Skip to main content
SpringerLink
Log in

Mass Conservation

  • Chapter
Multiphase Flow Dynamics 1

  • 2443 Accesses

Abstract

The creation of computer codes for modeling multiphase flows in industrial facilities is very complicated, time-consuming, and expensive. This is why the fundamentals on which such codes are based are subject to continuous review in order to incorporate the state of the art of knowledge into the current version of the code in question. An important element of the codes is the system of partial differential equations governing the flow. The understanding of each particular term in these equations is very important for the application.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, T.B., Jackson, R.: A fluid mechanical description of fluidized beds. Ind. Eng. Fundam. 6, 527 (1967)

    Article  Google Scholar 

  • Batchelor, G.K.: The stress system in a suspension of force-free particles. J. Fluid Mech. 42, 545–570 (1970)

    Article  MathSciNet  Google Scholar 

  • Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  • Delhaye, J.M., Giot, M., Reithmuller, M.L.: Thermohydraulics of two-phase systems for industrial design and nuclear engineering. Hemisphere Publishing Corporation, McGraw Hill, New York (1981)

    Google Scholar 

  • Deich, M.E., Philipoff, G.A.: Gas dynamics of two phase flows. Energoisdat, Moscow (1981) (in Russian)

    Google Scholar 

  • Faeth, G.M.: Spray combustion: a review. In: Proc. of 2nd International Conference on Multiphase Flow 1995, Kyoto, Japan, April 3-7 (1995)

    Google Scholar 

  • Fick, A.: Über Diffusion. Ann. der Physik 94, 59 (1855)

    Article  Google Scholar 

  • Gentry, R.A., Martin, R.E., Daly, B.J.: An Eulerian differencing method for unsteady compressible flow problems. J. Comp. Physics 1, 87 (1966)

    Article  MATH  Google Scholar 

  • Gray, W.G., Lee, P.C.Y.: On the theorems for local volume averaging of multi-phase system. Int. J. Multi-Phase Flow 3, 222–340 (1977)

    Article  Google Scholar 

  • Grigorieva, V.A., Zorina, V.M. (eds.): Handbook of thermal engineering, thermal engineering experiment, 2nd edn., Moskva, Atomisdat, vol. 2 (1988) (in Russian)

    Google Scholar 

  • Griffith, L.: A theory of the size distribution of particles in a comminuted system. Canadian J. Res. 21A(6), 57–64 (1943)

    Article  MathSciNet  Google Scholar 

  • Hetstrony, G.: Handbook of multi phase systems. Hemisphere Publ. Corp., McGraw-Hill Book Company, Washington, New York (1982)

    Google Scholar 

  • Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981)

    Article  MATH  Google Scholar 

  • Hirt, C.W.: Volume-fraction techniques: powerful tools for wind engineering. Journal of Wind Engineering and Industrial Aerodynmics 46&47, 327–338 (1993)

    Article  Google Scholar 

  • Ishii, M.: Thermo-fluid dynamic theory of two-phase flow. Eyrolles, Paris (1975) 38 1 Mass conservation

    Google Scholar 

  • Kataoka, I., Ishii, M., Mishima, K.: Transactions of the ASME 105, 230–238 (1983)

    Google Scholar 

  • Kocamustafaogulari, G., Ishii, M.: Interfacial area and nucleation site density in boiling systems. Int. J. Heat Mass Transfer 26(9), 1377–1387 (1983)

    Article  Google Scholar 

  • Kolev, N.I.: Transiente Drephasen Dreikomponenten Strömung, Teil 1: Formulierung des Differentialgleichungssystems. KfK Report 3910 (March 1985a)

    Google Scholar 

  • Kolev, N.I.: Transiente Dreiphasen Dreikomponenten Stroemung, Teil 2: Eindimensionales Schlupfmodell Vergleich Theorie-Experiment. KfK Report 3926 (August 1985b)

    Google Scholar 

  • Kolev, N.I.: Transiente Dreiphasen Dreikomponenten Strömung, Teil 3: 3D-Dreifluid-Diffusionsmodell. KfK Report 4080 (1986a)

