# Multiphase Flow studies using PIV

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24 Οκτ 2013 (πριν από 4 χρόνια και 7 μήνες)

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CVEN 679 Term Project Presentation

Multiphase Flow studies using PIV

Collaborators:

CHAMPA JOSHI

TIRTHARAJ BHAUMIK

PROJECT OBJECTIVE

The

PIV

(Particle

Image

Velocimetry)

measurement

method

is

used

to

obtain

relevant

parameters

in

the

study

of

multiphase

plumes

with

the

objective

of

validating

numerical

models

and

use

them

to

predict

field

phenomena
.

MULTIPHASE FLOW BASICS

Multiphase flows are fluid flows involving the
dynamics of more than one phase or constituent

One of the core areas of research in

Environmental Fluid Mechanics

Dispersed & Continuous Phases

Dispersed Phase : Bubbles, Droplets, Powder

Continuous Phase : Water, Air

Jets:

Driving force

Momentum flux of dispersed phase

Plumes:

Driving force

Buoyancy flux of dispersed phase

Applications

Bubble Breakwaters

Antifreeze measures in Harbors

Bubble curtains for Oil spill containment

CO
2

Sequestration in Ocean

Lake Aeration

Reservoir Destratification

SCHEMATIC OF A SIMPLE AIR
-
BUBBLE PLUME

Bubbles

Bubbles (Dispersed Phase)

Water (Continuous phase)

MULTIPHASE PLUMES IN STRATIFIED ENVIRONMENT

LIF Image of a Type 3 plume

N=((
-
g/
ρ
r
)*(d
ρ
a
/dz))
1/2

h
P

Dimensional Analysis:

h
T

= f (Q
init

, M
init

,
B
b_init
, B
w_init

,
u
s

,
N

, H
T

)

0

0

0

Total no. of variables = 4

Total no. of dimensions = 2 (L, T)

BUCKINGHAM
-
PI THEOREM

(4

2) = 2 non
-
dimensional groups

1

: Non
-
dimensional Trap Height

2

: Non
-
dimensional Bubble Slip Velocity

1

= h
T
/ (B/N
3
)
¼

2

= u
s

/ (BN)
¼

1

= g ( ∏
2

)

Single
-
phase plumes
: ∏
1

= 2.8

Two
-
phase plumes
:

Relationship between the non
-
dimensional parameters
validated from
experiments
:

1

= 2.8

0.27∏
2

1

= 5.2exp(
-
(
П
2

1.8)
2
/10.1)

Field Scale Complications:

Stratification profile may be non
-
linear

-

N varies with depth

There may be bubble expansion

-

u
s

varies with depth

There may be more than one dispersed phases
present

Poor correlation between lab and field scales!

REMEDY:

Numerical models with parameters validated from laboratory
experiments can include the field
-
scale complications

Governing Differential Equations:

Conservation of Mass flux

Conservation of Momentum flux

Conservation of Buoyancy flux of dispersed phase

Conservation of Buoyancy flux of continuous phase

Unknown parameters to be solved:

U
m

velocity

of continuous phase

2b

width

of plume

C
m

void fraction

of dispersed phase

g’

reduced gravity

of continuous phase

Gaussian and Top
-
Hat profiles:

Top
-
Hat Distribution

Gaussian Distribution

SELF

SIMILARITY ASSUMPTION

X: state variable of interest ( u, C, ∆
ρ
)

Derivation of the Governing Equations:

Entrainment Hypothesis

Dilute plume
assumption

Density locally invariant inside C.V

Balance of buoyant forces on two phases

Viscous Drag is negligible for water

Momentum of air bubbles is negligible

2b

Numerical models:

Mixed
-
fluid model :

McDougall (1978),

Asaeda & Imberger (1993)

-

Treats the dispersed and continuous phases as a single mixture

Two
-
fluid model :

-

Treats the dispersed and continuous phases as separate entities

Numerical Model Equations:

NUMERICAL SCHEME USED:
4
TH

ORDER RUNGE
-
KUTTA

Critical Model Issues:

Entrainment Coefficient

Initial conditions

U
m

, b and alpha are to be estimated using PIV measurements

Particle Image Velocimetry

Facilities & Equipments

Experimental Tank
(40 x 40 x 70 cm)

made of transparent acrylic glass (Plexiglas)

Diffuser source
(Airstone
-

1.4 cm dia)

produces bubbles of 3 mm dia above Q = 0.25 l/min

Electronic Mass Flowmeter
(Aalborg GFM 171)

and Needle valve

3.2 mm piping

Laser Light Source:
(Nd:YAG pulse laser)

-

Maximum power

(400 mJ/pulse)

-

Wavelength

(532 nm
-

green)

-

Pulse width

( 8 nanoseconds)

-

Time interval between pulses

( 4 ms )

-

Thickness of laser light sheet

(4 mm)

Optics

-

Cylindrical Lens

creates planar light sheet

Seeding Particles

Polyamide spheres (white, 50
μ
m diameter)

Camera (CCD)

Flowmaster 3S (3)

-

Frame rate

(8 fps)

-

Pixel

Resolution

(1280 x 1024)

-

Grayscale Resolution

(12
-
bit : 0 to 4095 grayscales)

-

Field of View

(18cm x 18 cm for each of the 3 cameras)

-

Controllable exposure time

(0.2 to 125 ms)

Computer

-

Data analysis software

DaVis (product of LaVision GmBH)

