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Original Articles

The Eddy Dissipation Turbulence Energy Cascade Model

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Pages 213-235 | Received 20 Feb 1999, Accepted 15 Dec 1999, Published online: 24 Oct 2007

References

  • Batchelor , G, K. and Townsend , A. A. ( 1947 ) Decay of vorticity in isotropic turbulence , Proc. Roy. Soc. London, Ser. A , 190 , 534 – 550 .
  • Batchelor , G. K. and Townsend , A. A. ( 1948 a) Decay of isotropic turbulence in the initial period , Proc. Roy. Soc. London, Ser. A , 193 , 539 – 558 .
  • Batchelor , G. K. and Townsend , A. A. ( 1948 b) Decay of isotropic turbulence in the final period , Proc. Roy. Soc. London, Ser. A , 194 , 527 – 543 .
  • Bennett , J. C. and Corrsin , S. ( 1978 ) Small Reynolds number nearly isotropic turbulence in a straight duct and a contraction , Phys. Fluids , 21 , 2129 – 2140 .
  • Bish , E. S. and Dahm , W.J.A. ( 1995 ) Strained dissipation and reaction layer analyses of nonequilibrium chemistry in turbulent reacting flows , Combustion and Flame , 100 , 457 – 464 .
  • Byggstøyl , S. ( 1984 ) Modelling of isotropic turbulent flow, in Mathematical modelling of turbulence-structure effects in reacting and non reacting flows , Dr. Ing. Thesis, Norwegian Institute of Technology, ;|Trondheim, pp. 1 – 14 .
  • Byggstøyl , S. and Magnussen , B. F. ( 1983 ) A model for flame extinction in turbulent flow. In Bradbury, L.J.S. et al. Turbulent Shear Flows 4 , Springer-Verlag, Berlin 1985, pp. 381 – 395 .
  • Chou P.-Y. and Huang Y.-N. ( 1975 ) On the statistical vorticity structure theory of homogeneous isotropic turbulence , Scientia Sinica , 18 , 199 – 222 .
  • Coleman , G. N. and Mansour , N. N. ( 1991 ) Simulation and modeling of homogeneous compressible turbulence under isotropic mean compression. In Durst , F. et al. (Eds.) Turbulent Shear Flows 8 , Springer Verlag, Berlin y 1993, pp. 268 – 282 .
  • Comte-Bellot , G. and Corrsin , S. ( 1966 ) The use of a contraction to improve the isotropy of grid-generated turbulence , J. Fluid Mech. , 25 , 657 – 682 .
  • Corrsin , S. ( 1962 ) Turbulent dissipation fluctuation , Phys. Fluids , 5 , 1301 – 1302 .
  • Dahm , W, J. A., Southerland , K. B. , and Buch , A. ( 1991 ) Direct, high resolution, four-dimensional measurements of the fine structure of Sc»1 molecular mixing in turbulent flows, Phys. Fluids A , 3 , 1115 – 1127 .
  • Ferziger , J. H. ( 1980 ) Homogeneous turbulent flow, in Kline , S. J. , Cantwell , B. J. , and Lilley , G.M. (Eds.) The 1980–81 AFOSR-HTTM-Stanford Conference on Complex turbulent flows: Comparison of computation and experiment I , Stanford , California 1981 . pp. 405 – 433 .
  • Frisch , U. , Sulem , P.-L. , and Nelkin , M. ( 1978 ) A simple dynamical model of intermittent fully developed turbulence , J. Fluid Mech. , 87 , 719 – 736 .
  • Furukawa , J. , Okamoto , K. , and Hirano . T. ( 1996 ) Turbulence characteristics within the local reaction zone of a high intensity turbulent premixed flame, Twenty-sixth Symp. (Int.) Comb. , Comb. Inst., Pittsburgh , Pennsylvania 1997 , pp. 405 – 412 .
  • Gran , I. R. and Magnussen , B. F. ( 1996 a) A numerical study of a bluff-body stabilized diffusion flame. Part 1. Influence of turbulence modeling and boundary conditions. Comb. Sci. Technol. , 119 , 171 – 190 .
  • Gran , I, R. and Magnussen , B. F. ( 1996 b) A numerical study of a bluff-body stabilized diffusion flame. Part 2. Influence of combustion modeling and finite-rate chemistry. Comb. Sci. Technol. , 119 , 191 – 217 .
  • Hanjalić , K. and Launder B. E. ( 1976 ) Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence, J. Fluid Mech. , 74 , 593 – 610 .
  • Jones , W P. and Launder , B. E. ( 1972 ) The prediction of laminarization with a two-equation model of turbulence , Int. J. Heat Mass Transfer , 15 , 301 – 314 .
  • Klebanoff , P. S. ( 1955 ) Characteristics of turbulence in a boundary layer with zero pressure gradient , Report 1247, NACA.
  • Kolmogorov , A. ( 1941 ) The local structure of turbulence in incompressible viscous fluid for very large Reynolds' number , C. R. Doklady Acad. Sci. URSS , 30 , 301 – 305 .
  • Kolmogorov , A. N. ( 1962 ) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , J. Fluid Mech. , 13 , 82 – 85 .
  • Kuo , A. Y. -S. and Corrsin , S. ( 1971 ) Experiments on internal intermittency and fine-structure distribution functions in fully turbulent fluid , J. Fluid Mech. , 50 , 285 – 319 .
