Oral presentation at ASME-ATI-UIT Symposium on Thermal-Fluid-Dynamics and Energy Systems (18/05/2010)

1. www.mbr-network.eu
Heat-and-Mass Transfer Relationship to
Determine Shear Stress in Tubular Membrane
Systems
Nicolas Ratkovich, Pierre Bérubé and Ingmar Nopens
ASME-ATI-UIT 2010
May 18th 2010, Sorrento – Italy

2. Outline
Introduction and Objectives
• Waste water treatment processes
• Reduction of fouling (two-phase flow)
• Dimensionless analysis (analogies)
Methodology
• Mass transfer (single- and two-phase flow)
• Heat-and-Mass transfer analogy
• Experimental set-up
Results and discussion
• Development of empirical model
Conclusions and future work
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3. Objectives
To quantify the mass transfer coefficient for
two phase flow
To validate the heat-and-mass transfer
analogy with the results obtained from
electrochemical shear probe measurements.
To propose an empirical correlation based on
heat transfer to determine the wall shear
stress
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4. Introduction
Waste water treatment processes
• Biological removal of organic substances and nutrients (bioreactor)
• Clean water-sludge separation:
- Conventional Activated Sludge (CAS) - Gravity
- Membrane Bioreactor (MBR) - Filtration
Immersed Side-stream
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5. Introduction
Membrane fouling
• Cake layer / pore blocking
• Decreases permeate flux
Reduction of fouling
• Introduction of air
- Two-phase (slug) flow
• Avoids reduction of permeate flux
- Surface shear stress → scouring effect
- Increases mass transfer (cake layer →
bulk region)
Slug flow
*Taha & Cui, 2006
• Large shear stress values
• Dynamic shear stress (liquid flows down-
& up-flow)
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6. Introduction
Dimensionless numbers
• Two physical phenomena are similar if they have the same
dimensionless forms of governing differential equations and
boundary conditions.
Similarities (internal flow)
Mass transfer Wall friction Heat transfer
Flow
mass heat
transfer transfer
shear stress
Cake layer
Membrane
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7. Introduction
Similarities (internal and single-phase flow)
Mass transfer Wall friction Heat transfer
Sh = function(d , Re, Sc ) f = function(d , Re ) Nu = function(d , Re, Pr )
km d µ 2 d ∆p 8τ w ρud hd cp µ
Dimensionless Sh = Sc = f = = Re = Nu = Pr =
numbers Df ρ Df L ρ u2 ρ u2 µ kc kc
1 0.14
Laminar
1
64  d 3  µB 
 d 3
f = Nu = 1.86  Re Pr   
(Re<2000) Sh = 1.62  Re Sc   L µ 
 L Re  W 
0.25 0.14
Turbulent
1 f = 1
µ 
Pr  B 
2 0.8
Sh = 0.04 Re 0.8 Sc 3   ε 5.74  Nu = 0.027 Re 3
µ 
(Re>4000) log10  + 0.9 
 3.7 d Re   W 
  
1
1
Sh  Sc  3
Analogy =   = Le 3
Nu  Pr 
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8. Single-phase flow
Mass transfer:
• Concentration polarization:
- Separation: Sludge ⇔ Solute
- Increase solute concentration near membrane surface
- Convection = Diffusion + Permeate
dC
J C = −D + J C per
dx
- Flux:
C 
J = km ln  m 
 Cb 
- Mass-transfer coefficient (km):
D
km =
δ
- Sh laminar correlation:
1
km d  d 3
Sh = = 1.62  Re Sc 
D  L
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9. Two-phase flow
Mass transfer
• Ghosh and Cui (1999) & Zheng and Che
(2006)
• Developed mass transfer correlations for:
- Falling film zone
- Wake zone
- Liquid slug zone
*Ghosh and Cui, 1999 9 www.mbr-network.eu

10. Heat-and-Mass transfer analogy
Developed shear stress correlation for:
- Gas slug zone (falling film + wake)
- Liquid slug zone
• Analogy: Transport of momentum, mass, heat and energy
- Lewis number:
1
1 Gas
Sh  Sc  3
slug (hTP)
=   = Le 3
Nu  Pr 
- Mass transfer coefficient:
2
Liquid
hTP − slug (hL)
km = Le 3
ρTP c p ,TP
- Heat transfer coefficient:
 0 .4 0.25 0.25 
 x   1 − Fp 
0 .1
 PrG   µL 
hTP = Fp hL 1 + 0.55     
 Pr 
 
µ 
 (I )
* 0.25

  1 − x   Fp

  L   G  
 
*Ghajar, 2010
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11. Experimental set-up at UBC
Tube diameter: 2 Shear probes (flow direction)
• 9.9 mm Conversion (Voltage → Shear)
3
 
Fluids used: 
τw = µL 
4.64 V
5 2


 ν e F π d e Co D 3 R G 

3

• Water + electrolyte
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12. Shear probes & Shear Stress Histograms
Conversion V → τ
V 4 IL  k  d
3
IL = km = 2 S =  m  e2 τ = µS
RG ν e F π d e Co  0.862  D
Correlation τ → km
1
de  τ w D 2
 3
k m = 0.862  
d  µ de



