Abstract
Soft drinks and champagne are examples of liquids containing sizable quantities of gases dissolved under pressure. In liquids usually used in technology there are dissolved inert gases and also micro-bubbles. It is known that at p = 105 Pa, T 2o = 298.15K the amount of dissolved gases and micro-bubbles in the coolant is α 1o ≅ 0.005, for boiling water nuclear reactors, and α 1o ≅ 0.001, for pressurized water reactor, see Malnes and Solberg (1973). Brennen (1995), p. 20, reported that it takes weeks of deaeration to reduce the concentration of air in the water tunnel below 3ppm (saturation at atmospheric pressure is about 15ppm). Wolf (1982- 1984) reported that it took him about 18 hours per single large scale test to increase the pressure to ~11MPa, to warm and mix the water inside the pressure vessel including 5 hours degassing of the water from 8mg O 2/l to a value of 2mg O 2/l before each test.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abramson, B., Sirignano, W.A.: Droplet vaporization model for spray combustion calculations. Int. Heat Mass Transfer 32, 1605–1618 (1989)
Acrivos, A., Taylor, T.D.: Heat and mass transfer from single spheres in stokes flow. The Physics of Fluids 5(4), 387–394 (1962)
Acrivos, A., Goddard, J.: Asymptotic expansion for laminar forced- convection heat and mass transfer. Part 1, J. of Fluid Mech. 23, 273 (1965)
Aksel’Rud, G.A.: Zh. fiz. Khim. 27, 1445 (1953)
Albring, W.: Angewandte Stroemungslehre, Verlag Theodor Steinkopf, Dresden, 4. Auflage (1970)
Al-Diwani, H.K., Rose, J.W.: Free convection film condensation of steam in presence of non condensing gases. Int. J. Heat Mass Transfer 16, 1959 (1973)
Avdeev, A.A.: Growth and condensation velocity of steam bubbles in turbulent flow. Teploenergetika, 1, 53–55 (1986) (in Russian)
Banerjee, S.: Turbulence structure and transport mechanisms at interfaces. In: Proc. Ninth Int. Heat Transfer Conference, Jerusalem, Israel, vol. 1, pp. 395–418 (1990)
Bankoff, S.S.: Some Condensation Studies Pertinent to LWR Safety. Int. J. Multiphase Flow 6, 51–67 (1980)
Batchelor, F.K.: The theory of homogeneous turbulence. The University Press, Cambridge (1953)
Berman, L.D.: Soprotivlenie na granize razdela fas pri plenochnoi kondensazii para nizkogo davleniya, Tr. Vses. N-i, i Konstrukt In-t Khim. Mashinost, vol. 36 p. 66 (1961)
Billet, M.L., Holl, J.W.: Scale effects on various types of limited cavitation. In: Parkin, B.R., Morgan, W.B. (eds.) Int. Symposium on Cavitation Inception ASME Winter Annual Meeting, New Orleans (1979)
Boussinsq, M.: Calcul du pourvoir retroidissant des courant fluids. J. Math. Pures Appl. 1, 285 (1905)
Brauer, H., et al.: Chem. Ing. Tech. 48, 737–741 (1976)
Brennen, C.E.: Cavitation and Bubble Dynamics. Oxford University Press, Oxford (1995)
Brumfield, L.K., Houze, K.N., Theofanous, T.G.: Turbulent mass transfer at free, Gas-Liquid Interfaces, with Applications to Film Flows. Int. J. Heat Mass Transfer 18, 1077–1081 (1975)
Bunker, R.S., Carey, V.P.: Modeling of turbulent condensation heat transfer in the boiling water reactor primary containment. Nucl. Eng. Des. 91, 297–304 (1986)
Calderbank, P.H., Moo-Young, M.B.: Chem. Eng. Sc. 16, 39 (1962)
Calderbank, P.H.: Gas absorption from bubbles. In: Chemical Engineering, October 1967, pp. CE209-CE233 (1967)
