Reflections on mathematical models and simulation of gas particle flows

Transcription

1 Reflections on mathematical models and simulation of gas particle flows Sankaran Sundaresan Princeton University Circulating Fluidized Beds 10 May 2, 2011

2 Outline Examples of flow characteristics Modeling issues Modeling approaches Outlook

3 With so many fine books and software products around, what is there to say? Why model? What to model?

4 Why model? What to model? To bag house fluidized bed Side-by-Side FCC unit Reaction Products Cyclone Regenerator : aeration ports Stripping Steam ir grid Riser-Reactor standpipe riser ir Regenerated Catalyst Standpipe Feed 4 Slide valve Lift-line air What phenomena would we like to understand?

5 To bag house Loop stability fluidized bed Low aeration rate (Stable flow) 0.55 : aeration ports standpipe Slide valve riser Solids volume fraction Time (seconds) Lift-line air Srivastava et al. Powder Tech., 100, 173 (1998)

6 Loop stability To bag house fluidized bed Higher aeration rate (Unstable flow) : aeration ports standpipe riser Slide valve Lift-line air What is the true mechanism for the instability? How does the stability transition change with scale up? Srivastava et al. Powder Tech., 100, 173 (1998)

7 Flow characteristics in the riser To bag house fluidized bed : aeration ports standpipe riser Slide valve Lift-line air How does the flow pattern change with scale up? How fast is the radial dispersion? How effective is the contacting between gas and particles?

8 Competing options Choice depends on: backmixing contacting efficiency attrition, erosion, etc. How do these issues change with scale up? How well can we control them?

9 Jet streaming How well can we predict them? How does such flow behavior change with scale up? Knowlton, et al., Powder Tech., 150, 72 (2005) ttributed to gas compression in deep beds operating at low pressures

10 Cyclone performance Strongly swirling flow aids separation Gas turbulence adversely affects separation Competition between swirl and turbulence? How do particle loading, design choices and throughputs affect this competition?

11 Mechanism and effect of liquid injection on flow Flow characteristics are affected by: gglomeration Gas evolution dapted from Bruhns & Werther, 2005.

12 Mechanism and effect of liquid injection on flow How well do we understand Flow characteristics are affected the local by: and global flows? gglomeration Gas evolution How will these flow structures change upon scale up? dapted from Bruhns & Werther, 2005.

13 Why is it difficult to model and simulate? To bag house fluidized bed Widely varying particle loading levels. s a result, different regimes of flow : aeration ports Need to quantify the physical processes reasonably well in all these regimes standpipe Slide valve riser Flow is invariably unsteady with a wide range of length and time scales. Cannot resolve all of them. Particle size distribution Changing particle characteristics Lift-line air Wet systems: agglomeration and breakup

14 Why model? What models? To bag house fluidized bed Understand physical processes Develop simpler models : eration ports Explore design alternatives Scale up and process retrofits Standpipe Riser Simulations: at the level of a few thousand particles at the device scale Slide valve Lift-line air Euler (fluid) Euler (particles) models Euler (fluid) Lagrange (particles)

15 Solids Fluid Solids Fluid t t ( ρφ ) s t s ( ρφ f f ) t Two fluid model equations ( ρφu ) 0 + = s s s ( ρφ f fu f ) 0 + = ( ) ( ) ( ) ( ) particle Phase stress effective buoyancy ρ φ u + ρ φ u u = σ φ σ + f + ρ φ g s s s s s s s s s f s s inertia interphase interaction gravity ρ φ u + ρ φ u u = φ σ f + ρ φ g f f f f f f f f f f f φ + φ = 1 s f Gas fluidized beds, risers and standpipes: fluid phase stress ~ pressure only

16 Solids Fluid Solids Fluid t t ( ρφ ) s t s ( ρφ f f ) t Two fluid model equations ( ρφu ) 0 + = s s s ( ρφ f fu f ) 0 + = ( ) ( ) ( ) ( ) effective buoyancy ρ φ u + ρ φ u u = σ φ P + f + ρ φ g s s s s s s s s s f s s inertia particle Phase stress interphase interaction gravity ρ φ u + ρ φ u u = φ P f + ρ φ g f f f f f f f f f f f φ + φ = 1 s f Gas fluidized beds, risers and standpipes: interphase interaction ~ drag force only

