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

2. Structure o Introduction to condensation in microchannels o 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

3. Structure o 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

4. Introduction o Condensation inside horizontal microchannels o Automotive air-conditioning, petrochemical industry o Reduce use of ozone-killing fluids o Increase heat transfer coefficient and pressure drop o Surface tension + Viscosity >>> gravitational forces Heat and Mass Transfer Laboratory 4

5. Pressure drop o Common parameters used by several correlations o Liquid Reynolds number o Vapor Reynolds number o Liquid-only Reynolds number o Vapor-only Reynolds number Heat and Mass Transfer Laboratory 5

6. Pressure drop o Common parameters used by several correlations o Single-phase friction factor (smooth tube) o Single-phase pressure gradients Heat and Mass Transfer Laboratory 6

7. Pressure drop prediction models o Friedel (1979;1980) o Considered Parameters o Liquid only single-phase pressure gradient o Liquid only and vapor only friction factor o Fluid and geometric properties o Range / applicability o D > 1 mm o Adiabatic o μ l /μ v < 1000 Heat and Mass Transfer Laboratory 7

8. Pressure drop prediction models o Friedel (1979;1980) Heat and Mass Transfer Laboratory 8

9. Pressure drop prediction models o Chen et al. (2001) o Modification of the Friedel correlation by adding two-phase multiplier o Considered Parameters o Two-phase pressure gradient by Friedel o We, Bo, Re v, Re lo o Range / applicability o 3.17 < D < 9 mm for R-410A o 5°C < T sat < 15°C o 50 < G < 600 kg/m 2 s Heat and Mass Transfer Laboratory 9

10. Pressure drop prediction models Heat and Mass Transfer Laboratory 10 o Chen et al. (2001)

11. Pressure drop prediction models o Cavallini et al. (2002) o Modification of the Friedel correlaction for annular flow. o Considered Parameters o Liquid only single-phase pressure gradient o Liquid only and vapor only friction factor o Fluid and geometric properties o Range / applicability o D = 8 mm for R-134a, R-410a and others o 30°C < T sat < 50°C o 100 < G < 750kg/m 2 s Heat and Mass Transfer Laboratory 11

12. Pressure drop prediction models o Cavallini et al. (2002) Heat and Mass Transfer Laboratory 12 Friedel

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

14. Pressure drop prediction models o Wilson et al. (2003) o Considered parameters o Single-phase pressure gradients (liquid-only) o Martinelli parameter o Range / applicabilty o Flattened round smooth, axial, and helical microfin tubes. o 1.84 < D < 7.79 mm for R-134a, R-410A o T sat = 35°C o 75 < G < 400 kg/m 2 s Heat and Mass Transfer Laboratory 14

15. Pressure drop prediction models o Wilson et al. (2003) Heat and Mass Transfer Laboratory 15 Model uses liquid-only two-phase multiplier of Jung and Radermacher (1989): X tt is the Martinelli dimensionless parameter for turbulent flow in the gas and liquid phases. Insert formulation

16. Pressure drop prediction models o Wilson et al. (2003) Heat and Mass Transfer Laboratory 16 Knowing the single-phase pressure gradient, the two-phase pressure grandient is: Single-phase friction factors are calculated using the Churchill correlation (1977): with

17. Pressure drop prediction models o Garimella et al. (2005) o Considered parameters o Single-phase pressure gradients o Martinelli parameter o Surface tension parameter o Fluid and geometric properties o Range / applicabilty o 0.5 < D < 4.91 mm for R-134a o T sat ~ 52°C o 150 < G < 750 kg/m 2 s Heat and Mass Transfer Laboratory 17

18. Pressure drop prediction models o Garimella et al. (2005) Heat and Mass Transfer Laboratory 18 Void fraction is calculated using the Baroczy (1965) correlation: Liquid and vapor Re values are given by:

19. Pressure drop prediction models o Garimella et al. (2005) Heat and Mass Transfer Laboratory 19 Liquid and vapor friction factors: Therefore, the single-phase pressure gradients are given and the Martinelli parameter is calculated:

20. Pressure drop prediction models o Garimella et al. (2005) Heat and Mass Transfer Laboratory 20 Liquid superficial velocity is given by: This velocity is used to evaluate the surface tension parameter:

21. Pressure drop prediction models o Garimella et al. (2005) Heat and Mass Transfer Laboratory 21 Interfacial friction factor: Laminar region: Turbulent region (Blasius):

