nach oben

Erschienen in:

2018 | OriginalPaper | Buchkapitel

46. Fundamental Equations for Two-Phase Flow in Tubes

verfasst von : Masahiro Kawaji

Erschienen in: Handbook of Thermal Science and Engineering

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Two-phase flow of gas and liquid is often encountered in the design and operation of heat exchangers, oil/gas transport lines, chemical and bioreactors, and mass transfer equipment. The two-phase pressure drop governs the pumping requirement in forced-circulation systems, while the pressure drop dictates the circulation rate and, hence, various system parameters in natural-circulation systems. All three components of pressure drop (gravitational, frictional, and accelerational) are dependent on void fraction or quality, so the design of energy systems and their performance are highly dependent on accurate predictions of both the two-phase pressure drop and void fraction. In this chapter, basic parameters are defined first, followed by descriptions of two-phase flow patterns, flow pattern maps and transition criteria, the conservation equations used in two-phase flow analyses, and the correlations and models available for predicting void fraction and pressure drop in simple flow channel geometries such as circular and noncircular tubes. In particular, advanced two-phase flow models including multidimensional two-fluid models and the constitutive relations for interfacial transfer terms are presented. Examples of two-dimensional and one-dimensional two-fluid models applied to predict radial void fraction distributions in bubbly flow and interfacial wave characteristics in inverted annular flow, respectively, are also described.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Boiling in Reagent and Polymeric Solutions

Nächstes Kapitel Flow Boiling in Tubes

Antal SP, Lahey RT Jr, Flaherty JE (1991) Analysis of phase distribution in fully developed laminar bubbly two-phase flow. Int J Multiphase Flow 17(5):635–652CrossRef

Armand AA (1946) Resistance to two-phase flow in horizontal tubes. Izv VTI 15(1):16–23

Baker O (1954) Simultaneous flow of oil and gas. Oil Gas J 53:185–195

Banerjee S, Chan AMC (1980) Separated flow models – I analysis of the averaged and local instantaneous formulations. Int J Multiphase Flow 6:1–24CrossRef

Bankoff SG (1960) A variable density single-fluid model for two-phase flow with particular reference to steam-water flow. J Heat Transf 82:265–272CrossRef

Baroczy CJ (1965) A systematic correlation of for two-phase pressure drop. Chem Eng Prog Symp Ser 62(44):232–249

Basset AB(1888) On the motion of a sphere in a viscous liquid. Philos Trans Royal Soc London, Ser A Math Phys Sci 179:43–63; also A treatise on hydrodynamics, 1961, Dover, New York, Chap. 22

Beattie DRH, Whalley PB (1982) A simple two-phase frictional pressure drop calculation method. Int J Multiphase Flow 8:83–87CrossRef

Bergles AE, Roos JP, Bourne JG (1968) Investigation of boiling flow regimes and critical heat flux. NYO-3304-13

Cheng L, Ribatski G, Thome JR (2008) Two-phase flow patterns and flow-pattern maps: fundamentals and applications. Appl Mech Rev 61(5):050802-050802-28. https://doi.org/10.1115/1.2955990CrossRef

Chichitti A, Lombardi C, Silvestri M, Soldaini G, Zavattarelli R (1960) Two-phase cooling experiments – pressure drop, heat transfer and burnout measurement. Energ Nucl 7(6):407–425

Chisholm D (1973) Pressure gradients due to friction during the flow of evaporating two-phase mixtures in smooth tubes and channels. Int J Heat Mass Transf 16:347–358CrossRef

Chisholm D, Laird ADK (1958) Two-phase flow in rough tubes. Trans ASME 80(2):276–286

Coddington P, Macian R (2002) A study of the performance of void fraction correlations used in the context of drift-flux two-phase flow models. Nucl Eng Design 215:199–216CrossRef

Collier JG (1972) Convective boiling and condensation. McGraw Hill, London

Collier JG, Thome JR (1994) Convective boiling and condensation. Oxford University Press, New York