Carlsow, H.S., Jaeger, J.C.: Condution of heat in solids, Oxford (1959)
Celata, G.P., Cumo, M., D’Annibale, F., Farello, G.E.: Direct contact condensation of steam on droplets. Int. J. Multiphase Flow 17(2), 191–211 (1991)
Cha, Y.S., Henry, R.E.: Bubble growth during decompression of liquids. Transaction of the ASME, Journal of Heat Transfer 103, 56–60 (1981)
Chiang, C.H., Sirignano, W.A.: Numerical analysis of convecting and interacting vaporizing fuel droplets with variable properties. Presented at the 28th AIAA Aerospace Sciences Mtg, Reno (November 1990)
Churchill, R.V.: Operational mathematics, pp. 132–134. McGraw Hill, New York (1958)
Churchill, S.W., Brier, J.C.: Convective heat transfer from a gas stream at high temperature to a circular cylinder normal to the flow. In: Chem. Engng. Progr. Simp. Ser. 51, vol. 17, pp. 57–65 (1955)
Clift, R., Ggarce, J.R., Weber, M.E.: Bubbles, drops, and particles. Academic Press, New York (1978)
Condie, K.G., et al.: Comparison of heat and mass transfer correlation with forced convective non equilibrium post-CHF experimental data. In: Dhir, V.K., Schrock, V.E. (eds.) Proc. of 22nd Nat. Heat Transfer Conf. & Exhibition. Basic Aspects of Two-Phase Flow and Heat Transfer, Niagara Falls, New York, August 5-8, pp. 57–65 (1984)
Daily, J.W., Johnson, J.R.: Turbulence and boundary-layer effect on cavitation inception from gas nuclei. Transactions of the ASME 78, 1695–1705 (1956)
Deitsch, M.E., Philiphoff, G.A.: Two-phase flow gas dynamics. Energoisdat, Moscu (1981) (in Russian)
Eddington, R.I., Kenning, D.B.R.: Comparison of gas and vapor bubble nucleation on brass surface in water. Int. J. Heat Mass Transfer 21, 855–862 (1978)
Epstein, P.S., Plesset, M.S.: On the stability of gas bubbles in liquid-gas solution. J. Chem. Phys. 18, 1505–1509 (1950)
Fedorovich, E.D., Rohsenow, W.M.: The effect of vapor subcooling on film condensation of metals. Int. J. of Heat Mass Transfer 12, 1525–1529 (1968)
Feng, Z.-G., Michaelides, E.E.: Unsteady heat transfer from a spherical particle at finite Peclet numbers. ASME Journal of Fluids Engineering 118, 96–102 (1986)
Fieder, J., Russel, K.C., Lothe, J., Pound, G.M.: Homogeneous nucleation and growth of droplets in vapours. Advances in Physics 15, 111–178 (1966)
Fortescue, G.E., Pearson, J.R.A.: On gas absorption into a turbulent liquid. Chem. Engng. Sci. 22, 1163–1176 (1967)
Ford, J.D., Lekic, A.: Rate of growth of drops during condensation. Int. J. Heat Mass Transfer 16, 61–64 (1973)
Fourier, J.: Theory analytique de la chaleur (1822)
Frenkel, F.I.: Selected works in gasdynamics. Nauka, Moscu (1973) (in Russian)
Friedlander, S.K.: A. I. Ch. Eng. J. 3, 43 (1957)
Friedlander, S.K.: A. I. Ch. Eng. J. 7, 347 (1961)
Froessling, N.: Beitr. Geophys. 32, 170 (1938)
Furth, R.: Proc. Cambr. Philos. Soc. 37, 252 (1941)
Gates, E.M., Bacon, J.: Determination of the cavitation nuclei distribution by holography. J. Ship Res. 22(1), 29–31 (1978)
Gibbs, J.W.: Thermodynamische Studien (1878); Leipzig: Amer. J. Sci. and Arts XVI, 454-455 (1982)
Gnielinski, V.: Berechnung mittlerer Waerme- und Stoffuebertragungskoeffizienten an laminar und turbulent ueberstroemenden Einzelkoerpern mit Hilfe einer einheitlichen Gleichung. Forsch. Ing. Wes. 41(5), 145–153 (1975)
