Sreekanth Pannala Computational Mathematics Computer Science and Mathematics Division

1. Micro-Mesoscopic Modeling of Heterogeneous Chemically Reacting Flows (MMMHCRF) over Catalytic/Solid Surfaces Sreekanth Pannala Computational MathematicsComputer Science and Mathematics Division

2. The team Oak RidgeNationalLaboratory National Energy Technology Laboratory Ames LaboratoryIowa State University Universityof Arizona Sreekanth Pannala Srdjan Simunovic StuartDaw PhaniNukala Rodney Fox Zhaoseng Gao George Frantziskonis SudibMishra PierreDeymier Krishna Muralidharan Thomas O’Brien DominicAlfonso MadhavaSyamlal

3. Goal Develop a multiphysics and multiscale mathematics framework for accurate modeling of heterogeneous reactingflows over catalytic surfaces

4. DFT: ~1 nm Flow over a catalyst surface • Chemically reactive flow over a surface is a basic building block that is central to many energy-related applications • Illustrative benchmark to demonstrate the capabilityto integrate scales of several orders of magnitude KMC: ~1 m LBM: ~1 mm Lattice Boltzmann (LBM) Kinetic Monte Carlo (KMC) Density Functional Theory (DFT) Closelycoupled Reactionbarriers Figure adapted from Succi et al., Computing in Science and Engineering, 3(6), 26, 2001

5. Approach: KMC–LBM couplingthrough Compound Wavelet Matrix y x-y y KMC contribution LBM viqi T x Compound Wavelet Matrix (CWM) x LBM contribution t viqi • Construct a CWM from LBM and KMC • Use CWM for coupling of mesoscopic and microscopic simulations in time and space • Use a Multiple Time Stepping (MTS) algorithm for higher-order accuracy in time • Use fractal projection to map the surface topographical information to constructthe KMC in one less dimension KMC x Fractalprojection Actualsurface x

6. CWM methodology in work:Transferring information from KMC to LBM Wavelettransformation Micro-informationKMC Homogenized properties at next scale Homogenization at the level correspondingto LBM, feedingfrom KMC to LBM Homogenized properties at next scale Increasing spatial or temporal scales

7. Recent results* • 1-D reaction/diffusion simulation performedat two different length and time scales: • Fine (KMC and diffusion equation using finite differenceat fine scale) • Coarse (analytical species solution and diffusion equationusing finite difference at coarse scale) • Pseudo-2-D reaction diffusion multiscale simulations with error analysis • A dynamic CWM implementation for non-stationary processes • Reconstructed the fine simulation results to reasonable accuracy using CWM at fraction of cost • Method allows for bi-directional transfer of information, i.e., upscaling and downscaling *Frantziskonis et al., International Journal for Multiscale Computational Engineering, 5-6, 755, 2006 Mishra et al. (SIAM J. of Sci. Comp. – under review), Muralidharan et al. (Phy. Rev. E – under review)

8. Example 1: 1-D reaction diffusionsystem* 100 50 50 80 CWMreconstruction 40 40 Transferring mean field Transferring mean field Coarse Species concentration A(0,t) 60 30 30 A(0,t) 20 20 40 Fine 10 10 0 0 20 100 100 200 200 300 300 400 400 Time, t 0 20 40 60 80 100 120 50 Time, t Transferring fine-scale statistics 40 30 A(0,t) • Successfully applied CWM strategyfor coupling reaction/diffusion system • A unique, rigorous, and powerful way to bridge temporal and spatial scales for multiphysics/multiscale simulations 20 10 0 25 500 100 200 Time, t *Frantziskonis et al., International Journal for Multiscale Computational Engineering, 5-6, 755, 2006

9. Example 2: 2-D diffusion with reacting boundary plane Fine Fine Coarse Coarse Evolution of reactants A and B

10. 45 45 (a) (b) T = 1 O = 5 T = 1 O = 5 30 30 T=2 O=2 T=1 O=5 T = 2 O = 2 CB CB 15 15 CWM solution Coarse solution 0 0 0 1.5 3.0 4.5 0 1 2 3 4 Time (s) Time (s) 45 (c) T = 1 O = 5 30 T = 2 O = 2 T = 3 O = 5 T=3 O=5 CB 15 0 0 1 2 3 4 Time (s) Example 2: 2-D diffusion with reacting boundary plane Reconstructed species profile (effect of overlap and thresholding)

