RTN PRATSOLIS (HPRN-CT-1999-0050) 7. DECEMBER 2001 BERLIN, Germany First training seminar Programme : Paschedag (TU Berlin) : Simulation of precipitation reactors using commercial CFD software (paschedag1.pdf) M. Signorino (TU Berlin) : Programme of investigation on mixing turbulent processes in non reactive solid-liquid systems (signorino.ppt) J. Derksen (TU Delft) : Large eddy simulations on the sample flow case (pitched-blade turbine in baffled tank at Re=7,300) (derksen1.ppt) H. Saint-Raymond (IRSID) and A. Alexiadis (IRSID) : Inclusion removal from liquid steel (saint-raymond1.ppt) M. Vanni, D. Marchisio, G. Baldi, A. Barresi (POLITO) : Precipitation in turbulent fluids (vanni1.ppt)
Simulation of Precipitation Reactors using Commercial CFD Software Anja Paschedag Technical University Berlin, Department of Chemical Engineering Content ~ Introduction ~ Models ~ Numerics ~ Results ~ Conclusions Simulation of 1 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Introduction Goal ~ Development of a code for numerical support of design of precipitation reactors ~ Modelling of the interaction between mixing and crystallization in a two phase system Basis ~ CFD codes (commercial or academic) with large number of models included (e.g. for turbulence) and stable numerical solution algorithms ~ Experimentally determined precipitation kinetics ~ Codes for solving the population balance without transport phenomena ~ Experimental setup for verification of test computations Simulation of 2 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Introduction Requirements Extention of models in CFD codes by ~ Improved turbulence models for * turbulent mass transfer / turbulent mixing * influence of a second phase on turbulent mixing ~ Kinetic models for * nucleation * crystal growth * agglomeration * others ~ Numerical handling of increase in dimensionality Simulation of 3 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Mass Balance Equations Mass balance for solved species c A t B v c A B D c A B B fa B lmin3 0 l Gn f A B l3d l Population balance with spacial dependencies n B v n B agg with and t l G B agg D agg l l l 2 2 n l 0 Gn l 0 β β l 3 l 3 l λ λ 3 λ 3 n 1 λ 2 Dagglmin λ 3 3 dλ n consumption by agglomeration formation by agglomeration For each of that equations appropriate boundary conditions and initial conditions have to be defined. l 3 λ3 1 3 n λ dλ Simulation of 4 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Turbulence Models RANS (URANS) LES DNS ~ Averaging in time ~ Resolving structures ~ Direct resolution of all over fluctuations above grid size, avera ging small structures scales in space and time ~ No requirements concer ~ Sufficient resolution of ~ Kolmogorov scale has to ning grid and time step large structures in space be resolved by grid, from the model and time required appropriate time step ~ Only resolution of macro ~ Direct resolution of micro mixing (implementation of mixing micromixing models possible) numerical effort accuracy Simulation of 5 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
k ε Model 1) Representation of all values Φ by Φ = Φ + Φ 2) Inserting into balance and averaging of the equations > Balance in terms of averaged values, but with an additional term containing fluctuation values 3) Application of closure model for that term required models available at different state of complexity, high Re standard k ε model most common and best tested Momentum balance: ρu i u j µ t u i x j Mass balance for species: c ρc u D t D t x i i u j x i δ i j 2 3 ρk µ t µ t ρsc t C µ ρ k2 ε Simulation of 6 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Probability Density Function Approach (PDF) Idea: define statistical measure for micromixing degree in the frame of RANS model Realization: ~ For each cell probability of all possible mixing states computed ~ Computation of reaction rate based on probabilities ~ Additional transport equations for PDF ~ Presentation of PDF * full PDF * moments of preassumed function * finite mode p A B A B Simulation of 7 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Kinetics Mixing of inlet flows fast chemical reaction Supersaturation Nucleation Number of crystals Crystal Growth / Agglomeration Approaches from literature available, but questions left about: ~ Accuracy of experimental determination (influence of mixing on the measured values) ~ Influence of activity coefficients ~ Influence of surface effects ( asymmetric behaviour for surplus components) ~ Influence of anisotropic growth Crystal size distribution Simulation of 8 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Two phase Models Pseudo