Study of hydrodynamic
cavitation by CFD modeling
Chemical and Materials Engineering
University of Alberta
Outline
 Background
 Milestone
 Cavitation modeling
 Cavitation experiments
 Future work
2
Background
 Objective: develop a system for enhancing fine particle flotation
using microbubbles generated by cavitation
 Mechanism proposed by Zhou et al. 1997
particle
particle
tiny bubble
Flotation-sized
bubbles
Two stage
attachment
tiny bubble
Enhanced coagulation
by Bubble bridging
 Hydrophobic particle surface in water is a good nucleation sites
for cavity generation
3
Milestone
 Develop a model for cavitation using CFD
 Apply the cavitation model in a high intensity agitation system
 Determine critical variables for hydrodynamic cavitation
 Determine bubble size distribution using population balance
equations
 Measure bubble size distribution
 Couple the cavitation and population balance equations with flow
equations
 Study floatation recovery
4
HIA Cell CFD modelling
Vessel diameter, Dt
7.65 cm
Vessel height, H
7.60 cm
Baffle width, J
1.34 cm
Baffle thickness
0.55 cm
No: of Baffles
2
Impeller diameter, D
5.76 cm
Bottom clearance, C
1.5 cm
D/Dt
0.7529
J/Dt
0.175
C/Dt
0.196
CFD Modelling of cavitation is performed for the laboratory HIA cell for
different impeller speeds and different dissolved gas content.
5
Contours of pressure and volume
fraction of vapor in the HIA cell
Pressure
Volume fraction of vapor
6
Geometries
 Orifice (R/r=2,3, R=2cm)
R
r
 Venturi (R/r=2, R=2cm)
R
r
 Contraction (R/r=2, R=2cm)
R
r
7
Pressure profile in venturi
Our model
Hu et al. 1998
 Minimum inlet velocity is 4 m/s for the studied venturi
8
Pressure and velocity profiles in venturi
Single phase model
Inlet velocity=4m/s
Pressure profile (Pa)
Velocity profile (m/s)
9
Pressure profiles in orifice
Single phase model
Inlet velocity=4m/s
10
2D and 3D comparison
Single phase model
Inlet velocity=4m/s
3D
2D
11
Cavitation models
 Schnerr-Sauer model
 Bubble number density
 Zwart-Gerber-Belamri
 Bubble diameter
 Evaporation coefficient
 Condensation coefficient
 Singhal et al. cavitation model
 Non-condensable gas fraction
12
Cavitation modelling
 Multiphase flow
 Continuity equation for mixture
 Momentum equation for mixture
 Cavitation model for vapor phase
 Bubble dynamics: growth of cavitation bubbles using Rayleigh-
Plesset equation
B  radius of bubble
PV =vapor pressure
P=pressure
L =liquid density
13
Cavitation model
 vapor transport equation
Evaporation
rate term
Condensation
rate term
When Pv ≥ P
When Pv ≤ P
V =Vapor volume fraction
k =Turbulence kinetic energy
 =Surface tension
Singhal et al. (2002): Ce=0.02, Cc=0.01
14
Multiphase modelling in orifice
 Continuity, turbulent flow model and Singhal et al. cavitation
model, inlet velocity: 4m/s
15
Multiphase modelling in orifice
 Singhal et al. and Zwart-Gelber-Belamri Cavitation models
(inlet velocity=4 m/s)
16
Multiphase modelling in orifice
 Continuity, turbulent flow model and Singhal et al. cavitation
model, inlet velocity: 4m/s and 4.5m/s
17
CFD analysis in orifice R/r=3
 Velocity contours in orifice (R/r=3)
Inlet velocity= 4 m/s
Max velocity= 51 m/s
 Pressure profile
Max pressure= 1.14 MPa
Min pressure= -98 kPa
 vapor fraction contours
Max vapor fraction= 0.92
Cavitation model:
Zwart-Gerber-Belamri
18
3D Multiphase modelling in orifice
19
20
Experimental Setup
21
Experimental Setup
 ID= 1 inch
 Variable speed slurry
pump
 Velocity range: 0-6 m/s
for 1 inch ID tube
22
Proposed setup
Type of contraction
Required Flow (GPM)
Required head pressure (ft)
Orifice
11.4 (1/2”)
3 (1/4”)
120 (1/2”)- 103 (1/4”)
Venturi
10 (1/2”)- 8 (1/4”)
 Pump:
 Centrifugal
 Max flow: 66 GPM
 Max head: 122 ft
 Price: $ 2000
 Flowmeter
 Coriolis Flow and Density Meter
23
Gas holdup measurements
 FBRM
 0.8 to 1000 micron
 Inline detection
 CCD
 Redlake Motionscope
 517 fps @ 1280 x 1024
 Min exposure time 1µs
R. J. N. Bernier, “Unsteady two-phase flow instrumentation and measurement,” Ph.D. dissertation, Cal.. Inst. Technol., Pasadena, 1982.
24
Gas holdup measurements
 Acoustic spectrometer
 Sonartrac
 2”-36”
 1-10 m/s
 1-20 %
 5 % accuracy
 $ 16500
R. J. N. Bernier, “Unsteady two-phase flow instrumentation and measurement,” Ph.D. dissertation, Cal.. Inst. Technol., Pasadena, 1982.
25
Gas holdup measurements
 Conductivity cell:
L
C=G
A
C: Specific conductivity of the solution
G: Measured conductivity of the solution
L: Distance between two plates
A: area of the plates
L/A: cell constant
Cell Constant (K)
Optimum Conductivity Range
(µS/cm)
0.1
0.5 to 400
1.0
10 to 2000
10.0
1000 to 200,000
http://www.coleparmer.ca/techinfo/techinfo.asp?htmlfile=Conductivity.htm&ID=78
26
Gas holdup measurements
 Electrods:
 Coaxial
 Parallel flat plate
 Wire grid
http://www.coleparmer.ca/techinfo/techinfo.asp?htmlfile=Conductivity.htm&ID=78
27
Future Work
 Implement physical experiments to evaluate parameters in
cavitation model and population balance model
 Use UDF in Fluent to model the generation of bubbles
 Implement the population balance in a bubble-particle
environment
 Determine bubble-particle and particle-particle collision rate
(frequency) and efficiency model parameters {experiments}
 Develop comprehensive model for flotation involving in-situ
bubble generation, bubble-particle interaction and the ultimate
flotation recovery.
 Study the effect design and operating parameters on fine
particle flotation
28
Acknowledgements
• Financial support for this work from:
NSERC-CAMIRO CRD Grant on Fine Particle
Flotation
NSERC-industrial Research Chair Program in Oil
Sands Engineering.
29
Thank you for your attention
30