turbulence in bubbly flows

• Void fraction distribution

jL =lrn/s 0.08 ja=0.025mls 0.06 a 0.04 0.02 0.00 0 0.5 2r/D

Vertical upflow

Vertical downflow

Microgravity

Void fraction distribution

Classical analysis based on Eulerian two-fluid models

Lance & Lapez de Bertodano, 1994; Chahed et al., 1999; Lucas et al. 2007, Hosokawa and Tomiyama., 2009 .. . )

1

0 _=PLa a(l-a)vi ₊ M Gr

ar

M₀ is the interracial momentum transfer : average of the forces acting on the bubbles

Hubble-turbulence interactions

Wall

2

aa

av'

2

au

~

effect

v'L-

=(l-a)

L- CL (Ua -UL)

L

+MGrt +Fwr

ar

ar \..

av

y

~

>0

>0

>0

Non-linear terms needed

<0

>0?

>0

>0

<0

f'Jo

especially in microgravity

Void fraction distribution

Classical analysis based on Eulerian two-fluid models

,2

aa

(l

)av'~

c (

)auL

v L -

=

-a

-

L u

G -

u L

+

M

Grt

+

Fwr

ar

ar

ar

~

a

o CM d Tr = - urPLkL - GTr = - -IULcl d - - - ra 11 ~ J d r dr G

Lance et Lapez de Bertodano (1994) Chahed et al. (2002)

[

a

~

'+2 1+2

ULG

]

da M G - L DTCp., -

d

u,.. r Ci. d [ '

-

~---- _J -a _{M- dr+ r G}

-Vertical upflow

>0

>0

<0

Vertical downflow

>0

<0

<0

Microgravity

>0

~o

_<0

Computation of the void fraction distribution in microgravity with a two-fluid

model (Chahed, Colin, Masbernat, JFE, 2002)

0.1 r----~---~~---., • data, Kamp et al {15)

.

.

..

.

• •

0---~---~---~---~ 0 0.2 0.4 y!R 0.6 0.8 1 0.1 r--~----~---,

o.oa • data, l<amp et al [t5]

• Cw= 1. CL= 0, C'T""' (t35 .a_ 0.06 'ii .... C12 "" o~ -~· c.;l= o.s-.~ C12= 1;-C1~"" 2 0.04 -·--~::: -

....

-

.... 0.02 0---~~---~~--~ 0 0.2 _{0.4 yiR} 0.6 0.8 1

Without the turbulent term in the added mass force

ja=O .025m/s

With the turbulent terms in the added mass force

Void fraction distribution

ODE for the void fraction distribution can be integrated in the transition region between the core and the wall region, neglecting the interaction of the bubbles with the wall

C₀ and Cg are 2 constantes depending on CL=0.288, CM 0.4, Ct=1.8 0.12 _<> <> <><>

<><>o

Conclusion

• Experiments on a turbulent bubbly pipe flow are performed in normal and microgravity conditions with the same set-up

• The wall shear stress in bubbly flow can be predicted versus Ri*d

• From local measurements, the effect of gravity on the flow structure has been highlighted with a dimensionless number Ri*

• When Ri* =0 (microgravity), the flow structure is similar to single-phase flow ( validity of the log law, linear shear stress)

• When Ri*> 1, buoyancy effects dominate (modification of the log law, reduction of the turbulent shear stress)

• The bubbly flow in upward and downward configuration displays two regions: a homogeneous core region and a wall region

• Void fraction distribution can be calculated from a radial momentum

balance, but the non linear term in the interfacial momentum transfer have to be taken into account to explain the void fraction distribution in

Thank you for your attention

Acknowledgements to:

Université de Toulouse

• CNES

• ESA

c

m

~

r

s

m m .1

cnes

G

e

sa

• CNRS

"C

CENTRE NATIONAL D'ÉTUDES SPATIALES

• European Community (Brite Euram project)

More details in Colin, Fabre, Kamp, Journal Fluid Mech. 2012

doi:10.1017/jfm.2012.401 and experimental data available on line