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MULTI-SCALE MODELING OF DENSE

PARTICLE-LADEN FLOWS

J.A.M. KUIPERS

M.A. VAN DER HOEF

M. VAN SINT ANNALAND

N.G. DEEN

EINDHOVEN UNIVERSITY OF TECHNOLOGY

FACULTY OF CHEMICAL ENGINEERING AND CHEMISTRY

MULTIPHASE REACTORS GROUP

THE NETHERLANDS

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DENSE GAS-PARTICLE FLOWS

shifting sands (Tanzania)

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clusters in co-current vertical gas-solid flows

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clusters in co-current vertical gas-solid flows

e = 1.0

µ = 0.0

e = 0.96

µ = 0.24

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fluidized bed family of gas-solid contactors

1: bubbling bed

2: turbulent bed

3: circulating bed

4: riser

5: downer

6: lateral staged bed

7: vertical staged bed

8: spouted bed

9: floating bed 10: twin bed

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POLY-DISPERSE DENSE GAS-PARTICLE FLOWS

fluidized bed spray granulation

Prof. Stefan Heinrich (TUHH)

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DENSE GAS-PARTICLE FLOWS & MODELLING

• GAS-PARTICLE SYSTEMS

+ very broad range of applications and related equipment geometries

+ occurence of both dilute and dense particle-laden flows (poly-disperse)

+ display a great variety of (very complex) flow structures

+ flows are inherently unsteady (bubbles, clusters)

• IMPLICATIONS FOR MODELLING

+ development of a single universal model far to ambitious (irrealistic)

+ multi scale approach is appropriate

+ closures for gas-particle and particle-particle interaction required

+ model should account for the transient nature of the flow

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MULTI-SCALE MODELLING

Van der Hoef et al., Annu. Rev. Fluid M., 2008

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MULTI-SCALE MODELLING

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LATTICE BOLTZMANN MODEL

• BASIC FEATURES

+ fictitious particles propagate in a three-dimensional (3D) lattice and

collide at surface of real particles (or walls): momentum exchange

+ particle-particle collisions can be accounted for (hard sphere model)

• ADVANTAGES

+ all details of the flow field are obtained: drag closure is computed

• DISADVANTAGES

+ number of particles is (very) limited (CPU limitations)

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RESULTS OF LATTICE BOLTZMANN MODEL

static array of bi-disperse particles at low Re p

example of initial particle

configuration for

a bi-disperse system

generated with a

Monte Carlo procedure

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static array of bi-disperse particles at low Re p

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static array of particles with log-normal PSD

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static array of particles with log-normal PSD

Re=0.1 Re=500

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final drag closure for mono-disperse and poly-disperse particles

good fit (deviation less then 8%) of basic LB simulation data

generated over wide range of εg and Re

strictly valid for homogeneous arrays of particles

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IB-DP MODEL

• FEATURES

+ Eulerian grid and Lagrangian force points on solid boundaries

• ADVANTAGES

+ all details of continuous phase flow field are captured

+ arbitrary shape of solid particles can be accounted for

• DISADVANTAGES

+ IB-DP simulations are CPU-demanding (especially in 3D)

+ limited to relatively small number of solid bodies (typically 103)

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RESULTS OF IB-DP MODEL

single and simple cubic array of particles (3D)

Re p=100 Re p=1

1003 Eulerian grid

N=(d p/h)=20

Dimensionless drag

F=10.9 (computed)

F=10.2 (analytical)

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fluidization of 1296 spherical particles (3D)

Fluid phase Density 1216 kg/m3

Viscosity 0.1 kg/(m.s)

Solid phase

Density 8000 kg/m3

Particle diameter 0.005 m

Collision parameters 0.9, 0.3, 0.10 (-)

U mf 1.2 cm/s

U t 40 cm/s

U 0 8.0 cm/s

Grid 400x12x800 (-)

Grid size 0.5 mm

∆t 0.2 ms

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DISCRETE PARTICLE MODEL

• BASIC FEATURES

+ individual particles are tracked in the computational domain taking

into account particle-particle and particle-wall encounters (collisions)

• ADVANTAGES

+ incorporation of arbitrary distribution of particle properties is easy

+ detailed particle-particle interaction models can be incorporated

• DISADVANTAGES

+ number of particles is (very) limited (CPU limitations)

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RESULTS DISCRETE PARTICLE MODEL

bubble formation in pseudo 2D bed

W=0.30 md p=1.5 mm

ρs=2526 kg/m3

U b=0.85 m/s

U j=15.0 m/s

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spouted bed

“CAPABILITIES” OF DPM

(COLLISION PARAMETERS!!!)

