Modelling Requirements for CFD. Calculations of Spray Dyers

Transcription

1 Title Modelling Requirements for CFD M. Sommerfeld Calculations of Spray Dyers Mechanische Verfahrenstechnik Zentrum für Ingenieurwissenschaften D Halle (Saale), Germany www-mvt.iw.uni-halle.de Campinas, Brazil, March 3-7, 015

2 Content of the Lecture Transport processes and physical phenomena in spray dryers Modelling requirements for numerical calculations of spray dryers Summary of Euler/Lagrange approach New droplet drying model Validation: single droplets and spray dryer Droplet/particle collision phenomena in spray dryers Stochastic inter-particle collision model Collisions of high-viscous droplets (experimental and modelling) Structure resolving particle agglomeration model Exemplary spray dryer calculations with agglomeration Conclusions and outlook

3 Introduction 1 Spray dryers are being used in many industrial areas (e.g. food, pharma, detergents and building) to convert a solution or suspension into a powder of defined properties. Injection of hot air with swirl Suspension or solution Atomisation Droplet break-up Droplet collisions Droplet motion Droplet drying Recycling of fine powder Collisions and agglomeration Air and fine particles Cyclone and bag filter Particle collisions Agglomeration Powder with defined properties

4 Introduction Brochure GEA Niro Spray Dryers A spray dryer is used for converting a solution or suspension into solid powder for further processing, transportation or commercial use. Quite often the main target is producing a powder of desired properties which has certain properties (particle design). Up to now the design of spray dryers and the determination of the operational conditions are based on a try-and-error approach in pilot-scale experiments. This procedure is however not very satisfactory since it is time consuming and rather costly. Since about 0 years, however, numerical approaches based on CFD (computational fluid dynamics) are increasingly applied for dryer design and optimization. Due to the importance of particle size distribution the Euler/Lagrange approach is beneficial for such simulations. A thorough computational tool is however not existing due to the numerous elementary processes influencing powder production in a spray dryer. Fletcher et al. Applied Mathematical Modelling 30 (006)

5 Introduction 3 Fluid Flow Simulation Two-Way Coupling Particle Phase Simulation Advantages of the Euler- Lagrange approach for spray dryer applications. Descriptive modelling of elementary processes Consideration of droplet/particle size distribution Grid generation URANS (unsteady Reynoldsaveraged conservation equations) Effect of particles on flow and turbulence LES (large-eddy simulations) Modification of sub-gridscale turbulence Gas phase properties (Vel, P, T, Species, ρ, µ) Atomisation model (droplet injection) Simple blob model Spatially resolved droplet size and velocity measurements Secondary break-up of droplets Wave, Rayleigh-Taylor, TAB, ETAB/CAB (Tanner 004) Comparison by Kumzerova et al (007) Droplet tracking Relevant fluid forces (i.e. drag, lift, particle shape) Turbulence effect (isotropic, anisotropic turbulence) Droplet drying Change of solids content and droplet properties (µ and σ) Turbulence effects (instantaneous temperature field seen by the droplets) Droplet collisions Bouncing Coalescence Separation (formation of satellite droplets) Collisions of partially dried particles Partial or full penetration Modelling of agglomerate structure Droplet/particle wall collisions Deposition or rebound collision (wall contamination)

6 Euler/Lagrange Approach 1 The fluid flow is calculated by solving the Reynolds-averaged conservation equations by accounting for two-way coupling (source terms). Turbulence model: k-ε turbulence model Conservation equations for: φ 1, u, v, w, k, ε, Y, T x y z x φ x y φ y z φ z ( ρuφ) + ( ρvφ) + ( ρwφ) Γ Γ Γ Sφ + Sφ, p,m + Sφ,p, ev The Lagrangian approach relies on the tracking of a large number of representative point-particles (parcels) through the flow field accounting for all relevant forces like: + models for small- scale phenomena Two-way coupling procedure with under-relaxation In-house code FASTEST/Lag-3D drag force gravity/buoyancy slip/shear lift slip/rotation lift torque on the particle Particle properties and Source Terms result from ensemble averaging