one phase Real multiphase ~ Particles handled like a solved ~ Particles desribed as an own phase chemical species ( concentration considered) ~ No relative velocity between ~ Seperate transport equations for particles and continuous phase both phases ~ Influence of particles on fluid flow ~ Interaction between phases included (esp. turbulence) has to be in balance equations and multiphase described by empirical relations turbulence model ~ Concentration of a species is a ~ In present models dispersed phases scalar and not a distribution constist of particles of unique size function > additional effort > additional effort to simulate size to simulate changes in size distribution ~ Numerical effort relatively high ~ Numerical effort very high Simulation of 9 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Numerics Discretization of balance equations in most commercial codes by finite volume method (FVM) Problem: discretization of population balance terms Method of moments Method of classes ~ Transport property: moments of a ~ Transport property: mass of particles distribution function in different size classes ~ Small number of equations ~ Large number of equations ~ Result: approximate continuous ~ Result: approximate discrete distribution function distribution function ~ Special derivation for the transport ~ Transport equations for classes result equations of moments from application of FVM on size coord. ~ Easy to derivate mean values of distr. ~ Some effort to derivate mean values ~ Some effort to reconstruct distribution ~ Easy to reconstruct distribution Simulation of 10 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Method of Classes Particle size distribution varies along an additional internal coordinate > Additional discretization along that direction using FVM > Number of PDE in usual coordinates coupled by source terms containing growth and agglomeration terms + boundary condition for l min containing nucleation Implementation into commercial CFD code ~ Coupling terms computed explicitely, even if equations solved implicitely > numerical stability reduced > inaccuracies in mass balance ~ Special description of agglomeration (discontinuous process) ~ Size distribution changes strongly in space and time, but adaptive discretization impossible Simulation of 11 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Configuration of the Tubular Reactor Chemical system Ba 2+ + SO 4 2 BaSO 4 Na + und Cl as counterions Geometry Inlet Concentrations R tot = 0.005 m c in,so4 = 100.0 mol/m 3 R nozzle = 0.0005 m c in,ba = 34.1 mol/m 3 L tot L nozzle = 2.1 m = 0.1 m Na 2 SO 4 BaCl 2 Simulation of 12 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Numerical Setup for the Tubular Reactor Model size classes: 45 transient ~ 1.5 residence times ~ t = 0.0005 s geometry mesh density section of the mesh 2d simulation: rotational symmetry, in angular reaction section of 4, 1 cell number of cells: 6580 (29 x 227) Simulation of 13 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Comparison of Results Relative integral curves of the size distribution at the outlet averaged over the cross section 1 mass fraction 0.8 0.6 0.4 0.2 simulation Torino experiments Torino simulation Berlin Simulation Torino CFD code FLUENT method of moments Experiments Torino turbidity measurements Simulation Berlin CFD code Star CD method of classes same kinetics as Torino 0 0 1e 06 2e 06 3e 06 particle diameter (in m) Simulation of 14 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Comparison of Results Differential size distribution at the outlet averaged over the cross section particle mass density (in kg/m3 m) 1e+07 8e+06 6e+06 4e+06 2e+06 0 simulation Torino simulation Berlin 0 1e 06 2e 06 3e 06 particle diameter (in m) Simulation of 15 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Conclusions ~ Results of our simulation in same order of magnitude like simulations and experiments from Torino ~ Slope to steep, average size lo large reasons? ~ Agglomeration has no significant influence on results in the tubular reactor Simulation of 16 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Prospect ~ Validation for different operating parameters (inlet concentrations with different concentration ratio, flow rate restricted by reasonable Re and residence time) ~ Application of improved kinetics if available ~ Implementation of PDF model ~ Implementation of model for influence of solid phase on turbulence when available ~ Simulation of stirred tank longer residence times relevant agglomeration more complicated turbulent structures data for validation have to be available ~ Use of a non commercial code Simulation of 17 Technical University Berlin Precipitation Reactors Department of Chemical Engineering
