Heat and Mass Transfer Laboratory 1

Hussein DhananiSebastian SchmidtChristian Metzger

Assistant: Marcel Christians-Lupi

Teacher: Prof. J.R Thome

Condensation in mini- and microchannels

20 December 2007

Structureo Introduction to condensation in

microchannelso Pressure drop

o Prediction models• Friedel (1979;1980)• Chen (2001)• Cavallini (2001;2002)• Wilson (2003)• Garimella (2005)

o Graph analysis

Heat and Mass Transfer Laboratory 2

Structureo Heat transfer

o Prediction models• Shah (1979)• Dobson & Chato (1998)• Cavallini (2002)• Bandhauer (2005)

o Graph analysis

o Questions

Heat and Mass Transfer Laboratory 3

Introductiono Condensation inside horizontal microchannels

oAutomotive air-conditioning, petrochemical industry

oReduce use of ozone-killing fluids

o Increase heat transfer coefficient and pressure drop

oSurface tension + Viscosity >>> gravitational forces

Heat and Mass Transfer Laboratory 4

Pressure dropo Physical basics

Heat and Mass Transfer Laboratory 5

frictionalmomentumstatictotal PPPP

Inclination of the tube

(pressure head)

Acceleration of the flow

(change of densitiy or mass flux)

Friction on the wall

Pressure dropo Common parameters used by several

correlations

o Liquid Reynolds number

oVapor Reynolds number

o Liquid-only Reynolds number

oVapor-only Reynolds number

Heat and Mass Transfer Laboratory 6

ll

xGD

)1(

Re

vv

GDx

Re

llo

GD

Re

vvo

GD

Re

Pressure dropo Common parameters used by several

correlations

oSingle-phase friction factor (smooth tube)

oSingle-phase pressure gradients

Heat and Mass Transfer Laboratory 7

volovlvolovlXfor

X

X

XX

fandfff

f

,,

Re

37530

7

Reln457,2

Re

88

,,,

12

15,1

16169,012

v

vo

vol

lo

lo

v

v

vl

l

l

D

Gf

dz

dP

D

Gf

dz

dP

D

xGf

dz

dP

D

xGf

dz

dP

2

²

2

²

2

²²

2

)²1²(

Pressure drop prediction modelso Friedel (1979;1980)

o Considered Parameterso Liquid only single-phase pressure gradient o Liquid only and vapor only friction factoro Fluid and geometric properties

o Range & applicabilityo D > 1 mmo Adiabatico μl/μv < 1000

Heat and Mass Transfer Laboratory 8

Pressure drop prediction modelso Friedel (1979;1980)

Heat and Mass Transfer Laboratory 9

lodz

dPlodz

dP

WeFr

FHElo

WeandFrgDGwith

l

x

v

xTP

l

v

l

v

v

lHxxFlofv

voflxxE

2

035,0045,024,32

,,,1

1

7,0

1

19,091,0

;24,0

)1(78,0

;²)²1(

Pressure drop prediction models

o Chen et al. (2001)

o Modification of the Friedel correlation by adding two-phase multiplier

o Considered Parameterso Two-phase pressure gradient by Friedelo We, Bo, Rev, Relo

o Range & applicabilityo 3.17 < D < 9 mm for R-410Ao 5°C < Tsat < 15°C

o 50 < G < 600 kg/m2s

Heat and Mass Transfer Laboratory 10

Pressure drop prediction models

Heat and Mass Transfer Laboratory 11

22²

2,0

09,0

45,0

5,206,05,2

5,24,01Re

Re0333,0

;

D

vlgBoandm

DGWewith

Bov

lo

Friedel BoBo

We

Boe

dz

dP

dz

dP

o Chen et al. (2001)

Pressure drop prediction models o Cavallini et al. (2002)

o Modification of the Friedel correlaction for annular flow.

o Considered Parameterso Liquid only single-phase pressure gradient o Liquid only and vapor only friction factoro Fluid and geometric properties

o Range & applicabilityo D = 8 mm for R-134a , R-410a and otherso 30°C < Tsat < 50°C

o 100 < G < 750kg/m2sHeat and Mass Transfer

Laboratory 12

Pressure drop prediction models o Cavallini et al. (2002)

Heat and Mass Transfer Laboratory 13

lodz

dPlodz

dP

WeFr

FHElo

WeandFrgDGwith

l

x

v

xTP

l

v

l

v

v

lHxxFlofv

voflxxE

2

035,0045,024,32

,,,1

1

7,0

1

19,091,0

;24,0

)1(78,0

;²)²1(

Friedel

Pressure drop prediction models o Cavallini et al. (2002)

Heat and Mass Transfer Laboratory 14

lodz

dPlodz

dP

We

FHElo

WegDGwith

v

l

v

l

v

v

lHxFlofv

voflxxE

2

1458,0262,12

,,,

477,3

1

181,13278,0

;6978,0

;²)²1(

Pressure drop prediction modelso Wilson et al. (2003)

o Considered parameterso Single-phase pressure gradients (liquid-only)o Martinelli parameter

o Range & applicabiltyo Flattened round smooth, axial, and helical microfin tubes.o 1.84 < D < 7.79 mm for R-134a, R-410Ao Tsat = 35°C

o 75 < G < 400 kg/m2s

Heat and Mass Transfer Laboratory 15

Pressure drop prediction modelso Wilson et al. (2003)

Heat and Mass Transfer Laboratory 16

Model uses liquid-only two-phase multiplier of Jung and Radermacher (1989):

Xtt is the Martinelli dimensionless parameter for turbulent flow in the gas and liquid phases.

lo2 12.82Xtt

1.47 (1 x)1.8

Insert formulation

Pressure drop prediction modelso Wilson et al. (2003)

Heat and Mass Transfer Laboratory 17

Knowing the single-phase pressure gradient, the two-phase pressure grandient is:

P

Llo

2 dP

dz

lo

dP

dz

lo

floG

2

2Dl

Single-phase friction factors are calculated using the Churchill correlation (1977):

f 88

Re

12

2.457gln1

7

Re

0.9

0.27 / D

16

37530

Re

16

1.5

1/12

with

Pressure drop prediction modelso Garimella et al. (2005)

o Considered parameterso Single-phase pressure gradientso Martinelli parametero Surface tension parametero Fluid and geometric properties

o Range & applicabiltyo 0.5 < D < 4.91 mm for R-134ao Tsat ~ 52°C

o 150 < G < 750 kg/m2s

Heat and Mass Transfer Laboratory 18

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 19

113.065.074.011

v

l

l

vx

x

Void fraction is calculated using the Baroczy (1965) correlation:

Liquid and vapor Re values are given by:

l

xGDl

1

1Re

v

GDxv

Re

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 20

ll

fRe

64

Liquid and vapor friction factors:

Therefore, the single-phase pressure gradients are given and the Martinelli parameter is calculated:

21

vdzdPldzdP

X

25.0Re316.0 vv

f

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 21

1

1

l

xGl

j

Liquid superficial velocity is given by:

This velocity is used to evaluate the surface tension parameter:

ll

j

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 22

lfcb

laAX

if Re

Interfacial friction factor:

Laminar region:

121.0,930.0,427.0,10308.1:2100Re 3 cbaAl

Turbulent region (Blasius):

021.0,327.0,532.0,64.25:3400Re cbaAl

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 23

Dv

xGi

fdz

dP 15.2

22

2

1

The pressure gradient is determined as follows:

Pressure drop prediction modelso Graph analysis for R-134a

Heat and Mass Transfer Laboratory 24

G = 400 kg/m2s G = 800 kg/m2s

Tsat = 40°C , D = 1.4 mm

Pressure drop prediction modelso Graph analysis for R-410A

Heat and Mass Transfer Laboratory 25

G = 600 kg/m2s G = 1000 kg/m2s

Tsat = 40°C , D = 1.4 mm

Heat transfero Common parameters used by several

correlations

oPrandtl number

oReduced pressure

oMartinelli parameter

Heat and Mass Transfer Laboratory 26

Heat transfer prediction models o Shah (1979)

o Considered parameterso Vapor Velocity o Liquid-only Reynolds numbero Liquid Prandtl numbero Reduced pressureo Fluid and geometric properties

o Range & applicabilityo 7 < D < 40 mm o Various refrigerantso 11 < G < 211 kg/m2so 21 < Tsat < 310°C

Heat and Mass Transfer Laboratory 27

Heat transfer prediction models o Shah (1979)

Heat and Mass Transfer Laboratory 28

Applicability range:

If range is respected, compute liquid-only transfer coefficient:

