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Some single-phase boundary layer theory basics

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Multiphase Flow Dynamics 4

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Abstract

Hundreds of very useful constitutive relations that describe the interactions in multiphase flows are based on the achievements of single-phase boundary layer theory. That is why it is important to recall at least some of them, before moving on to more complex interactions in multiphase flow theory. My favorite book to start learning the main ideas of single-phase boundary layer theory is the famous monograph by Schlichting (1982). This chapter gives only the basics required to understand the rest of the book.

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References

  • Alshamani, K.M.M.: Correlation among turbulent shear stress, turbulent kinetic energy, and axial turbulence intensity. AIAA J. 16(8), 859–861 (1978)

    Article  Google Scholar 

  • Avdeev, A.A.: Teploenergetika 3, 23 (1982)

    Google Scholar 

  • Azer, N.Z., Chao, B.T.: A mechanism of turbulent heat transfer in liquid metals. Int. J. Heat Mass Transfer 1, 121–138 (1960)

    Article  Google Scholar 

  • Baehr, H.D., Stephan, K.: Wärme- und Stoffübertragung. Springer, 4. Auflage, Berlin (2004)

    Google Scholar 

  • Bendiksen, K.H.: On the motion of long bubbles in vertical tubes. Int. J. Multiphase Flow 11, 797–812 (1985)

    Article  MATH  Google Scholar 

  • Bergant, A., Simpson, A.R., Vitkovsky, J.: Review of unsteady prediction models in transient pipe flow. In: 9th IAHR Int. Meeting, Brno, Czech Republic, September 7-9 (1999)

    Google Scholar 

  • Bishop, A.A., Sandberg, R.O., Tong, L.S.: Forced convection heat transfer to wa-ter at near-critical temperatures and super-critical pressures. WCAP-2056, Westing-house Electric Corporation, Atomic Power Division (December 1964)

    Google Scholar 

  • Bobkov, V.P., Gribanov, Y.I.: Statisticheskie izmerenija v turbolentnyh potokax. Energoatomizdat, Moskva (1988)

    Google Scholar 

  • Borstevskij, J.T., Rudin, S.N.: Upravlenie turbulentnom pograniznom sloe. Visha skola, Kiev (1978)

    Google Scholar 

  • Bradshaw, P.: The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625–645 (1967)

    Article  Google Scholar 

  • Brunone, B., Golia, U.M., Greco, M.: Some remarks on the momentum equations for transients, Int. Meeting on Hydraulic Transients with Column Separation. In: 9th Round Table, IAHR, Valencia, Spain, pp. 140–148 (1991)

    Google Scholar 

  • Bühne, W.: Wärme 61, 162 (1938)

    Google Scholar 

  • Buleev, N.I.: Trudy 3-j mejdunarodnoj konferenzii po mirnomu ispol’zovaniju atomnoj energii 5, 305-313 (1965)

    Google Scholar 

  • Colebrook, C.F.: Turbulent flow in pipes with particular reference to the transition region between the smooth and the rough pipe lows. J. Institution Civil Engineers (1939)

    Google Scholar 

  • Collins, R., De Moraes, F.F., Davidson, J.F., Harrison, D.: The motion of large gas bubble rising through liquid flowing in a tube. J. Fluid. Mech. 89, 497–514 (1978)

    Article  Google Scholar 

  • Dittus, F.V., Boelter, L.M.K.: Engng., vol. 2(13), p. 443. Univ. of Calif. Publ. (1930)

    Google Scholar 

  • Gnielinski, V.: New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng. 16(2), 359–368 (1976)

    Google Scholar 

  • Grim, H.: A new procedure for the prediction of forced convection heat transfer at near- and supercritical pressure. Heat and Mass Transfer 31, 301–305 (1996)

    Article  Google Scholar 

  • Grötzbach, G.: Anisotropy and buoyancy in nuclear turbulent heat transfer – crit-ical assessment and needs for modeling. Forschungszentrum Karlsruhe, FZKA 7363 (December 2007)

    Google Scholar 

  • Hammond, G.P.: Turbulent Prandtl number within a near-wall flow. AIAA J. 23(11), 1668–1669 (1985)

    Article  MathSciNet  Google Scholar 

  • Harsha, P.T., Lee, S.C.: Correlation between turbulent shear stress and turbulent kinetic energy. AIAA J. 8(5), 1508–1510 (1970)