Ing. Manfredi Signorino, PhD student TU-Berlin Precipitation and Agglomeration in Turbulent Solid Liquid Systems Ing. Manfredi Signorino 1 Technische Universität Berlin Institut für Verfahrenstechnik
Status Aim: Investigation of mixing turbulent processes in non reactive solid-liquid systems. First step: Experimental investigation in a pipe reactor. Experimental Technique: Characterisation of mixing by temperature measurements (analogy between heat and mass-transfer). Ing. Manfredi Signorino 2 Technische Universität Berlin Institut für Verfahrenstechnik
Experimental Setup A L = 1500 mm; 1000 mm D = 7 mm d = 4.6mm d D L Fluid: Water + Suspended particles (glass particles, volume concentration up to 10%, diameter less then 0,1mm). Experimental technique: Temperature measurements Five measurements point per cross-section. Radial and Axial temperature profile reconstruction. Ing. Manfredi Signorino 3 Technische Universität Berlin Institut für Verfahrenstechnik
Particles considerations Biot Number (glass particles a = 0.1mm, l m = 0.8 W/mK) Bi = h f a 6λ m 0.83 ; Not negligible thermal-inertia Heat-balance: The particles are reactive from the heat-exchange point of view. Particles influence expected : Turbulent temperature fluctuation (Kolmogorov scale of the problem ~ 17.5 µm, for Re = 15000). Mixing length (variation in the radial and axial temperature profile). Ing. Manfredi Signorino 4 Technische Universität Berlin Institut für Verfahrenstechnik
Thermocouples test Thermocouples Test: Re=18.000, U=2,5 m/s 32,8 A 32,6 32,4 C 32,2 32 31,8 0 cm d 31,6 31,4 50 60 70 80 90 100 cm 50 cm D L Global Accuracy (Thermocouples+Data Acquisition System) ±0,1 C. 100 cm Maximum Sample Rate = 10 khz (per thermocouple). Ing. Manfredi Signorino 5 Technische Universität Berlin Institut für Verfahrenstechnik
Summary What we want to measure is Mean temperature distribution in each pipe section Mixing length?mixing temperature fluctuations Ing. Manfredi Signorino 6 Technische Universität Berlin Institut für Verfahrenstechnik
Prospect Better understanding of the particles influence on the flow field (turbulence, mixing, ). Formulation of a model for the influence of solid particles on turbulent flow and mixing. Implementation of the model in the CFD code. Simulation of different reactors, with different particle size. One particle size Particle size distribution Validation of the model by experiments. Application to large scale reactors. Ing. Manfredi Signorino 7 Technische Universität Berlin Institut für Verfahrenstechnik
Large-eddy simulations on the sample flow case pitched blade turbine in baffled tank at Re=7,300 Jos Derksen Kramers Laboratorium voor Fysische Technologie Department of Applied Physics Delft University of Technology The Netherlands email: jos@klft.tn.tudelft.nl Kramers Laboratorium voor Fysische Technologie
Introduction Outline why large-eddy simulations (LES) in stirred tanks? Subgrid-scale modeling Smagorinsky model structure function model wall damping The sample case pitched blade turbine case (experiments by Schäfer et al. 1998) Summary Kramers Laboratorium voor Fysische Technologie
Why LES in stirred tanks? Intrinsically unsteady flow v tip Velocity time series 0 1 2 3 4 5 t N Applications e.g. agglomeration micro-mixing Kramers Laboratorium voor Fysische Technologie
Example: agglomeration in crystallizers Particle-particle collisions Contact time (to grow a bond) Elco Hollander sheared turbulence γ& agglomeration rate (#/m 3 s) : J aggl = βm 2 β 2 simple shear (10-14 m 3 /s) β collision d 3 ε 1.29 ν 2.2 1.33γ& + ε / ν 2.2 1/2.2 β collision β β 0 0 10 (s -1 ) γ& averaged instantaneous Kramers Laboratorium voor Fysische Technologie
Agglomeration (2) Evolution of the particle number concentration during 10 impeller revolutions Kramers Laboratorium voor Fysische Technologie
Example: micro-mixing LES combined with (particle based) PDF methods Modeling scalar transport with competitive chemical reactions k 1 A + B P A + C k 2 Q forced turbulence η K 0.1 Eelco van Vliet k 1 >>k 2 consumed reactant A Da=8 t=0 t=0.5t turb t=2t turb (slow) product Q yield of the slow product 0.5 0 10-2 10 0 Damkohler: t turb/tchem 10 2 Kramers Laboratorium voor Fysische Technologie
temporal evolution of species concentrations Da=8 Kramers Laboratorium voor Fysische Technologie
