experiments and model development for polydisperse, gas ...€¦ · ibm-based model for...

Experiments and Model Development forPolydisperse, Gas-fluidized Systems

NETL 2010 Workshop on Multiphase Flow Science4 May 2010

Pittsburgh, PA

S. TennetiR. GargShankar Subramaniam

Jia-Wei ChewR. Brent RiceChristine M. Hrenya

Vicente Garzó

Project Scope: Work Breakdown Structure Development, Verification, and Validation of Multiphase Models for Polydisperse Flows

TheoryDevelopment

DataCollection

ModelValidation

ProgramManagement Deliverables

1. Solid-PhaseContinuum

Theory

2. Gas-SolidDrag

3. Gas-PhaseTurbulence

Simulations

Experiments

4.1 DEM (solids)

4.2 Eulerian-DEM (gas-solid)

4.3 Low-velocity fluidized bed

4.4 Cluster Probe Development

1.1 Kinetic Theory

1.2 DQMOM

1.3 Incorporation of KT and DQMOM into MFIX

1.4 KT extension to multiphase

2.1 LBM/DTIBM: zero-mean vel.

2.2 LBM/DTIBM: non-zero rel. vel.

2.3 LBM/DTIBM: freely evolving

3.1 Polydisperse DNS

3.2 Multiphase Turb. Model

4.5 High-velocity fluidized bed (PSRI)

4.6.1 Compare with DEM data (4.1) and low-velocity bed (4.3)

4.6.2 Liaison to NETL riser data

4.6.3 Compare with high- velocity data from Eulerian-DEM (4.2), PSRI (4.5), and NETL (4.6.2)

5.1 DevelopManagement Plan

Monthly email updates

Quarterly reports

Annual reports

Final report

ApproachScopeCost EstimatesScheduleRiskConstraintsAssumptionsCommunication

New theory into MFIX

Univ. Colorado Tasks for Year 3

Validation data1) Bubbling-bed experiments (Colorado)

2) DEM simulations of simple shear (Colorado)

3) Riser experiments (Colorado & PSRI)Ray Cocco (PSRI) – Thursday

Theory4) Application of polydisperse kinetic theory to clustering

(Princeton & NETL & Colorado)Bill Holloway (Princeton) - Tuesday

5) Kinetic Theory Extension to Gas-Solid Flows (Colorado & Iowa State)

Overview: Bubbling Bed Experiments

ObjectiveTo characterize segregation and bubbling behavior of bubbling beds with continuous size distributions• Do continuous PSD’s behave like binary mixtures?• Is there a direct link between the segregation and bubbling levels?

System

Measurements: Segregation and Bubbling

Segregation: sieving of thin vertical sections1. High velocity (3 Ucf) to mix bed2. Low velocity (1.2 Ucf) for segregation3. Shut down, vacuum sections, sieve

Bubbling: fiber optic probe1. 7 axial x 9 radial positions2. Bubble frequency, velocity & size

Continuous PSD’s Investigated

Width of distribution: σ/dave (%)

Material: sand

Gaussian lognormal

Results: Segregation

scont = 0 perfect mixingscont = 1 perfect segregation

scont =S −1

Smax −1

Smax =2xlarge + xsmall

xlarge

S = < hsmall >< hlarge >

perfectly mixed

Gaussian: as PSD width increases ↑, segregation ↑lognormal: non-monotonic variation of segregation with PSD width

Chew, Wolz & Hrenya, AIChE J (in press)

Results: Bubbling

Gaussian lognormal

Gaussian: as PSD width increases ↑, all bubble parameters ↑ (some not shown)lognormal: same as Gaussian (monotonic variation)

Chew & Hrenya, I&ECR (submitted)

Reconciliation: Segregation and Bubbling Measurements

Explanation• presence of bubble-less layer in some systems• size of bubble-less layer correlates with degree of segregation

Gaussian lognormal

Objective

Assess the impact of polydispersity on clustering in granular flows• How does polydispersity affect the prominence of clusters?• Does species segregation occur in a transient cluster?

System: Simple Shear Flow

Approach: MD simulations

MD Simulations

Simulation Description• 2D, event-driven• Inelastic, frictionless, hard disks• Size distributions: binary, Gaussian, lognormal

Concentration mapping

Resulting Quantities: νclus νdil Tclus TdilνL,clus νL,dil TL,clus TL,dil

νavg = 0.2 Cluster Region: ν > νavgDilute Region: ν > νavg

Greater Conc. DifferenceIncreased Prominence

Lesser Conc. Difference

Decreased Prominence

0.4 0.5 0.57

0.9 0.95

Cluster prominence greater for systems with more than

one species

Tendency increases with deviation from

monodisperse limit

Results: Cluster Prominence

binary

GaussianLognormal

Results: Cluster Prominence

binary continuous

Cluster prominence greater for systems with more than

one species

Tendency increases with deviation from

monodisperse limit

Rice & Hrenya Phys. Rev. E (2010)

Large Particles segregate preferentially toward the

clustered regions

Tendency increases with increasing size disparity

Results: Species Segregation

binary


0.4 0.5 0.57

0.9 0.95

Greater Conc. DifferenceGreater Species Segregation

Lesser Conc. Difference

Less Species Segregation

GaussianLognormal

Large Particles segregate preferentially toward the

clustered regions

Tendency increases with increasing size disparity

Results: Species Segregation

binary continuous


Modeling of Gas-solid Flows

Continuum (“Two-fluid”) Description• Gas phase: Navier-Stokes + turbulence + drag force• Solids phase: Kinetic-theory-based models + fluid-phase interactions