    Google Scholar 

  • Kolev, N.I.: Transient three-dimensional three-phase three-component nonequilibrium flow in porous bodies described by three-velocity fields. Kernenergie 29, 383–392 (1986b)

    Google Scholar 

  • Kolev, N.I.: A three field-diffusion model of three-phase, three-component flow for the transient 3D-computer code IVA2/001. Nucl. Tech. 78, 95–131 (1987)

    Google Scholar 

  • Kolev, N.I.: Derivatives for the state equations of multi-component mixtures for universal multi-component flow models. Nucl. Sci. Eng. 108, 74–87 (1990)

    Google Scholar 

  • Kolev, N.I.: A three-field model of transient 3D multi-phase, three-component flow for the computer code IVA3, Part 1: Theoretical basics: conservation and state equations, numerics. KfK Report 4948 (September 1991a)

    Google Scholar 

  • Kolev, N.I.: IVA3: A transient 3D three-phase, three-component flow analyzer. In: Proc. of the Int. Top. Meeting on Safety of Thermal Reactors, Portland, Oregon, July 21-25, pp. 171–180 (1991b); Presented at the 7th Meeting of the IAHR Working Group on Advanced Nuclear Reactor Thermal-Hydraulics, Kernforschungszentrum Karlsruhe, August 27-29 (1991)

    Google Scholar 

  • Kolev, N.I.: Fragmentation and coalescence dynamics in multi-phase flows. Exp. Thermal Fluid Sci. 6, 211–251 (1993a)

    Article  Google Scholar 

  • Kolev, N.I.: The code IVA3 for modelling of transient three-phase flows in complicated 3D geometry. Kerntechnik 58(3), 147–156 (1993b)

    Google Scholar 

  • Kolev, N.I.: IVA3 NW: Computer code for modeling of transient three phase flow in complicated 3D geometry connected with industrial networks. In: Proc. of the Sixth Int. Top. Meeting on Nuclear Reactor Thermal Hydraulics, Grenoble, France, October 5-8 (1993c)

    Google Scholar 

  • Kolev, N.I.: Berechnung der Fluiddynamischen Vorgänge bei einem Sperrwasserkühlerrohrbruch. Projekt KKW Emsland, Siemens KWU Report R232/93/0002 (1993d)

    Google Scholar 

  • Kolev, N.I.: IVA3-NW A three phase flow network analyzer. Input description. Siemens KWU Report R232/93/E0041 (1993e)

    Google Scholar 

  • Kolev, N.I.: IVA3-NW Components: relief valves, pumps, heat structures. Siemens KWU Report R232/93/E0050 (1993f)

    Google Scholar 

  • Kolev, N.I.: The influence of the mutual bubble interaction on the bubble departure diameter. Exp. Thermal Fluid Sci. 8, 167–174 (1994a)

    Article  Google Scholar 

  • Kolev, N.I.: The code IVA4: Modeling of mass conservation in multi-phase multicomponent flows in heterogeneous porous media. Kerntechnik 59(4-5), 226–237 (1994b)

    Google Scholar 

  • Kolev, N.I.: Three fluid modeling with dynamic fragmentation and coalescence fiction or daily practice? In: 7th FARO Experts Group Meeting Ispra, October 15-16 (1996); Proceedings of OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, MD, November 5-8 (1996); 4th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, ExHFT 4, Brussels, June 2-6 (1997); ASME Fluids Engineering Conference & Exhibition, The Hyatt Regency Vancouver, British Columbia, June 22-26 (1997); Invited Paper; Proceedings of 1997 International Seminar on Vapor Explosions and Explosive Eruptions (AMIGO-IMI), May 22-24. Aoba Kinen Kaikan of Tohoku University, Sendai-City, Japan (1997)

    Google Scholar 

  • Kolev, N.I.: Can melt-water interaction jeopardize the containment integrity of the EPR? Part 3: Fragmentation and coalescence dynamics in multi-phase flows, KWU NAT/1998/E083a, Project EPR (1998)

