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

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

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

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 0.4 - 0.7 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

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

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

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

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 25000 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

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

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

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

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

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

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

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

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. Heat and Mass Transfer Laboratory 16

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 Heat and Mass Transfer Laboratory 34

Heat transfer prediction models Calculation of the shear stress Dimensionless film thickness Heat and Mass Transfer Laboratory 35

Heat transfer prediction models Dimensionless temperature Heat transfer coefficient Heat and Mass Transfer Laboratory 36

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

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

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

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

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 Heat and Mass Transfer Laboratory 41

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 Heat and Mass Transfer Laboratory 42

Questions ?

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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.