7 Dispersed phase (particles): d x p u p dt m P d u d t P,i 3 4 ρ + ρ ρ D F P π 4 Euler/Lagrange Approach P D drag force slip-shear lift slip-rotation lift m p P C C LR D ρf π ( u u ) u u + D C D (( u u ) ω ) i P,i Depending on the nature of the dispersed phase and the density ratio different relevant forces have to be used. P Ω ( u F u P ) ρ u F u P + mp gi 1 + Fi Ω ρp gravity/ buoyancy other forces, e.g. electrostatic 4 p LS P F p F The instantaneous fluid velocity is generated by a single-step Langevin model. u f i,n+ 1 R P,i f ( t, r) ui,n + σi 1 R P,i( t, r) ξi I p d ω dt p ρ F D p Rotation: 5 C R Ω Ω

8 Lecture Content New droplet drying model with validation for a spray dryer

9 Droplet Drying Model 1 Drying stages of a spherical solution or suspension droplet falling rate period t 0 s t 400 s t 1800 s B-C constant rate period Wet-bulb temperature droplet suspended particles Crust and enclosures Two possible paths of droplet drying

10 Droplet Drying Model A Mechanistic model is used to describe the four stages of droplet drying (Darvan & Sommerfeld, IDS 014) Stage A-B, initial heat-up period (sensible heating) T S equilibrium temperature (wet bulb temperature) Temperature distribution inside the droplet: T d t α r r r d T r T 0 r T k r h at : r 0 ( T T ) at : r R s α: droplet thermal diffusivity k: thermal conductivity h: air heat transfer coefficient

11 Droplet Drying Model 3 Stage B-C, quasi-equilibrium evaporation (like liquid droplets), change of droplet temperature (constant rate period): T S is slightly higher than the bulb temperature Constant further increase due to rising solids concentration Change of droplet temperature: ( T T ) π R Nu λ s m Cv d T d r air + L d m d t Nu Re 0.5 Pr 0.33 Rate of evaporation by diffusion of vapour through the boundary layer around the droplet (gas phase resistance) depending on vapour concentration γ [kg/m 3 ]: d m d t π R Sh s D air ( γ ) γ Sh Re 0.5 Sc 0.33

12 Droplet Drying Model 4 Stage C-D, crust formation and boiling (falling rate period): Surface concentration C S reaches the saturation C sat Crust formation due to crystallisation droplet shrinkage is stopped Two regions: dry outer crust and inner wet core (fully saturated) Discretisation of core and crust region Interface tracking Calculation of temperature distribution (crust and core region) T d t r R d R d t T r α + r r r d int int T r T r 0 at : r 0 α: droplet thermal diffusivity k: thermal conductivity h: air heat transfer coefficient T k r T T wb h ( T T ) s at : r R int at : r R

13 Droplet Drying Model 5 The heat balance at the interface (R int ) is used to track the interface in time (depending on thermal conductivity of crust and core): d R T int ( ω ) 0 ωb L ρav k crust r R,int k core r R, int d t r r Vapour diffusion through boundary layer around liquid core and through the crust: dm dt + π ( γ γ ) s R cri 1 Sh D air D δ R Solids concentration distribution within the droplet (diffusion): crust cri ( R δ) cri T C r Internal diffusion of solids for skimmed milk 1 C r D AB r r r ( ωa ) H 1 1 DAB ( ω ) R T 303 ω A : moisture content droplet H: activation energy diffusion A

14 Droplet Drying Model 6 Stage D-E, porous particle drying: Bounded liquid is evaporated with decreasing rate Temperature asymptotically approaches surrounding gas temperature Temperature distribution inside the dried particle estimated by taking into account only the crust thermo-physical properties: t α d r r d r T d T d r d T d r k 0 d T d r h at : r 0 ( T T ) at : r R s

