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The Research of Multiphase Flow Distributed in Microchannel and Stability

Reporter ： Dongyue Peng

Mentor ： Feng Xin

Contents

Introduction

Goals

Flow resistance modeland nonlinear dynamic system

Relevant references

Next plan

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IntroductionIntroduction11

What is microchannel ?

Microchannel is fabricated by micromachining and

precision machining technology. The dimension of channel

cross-section is 0.5mm(500um) or less, which makes it

different from others.

Advantage:

1 、 Have a large specific surface

2 、 Enhancing heat and mass transfer progress

3 、 less reagents

4 、 Much safer and easier to control

5 、 Numbering-up

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Compared to the traditional approach of

scale up, numbering-up avoids the route from

laboratory-scale to pilot plant scale to

commercial plant. However, one key

challenge of numbering up is non-uniformity

flow distributed in microchannel .

Reason ： there exists feedback among

these channels and this feedback combined

with the amplification of a slight difference in

resistances of these channels.

This negative effect leads to non-

uniformity ,sometimes, even chaotic

disturbance . Fig. 1. Photos of CO2 -water flow pattern in 16 parallel microchannels Adopted from Yue. Boichot et al. (2009)

IntroductionIntroduction

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GoalsGoals22

1 、 Present a valid model or method to describe the microchannel system, which

can explain the ratio of fluid in each channel and flow state(stable, periodic, or

chaos).

2 、 Introduce some disturbances into the system and study its capacity to resist the

interference.

Fig. 2. Schematic view of ideal description flow distribution

Fig. 3. schematic view when introducing external interference

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Relevant referencesRelevant references33

Fig. 4. Schematic representation of gas–liquid flow distribution over parallel microchannels ： (A)external distribution (B) internal distribution . Adopted from Al-Rawashdeh ,M et al.(2012).

A B

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Analysis of the microchannelAnalysis of the microchannel22

the Multi-phase flow in microchannel results in different flow regimes. Among them, taylor

flow is attractive due to its well defined gas-liquid interface reduced axial dispersion approaching

ideal plug flow, and its excellent mass transfer and heat transfer characteristics.

Fig. 5. Photos of CO2-water flow pattern in 16 parallel microchannels (A) low speed of gaseous phase (B) high speed of gaseous phase. Adopted from Yue ,Boichot et al.(2009)

A B

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Fig. 6. (A) Schematic representation of barrier-based gas–liquid

flow distributor for four parallel microchannels.

Adopted from Al-Rawashdeh, Fluitsma et al.(2012)

(B) Schematic of the distribution unit with a PTFE.

Adoped from Matthias Mendorf et al.(2010) (C) Schematic view of the railroad-like channel network. Adopted from Ahn, Lee et al.(2011)

A B

C

Relevant referencesRelevant references

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A B

Fig. 7. The selection of paths by bubbles, at multiple bubble density levels.

Adopted from Choi,Hashimoto et al. (2011)

A micrograph of the experimental setup and a graph of the mean ratio of the numbers of drop-lets traveling through

each of the two arms of the loops.

Adopted from Jousse, Farr et al.(2006)

Relevant referencesRelevant references

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Resistance modelResistance model44

Fundamental formula

Fig. 8. Simplified resistance network model.

Adopted from Pan, M., Y. Tang, et al. (2009).

Schematic view for gas–liquid flow in multiple parallel microchannels.

Adopted from Al-Rawashdeh, Fluitsma et al.(2012)

ΔP = R×Q

A

B

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Fundamental Assumptions:

1 fixed physical properties;

2 the pressure of outlet equals to atmosphere;

3 ignore pressure drop when two phases mix

4 Only consider the influence of channel size on the fluid distribution

Fig. 9. Schematic view for gas–liquid flow in multi-parallel microchannels.

Resistance modelResistance model

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P-P0=P-P0

(Ql1, Ql2, Qg1, Qg2,)

Rl1 Ql1+ Rm1(Ql1+ Qg1)= Rl2 Ql2+ Rm2(Ql2+ Qg2)

Rg1 Qg1+ Rm1(Ql1+ Qg1)= Rg2 Qg2+ Rm2(Ql2+ Qg2)

Ql1+ Ql2=Ql

Qg1+ Qg2=Qg

Resistance modelResistance model

parameter Liquid(water) Gas(nitrogen) unit

Viscosity 893.7 17.812 mPa.s

Density 997 1.25 Kg/m3

Surface tension 0.07197 N/m

Rate of flow 0.5 1 ml/min

channel width height L

Cl1,Cl2,Cg1,Cg2 200um 50um 40mm

Cm1~Cm2 200um 50um 30mm

Table.1.Experimental parameter ( 25℃)

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start

Input physical properties and flow rates

Input the size of channels

Assumed Rm1=0,Rm2=0,calculated Rl1,Rl2,Rg1,Rg2,then calculate initial value Ql1, Ql2, Qg1,Qg2.

According to the pressure equilibrium, calculate value Q l1, Ql2, Qg1,Qg2 again.

