Abstract
A theoretical analysis of direct contact hygroscopic-condensation of cold vapor on hot films is presented. The condensation of the relatively low temperature, low pressure, vapors on a hot film of an hygroscopic brine solution may occur due to the reduced vapor pressure of a sufficiently concentrated solution.
The driving force for condensation is the difference between the partial pressure of water in the brine and the partial pressure of the condensing water vapor. The condensation is also governed by simultaneous mass transfer mechanisms, due to a non-isothermal absorption, with a possible opposing thermal driving force in the condensing vapor phase. The overall performance is determined by the accumulating effects of the various resistances to heat and mass transfer. The present study is aimed to elucidate the controlling mechanisms associated with this absorption-condensation process, and suggest overall transfer rates at the laminar and turbulent flow regimes.
Zusammenfassung
Es wird eine theoretische Analyse der hygroskopischen Kondensation eines kalten Dampfes auf heißem Film bei unmittelbarem Kontakt vorgestellt. Diese Kondensation bei relativ niedriger Temperatur, niedrigem Druck des Dampfes auf heißem Film einer hygroskopischen Sole-Lösung kann auftreten durch Druckerniedrigung über einer genügend hoch konzentrierten Lösung.
Die treibende Kraft für die Kondensation ist der Unterschied zwischen dem Partialdruck des Wassers in der Sole und dem Partialdruck des kondensierenden Wasserdampfes. Die Kondensation wird auch durch gleichzeitig auftretende Stofftransportmechanismen gesteuert, resultierend aus einer nichtisothermen Absorption, die durch eine entgegengesetzte, thermische treibende Kraft in der kondensierenden Dampfphase ermöglicht wird. Das gesamte Verhalten wird bestimmt durch die akkumulierenden Effekte der verschiedenen Widerstände auf den Wärmeund den Stofftransport. Die vorliegende Studie hat zum Ziel, diese steuernden Mechanismen, die mit Absorptions- und Kondensationsprozessen verbunden sind, zu klären und es wird ein mittlerer Wärmeübergangskoeffizient für laminare und turbulente Strömungsbereiche vorgeschlagen.
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Abbreviations
- C b :
-
salt concentration in the brine, kg salt/kg solution
- C * b :
-
equilibrium salt concentration, kg salt/kg solution
- C * bm :
-
equilibrium salt concentration at temperatureT m and pressureP ci
- C s :
-
interfacial salt concentrationC s =C * b (T b ,P c ) kg salt/kg solution
- C w :
-
water concentration in the brine, kg water/kg solution
- c p :
-
specific heat kJ/kg‡C
- d c :
-
plate spacing, m
- D :
-
diffusion coefficient of salt in the brine, m2/sec
- D H :
-
hydraulic radius for vapor flow, m
- F :
-
heat transfer amplification factor due to waviness, Eq. (B.8)
- g :
-
gravitational acceleration, m/sec2
- h m :
-
heat transfer coefficient to the wall, kJ/sec m2 ‡ C
- h s :
-
interfacial heat transfer coefficient, kJ/scc m2 ‡ C
- j :
-
enthalpy, kJ/kg
- k :
-
thermal conductivity, kJ/sec m ‡C
- K b :
-
absorption mass transfer coefficient, m/$ec
- L :
-
required plate length, m
- m :
-
local condensation flux, kg/sec m2
- M :
-
overall condensation rate, kg/sec m
- \(Nu_c ,\overline {Nu} _c\) :
-
nondimensional local and average condensation heat flux, Eqs. (8), (9)
- \(\overline {Nu} _m\) :
-
nondimensional average heat flux through the wall, Eq. (10)
- P c :
-
local vapor pressure, N/m2
- Pr :
-
Prandtl number,c p Μ/k
- q m :
-
local heat flux transferred through the wall, kJ/m2 sec
- q s :
-
local interfacial heat flux, kJ/m2 sec
- Q m :
-
overall heat transferred through the wall, kJ/sec
- Q c :
-
overall heat released during condensation, kJ/sec
- Sc :
-
Schmidt number,Μ/ΝD
- \(Sh_c ,\overline {Sh} _c\) :
-
nondimensional local and average condensation mass flux, Eqs. (6), (7)
- T :
-
temperature, ‡C
- T * bi :
-
equilibrium brine temperature at initial brine concentrationC bi
- T m :
-
wall temperature, ‡ C
- u c :
-
vapor velocity, m/sec
- W c :
-
local vapor mass flow rate (per unit width), kg/sec m
- z :
-
downstream distance, m
- γ :
-
nondimensional concentration
- γ :
-
mass flow rate (per unit width) kg/sec m
- δ :
-
film thickness, m
- δHdil :
-
heat of dilution, kJ/kg
- λ :
-
latent heat of pure water vaporization, kJ/kg
- λ* :
-
latent heat of vaporization of brine, kJ/kg
- λ *ef :
-
effective latent heat of condensation, Eqs. (A.14)-(A. 16)
- Μ :
-
viscosity, kg/m sec
- ξ :
-
nondimensional downstream distance
- χ :
-
stream quality, kg vapor/kg mixture
