A review of EMMS drag
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1 12 th Int. Conf. Fluidized Bed Technology May 23-26, 2017, Krakow, Poland A review of drag Bona Lu, Fei Li, Wei Wang, Xinhua Liu, Junwu Wang, Ning Yang, Wei Ge, Jinghai Li Institute of Process Engineering Chinese Academy of Sciences
2 Development of drag model Cluster-based drag Yang et al. CEJ, 2003 (96): 71 Wang & Li, CES, 2007 (62): 208 Lu et al., CES, 2009 (64): 3431 Cluster modification Wang et al. CES, 2008(63): 1553 Hu et al. CEJ, 2017(307): 326 Li & Kwauk, 1994 Li et al. CFBII, 1988 Bubble-based drag Shi et al., CES, 2011 (66): 5541 Hong et al., CES, 2013(99):191 Luo et al., CEJ, 2017 (accepted) Bubble modification Liu et al. IECR, 2014(53):
3 model equations F F F 3 1 = ( 1 )( ) 4 C ε ρ U = ε ρ ρ g c 2 dc Dc f slip,c g p f dp 3 1 ε = C ρ U = ε ρ ρ ( 1 )( ) f 2 df Df f slip,f f p f 4 dp = 3 f C f ( 1 f )( )( ) g d ρ U = ε ε ρ ρ 2 di Di f slip,i f c p f 4 cl ( 1 f ) U = fu + U g gc gf ( 1 f ) U = fu + U d cl p pc pf = ( U /1 ( ε ) ( U + U ε /1 ( ε )) ) d g g p p max mf p mf mf N ( ) ( U + U ( )) ρ / ρ ρ ε /1 ε st p p f mf p mf mf g g Subject to stability condition: N st min 3
4 Numerical method X = { x 1, x 2,, x n } NLP code: GRG min E j (X) E k (X) Analytical solution 1996 s.t. F i (X)=0, i=1, 2,, m Full-range search 2002 Li et al., CES, 2003(58): 521 4
5 Numerical method: full-range search 1. Calculate U sf from Eq.(2); 2. Traverse ε c and f with the range of [ε mf, ε max ], and [0,1] respectively; 3. Calculate U sc from Eq.(1); 4. With the definitions of U sf and U sc ; U gf, U gc, U pf and U pc can be solved from Eqs.(4)-(5); 5. Calculate d cl from Eq.(6); 6. Calculate U si from its definition and Eq.(3) respectively, denote the difference as U si ; 7. Compare U si with the convergence criteria, if converged then store the value and continue the search until finished, else directly go back to step 3; 8. Find the optimal root through the minimization of N st among all the possible roots. Ge et al., CES, 2002 (57):
6 Basic equations of drag ε 1 π F = C ρ U U d = ρ ρ ε a g ( )( 1 )( ) c 2 dc 3 Dc g slip,c slip,c p p g g c π dp f 1 π F = C ρ U U d = f ρ ρ ε ε a g ( )( )( ) 2 di 3 Di g slip,i slip,i cl p g g c i π dcl ε 1 π F = C ρ U U d = ρ ρ ε a g ( )( 1 )( ) f 2 df 3 Df g slip,f slip,f p p g f f π dp ( 1 f ) U = fu + U g gc gf ( 1 f ) U = fu + U d d s sc sf cl U s ε mf U s Umf + g 1 εmax 1 εmf = ρ ε U N g U + p p mf s st mf ρp ρg 1 εmf ( 1 f ) ε = fε + ε g c f Subject to stability condition: N st min 6
7 Definition of drag coefficient drag coefficient ε ε β = = + + U 2 2 g g FD cfc ifi fff slip Uslip ( ) slip ( fm m ( 1 f ) m ) 2 ρp ρg εg = f + f + f U ( 1 ε ) 3 ε β ρ ε ( 1 εg )( ac g) ( εg εgc )( ai g) ( 1 )( 1 εgf )( af g) Wen & Yu model for homogeneous fluidization g g = gcd0 ug up g 4 dp Drag correction factor (heterogeneity index) H D β β 0 is a bivariate function of (u slip, ε g ) 7
8 2.0 : named /Classic ; drag: H D =f(ε g ), named /Global drag: H D =f(ε g, U slip ), named /matrix
9 /classic for flow regime map At given gas velocity Sweeping a range of solid flux 9
10 A flow regime map for a CFB Physical properties (µ g = Pa s, ρ g =0.766 kg/m 3, d p =97 µm, ρ s =1500 kg/m 3 ) For an industrial reactor where the circulating solid flux is hard to obtain, this map can help to evaluate the solid flux at a given gas velocity. 10
11 How to get the drag coefficient? Taking /matrix module as an example 11
12 The program is running The running interface The results interface 12
13 The drag correction factor, H D ( ) H f u ε D = slip, g 13
14 Fitting functions for H D 1.0 H D ~ Re or U slip 1.0 a, b, c ~ ε g 0.8 ε g 0.8 H D ε g =0.60 ε g =0.65 ε g =0.70 ε g =0.75 ε g =0.80 ε g =0.85 ε g =0.90 ε g =0.92 ε g = Re Coefficients a, b, c a c 0.2 b Voidage Power functions H D = a( Re + b) c b or H = are The coefficients a, b and c D depend on ε g 14
15 Comparison of H D (a) before the fitting (b) after the fitting 15
16 The fitting formulae for H D ANSYS FLUENT Define_exchange_properties UDF (user defined function) 16
17 Coupling with FLUENT Tips: Firstly chose the drag correlation included in FLUENT(i.e. Wen & Yu), run for several steps Then change it to drag 17
18 Test: ETH-CFB with Geldart B particles A CFB from ETH, rebuilt at IPE in