    Article  Google Scholar 

  • Hoffman, E.: Z. Ges. Kälte-Ind. 44, 99–107 (1937)

    Google Scholar 

  • Hollingsworth, D.K., Kays, W.M., Moffat, R.J.: Measurement and prediction of the turbulent thermal boundary layer in water on flat and concave surfaces. Report no. HMT-41, Thermosciences Division, Dep. of Mech. Engr., Stanford Univ., CA (September 1989)

    Google Scholar 

  • Hurlburt, E.T., Fore, L.B., Bauer, R.C.: A two zone interfacial shear stress and liquid film velocity model for vertical annular two-phase flow. In: Proc. of FEDSM 2006 2006 ASME Joint U.S. – European Fluids Engineering Summer Meeting, Miami, FL, July 17-20. FEDSM2006-98512 (2006)

    Google Scholar 

  • Jaster, H., Kosky, P.G.: Condensation heat transfer in mixed flow regime. Int. J. Heat Mass Transfer 19, 95–99 (1976)

    Article  Google Scholar 

  • Johansen, S.T.: The deposition of particles on vertical walls. Int. J. Multiphase Flow 17, 335–376 (1991)

    Article  Google Scholar 

  • Jukauskas, A., Jyugja, I.: Teplootdacha v laminarnom potoke jidkosti. Mintis, Vil’nyus (1969)

    Google Scholar 

  • Kader, B.A., Yaglom, A.M.: Int. J. Heat Mass Transfer 15(12), 2329–2351 (1972)

    Article  Google Scholar 

  • Kalinin, E.K., Dreitser, G.A.: Unsteady convective heat transfer and hydrodynamics in channels. In: Hartnet, G.P., Ervine, G.S. (eds.) Advances in Heat Transfer, vol. 6 (1970)

    Google Scholar 

  • Kao, M.-T., Lee, M., Ferng, Y.-M., Chieng, C.-C.: Heat transfer deterioration in a su-percritical water channel. Nuclear Engineering and Design 240, 3321–3328 (2010)

    Article  Google Scholar 

  • Kays, W.M.: Konvektivnyj teplo- i masoobmen. Miskva, Energia, 207 (1972), translation from English

    Google Scholar 

  • Kays, W.M.: Turbulent Prandtl number – where are we? Transaction of the ASME 116, 284–295 (1994)

    Article  Google Scholar 

  • Kays, W.M., Crawford, M.E.: Convective heat and mass transfer, 3rd edn. McGraw-Hill, New York (1993)

    Google Scholar 

  • Kawamura, H.: Transient hydraulics and heat transfer in a turbulent flow. Kernforschungszentrum Karlsruhe, Report KFK 2166 (Juni 1975)

    Google Scholar 

  • Kim, D.E., Kim, M.H.: Experimental study of the effect of flow acceleration and buoyancy on heat transfer in supercritical fluid flow in circular tube. Nuclear Eng. Design 240, 3336–3349 (2010)

    Article  Google Scholar 

  • Kim, J., Moin, P., Moser, R.: Turbulent statistics in a fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    Article  MATH  Google Scholar 

  • Kirillov, P.L.: Analiz razchetnyh formul po teploobmenu pri turbulentnom techenii v rtubach. Obsor FEI-0230, Moskva, ZNIIatominform, 80s (1988)

    Google Scholar 

  • Kirillov, P.L., Markov, Y.M., Slobodchuk, V.I.: Rasrpredelenie temperatury i zakon teploobmena pri turbulentnom techenii v krugloj trube: Preprint FEI-1703 (1985)

    Google Scholar 

  • Kirilov, P.L., Pomet’ko, R.S., Smirnov, A.M., Grabezhnaia, V.A.: Investigation on heat transfer to water at supercritical pressures in tubes and rod bundles. FEI-3051, Institute of physics and power engineering (FEI) (2005) (in Russian)

    Google Scholar 

  • Knudsen, J.G., Katz, D.L.: Fluid dynamics and heat transfer, pp. 394, 485–486. McGraw-Hill, New York (1958)

    MATH  Google Scholar 

  • Kutateladze, S.S.: Osnovy teorii teploobmena, 5th edn. Atomizdat, Moskva (1979)

