reverse electrodialysis Gurreri L. * , Tamburini A., Cipollina A., - - PowerPoint PPT Presentation

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CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Scuola Politecnica Dipartimento di Ingegneria Chimica, Gestionale, Informatica e Meccanica (DICGIM), viale delle Scienze (Ed.6), 90128 Palermo, Italy

Gurreri L.*, Tamburini A., Cipollina A., Micale G., Ciofalo M.

*e-mail address: luigi.gurreri@unipa.it

Second International Conference on

Salinity Gradient Energy

September 10th-12th, 2014, Leeuwarden, The Netherlands

Objectives and background

RED CHANNELS

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Channel geometry Fluid Dynamics Performance

• Hydraulic friction
• Concentration Polarization

Net spacers for membranes separation Mixing promotion X Higher friction factor Two layers (overlapped) filaments Woven filaments

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Objectives and background

OBJECTIVES, TOOLS AND ACTIVITIES

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Objective: prediction of fluid flow and mass transfer in spacer-filled channels for RED applications Process optimization Tools: 3D-Computational Fluid Dynamics (CFD) modelling Activities: parametric analysis

• Wires shape: woven and non woven spacers
• Pitch to height ratio (l/h)
• Channel orientation (fluid flow direction)
• Reynolds numbers typical of RED applications

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

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NUMERICAL METHODOLOGIES

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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CASES INVESTIGATED

Filaments shape

• Overlapped (o)
• Woven (w)

Fluid flow direction α

• 0°
• 45°

Reynolds number Re

1, 4, 16, 64

Size

Pitch to height ratio l/h = 2, 3, 4 (h = 0.3 mm)

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

α0 l

Diamond spacers

l α45 α0 α45

Overlapped Woven

Numerical methodologies

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CFD MODELING

The finite volumes code Ansys-CFX 14 was employed to discretize and solve the governing equations (Newtonian and incompressible fluid). Steady regime at all flow rates investigated NaCl solution at T = 25 °C

Molarity [mol/l] Density [kg/m3] Viscosity [Pa s] Diffusivity [m2/s] Seawater 0.5 1017.2 9.31e-04 1.47e-09

u  

2

u u u p u P t            

Body force → fluid motion in a periodic domain

 

 



s e

b Cu D C ku b a M C ks                

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

For details see L. Gurreri, A. Tamburini, A. Cipollina, G. Micale, M. Ciofalo, CFD prediction of concentration polarization phenomena in spacer-filled channels for reverse electrodialysis, J. Membr. Sci., 468 (2014) 133-148.

Numerical methodologies

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BASIC EQUATIONS*

Transport equation for a binary electrolyte

Accumulation Convection Diffusion Migration

 

ln 1 ln

i i i

d C i t C Cu D C t d C z F                      

salt diffusivity solvent concentration solvent velocity ≈ u transport number *J.S. Newman, Electrochemical Systems, Second Edition, 2nd edition, Prentice Hall, Englewood Cliffs, NJ (1991)

• K. Kontturi, L Murtomäki, J.A. Manzanares, Ionic Transport Processes In Electrochemistry and Membrane Science, Oxford University Press (2008)

   

i j i i ij j i j i j j T ij

C C C K u u RT u u C D      

 

z C z C

   

 

Electroneutrality condition binary electrolyte Multicomponent diffusion equation (Stefan-Maxwell)

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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CFD MODELLING DEVELOPMENT

Implementation of transport equations

Assuming density as a linear function of C  C

M a b b M C dC d C C d C d

C

            ln ln 1  

b aC   

0.95 1.00 1.05 1.10 1.15 1.20 1 2 3 4 5 6

Density [kg/l] Molarity [mol/l]

Diffusive term

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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CFD MODELLING DEVELOPMENT

Implementation of transport equations

• Current density
• Equations system not closed
• Above transport equation can be solved
• when coupled with other equations → entire stack as domain
• or when current density distribution is known (spacer-less channel)

Migrative term

 

 

i C i i

i t C b Cu D C t b a M C z F                   

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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CFD MODELLING DEVELOPMENT

Implementation of transport equations

• Concentration profiles were unaffected by the migrative term
• Migrative term is negligible compared to the diffusive one
• → Migrative flux is quite uniform

Simulations of an empty channel

 

