1. Condensation in mini- and microchannels
Hussein Dhanani
Sebastian Schmidt
Christian Metzger
Assistant: Marcel Christians-Lupi
Teacher: Prof. J.R Thome
20 December 2007
Heat and Mass Transfer Laboratory

2. Heat and Mass Transfer Laboratory
Structure
Introduction to condensation in microchannels
Pressure drop
Prediction models
Friedel (1979;1980)
Chen (2001)
Cavallini (2001;2002)
Wilson (2003)
Garimella (2005)
Graph analysis
HUSSEIN STARTS
Heat and Mass Transfer Laboratory

3. Heat and Mass Transfer Laboratory
Structure
Heat transfer
Prediction models
Shah (1979)
Dobson & Chato (1998)
Cavallini (2002)
Bandhauer (2005)
Graph analysis
Questions
Heat and Mass Transfer Laboratory

4. Heat and Mass Transfer Laboratory
Introduction
Condensation inside horizontal microchannels
Automotive air-conditioning, petrochemical industry
Reduce use of ozone-killing fluids
Increase heat transfer coefficient and pressure drop
Surface tension + Viscosity >>> gravitational forces
microchannel increasingly use in industry to yield compact geometries for heat transfer in a wide variety of application. Use for the purpose of reducing inventories of hasardous fluids in components and for reducing consumption for component fabrication. ecological by reducing the amounts of harmful fluids.
Knowledge of the two-phase frictional characteristics is essential since it would certainly improve the accuracy of the design of a thermal system.
At some mass velocity higher heat transfer coeff can be obtained when reducing the hydraulic diameter at the expense of higher frictional pressure drop.
large use in compact condensers for the air-conditioning systems in automobiles for many years. they have hydraulic diameters of mm range. Compactness is valuable because it provides large condensation heat transfer coefficient, high surface-to-volume ratios and reduced air-side pressure to the use of microchannels. -> Heat transfer coeff and pressure gradients increase with decreasing hydraulic diameter.
where surface tension and viscous forces dominate over gravitational forces so flow patterns are independent of channel orientation that is why we do experiments on horizontal tubes.
Micro and Mini channel transition is not easy to determine.
Heat and Mass Transfer Laboratory 4

5. Pressure drop Physical basics Inclination of the tube
(pressure head)
Acceleration of the flow
(change of densitiy or mass flux)
Friction on the wall
CHRISTIAN ..
The total pressure drop of a fluid is due to the variation of kinetic and potential energy of the fluid and that due to friction on the walls of the flow channel. The total pressure drop is a sum of the static pressure drop(elevation head), the momentum pressure drop (acceleration due to variation of density) and the frictional pressure drop (friction on the wall).
The static pressure drop equals zero since these methods were set up for horizontal tubes (minichannel) or the effect of gravity can be neglected according to the microchannel assumption.
For a condensing flow the kinetic energy of the outgoing flow is smaller than that of the incoming flow. Hence, the momentum pressure drop results in an increase in pressure at the exit, i.e. pressure recovery. For condensing flows, it is common to ignore the momentum recovery as only some of it may actually be realized in the flow and ignoring it provides some conservatism in the design.
The following methods only predict the frictional pressure drop
Heat and Mass Transfer Laboratory

6. Heat and Mass Transfer Laboratory
Pressure drop
Common parameters used by several correlations
Liquid Reynolds number
Vapor Reynolds number
Liquid-only Reynolds number
Vapor-only Reynolds number
CHRISTIAN ..
Reynolds is the ratio between mass flux and viscosity.
The « only » number is when you considered tubes filled with only vapor or liquid. Independant of vapor quality.
Heat and Mass Transfer Laboratory

7. Heat and Mass Transfer Laboratory
Pressure drop
Common parameters used by several correlations
Single-phase friction factor (smooth tube)
Single-phase pressure gradients
Friction factor is a strong functio of the Reynolds. Empirical equation.
Heat and Mass Transfer Laboratory

