Condensation in mini- and microchannels

Heat and Mass Transfer Laboratory 1

Hussein DhananiSebastian SchmidtChristian Metzger

Assistant: Marcel Christians-LupiTeacher: 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

,,

Re37530

7Reln457,2

Re88

,,,

121

5,116169,012

v

vo

vol

lo

lo

v

v

vl

l

l

DGf

dzdP

DGf

dzdP

DxGf

dzdP

DxGf

dzdP

2²

2²

2²²

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 μl/μv < 1000

Heat and Mass Transfer Laboratory 8

Pressure drop prediction modelso Friedel (1979;1980)

Heat and Mass Transfer Laboratory 9

lodzdP

lodzdP

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

another 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°Co 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

5,24,01ReRe0333,0

;

D

vlgBoandm

DGWewith

Bov

lo

Friedel BoBo

We

Boe

dzdP

dzdP

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°Co 100 < G < 750kg/m2s

Heat and Mass Transfer Laboratory 12

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

Heat and Mass Transfer Laboratory 13

lodzdP

lodzdP

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

lodzdP

lodzdP

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°Co 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

1.05.09.01

GL

LG

xxX tt

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:

PL

lo2 dP

dz

lo

dPdz

lo

floG

2

2Dl

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

f 88Re

12

2.457gln 17Re

0.9

0.27 / D

16

37530Re

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°Co 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

llf Re

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 vvf

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 21

11

l

xGlj

Liquid superficial velocity is given by:

This velocity is used to evaluate the surface tension parameter:

llj

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 22

lfcb

laAXif 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

For the transition region an interpolation based on G and x is used.

Pressure drop prediction modelso Garimella et al. (2005)

Heat and Mass Transfer Laboratory 23

Dv

xGifdz

dP 15.2

22

21

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

L

LLL k

Cp

Pr

1.05.09.01

GL

LG

xxX tt

crit

satred P

PP

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 0.4421 Tsat 310C

3 Vv xGv

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 parameters

o 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

xv

l

2 /3

1

Ga gl (l v )D 3l2

)12arccos(1

strat

LG

wsatpLl h

TTcJa

gDmFrL

L 2

2

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 12.22Xtt0.89

And the resulting heat transfer coefficient is:

h Nu kl

D

Heat transfer prediction models o Dobson and Chato (1998)

Heat and Mass Transfer Laboratory 34

For Frso < 20 and G < 500 kg/m2s the stratified-wavy flow correlation proposed is

Where the forced convection term is given by:

forcedl

l

ll

tt

vo NuJa

GaX

xNu

1Pr

11.11Re23.0)(

25.0

58.0

12.0

2

14.080.0 376.1PrRe0195.0 ctt

LLforced XcNu

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 35

Heat transfer prediction models

Heat and Mass Transfer Laboratory 36

4D

dzdP

Cav

o Calculation of the shear stress

o Dimensionless film thickness

1145ReRe0504,0

1145Re2Re

87

5,0

ll

ll

for

for

Heat transfer prediction models

Heat and Mass Transfer Laboratory 37

oDimensionless temperature

3030

ln495,0Pr51lnPr5

30515

Pr1lnPr5

5Pr

ll

ll

l

T

oHeat transfer coefficient

T

Ch l

pll

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 38

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

Heat and Mass Transfer Laboratory 39

Interfacial shear stress:

4D

LP

i

Friction velocity is now calculated:

l

iu

*

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

Heat and Mass Transfer Laboratory 40

Film thickness is directly calculated from void fraction:

2

1 D

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 41

Turbulent dimensionless temperature is given by:

11

5Prln5Pr5

llT

Therefore, the heat transfer coefficient is:

TuCp

h ll*

2100Re lif

Heat transfer

Heat and Mass Transfer Laboratory 42

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 43

oGraph analysis for R410a

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

D=2.75mm, Tsat=35°C

Questions ?

Thank you for your attention !

Bibliographyo Heat Transfer and fluid flow in Minichannels and Microchannels. Kandlikar S.G., Garimella Srinivas, Li Dongqing, Colin Stephane, King Michael R. Elsevier Science & Technology (Netherlands), 2005o A general correlation of heat transfer during film condensation, M.M Shah, 1978/ Int. J. Heat Mass Transfer vol.22, pp 547 – 556o Refrigerant charge, pressure drop, and condensation heat transfer in flattened tubes. M.J. Wilson, T.A. Newell, J.C. Chato, C.A. Infante Ferreira, 2002, International Journal of Refrigeration 26 (2003) 442–451o Two-phase frictional pressure gradient of R236ea, R134a and R410A inside multi-port mini-channels. A. Cavallini , D. Del Col, L. Doretti, M. Matkovic, L. Rossetto, C. Zilio, 2005, Experimental Thermal and Fluid Science 29 (2005) 861–870

o Engineering Databook III. J.R Thome, 2006,Wolverine Tube, inc.