Numerical Simulation of Gas-Liquid-Reactors with Bubbly Flows using a Hybrid Multiphase-CFD Approach TFM Hybrid Interface Resolving Two-Fluid Model (HIRES-TFM) by Coupling of the Volume-of-Fluid (VOF) method and the Two-Fluid model (TFM) VOF using. Dipl.-Ing. Holger Marschall Chair of Chemical Engineering Technische Universität München
Outline background & motivation problem statement state-of-the-art (VOF & TFM) hybrid approach (HIRES-TFM) governing equations basic equation (VOF & TFM) basic idea & switch criterion (HIRES-TFM) numerical results prototype examples (HIRES-TFM) outlook CFD in Chemical Reaction Engineering V June 15-20, 2008 2
Background Phenomenology of Multiphase-Flows Process Technology droplet flow churn flow stratified flow dense bubbly flow dilute bubbly flow liquid spray gas/ liquid flow fluidized bed gas liquid/ solid flow gas/ solid flow sedimentation smoke flow porous medium solid fixed solid in motion fixed bed dust flow dilute particle flow dense particle flow solid in motion solid fixed solid granular flow [Laurien, 2004] CFD in Chemical Reaction Engineering V June 15-20, 2008 3
Background & Motivation Problem Statement Governing Equations Numerical Results Outlook Motivation Phenomenology of Multiphase-Flows Bubble Column Reactors V& G [Fan, 1990], [Mudde, 2003] CFD in Chemical Reaction Engineering V June 15-20, 2008 4
Motivation Phenomenologyof Multiphase-Flows Bubble Column Reactors fluid dynamics of two-phase flow systems in process apparatus and chemical reactors with transient flow structures fluid dynamics, reaction and mass transfer at gas-liquid interfaces of two-phase flow systems with spatial and/or temporal scales over more than 6orders of magnitude [Fan, 1990], [Mudde, 2003] CFD in Chemical Reaction Engineering V June 15-20, 2008 5
Problem Statement State-of-the-Art Current Frontiers reactor inlet modelling, empiricism -porous plates, perforated plates, single orifice nozzles -multiple orifice nozzles, perforated rings, spider-type spargers reactor interior flow structure reactor performance slurryconcentration high low g/l interface wake interface particle flow vortex shedding requirements Higher Accuracy, Cutback of Conservatisms & Uncertainties Portability to New Geometries and Range of Parameters Enhanced Scale-Up Options [Deckwer, 1985], [Fan, 1990] CFD in Chemical Reaction Engineering V June 15-20, 2008 6
Problem Statement State-of-the-Art Hierarchyof Numerical Methods macroscopic & mesoscopic level Modelling Effort & Complexity field averaging models (EE) entity tracking models (EL) interface resolving methods (EE) microscopic level Lattice Boltzmann Monte Carlo Degree of Detail & Computational Costs [Paschedag, 2007] CFD in Chemical Reaction Engineering V June 15-20, 2008 7
Problem Statement Hybrid Approach challenge Multiscale CMFD Large-scale CMFD conceptual approach adaptive: as coarse as possible & as detailed as required HIRES-TFM = Hybrid Interface-Resolving Two-Fluid Model interface resolving algorithm VOF for free surface flow regions as long as local computational grid density allows interface capturing extended two-fluid model TFM for dispersed flow regions where dimensions of fluid parts are comparable to or smaller than grid spacing [Tomiyama, 1998] CFD in Chemical Reaction Engineering V June 15-20, 2008 8
Problem Statement Hybrid Approach challenge Multiscale CMFD VOF TFM II Large-scale CMFD VOF conceptual approach adaptive: as coarse as possible & as detailed as required TFM TFM I HIRES-TFM = Hybrid Interface-Resolving Two-Fluid Model interface resolving algorithm VOF for free surface flow regions as long as local computational grid density allows interface capturing extended two-fluid model TFM for dispersed flow regions where dimensions of fluid parts are comparable to or smaller than grid spacing CFD in Chemical Reaction Engineering V June 15-20, 2008 9