    Google Scholar 

  • Kolev, N.I.: Verification of IVA5 computer code for melt-water interaction analysis, Part 1: Single phase flow, Part 2: Two-phase flow, three-phase flow with cold and hot solid spheres, Part 3: Three-phase flow with dynamic fragmentation and coalescence, Part 4: Three-phase flow with dynamic fragmentation and coalescence – alumna experiments. In: CD Proceedings of the Ninth International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, CA, October 3-8 (1999); Log. Nr. 315

    Google Scholar 

  • Kolomentzev, A.I., Dushkin, A.L.: Vlianie teplovoj i dinamiceskoj neravnovesnosty faz na pokasatel adiabatj v dwuchfasnijh sredach. TE 8, 53–55 (1985)

    Google Scholar 

  • Mugele, R.A., Evans, H.D.: Droplet size distribution in sprays. Ing. Eng. Chem. 43, 1317–1324 (1951)

    Article  Google Scholar 

  • Nukiama, S., Tanasawa, Y.: Trans. Soc. Mech. Engrs. (Japan) 4(14), 86 (1931)

    Google Scholar 

  • Pilch, M., Erdman, C.A., Reynolds, A.B.: Acceleration induced fragmentation of liquid drops. Department of Nucl. Eng., University of Virginia, Charlottesville, VA, NUREG/CR-2247 (August 1981)

    Google Scholar 

  • Reid, R.C., Prausnitz, J.M., Sherwood, T.K.: The properties of gases and liquids, 3rd edn. McGraw–Hill Book Company, New York (1982)

    Google Scholar 

  • Reynolds, O.: On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Cambridge Phil. Trans., 123–164 (May 1894)

    Google Scholar 

  • Riznic, J.R., Ishii, M.: Bubble number density and vapor generation in flushing flow. Int. J. Heat Mass Transfer 32(10), 1821–1833 (1989)

    Article  Google Scholar 

  • Rosin, P., Rammler, E.: Laws governing the fineness of powdered coal. J. Inst. Fuel 7, 29–36 (1933)

    Google Scholar 

  • Sauter, J.: NACA Rept. TM-518 (1929)

    Google Scholar 

  • Serizawa, A., Kataoka, I., Michiyoshi, I.I.I.: Turbulence structure of air-water bubbly flow – I. Transport properties. Int. J. Multiphase Flow 2, 247–259 (1975)

    Article  Google Scholar 

  • Sha, T., Chao, B.T., Soo, S.L.: Porous-media formulation for multi-phase flow with heat transfer. Nucl. Eng. Des. 82, 93–106 (1984)

    Article  Google Scholar 

  • Slattery, J.C.: Flow of viscoelastic fluids through porous media. AIChE J. 13, 1066 (1967)

    Article  Google Scholar 

  • Slattery, J.C.: Interfacial transport phenomena. Springer, Heidelberg (1990)

    Book  Google Scholar 

  • Teletov, S.G.: On the problem of fluid dynamics of two-phase mixtures, I. Hydrodynamic and energy equations. Bull. Moscow Univ. (2), 15 (1958)

    Google Scholar 

  • Wallis, G.B.: One-dimensional two-phase flow. McGraw–Hill Book Company, New York (1969)

    Google Scholar 

  • Whitaker, S.: Diffusion and dispersion in porous media. AIChE J. 13, 420 (1967)

    Article  Google Scholar 

  • Whitaker, S.: Advances in theory of fluid motion in porous media. Ind. Eng. Chem. 61(12), 14–28 (1969)

    Article  Google Scholar 

  • Whitaker, S.: Experimental principles of heat transfer. Pergamon Press, New York (1977)

    Google Scholar 

  • Whitaker, S.: A simple geometrical derivation of the spatial averaging theorem. Chem. Eng. Edu., 50–52 (1985)

    Google Scholar 

  • Zemansky, M.W.: Heat and thermodynamics, 5th edn. McGraw-Hill Book Company, New York (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Möhrendorferstr, Herzogenaurach, Germany

    Nikolay Ivanov Kolev

Authors
  1. Nikolay Ivanov Kolev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolay Ivanov Kolev .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Kolev, N.I. (2015). Mass Conservation. In: Multiphase Flow Dynamics 1. Springer, Cham. https://doi.org/10.1007/978-3-319-15296-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15296-7_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15295-0

  • Online ISBN: 978-3-319-15296-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation