condensation in mini- and microchannels
DESCRIPTION
Condensation in mini- and microchannels. Hussein Dhanani Sebastian Schmidt Christian Metzger Assistant: Marcel Christians-Lupi Teacher: Prof. J.R Thome. 20 December 2007. Structure. Introduction to condensation in microchannels Pressure drop Prediction models Friedel (1979;1980) - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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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
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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
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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
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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(
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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
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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(
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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°C
o 50 < G < 600 kg/m2s
Heat and Mass Transfer Laboratory 10
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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)
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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
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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
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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(
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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
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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
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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
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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
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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
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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
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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
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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
For the transition region an interpolation based on G and x is used.
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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:
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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
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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
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Heat transfero Common parameters used by several
correlations
oPrandtl number
oReduced pressure
oMartinelli parameter
Heat and Mass Transfer Laboratory 26
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
*
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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
*
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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
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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
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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
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Questions ?
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Thank you for your attention !
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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), 2005
o A general correlation of heat transfer during film condensation, M.M Shah, 1978/ Int. J. Heat Mass Transfer vol.22, pp 547 – 556
o 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) 442–451
o 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.