19 Simulation Results Axial profiles Solid flux Bed height (m) 8 69*283 34*142 23*94 17*71 6*7 6 Exp. 4 2 WenYu&Ergun Model G 8 69*283 34*142 23*94 17*71 Exp Model M Solids flux (kg/(m 2 s)) Model G Model M Exp. WenYu&Ergu P(mbar) P(mbar) Decreasing grid size Air- glass beads, U g =7.7m/s, d p =300µm Lu et al. (2011) Chem. Eng. Sci. 66, Axial voidage profile is well predicted by using both homogeneous and drag Solid flux is better predicted by using the drag
20 drag in Barracuda Barracuda provide 3 approaches to use drag: Predefined drag models /Global model /Matrix model Import drag file from software User defined correlations
21 Predefined drag models /Global The /Global model is named -Yang-2004 in Barracuda. Open the Drag Models in the left column, you can find -Yang Choose -Yang-2004 in Particle Species Properties to use this model.
22 Predefined drag models /Global Step by step: 1. Click Particle Species in the left column; 2. Click a particle species in the right column to open Particle species properties dialog; 3. Choose -Yang-2004 in the Model Name dropdown list; 4. Click OK button.
23 Predefined drag models /Matrix The /Matrix model is implemented as Multiplier in Barracuda. Open the Particle species properties dialog, you can find Multiplier. Make sure that Wen-Yu drag model have been chosen to use Multiplier.
24 Predefined drag models /Matrix Step by step: 1. Click Particle Species in the left column; 2. Click a particle species in the right column to open Particle species properties dialog; 3. Choose Wen-Yu in the Model Name dropdown list; 4. Select Multiplier (predefined) and click to open the dropdown list; 5. Choose an operating type closest to your case; 6. Click OK button. Some typical operating conditions including fast fluidized bed, bubbling fluidized bed, turbulent fluidized bed etc. have been implemented with /Matrix.
25 Import drag file from software This approach is also implemented by Multiplier, with two main steps: 1. Prepare the drag file from software; 2. Import the drag file in Barracuda.
26 Generate drag file from software In software We assume you have finished calculation with /Matrix in software Step by step: 1. Right click Hete in the left column; 2. Click Export Data ; 3. Fill the file name i.e Hd.dat, click Save. Content of drag file
27 Import drag file in Barracuda In Barracuda Step by step: 1. Click Particle Species in the left column; 2. Click a particle species in the right column to open Particle species properties dialog; 3. Choose Wen-Yu in the Model Name dropdown list; 4. Select Multiplier (from file) and click to open the file dialog; 5. Choose the drag file i.e Hd.dat you have prepared before; 6. Click OK button.
28 User defined drag correlations Define drag correlations This approach is also implemented by two main steps: 1. Defined your own drag correlation in Drag Models ; 2. Use your defined drag correlation in Particle species properties dialog.
29 Define your own drag correlations Step by step: 1. Click Drag Models in the left column to open Drag Model Manager ; 2. Click Add button to open Drag Model Editor dialog; 3. Fill the Name blank to name your model, i.e my; 4. Fill the Comment to give your model a short discription; 5. Define constants by click Add Row button; 6. Fill the F custom () with your drag correlation; 7. Click OK button. Note: Drag correlation should be written like: F = 3πµ d u u F ( ) ( ) drag p f s custom
30 Use your defined correlation Step by step: 1. Click Particle Species in the left column; 2. Click a particle species in the right column to open Particle species properties dialog; 3. Choose your defined model i.e my in the Model Name dropdown list; 4. Click OK button.
31 Barracuda simulation with drag Solid flux Axial solid fraction G s (kg/m 2 s) Homogeneous drag Exp. drag t (s) H (m) Homo. Exp ε s (-) 20 s Averaged Barracuda with drag improves riser simulation
32 About determination of G s In case both U g and G s are known, in drag, heterogeneity index H D is obtained in 2 steps: 1 Operating condition Your own d cl, ε c models d cl, ε c U g, G s 2 Local parameter v g, v s, ε s H D You can also use your own cluster models
33 About determination of G s In case G s is not known when simulating the whole CFB system, G s can be determined from full-loop computation of CFB as follows: U g, I m Try a G s Modeling Riser Downcomer Loop seal etc. ƩΔP = 0 ƩI m = 0 G' s Liu et al., Chem. Eng. J (278): G s U g H D
34 Thank you for your attention! This ppt can be downloaded after this conference on our website:
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