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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 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