11. Example 2: 2-D diffusion with reacting boundary plane 0.20 0.20 Diffusion Error CWM Error Diffusion Error 0.15 0.15 Relative Error, e(n) Relative Error, e(n) 0.10 0.10 0.05 0.05 (b) 0 0 1 2 3 4 5 1 2 3 4 5 Number of Overlap Scales, n Number of Overlap Scales, n The error is dominated by the discretization errors in solving the diffusion equation

12. Dynamic CWM (dCWM): Dynamic coupling of coarse and fine methods • Coupling of the dynamics of both coarse and fine methods for non-stationary problems (similar to gap-tooth method) • Better exploration of phase-space due to inclusion of stochasticity from fast scales • Long-term behavior feedback to fast scales from coarse representation coarse Nc CWM Cn fine Nf 1≤ n ≤ N (iterations)

13. Example 3: 1-D diffusion withreacting boundary plane with dCWM Nc = 16384; Nf = 2048; N = 8 2500 compound coarse compound 2000 1500 CA coarse 1000 500 0 0 50 100 150 200 250 Time (non-dimensional units)

14. Example 3: 1-D diffusion with reacting doundary plane with dCWM Nc = 16384; Nf = 2048; N = 8 140 130 compound 120 Mean Trajectory 110 100 CA 90 80 70 60 50 50 100 150 200 Time (non-dimensional units) dCWM is able to capture the later-time fluctuations in the mean trajectory when there is competition between diffusion and reaction processes

15. Work in progress: Reactive boundary with LBM • Chemical reactions in the flow are represented by mass source on RHS • Development of new boundary conditions for reactive boundary: • Transport from bulk fluid to boundary (flux/Neumann) • Reaction (concentration/Dirichlet) • Transport from boundary to bulk fluid (flux/Neumann) • Reactive term must reproduce correct density change rates for reactants, and total heat/release absorption per surface area • Development of new combined flow-species transport with non-reflecting boundary conditions (absorbing layer, extrapolation method)

16. Applications • Fibrous substrate for discontinuous fiber substrate • The voids found by probing the substratewith a fixed-size sphere are denoted by spheres a a a  r b p radiation z z Coal particle Gas phase Schematic of burning of coalparticle using laser heating in microgravity environment showingthe various regimes of combustion[Wendt et al.; Proc. Combust. Inst., 29, 449 (2002)] Gas flow in the char Pyrolysis front Not yet reacted coal

17. Additional applications:Nuclear fuel coating process Spouted bed coater (device scale) Coated fuel particle (small scale) • Design challenge:Maintain optimal temperatures, species, residence times in each zone to attain right microstructureof coating layersat nm scale • Truly multiscale problem: ~O(13) time scales~O(8) length scales ~10-1 m Amorphous C Si-C Ballistic zone Kernel UO2 Inner Pyrolitic C Transportreaction zone (~10-6-10-2s) ~10-3 m Hopperflowzone (~s) Pickup zone (~10-6-10-2s) Pickup zone (~10-6-10-2s) ~10-3 m Links multiscale mathematicswith petascale computingand GNEP • 0.5- to 1-mm particles • Coating encapsulatesfission products • Failure rate < 1 in 105 • Quality depends on surface processes at nm length scale and ns time scales Inlet gas • Coating at high temperature (1300–1500°C) in batch spouted bed reactor for ~104 s • Particles cycle thru deposition and annealing zones where complex chemistry occurs

18. Going forward • Generalize the process of constructing the CWM in the overlapping scales • Energy matching • Smooth variation of cross-correlation across the bridging scales • Invoke conservation laws? • Thermal LBM with chemistry • LBM coupled with KMC and CWM • Coarsening of KMC in space • MTS comparison to dCWM for time coupling • Application to NiO system and other realistic systems • Parallel framework to couple multiphysics code • Will be released as open source on completion • Advertise to have other groups (applied math and computational scientists) involved to make additional improvements 18 Pannala_MM_0611

19. Contacts Sreekanth Pannala Computational MathematicsComputer Science and Mathematics Division(865) 574-3129pannalas@ornl.gov Srdjan Simunovic Computational Materials Computer Science and Mathematics Division(865) 241-3863simunovics@ornl.gov 19 Pannala_MM_SC07