8. Pressure drop prediction models
Friedel (1979;1980)
Considered Parameters
Liquid only single-phase pressure gradient
Liquid only and vapor only friction factor
Fluid and geometric properties
Range & applicability
D > 1 mm
Adiabatic
μl/μv < 1000
The calculation of the frictional pressure drop in this method (as in the following) bases on the separated flow model. This model considers that the two phases are artificially separated into two streams, each flowing in it’s own pipe. The areas of the two pipes are proportional to the void fraction.
Developed from database of points
Includes surface tension effects
Calculated vs experimental pressure gradient is +- 30% for R-134a and more than 30 % for R-410A.
MINICHANNEL
Heat and Mass Transfer Laboratory

9. Pressure drop prediction models
Friedel (1979;1980)
H is a type of « martinelli parameter »
Martinelli parameter is a ratio of pressure gradient between liquid and gas phase. Depends on the state of the phases (turbulent- laminar)
Froude number = Inertia / gravitation
Weber = Inertia / surface tension
Heat and Mass Transfer Laboratory

10. Pressure drop prediction models
Chen et al. (2001)
Modification of the Friedel correlation by adding two-phase multiplier
Considered Parameters
Two-phase pressure gradient by Friedel
We, Bo, Rev, Relo
Range & applicability
3.17 < D < 9 mm for R-410A
5°C < Tsat < 15°C
50 < G < 600 kg/m2s
Accuracy outside the +-30% interval.
MINICHANNEL
Heat and Mass Transfer Laboratory

11. Pressure drop prediction models
Chen et al. (2001)
Bo = Buoyancy (densities difference)/ surface tension
We = Intertia / surface tension
Heat and Mass Transfer Laboratory

12. Pressure drop prediction models
Cavallini et al. (2002)
Modification of the Friedel correlaction for annular flow.
Considered Parameters
Liquid only single-phase pressure gradient
Liquid only and vapor only friction factor
Fluid and geometric properties
Range & applicability
D = 8 mm for R-134a , R-410a and others
30°C < Tsat < 50°C
100 < G < 750kg/m2s
MINICHANNEL
Heat and Mass Transfer Laboratory

13. Pressure drop prediction models
Cavallini et al. (2002)
Friedel
Heat and Mass Transfer Laboratory

14. Pressure drop prediction models
Cavallini et al. (2002)
Heat and Mass Transfer Laboratory

15. Pressure drop prediction models
Wilson et al. (2003)
Considered parameters
Single-phase pressure gradients (liquid-only)
Martinelli parameter
Range & applicabilty
Flattened round smooth, axial, and helical microfin tubes.
1.84 < D < 7.79 mm for R-134a, R-410A
Tsat = 35°C
75 < G < 400 kg/m2s
HUSSEIN…
DP increases as tube approaches rectangular shape
There are not geometrical factor of fin or shape. Assume Dh allows it to work with everything. Dh = 4* area / perimeter
Heat and Mass Transfer Laboratory 15

16. Pressure drop prediction models
Wilson et al. (2003)
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.
The liquid only formulation treats all refrigerant mass flow as if it is in the liquid phase.
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17. Pressure drop prediction models
Wilson et al. (2003)
Knowing the single-phase pressure gradient, the two-phase pressure grandient is:
with
Single-phase friction factors are calculated using the Churchill correlation (1977):
Espsilon = 0 for smooth tubes
Heat and Mass Transfer Laboratory 17

18. Pressure drop prediction models
Garimella et al. (2005)
Considered parameters
Single-phase pressure gradients
Martinelli parameter
Surface tension parameter
Fluid and geometric properties
Range & applicabilty
0.5 < D < 4.91 mm for R-134a
Tsat ~ 52°C
150 < G < 750 kg/m2s
SEBASTIAN..
87% of the data within +- 20%
MICROCHANNELS
Heat and Mass Transfer Laboratory 18