Subgrid-scale modeling Single-phase, turbulent flow: η K /L Re -3/4 Computational grid: spatial low-pass filter filter width: λ filter =2 Subgrid-scale motion: diffusive ν e Smagorinsky model ν Sm e = 2 ( c ) 2SijSij s Structure function model* ν 3 / 2 1/ 2 ( x, ) = 0. 105C [ F ( x ) ] SF e K 2, S ij = 1 u 2 x i j + u x i j F 2 ( x, ) = u( x,t) u( x + r,t ) F 2 : structure function 2 r = *Métais&Lesieur, JFM 239, 1992 Kramers Laboratorium voor Fysische Technologie
Subgrid-scale modeling (2) Isotropic, equilibrium turbulence, in the inertial subrange c s =0.165 C K =1.4 Smagorinsky model versus structure function model SF e 2 ( c ) SijSij + ωi i ν 0. 77 2 ω s Sm ν e Stirred tanks: anisotropic, off-equilibrium turbulence is there an inertial subrange? how to chose? c s =0.1 C K =2.7 Kramers Laboratorium voor Fysische Technologie
Subgrid-scale modeling (3) Fully developed turbulence at Re=7,300? possibly partly turbulent, partly transitional flow Selective subgrid-scale modeling*: Sm sel Sm ν 1 e νe = νe βν exp βν with β = 2 2 9 ν e ν 1 Smag. selective 0 0 50 100 r 2 1/ 2 ( S ) ν 2 2 = / *Voke, Theoret. Comput. Fl. Dyn. 8 (1996) Kramers Laboratorium voor Fysische Technologie
Subgrid-scale modeling (4) No-slip walls Wall damping functions (Van Driest, 1956) + + ν = ν 1 y / A e,damped e e A + =26 2 y + anisotropy vanishing sgs stresses at the wall Kramers Laboratorium voor Fysische Technologie
The sample flow LDA data at Re=7,300* angle-averaged angle-resolved mean velocity values RMS values (Reynolds normal stresses) Pitched blade turbine revolving in a baffled tank Re 2 ND = ν with D the impeller diameter *Schäfer et al., AIChE J 44, 1998 Kramers Laboratorium voor Fysische Technologie
Experimental validation (1) (angle-averaged velocity field midway between baffles) experiment 120 3 240 3 360 3 Smagorinsky model 0.5v tip simulations interpolated to the experimental grid 0.5v tip structure function model Smagorinsky model with wall damping Kramers Laboratorium voor Fysische Technologie
Intermezzo: Re-number effects* LES on a 240 3 grid (Smagorinsky model with wall damping) Re=7,300 35,000 70,000 140,000 0.5v tip *see also the experiments by Bittorf&Kresta (European Mixing 10, 2000) Kramers Laboratorium voor Fysische Technologie
Experimental validation (2) (angle-resolved velocity field) experiment v tip LES, Smag. 240 3 mesh simulations interpolated to the experimental grid LES, SF 240 3 mesh 0 o 30 o 60 o Kramers Laboratorium voor Fysische Technologie
Experimental validation (3) (angle-resolved tke field) 20 o experiment 40 o 60 o k/v tip 2 0.048 0.036 0.024 LES, Smag. 240 3 mesh 0.012 0.0 LES, SF 240 3 mesh Kramers Laboratorium voor Fysische Technologie
Summary LES for stirred tanks: detailed flow information time dependence micro-scale physics and chemistry Subgrid-scale models equilibrium turbulence / inertial subrange wall effects what resolution to chose? experimental validation Smagorinsky versus Structure Function model no significant differences for the average flow with respect to tke: no clear conclusion Kramers Laboratorium voor Fysische Technologie
Inclusions Removal from Liquid Steel Cooperative work between : SPIN Laboratory : Pr. M. Cournil, F. Gruy, P. Cugniet IRSID : H. Saint-Raymond, P. Gardin, A. Alexiadis PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1
Steelmaking route Flat carbon steels for automotive and packaging application PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2
A major Challenge : Clean Steel Elaboration Deoxidizing process One of the last stage before Continuous Casting addition of deoxidizing agent (Mn, Si, Al, Ca, ) in liquid steel Formation of oxide particles in bath : Inclusion solid (Al 2 O 3 ) liquid (CaO-Al 2 O 3 ) Formation of clusters by aggregation Defects in steel products Process perturbations PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3
Alumina cluster in steel PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 4
Objectives Development of knowledge about elementary mechanisms on solid inclusion elimination : Cluster Flotation V flottation Bubble - cluster interaction bubble bulle cluster SLAG Slag entrapment Wall deposit WALL Inclusion aggregation PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 5
Successive steps Particle-particle interaction non wetting effect Formation and removal of inclusion clusters aggregation - fragmentation - flotation Experimental validation representative cold model : turbidimetric study of SiO 2 aggregation in water - ethanol mixture Simulation of industrial treatment Simulation of inclusions removal in steel Fluid flow calculations in industrial reactor PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 6