22. Pressure drop prediction models o Garimella et al. (2005) Heat and Mass Transfer Laboratory 22 The pressure gradient is determined as follows:

23. Pressure drop prediction models o Graph analysis for R-134a Heat and Mass Transfer Laboratory 23 G = 400 kg/m 2 sG = 800 kg/m 2 s T sat = 40°C, D = 1.4 mm

24. Pressure drop prediction models o Graph analysis for R-410A Heat and Mass Transfer Laboratory 24 G = 600 kg/m 2 sG = 1000 kg/m 2 s T sat = 40°C, D = 1.4 mm

25. Heat transfer o Common parameters used by several correlations o Prandtl number o Reduced pressure o Martinelli parameter Heat and Mass Transfer Laboratory 25

26. Heat transfer prediction models o Shah (1979) o Considered parameters o Vapor Velocity o Liquid-only Reynolds number o Liquid Prandtl number o Reduced pressure o Fluid and geometric properties o Range / applicability o 7 < D < 40 mm o Various refrigerants o 11 < G < 211 kg/m 2 s o 21 < T sat < 310°C Heat and Mass Transfer Laboratory 26

27. Heat transfer prediction models o Shah (1979) Heat and Mass Transfer Laboratory 27 Applicability range: If range is respected, compute liquid-only transfer coefficient:

28. Heat transfer prediction models o Shah (1979) Heat and Mass Transfer Laboratory 28 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.

29. Heat transfer prediction models Heat and Mass Transfer Laboratory 29 o Dobson and Chato (1998) o Considered parameters o Liquid, vapor-only Reynolds number o Martinelli parameter o Zivi’s (1964) void fraction o Galileo number o Modified Soliman Froude number o Liquid Prandtl number o Range / applicability o D = 7.04 mm o 25 < G < 800 kg /m 2 s o 35 < T sat < 60°C

30. Heat transfer prediction models o Dobson and Chato (1998) Heat and Mass Transfer Laboratory 30 Calculate the modified Soliman Froude number:

31. Heat transfer prediction models o Dobson and Chato (1998) Heat and Mass Transfer Laboratory 31 With:

32. Heat transfer prediction models o Dobson and Chato (1998) Heat and Mass Transfer Laboratory 32 For Fr so > 20, the annular flow correlation proposed is And the resulting heat transfer coefficient is:

33. Heat transfer prediction models o Cavallini et al. (2002) Applicable for annular regime only o Considered Parameters o Pressure drop o Dimensionless film thickness o Dimensionless temperature o Re, Pr o Fluid and geometric properties o Range / applicability o D = 8 mm o R134a and R410a o 100 < G < 750 kg/m 2 s o 30 < T sat < 50°C Heat and Mass Transfer Laboratory 33

34. Heat transfer prediction models Heat and Mass Transfer Laboratory 34 o Calculation of the shear stress o Dimensionless film thickness

35. Heat transfer prediction models Heat and Mass Transfer Laboratory 35 o Dimensionless temperature o Heat transfer coefficient

36. Heat transfer prediction models o Bandhauer et al. (2005) o Considered parameters o Pressure drop o Dimensionless film thickness o Turbulent dimensionless temperature o Pr o Fluid and geometric properties o Range / applicability o 0.4 < D < 4.9 mm o R134a o 150 < G < 750 kg/m 2 s Heat and Mass Transfer Laboratory 36

37. Heat transfer prediction models o Bandhauer et al. (2005) Heat and Mass Transfer Laboratory 37 Interfacial shear stress: Friction velocity is now calculated:

38. Heat transfer prediction models o Bandhauer et al. (2005) Heat and Mass Transfer Laboratory 38 Film thickness is directly calculated from void fraction: This thickness is used to obtain the dimensionless film thickness:

39. Heat transfer prediction models o Bandhauer et al. (2005) Heat and Mass Transfer Laboratory 39 Turbulent dimensionless temperature is given by: Therefore, the heat transfer coefficient is:

40. Heat transfer Heat and Mass Transfer Laboratory 40 o Graph analysis for R134a G=175 kg/m 2 sG=400 kg/m2s D=2.75mm, T sat =35°C

41. Heat transfer Heat and Mass Transfer Laboratory 41 o Graph analysis for R410a G=175 kg/m 2 sG=400 kg/m2s D=2.75mm, T sat =35°C

42. Questions ?

43. Thank you for your (hard) attention !