- g9 :
-
density, kg/m3
- gs :
-
surface tension, N/m
- θ :
-
nondimensional temperature
- Τ s :
-
interfacial shear stress, N/m2
- b :
-
brine film
- c :
-
condensing vapor
- i :
-
at inlet
- m :
-
wall
- N :
-
Nusselt's solution
- o :
-
at bottom (outlet)
- s :
-
interfacial
- *:
-
at thermodynamic equilibrium
References
Moalem-Maron, D.; Sideman, S.: Theoretical analysis of a horizontal condenser-evaporator tube. Int. J. Heat Mass Transfer 19 (1976) 259–270
Moalem-Maron, D.; Sideman, S.: Theoretical analysis of a horizontal condenser elliptical tube. Trans. ASME J. of Heat Transfer 97 (1975) 352–359
Moalem-Maron D.; Brauner, M.: Analysis of power cycle based on absorption condenser evaporator. Report 1. Project 0251. School of Engineering, Tel-Aviv University, submitted to ORMAT Turbines, Ltd. (1983)
Brauner, K.; Moalem-Maron, D.; Harel, Z.: Wettability, rewettability and breakdown of thin film of aqueous salt solutions. Desalination 52 (1985) 295–307
Henstock, W. H.; Hanratty, T. J.: Gas absorption by a liquid layer flowing on the wall of a pipe. AIChE J. 25 (1979) 122–131
Bakopoulos, A.: Liquid-side controlled mass transfer in wetted-wall tubes. German Chem. Eng. 3 (1980) 241–252
Chung, D. K.; Mills, A. F.: Experimental study of gas absorption into turbulent falling films of water and ethylene glycolwater mixtures. Int. J. Heat Mass Transfer 19 (1976) 51–59
McCready, M. J.; Hanratty, T. J.: Concentration fluctuations close to a gas-liquid interface. AIChE J. 30(5) (1984) 816–817
King, C. J.: Turbulent liquid phase mass transfer at a free gas-liquid interface. I/EC Fundamentals 5 (1966) 1–8
Bin, A. K.: Mass transfer into turbulent liquid film. Int. J. Heat Mass Transfer 26 (1983) 981–991
Kastwia, G.; Stepanek, J. B.: Two phase flow-IV. Gas and liquid side mass transfer coefficients. Chem. Eng. Sci. 29 (1974) 1849
McCready, M. J.; Hanratty, T. J.: Gas effect of air shear on gas absorption by liquid film. Private communication (1985)
Brumfield, L. K.; Houze, R. N.; Theofanous, T. G.: Turbulent mass transfer at free, gas-liquid interfaces, with applications to film flows. Int. J. Heat Mass Transfer 18 (1975) 1077–1081
Brauner, N.; Moalem-Maron, D.: Characteristics of inclined thin films, waviness and the associated mass transfer. Int. J. Heat Mass Transfer 25 (1982) 99–110
Brauner, N.; Moalem-Maron, D.: Mass transfer in inclined thin films with intermittent feed. Chem. Eng. J. 28 (1984) 139–150
Brauner, N.; Moalem-Maron, D.: Modelling of wavy flow in inclined thin films. Chem. Eng. Sci. 38 (1983) 775–788
Yih, S. M.; Seagrave, R. C.: Mass transfer in laminar falling liquid films with accompanying heat transfer and interfacial shear. Int. J. Heat Mass Transfer 23 (1980) 749–758
Grigor'eva, N. I.; Nakoryakov, V. E.: Exact solution of combined heat and mass transfer problem during film absorption. Inzh.-fiz. zh. 33 (1977) 983–989
Nakoryakov, V. E.; Grigor'eva, N. I.: Calculation of heat and mass transfer in non-isothermal absorption in the entrance region of a falling film. Osn. Khim. Tekhnol. 14 (1980) 483–488
Grossman, G.: Heat and mass transfer in film absorption. Handbook of Heat and Mass Transfer. Gulf Publishing, pp. 211–257, 1986
Yih, S. M.; Chen, K. Y.: Gas absorption into wavy and turbulent falling liquid films in a wetted wall column. Chem. Eng. Commun. 17 (1982) 123–136
Kutadeladze, S. S.: Fundamentals of heat transfer. London: Edward Arnold 1963
Chun, K. R.; Seban, R. A.: Heat transfer to evaporating liquid films. J. of Heat Transfer., Trans. ASME, Series C, 93(4) (1971) 391
Groothuis, G.; Hendal, W. P.: Heat transfer in two phase flow. Chem. Eng. Sci. 11 (1959) 212–220
Wallis, G. B.: One dimensional two phase flow. New York: McGraw-Hill 1969
Feind, K.: Stromungsuntersuchungen bei gegenstrom van rieselfilmen und gas lotrechten rohresn. VDI-Forschungsheft, 481 (1960)
Brauner, N.; Moalem-Maron, D.; Sideman, S.: Simultaneous mass and heat transfer in direct contact hygroscopic condensation. Proc. 8th Int. Heat Transfer Conf. San Francisco: Tien, C. L.; Carey, V. P.; Ferrell, J. K. (Ed.). New York: 1986, Hemisphere, Vol. 4, pp. 1647–1652
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Dedicated to Prof. Dr.-Ing. U. Grigull's 75th birthday
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Brauner, N., Maron, D.M. & Sideman, S. Heat and mass transfer in direct contact hygroscopic condensation. Wärme- und Stoffübertragung 21, 233–245 (1987). https://doi.org/10.1007/BF01004026
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DOI: https://doi.org/10.1007/BF01004026