First and Second Laws of the Thermodynamics Local

  • Nikolay Ivanov KolevEmail author


As in Chapters 1 and 2, from the large number of formulations of the conservation equations for multi-phase flows the local volume averaging as founded by Anderson and Jackson, Slattery, and Whitaker was selected to derive rigorously the energy conservation equations for multi-phase flows conditionally divided into three velocity fields. The heterogeneous porous-media formulation introduced by Gentry et al., commented by Hirt, and used by Sha, Chao and Soo, is then implanted into the formalism as a geometrical skeleton.


Velocity Field Turbulent Kinetic Energy Energy Conservation Equation Mass Conservation Equation Specific Entropy 
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  1. Albring, W.: Angewandte Strömungslehre. Verlag Theodor Steinkopf, Dresden (1970)Google Scholar
  2. Bird, B.R., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena. John Wiley & Sons, New York (1960)Google Scholar
  3. Bohl, W.R., et al.: Multiphase flow in the advanced fluid dynamics model. In: ANS Proc. 1988 Nat. Heat Transfer Conf., HTC, Houston, Texas, July 24-27, vol. 3, pp. 61–70 (1988)Google Scholar
  4. Boussinesq, J.: Essai sur la théorie des eaux courantes, Mem. Acad. Sci. Inst. Fr. 23(1), 252–260 (1877)Google Scholar
  5. Chandesris, M., Serre, G., Sagaut: A macroscopic turbulence model for flow in porous media suited for channel, pipe and rod bundle flows. In: 4th Int. Conf. on Computational Heat and Mass Transfer, Paris (2005)Google Scholar
  6. Fick, A.: Über Diffusion. Ann. der Physik 94, 59 (1855)CrossRefGoogle Scholar
  7. Gibbs, W.J.: Thermodynamische Studien. Verlag von Wilhelm Engelmann, Leipzig (1892)zbMATHGoogle Scholar
  8. 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
  9. Hammond, G.P.: Turbulent Prandtl number within a near-wall flow. AIAA Journal 23(11), 1668–1669 (1985)MathSciNetCrossRefGoogle Scholar
  10. Kelly, J.M., Kohrt, R.J.: COBRA-TF: Flow blockage heat transfer program. In: Proc. Eleventh Water Reactor Safety Research Information Meeting, Gaithersbury - Maryland, NUREG/CP-0048, October 24-28, vol. 1, pp. 209–232 (1983)Google Scholar
  11. Kolev, N.I.: Transiente Drephasen Dreikomponenten Stroemung, Teil 1: Formulierung des Differentialgleichungssystems, KfK 3910 (March 1985)Google Scholar
  12. Kolev, N.I.: Transient three-dimensional three-phase three-component non equilibrium flow in porous bodies described by three-velocity fields. Kernenergie 29(10), 383–392 (1986)Google Scholar
  13. Kolev, N.I.: Transiente Dreiphasen Dreikomponenten Stroemung, Part 3: 3D-Dreifluid-Diffusionsmodell, KfK 4080 (1986)Google Scholar
  14. Kolev, N.I.: A Three Field-Diffusion Model of Three-Phase, Three-Component Flow for the Transient 3D-Computer Code IVA2/01. Nuclear Technology 78, 95–131 (1987)Google Scholar
  15. 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 4948 Kernforschungszentrum Karlsruhe (September 1991)Google Scholar
  16. 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 (1991)Google Scholar
  17. Kolev, N.I.: Berechnung der Fluiddynamischen Vorgänge bei einem Sperrwasserkühlerrohrbruch, Projekt KKW Emsland, Siemens KWU Report R232/93/0002 (1993a)Google Scholar
  18. Kolev, N.I.: IVA3-NW A three phase flow network analyzer. Input description, Siemens KWU Report R232/93/E0041 (1993b)Google Scholar
  19. Kolev, N.I.: IVA3-NW components: Relief valves, pumps, heat structures, Siemens KWU Report R232/93/E0050 (1993c)Google Scholar
  20. Kolev, N.I.: The code IVA3 for modelling of transient three-phase flows in complicated 3D geometry. Kerntechnik 58(3), 147–156 (1993d)Google Scholar
  21. Kolev, N.I.: IVA3 NW: Computer code for modelling 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 (1993e)Google Scholar