Calculate multiphase flow distribution

Choose the valid model to calculate Rm1,Rm2

end

Yes

Fig. 9. Sequence procedures for solving the resistance model.

Resistance modelResistance model

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To ensure an accurate result, the key of the progress is to choose

a valid and accurate model to calculate Rm1 and Rm2

HFM model and SFM model

SFM :

Resistance modelResistance model

Adopted from Choi and Kim et al. (2011)

Adopted from Fuerstman, Lai et al.(2007)

Bubble model

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44 Resistance modelResistance model

GroupChannel

number

Size(σ=0~0.05) Flow rate Rm model

width/um Height/um ml/min

Group 1

Cl2 200×(1-σ) 50

Ql=0.5 ， Qg=1 SFMCg2200×(1-σ) 50

Group 2

Cl2 200 50×(1-σ)

Ql=0.5 ， Qg=1 SFMCg2200 50×(1-σ)

Group 3

Cl2 200×(1-σ) 50

Ql=0.5 ， Qg=0.

6

SFMCg2200×(1-σ) 50

Group 4

Cl2 200×(1-σ) 50

Ql=0.5 ， Qg=1 Bubble modelCg2200×(1-σ) 50

Table.2. Experimental Variables

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Fig. 10. the relationship of channel size and gas phase flow distributuion:（ A ） change the width of liquid and gas channel,(B) change the width of gas channel and height of liquid channel,(C) change the height of liquid and gas channel.

A B

Conclusion:1 Gas-phase of fluid distributed in channel is much

more sensitive to the changed size of liquid channel than that of gas channel.

2 The deviation from height contributes more to non-uniform distribution than that from the width.

3 On the same deviation, the distribution of liquid is more uniform than that of gas

4 The influence of manufacturing tolerance should be care more.

Resistance modelResistance model

C

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Conclusion1 The result of bubble model is a little bigger than that of SFM model.2 Decrease the rate of gas, the deviation will enlarge.

Fig. 11. the relationship of channel size and gas phase flow distribution: （ A ） change the width of liquid and gas channel in SFM model (B) change the width of gas and liquid channel in Bubble model, (C) change the width of liquid and gas channel in a smaller flow rate of gas.

Resistance modelResistance model

A B

C

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The progress of iteration is always non-convergence

Initial value of Ql1, Ql2 Qg1 Qg2

Output the value of Ql1, Ql2 Qg1 Qg2

Fig. 12. Schematic view of iteration procedure.

0 8 160.00

0.05

0.10

0.15

flow

rat

e10-7

m3 /s

iterations n

channelg1 channelg2 channell1 channell2

Resistance modelResistance model

Fig. 13. The value of flow rate during iteration

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In our nature, almost everything have relationship with each other and

most of these relationships are nonlinear, like the butterfly effect.

In my opinion, the application of nonlinear dynamical system can be

divided into two classes, one of which adopts chaotic time series. We can

obtain the Largest Lyapunov exponent, fraction dimension, Kolmogorov

entropy and phase diagram and so on, which can ensure us a systematic

system analysis and prediction.

(Schembri,Sapuppo et al.2011)

Another method is applying existed equations to represent the nonlinear

system. That is to say, It mainly relies on the experimental data to obtain

related equation parameters.

(Barbier, Willaime et al.2006)

Nonlinear dynamic systemNonlinear dynamic system

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Fig. 13. (A) Time series for Vair=0.12ml/min ， V water=0.63ml/min and for Vair=1.2ml/min ， Vwater=6.3ml/min (B) Schematic of a microfluidic snake channel.(C) contour plot of Largest Lyapunov exponent versus Air Fraction (D) Phase diagrams for Vair = 7.43 ml/min, Vwater = 1.57 ml/min and for Vair = 0.17 ml/min, Vwater = 0.15 ml/min.Adopt from Schembri, Sapuppo et al.(2001)

The discrete conditions of chaos are often performed by chaotic time series, and this chaotic time series contains a plenty of system dynamic information.

Nonlinear dynamic systemNonlinear dynamic system

A

B

D

C

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A B

Fig. 13. (A) Sketch of the parallelized system,(B) Dynamic behaviors in two microfluids with different flow rate: (a) Qo=4 L/min,Qw=0.6 L/min, Qw’ =0.5 L/min; (b) Qo=4 L/min, Qw=1.2 L/min, Qw ’ =0.5 L/min. Adopted from Barbier, Willaime et al. (2006)

Nonlinear dynamic systemNonlinear dynamic system

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55 Next planNext plan

1 、 A lot of improvements should consider in order to design a more

accurate model . It should consider pressure value of the bubbles and

two phases mix. After that , the influence coming from feedback should

be added in the model.

2 、 Attempt to use the method of nonlinear dynamic system to describe

the microchannel system, and then make some accurate predictions.

3 、 Wish to verify some assumptions by experiment, like the actual

situation of flow disturbance and the its capacity to resist the

interference.