Current Objective: Incorporation of gas-phase (drag) effects intokinetic-theory-based models for solid phase

new termsmodifications to kinetic-theory closures

Physical Picture

Recall fluid-solid interaction force (drag force)

Mean fluid force on single particle

Velocity & pressure fields (& thus fluid force) change with:

• Fluctuations in particle velocity• Fluctuations in gas velocity

Mean vs. Instantaneous Fluid Force

( )2

2

0 0

cos sinfluid n t r RF F F p R d dπ π

θ θ θ φ=

= + = −∫ ∫

( )2

2

0 0

sin sinr r R R d dπ π

θτ θ θ θ φ=+ ∫ ∫

U

Ug

( )fluid gF f U U= −

= f (velocity & pressureat surface) pressure field

U

Incorporation of Instantaneous Fluid Force

Alternative 1: DEM (solids) /DNS (fluid) – resolve flow field around particles+ fluid force is “output”- too computationally expensive

(no-slip BC at each moving particle surface)

Alternative 2: Two-fluid model – “averaged” flow field over several particles+ computationally feasible (single equation of motion for each phase)- fluid effects are “input” – model is needed to subsume instantaneous effects

Q1: Impact on governing equations (additional terms)?

Q2: Impact on constitutive relations for solid phase (P, q, ζ )?

Current Approach(i) use DEM/DNS simulations to develop model for instantaneous force(ii) incorporate this force model into starting kinetic equation & derive

hydrodynamic description

More details…

Basic Idea: Incorporation of fluid force into Enskog kinetic equation

DEM/DNS technique for closure: IBM (Immersed Boundary Method)based model of Ffluid,i as function of:- Hydrodynamic variables: φ, Ui, T, Ugi- Physical parameters: m, d, α, µg , ρg

,fluid ii i

i i i

Fff v g f Jt x v m v

∂ ∂ ∂ ∂+ + + = ∂ ∂ ∂ ∂

instantaneous fluid forceon single particle

gravity collisionsconvectivetransient

IBM-based model for acceleration

Use IBM simulations to find β∗, γij∗, and Bij∗ as functions of • φ solids volume fraction • ρs/ρf density ratio

• particle Re based on mean flow

• particle Re based on particle velocity fluctuations

( ), 1fluid i i i giIBM i ijj jjF

A BU U V dWm m m

β γ= = − − − −

instantaneous particle acceleration

meanparticle velocity

mean gas

velocity

fluctuatingparticlevelocity

Wiener process increment(stochastic model for fluctuating

fluid velocity)

coefficients extractedfrom IBM simulations

( )1 gm

g

dRe

φ ρ

µ

−= g

U - U

g

T

g

dRe

Tm

ρ

µ=

Resulting Hydrodynamic Description

Balance Equations (Solid-Phase Momentum & Granular Energy)

Explicit Constitutive relations obtained for ζ, P, and q:

• Cooling rate• Cooling rate TC• Shear viscosity• Bulk viscosity• Conductivity• Dufour coefficient

( )1 Mt gIBD mn mβ

+ ∇ = − − +U U UP g

( )2 23 3 3k

t ij j ij ij iji ijD T P U T P nB

nBρ

ργζ+ ∇ ⋅ + ∇ = − − +q

sink due to viscous drag

mean drag

source due to fluid-particlefluctuations

( )(0) (0) ijBζ ζ=

( ),ij ijBη η γ=( )ijBλ λ=( ),ij ijBκ κ γ=( ),ij ijBµ µ γ=

( ),U U ij ijBζ ζ γ=

Base Case: Massive Particles (St>>1) and Stokes flow (Rem

1500 2000 2500

1.010

1.015

1.020

Shear Viscosity

0.0 0.1 0.2 0.3 0.4 0.51.00

1.02

1.04

1.06

1.08

y f

η /ηdry

ρs / ρf

φ

η /ηdry

ReM = 0.1ReT = 0.5φ = 0.2

ReM = 0.1ReT = 0.5ρs/ρf = 1000

α

α

Dufour Coefficient

1500 2000 2500

1.4

1.6

1.8

2.0

2.2f

0.1 0.2 0.3 0.4 0.51.5

2.0

2.5

ReM = 0.1ReT = 0.5ρs/ρf = 1000

ReM = 0.1ReT = 0.5φ = 0.2

µ / µ dry

ρs / ρf

φ

µ / µ dry

α

α

Summary

IBM-based model for instantaneous fluid acceleration has been incorporated into Enskog equation, and corresponding hydrodynamic description derived

• Additional source/sink in momentum and granular energy balances

• Modification of constitutive closures- For limiting case of Rem >1: non-negligible gas-

phase influence on shear viscosity and Dufour coefficient

• Framework extendible to non-limiting cases once IBM coefficients are extracted (coming soon…)

Experiments and Model Development for�Polydisperse, Gas-fluidized SystemsProject Scope: Work Breakdown StructureUniv. Colorado Tasks for Year 3Univ. Colorado Tasks for Year 3Overview: Bubbling Bed ExperimentsMeasurements: Segregation and BubblingContinuous PSD’s InvestigatedResults: SegregationResults: BubblingReconciliation: Segregation and Bubbling MeasurementsUniv. Colorado Tasks for Year 3ObjectiveMD SimulationsResults: Cluster ProminenceResults: Cluster ProminenceResults: Species SegregationResults: Species SegregationUniv. Colorado Tasks for Year 3Modeling of Gas-solid FlowsPhysical PictureIncorporation of Instantaneous Fluid ForceMore details…IBM-based model for acceleration Resulting Hydrodynamic DescriptionBase Case: Massive Particles (St>>1) and Stokes flow (Rem

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