De Jarlais G (1983) An experimental study of inverted annular flow hydrodynamics utilizing an adiabatic simulation. NUREG/CR-3339, ANL-83-44

Drew DA, Lahey RT Jr (1987) The virtual mass and lift force on a sphere in rotating and straining inviscid flow. Int J Multiphase Flow 13:113–121CrossRef

Dukler AE, Taitel Y (1977) Flow regime transitions for vertical upward gas liquid flow: a preliminary approach through physical modeling. Progress Report No. 1, NUREG-0162

Dukler AE, Wicks M, Cleveland RG (1964) Frictional pressure drop in two-phase flow: an approach through similarity analysis. AICHE J 10:44–51CrossRef

Faghri A, Zhang Y (2006) Transport phenomena in multiphase systems. Elsevier, Burlington

Franca F, Lahey RT (1992) The use of drift-flux techniques for the analysis of horizontal two-phase flows. Int J Multiphase Flow 18(6):787–801CrossRef

Friedel L (1977) Momentum exchange and pressure drop. In: Whalley PB (ed) Two-phase flows and heat transfer. Oxford University Press, Oxford

Friedel L (1979) Improved friction drop correlations for horizontal and vertical two-phase pipe flow. Paper E2 presented at the European Two-phase Flow Group Meeting, Ispra

Friedel L, Diener R (1998) Reproductive accuracy of selected void fraction correlations for horizontal and vertical up flow. Forsch im Ingenieurwes 64:87–97CrossRef

Godbole PV, Tang CC, Ghajar AJ (2011) Comparison of void fraction correlations for different flow patterns in upward vertical two-phase flow. Heat Transf Eng 32(10):843–860CrossRef

Govier GW, Aziz K (1972) The flow of complex mixtures in pipes. Van Nostrand Reinhold, New York

Hasan AR, Kabir CS (1992) Two-phase flow in vertical and inclined annuli. Int J Multiphase Flow 18(2):279–293CrossRef

Hewitt GF (1982) Flow regimes. “Pressure drop” and “void fraction”, sections 2.1–2.3. In: Hetsroni G (ed) Handbook of multiphase systems. McGraw-Hill, New York

Hewitt GF, Roberts DN (1969) Studies of two-phase flow patterns by simultaneous X-ray and flash photography. UKAEA Report AERE-M2159

Hubbard MG, Dukler AE (1966) The characterization of flow regimes for horizontal two-phase flow. In: Saad MA, Miller JA (eds) Proceedings of the 1966 heat transfer and fluid mechanics institute, Stanford University Press, Palo Alto, pp 100–121

Idzinga W, Todreas N, Bowring R (1977) An assessment of two-phase pressure drop correlations for steam-water systems. Int J Multiphase Flow 3:401–413CrossRef

Ishii M (1975) Thermo-fluid dynamic theory of two-phase flow. Eyrolles, ParisMATH

Ishii M (1977) One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes. ANL Report ANL-77-47

Ishii M, Chawla TC (1979) Local drag laws in dispersed two-phase flow. ANL-79-105, NUREG/CR-1230

Ishii M, De Jarlais G (1986) Flow regime transition and interfacial characteristics of inverted annular flow. Nucl Eng Des 95:171–184CrossRef

Ishii M, Hibiki T (2006) Thermo-fluid dynamics of two-phase flow. Springer US. 10.1007/978–0–387-29187-1. http://www.springer.com/us/book/9780387283210

Ishii M, Mishima K (1980) Study of two-fluid model and interfacial area. Argonne National Laboratory Report, ANL-80-111, NUREG/CR-1873

Ishii M, Mishima K (1984) Two-fluid model and hydrodynamic constitutive relations. Nucl Eng Des 82:107–126CrossRef

Ishii M, Zuber N (1979) Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AICHE J 25:843–855CrossRef

Ishii M, Kim S, Uhle J (2002) Interfacial area transport equation: model development and benchmark experiments. Int J Heat Mass Transf 45(15):3111–3123CrossRef