(Link et al., CES, 2005)

REGIME PREDICTION

GAS BUBBLES BEHAVIOUR

PRESSURE FLUCTUATIONS

SOLIDS MOTION

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spouted bed

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spouted bed

/ 16.0 / 1.2sf mf bf mf u u u u= ↔ =

particle configuration particle velocity map

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spouted bed

experimental simulated

/ 16.0 / 1.2sf mf bf mf u u u u= ↔ =

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spouted bed

DPM PEPT

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1 bar 2 bar 4 bar 8 bar 16 bar 32 bar 64 bar


effect of operating pressure

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effect of operating pressure

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Porosity

P D F

1 bar

2 bar

4 bar

8 bar

16 bar

32 bar

Dense emulsion Intermediate Bubbles

p p

p

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Courtesy: Prof. Heinrich (TUHH)

• wide residence time distribution

• stochastic flow profile

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Courtesy: Prof. Heinrich (TUHH)

• wetting cycles

• narrow residence time distribution

• stationary flow profile in spray zone

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TWO-FLUID MODEL BASED ON KINETIC THEORY

• BASIC FEATURES

+ statistical mechanical description of particle-particle encounters

• ADVANTAGES

+ based on more fundamental description of particle-particle interaction

compared to classical two-fluid model and the discrete bubble model

• DISADVANTAGES

+ incorporation of different particle properties (polydispersity) is quite

difficult and leads to (many) additional equations (CPU limitations)

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• DEFINITION OF PARTICLE VELOCITIES

+ instantaneous particle velocity:

+ ensemble averaged particle velocity:

+ fluctuating particle velocity:

• DISTRIBUTION OF FLUCTUATING VELOCITIES (KTG)

vcC −=

v

c

)2

exp()2

(2

2/3

kT

mC

kT

mn f −

π

= Maxwell’s velocity distribution

Boltzmann constantnumber density

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RESULTS TWO-FLUID MODEL

bubble formation: 15 cm bed

W=0.15 m

d p=1.5 mm

ρs=2526 kg/m3

U b=0.85 m/s

U j=15.0 m/s N p=120000

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RESULTS TWO-FLUID MODEL

bubble formation: 30 cm bed

W=0.30 m

d p=2.5 mm

ρs=2526 kg/m3

U b=1.20 m/s

U j=20.0 m/s N p=60000

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Geldart A type fluidization

grid size

0.8 mm

grid size0.2 mm

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SEGREGATION IN BIDISPERSE SYSTEMS

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experimental technique

DIGITAL IMAGE ANALYSIS

USING TWO PARTICLE TYPES

WITH DIFFERENT COLORS

COLOR INTENSITY MEASURE

FOR PARTICLE FRACTION

CAREFUL CALLIBRATION

ESSENTIAL

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RESULTS DPM MODEL

segregation in bidisperse systems

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RESULTS DPM MODEL


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RESULTS DPM MODEL


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MULTI-FLUID MODEL (MFM) BASED ON KINETIC THEORY

• BASIC FEATURES OF CURRENT MFM

all particle species are assumed to possess a nearly Maxwellian

velocity distribution with respect to the particle mixture velocity

and the particle mixture granular temperature

in the corresponding equilibrium situation (no external forces and

absence of gradients in porosity, velocity and granular temperature)

interaction between different particle species already exists

differences in the mean velocities and granular temperatures of the

particle species result from higher order perturbation terms in theChapman-Enskog solution method of the Boltzmann equations

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simulation with multi-fluid model

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RESULTS MFM MODEL


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RESULTS MFM MODEL


New MFMOld MFM

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RESULTS MFM MODEL


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CONCLUSIONS

• MULTI –SCALE SIMULATION APPROACH

+ closures for gas-particle and particle-particle interaction are critical

+ LBM provides closures for gas-particle interaction

+ DPM essential………but should be viewed as a “learning model”

+ incorporation of friction in kinetic theory models (encounter model)

• EXPERIMENTAL VALIDATION

+ important role for non-invasive monitoring (CARPT, MRI, PEPT)

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FUTURE WORK

• MULTI-SCALE SIMULATION APPROACH

+ readily applicable to non-spherical particles

+ extension to mass and heat transport (ERC Advanced Grant)

+ incorporation of liquid phase (droplets) (Prof. Heinrich TUHH)

+ filtered two-fluid models (Geldart A)

+ other multiphase flows (gas-liquid + gas-liquid-solid)

+ hybrid models (particle based + continuum)

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EXTENSION TO BUBBLY FLOW

O(105) bubblesO(102) bubbles

( ),

( , )1 25.88 exp( / 2)

D g

g l

D

C Eo Eo

C

ε ε ε

∞

= + −

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ACKNOWLEDGEMENTS

PhD’s + PD’s

Renske BeetstraAlbert Bokkers

Maureen van Buitenen

Willem Godlieb

Matthijs Goldschmidt

Bob HoomansJeroen Link

Daneshwar Patil

Junwu Wang

Mao Ye

Funding

Akzo NobelCorus

DSM

FOM

NWO-CW

SabicShell

STW

Unilever

Yara

Documents

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