  22. Kolev, N.I.: IVA4: Modelling of mass conservation in multi-phase multi-component flows in heterogeneous porous media. Siemens KWU Report NA-M/94/E029, July 5, 1994 also in Kerntechnik 59(4-5), 226–237 (1994)Google Scholar
  23. Kolev, N.I.: IVA4: Modelling of momentum conservation in multi-phase flows in heterogeneous porous media. Siemens KWU Report NA-M/94/E030, July 5, also in Kerntechnik 59(6), 249–258 (1994)Google Scholar
  24. Kolev, N.I.: The influence of the mutual bubble interaction on the bubble departure diameter. Experimental Thermal and Fluid Science 8, 167–174 (1994)CrossRefGoogle Scholar
  25. 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)Google Scholar
  26. Kolev, N.I.: Derivatives for the equation of state of multi-component mixtures for universal multi-component flow models. Nuclear Science and Engineering 108, 74–87 (1991)Google Scholar
  27. Kolev, N.I.: The code IVA4: Second law of thermodynamics for multi-phase multi-component flows in heterogeneous media. Kerntechnik 60(1), 1–39 (1995)Google Scholar
  28. Kolev, N.I.: Comments on the entropy concept. Kerntechnik 62(1), 67–70 (1997a)Google Scholar
  29. Kolev, N.I.: Three fluid modeling with dynamic fragmentation and coalescence fiction or daily practice? In: Proceedings of OECD/CSNI Workshop on Transient Thermal-Hydraulic and Neutronic Codes Requirements, Annapolis, Md, U.S.A., November 5-8 (1997b); 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, Vancouver, British Columbia, CANADA June 22-26 (1997), Invited Paper; Proceedings of 1997 International Seminar on Vapor Explosions and Explosive Eruptions (AMIGO-IMI), Aoba Kinen Kaikan of Tohoku University, Sendai-City, Japan, May 22-24 (1997)Google Scholar
  30. Kolev, N.I.: On the variety of notation of the energy conservation principle for single phase flow. Kerntechnik 63(3), 145–156 (1998)Google Scholar
  31. 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, California, October 3-8 (1999); Log. Nr. 315Google Scholar
  32. Liles, D.R., et al.: TRAC-P1: An advanced best estimate computer program for PWR LOCA analysis. I. Methods, Models, User Information and Programming Details, NUREG/CR-0063, LA-7279-MS, vol. 1 (June 1978)Google Scholar
  33. Liles, D.R., et al.: TRAC-FD2 An advanced best-estimate computer program for pres-surized water reactor loss-of-coolant accident analysis. NUREG/CR-2054, LA-8709 MS (April 1981)Google Scholar
  34. Oswatitsch, K.: Gasdynamik, Berlin, Göttingen, Heidelberg (1952)Google Scholar
  35. 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
  36. Sha, T., Chao, B.T., Soo, S.L.: Porous media formulation for multi phase flow with heat transfer. Nuclear Engineering and Design 82, 93–106 (1984)CrossRefGoogle Scholar
  37. Shapiro, A.H.: The dynamics and thermodynamics of compressible fluid flow. The Roland Press Company, New York (1953)Google Scholar
  38. Solbrig, C.W., Hocever, C.H., Huges, E.D.: A model for a heterogene-ous two-phase unequal temperature fluid. In: 17th National Heat Transfer Conference, Salt Lake Sity, Utah, August 14-17, pp. 139–151 (1977)Google Scholar
  39. Stefan, J.: Versuche über die Verdampfung. Wiener Berichte 68, 385 (1874)Google Scholar
  40. Taylor, G.I.: Proc. Roy. Soc. A 151, 429 (1935)Google Scholar
  41. Thurgood, M.J., et al.: COBRA/TRAC - A thermal hydraulic code for transient analysis of nuclear reactor vessels and primary coolant systems. NUREG/CR-346, vol. 1-5 (1983)Google Scholar
  42. Zierep, J.: Einige moderne Aspekte der Stroemungsmechanik. Zeitschrift fuer Flugwissenschaften und Weltraumforschung 7(6), 357–361 (1983)zbMATHGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.MöhrendorferstrHerzogenaurachGermany

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