Hadamard, J.: Dokl. Akad. Nauk, SSSR 152, 1734 (1911)
Hammitt, F.G.: Cavitation and multiphase flow phenomena. McGraw-Hill Inc., New York (1980)
Hausen, H.: Darstellung des Waermeueberganges in Roehren durch verallgemeinerte Potenzgleichungen. Verfahrenstechnik 9(4/5), 75–79 (1958)
Hertz, H.: Wied. Ann. 17, 193 (1882)
Hobbhahn, W.K.: Modeling of condensation in light water reactor safety. In: Mueller, U., Rehme, K., Rust, K., Braun, G. (eds.) Proc. of the Fourth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics, Karlsruhe, October 10-13, vol. 2, pp. 1047–1053 (1989)
Huang, T.T.: The effect of turbulence simulation on cavitation inception of axisymmetric headforms. In: Parkin, B.R., Morgan, W.B. (eds.) Int. Symposium on Cavitation Inception ASME Winter Annual Meeting, New Orleans (1984)
Hughes, E.D., Paulsen, M.P., Agee, L.J.: A drift-flux model of two-phase flow for RETRAN. Nuclear Technology 54, 410–420 (1981)
Hunt, D.L.: The effect of delayed bubble growth on the depressurization of vessels Containing high temperature water. UKAEA Report AHSB(S), R 189 (1970)
Isenberg, J., Sideman, S.: Direct contact heat transfer with change of phase: Bubble condensation in immiscible liquids. Int. J. Heat Mass Transfer 13, 997–1011 (1970)
Jakob, M., Linke, W.: Der Waermeübergang von einer waagerechten Platte an sidendes Wasser. Forsch. Ing. Wes. 4, 75–81 (1933)
Jensen, R.J., Yuen, M.C.: Interphase transport in horizontal stratified concurrent flow, U.S. Nuclear Regulatory Commission Report NUREG/CR-2334 (1982)
Katz, J.: Determination of solid nuclei and bubble distribution in water by holography, Calif. Inst. of Techn., Eng. and Appl. Sci. Div. Rep. No. 183-3 (1978)
Keller, A.P.: Cavitation inception measurements and flow visualization on asymetric bodies at two different free stream turbulence levels and test procedures. In: Int. Symposium on Cavitation Inception, ASME Winter Annual Meeting, New York (1979)
Kendouch, A.A.: Theoretical and experimental investigations into the problem of transient two-phase flow and its application to reactor safety, Ph.D.Thesis, Department of Thermodynamics and Fluid Mechanics, University of Strathclyde, U.C (1976)
Kim, H.J., Bankoff, S.G.: Local heat transfer coefficients for condensation in stratified countercurrent steam - water flows. Trans. ASME 105, 706–712 (1983)
Kim, M.H., Corradini, M.L.: Modeling of condensation heat transfer in a reactor containment. Nucl. Eng. and Design 118, 193–212 (1990)
Knapp, R.T., Levy, J., Brown, F.B., O’Neill, J.P.: The hydrodynamics laboratory at the California Institute of Technology. Trans. ASME 70, 437 (1948)
Knowles, J.B.: A mathematical model of vapor film destabilization, Report AEEW-R-1933 (1985)
Knudsen, M.: Ann. Physic 47, 697 (1915)
Kolev, N.I.: Multiphase Flow Dynamics 2. Mechanical and Thermal Interactions. Springer, Heidelberg (2002, 2004)
Kremeen, R.W., McGraw, J.T., Parkin, B.R.: Mechanism of cavitation inception and the released scale effects problem. Trans. Am. Soc. Mech. Engs. 77, 533 (1955)
Kuiper, G.: Some experiments with distinguished types of cavitation on ship properties. In: Morgan, W.B., Parkin, B.R. (eds.) Int. Symposium on Cavitation Inception ASME Winter Annual Meeting, New Orleans (1979)
