Important length scales in dense gas- par3cle flows

Transcription

1 Imoran lenh scales in dense as- ar3cle flows Sefan Radl, Chris Milioli, Fernando Milioli & Sankaran Sundaresan Princeon Universiy Paer 17c, 03B09 Secial session o celebrae John Chen s career lon accomlishmens Monday, Ocober 9, 01 Conference C (Omni) 1

2 Ouline Backround on dimensional analysis of fluidized beds Characeris3c lenh a small scales Characeris3c lenh a larer scales Proosed hierarchy of imorance for he dimensionless rous in scale- u and scale- down of urbulen fluidized beds and CFB risers

3 Fluidized bed scale- u or scale- down Wha are imoran dimensionless rous ha mus be mached while scalin urbulen and fas fluidized beds? Dimensional quan33es: Densi3es of as (a inle) and solid (ρ and ρ s ) G i = i U i, Mass fluxes of as (a inle) and solid (G and G s ) i = s, Par3cle diameer, d (more accuraely, PSD) Gas viscosiy, μ Sysem size, D Gravia3onal consan,, ma\ers, bu is fixed. Exen of as densiy varia3on as i flows hrouh he bed Low ressure vs. hih ressure Microscoic, bu dimensionless, arameers: Fric3on coefficien and coefficien of res3u3on Par3cle- ar3cle: μ and e Par3cle- wall: μ w and e w Par3cle shae, aseriy 3

4 Dimensional analysis Dimensionless rous Gas and solid velociy ra3o Gas and solid densiy ra3o Par3cle- o- bed size ra3o Froude number (bed- scale) Froude number (ar3cle scale) Par3cle Reynolds number U,, d U s s D, Fr b = U D, Fr = v, Re = v d, PSD, Geomery d µ " Ar = % 3 s 1 d " = % 3/ Re s 1, Re = d = Re 1/ # $ &' µ # $ &' Fr µ Fr Fr = U = Fr b d " # $ d D % &' 1 U,, d U s s D, Fr, Ar, Re, PSD, Geomery If only viscous dra Microscoic arameers: µ w,e w,µ,e Canno mach all of hese 4

5 Use model equa3ons o examine scalin Glicksman (1984, 1994, ) Two- fluid model con3nuiy and momenum balance Nelec ar3cle hase sress µ w,e w,µ,e U,, d U s s D, Fr, Ar, Re, PSD, Geomery Deamore e al. (001) Kine3c heory model, seady sae simula3ons Mus ay a\en3on o ar3cle inerac3on arameers: e w,e 5

6 Use model equa3ons o examine scalin Qi, Zhu & Huan (Chem. En. Sci., 63, 5613, 008) Hydrodynamic similariy of riser flows U Global quan33es mach if we mach: $ D Nohin relaed o ar3cle diameer "# %& or as viscosiy Naren & Ranade (Par3cuoloy, 9, 11-19, 011) Tesed hrouh simula3ons Yes, bu radial rofiles don mach '0.3 Us U 6

7 Objec3ve of our sudy Dimensionless rous : U,, d U s s D, Fr b = U D, Fr = v, Re = v d, PSD, Geomery d µ µ w,e w,µ,e Grou hese in erms of heir shere of influence Imoran for similariy of macro- scale flow characeris3cs Influence limied o smaller scales Goal: Undersand wha erms (in he wo- fluid model) are come3n a differen scales? 7

8 Two- fluid model: Momenum balance & ( ' (" s v s ) + $ %(" s v s v s ) ) + * =, $ %-, # $ %- +. v, v s s s ( ) + " s Princially viscous dra ood arox. for mos TFB and CFB = µ d f " 1 ( s ) = # s f v (" s ) & ( ' (" # v ) + $ %(" # v v ) Le us cas hese in dimensionless form ) + * =,# $ %-,. v, v s ( ) + " # 8

