How To Calculate The Power Of A Bubble Swarm

Transcription

1 Hgh Performance Smulaton of Bubbly Flows: Pushng the mt by Usng Conventonal CFD and BGK Stefan Radl, 1,2 Radompon Sungkorn, 1 Danele Suzz, 2 Jos Derksen, 3 Johannes G. Khnast 1,2 1 Insttute for Process and Partcle Engneerng, Graz Unversty of Technology, Austra 2 Research Center Pharmaceutcal Engneerng GmbH, Austra 3 Department of Chemcal and Materals Engneerng, Unversty of Alberta, Edmonton, Canada MSM Symposum 2009 December 8, Melbourne 1

2 Introducton Motvaton Novel Tools New strateges to solve (or to mmc the behavor of) the Naver- Stokes equaton (e.g., BM) Relable Open-source software (e.g., OpenFOAM) (relatvely) cheap computers Ths makes, e.g., agrangan Partcle Trackng (PT) for large bubbles swarms possble Applcaton Areas J.J. Derksen, H.E.A. van den Akker. AIChE J 45, 1999, S. Radl, J. Khnast. AIChE J, 2009, n press. fne chemcals ndustry catalytc hydrogenaton and oxdaton pharmaceutcal ndustry Qualty by Desgn (QbD) ntatve boreactors shear damage to cells, oxygen supply n yeast and antbotcs producton, CO 2 supply n mcroalgae cultvaton synfuels modelng of Fscher-Tropsch synthess MSM Symposum 2009 December 8, Melbourne 2

3 Part I Multphase Flow Normalzed energy dsspaton rate and flow feld n a 250 m² ndustral fermenter MSM Symposum 2009 December 8, Melbourne 3

4 ES-PT Meso-scale Smulaton of Bubble Swarms: agrangan Partcle Trackng (PT) combned wth arge Eddy Smulaton (ES) Governng Equatons (Euler Grd) ε + ε u t m ( ε ρ u) p t du dt = F + G + Fp + FD + F + F A,.. & Φ Φ ( ) 0 = ( ε ρ uu) = ε p ( ε τ ) + ε ρ g Φ N r j.. F G F p.. F D.. F.. F A.. sources due to dsperse phase reacton rate of reacton j gravty force force due to pressure gradent drag force lft force added mass force + ( ε Y ) + ( ε uy ) = ( ε D Y ) + Φ + ε t Newton s Equaton of Moton (agrangan Grd) vald for dlute and dense systems as we consder ε on the Euleran grd! MSM Symposum 2009 December 8, Melbourne 4 eff, N& ν, j j total lqud-phase stress: 2 τ = µ µ SGS, u 3 T ( + ) ( u + u ) I ( ) r j Sketch of forces actng on a bubble

5 ES EXPERIMENT ES-PT Bubble Swarms: Valdaton of Flow Setup Becker case doman sze 0.5 x 0.08 x 1.5 [m] 1.6 [l/mn] gas flow rate 1.6 [mm] bubble sze excentrc sparger Results strongly unsteady moton of the gas plume reproduced (t osc = 40 [s]) gas hold-up between 0.24 % and 0.34 % (70k 95k bubbles n doman) Guness effect: small bubbles move downwards near wall Snapshot of bubble postons for two dfferent tmes (exp. Data by Sokolchn and Egenberger, 1999) Bubble velocty (bubble dameter magnfed by a factor of 3) MSM Symposum 2009 December 8, Melbourne 5

6 ES-PT Bubble Swarms: Valdaton of Flow Euler-Euler ES-PT Quanttatve Results excellent agreement wth mean velocty feld publshed by S&E for PT-ES and Euler-Euler smulaton wth κ-ζf turbulence model some space for mprovement near the walls for both approaches Influence of the Grd Tme-averaged velocty profles (left) at z/h=0.22 and vector plot of the tme-averaged veloctes (rght) for (top) Euler-Euler Smulaton and (bottom) ES-PT Tme-averaged velocty profles z/h=0.35 for dfferent grds usng BT-ES (mesh 0: 122,880 cells, mesh 2: 820,800 cells) Mesh 0 Mesh 2 coarse fne MSM Symposum 2009 December 8, Melbourne 6

7 BGK Bubble Swarms: Results wth a new BGK code u [m/s] Challenges when usng BGK Stablty (when mposng forces, the densty feld may start to oscllate) To take nto account the local gas hold-up n the NS Eqn. Effcent handlng of partcle nformaton 0s 5s 10s Instantaneous fltered velocty feld, BGK code 15s Speed-up of the BGK flow solver (smulatons performed at the ccluster of the Graz Unversty of Technology) Speed-up (t seral /t parallel ) (b) BGK... attce Boltzmann Bhatnagar-Gross-Krook Number of processors MSM Symposum 2009 December 8, Melbourne 7