17 Solids Fluid Solids Fluid t t ( ρφ ) s t s ( ρφ f f ) t Two fluid model equations ( ρφu ) 0 + = s s s ( ρφ f fu f ) 0 + = ( ) ( ) ( ) ( ) effective buoyancy ρ φ u + ρ φ u u = σ φ P + f + ρ φ g s s s s s s s s s f d s s inertia particle Phase stress interphase interaction gravity ρ φ u + ρ φ u u = φ P f + ρ φ g f f f f f f f f f d f f φ + φ = 1 s f Good text book drag force models are available in the literature for nearly homogeneous systems: e.g., Wen and Yu (1966) Wen & Yu, Chem. Eng. Prog. Symp. Ser., 62, 100 (1966)

18 Solids Fluid Solids Fluid t t ( ρφ ) s t s ( ρφ f f ) t Two fluid model equations ( ρφu ) 0 + = s s s ( ρφ f fu f ) 0 + = ( ) ( ) ( ) ( ) effective buoyancy ρ φ u + ρ φ u u = σ φ P + f + ρ φ g s s s s s s s s s f d s s inertia particle Phase stress interphase interaction gravity ρ φ u + ρ φ u u = φ P f + ρ φ g f f f f f f f f f d f f φ + φ = 1 s f force chains at high particle loading binary collisions between particles particle streaming Important in hoppers, bins, standpipes Less so in fluidized beds and risers Even less in freeboard region & cyclones

19 2D Domain size : 64 cm x 64 cm 256 x 256 Fine structure Instability driven by: inertia, dependence of drag force on particle loading level, inelastic collisions 3D Domain size : 8 cm x 8 cm x 8 cm 64x64x64 Stabilized by: weak particle phase stress Weak stabilization small length scale 75 μm particles in air verage particle volume fraction: 0.05 Resolve or not resolve? Simulations performed with MFIX

20 Simple example: turbulent fluidized bed V g = 0; V p = V t Sedimentation of a single particle V g = V t ; V p = 0 Levitation of a single particle V g > V t ; V p =? Vertical conveying of a single particle V g > V t Presence of other particles typically hinder! Bed emptying time for turbulent fluidized beds are much longer than predicted by this model

21 Simple example: turbulent fluidized bed Standard form f homo ( u u ) = β d f s Modified form Bed expansion decreases as one improves resolution * When one does not resolve all the flow structures, one must correct the drag force model O Brien & Syamlal, CFB 4 (1993) Li & Kwauk (1994) EMMS model McKeen & Pugsley (2003) tune cluster size homo ( u u )( 1 ( ) ( φ )) f = β c Δ h d f s Function of resolution Extent of correction depends on chosen resolution *,# * Parmentier et al., ICHE J. (2011); Igci et al., ICHE J. (2010)

22 Newly emerging drag force models ( u u )( 1 ( ) ( φ )) f = β c Δ h d f s homo h ( φ ) 0 as 0 c Δ 1 as Δ Further refinements Parmentier et al. (2011) dynamically adjust c. h 2D Particle volume fraction Igci et al. add wall correction We typically use different grid resolutions when simulating pilot scale and commercial scale units The effective drag law is now different for the two cases! * Parmentier et al., ICHE J. (2011); Igci et al., ICHE J. (2010, 2011)

23 Newly emerging drag force models ( u u )( 1 ( ) ( φ )) f = β c Δ h d f s homo h ( φ ) 0 as 0 c Δ 1 as Δ EMMS model * h 2D Particle volume fraction f homo ( u u )( 1 h ( φ )) = β d f s EMMS * Li & Kwauk (1994)

24 Solids t ( ) ( ) Particle phase stress particle phase stress effective buoyancy ρ φ u + ρ φ u u = σ φ P + f + ρ φ g s s s s s s s s s f d s s inertia interphase interaction gravity Campbell, JFM, 465, 261 (2002); Tardos et al., Powder Technol., 131, 23 (2003): Lois & Carlson, Euro. Phys. Lett., 80, (2007).

25 Discrete Element Method Newton s equations Spring dashpot contact model Open domain (LMMPS * ) + commercial Can include cohesion, liquid bridge, nonspherical shape, size distribution * LMMPS code. Plimpton, J. Comp. Phys., 117, 1 (1995) Cundall & Strack, Geotechnique, 29, 47 (1979); Zhu et al., CES, 63, 5728 (2008).

26 DEM simulations of simple shear flow Scaled Pressure Scaled Shear Stress Quasi static intermediate Quasi static intermediate inertial inertial Scaled shear rate Chialvo et al. (2011).

27 DEM simulations of simple shear flow Quasi static Rescaled Pressure Quasi static Rescaled Shear Stress interme diate intermediate inertial inertial Rescaled shear rate Chialvo et al. (2011).