Problem Statement Hybrid Approach - interfacial friction - interfacial tension - turbulence - mass transfer - economic resolution of interfacial structures and dynamics: local adaptive mesh refinement (AMR) VOF interfoamext TFM II VOF TFM bubblefoamext - interfacial forces drag force non-drag forces (lift force, turbulent drag force) - polydispersity (class method) (method of moments) (Monte-Carlo method) interfacial area conc. - coalescence and breakup TFM I HIRES-TFM - turbulence incl. BIT - mass transfer CFD in Chemical Reaction Engineering V June 15-20, 2008 10
Governing Equation Coupling of the VOF method and the TFM basic equations - continuity equation U = 0 - momentum equation ρu + ( ρuu ) = t p + µ + + ρ + T ( U U ) g Fσ - topological equation (continuity) α + = t ( U α ) 0 - mixture density & mixture viscosity µ = αµ + (1 α ) µ a ρ = αρ + (1 α) ρ a b b VOF - phase fraction equation (continuity) α t ϕ ( Uϕαϕ) + = 0 - momentum equation TFM αϕuϕ eff + ( αϕuu ϕ ϕ ) + ( αϕrϕ ) = t p + α g + M α ϕ ρ ϕ ϕ α ϕ ρ ϕ ϕ +constitutive equations interfacial momentum transfer +model equation interfacial tension CFD in Chemical Reaction Engineering V June 15-20, 2008 11
Governing Equation Coupling of the VOF method and the TFM interface compression problem of VOF methods: accuracy and reliability of the numerical approach to ensure the interface remains sharp basic idea for a sharp interface: convective transport term, counter gradient (against num. diffusion), conservative & bounded ( U r c (1 c ) ) - scalar flux second-moment closure in complex combustion models for turbulent flames U r relative velocity between burnt and unburnt gases c progress variable CFD in Chemical Reaction Engineering V June 15-20, 2008 12
Governing Equation Coupling of the VOF method and the TFM interface compression problem of VOF methods: accuracy and reliability of the numerical approach to ensure the interface remains sharp basic idea for a sharp interface: convective transport term, counter gradient (against num. diffusion), conservative & bounded α t a where ( U r c (1 c ) ) ( Uaαa) ( Ucαa ( αa )) + + 1 = 0 U c = c α α U α α ( ) U = c min c α U,max U 1 c 4 a a α α a a - convection-based sharpening algorithm in the phase fraction equation for interface capturing U c artificial compression term acting normal to the interface α a volume fraction of phase a CFD in Chemical Reaction Engineering V June 15-20, 2008 13
Governing Equation Coupling of the VOF method and the TFM switch criterion α t Γ d a ( Uaαa) d ( Ucαa ( αa )) + + Γ 1 = 0 switch factor, that ( α, α,,,..., ) Γ = f a V We d a a i - carries the information about the interface shape - quantifies the local dispersion of the twophase flow structure - estimates the interface reconstruction correctness of the VOF method Γ = d nb nb Γ d A A i i CFD in Chemical Reaction Engineering V June 15-20, 2008 14
Numerical Results Prototype Examples HIRES-TFM small bubble region d sb= 0.3 mm 3% gas fraction 45 mm 50 mm large bubble region d= lb 5.0 mm 100% gas fraction 5 mm Interaction among a 5 mm bubble and many small bubbles of 0.25 mm in diameter in a 2D air-water system [Tomiyama, 2003] 20 mm CFD in Chemical Reaction Engineering V June 15-20, 2008 15
Numerical Results Prototype Examples HIRES-TFM CFD in Chemical Reaction Engineering V June 15-20, 2008 16
Numerical Results Prototype Examples HIRES-TFM small bubbles d sb= 0.3 mm 5% gas fraction 100 mm large bubbles d lb = 6-10 mm 100% gas fraction 30 mm t=0s t=0.1s t=0.2s CFD in Chemical Reaction Engineering V June 15-20, 2008 17
Outlook Plans HIRES-TFM simulation of a lab-scale bubble column with sparger vs. experimental validation 200 mm BODY H D d h = 2000 mm = 200 mm = 10 mm 200 mm CFD in Chemical Reaction Engineering V June 15-20, 2008 18
Outlook Future Challenges HIRES-TFM spray formation & jets phase inversion CFD in Chemical Reaction Engineering V June 15-20, 2008 19
Thanks for your attention Acknowledgements Prof. Dr.-Ing. Olaf Hinrichsen & Prof. Wolfgang Polifke (TU München) Dr. Henry G. Weller (OpenCFD Ltd.) Prof. Dr. Hrvoje Jasak (FSB Zagreb, Wikki Ltd.) Contact Dipl.-Ing. Holger Marschall Lehrstuhl I für Technische Chemie Technische Universität München Lichtenbergstr. 4 D-85747 Garching Tel.: +49 89 289-13512 Email: holger.marschall@ch.tum.de CFD in Chemical Reaction Engineering V June 15-20, 2008 20