9 Two- fluid model: Momenum balance & ( ' (" s v s ) + $ %(" s v s v s ) In fluidized flows, dra nearly balances he weih of he ar3cles. So, v is a naural characeris3c velociy Par3cle densiy is a naural densiy scale Wha abou lenh scale? Many choices Iner3a ~ Graviy ) + * =, $ %-, # $ +# $ %. + " s f s s s v L 1 ~ v ( ) v, v s ( ) + " s 9

10 Two- fluid model: Par3cle hase sress & ( ' (" s v s ) + $ %(" s v s v s ) ) + * =, $ %-, # $ +# $ %. + " s f s s s v ( ) v, v s ( ) + " s Par3cle hase sress: µ s ~ s v d µ s ~ s T 1/ d Par3cle hase deviaoric sress ~ Graviy Par3cle hase deviaoric sress ~ Iner3a L ~ v ( Fr ) n,n = 1, 3,1, 4 3 ; Fr = v d 10

11 Two- fluid model: Momenum balance & ( ' (" s v s ) + $ %(" s v s v s ) In fluidized flows, dra nearly balances he weih of he ar3cles. So, v is a naural characeris3c velociy Par3cle densiy is a naural densiy scale Wha abou lenh scale? ) + * =, $ %-, # $ +# $ %. + " s f s s s v L ~ v ( ) v, v s Each corresonds o come33on beween differen airs. ( ) + " s ( Fr ) n,n = 0, 1, 3,1, 4 3 Ques3on: As one examines roressively larer scale, how does his come33on shi? 11

12 CFD- DEM simula3ons Sysem 1 Given: s1,d 1,1,µ1 Periodic box size: d1 x d1 x 4d1 Fluid rid size: f 1 Deermine dimensionless domain- averae sli velociy: Vsli, 1 V1 ρs1 / ρ / 1.3 [k/m³] µ [Pa.s] Δd1 / Δf1 4 / 0.5 [mm] d1 75 [µm] φs 0.05 (0.5) v1/ 4.86 [mm] Fr (φs = 0.5, ar3cles colored accordin local ar3cle volume frac3on) 1

13 How should we scale he CFD- DEM simula3ons? Sysem 1 Sysem Given: s1,d 1, 1,µ 1 Given: s,d,,µ Periodic box size: d1 x d1 x 4 d1 Periodic box size: d x d x 4 d Fluid rid size: f 1 Fluid rid size: f d = d1 Deermined dimensionless L d L domain- averae sli velociy d1 Wan: V sli, V = V sli, 1 V 1 f L f = f 1 L f 1 Which of hese make sense? L d ~ v L f ~ v ( Fr ) n d ( Fr ) n f,n d = 0, 1, 3,1, 4 3,n f = 0, 1, 3,1,

14 How should we scale he CFD- DEM simula3ons? Sysem 1 Sysem Given: s1,d 1,1,µ1, 1 Given: s,d,,µ, Periodic box size: d1 x d1 x 4d1 Periodic box size: d x d x 4d Fluid rid size: f 1 Fluid rid size: f Wan: Vsli, V = Vsli, 1 V1 ( ) v Ld ~ Fr ( ) v Lf ~ Fr d d1 = Ld Ld1 f f1 = Lf Lf1 nd 1 4,nd = 0,,,1, 3 3 nf 1 4,n f = 0,,,1,

15 How should we scale he CFD- DEM simula3ons? A small scale, boh resolu3on requiremen and filered sa3s3cs scale as v ( Fr ) /3 Par3cle hase sress - kine3c heory: Wha hysical icure does his imly? Plus, Par3cle hase deviaoric sress ~ Graviy µ s ~ s T 1/ d & ( ' (" s v s ) + $ %(" s v s v s ) ) + * =, $ %-, # $ +# $ %. + " s f s s s v ( ) v, v s ( ) + " s 15

16 Grid resolu3on requiremen of TFM simula3ons A small scale, boh resolu3on requiremen and filered sa3s3cs scale as v ( Fr ) /3 Par3cle hase sress - kine3c heory: Grid resolu3on requiremen of TFM is se by he need o resolve he come33on beween dra and viscous forces Now swich o simula8on in larer domains usin TFM µ s ~ s T 1/ d & ( ' (" s v s ) + $ %(" s v s v s ) ) + * =, $ %-, # $ +# $ %. + " s f s s s v ( ) v, v s ( ) + " s 16