15 Droplet Drying Model 7 Comparison of the new drying model with experiments and classical models Temperature [K] Experiment 300 new model Farid model 90 Nesic model Sano model Time [s] Mass [kg] 4x10-6 3x10-6 x10-6 Experiments for skim milk (solids 0% mass) by Chen et al. (1999): V air 1.0 m/s T air 343 K T drop,0 8 K D mm Experiment new model Farid model Nesic model Sano model 1x Time [s]

16 Mass [kg] Droplet Drying Model 8 Comparison of the new drying model with experiments: 5x10-6 4x10-6 3x10-6 x10-6 1x Time [s] Sodium sulphate in water, x % mass (Nesic & Vodnik 1991) V air 1.0 m/s 1x10-6 T air 383 K T drop,0 97 K 0 D mm Time [s] Mass [kg] 3x Temperature [K] Colloidal silica, 30 % mass (Nesic & Vodnik 1991) V air 1.4 m/s T air 451 K T drop,0 93 K D 0 mm Temperature [K]

17 Droplet Drying Model 9 Radial distribution of mass and temperature within the droplet Mass [kg solid /kg total ] Temperature [K] t 0 s t 40 s t 60 s R / R 0 [ - ] Temperature [K] Experiments for skim milk (solids 30% mass) by Sano & Keey (1985) V air 1.0 m/s T air 43 K T drop,0 301 K D mm t 0 s t 40 s t 60 s R / R 0 [ - ] Time [s] 14:50

18 Spray Dryer 1 Dryer geometry: H 980 mm H cyl 10 mm D 900 mm D out 95 mm Annular Air Inlet D o 100 mm R i 3.05 mm 718,706 control volumes Number [ - ] Air flow, no swirl: ṁ air 6.8 kg/h T air 444 K U ax 8.87 m/s U tan 0.0 m/s Droplet Diameter [µm] Two-Fluid Nozzle: Spray angle β 9 o D nozzle,air,o 3.05 mm D nozzle,air,i 1.73 mm H nozzle 00 mm Whey Based Solution: 30 mass-% solids ρ drop 100 kg/m 3 ṁ solution 7.31 kg/h T solution 93 K U air, av 9. m/s

19 Spray Dryer Comparison of present calculations with results obtained with Fluent Droplet Velocity [m/s] Particle Diameter 30 µm z 0.4 m z 1.0 m z.1 m Radius [m] Droplet Temperature [K] Particle Diameter 30 µm z 0.4 m 330 z 1.0 m z.1 m Radius [m]

20 Lecture Content Droplet and particle collisions in spray dryer stochastic inter-particle collision model experiments for viscous droplets

21 Inter-Particle Collisions in Spray Dryers Properties of droplets injected into a spray dryer (i.e. viscosity and surface tension) are strongly changing along their way through the dryer caused by drying of solution and suspension droplets (increasing solids content). Collisions of droplets/particles with different drying state Surface tension dominated droplets Vicinity of atomiser Droplets and solid particles Penetration Agglomerate formation Particle coating Viscosity dominated droplets Middle region of dryer Solid particles (low moisture content) Agglomeration van der Waals forces

22 Stochastic Inter-Particle Collision Model 1 Stochastic Inter-Particle Collision Model (Sommerfeld 001) In the trajectory calculation of the considered particle a fictitious collision partner is generated for each time step. The properties of the fictitious particle are sampled from local distribution functions and correlations with the particle size. In sampling the fictitious particle velocity fluctuation the correlation of the fluctuating velocity is respected (LES of Simonin): ( ) ( ) n u fict,i R τp, TL u real,i + σi 1 R τp, TL ξ ( ) 0.4 τp R τ p, TL exp 0.55 TL Calculation of collision probability between the considered particle and the fictitious particle: π P fc t ( DP1 + DP ) u P1 u P n P t 4 A collision occurs when a random number in the range [0-1] becomes smaller than the collision probability. particle diameter particle velocities particle temperature solids content

23 Stochastic Inter-Particle Collision Model The collision process is calculated in a co-ordinate system where the fictitious particle is stationary. L φ Y + Z arcsin( L) 0 < Ψ < π with : L 1 1 L u rel φ collision cylinder 1 Ψ Consideration of impact probability (small and large particles): d p Yc η DK + dp ρp u p1 u Ψi 18 µ D ( ) p K d Collision occurs if: p Ψi Ψ + a i b La Y C Stream lines Boundary particle Y c U 0 L a Separated particle collector D K