Labunzov, D.A.: State of the art of the nuclide boiling mechanism of liquids. In: Heat Transfer and Physical Hydrodynamics, Moskva, Nauka, pp. 98–115 (1974) (in Russian)
Labunzov, D.A., Krjukov, A.P.: Processes of intensive flushing. Thermal Engineering 24(4), 8–11 (1977) (in Russian)
Lamont, J.C., Scott, D.S.: An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE Journal 16(4), 513–519 (1970)
Lamont, J.C., Yuen, M.C.: Interface transport in horizontal stratified concurrent flow, U.S. Nuclear Regulatory Commission Report NUREG/CR-2334 (1982)
Langmuir, I.: Physik. Z. 14, 1273 (1913)
Langmuir, I.: Jones HA and Mackay GMJ. Physic. Rev. 30, 201 (1927)
Lienhard, J.: A heat transfer textbook. Prentice-Hall, Inc., Engelwood Cliffts
Lee, K., Ryley, D.J.: The evaporation of water droplets in superheated steam. J. of Heat Transfer 90 (November 1968)
Levich, V.G.: Physicochemical Hydrodynamics. Prentice-Hall, Englewood Cliffs (1962)
Lochiel, A.C.: Ph. D. Thesis, University of Edinburgh (1963)
Ludvig, A.: Untersuchungen zur spontaneous Kondensation von Wasserdampf bei stationaerer Ueberschalllstroemung unter Beruecksichtigung des Realgasverhaltens. Dissertation, Universitaet Karlsruhe, TH (1975)
Mason, B.J.: Spontaneous condensation of water vapor expansion chamber experiments. Proc. Phys. Soc. London, Serie B 64, 773–779 (1951)
Mason, B.J.: The Physics of Clouds. Clarendon Press, Oxford (1957)
Michaelides, E.E.: Hydrodynamic force and heat/mass transfer from particles, bubbles and drops – The Freeman Scholar Lecture. ASME Journal of Fluids Engineering 125, 209–238 (2003)
Mills, A.F.: The condensation of steam at low pressure, Techn. Report Series No. 6, Issue 39. Space Sciences Laboratory, University of California, Berkeley
Mills, A.F., Seban, R.A.: The condensation coefficient of water. J. of Heat Transfer 10, 1815–1827 (1967)
Malnes, D., Solberg, K.: A fundamental solution to the critical two-phase flow problems, applicable to loss of coolant accident analysis. SD-119, Kjeller Inst., Norway (May 1973)
Nabavian, K., Bromley, L.A.: Condensation coefficient of water. Chem. Eng. Sc. 18, 651–660 (1963)
Nigmatulin, R.I.: Basics of the mechanics of the heterogeneous fluids, Moskva, Nauka (1978) (in Russian)
O’Hern, T.J., Katz, J., Acosta, A.J.: Holographic measurements of cavitation nuclei in the see. In: Proc. ASME Cavitation and Multiphase Flow Forum, pp. 39–42 (1988)
Parkin and Kermeen RW, The roles of convective air diffusion and liquid tensile stresses during cavitation inception. In: Proc. IAHR Symposium of Cavitation and Hydraulic Machinery, Sendai, Japan (1963)
Peterson, F.B., et al.: Comparative measurements of bubble and particulate spectra by three optical measurements methods, Proc. 14th Int. Towing Conf. (1975)
Petukhov, B.S., Popov, V.N.: Theoretical calculation of heat exchange and friction resistance in turbulent flow in tubes of an incompressible fluid with variable physical properties. High Temperature 1, 69–83 (1963)
Pohlhausen, E.: Der Waermeaustausch zwischen festen Koerpern und Fluessigkeiten mit kkleiner Reibung und kleiner Waermeleitung. Z. angew. Math. Mech. 1(2), 115–121 (1921)
Ranz, W., Marschal Jr., W.: Evaporation from drops. Ch. Eng. Progress 48, 141–146 (1952)
