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Study of hydrodynamic cavitation by CFD modeling

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Study of hydrodynamic cavitation by CFD modeling

Chemical and Materials Engineering

University of Alberta

Outline

- Background
- Milestone
- Cavitation modeling
- Cavitation experiments
- Future work

Background

- Objective: develop a system for enhancing fine particle flotation using microbubbles generated by cavitation
- Mechanism proposed by Zhou et al. 1997
- Hydrophobic particle surface in water is a good nucleation sites for cavity generation

particle

particle

tiny bubble

tiny bubble

Flotation-sized bubbles

Enhanced coagulation by Bubble bridging

Two stage attachment

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

HIA Cell CFD modelling

CFD Modelling of cavitation is performed for the laboratory HIA cell for different impeller speeds and different dissolved gas content.

Volume fraction of vapor

Contours of pressure and volume fraction of vapor in the HIA cell

Pressure

Geometries

- Orifice (R/r=2,3, R=2cm)
- Venturi (R/r=2, R=2cm)
- Contraction (R/r=2, R=2cm)

R

r

R

r

R

r

Pressure profile in venturi

Our model

Hu et al. 1998

- Minimum inlet velocity is 4 m/s for the studied venturi

Pressure and velocity profiles in venturi

Single phase model

Inlet velocity=4m/s

Pressure profile (Pa)

Velocity profile (m/s)

Pressure profiles in orifice

Single phase model

Inlet velocity=4m/s

2D and 3D comparison

Single phase model

Inlet velocity=4m/s

2D

3D

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

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

Cavitation model

- vapor transport equation

Evaporation rate term

Condensation rate term

When Pv ≥ P

When Pv ≤ P

Singhal et al. (2002): Ce=0.02, Cc=0.01

Multiphase modelling in orifice

- Continuity, turbulent flow model and Singhal et al. cavitation model, inlet velocity: 4m/s

Multiphase modelling in orifice

- Singhalet al. and Zwart-Gelber-Belamri Cavitation models (inlet velocity=4 m/s)

Multiphase modelling in orifice

- Continuity, turbulent flow model and Singhal et al. cavitation model, inlet velocity: 4m/s and 4.5m/s

CFD analysis in orifice R/r=3

- Velocity contours in orifice (R/r=3)
- Pressure profile
- vapor fraction contours

Inlet velocity= 4 m/s

Max velocity= 51 m/s

Max pressure= 1.14 MPa

Min pressure= -98 kPa

Max vapor fraction= 0.92

Cavitation model:

Zwart-Gerber-Belamri

3D Multiphase modelling in orifice

Experimental Setup

Experimental Setup

- ID= 1 inch
- Variable speed slurry pump
- Velocity range: 0-6 m/s for 1 inch ID tube

Proposed setup

- Pump:
- Centrifugal
- Max flow: 66 GPM
- Max head: 122 ft
- Price: $ 2000

- Flowmeter
- Coriolis Flow and Density Meter

Gas holdup measurements

- FBRM
- 0.8 to 1000 micron
- Inline detection

- CCD
- RedlakeMotionscope
- 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.

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.

Gas holdup measurements

- Conductivity cell:

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

http://www.coleparmer.ca/techinfo/techinfo.asp?htmlfile=Conductivity.htm&ID=78

Gas holdup measurements

- Electrods:
- Coaxial
- Parallel flat plate
- Wire grid

http://www.coleparmer.ca/techinfo/techinfo.asp?htmlfile=Conductivity.htm&ID=78

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

Acknowledgements

- Financial support for this work from:
- NSERC-CAMIRO CRD Grant on Fine ParticleFlotation
- NSERC-industrial Research Chair Program in Oil Sands Engineering.

Thank you for your attention