0.002 Pred 0.4421Tsat 310C

3 Vv xG

v

300 m s 10.83 G 210.56

hlo 0.023Relo0.8Prl

0.4kl

D

Heat transfer prediction models o Shah (1979)

Heat and Mass Transfer Laboratory 29

For heat transfer coefficient, apply multiplier:

Widely used for design. Improvement needed for results near critical pressure and vapor quality from 0.85 to 1.

h hlo (1 x)0.8 3.8x0.76 (1 x)0.04

Pred0.38

Heat transfer prediction models

Heat and Mass Transfer Laboratory 30

o Dobson and Chato (1998)

o Considered parameterso Liquid, vapor-only Reynolds number o Martinelli parametero Zivi’s (1964) void fractiono Galileo numbero Modified Soliman Froude numbero Liquid Prandtl number

o Range & applicabilityo D = 7.04 mmo 25 < G < 800 kg /m2so 35 < Tsat < 60°C

Heat transfer prediction models o Dobson and Chato (1998)

Heat and Mass Transfer Laboratory 31

Calculate the modified Soliman Froude number:

Frso 0.025Rel1.59 11.09Xtt

0.039

Xtt

1.5

1

Ga0.5for Rel 1250

Frso 1.26Rel1.04 11.09Xtt

0.039

Xtt

1.5

1

Ga0.5for Rel 1250

Heat transfer prediction models o Dobson and Chato (1998)

Heat and Mass Transfer Laboratory 32

With:

Rel GD(1 x)

l

11 x

x

v

l

2 /3

1

Ga gl (l v )D 3l2

Heat transfer prediction models o Dobson and Chato (1998)

Heat and Mass Transfer Laboratory 33

For Frso > 20, the annular flow correlation proposed is

Nuannular 0.023Rel0.8Prl

0.4 12.22

Xtt0.89

And the resulting heat transfer coefficient is:

h Nu kl

D

Heat transfer prediction models o Cavallini et al. (2002) Applicable for annular regime

only

o Considered Parameterso Pressure drop o Dimensionless film thicknesso Dimensionless temperatureo Re, Pro Fluid and geometric properties

o Range & applicabilityo D = 8 mm o R134a and R410ao 100 < G < 750 kg/m2so 30 < Tsat < 50°C

Heat and Mass Transfer Laboratory 34

Heat transfer prediction models

Heat and Mass Transfer Laboratory 35

4

D

dz

dp

f

o Calculation of the shear stress

o Dimensionless film thickness

1145ReRe0504,0

1145Re2

Re

8

7

5,0

ll

ll

for

for

Heat transfer prediction models

Heat and Mass Transfer Laboratory 36

oDimensionless temperature

3030

ln495,0Pr51lnPr5

30515

Pr1lnPr5

5Pr

ll

ll

l

T

oHeat transfer coefficient

T

C

h lpll

5,0

Heat transfer prediction models o Bandhauer et al. (2005)

o Considered parameterso Pressure drop o Dimensionless film thicknesso Turbulent dimensionless temperatureo Pro Fluid and geometric properties

o Range & applicabilityo 0.4 < D < 4.9 mmo R134ao 150 < G < 750 kg/m2s

Heat and Mass Transfer Laboratory 37

Heat transfer prediction models o Bandhauer et al. (2005)

Heat and Mass Transfer Laboratory 38

Interfacial shear stress:

4

D

L

Pi

Friction velocity is now calculated:

l

iu

*

Heat transfer prediction models o Bandhauer et al. (2005)

Heat and Mass Transfer Laboratory 39

Film thickness is directly calculated from void fraction:

2

1D

This thickness is used to obtain the dimensionless film thickness:

l

l u

*

Heat transfer prediction models o Bandhauer et al. (2005)

Heat and Mass Transfer Laboratory 40

Turbulent dimensionless temperature is given by:

11

5Prln5Pr5

llT

Therefore, the heat transfer coefficient is:

T

uCph ll

*

2100Re lif

Heat transfer

Heat and Mass Transfer Laboratory 41

oGraph analysis for R134a

G=175 kg/m2s G=400 kg/m2s

D=2.75mm, Tsat=35°C

Heat transfer

Heat and Mass Transfer Laboratory 42

oGraph analysis for R410a

G=175 kg/m2s G=400 kg/m2s

D=2.75mm, Tsat=35°C

Questions ?

Thank you for your attention !