Rohsenow, W.M., Choi, H.: Heat, mass and momentum transfer. Prentice - Hall Publishers, New Jersey (1961)
Rosenberg, B.: Report no 727. The David Taylor Model Basin, Washington DC (1950)
Rouse, H.: Cavitation in the mixing zone of a submerged jet, La Houille Blanche (January-February 1953)
Saha, P.: Int. J. Heat and Mass Transfer 23, 481 (1980)
Samson, R.E., Springer, G.S.: Condensation on and evaporation from droplets by a moment method. J. Fluid Mech. 36, 577–584 (1969)
Siddique, M., Golay, M.W.: Theoretical modeling of forced convection condensation of steam in a vertical tube in presence of non condensable gas. Nuclear Technology 106 (May 1994)
Simoneau, R.J.: Depressurization and two-phase flow of water containing high levels of dissolved nitrogen gas, NASA Technical Paper, USA (1981)
Skripov, W.P., Sinizyn, E.N., Pavlov, P.A., Ermakov, G.W., Muratov, G.N., Bulanov, N.B., Bajdakov, W.G.: Thermophysical properties of liquids in meta-stable state, Moscu, Atomisdat (1980) (in Russia)
Slattery, J.C.: Interfacial transport phenomena. Springer, Heidelberg (1990)
Soo, S.L.: Fluid dynamics of multiphase systems, Massachusetts, Woltham (1969)
Spalding, D.B.: The combustion of liquid fuels. In: Proc. 4th Symp (Int.) on Combustion, pp. 847–864. Williams & Wilkins, Baltimore (1953)
Tanaka, M.: Heat transfer of a spray droplet in a nuclear reactor containment. Nuclear Technology 47, 268 (1980)
Takadi, T., Maeda, S.: Vhem. Engng. 25, 254 (1961)
Taylor, G.I.: Proc. Roy. Soc. A 151, 429 (1935)
Taylor, G.I.: The mean value of the fluctuation in pressure and pressure gradient in a turbulent flow. In: Proceedings of the Cambridge Philosophical Society, pp. 380–384 (1936)
Theofanous, T.G., Houze, R.N., Brumfield, L.K.: Turbulent mass transfer at free gas-liquid interfaces with applications to open-channel, bubble and jet flows. Int. J. Heat Mass Transfer 19, 613–624 (1975)
Uchida, U., Oyama, A., Togo, Y.: Evolution of post - incident cooling system of light water reactors. In: Proc. 3th Int. Conf. Peaceful Uses of Atomic Energy, International Atomic Energy Agency, Vienna, Austria, vol. 13, p. 93 (1964)
Van Vingaarden, L.: On the growth of small cavitation bubbles by convective diffusion. Int. J. Heat Matt Transfer 10, 127–134 (1967)
VDI-Waermeatlas, 4. Auflage VDI-Verlag (1984)
Volmer, M.: Kinetik der Phasenbildung, Dresden und Leipzig, Verlag von Theodor Steinkopff (1939)
Ward, D.M., Trass, O., Johnson, A.I.: Can. J. Chem. Eng. 40, 164 (1962)
Wilson, J.F.: Primary separation of steam from water by natural separation. US/EURATOM Report ACNP-65002 (1965)
Wolf, L., et al. (1982-1984) HDR Sicherheitsprogramm (Investigations of RPV internals during blow down) Kernforschungszentrum Karlsruhe. Reports in German
Zeldovich, J.B.: To the theory of origination of the new phase, cavitation. Journal of Experimental and Theoretical Physics 12(11/12), 525–538 (1942)
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kolev, N.I. (2011). Transient solution and dissolution of gasses in liquid flows. In: Multiphase Flow Dynamics 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20749-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-20749-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20748-8
Online ISBN: 978-3-642-20749-5
eBook Packages: EngineeringEngineering (R0)