24 Stochastic Inter-Particle Collision Model 3 In the case of rebound the new velocities of the considered particle are calculated by solving the momentum equations for an oblique collision in connection with Coulombs law of friction. u P1 u P1 1+ e 1 1+ mp1 m Sliding collision P Non-sliding collision v u P1 P1 < 7 µ ( 1 e) v P1 v P1 1 µ u 1 P1 ( 1+ e) v + P1 1 mp1 mp v P1 v P m P1 m P Re-transformation of the new particle velocities in the laboratory frame of reference. Particle rotation is not considered in agglomeration studies, due to the complex momentum exchange for structured agglomerates.

25 Droplet Collision Modelling 1 The outcome of a droplet collision depends on numerous parameters, namely, the kinetic properties and the thermo-physical properties of gas and droplets. Droplet velocities Droplet diameter ratio Impact angle Droplet liquid (density and viscosity) Surface tension Type of gas phase Gas phase pressure and temperature Governing non-dimensional parameters for the collision process: ρl DS Urel We b C DS B σl D S + D L D L µ l Oh C φ arcsin( B) 1 ρ σ D l l S S: small L: large The different collision scenarios are generally summarised in a phase diagram, i.e. B f (We C ) Due to the large number of relevant properties a unique solution for the collision regimes was not introduced so far!!! bl u rel φ collision cylinder

26 Droplet Collision Modelling Determination of the outcome of droplet collision based on B f(we) Calculation of post-collision droplet sizes and velocities bouncing B [ - ] 0.6 stretching separation 0.4 coalescence 0. reflexive separation We [ - ] Not universally applicable experiments to generalise the effect of viscosity Relative velocity substances (PVP K30, K17, Saccharose, series of alcohols, FVA 1 reference oil

27 Water for Validation Images for We 30 σ ρ σ µ + 1 l d l l l b 1 d a D C 1 We C B C a.33 and C b 0.41 Kuschel & Sommerfeld Exp. in Fluids, 013

28 PVP K30 5 Ma% PVP K30: 5 Ma%, η 60.0 mp s Images for We 30 C a.3378 and C b 0.4 The oscillation of the droplets after coalescence is reduced with increasing dynamic viscosity

29 Modelling - Characteristic Points u rel [m/s] Extraction of characteristic Triple Points (bouncing, coalescence and stretching separation collapse in one region) from the measurements for all substances The crossing point shows a clear dependence on viscosity (solids content) Development of a maximum or minimum for u rel and B, respectively Alcohol Saccharose 1. K17 K30 FVA1 ref. oil η [mpa s] maximum/minimum location at: u σ µ l relax l 3.47 m s B [ - ] Alcohol Saccharose K17 K30 FVA1 ref. oil η [mpa s] Sommerfeld & Kuschel ICMF Korea, 013

30 Re [ - ] Modelling Onset of Stretching Separation Summary of Triple Point location for all systems Onset of stretching separation: Resulting from a theory on maximum 1 K 1 of information entropy for competing e Re Ca We processes, i.e. interaction of flow C structures with the mean flow K6.9451* K We for bubble break-up K critical Re for laminar- Alcohols turbulent pipe flow 100 left right Ca [ - ] Saccharose PVP K17 PVP K30 FVA 1 Oil Water Correlation Qian Tetradecane 1 atm N (1997) Re ρ µ l Ca Urel σl *Naue, G. and Bärwolff, G.: Transportprozesse in Fluiden, Deutscher Verlag für Grundstoff-Industrie, Leipzig, 199. l DS µ l U rel U u rel relax sliding of two fluid surfaces