19. Pressure drop prediction models
Garimella et al. (2005)
Void fraction is calculated using the Baroczy (1965) correlation:
Liquid and vapor Re values are given by:
Heat and Mass Transfer Laboratory 19

20. Pressure drop prediction models
Garimella et al. (2005)
Liquid and vapor friction factors:
Therefore, the single-phase pressure gradients are given and the Martinelli parameter is calculated:
Laminar liquid film
Turbulent vapor film
Heat and Mass Transfer Laboratory 20

21. Pressure drop prediction models
Garimella et al. (2005)
Liquid superficial velocity is given by:
This velocity is used to evaluate the surface tension parameter:
Heat and Mass Transfer Laboratory 21

22. Pressure drop prediction models
Garimella et al. (2005)
Interfacial friction factor:
Laminar region:
Interpolation of G and x
Turbulent region (Blasius):
Heat and Mass Transfer Laboratory 22

23. Pressure drop prediction models
Garimella et al. (2005)
The pressure gradient is determined as follows:
Heat and Mass Transfer Laboratory 23

24. Pressure drop prediction models
Graph analysis for R-134a
SEBASTIAN…
When mass flux increases -> pressure drop increase
Usual to have huge deviation for pressure drop.
Result are not accurate because you describe two phases phenomenon with single-phase model.
Due to very sensitive experimental conditions, measurement can be false.
Consider only from x = 0.05 – 0.95
Wilson is irrelevant because it is outside the G range
Garimella steps are due to transition region.
Predicted pressure drop vary considerably. Large variation is due to different two-phase multipliers from diff investigators. Only recommendation : choose a model based on geometry, fluid and operation conditions similar to those of interest.
G = 400 kg/m2s
G = 800 kg/m2s
Tsat = 40°C , D = 1.4 mm
Heat and Mass Transfer Laboratory 24

25. Pressure drop prediction models
Graph analysis for R-410A
When mass flux increases -> pressure drop increase
Usual to have huge deviation for pressure drop.
G = 600 kg/m2s
G = 1000 kg/m2s
Tsat = 40°C , D = 1.4 mm
Heat and Mass Transfer Laboratory 25

26. Heat and Mass Transfer Laboratory
Heat transfer
Common parameters used by several correlations
Prandtl number
Reduced pressure
Martinelli parameter
HUSSEIN…
(Use reduced pressure for accurate radial distribution of void fraction.)
Heat and Mass Transfer Laboratory 26

27. Heat transfer prediction models
Shah (1979)
Considered parameters
Vapor Velocity
Liquid-only Reynolds number
Liquid Prandtl number
Reduced pressure
Fluid and geometric properties
Range & applicability
7 < D < 40 mm
Various refrigerants
11 < G < 211 kg/m2s
21 < Tsat < 310°C
Large database from 21 sources
Widely used general purpose empirical correlation
R11, R12, R22, R113, ethanol, methanol
Heat and Mass Transfer Laboratory 27

28. Heat transfer prediction models
Shah (1979)
Applicability range:
If range is respected, compute liquid-only transfer coefficient:
In heat transfer problems, the Prandtl number controls the relative thickness of the momentum and thermal boundary layers.
When Pr is small, it means that the heat diffuses very quickly compared to the velocity (momentum). This means that for liquid materials the thickness of the thermal boundary layer is much bigger than the velocity boundary layer.
Re describes the flow boundary layer. Prandtl allows to deduct flow BL from thermal BL
Shear-driven because there is Reynolds and Pr.
Heat and Mass Transfer Laboratory 28

29. Heat transfer prediction models
Shah (1979)
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.
Shah use the reduced pressure Pred = Psat / P crit.
Thome recommend use Shah when G > 200
Heat and Mass Transfer Laboratory 29

30. Heat transfer prediction models
Dobson and Chato (1998)
Considered parameters
Liquid, vapor-only Reynolds number
Martinelli parameter
Zivi’s (1964) void fraction
Galileo number
Modified Soliman Froude number
Liquid Prandtl number
Range & applicability
D = 7.04 mm
25 < G < 800 kg /m2s
35 < Tsat < 60°C
Fluid properties effect not very significant
No significant effect of diameter reduction
Considered for annular flow only !!
Heat and Mass Transfer Laboratory 30

