CVEN 679 Term Project Presentation
Multiphase Flow studies using PIV
Collaborators:
CHAMPA JOSHI
TIRTHARAJ BHAUMIK
RAMAKRISHNAN HARI PRASAD
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
LEADS TO:
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 :
Socolofsky & Adams (2001)

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
Schladow,
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
.
&
Adams,
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
Links
:
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
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