1. 1 Multiscale Simulations and Modeling of Particulate Flows in Oxycoal Reactors Sourabh Apte Department of Mechanical Engineering Funding: DoE National Energy Technology Laboratory A Cihonski, M. Martin, E. Shams, J. Finn

2. 2 National Energy Technology Lab. US Bureau of Mines---> Albany Metallurgy Research Center ---> Albany Research Center---> Now, NETL-Albany.

3. 3 Oxy-Coal Reactors Pulverized coal combustion in recirculated mixture of flue gas and oxygen (oxygen rich environment) Nitrogen depleted environment eliminates NOx Completion of combustion leading to products rich in water vapor and CO2 Reduced CO and flue gases means efficient control of emissions Need for carbon capture and sequestration O2 enriched environments lead to increased reactor temperatures and thermal effects Cost of production of pure O2 could be high

4. 4 Combustion/Gasification Hybrid Flue gases from coal gasifier linked with a combustor Char from gasification burned in a Fluidized Bed for steam http://fossil.energy.gov/programs/powersystems/combustion/combustion_hybridschematic.html

5. 5 Modeling Needs Multiphase, multiple species, multicomponent heat transfer and turbulent flow problem Multiple spatio-temporal scales Particle-turbulence interactions Coal volatization Turbulent combustion Modeling of ash, soot particles Complex geometry Radiative heat transfer through participating media Burnout => Metals

6. 6 Modeling Needs: Particulate Flows Grace et al. Dilute and dense clusters of coal particles Arbitrary shapes Particle dispersion and interactions with turbulence Particle-particle interactions, preferential concentrations and structure formation Spatio-temporal variations in solid volume fractions Detailed experimental data for validation

7. 7 Modeling Challenges: Particulate Flows Grid Based Classification Fully Resolved: particles larger than the grid Sub-grid: particles smaller than the grid resolution Partially resolved: particles resolved in one or more directions and under- resolved in others Temporally evolving regions Physics-Based Classification Particle size smaller than smallest resolved scale (Kolmogorov scale for DNS or filter size for LES) Particle size comparable to energetic eddies

8. 8 Simulation Techniques: Particulate Flows Van der Hoeff et al. Annual Review of Fluid Mechanics, 2008 Resolved Bubbles Two-Fluid Under-resolved discrete particle Resolved Particles Molecular Dynamics

9. 9 Particulate Flow Modeling Fully Resolved Direct Numerical Simulation Develop an efficient approach for fully resolved simulation (FRS) of particle-laden turbulent flows (heavier-than fluid particles) Apply FRS to study interactions of sedimenting particles with turbulent flow and quantify drag and lift correlations in “inhomogeneous” clusters Large-eddy Simulation (LES) with under-resolved particle dynamics Develop an efficient approach for LES of turbulent flows with dense particle-laden flows with Discrete Element Modeling (DEM) Apply LES-DEM to investigate particle-turbulent interactions in realistic oxycoal reactors. Further advance LES-DEM for turbulent reacting flows Fully resolvedSubgrid

10. 10 Background Resolved Simulations of Particle-Laden Flows  Arbitrary Lagrangian Eulerian Schemes (ALE) ( Hirt, Hu et al.)  Fictitious Domain Method ( Glowinski, Hu, Patankar, Minev )  Overset Grids ( Burton )  Lattice-Boltzmann ( Ladd, ten Cate etal.)  Immersed Boundary Methods ( Peskin, Ulhmann, Mittal )  Immersed Boundary with Spectral Model ( PHYSALIS: Prosperetti )  Immersed Boundary + Lattice Boltzmann ( Proteus: Michaelides )  …. None show simulations with large density ratios (particle-air~ 2000) Fully resolved

11. 11 Fictitious-Domain Based Approach - Fixed background grid (structured or unstructured) - Particle sizes are assumed larger than grid resolutions - Assume the entire domain (even the particle regions) filled with a fluid - Solve Navier-Stokes over the entire domain (finite volume) - Impose additional constraints obtained from restricting the particle domain to undergo rigid body motion (translation and rotation)

12. 12 Algorithm - Define material points/volumes within the particle domain - Use color functions to identify particle domain (volume fraction) - Use conservative kernels (second order) for interpolation of all quantities between material volumes and grid CVs (Roma et al.) - Compute density using the color function

13. 13 Fractional Time-Stepping for Rigidity Constraint Momentum equation over entire domain Solve variable coefficient Poisson equation to enforce divergence-free constraint Reconstruct pressure gradient and update velocity fields

14. 14 Fractional Time-Stepping for Rigidity Constraint Patankar (2001) Apte et al. (JCP, 2008 under review) Rigid body motion and rigidity constraint Enforce rigidity constraint Compute rigidity constraint force Advance particle positions and repeat Requires interpolations from grid to particles