31. Heat transfer prediction models
Dobson and Chato (1998)
Calculate the modified Soliman Froude number:
Distinguish which heat transfer regime to apply. Transition from annular to stratified flow using a criterion based on froude number.
Dobson & chato noted 20 as the transition value for their method.
Annular flow correlation is utilized
When G >500
When G < 500 and Frso > 20 otherwise use stratified correlation
Heat and Mass Transfer Laboratory 31

32. Heat transfer prediction models
Dobson and Chato (1998)
With:
Heat and Mass Transfer Laboratory 32

33. Heat transfer prediction models
Dobson and Chato (1998)
For Frso > 20, the annular flow correlation proposed is
And the resulting heat transfer coefficient is:
Heat and Mass Transfer Laboratory 33

34. Heat transfer prediction models
Cavallini et al. (2002) Applicable for annular regime only
Considered Parameters
Pressure drop
Dimensionless film thickness
Dimensionless temperature
Re, Pr
Fluid and geometric properties
Range & applicability
D = 8 mm
R134a and R410a
100 < G < 750 kg/m2s
30 < Tsat < 50°C
-CHRISTIAN…
Own data and database from others used for correlations
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35. Heat transfer prediction models
Calculation of the shear stress
Dimensionless film thickness
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36. Heat transfer prediction models
Dimensionless temperature
Heat transfer coefficient
Heat and Mass Transfer Laboratory 36

37. Heat transfer prediction models
Bandhauer et al. (2005)
Considered parameters
Pressure drop
Dimensionless film thickness
Turbulent dimensionless temperature Pr
Fluid and geometric properties
Range & applicability
0.4 < D < 4.9 mm
R134a
150 < G < 750 kg/m2s
SEBASTIAN…
Addresses annular, mist and disperse wave regimes
Interfacial shear stress from models developed specifically for microchannels
Only for laminar flows
Heat and Mass Transfer Laboratory 37

38. Heat transfer prediction models
Bandhauer et al. (2005)
Interfacial shear stress:
Friction velocity is now calculated:
Heat and Mass Transfer Laboratory 38

39. Heat transfer prediction models
Bandhauer et al. (2005)
Film thickness is directly calculated from void fraction:
This thickness is used to obtain the dimensionless film thickness:
Heat and Mass Transfer Laboratory 39

40. Heat transfer prediction models
Bandhauer et al. (2005)
Turbulent dimensionless temperature is given by:
Therefore, the heat transfer coefficient is:
Heat and Mass Transfer Laboratory 40

41. Heat and Mass Transfer Laboratory
Heat transfer
Graph analysis for R134a
CHRISTIAN..
With increasing mass flux the heat transfer coefficient increases
More accurate than pressure drop.
Peaks at high x don’t have physical meaning.
Shah methods have conditions over vapor velocity which reduced its applicability zone.
Dobson & Chato…
Cavallini
G=175 kg/m2s
G=400 kg/m2s
D=2.75mm, Tsat=35°C
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42. Heat and Mass Transfer Laboratory
Heat transfer
Graph analysis for R410a
With increasing mass flux the heat transfer coefficient increases
Heat transfer increase with decreasing hydraulic diameter
Reasons of deviation is because methods are applied outside of the range.
All models except bandhauer were based on diameter in the ~8mm range. Less correlation based on diameter ~ 3 mm
G=175 kg/m2s
G=400 kg/m2s
D=2.75mm, Tsat=35°C
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43. Questions ?

44. Thank you for your attention !

45. Bibliography
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
A general correlation of heat transfer during film condensation, M.M Shah, 1978/ Int. J. Heat Mass Transfer vol.22, pp 547 – 556
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
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
Engineering Databook III. J.R Thome, 2006,Wolverine Tube, inc.