-

Synchronization unit

controls timing of laser pulse triggering and camera exposure

-

Frame Grabber

captures frames and transfers to computer RAM and then to Hard Disk

-

Utilities

Matlab

PIV E
XPERIMENTAL

S
ETUP

M
EDIAN
F
ILTERING FOR
PIV
DATA

U
MEDIAN

1.5U
RMS

< U < U
MEDIAN

+ 1.5U
RMS

Interrogation Window

16 X 16 pixels, 50% overlap

PTV A
NALYSIS BY
T
HRESHOLD

Grayscale intensity Threshold Range for a 12
-
bit CCD camera: 0

4095

Intensity Threshold for the brighter bubbles: 2500

F
LUID &
B
UBBLE
V
ELOCITY

P
ROFILES

Fluid velocity profile:

Resembles Gaussian

Bubble velocity profile:

Resembles Top
-
Hat

E
NTRAINMENT
C
OEFFICIENT FROM PIV

IMPORTANT FINDING:
Alpha is not constant and varies non
-
linearly with depth

COMPARISON W/TWO
-
FLUID MODEL

Model and experimental results agree appreciably well

COMPARISON W/MIXED
-
FLUID MODEL

Model overpredicts the velocity of continuous phase and the momentum flux

RESULTS:

PIV of unstratified bubble plume successful

Entrainment coefficient depends on bubble concentration

Two
-
fluid models appear to match plume physics better than mixed fluid models

ONGOING WORK:

Combining three different FOV to get better aligned data

Application of PIV to stratified bubble plume

Extending single plume numerical model to double plume

Obtaining appropriate initial conditions

FUTURE SCOPE OF WORK:

PIV
-
LIF Combined study for the bubble plume

Develop LES (Large Eddy Simulation) numerical models

REAL
-
LIFE SCENARIOS:

Ocean Sequestration
of Liquid CO
2

(constitutes
64% of global greenhouse gas
emissions)

Other Applications:

Aeration of Lake/Aquariums

Fate of oil/chemicals released in
deep sea due to accidental
leakages and blowouts

Bio
-
medical Engineering

-

blood flow modeling in a ventricular assist
device

Chemical industries

-

two
-
phase flow modeling due to
countercurrent chromatography

Metallurgy

-

gas stirring of molten metals in ladles, in
nuclear devices and chemical reactors

References:

Asaeda,

T
.

&

Imberger,

J
.

(
1993
),

‘Structure

of

bubble

plumes

in

linearly

stratified

environments’,

J
.
Fluid

Mech
.

249
,

35
-
57
.

Bergmann

C
.

(
2004
),

‘Physical

and

Numerical

studies

on

multiphase

plumes’,

MS

Thesis,

Dept
.

of

Civil

Engrg,,

Coastal

&

Ocean

Engrg
.

Program,

Texas

A&M

University,

College

Station,

TX
.

Bergmann

C
.
,

Seol

D
.
-
G
.
,

Bhaumik

T
.

&

Socolofsky

S
.

A
.

(
2004
),

‘Entrainment

and

mixing

properties

of

a

simple

bubble

plume’,

Abstract

#

272
,

4
th

International

Symposium

on

Environmental

Hydraulics,

IAHR,

Hong

Kong,

China
.

Lemckert,

C
.

J
.

&

Imberger,

J
.

(
1993
),

‘Energetic

bubble

plumes

in

arbitrary

stratification’,

J
.
Hydraulic

Engrg
..

119
(
6
),

680
-
703
.

McDougall,

T
.
J
.

(
1978
),

‘Bubble

plumes

in

stratified

environments’,

J
.
Fluid

Mech
.

85
(
4
),

655
-
672
.

Milgram,

J
.
H
.

(
1983
),

‘Mean

flow

in

round

bubble

plumes’,

J
.
Fluid

Mech
.

133
,

345
-
376
.

Morton,

B
.

R
.
,

Taylor,

S
.

G
.

I
.

&

Turner,

J
.

S
.

(
1956
),

‘Turbulent

gravitational

convection

from

maintained

and

instantaneous

sources’,

Proc
.

of

the

Royal

Soc
.

A
234
,

1
-
23

S
.

G
.
(
1993
),

‘Lake

destratification

by

bubble
-
plume

systems
:

Design

methodology’,

J
.

Hydr
.

Engrg
.

119
(
3
),

350
-
368
.

Socolofsky

S
.

A
.

(
2001
),

‘Laboratory

Experiments

of

Multi
-
phase

plumes

in

Stratification

and

Crossflow’,

Ph
.
D

Thesis,

Dept
.

of

Civ
.

Env
.

Engrg
.
,

MIT,

Cambridge,

MA
.

Socolofsky,

S
.

A
.
,

Crounse,

B
.

C
.

&

E
.

E

(
2002
),

‘Multi
-
phase

plumes

in

uniform,

stratified

and

flowing

environments,

in

H
.

Shen,

A
.

Cheng,

K
.
-
H
.

Wang

&

M
.

H
.

teng,

eds,

‘Environmental

Fluid

Mechanics

Theories

and

Applications’,

ASCE/Fluids

Committee,

Chapter

4
,

pp
.

84
-
125
.

Wuest,

A
.
,

Brooks,

N
.

H
.

&

Imboden,

D
.

M
.

(
1992
),

‘Bubble

plume

modeling

for

lake

restoration’,

Water

Resour
.

Res
.

28
(
12
),

3235
-
3250
.

Related

:

http
:
//vtchl
.
uiuc
.
edu/basic/r/bp/

http
:
//www
.
dantecdynamics
.
com/PIV/System/Index
.
html

http
:
//archive
.
greenpeace
.
org/politics/co
2
/co
2
dump
.
pdf

www
.
umanitoba
.
ca/institutes/fisheries/eutro
.
html

http
:
//bss
.
sfsu
.
edu/ehines/geog
646
/Marine
%
20
Pollution
.
pdf

http
:
//www
.
sealifesupply
.
com/aquaria
.
htm

Questions ?