17 Coarser srucures resolved in KT- TFM simula3ons Wha is he correc lenh scale for he filer size? L filer ~ v ( Fr ) n filer,n filer =? Grid resolu3on requiremen of TFM is se by he need o resolve he come33on beween dra and viscous forces L rid ~ v ( Fr ) /3 rid << fil << domain 17

18 Coarser srucures resolved in KT- TFM simula3ons Wha is he correc lenh scale for he filer size? L filer ~ v ( Fr ) n filer,n filer =? How did we es?: Perform simula3ons wih differen ar3cle sizes ( μm), scalin he filer and domain sizes usin differen values. n filer rid L rid = fixed L rid ~ v rid << fil << domain ( Fr ) "/3 Domain- averaed ar3cle volume frac3on =

19 Coarser srucures resolved in KT- TFM simula3ons Wha is he correc lenh scale for he filer size? L filer ~ v ( Fr ) n filer,n filer =? Examine resul3n filered ar3cle hase sress and filered fluid- ar3cle dra coefficien rid L rid = fixed L rid ~ v rid << fil << domain ( Fr ) "/3 Domain- averaed ar3cle volume frac3on =

20 Dimensionless filered ar3cle hase viscosiy & ( ' L filer ~ v Normalized dimensionless solid hase effecive viscosiy ( Fr ) n filer µ s, dim.less µ s, dim.less, 75µm Filer = 1/8D 15% of solid filer L filer = consan, bu larer µ ( s, fil s v L ) filer n fil = -/3 n fil = Fr d (" s v s ) + $ %(" s v s v s ) ) + * =, $ %-, # $ +# $ %. + " s f s s s v Comare resuls obained wih differen dimensional ar3cle sizes, and subsequenly cas in dimensionless form ( ) v, v s ( ) + " s 0

21 Wha does i all mean? & ( ' & ( ' (" s v s ) + $ %(" s v s v s ) (" # v ) + $ %(" # v v ) ) + * =, $ %-, # $ %- + " s f s s v ) + * =,# $ %-, " s f v ( ) v, v s ( ) + " s ( ) + " # ( ) v, v s For TFBs and CFB risers, he ar3cle hase sress and he deviaoric ar of he fluid hase sress have li\le influence on coarse srucures. "# ~ Now consider a real hysical sysem Characeris3c lenh for macro- scale srucures in TFB/CFB riser is U. 1

22 Wha does i all mean? U U s D U is an imoran dimensionless rou o mach he macro- scale characeris3cs immediaely arises via flux secifica3on Qi, Zhu & Huan (Chem. En. Sci., 63, 5613, 008) Hydrodynamic similariy of riser flows U Global quan33es mach if we mach: $ D Nohin relaed o ar3cle diameer "# %& or as viscosiy '0.3 Us U

23 Wha does i all mean? U U s U D U v is an imoran dimensionless rou o mach he macro- scale characeris3cs immediaely arises via flux secifica3on arises via correc3on o he dra force resul3n from small scale srucures (clusers and sreamers) s Le = K. may ener only via lobal arumens. Usually " << s " s. s Then, if, he densiy ra3o is no imoran. KH << 1 (Violaed by dee beds a low ressures) 3

24 Fluidized bed scale- u or scale- down Revisied scale-u and scale-down. For sysems wih " << s " s. Usin a combinaion of CFD-DEM and TFM simulaions, we have examined he comeiion beween erms in he momenum balance equaions. Model analysis sues he followin hierarchy: Mos imoran: U D, U s U PSD, Geomery Nex imoran: U s v Then: s KH, when i is no much smaller han 1. 4

25 Fundin from: S. Radl: Erwin- Schrödiner fellowshi Milioli: FAPESP - São Paulo Sae Research Founda3on (Brazil) ExxonMobil Research & Enineerin Co. 5