31 Modelling Onset of Stretching Separation Adaptation of the model of Jiang et al. (199) to match triple B C We a C b µ σ l l ρl D σl d 1 Optimal set of parameters for the Jiang model is a function of normalised relaxation velocity (here u* relax (σ/µ)* 3.47 m/s) C a [ - ], C b [ - ] 10 1 water PVP K17 PVP K30 Saccharose alcohols FVA 1 Oil C C a b u.76 u relax * relax u u relax * relax correlation C a correlation C b * * σ/η [ - ] u ( σ η) (σ/η) relax u relax σ η

32 Modelling - Onset of Reflexive Separation Critical We for the beginning of reflexive separation (at B 0) A correlation for all data can be found for We f(ca): We K 3 3 Ca + K K Deformation of the droplets Modifying the model of Ashgriz and Poo to match critical We crit : We We crit We [ - ] K17 K30 Alcohols 1000 Saccharose FVA1 Reference Oil Gotaas 007 (MEG, DEG) Willis 00 (Silicon oil) Jiang 199 (Alcane) ( ) ( ) ( ) ηs + η L Ca [ - ] own exp, Park 1970, Ashgriz 1990 (water) Qian 1997 (Tetradecan) We K 3 /3 Ca + K

33 Models Versus Experiments 1 B [ - ] Bouncing Coalescence Separation Estrade Jiang et al. Ashgriz & Poo The model of Ashgriz and Poo combined with the correlation for reflexive separation predicts the shift of the regime correctly We [ - ] FVA 1, 60 η 6.7 mpa s The adapted model of Estrade et al. is reasonably good for higher We but shows systematic deviations for lower We B [ - ] PVP K30, 15 % η 1.5 mpa s We [ - ]

34 Models Versus Experiments 1.0 B [ - ] For most of the substances the extended Jiang et al. model correctly predicts the boundary between coalescence and stretching separation 0. Bouncing Koaleszenz Separation Saccharose 60 % η 57.3 mpa s We [ - ] Estrade Jiang PVP K30, 5 % η 60 mpa s Further studies are necessary for developing a general model for lower boundary of bouncing valid for the entire range of We B [ - ] We [ - ]

35 Lecture Content New structure agglomeration model with preliminary validation for a spray dryer 15:10

36 Sommerfeld & Stübing ETMM 9, 01 Agglomeration Model for Solid Particles Agglomeration models Point-particle assumption Simple agglomeration model Sequential agglomeration model Agglomerate structure model Volume equivalent sphere Number of primary particles Penetration depth Number of primary particles Hull volume/diameter Porosity of hull Contact forces Location vectors Convex hull V ε 1 V Part Hull Agglomerate structure Effective surface area Volume of convex hull Porosity of the agglomerate

37 Agglomerate Structure Model 1 In order to obtain more detailed information on the agglomerate structure, location vectors for all primary particles in the agglomerate with respect to a reference particle are stored. The agglomerate structure is stored in a linked list The agglomerate is still treated as point-particle!!! Most important agglomerate properties Porosity of the agglomerate (convex hull) Effective surface area Agglomerate structure; Shape indicators

38 Agglomerate Structure Model Assumptions for the stochastic collision model with respect to structure modelling Agglomerates can only collide with primary particles (number concentration of the resulting agglomerates is very low). The fictitious particle cannot be an agglomerate, hence it is only sampled from the primary particle size distribution. Extension of the stochastic collision model The collision probability (based on a selected collision sphere of the agglomerate) predicts whether a collision occurs. The collision process is calculated in a coordinate system where the agglomerate is stationary. The point of impact on the surface of the selected collision sphere of the agglomerate is sampled stochastically L

39 Agglomerate Structure Model 3 A collision occurs if the lateral displacement L is smaller than the boundary trajectory Y C (impact efficiency). Random rotation of the agglomerate in all three directions (since rotation is neglected). 1 1 L The particle collides with the primary particle in the agglomerate being closest to the impact point (tracking). Possible collision scenarios: 1 L 1 sticking rebound Viscous particles: penetration