    Google Scholar 

  • Kutateladze, S.S., Khabakhpasheva, W.M., Orlov, V.V., Perepelitsa, V.V., Michailova, E.S.: In Turbulent Shear Flows I, pp. 9–103. Springer, Berlin (1979)

    Google Scholar 

  • Laufer, J.: Investigation of turbulent flow in a two-dimensional channel. NACA Report 1053 (1952)

    Google Scholar 

  • Laufer, J.: The structure of turbulence in fully developed pipe flow. NACA Report 1273 (1953)

    Google Scholar 

  • Laufer, S.L.: The structure of turbulence in fully developed pipe flow. NASA Techni-cal Note No. 2954 (1953)

    Google Scholar 

  • Lee, S.L., Durst, F.: On the motion of particles in turbulent flow. US Nuclear Regulatory Commission Report NUREG/CR-1556 (1980)

    Google Scholar 

  • Lee, S.J., Lahey Jr., R.T., Jones Jr., O.C.: The prediction of two phase turbulence and phase distribution phenomena using k-e model. Int. J. of Multiphase Flow (1986)

    Google Scholar 

  • Levy, S.: Forced convection subcooled boiling – prediction of the vapor volumetric fraction. Int. J. Heat Mass Transfer 10, 951–965 (1967)

    Article  Google Scholar 

  • Ludwig, H.Z.: Z. Flugwiss. 4, 73–81 (1956)

    Google Scholar 

  • Martinelli, R.C.: Heat transfer to molten metals. Trans. Am. Soc. Mech. Eng. 69, 947–959 (1974)

    Google Scholar 

  • Matida, E.A., Tori, A., Nishino, K.: Proc. of the 35th Nat. Heat Transfer Symposium of Japan, vol. 2, pp. 495–496 (1998)

    Google Scholar 

  • Marek, J., Mensinger, E., Rehme, K.: Experimental friction factors of transient flows through circular tubes (Final report). Primärbericht, Institut für Neutronenphysik und Reaktortechnik, INR-910, Kernforschungszentrum Karlsruhe (März 1979)

    Google Scholar 

  • Migay, V.K.: Toploobmen v trubah pri turbulentnom techeniy. Tr. ZKTI vyp. 206 (1983)

    Google Scholar 

  • Miheev, M.H.: Izv. AN SSSR (10), 1448–1454 (1952)

    Google Scholar 

  • Miheev, M.A.: Izvestiya AN SSSR. Energetika i transport (5) (1966)

    Google Scholar 

  • Miheev, M.A., Miheeva, I.M.: Osnovy teploperedachi. Energiya, Moskva (1973)

    Google Scholar 

  • Mokry, S.J., Kirilov, P.L., Pioro, I.L., Gospodinov, Y.K.: Supercritical water heat transfer in vertical bare tube: normal, improved, and deteriorated regimes. Nuclear Technology 172, 60–70 (2010)

    Google Scholar 

  • Na, T., Habib, I.S.: Heat transfer in turbulent pipe flow based on a new mixing length model. Appl. Sci. Res. 28, 302–314 (1973)

    Google Scholar 

  • Nikuradse, J.: Gesetzmäßigkeit der turbulenten Strömung in glaten Rohren, Forsch. Arb. Ing.-Wes. No 1932 (1932)

    Google Scholar 

  • Nikuradse, J.: VDI – Forschungsheft, no 361 (1933)

    Google Scholar 

  • Notter, R.H., Sleicher, C.H.: A solution of the turbulent Graetz-problem III fully de-veloped and entrance region heat transfer rates. Chem. Eng. Sci. 27, 2073–2093 (1972)

    Article  Google Scholar 

  • Petukhov, B.S., Kirillov, P.L.: About heat transfer at turbulent fluid flow in tubes. Thermal Engineering 4, 63–68 (1958) (in Russian)

    Google Scholar 

  • Petukhov, B.S.: Heat transfer and friction in turbulent pipe flow with variable physical properties. In: Advances in Heat Transfer, vol. 6, pp. 503–564. Academic Press, New York (1970)

    Google Scholar 

  • Petukhov, B.S., Genin, L.G., Kovalev, S.A.: Teploobmen v jadernych energeticheskih ustanovkax. Atomizdat, Moskva (1974)

    Google Scholar 

  • Prandtl, L.: Physik. Zeitachrift 11, 1072–1078 (1910); 29, 487-489 (1928)