Ishii M, Kim S, Kelly J (2005) Development of interfacial area transport equation. Nucl Eng Technol 37(6):525–536

Jones OC, Zuber N (1975) The interrelation between void fraction fluctuations and flow patterns in two-phase flow. Int J Multiphase Flow 2:273–306CrossRef

Kawaji M, Banerjee S (1987) Application of a multifield model to reflooding of a hot vertical tube, part 1. Model structure and interfacial phenomena. J Heat Transf 109(1):204–211CrossRef

Kawaji M, Anoda Y, Nakamura H, Tasaka T (1987) Phase and velocity distributions and holdup in high-pressure steam/water stratified flow in a large diameter horizontal pipe. Int J Multiphase Flow 13(2):145–159CrossRef

Kim S, Ishii M, Sun X, Beus SG (2002) Interfacial area transport and evaluation of source terms for confined air water bubbly flow. Nucl Eng Des 219(1):61–65CrossRef

Kocamustafaogullari G, Ishii M (1995) Foundation of the interfacial area transport equation and its closure relation. Int J Heat Mass Transf 38(3):481–493CrossRef

Koizumi Y, Yamamoto N, Tasaka K (1990) Air/water two-phase flow in a horizontal large-diameter pipe (1st Report, Flow regime). Trans. JSME 56(532, B):3745–3749CrossRef

Lahey RT Jr, Lopez de Bertodano M, Jones OC Jr (1993) Phase distribution incomplex geometry conduits. Nucl Eng Des 141:117–201

Lamb H (1932) Hydrodynamics, 6th edn. Cambridge University Press, Cambridge, UKMATH

Liu TJ, Bankoff SG (1993) Structure of air-water bubbly flow in a vertical pipe – II. Void fraction, bubble velocity and bubble size distribution. Int J Heat Mass Transf 36:1061–1072CrossRef

Lockhart RW, Martinelli RC (1949) Proposed correlation of data for isothermal two-phase, two-component flow in pipes. Chem Eng Prog 45:39–48

Mandhane JM, Gregory GA, Aziz K (1974) Critical evaluation of holdup prediction methods for gas–liquid flow in horizontal pipes. J Pet Technol 27:1017–1026CrossRef

Martinelli RC, Nelson DB (1948) Prediction of pressure drop during forced-circulation boiling of water. Trans ASME 70:695–702

McAdams WH, Wood WK, Bryan RL (1942) Vaporization inside horizontal tubes: II, benzene-oil mixtures. Trans ASME 64:193–200

Mei R, Adrian RJ, Hanratty J (1991) Particle dispersion in isotropic turbulence under stokes drag and Basset force with gravitational settling. J Fluid Mech 225:481–495CrossRef

Michaelides EE (1997) Review-the transient equation of motion for particles, bubbles and droplets. J Fluids Eng 119:233–247CrossRef

Mishima K, Ishii M (1984) Flow regime transition criteria for upward two-phase flow in vertical tubes. Int J Heat Mass Transf 27(5):723–737CrossRef

Müller-Steinhagen H, Heck K (1986) A simple friction pressure correlation for two-phase flow in pipes. Chem Eng Process 20:297–308CrossRef

Nakoryakov VE, Kashinskii ON, Koz’myenko BK, Goryelik RS (1986) Study of upward bubbly flow at low liquid velocities. Izv Sib otdel Akad nauk SSSR 16:15–20

Nigmatulin RI (1979) Spatial averaging in the mechanics of heterogeneous and dispersed systems. Int J Multiphase Flow 4:353–385CrossRef

Noghrehkar GR, Kawaji M, Chan AMC (1999) Investigation of two-phase flow regimes in tube bundles under cross-flow conditions. Int J Multiphase Flow 25:857–874CrossRef

Oshinowo T, Charles ME (1974) Vertical two-phase flow: part 11. Holdup and pressure drop. Can J Chem Eng 56:438–448CrossRef

Owens WL (1961) Two-phase pressure gradient. ASME Int Develop Heat Transf Part II 363–368