Particle-particle interaction in non wetting conditions Thermodynamic Analysis (Kozakevitch et al. 1968) Gaseous cavities could exist in particle porosity Propagation of the cavities during a collision Gas bridge formation Experimental observation (Yaminski et al. 1983) They observed a cavity between a glass sphere immerged in mercury and a glass wall α Solid particle Solid Particle glass Gas Liquid Gas θ Hg Liquid Gas bridge PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 7
Population balance Smoluchowski equation dn dt i = i 1 i K ji jnjni j Kiknink + Bikni k 1 1 2 + j = 1 k= 1 k= 1 k= 1 B ki-k n i F i K ij : aggregation kernel B ij : fragmentation kernel F i : aggregate removal term by flotation PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 8
Flotation Fractal description of clusters R cluster = a 0 N 1 d f U t = ( ρ ρ ) f ρ f cluster 4g 3 2R C d R Number of particles in cluster 1000 10000 100000 Fractal dimension d f 2.9 2 2.9 2 2.9 2 Terminal velocity U t (m/s) 2.8 10-5 8.6 10-6 1.3 10-4 2.6 10-5 5.7 10-4 7.8 10-5 R cluster (microns) 5.4 20.1 12.0 63.7 26.5 201 radius of elementary particle a 0 : 0.5 µm PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 9
Aggregation kernel: K ij collision frequency between two aggregates of size i and j (no interaction) 0 4 ( ) 3 local velocity gradient γ& Jij = γ& ai + a j nj 3 collision efficiency to build an cluster of size i+j Turbulent flow J t Hydrodynamic interaction no interaction G(r)=1 J 0 ij = a ij J ij = 4πr 2 n G( r ) b ( ε 1 ) 2 r ν 2 r + 2n 6πaµ dv dr V : interaction potential Van der Waals attractive force PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 0
Aggregation - Fragmentation Current aggregation-fragmentation models Van der Waals attractive force between particles hydrodynamic interactions (turbulent flow) cluster morphology : fractal description Adaptation to a non wetting system gas cavities : low breakage probability liquid - gas - particle interface : slipping condition (parameter b) PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 1
Liquid-gas-particle interface Wetting system: liquid-solid interface Non slipping condition Non wetting system: liquid-gas-solid interface Slipping condition with parameter b b z z liquid Gas layer? solid PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 2
Slipping parameter a b Fluid Particle v Hydrodynamic force acting on the fixed particle : h F h =f h v When h >> a : When h<<a : f h a + 2b f h 6πµ a a + 3b 2 6 πa µ ( 1) f with 4h with f ( 1) = (based on Vinogradova s work) Re p <<1 ( 1+ h / 6b) ln( 1+ 6b / h) 3b / h 1 PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 3
Calculated collision efficiency 1,8 Collision efficiency 1,6 1,4 1,2 1 0,8 0,6 0,4 X X X X X X X X X X X X X X X X X X X b/a = 10 6 b/a = 10 1 b/a = 1 b/a = 10-2 b/a = 10-4 0,2 0 0,00001 0,0001 0,001 0,01 0,1 1 10 Steelmaking application C A = A 36π µ a 3 γ& PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 4
Non wetting effect Similar collision trajectories in both cases Calculated collision efficiencies of the same order of magnitude Small effect of non wetting conditions on aggregation Non wetting conditions affect: cluster cohesion breakage probability (negligible in the case of steel) cluster morphology (reorganization?) PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 5
Experimental method the Turbidimetry In-situ measurement of light scattered by particles or clusters τ 1 ( λ) = Ln blank L Isuspension Turbidity depends on the particle size distribution f(d) τ = ( λ) ( λ, D, m) f ( D) dd C sca A good knowledge of the optical properties of fractal clusters is required I PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 6
Experimental apparatus Mono dispersed silica particles naturally hydrophilic hydrophobic by means of a surface treatment (silanation) 1 µm 1 µm 0.5µm 1.5µm PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 7
Experimental apparatus Wetting properties (contact angle) depend on waterethanol mixture composition Xe-Hg Lamp Optical fiber Tank ethanol content in water ethanol mixture (%) Contact angle 0% 125 3.45% 118.5 5% 116.4 10% 140.8 15% 89.9 20% 79.1 Turbidity sensor Light detector Data acquisition Spectrophotometer Monochromator (grating) PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 8
Experimental results At the beginning : similar evolution in both cases dominating phenomenon : primary particles aggregation Then different evolutions In non wetting conditions, clusters are bigger with different optical properties (gas bridge) Different final levels aggregation - breakage competition turbidity (cm -1 ) 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Wetting conditions Non wetting conditions 0 0 400 800 1200 1600 2000 time (s) Silica 0.5 µm PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 1 9