Gas
slug
Liquid
slug
Correlation Sh → τ
1.561 µ D
τw = 2
Sh 3
de
Correlation Nu → τ
1
 Sc  3
Sh = Nu  
 Pr 
1.561 µ D  Sc  3
τw = 2   Nu
de  Pr 
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13. Electrochemical measurements
Single-phase flow
Shear stress Sherwood number
0.1 35 1
Theory Experimental data
 d 3
Shear probes Lévêque correlation Sh = 1.62  Re Sc 
0.09
This work  L
30
0.08
25 1
0.07
 d 3
Shear stress (Pa)
Sh = 1.495  Re Sc 
0.06  L
8 ρ u2 20
τw =
Sh
0.05
Re
15
0.04
0.03 10
0.02
5
0.01
0 0
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 1400
Re Re
Difference of 8 % between theory and experimental data
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14. Empirical model
Two-phase flow
1.561 µ D  ScTP  3
• Gas slug τ w, gs = 2

 Pr  φ gs NuTP 3

de  TP 
• Liquid slug 1.561 µ D  Sc L  3
τ w,ls = 2

 Pr  φls Nu L 3

de  L 
• Correction factors:
- Coalescence
- Bubble length
- Hydraulic diameter
- Transition regime (calibration under laminar conditions)
- φgs & φls
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15. Empirical model
Correction factor 140 2.8
• Power law expression
120 2.4
φ = a1 Re L a 2
100 2
• Based on experimental
measurements
a1,gs ReLa2,gs
-0.2945
a2,ls
y = 545.7382x
80 2
R = 0.9461
1.6
a1,ls ReL
60 1.2
Final expression 40 0.8
• Liquid slug Liquid slug
y = 1508.7567x
-1.1957
20 Gas slug 0.4
( ) Nu
2
−0.295 3 3 R = 0.9113
τ w,ls = 48.900 Re L L
Power (Gas slug)
Power (Liquid slug)
0 0
• Gas slug 0 200 400 600 800 1000 1200
( )
3
τ w, gs = 138.741Re L −1.196 NuTP 3 ReL
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16. Empirical model
ReSG Reff
140 2.8
140 2.8
120 2.4
120 2.4
100 2
100 2
a2,gs
a2,ls
80 1.6
a2,gs
a2,ls
a1,gs ReSG
a1,ls ReSG
80 1.6
a1,gs Reff
a1,ls Reff
60 1.2
60 1.2
40 0.8
40 0.8
Liquid slug
20 0.4 Liquid slug
Gas slug
20 Gas slug 0.4
Power (Gas slug)
Power (Gas slug)
Power (Liquid slug)
0 0 Power (Liquid slug)
0 0
0 5 10 15 20 25 30 35 40 45
186 188 190 192 194 196 198 200
ReSG
Rem 140 2.8
Resf 140
Reff
2.8
120 2.4 120 2.4
100 2 100 2
a2,gs
a2,ls
a1,gs Rema2,gs
a2,ls
80 1.6 80 1.6
a1,gs Resf
a1,ls Resf
a1,ls Rem
60 1.2 60 1.2
40 0.8 40 0.8
Liquid slug Liquid slug
20 0.4 20 Gas slug 0.4
Gas slug
Power (Gas slug) Power (Gas slug)
Power (Liquid slug) Power (Liquid slug)
0 0 0 0
0 200 400 600 800 1000 1200 1400 1600 1800 0 500 1000 1500 2000 2500 3000
Rem Resf
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17. Conclusions
Shear stress values were obtained from shear probes
(electrochemical method) using the Sherwood number
Using the analogy between heat-and-mass transfer an
empirical correlation was developed for two-phase flow to
determine the wall shear stress:
• Two zones: liquid (L) and gas slug (TP)
• Predictions:
- Single phase flow is acceptable (10 % error)
- Two-phase flow: error up to 60 %
> Heat transfer coefficient correlation for TP has errors up to 30%
> The correlation is mainly designed for turbulent regime
> Common membrane operation is in laminar-transition regime
Analogies are determined mainly for turbulent regime;
operation of tubular air lift membranes is in laminar-transition
regime
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18. Future work
Non-Newtonian liquids (i.e. sludge)
• Use of CMC as a non-Newtonian liquid to mimic the
properties of Sludge.
• Viscosity (flow in a pipe)
n n −1 n −1 n −1
 3 n + 1   8 u SL   3n +1  8 u SL 
µB = K  
 4n   d  µW = K 
 4n    
       d 
• Reynolds and Prandtl number
ρ L u SL d cp µB
Re MR = Pr =
µB kc
• Nusselt number correction
1
Nu non− New  3 n + 1  3
=
 4n  
Nu New  
• Viscosity correction:
0.14
 µB 

µ 

 W 
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19. Acknowledgement
MBR-TRAIN is a Marie Curie Host Fellowship for Early
Stage Research Training supported by the European
Commission under the 6th Framework Programme
(Structuring the European Research Area - Marie Curie
Actions)
Contract No. MEST-CT-2005-021050
Duration: 01/01/06 - 31/12/09
MBR-TRAIN is part of the MBR-NETWORK Cluster
More info: www.mbr-network.eu and www.mbr-train.org
Funding for the infrastructure used to measure
surface shear forces was provided by the Natural
Science and Engineering Research Council of
Canada (NSERC).
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