8 Part II Mxng MSM Symposum 2009 December 8, Melbourne 8

9 ES-PT Bubble Swarms: Mxng wthout Mass Transfer Setup ar bubbles movng n water, Becker case Sc = 500, Sc SGS = 0.7 (nfluence of Sc SGS s small) Quantfcaton of mxng Potental for dffusve mxng Φ [1/m] (Bothe et al., 2006), the nverse s a measure for the scale of segregaton. The ntensty of segregaton s quantfed by the varance σ². D. Bothe, C. Stemch, H.-J. Warnecke. Flud Mxng n a T-shaped mcro-mxer. Chem Eng Sc 61 (2006) Φ = σ 1 ε, V mean = 2 1 ε tot V Y ε dv V tot ( Y Y, mean ) V tot, mean tot 2 ε dv (a1) (a2) (a3) (a4) (b) (c) Analyss of mxng metrcs for dfferent ntal dstrbutons of an nert scalar wthout mass transfer (a: ntal dstrbutons used for the analyss; b: normalzed scale of segregaton vs. tme, c: log-normal ft of the dstrbuton of after a tme of 15s for case a1) MSM Symposum 2009 December 8, Melbourne 9

10 ES-PT Bubble Swarms: Dssoluton and Mxng of Gas Setup ar s dssolvng n water (no reactons) Sc = 500, Sc SGS = 0.7 Quantfcaton of mxng σ² Contour plots of (a) concentraton feld Y, (b) local dstrbuton of the varance σ², and (c) potental for dffusve mxng Φ (left: t=5[s], rght: t=15[s]) MSM Symposum 2009 December 8, Melbourne 10

11 ES-PT Bubble Swarms: Dssoluton and Mxng of Gas Scale of segregaton Very fast dynamc behavor, for long tmes perfectly log-normal dstrbuted Intensty of segregaton ntermedate tme scale, strong fluctuatons n tme σ² and Φ decrease n tme accordng to (Y eq -Y mean ),.e., exponentally Dstrbuton of the scale of segregaton, top: comparson of dstrbutons for dfferent tmes, bottom: Tme profles for the mxng metrcs σ² and Φ log-normal ft of the dstrbuton after a tme of 15 [s] MSM Symposum 2009 December 8, Melbourne 11

12 ES-PT Bubble Swarms: Dssoluton and Mxng of Gas The mechansm leadng to fluctuatons of σ² A cloud of hgh concentraton forms at the top due to hgh gas hold-up εg Interfacal area a and mass transfer decrease qud-phase mxng s not much nfluenced. Cloud s mxed wth the bulk lqud t=36s t=30s t=30s t=36s Tme profles for (top) σ² and (bottom) specfc nterfacal area a for dfferent bubble szes 30s MSM Symposum s 34s 36s December 8, Melbourne Concentraton contour plots and bubble postons for dfferent tmes (dp=1.6mm) 12

13 ES-PT Bubble Swarms: Scalar Varance n Multphase Systems Defnton, ts Transport Equaton and Results Y = V, = YY ( ε Y ) t Y Y ( ε D Y ) V, + 2 ε D 2 ε s + 2 α Y wth: C eff, χ V, + eff, Φ N & Y Φ s χ = Y V, τ Φ ( ε uy ) V, Y Y V, Dmensonless concentraton (a1, a2) and scalar varance (b1, b2) contour plots after 2 [s] (left) and 10 [s] (rght) for an nert scalar (α = 0). A Remanng Challenge To model the generaton of varance due to mass transfer 2 α YV, MSM Symposum 2009 December 8, Melbourne 13 Φ N & Y

14 Part III Brdgng the Scale Gap Göz et al., 2001 MSM Symposum 2009 December 8, Melbourne 14

15 ES Extenson Flm Model What s gong on at the Interface? Comparng DNS wth mass transfer correlatons 3D DNS s able to perfectly reproduce correlatons for Sc = 1 For hgher Sc numbers, extreme grd refnement near the nterface s needed Streamlnes and dstrbuton of dssolved gas around a sphercal bubble H 2 and product dstrbuton n the wake of a sphercal bubble MSM Symposum 2009 December 8, Melbourne 15

16 ES Extenson Flm Model Model Concept Overvew The multphase reactor s separated nto a dspersed and a contnuous phase The dspersed phase conssts of partcles (or parcles of partcles) that are ndvdually tracked (agrangan grd) The contnuous phase conssts of a stagnant flm (smlar to Keng et al.) and a bulk phase (Euleran grd) Features Very detaled hydrodynamcs n the bulk phase consdered Fully predctve and flexble Mcromxng effects near the nterphase and n the bulk phase consdered Rgorous nterface model for dspersed-flow multphase reactors Governng Equatons Partcle (non-reactve speces transport) Flm (quas-steady-state assumpton) 2 c 0 = 2 x D = r 2 r r + Ha nk ( c ) MSM Symposum 2009 December 8, Melbourne 16 c t 2 2 j Da Da j 1 c r ν j Keng et al., CEP, 2009 k k