Experimental results 20 20 µm µm Different final levels aggregation - breakage competition High level (limit size) small aggregates Low level big aggregates formation turbidity (cm -1 ) 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Wetting conditions Non wetting conditions 0 0 400 800 1200 1600 2000 time (s) Silica 0.5 µm PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 0
Simulations Good agreement between measurements and simulations (turbidity at different wavelength) description of the time evolution of the particle size distribution The non wetting effect is correctly predict compare to experimental results 1,6 Turbidity (cm -1 ) 1,4 1,2 1 0,8 0,6 0,4 0,2 0 λ= 501 nm λ= 752 nm Silica 1,5 µm 0 5 10 15 20 25 30 35 Time (min) Wetting conditions Measurements Model Turbidity (cm -1 ) 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0,0 Wetting system Non wetting system Silica 1,5 µm 0 5 10 15 20 25 30 Time (min) Simulation in non wetting conditions PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 1
ε, m 2 /s 3 Simulation of industrial treatment ε 1 ε 2 ε 3 ε 5, V up ε 4 Population balance in each reactor zone Fluent package - Lagrangian Approach PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 2
Application Cluster number / m 3 10 14 10 13 10 12 10 11 10 10 Effect of model parameters t=100 s d f =2 loose aggregate d f =3 compact aggregate Total oxygen of metal (ppm) 400 300 200 Q g =40 Nm 3 /h Q g =114 Nm 3 /h 100 0 50 100 150 200 Effect of industrial process parameters t (s) 10 09 1 10 100 1000 Particle number in cluster PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 3
Particle interaction modelling Part I - Bubble size distribution in a gas plume Final objective : implementation in a CFD package of specific module for : coalescence (bubbles, droplets), aggregation (solid particles), fragmentation PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 4
Steps Identification of the best models (literature, other Pratsolis project) Selection among different models Implementation in CFD packages of specific modules for coalescence and break-up Validation PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 5
Why study bubble size distribution? Physical proprieties related with the interfacial surface Drag coefficient for the velocity pattern PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 6
Bubble interactions Coalescence Break-up PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 7
Coalescence mechanism Turbulent Collision Buoyancy collision Coalescence efficiency PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 8
Mechanism of collision PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 2 9
Rate of turbulent collision (s -1 m -3 ) θ ( ) ( ) 2 1 3 2 3 2 3 d + d d d 1 2, j =. 2796n in j bi bj ε bi + T i 0 bj Prince et al.,1990 PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3 0
Rate of buoyancy collision (s -1 m -3 ) θ B i j ( ) 2( ) d d u u = 0. 1963n n + +, i j bi bj ri Friedlander,1977 rj PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3 1
Coalescence efficiency λ = exp( t τ i j i, j i,, j ) Coulaloglou and Tavlarides; 1977 PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3 2
Break-up Turbulent break-up due to eddies collision Small eddies haven t enough energy Large eddies just transport the bubbles Efficient eddy size = 0,2D B D B Luo and Svensen, 1996 ΩB ( v : u) ( 1 α ) n b = 0.923 ε d 2 b ( 1+ ξ ) 1 3 2 1 fσ ξ 11 3 3 5 3 11 3 min ξ db ξ 12c exp 2 2.41ρlε dξ PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3 3
07/12/2001 3 4 PRATSOLIS Meeting HSR - AA / CP / IRSID Local bubbles population balance dt dt n n N k i k i Br i k Br i k k i N i C i k k i j C j i k k + + = + = = = = = τ τ θ θ θ θ τ 0 1 1 1,, 0 1 1 0, 1, 2 1 (0) ) (
Example 1 w g = 0,3 m s -1, ε = 0,2 m 2 s -3, τ = 1 s, N TOT = 2.000.000 bubbles d 0 = 2mm 1,00E+06 9,00E+05 ndt=1 [bulles m-3] 8,00E+05 7,00E+05 6,00E+05 5,00E+05 4,00E+05 3,00E+05 2,00E+05 1,00E+05 0,00E+00 0 0,001 0,002 0,003 0,004 0,005 0,006 PRATSOLIS Meeting db[m] 07/12/2001 HSR - AA / CP / IRSID 3 5
Example 2 w g = 0,3 m s -1, ε = 0,2 m 2 s -3, τ = 1 s, N TOT = 23.000.000 bubbles. d 0 = 2 mm 1,60E+06 1,40E+06 ndt [bolle m-3] 1,20E+06 1,00E+06 8,00E+05 6,00E+05 4,00E+05 2,00E+05 0,00E+00 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 d [m] PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3 6
Conclusion Aggregation of primary particles is not very much influenced by wetting conditions. For high contact angle, fragmentation phenomenon appears to be less significant and big clusters can be formed. The aggregation model developed for wetting conditions has been adapted for non wetting system. Results are in good agreement with multi-wavelengths turbidity measurements. In the future, we want to improve the model with new developments concerning: - bubble description in reactor and interaction with inclusions - wall caption and behavior of cluster near the slag steel interface PRATSOLIS Meeting 07/12/2001 HSR - AA / CP / IRSID 3 7
Precipitation in Turbulent Fluids D. Marchisio,, G. Baldi,, A. Barresi,, M.Vanni Politecnico di Torino Berlin, Pratsolis Meeting December 7th, 2001
Precipitation and reactive crystallization Precipitation is a multi-step process: Chemical reaction and nucleation Crystal growth Aggregation and breakage
Nucleation Nucleation is a very fast process Its rate is non-linear with respect to supersaturation Usually expressions are empirically based: J c, c ( ) A B 2.83 10 ( cc ) A B ks 10 = 3 2.53 10 ( cc ) A B ks 1.775 15
Crystal growth Usually two processes control the over-all phenomenon In the case of diffusion and surface reaction: G c c k c c k (, ) ( ) A B = r As Bs s G c, c = k c c ( ) ( ) A B d A As G c, c = k c c ( ) ( ) A B d B Bs 2 k d = ShDM d ρ p
Aggregation and Breakage Crystals can aggregate (with possible further cementation: agglomeration) or break up Aggregation is a second-order process with respect of particle concentration BL ( ) = L 2 β λ λ λ λ λ λ 3 3 1 1 3 3 3 3 L ( L ), n ( L ), n( ) d 0 3 3 2 ( L λ ) DL ( ) = nl ( ) β( L, λ) n( λ) dλ 0 2 3
Aggregation and breakage The Brownian mechanism has been considered for aggregation Aggregation kernel β L, λ ( ) = 2kT B ( L + λ ) 2 3µ Lλ In the considered case the effect of breakage is negligible λ L
Mixing effects: CFD approach The CRE approach defines: macro-mixing meso-mixing micro-mixing Using CFD macro- and meso- mixing are solved together but what about micro-mixing? Micromixing is a sub-grid scale phenomenon Only introducing a SGS model micromixing is taken into account
Governing equations The main challenge in turbulent reacting flow is to find a closure for the chemical source term appearing in the last equation ( ) φ + φ φ = φ + φ ρ ν = + = φ φ k k S u x x D x x u t u u x x p x u x x u u t u x u k j j j k j j k j k j i j j j i j j i j i i i ' ' ' 1 0 Reynolds-averaged transport equations:
j PDF methods: full PDF Transport equation of the composition-pdf: fφ fφ ' + u j + ui ψ fφ = t x x α 2 Dα φα ψ fφ Sα fφ ψα The problem is intractable with standard methods Monte-Carlo solvers i + ( ψ) ψ
Presumed PDF methods ε ξ ξ ξ Γ + ξ Γ = ξ + ξ ξ Γ = ξ + ξ 2 2 ' ' ' 2 2 2 i i t i t i i i i t i i i x x x x x u t x x x u t The functional form of the PDF can be assumed a priori in terms of the mixture fraction, that is a non-reacting scalar The problem of mixing and reaction can be shifted to the problem of mixing of a conserved scalar:
Presumed PDF methods For two non-premixed streams the mixture fraction is defined to be zero in one feed stream and equal to unity in the other Non-reacting system c c o A Ao = ξ Instantaneous reaction ξ s = c Ao c Bo + c Bo c c c c o A Ao o A Ao = = 0 ξ ξ 1 ξ s s if if ξ ξ < ξ > ξ s s
Finite-mode PDF The mixture fraction PDF can be expressed in terms of a finite set of delta functions: N e f ( ; xt,) p ( xt,) ξ ζ n δ ζ ξ n= 1 ( ) N e affects the ability to approximate the real PDF The advantage of this method is to give an accurate description with a small N e n
Comparison between the models f ξ (ζ) I s =0.95 0 ζ 1 f ξ (ζ) I s =0.2 f ξ (ζ) I s =0.01 0 ζ 1 0 ζ 1
Comparison between the models The finite mode PDF has been validated by comparison with Full PDF and beta PDF predictions The effect of the number of modes (N e ) has been investigated and N e =3 was found to give an accurate description of mixing the Full PDF (--------), Beta PDF ( _ ) and Finite Mode PDF ( )
Finite-mode pdf transport eqs. Transport equations are written for volume fractions/probabilities of modes 1 and 2 and for weighted concentrations ( ) ( ) ( ) ( ) 2 2 3 2 2 2 1 1 3 1 1 1 1 1 p p p x p x p u x t p p p p x p x p u x t p s i t i i i s i t i i i γ + γ Γ = + γ + γ Γ = + The model parameters (γ, γ s ) are determined by forcing the variance to follow an adequate transport equation 2 ' C k φ φ ε ε φ = s α
Population balance Population balance is a continuity statement based on the number density function n n + ui n + Gn = Γ t + Bn Dn t xi L xi xi Different approaches can be used: ( ) ( ) () () Classes methods: good accuracy, high computational costs (30-50 scalars) Standard Moment Method: poor accuracy (expecially for aggregation problems) but low computational costs (4-6 scalars) Quadrature method of moments
Population balance The SMM solves the population balance in terms of the moments of the CSD m j = Lower-order moments are of particular interest N = m, A = km, V = km, d = t 0 t a 2 t v 3 43 + 0 j n( L) L dl With the SMM only size-independent growth and simple aggregation problems can be solved m 4 m 3
Population balance In order to close the problem the QMOM can be used The method is based on an ad hoc quadrature formula in which abscissas and weights are obtained from the lower-order moments themselves + m nlldl ( ) j wl j = j k k 0 k = 1 3
Validation of the QMOM Comparison of QMOM predictions with rigorous population balance solution (CM) in the case of perikinetic aggregation
Population balance The QMOM has been formulated for size-dependent growth rate The method has been validated for modeling aggregation by comparison with a Classes Method In this work the SMM has been used to model barium sulfate precipitation
Experimental setup and validation Precipitation of BaSO 4 in: Semi-batch Taylor- Couette reactor Continuous tubular reactor
Experimental setup and validation CFD has been used to model the flow field (Fluent) The micromixing model and the population balance (SMM and/or QMOM) were included in the code itself by using user-defined scalars
Case Study 1: Couette reactor Validation of CFD predictions concerning the flow and turbulence field Validation of CFD predictions concerning dispersion of an inert tracer Validation of the model for parallel reactions and for barium sulfate precipitation
Flow field investigation Glass static cylinder Teflon rotating cylinder Glass window Difraction lences Mirror LASER Collimating lens TRANSMITOR x z y Optic fiber Transmitting lens Receiving lens w v Receiving fiber RECEPTOR
H/2
CFD validation: flow field 2D and 3D simulations by using different turbulence models and different near wall treatments with (FLUENT ) release 5.2 Comparison was made in terms of number of vortices and mean velocities and Reynolds stress tensor components u uu uu 2 x x z x uu u uu 2 x z z z uu uu u x 2 θ z θ θ θ θ u z x z y u θ
CFD validation: flow field Comparison showed that the RSM with standard wall functions gives the best agreement Experimental CFD predictions Mean axial velocity, m/s
CFD validation: tracer dispersion Tracer dispersion was investigated at different injection positions (FP) FP1 FP2 M10 M7 FP3 FP4 M5 M1
Mixing properties During injection, p 1 enters into the reactor Within 1 second, p 2 disappears
Effect of operating conditions Effect of rotation speed of the inner cylinder Increasing the rotation speed, the degree of segregation is reduced This results in a slightly higher number of particles with lower dimension
Effect of operating conditions Effect of initial nominal supersaturation (S o ) An increase in S o results in an increase of the mean crystal size, because in these operating conditions growth is favored in respect of nucleation
Case Study 2: Tubular reactor The reactor was modeled by using a commercial CFD code (FLUENT ) release 5.2 The standard k-ε model was used in a 2D axysimmetric geometry Computational domain: 130 55 (8416 live cells)
Reactor geometry and operating conditions Internal diameter (main flow) = 10 mm Length = 1500 mm Internal diameter = 1 mm Outer diameter = 1.5 mm Velocity = 1 m/s Re = 10000 The two reactants were fed alternatively in the main flow and in the small coaxial tube The inlet concentrations were varied in order to study the effect on the CSD
Effect of ion excess on crystal size Re = 10000; VR = 1; c A0 = 34.101 mol/m 3 Exp. data with BaCl 2 in nozzle Exp. data with Na 2 SO 4 in nozzle
Crystal morphology at high sulfate concentration At higher concentrations aggregation becomes important c BO = 34.101 mol/m 3 Aggregates morphology Model predictions w/o aggregation Model predictions with aggregation
Conclusions A model for investigating turbulent precipitation has been presented The model developed is CFD based Micro-mixing has been included with a presumed PDF model (finite-mode PDF) The population balance has been modelled by using the Standard Moment Method but a new approach (QMOM) has been presented The model has been validated through comparison with experimental data
Conclusions The finite-mode PDF model has been shown to describe with sufficient accuracy mixing and reaction in liquid turbulent media The role of the micro-mixing in CFD modeling has been investigated and cleared Kinetics expressions for barium sulfate nucleation and growth have been shown to be inadequate The SMM has been shown to be inadequate for high aggregation rate An alternative is constituted by the QMOM which has been partially validated