  • Kuo. A. Y.-S. and Corrsin , S. ( 1972 ) Experiment on the geometry of the fine-structure regions in fully developed turbulence , J. Fluid Mech. , 56 , 447 – 479 (1972).
  • Launder , B. E. , and Spalding , D. B. ( 1974 ) The numerical computation of turbulent flows , Computer Methods in Appl. Mech. and Eng. , 3 . 269 – 289 .
  • Lesieur , M. ( 1990 ) Turbulence in Fluids , 2nd. ed., Kluwer, Dordrecht , The Netherlands.
  • Lumley , J, L. ( 1992 ) Some comments on turbulence , Phys. Fluids A , 4 , 203 – 211 .
  • Lumley , J. L. , Berkooz , G. , Elezgaray , J. , Holmes , P. , Poje , A. , and Volte , C. ( 1996 ) Fundamental aspects of incompressible and compressible turbulent flows. In Gatski , T. B. , Hussaini , M. Y , and Lumley , J. L. (Eds.) Simulation and Modeling of Turbulent Flows , Oxford University Press, New York , pp. 5 – 78 .
  • Magnussen , B. F. ( 1981 a) On the structure of turbulence and a generalized eddy dissipation concept for chemical reaction in turbulent flow , 19th. AIAA aerospace science meeting, Jan. 12 – 15 , 1981 , St . Louis, Missouri .
  • Magnussen , B. F. ( 1981 b) Modeling of reaction processes in turbulent flames with special emphasis on soot formation and combustion. In Siegla , D. C. and Smith , G. W. (Eds.) Particulate carbon formation during combustion. , Plenum Publishing Corp., pp. 321 – 335 .
  • Magnussen , B. F. Modeling of NOx and soot formation by the Eddy Dissipation Concept , Int. Flame Research Foundation , 1st Topic Oriented Technical Meeting, 17 – 19 Oct. ,( 1989 ) Amsterdam , Holland . (Also: Report No. STF15 A90014, SINTEF , Trondheim , Norway 1990 .).
  • Magnussen , B. F. and Hjertager , B. H. ( 1976 ) On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Sixteenth Symp. (Int.) Comb., Comb. Inst. , Pittsburgh , Pennsylvania , pp. 719 – 729 .
  • Magnussen , B. F. , Hjertager , B. H. , Olsen , J. G. , and Bhaduri , D. ( 1978 ) Effects of turbulent structure and local concentrations on soot formation and combustion in C2H2 diffusion flames, Seventeenth Symp. (Int.) Comb., Comb. Inst. , Pittsburgh , Pennsylvania 1979 , pp. 1383 – 1393 .
  • Mansour , N. N. and Wray , A. A. ( 1994 ) Decay of isotropic turbulence at low Reynolds number , Phys. Fluids , 6 , 808 – 814 .
  • Onsager , L. ( 1945 ) The distribution of energy in turbulence, (Abstract) , Phys. Rev , 68 ,286.
  • Onsager , L. ( 1949 ) Statistical hydrodynamics , Nuovo Cimento, Suppl , 6 , 279 – 287 ,
  • Richardson , L. F. ( 1922 ) Weather prediction by numerical process , London (reprint: Dover, New York y 1965).
  • Rotta , J. ( 1951 a) Statistische Theorie nichthomogener Turbulenz - 1. Mitteilung , Z. Phys. , 129 , 547 – 572 .
  • Rotta , J. ( 1951 b) Statistische Theorie nichthomogener Turbulenz - 2. Mitteilung , Z. Phys. , 131 , 51 – 77 .
  • Schumann , U. and Patterson , G. S. ( 1978 ) Numerical study of pressure and velocity fluctuations in nearly isotropic turbulence , J. Fluid Mech. , 88 , 685 – 709 .
  • She , Z. -S. and Jackson , E. ( 1993 ) On the universal form of energy spectra in fully developed turbulence , Phys. Fluids , 5 , 1526 – 1528 .
  • Sirovich , L. , Smith , L. , and Yakhot , V. ( 1994 ) Energy spectrum of homogeneous and isotropic turbulence in far dissipation range , Phys. Rev. Lett. , 72 , 344 – 347 .
  • Smith , L. M , and Reynolds , W, C. ( 1991 ) The dissipation-range spectrum and the velocity-derivative skewness in turbulent flows , Phys. Fluids A , 3 , 992 – 994 .
  • Sreenivasan , K. R. ( 1995 ) On the universality of the Kolmogorov constant , Phys. Fluids , 7 , 2778 – 2784 .
  • Tennekes , H. ( 1968 ) Simple model for the small-scale structure of turbulence , Phys. Fluids , 11 , 669 – 671 .
  • Tennekes , H. and Lumley , J. L. ( 1972 ) A first course in turbulence , (p:MIT Press,| Cambridge , Massachusetts , 9th printing 1983 ).
  • Wei Z. , Zhu Q. , Niu Z. , and Yu D. ( 1988 ) The experimental results of micro-structure in grid-produced turbulence , Acta Mech. Sinica , 4 , 8 – 14 .
  • Yakhot , V. and Zakharov , V. ( 1993 ) Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence , Physica D , 64 , 379 – 394 .
  • Zhou , Y. ( 1993 ) Interacting scales and energy transfer in isotropic turbulence. Phys. Fluids A , 5 , 2511 – 2524 .
  • * E-mail: [email protected] Fax. No.: +47 73 59 35 80

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