17 ES Extenson Flm Model Model Detals Structure The reacton knetcs and stochometry are fxed. For the calculaton of the concentraton profle n the flm we need the flm thckness (from bubble moton), the nterface concentraton (partcle couplng) and the bulk concentraton (bulk couplng) Calculaton Strategy Solve flm equatons n Matlab before smulaton and save data Calculate flm thckness and nterpolate bulk concentraton n ES-PT Solve partcle model and nterpolate flm model output from look-up table n ES- BT Tme savngs: 0.04 [s] vs [s] per tme step (factor ~20) Varables (orange) and constants (green) nvolved n the flm model Calculaton strategy (a data base s provded by Matlab, whch s then used as a look-up table by OpenFOAM) MSM Symposum 2009 December 8, Melbourne 17

18 Acknowledgement - FWF (Project P19639 Reactve Mass Transfer n Bubble Swarms, - NSF Grant CTS EU Mare Cure Char MEXC-CT Athanas Koynov, Gretar Tryggvason, Mchael C. Gruber, Hannes Pucher, Andreas Etzlmayer Questons? References Parts of ths project were realzed usng OpenFOAM s a regstered trade mark of OpenCFD mted 1. A. Koynov, G. Tryggvason, J. Khnast; Characterzaton of the localzed hydrodynamc shear forces and dssolved oxygen dstrbuton n sparged boreactors, Botechnol Boeng 97 (2007), S. Radl, G. Tryggvason, J. Khnast; Flow and Mass Transfer of Fully Resolved Deformable Bubble Swarms n non-newtonan Fluds, AIChE J 53 (2007), S. Radl, A. Koynov, G. Tryggvason, J. Khnast; DNS-based Predcton of the Selectvty of Fast Multphase Reactons: Hydrogenaton of Ntroarenes, Chemcal Engneerng Scence 63 (2008), S. Radl, D. Suzz, J. Khnast; Assessment of Mcro- and Mesomxng n Bubble Swarms va Smulatons, Chemcal Engneerng Transactons (2009). 5. S. Radl, J. Khnast; Multphase Flow and Mxng n Dlute Bubble Swarms, AIChE Journal (2009), n press. MSM Symposum 2009 December 8, Melbourne 18

19 Hgh Performance Smulaton of Bubbly Flows: Pushng the mt by Usng Conventonal CFD and BGK Stefan Radl, 1,2 Radompon Sungkorn, 1 Danele Suzz, 2 Jos Derksen, 3 Johannes G. Khnast 1,2 1 Insttute for Process and Partcle Engneerng, Graz Unversty of Technology, Austra 2 Research Center Pharmaceutcal Engneerng GmbH, Austra 3 Department of Chemcal and Materals Engneerng, Unversty of Alberta, Edmonton, Canada MSM Symposum 2009 December 8, Melbourne 19

20 ES-PT Bubble Swarms: Reactons n the qud Phase Effect of the reacton rate In boreactors, typcal reacton tme scales range from 1 to 10 3 s. We would lke to dentfy regons starvng nutrents, e.g., oxygen. The queston thus s: Is the reactor well mxed and can we supply enough nutrents? Φ and σ² are much smaller, however, ths does not mean the reactor s well mxed! Thus, we cannot employ Φ and σ² for ths analyss! τ R =100s (d) τ R =100s τ R =200s τ R =100s (a) (b) (c) Dmensonless mean concentraton profles (a: τ R =100[s], b: τ R =200[s]), (c) mxng metrcs for the case wth τ R =100[s], and (d) snapshot of the concentraton profle and bubbles for the case wth τ R =100[s]. MSM Symposum 2009 December 8, Melbourne 20

21 ES Extenson Flm Model Verfcaton & Valdaton Strategy Flm Model Verfcaton va sem-analytcal solutons from lterature Valdaton of the flm model wth expermental data s extremly dffcult. Instead, we use drect numercal smulatons to detal on the accuracy of the flm model. Bulk Phase Flow Mean and fluctuatng velocty feld Scalar mxng: ph and conductvty measurements Reactve mxng: 4 th Bourne reacton (neutralzaton vs. acd hydrolyss) Total Performance 2D DNS of bubble swarms Reactve multphase mxng: 4 th Bourne reacton n bubble column [%] Comparson of flm model predcton wth DNS data Expermental setup for the nvestgaton of reactve mxng MSM Symposum 2009 December 8, Melbourne 21