Gas absorption into a spherical liquid droplet: numerical ... fileGas absorption into a spherical liquid droplet: numerical and theoretical study C. Wylock, P. Colinet, B. Haut 22th

Gas absorption into a spherical liquid droplet: numerical

and theoretical study C. Wylock, P. Colinet, B. Haut

22th International Symposium on Chemical Reaction Engineering

Maastricht, The Netherlands

September, the 3rd, 2012 ISCRE 22

Framework

Spray absorbers

• Absorption of gas materials by reactive liquid droplets

• Important mass transfer devices for several industrial applications, such as air pollution control (e.g. scrubbing of SO2 by limestone slurry)

• Nowadays, efficient design and optimization require deep understanding of phenomena taking place during the gas-droplet mass transfer BUT complex problem

Transfers, Interfaces and Processes

Ecole Polytechnique de Bruxelles 2

Framework

Multiscale problem

Several coupled phenomena in an absorbing droplet

• Interactions gaseous flow – liquid flow

• Interactions flow – mass transfer

• If enhanced interactions reactions - mass transfer



Spray absorber Droplet cloud Droplet Gas-liquid interface

This work

Framework

Development of mass transfer model

• Detailed modelling of phenomena and their interactions

fundamental interest for spray absorber modelling

• Looking for «simplicity» (simple but not simplistic) of the mass transfer model in order to be applicable in an absorber model (e.g. for the scaling)

• Approach :



"Complex" model

Analysis "Simplified"

model Comparison

Studied case

Liquid water droplet in free fall in gaseous air

• Non-deformable sphere

• Non-oscillating interface

• Incompressible laminar flows

• At terminal velocity (stationary flow)

A gaseous component A is transferred from the gas into

the liquid droplet

Possibly irreversible chemical reaction with a

component B in the liquid phase following:

A + B C

Problem studied by Direct Numerical Simulation (DNS)



dd ≤ 1mm ; Re ≤ 250

Outline

Mathematical modelling

• Domain and equations

Physical absorption

• Simulation results and discussion

• Development of analytical solutions

• Summary

Absorption coupled with a chemical reaction


• Summary

Final conclusion



Outline



Physical absorption



• Summary



• Summary

Final conclusion




Computational domain

• 2-D axisymmetric domain

• Meshing with boundary layer meshes




Equations in the gaseous phase

• Navier-Stokes and continuity

• Concentration transport



with


Equations in the liquid phase





Physical absorption : Ha=0

with


Conditions at the gas-liquid interface






Numerical resolution

• Finite element resolution with COMSOL Multiphysics 3.4

Simulations realized for:

• Physical absorption : various flow regimes <-> various Re

• Absorption coupled with a reaction : various flow and chemical regimes <-> various Re and Ha




Post-processing: study of time evolution of

• Saturation



Physical absorption


* see our paper doi/10.1016/j.cej.2012.07.085

*

*


Post-processing: study of time evolution of

• Saturation

• Time-averaged Sherwood number



* see our paper doi/10.1016/j.cej.2012.07.085

*

If physical absorption:

Outline



Physical absorption (Ha=0)



• Summary



• Summary

Final conclusion



Physical absorption: simulation results

Time evolution of



Saturation Time-averaged Sherwood number

Analysis of time evolution of concentration fields

• Re = 0.1

Similar to a pure diffusive process in a sphere

Physical absorption: discussion




• Re = 200

1. Fast saturation of the vortex periphery

2. Mainly ‘diffusive’ process through toroidal vortex





• Re=5

Combination of diffusive and convective transport




Outline






• Summary



• Summary

Final conclusion



Physical absorption: analytical solutions

1. Limit case Re 0 : diffusion in a sphere

Model equation:




2. Limit case Re ∞

• ‘Instantaneous’ saturation of a vortex periphery

• ‘Diffusion’ through a toroidal vortex

• Torus cut and unfold gives a cylinder




2. Limit case Re ∞ : diffusion in a cylinder representing

a toroidal vortex

– Model equation:

with and



Adjustable parameters Fitted from DNS results

0.97 2.4


3. Intermediate Re

i. Diffusion in a boundary layer (thiner if Re larger)

similar to penetration-film model with thickness df

Model equation:



df

x


3. Intermediate Re

i. Diffusion in a boundary layer (thiner if Re larger)

similar to penetration-film model with thickness df

with

ii. Diffusion through the toroidal vortex



Adjustable parameter Fitted from DNS results

𝛿𝑓 = 0.1825 Re−0.587


Comparison of the analytical expressions for the mass

transfer rate (continuous lines) with the DNS results (dashed

lines)



Outline






• Summary



• Summary

Final conclusion



Physical absorption: summary

3 steps can be observed:

1. Diffusion at interface vicinity directed towards the droplet center.

2. Convection enhancing the transfer by depleting the interface boundary layer

3. Saturation of the vortex periphery. The transfer rate becomes limited by diffusion towards the vortex inside.

Following the flow regime:

• Re 0 : only the 1st step is observed.

• Re ∞ : the 3rd step is directly observed.

• Intermediate Re : mass absorption rate controlled successively by these 3 limiting steps, transition time decreases as Re increases.

Enables to propose simplified mechanisms to describe the mass transfer rate evolution for any flow regime

Analytical solutions for



Outline



Physical absorption



• Summary

Absorption coupled with a chemical reaction (Ha>0)


• Summary

Final conclusion



Absorption coupled with chemical reaction:

simulation results and discussion

Time evolution of Sh and f and concentration fields

analysis

• Re = 0.1

30




analysis

• Re = 0.1

Ha = 0.1

31

CA CB




analysis

• Re = 0.1

Ha = 10

32

CA CB




analysis

• Re = 100

33




analysis

• Re = 100

Ha = 0.1

34

CA CB




analysis

• Re = 100

Ha = 10

35

CA CB




analysis

• Re = 1






analysis

• Re = 10



Outline



Physical absorption



• Summary

Absorption coupled with a chemical reaction (Ha>0)


• Summary

Final conclusion



Absorption with reaction : summary

Prevalent mass transport mechanism: depends on Re

Slow reaction (Ha<<1)

• Saturation is delayed by B as it increases absorption capability

• Transfer rate remains mostly controlled by transport of A

Fast reaction (Ha>>1)

• Saturation not delayed

• Transfer rate is first controlled by the transport of B and becomes controlled by transport of A when B is depleted

Moderate reaction (Ha~1) : intermediate situation

• Saturation possibly delayed

• Transfer rate gets influenced by the transport of A and B



Outline



Physical absorption



• Summary



• Summary

Final conclusion



Final conclusion

Results show the importance of taking into account all the

phenomena simultaneously in gas-droplet mass transfer

modeling

Detailed analysis enables looking “smartly” for simplified

approaches:

• Approximate analytical expressions for physical absorption: OK

• Expressions when coupled with an instantaneous reaction: in development





Thanks for your kind attention

Documents

Gas absorption into a spherical liquid droplet: numerical ... fileGas absorption into a spherical liquid droplet: numerical and theoretical study C. Wylock, P. Colinet, B. Haut 22th