15. 15 Verification Studies for Fully Resolved Simulation (FRS)

16. 16 Taylor Problem - Stationary, decaying vortices - A rotating rigid body (cube) - Initial condition (velocity & pressure) and velocity at material points specified Error in pressure Error in velocity

17. 17 Flow Over a Fixed Sphere

18. 18 Flow Over a Fixed Sphere

19. 19 Flow Over an Oscillating Sphere

20. 20 Freely Falling Sphere Experiments by Ten Cate et al. (PoF 2005) t=0.15 st=0.6 st=0.96 s Velocity Magnitude Grid: 100x100x160 Time Step:0.75 ms

21. 21 Freely Falling Sphere Experiments by Ten Cate et al. (PoF 2005)

22. 22 Wake Interactions (Drafting-Kissing-Tumbling) Same density particles

23. 23 Wake Interactions Density ratio ~1.5 Heavy particle Re p ~100

24. 24 Decaying Isotropic Turbulence cubesspheres 96x96x96, 10 cvs per particle 125 particles,  p/  f = 9,  = 0.05 Re ~ 30 St ~ 5, 64 proc. Approx. 6 sec per time-step

25. 25 Isotropic Turbulence time KE fluid particle

26. 26 Can We Simulate Large Number of Particles? - Overhead ~ 20% - Simulations of 10,000 particles may require around 10 million grid points

27. 27 Subgrid Particles

28. 28 Mixture theory based formulation [Joseph and Lundgren, 1990] Continuum phase: Eulerian; Dispersed Phase: Lagrangian Continuity Locally non-zero divergence field Momentum Interphase interaction force Subgrid Particles (LES-DEM)

29. 29 Mixture theory based formulation [Joseph and Lundgren, 1990] Continuum phase: Eulerian; Dispersed Phase: Lagrangian Subgrid Particles (LES-DEM) Time scales Based on a drag model Flow around particle not resolved

30. 30 Search Path DropletCV Centroid InitialFinal Criterion for Locating – Compare face-normal vectors Brute Force – Compute Minimum Distance of Droplet from CV Centroids – Search CV and Neighbors to Locate Droplet Known Vicinity Algorithm: Neighbor to Neighbor Search Lohner, R. (JCP, Vol. 118, 1995) – Requires Good Guess of Initial Location of Droplet – Search in the Direction of Particle Motion – Most Efficient if Particle Located in < 10-15 attempts – Scalar in Nature n Searching and Locating Particles

31. 31 Performance of Search Algorithm

32. 32 Experiments by Sommerfeld et al. (1991) Gas Phase (Air)Particle Phase (Glass) Flow rate in primary jet, g/s9.9Loading ratio in primary jet0.034 Flow rate in secondary jet, g/s38.3Flow rate, g/s0.34 Inlet Reynolds number26200Density ratio2152 Swirl number0.47Length scale, m0.032 Particle-laden Swirling Flow Dilute Loading (particle-particle interactions negligible)

33. 33 1.6 million total hexahedral cells; nearly 1.2 million cells in region of interest Convective Boundary condition Convective Boundary Condition Particle-laden Swirling Flow

34. 34 Coaxial combustor: Re=26,200 Apte et al, IJMF 2003 Particle-laden Swirling Flow

35. 35 Gas Phase Statistics Apte et al, IJMF 2003 Mean Axial Velocity Mean Swirl Velocity Mean Radial Velocity RMS of Axial Velocity RMS of Radial Velocity RMS of Swirl Velocity Particle-laden Swirling Flow

36. 36 Particle Statistics Apte et al, IJMF 2003 Mean Radial Velocity RMS of Radial Velocity Mean Swirl Velocity RMS of Swirl Velocity Mean Particle Diameter RMS of Particle Diameter Mean Axial Velocity RMS of Axial Velocity Particle-laden Swirling Flow

37. 37 Densely Loaded Regions Ongoing Developments Issues: Need to model inter-particle interactions Models for collision Load imbalance (only few processors have particles) leading to loss of computing efficiency - Sparse block grid - Partition particles on a simple Cartesian mesh (boxes) - Redistribute boxes among processors to “balance load” - Solve particle equations and advance particle locations (searching and locating simple as Cartesian boxes) - Transfer particles to appropriate processors partitioned based on the unstructured grid (Octree searches) - Compute particle-fluid interactions forces - Solve fluid equations.

38. 38 Gravitational Settling Particle Evolution Apte et al, IJMF 2008

39. 39 Rayleigh-Taylor Instability (preliminary study) Particle void fraction Particle Evolution