microchannels

8/7/2019 microchannels

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University of Illinois


Modeling Heat Transfer and Pressure

Drop for Liquid-Vapor Flows in theElongated-Bubble Flow Regime

Anthony M. JacobiRichard W. Kritzer Distinguished Professor of Mechanical Engineering

Co-Director ACRCUniversity of Illinois at Urbana-Champaign


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Motivation A vapor-compression system


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Motivation Heat exchangers


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Motivation Integrated as the IMCC


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Motivation Personal cooling systems


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Outline

Statement of goals

Summary of a heat transfer model

Background for modeling

Focus on the physical model

Review some validation

Pressure drop modeling

How is two-phase pressure-drop modeling approached?

A directly mechanistic model is superior

There are problems with our mechanistic models.

Some ideas for modelingrather loose ideas that you might shoot down.

Field and Hrnjak 2007, ACRC TR-271


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Statement of goals

Shamelessly promote the heat transfer model?

The apparent success of the model might say something about physics.

Present a loose overview of pressure-drop models.

Their apparent success might not say something about physicsIdentify problems in our mechanistic descriptions

There appear to be obvious weakness in our descriptions of the flows

Propose some ideas that might improve our models.

Backward boundary layers and surface tensionRelate back to application

To show that everything I presented might be meaningless


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Flow regime observations

Observations of flow regimes in microchannel f lows (modified from Qu et al . (2005) elongated bubble flow and annular flowdominate.


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A two-zone model of heat transfer to elongated-bubble flow (Jacobi and Thome 2002)

LPLV

LL

D

q

U

Initial bubble growth per Plessets theory gives the time required to generate apair, with Teff prescribed. With this period known, initial conditions on thepair geometry are determined for a known mass flux. An energy balance isapplied to the pair, and heat transfer is modeled as thin-film evaporation througho;


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1111


2

)(

))()((

+=R

t Lt LqD

dt

dL

V

LV V

Conservation of energy yields coupled ODEs for pair geometry

With pair geometry known at all times (locations), a thin-filmevaporation model is used to calculate heat transfer coefficient.

1

)(4

)();(

=

t U

t qLk t sh

L

poL


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0

5000

10000

15000

20000

40000 80000 120000 160000 200000

q (W/m 2)

Teff

=30 oC Teff

=38 oC

Teff

=45 oC

h (W/ m2K)

q (W/m2)


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0

5000

10000

15000

20000

150 200 250 300 350 400 450

m (kg/m 2s)

T=30 oC

T=38 oC

T=45 oC

h (W/m 2K )

G (kg/m2s)


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0

5000

10000

15000

20000

0 50000 100000 150000 200000

Current ModelData of Bao et al. (2000)

q (W/m 2)

A simple thin-film heattransfer model predictsthe observed trends. It isunnecessary--probably

wrong--to extrapolateconventional-scale datainterpretations to themesoscale. The successof this model suggestsnucleate boiling might

not dominate.h (W/ m2K )

q (W/m2)


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A three-zone model of heat transfer to elongated-bubble flow (Thome et al. 2004)


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Initial conditions

Pair length and velocity evolve

Down the tube

1p

v l

G x xL

f = +


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Two or three zones?

Motivated by Moriyama and Inoue (1996):

The constant C o is left as a free parameter


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Two or three zones?

Minimum film thickness, min, left as adjustable parameter


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Two or three zones?

,dry film vt t >If

,dry film vt t > , )

0, CS=V0(cos cos )

( ) ( )

c f b shear

pl l v v c p l l v v c

pA P F

dU d L L A U L L A

dt dt

+

+ = +

, ,( )sx bx rf x X X X X CS C C CS

F F a d V d V V V dAt

+ = +


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Pressure Drop

A proposal. 3 31

0

pv

v

LLv v p l l p

shear L

U U F C P dx dx

x x

= +

3 / 248( )

2

pv v l l v l l l

p p p

p l vp l v

p p

U pL L

L DL DL

dU L LU

dz L L

+ + +

+

:

Then


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Pressure Drop

Surface tension:

Shear:

Growth and acceleration of the triplet:

8

p pDL DL

3 / 24( )p pv v l l v l l l

p

U LL L

DL D +

2 p l vp l vp p

dU L LU yuk

dz L L

+

(cos )


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Pressure Drop

Will it work?

1/ 2

( )4 8

16

0 1

p

l v v l l v l l l l p p l p

p l vl v

l p p

U L L

L U L

dU L LDdz L L

C C

= + + +

+


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Outline

Statement of goals

Summary of a heat transfer model

Background for modeling

Focus on the physical model

Review some validation

Pressure drop modeling

How is two-phase pressure-drop modeling approached?

A directly mechanistic model is superior

There are problems with our mechanistic models.Some ideas for modelingrather loose ideas that you might shoot down.

Field and Hrnjak, 2007 ACRC TR-261.


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Field and Hrnjak, 2007, ACRC TR-261


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Mechanistic Adjusted S.F.

microchannels

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