Condensation in mini- and microchannels
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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.
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