Fine Grid Simulations of Gas SolidsFine-Grid Simulations of Gas-Solids Flow in a Circulating Fluidized Bed

Sofiane Benyahiaf yUS DOE, National Energy Technology Laboratory

Multiphase Flow Science WorkshopMultiphase Flow Science WorkshopAugust 16-18, 2011

Introduction

Two-fluid or continuum model based simulations are l d t d t ti l hcommonly conducted on coarse computational mesh

requiring subgrid model.

Based on some publications1, some doubts still remain if finely resolved two-fluid simulations can capture basic experimental observations of solids hold-up and pressure d fil i idrop profiles in risers.

We will first show some results2 using subgrid models and then attempt to obtain similar results using grid-refined two-fluid simulations with no subgrid corrections.

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1 Lu, B.; Wang, W.; Li, J. Chem. Eng. Sci. 2009; 64; 3437-3447.2 Benyahia, S. AIChE J. doi: 10.1002/aic.12603

Purpose of this presentation

First show that coarse two-fluid simulations can provide bl ith th h l f b id d l (thireasonable accuracy with the help of subgrid models (this

is a continuation of my last year presentation.)

Then, demonstrate that two fluid simulations without subgrid models will predict the correct experimental observations as the grid is refined

Finally, show the necessity to invest more research in the development of subgrid models due to significant computer time requirements to conduct these fine grid simulations.

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Two-fluid simulation conditions1

Two gas‐solids outlets

0.35 m

0.14 m

Process temperature 297 K

Process pressure 1.01 x 105 Pa

Air density ~1.2 kg/m3

0 09 m

Air viscosity 1.8 x 10-5 Pa·s

Gas-phase turbulence length-scale 0.01 m

Solids density 930 kg/m3

0.09 m

60, 90 cells

10.5 m

450, 4500, 10500 cells

Particle diameter 54 micron

Single-particle terminal velocity 0.074 m/s

Particle-particle restitution coefficient 0.9

P ti l ll tit ti ffi i t

2.78 m

Particle-wall restitution coefficient 0.7

Specularity coefficient 0.0001

Particle-particle angle of internal

frictionpi/6

Gas inlet

Two solids side inlets

0.35 m

0.14 meps_mf =0.4

eps = 0.3 ,  Vs: computed

friction

Particle-wall angle of friction pi/16

Void fraction at maximum packing 0.4

Void fraction at minimum fluidization 0.6

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Gas inlet

Vg = 1.5 m/s1 Lu, B.; Wang, W.; Li, J. Chem. Eng. Sci. 2009; 64; 3437-3447.

Coarse grid simulation resultsDrag model Wen-Yu EMMS Experimental

Solids mass flux (kg/m2s)

205 16.9 14.3( g )

Standard deviation (kg/m2s)

25.2 5.59 -

10EMMS (pressure)

8

EMMS (pressure)

Wen‐Yu (pressure)

experiment (pressure)

EMMS (voidage)

Wen‐Yu (voidage)

4

6Heigh

t  (m

)

Wen-Yu drag EMMS drag

2

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g EMMS drag

Time-averaged 0

0.7 0.8 0.9 1Void fraction 

Coarse-grid simulation results

There is clearly a need to “correct” the drag force as id i l ti f il t di t th lid h ldcoarse-grid simulations fail to predict the solids hold-up.

There is a significant difference in the computed solids hold-up and the one deduced from pressure-gradient. Note that measurements are based on pressure*.

So even with drag corrections, there is still disagreements between measurements and simulation data, which will be investigated in the next slides…

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*All subsequent results will be based only on our computed pressure gradient data.

Effect of particle-particle friction10

e = 0.9

0 79 ( i l d hi h f i i )8

e = 0.79 (simulated higher friction)

experiment

4

6Heigh

t  (m

)

2

0

0.7 0.8 0.9 1Void fraction 

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Effect of particle-wall friction10

phi = 0.0001

phi = 0 01

6

8

phi = 0.01

phi = 0.1

experiment

4

6Heigh

t  (m

)

2

0

0.7 0.8 0.9 1Void fraction 

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3 Li, T; Benyahia, S. AIChE J. doi: 10.1002/aic.12728

Effect of polydispersity10

Monodisperse (EMMS)

Monodisperse (Wen‐Yu)

10dp30

dp60

6

8

)

Polydisperse (EMMS)

Polydisperse (Wen‐Yu)

experiment

6

8dp115

solids hold‐up  (polydisperse)

solids hold‐up  (monodisperse)

4

6

Heigh

t  (m

)

4

6

Heigh

t  (m

)

2 2

0

0.7 0.8 0.9 1Void fraction 

0

0 1 2 3Scaled solids volume fraction 

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Coarse-grid simulation results

There is clearly a need to correct the drag force for both d l di t ith idmono- and poly-disperse systems with a coarse grid.

Next we present results of refined two-fluid simulations using a standard homogeneous drag correlation.

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Fine-grid simulation results

Grid resolutionSolids mass flux

(kg/m2s)

60x450 205

60x4500 200

90x10500 14090x10500

EMMS 16.9

Experimental 14.3

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Coarse 60x450

60x4500 90x10500 or 1 mm2 cells

Fine-grid simulation results

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Summary

This study shows that more accurate results are obtained as the grid is refined, but a grid-converged3 solution was not obtained even with 1 M cells!with 1 M cells!

It is, therefore, necessary to include sub-grid corrections due to the large computational requirements and time needed to conduct fully-resolved simulations.fully resolved simulations.

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3 Wang, J.; van der Hoef, MA.; Kuipers, JAM. Chem. Eng. Sci. 2009; 64; 622-625.