40 Penetration Model for High Viscous Droplets High viscous droplets penetrates into the low viscous droplet (spherical frame) - Contact Area: u ϑ d cont h d Low h h u ϕ -u r A c Calculation of time-dependent penetration depth: m Radial: Low viscosity Motion of sphere in viscous liquid High du dt r 3 π µ dr dt u r Low d cont - Penetration depth: u r d h Tangential: Shear force across contact area m High du dt ϑ X h P X µ dϑ dt d P Low Low u r High ϑ + for r d d cont Low for u r > 0 ϑ r r 0

41 Agglomeration Model for Solid Particles The occurrence of agglomeration may be decided on the basis of an energy balance (dry particles only Van der Waals forces): E E + k1 vdw E d E d ( 1 k pl ) Ek1 Ho and Sommerfeld (00) h Van der Waals Energie: A E vdw π a dz 3 6 π z z 0 Restitution ratio: Ek1 Ed k pl E k1 R1: smaller particle R 1 a z o R Critical impact velocity: U kr 1 R 1 ( 1 k ) k pl pl 1/ π z 0 A 6 P pl ρ p Agglomeration if: U cosφ rel U kr

42 Geometry of the Spray Dryer 1 Geometry and operational conditions of spray dryer (NIRO Copenhagen): Dryer geometry: H 4096 mm H cyl 1960 mm D 700 mm H out 3303 mm D out 10 mm Annular Air Inlet R o 57 mm R i 447 mm Air flow with swirl: ṁ air 1900 kg/h φ air 1.1 mass-% T air 45.5 K U ax 9.8 m/s U tan.4 m/s Fines return: Annular inlet around the nozzle D o 7 mm D i 63 mm U fine 37 m/s ρ fine 440 kg/m³ Pressure nozzle: Hollow cone nozzle p nozzle 85 bar Spray angle β 5 o D nozzle mm H nozzle 70 mm Maltodextrine DE-18 Solution: 9 mass-% solids ρ drop 1090 kg/m 3 ṁ solution 9 kg/h T solution 93 K U av 17 m/s

43 Geometry of the Spray Dryer Numerical discretisation and boundary conditions of the spray dryer: Number [ - ] Droplet and Particle Sizes Discretisation: 138 blocks meshes Spray Droplets Fines Return Particle Diameter [µm] Inlet and boundary conditions: Inlet: assumed velocity profiles Walls: no-slip velocity heat transfer coefficient measurements h 10.5 W/(K m²), Outlet pipe: gradient free

44 Numerical Results Spray Dryer 1 Calculated flow structure and temperature field in the dryer: Velocity field Water vapour concentration Temperature field

45 Numerical Results Spray Dryer Particle phase properties throughout the spray dryer Particle trajectories Particle concentration [kg/kg]

46 Numerical Results Spray Dryer 3 Particle-phase properties throughout the spray dryer Solids content in the particles Local particle mean diameter

47 Numerical Results Spray Dryer 4 Properties of the agglomerates produced in the spray dryer Number [ - ] Number Primary Particles N PP [ - ] 00 Number [ - ] high -u r u ϑ Relative Penetration x P / D P, high [%] h u ϕ a A c low Number [ - ] Porosity ε [ - ] Porosity: V ε 1 V Part Hull 30 primary particles ε hull 0.61

48 Numerical Results Spray Dryer 5 Simulated agglomerates compared with agglomerates collected from the spray dryer

49 Outlook 1 Sub-models for describing the behaviour of droplets and particles in a spray dryer have been developed and validated; i.e. drying, viscous droplet collisions and agglomeration model. The models will be jointly implemented in the in-house code FASTEST/Lag-3D and further validated. Extension of the droplet collision model for very high viscosities; i.e. up to several Pa s. a Feeding Liquid (up to 16bar) Outlet b c d Coalescence Stretching Separation

50 Outlook Validation of the droplet collision models using a special laboratory spray dryer with interacting sprays.

51 Acknowledgements The financial support of projects by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged. The following Ph.D. students have contributed to the presented research: Dipl.-Ing. Stefan Blei M.Sc. Ali Darvan M.Sc. Chi-Ahn Ho Dipl.-Ing. Matthias Kuschel Dr.-Ing. Hai Li Dipl. Ing. Sebastian Stübing

52 Workshop 015