    Google Scholar 

  • Quarmby, A., Quirk, R.: Axisymmetric and non-symmetric turbulent diffusion in a plain circular tube at high Schmidt number. Int. J. Heat Mass Transfer 17, 143–148 (1974)

    Article  Google Scholar 

  • Rehme, K.: The structure of turbulence in rod bundles and the implications on natural mixing between the subchannels. Int. J. Heat Mass Transfer 35(2), 567–581 (1992)

    Article  Google Scholar 

  • Reichardt, H.: Vollständige Darstellung der turbulenten Geschwindigkeiten in glaten Leitungen. Z. angew. Math. Mech. 31(7), 208–219 (1951)

    Article  MATH  Google Scholar 

  • Reynolds, O.: Proc. Manchester Phil. Soc., rep¬rint of “Scientific Papers of O. Reynolds”, vol. II, Cambridge (1974)

    Google Scholar 

  • Sani Rle, R.: Down flow boiling and non-boiling heat transfer in a uniformly heated tube, 15th edn. University of California, URL-9023, Chemistry-Gen. UC-4, TID-4500, January 4 (1960)

    Google Scholar 

  • Schlichting, H.: Grenzschicht-Theorie, Braun, Karlsruhe, 8 Auflage (1982)

    Google Scholar 

  • Sidorov, A.E.: Calculation of resistance and convective heat transfer. Teploenergetika (4), 79–80 (1959)

    Google Scholar 

  • Sleicher, C.A., Rouse, M.W.: A convenient correlation for heat transfer to constant and variable property fluids un turbulent pipe flow. Int. J. Heat Mass Transfer 18, 677–683 (1975)

    Article  Google Scholar 

  • Stokes, G.G.: On the theories of the internal friction of fluids in motion and of the equilibrium and motion of elastic solids. Trans. Cambridge Phil. Soc. 8, 287–305 (1845)

    Google Scholar 

  • Taylor, G.I.: Brit. Aeronaut. Comm. Rept. Mem. 272, 423–429 (1916)

    Google Scholar 

  • Traviss, D.P., Rohsenow, W.M., Baron, A.B.: Forced convection condensation inside a tubes: A heat transfer equation for condenser design. ASHRAE Trans., no 2272 Rp-63 (1973)

    Google Scholar 

  • Vardy, A.E., Brown, J.M.B.: On turbulent, unsteady, smooth-pipe flow. In: Proc. Int. Conf. on Pressure Surges and Fluid Transients, pp. 289–311. BHR Group, Harrogate, England (1996)

    Google Scholar 

  • Vames, J.S., Hanratty, T.J.: Turbulent dispersion of droplets for air flow in a pipes. Exports Fluids 6, 94–104 (1988)

    Google Scholar 

  • van Driest, E.R.: On turbulent flow near a wall. Heat Transfer and Fluid Mech. Institute (1955)

    Google Scholar 

  • von Karman, T.: Trans. ASME 61, 705–710 (1939)

    Google Scholar 

  • Weisman, J.: Heat transfer to water flowing parallel to tube bundles. Nucl. Sci. Eng. 6, 79 (1959)

    Google Scholar 

  • White, F.M.: Viscous fluid flow, 3rd edn. McGraw-Hill, New York (2006)

    Google Scholar 

  • Yakhot, Y., Orszag, S.A., Yakhot, A.: Heat transfer in turbulent fluids-1. Pipe flow, Int. J. of Heat and Mass Transfer 35(1), 15–22 (1987)

    Article  Google Scholar 

  • Yamagata, K., Nishikawa, K., Hasegawa, S., Fujii, T., Yoshida: Forced convective heat transfer to supercritical water flow in tubes. Int. J. Heat Mass Transfer 15, 2575–2593 (1972)

    Article  Google Scholar 

  • Yu, B., Ozoe, H., Churchill, S.W.: The characteristics of fully developed turbulent convection in round tube. Chem. Eng. Sci. 56, 1781–1800 (2001)

    Article  Google Scholar 

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  1. Nikolay Ivanov Kolev
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Kolev, N.I. (2011). Some single-phase boundary layer theory basics. In: Multiphase Flow Dynamics 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20749-5_1

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  • DOI: https://doi.org/10.1007/978-3-642-20749-5_1

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