28 Standpipe flow of FCC particles 0.60 verage solids volume fraction External aeration rate (m 3 /hr) Increasing external aeration unstable Friction s s s u Srivastava et al. Powder Tech., 100, 173 (1998) 0% 12% 24% 36% 48% 60%

29 DEM simulations of simple shear flow Scaled Pressure Do such small Scaled levels Shear of stress Stress matter in fluidized beds and CFBs? They influence the size of the small clusters and streamers When not resolving all the flow structures, one must correct : the drag force model + effective stresses due to fluctuating meso scale structures Chialvo et al. (2011).

30 Coker model simulation Instantaneous Time veraged How to go from scaled down unit to full commercial scale? Traditional keep the same grid size; not practical Remedy: Use larger grids with appropriately scaled constitutive laws Chen et al., pplication of Coarse Grained Drag Law in Computational Fluid Dynamics Simulations of Fluidized 325,000 grids; 32 processors 1 computational day per second of real time Beds, IChE nnual Meeting (2008) Fully cylindrical cold flow model of Syncrude coker 1/19 th scale. Song et al., Powder Tech, 147, 126 (2004).

31 Handling particle size distribution Inherent size distribution Changing particle properties Euler Euler approach Multiple particle phases Method of moments Generalize kinetic theory Generalize drag law Cast the particle phase balance equations in a Lagrangian framework Follow the motion of a few million test particles, referred to as parcels, while treating the remaining (ghost) particles through mean field Multi Phase Particle In Cell method * Much easier to handle particle size distribution and changing particle properties; faster computations * Originally derived directly from a probabilistic approach: D.M. Snider, J. Comp. Phys., 170, 523 (2001)

32 ρ v Discrete Particle Model pproach du v = σ v σ p p p p s p f dt φ s Effective buoyancy particle phase stress + ρ v g weight vp f φ { s p p d all other fluid-particle interactions What are the right drag law and effective stresses to use when all flow structures are not resolved? Particle phase stress term captures the effects of all collisions No need to track collisions between parcels Different parcels can have different underlying particle size, property, etc. Parcels can be allowed to interact in the mean: mimic kinetic theory, transfer liquids, etc. Snider, J. Comp. Phys., 170, 523 (2001); O Rourke & Snider, CES, 65, 6014 (2010); O Rourke et al., CES, 64, 1784 (2009).

33 CPFD Simulation of a Settler Courtesy: Dale Snider & Ken Williams, CPFD Software, LLC.

34 ρ v Discrete Particle Model pproach d u v = σ v σ p p p p p s p f dt φ s Effective buoyancy particle phase stress + ρ v g weight vp f φ { s p p d all other fluid-particle interactions If parcel size = particle size: Track all collisions CFD DEM * MP PIC: Particle phase stress term captures the effects of all collisions No need to track collisions between parcels What if we track collisions between parcels? # Pretty well in quasi static regime Much less accurately in the inertial regime # Patankar & Joseph, IJMF, 27, 1659 (2001); # Benyahia & Galvin, IECR, 49, (2010); * Chu et al., CES, 66, 834 (2011)

35 U r p,0 Discrete Particle Model with Collision Tracking y x particle reservoir (d p, φ p ) R sample y jet D tar Pros and cons for tracking collisions between parcels? Still evolving Compare scattering angles predicted with experimental data Cheng et al., PRL, 99, (2007); Radl et al. (2011)

36 Verification vs. Validation Can the simulator correctly reproduce analytically obtainable results for some test problems? Can the independence of the predictions to simulator parameters be ascertained? Grid size, parcel size, etc. Model vs. model: CFD DEM, Euler Euler, MP PIC, etc. Begin with a kinetic theory based Euler Euler model and filter to obtain a coarse grained Euler Euler model Show that both model yield the same solution Comparison against experimental data Many early validation studies were based on 2D simulations Quantitative differences between 2D and 3D Often validation are with data in pilot scale units with some tuning How do we know that the same tuning will work for larger scale where we will have coarser grid resolution?

37 Things to consider in validation Comparison against experimental data at a minimum of two different scales Flow regime maps covering turbulent to fast fluidization Good data base for riser flows: Vary gas flux while holding solids flux constant Vary solids flux while holding gas flux constant Good database for standpipes are needed as well

38 Outlook More and more 3D simulations of the full CFB loop GPU based computing Standpipe flows: detailed experimental characterization and validation of simulations more needed Both Euler Euler and Euler Lagrange will continue to develop; but, Euler Lagrange approach (Parcel based: with or without collision tracking) is very likely to gain more traction: Ease of handling PSD and changing particle properties How to adapt the ideas on microscale modeling (such as kinetic theory) and coarse simulations developed for Euler Euler approach to the discrete methods fertile topic Carbon capture, chemical looping, methanol to olefin More and more effort on wet systems + More case studies on reacting flows Old, but still very relevant problems