Rouhani SZ, Axelsson E (1970) Calculation of void volume fraction in the sub cooled and quality boiling regions. Int J Heat Mass Transf 13:383–393CrossRef

Rouhani SZ, Sohal MS (1983) Two-phase flow patterns: a review of research results. Prog Nucl Energy 11(3):219–259CrossRef

Saadatomi M, Sato Y, Saruwatari S (1982) Two-phase flow in vertical non-circular channels. Int J Multiphase Flow 8(6):641–655CrossRef

Sadatomi M, Kawaji M, Lorencez CM, Chang T (1993) Prediction of liquid level distribution in horizontal gas-liquid stratified flows with interfacial level gradient. Int J Multiphase Flow 19(6):987–997CrossRef

Sato Y, Sadatomi M (1986) Two-phase flow in vertical non-circular channels. In: Cheremisinoff NP (ed) Encyclopedia of fluid mechanics, vol 3. Gulf Publishing, Houston, pp 651–664

Serizawa A, Kataoka I, Michiyoshi I (1975) Turbulence structure of air-water bubbly flow, part II: local properties. Int J Multiphase Flow 2:235–246CrossRef

Stuhmiller JH (1977) The influence of interfacial pressure on the character of two-phase flow model equations. Int J Multiphase Flow 3:551–560CrossRef

Taitel Y, Dukler AE (1976a) A model for predicting flow regime transition in horizontal and near horizontal gas-liquid flow. AICHE J 22:47–55CrossRef

Taitel Y, Dukler AE (1976b) A theoretical approach to the Lockhart-Martinelli correlation for stratified flow. Int J Multiphase Flow 2:591–595CrossRef

Taitel Y, Bornea D, Dukler AE (1980) Modelling flow pattern transitions for steady upward gas-liquid flow in vertical tubes. AICHE J 26(3):345–354CrossRef

Thom JRS (1964) Prediction of pressure drop during forced circulation boiling of water. Int J Heat Mass Transf 7:709–724CrossRef

Tomiyama A, Kataoka I, Zun I, Sakaguchi T (1998) Drag coefficients of single bubbles under normal and micro gravity conditions. JSME Int J, Ser B 41(2):472–479CrossRef

Tomiyama A, Tamai H, Zun I, Hosokawa S (2002) Transverse migration of single bubbles in simple shear flows. Chem Eng Sci 57:1849–1858CrossRef

Wallis GB (1969) One-dimensional two-phase flow. McGraw-Hill, New York

Wang X, Sun X (2010) Three-dimensional simulations of air–water bubbly flows. Int J Multiphase Flow 36:882–890CrossRef

Weisman J, Duncan D, Gibson J, Crawford T (1979) Effects of fluid properties and pipe diameter on two-phase flow patterns in horizontal lines. Int J Multiphase Flow 5:437–462CrossRef

Woldesemayat MA, Ghajar AJ (2007) Comparison of void fraction correlations for different flow patterns in horizontal and upward inclined pipes. Int J Multiphase Flow 33:347–370CrossRef

Wu Q, Kim S, Ishii M, Beus SG (1998) One-group interfacial area transport in vertical bubbly flow. Int J Heat Mass Transf 41(8–9):1103–1112CrossRef

Zuber N (1964) On the dispersed flow in the laminar flow regime. Chem Eng Sci 19:897–917CrossRef

Zuber N, Findlay JA (1965) Average volumetric concentration in two-phase flow systems. J Heat Transf 87:453–468CrossRef

Zun I (1980) The transverse migration of bubbles influenced by walls in vertical bubbly flow. Int J Multiphase Flow 6:583–588CrossRef

Titel: Fundamental Equations for Two-Phase Flow in Tubes
verfasst von: Masahiro Kawaji
Verlag: Springer International Publishing
Buch: Handbook of Thermal Science and Engineering
Print ISBN: 978-3-319-26694-7

Electronic ISBN: 978-3-319-26695-4

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-26695-4_46

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht