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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

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National Energy Technology Lab.

US Bureau of Mines---> Albany Metallurgy Research Center ---> Albany Research Center---> Now, NETL-Albany.

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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

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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

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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

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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

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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

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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

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Particulate Flow ModelingFully 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 resolved

Subgrid

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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

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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)

Ωg

Ωp

Ωp

Ω =Ωg ∪Ωp

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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

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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

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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

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Verification Studies for Fully Resolved Simulation (FRS)

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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

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Flow Over a Fixed Sphere

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Flow Over a Fixed Sphere

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Flow Over an Oscillating Sphere

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Freely Falling Sphere

Experiments byTen Cate et al. (PoF 2005)

t=0.15 s t=0.6 s t=0.96 s

Velocity Magnitude

Grid: 100x100x160Time Step:0.75 ms

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Freely Falling Sphere

Experiments byTen Cate et al. (PoF 2005)

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Wake Interactions(Drafting-Kissing-Tumbling)

Same density particles

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Wake Interactions

Density ratio ~1.5

Heavy particle

Rep~100

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Can We Simulate Large Number of Particles?

- Overhead ~ 20%

- Simulations of 10,000 particles may require around 10 million grid points

0%

10%

20%

30%

40%

50%

60%

ParticleTracking

Rigid MotionComputation

Collisions MomentumSolve

PressureSolve

Time

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Subgrid Particles

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Mixture theory based formulation [Joseph and Lundgren, 1990]

Continuum phase: Eulerian; Dispersed Phase: Lagrangian

Continuity

Locally non-zero divergence fieldMomentum

Interphase interaction force

Subgrid Particles (LES-DEM)

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Mixture theory based formulation [Joseph and Lundgren, 1990]

Continuum phase: Eulerian; Dispersed Phase: Lagrangian

Subgrid Particles (LES-DEM)

Time scales

Based on a drag modelFlow around particle not resolved

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Search Path

Droplet CV Centroid

Initial Final

• 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

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Performance of Search Algorithm

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• Experiments by Sommerfeld et al. (1991)

Gas Phase (Air) Particle Phase (Glass)

Flow rate in primary jet, g/s 9.9 Loading ratio in primary jet 0.034

Flow rate in secondary jet, g/s

38.3 Flow rate, g/s 0.34

Inlet Reynolds number 26200 Density ratio 2152

Swirl number 0.47 Length scale, m 0.032

Particle-laden Swirling Flow

Dilute Loading (particle-particle interactions negligible)

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• 1.6 million total hexahedral cells; nearly 1.2 million cells in region of interest

ConvectiveBoundary conditionConvective

BoundaryCondition

Particle-laden Swirling Flow

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Coaxial combustor: Re=26,200

Apte et al, IJMF 2003

Particle-laden Swirling Flow

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• Gas Phase StatisticsApte 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

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• 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

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Densely Loaded RegionsOngoing 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.

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Gravitational SettlingParticle Evolution

Apte et al, IJMF 2008

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Rayleigh-Taylor Instability(preliminary study)

Particle void fraction Particle Evolution