 

i C i i

i t C b Cu D C t b a M C z F                   

10 12 14 16 18 20 22 24 26 28 0.0 0.2 0.4 0.6 0.8 1.0

C [mol/m3] y/H [-]

Without migrative term With migrative term

18 19 19 20 20 21 0.14 0.15 0.16 0.17 0.18 0.19

• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5 0.0 0.2 0.4 0.6 0.8 1.0

Diffusive and Migrative terms [mol/m3 s] y/H [-]

Diffusive term Migrative term x 100

Migrative term neglected

most unfavourable case (low concentration and high current density)

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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MODELLING APPROACH

Transport equation implemented for Unit Cell

( , , , ) C C x y z t k s   

Periodic concentration Fully developed flow → Linear variation of concentration along the flow direction (s) Periodic boundary conditions despite the change of the bulk concentration

Transport equation for the electrolyte in unit cell

, TOT s ave

Q k V u   ( )

TOT CEM AEM

Q J A A   

Ingoing flux throug membrane Fluid flow direction

 

 



s e

C b Cu D C ku t b a M C ks                  

• Conc. gradient

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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MODELLING APPROACH

Computational domain

Brine Sea water Brine

One channel No double layer

+ + -

• 0.3 mm

0.3 mm Overlapped

Unit Cell

Woven

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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MODELLING APPROACH

Wall boundary at membrane-solution interface

CEM NaCl

, , , , , ,

1 0.5

m i i i tot d m CEM CEM CEM d m CEM CEM d CEM d CEM

t J i z F J J J t J J i z F J t J i i z F F   

           

             

i

, d CEM

J

, d CEM

J

, m CEM

J

, m CEM

J

Uniform flux at the membrane-solution interfaces

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Numerical methodologies

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MODELLING APPROACH

Mesh and grid dependence analysis

Grid dependence by varying the size

• results independent of the discretization degree
• accuracy
• computational savings

Size = 0.006 mm 420,000 - 5,760,000 vol.

Overlapped Woven

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

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RESULTS

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

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Pressure drop

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Results: pressure drop

0.1 1 10 100 1000 0.7 7 70

f [-] Re [-]

w-l/h2-α0 w-l/h3-α0 w-l/h4-α0 w-l/h2-α45 w-l/h3-α45 w-l/h4-α45 empty

0.1 1 10 100 1000 0.7 7 70

f [-] Re[-]

• -l/h2-α0
• -l/h3-α0
• -l/h4-α0
• -l/h2-α45
• -l/h3-α45
• -l/h4-α45

empty

FRICTION FACTOR

• The presence of obstacles causes f higher than the

empty ch.

• α has irrelevant effects
• f reduces by increasing the pitch

n

f ARe 

• W-shape implies f higher than the o
• At the lowest Re numbers, n = -1 → creeping flow
• At higher Re, n deviates from -1, since the
• bstacles induce increasing inertial effects → flow

fields not self-similar

Woven

2 ,

2

h s mean

d p f l u   

Overlapped

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Results: pressure drop

5 10 15 20 25 0.7 7 70

f/(24/Re) [-] Re[-]

• -l/h2-α0
• -l/h3-α0
• -l/h4-α0
• -l/h2-α45
• -l/h3-α45
• -l/h4-α45

108-140%

5 10 15 20 25 0.7 7 70

f/(24/Re) [-] Re [-]

w-l/h2-α0 w-l/h3-α0 w-l/h4-α0 w-l/h2-α45 w-l/h3-α45 w-l/h4-α45

PRESSURE DROP NORMALIZED

• Spacers provide f 3-20 times higher than

the empty ch.

• α is irrelevant at these Re

1

24

empty

f Re 

33-39% 190-210% 46-48%

• The pitch has significant effects, especially for

the w-shape

• W-shape leads to pressure drop increase

by 106%, 67%, 54%, for l/h=2,3,4 respectively

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Woven

Overlapped

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Mass transfer

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Results: mass transfer

MASS TRANSFER COEFFICIENT

Effect of Re and l/h

Re l/h

1 4 16 64 2 3 4

w-α45

Fluid flow Fluid flow

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

( )

i bulk

J k C C  

kave kave

Results: mass transfer

MASS TRANSFER COEFFICIENT

Effect of α in w-shape

kw-α45>kw-α0 w-l/h2-α0

Re=16

α45

w-l/h2-α45

Fluid flow

w-α45

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Fluid flow

w-α0

Results: mass transfer

Fluid flow

MASS TRANSFER COEFFICIENT

Effect of filaments shape

• -l/h2-α45

Re=16

w-l/h2-α45

Fluid flow

w-α45

• -α45

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

kw>ko

Results: mass transfer

Fluid flow

MASS TRANSFER COEFFICIENT

Effect of α in o-shape

• -l/h2-α45

Re=16

Fluid flow

• -α45

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Different distribution, but similar kave

• -l/h2-α0
• -α0

Results: mass transfer

MASS TRANSFER COEFFICIENT

Effect of α in o-shape

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

• -l/h2-α0
• -l/h2-α45

Re=16

Fluid flow

• -α0
• -α45

Significant effect

• f the asymmetry

for o-α0

Fluid flow

Results: mass transfer

SHERWOOD NUMBER

• Mixing not favored at very low Re due to the

calm regions caused by the filaments, especially for α0. Sh much higher at higher Re

• : Shw-α45 > Shw-α0; for o-shape the effect is

slighter, but the influence of Re is more complex

h

k d Sh D 

• Shw-α45 reduces by increasing l/h, for α0 this
• ccurs only at the highest Re; for o-shape the

dependence on l/h is not significant

• Shw > Sho

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

5 50 0.7 7 70

Sh [-] Re[-]

• -l/h2-α0
• -l/h3-α0
• -l/h4-α0
• -l/h2-α45
• -l/h3-α45
• -l/h4-α45

empty

5 50 0.7 7 70

Sh [-] Re [-]

w-l/h2-α0 w-l/h3-α0 w-l/h4-α0 w-l/h2-α45 w-l/h3-α45 w-l/h4-α45 empty

Woven

Overlapped

Results: mass transfer

5 50 0.7 7 70

Sh [-] Re[-]

• -l/h2-α0-h
• -l/h2-α0-l
• -l/h3-α0-h
• -l/h3-α0-l
• -l/h4-α0-h
• -l/h4-α0-l

empty

5 50 0.7 7 70

Sh [-] Re[-]

• -l/h2-α0
• -l/h3-α0
• -l/h4-α0

empty

SHERWOOD NUMBER

Overlapped-α0

h

k d Sh D 

• Overlapped-α0 is the only case with asymmetry → distribution and average Sh different at the

two walls

• Very different behavior for the high and the low walls
• Trend not straightforward with Re

Average Sh Sh on high and low walls

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

Results: mass transfer

SHERWOOD NUMBER

h

k d Sh D 

• Qualitatively, the same considerations can be

applied as before

• As a difference, the pitch has not a significant

effect for the w-α0

2 4 3 3

1 SPC 8 h Pn f Re    

,

SPC

s mean

p u l  

Power number

• Pn: dimensionless pumping power

consumption

• In a quantitative analysis, the trends of

Sh=f(Pn) are different with respect to Sh=f(Re)

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

5 50 1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06

Sh [-] Pn[-]

• -l/h2-α0
• -l/h3-α0
• -l/h4-α0
• -l/h2-α45
• -l/h3-α45
• -l/h4-α45

empty

5 50 1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+06

Sh [-] Pn [-]

w-l/h2-α0 w-l/h3-α0 w-l/h4-α0 w-l/h2-α45 w-l/h3-α45 w-l/h4-α45 empty

Woven

Overlapped

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CONCLUSIONS

Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

CONCLUSIONS

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Second International Conference on Salinity Gradient Energy, September 10th-12th, 2014, Leeuwarden, The Netherlands CFD analysis of mass transfer in spacer-filled channels for reverse electrodialysis

CFD modelling of spacer filled ch. for RED

• Fluid flow and mass transfer behaviour
• Parametric analysis of:

· Wires shape: woven and non woven spacers · Pitch to height ratio (l/h) · Channel orientation (fluid flow direction) · Re effects

• Process efficiency: Pn and Sh

OPTIMAL CHANNEL CONFIGURATION

Influence of various factors on efficiency. Simulation results as input data for a process simulator → Optimal channel configuration and Re

EuroMed 2015 Desalination for Clean Water and Energy Palermo, Italy, 10-14 May 2015

Thank you for your attention

Luigi Gurreri luigi-gurreri@unipa.it