Johnson-Edgeworth Translation for Probability Modeling of Binary Scalar Mixing in Turbulent Flows

References

• Abramowitz , M. and Stegun , I. A. ( 1972 ). Handbook of Mathematical Functions and Formulas, Graphs, and Mathematical Tables . Government Printing Office , Washington , D.C .
   Google Scholar
• Bilger , R. W. ( 1980 ). Tlirbulent flows with nonpremixed reactants . In Libby, P. A. and Williams, F. A., editors , Turbulent Reacting Flows , chapter 3 , pages 65 – 113 . Springer-Verlag , Heidelberg .
   Google Scholar
• Brodkey , R. S. ( 1981 ). Fundamental of turbulent motion . Chem. Eng. Comm. 8 , 1 – 23 .
   Web of Science ®Google Scholar
• Casella , G. Berger , R. L. ( 1990 ). Statistical Inference . Brooks/Cole Publishing Company , Belmont , CA .
   Google Scholar
• Chen , H. , Chen , S. , and Kraichnan , R. H. ( 1989 ). |atProbability distribution of a stochastically advected scalar field|ot. Phys, Rev. Lett. , 63 , 2657 – 2660 .
   PubMed Web of Science ®Google Scholar
• Curl , R. L. ( 1963 ). Dispersed phase mixing I. Theory and effects in simple reactors . AIChE J. , 9 , 175 – 181 .
   Web of Science ®Google Scholar
• Dopazo , C. ( 1973 ), Non-Isothermal Turbulent Reactive Flows: Stochastic Approaches . Ph.D. Thesis , Department f Mechanical Engineering , State University of New York at Stony Brook , Stony Brook , NY .
   Google Scholar
• Dutta , A. and Tarbell , J. M. ( 1989 ). Closure models for turbulent reacting flows . AIChE J. , 35 , 2013 – 2027 .
   Web of Science ®Google Scholar
• Edgeworth , F. Y. ( 1907 ), On the representation of statistical frequency by a series . Journal of the Royal Statistical Society , Series A . 70 , 102 – 106 .
   Google Scholar
• Erlebacher , G. , Hussaini , M. Y. , Speziaie , C. G. , and Zang , T. A. ( 1987 ). Toward the large eddy simulation of compressible turbulent flows . ICASE Report 87-20 , NASA Langley Research Center , Hampton , VA . Also available as NASA CR 178273 .
   Google Scholar
• Erlebacher , G. , Hussaini , M. Y. , Speziale , C. G. , and Zang , T. A. ( 1990a ). Toward the large eddy simulation of compressible turbulent flows . ICASE Report 90-76 , NASA Langley Research Center , Hampton , VA . Also available as NASA CR 187460 .
   Google Scholar
• Erlebacher , G. , Hussaini , M.Y. , Kreiss , H. O. , and Sarkar , S. ( 1990b ). The analysis and simulation of compressible turbulence . Theoret. Comput. Fluid Dynamics 2 , 73 – 95 .
   Google Scholar
• Eswaran , V. and Pope , S. B. ( 1988 ). Direct numerical simulations of the turbulent mixing of a passive scalar . Phys. Fluids 31 , 506 – 520 .
   Web of Science ®Google Scholar
• Frankel , S. H. , Jiang , T.-L. , and Givi , P. ( 1992a ). Modeling of isotropic reacting turbulence by a hybrid mapping-EDQNM closure . AIChE J. 38 , 535 – 543 .
   Web of Science ®Google Scholar
• Frankel , S. H. , Madnia , C. K. , and Givi , P. ( 1992b ). Modeling of the reactant conversion rate in a turbulent shear flow . Chem. Eng. Comm. , 113 , 197 – 209 .
   Web of Science ®Google Scholar
• Frankel , S. H. ( 1992 ). Ph.D. Thesis , Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo , Buffalo , NY . in preparation .
   Google Scholar
• Gaffney , R. L. , White , J. A. , Girimaji , S. S. , and Drummond , J. P. ( 1992 ). Modeling of turbulent/chemistry interactions using assumed pdf methods . AIAA paper AIAA-92-3638 .
   Google Scholar
• Gao , F. ( 1991 ). Mapping closure and non-Gaussianity of the scalar probability density functions in isotropic turbulence . Phys. Fluids A 3 , 2438 – 2444 .
   Web of Science ®Google Scholar
• Girimaji , S. S. ( 1991a ). Assumed β-pdf model for turbulent mixing Validation and extension to multiple scalar mixing . Combust. Sci. and Tech. 78 , 177 – 196 .
   Web of Science ®Google Scholar
• Girimaji , S. S. ( 1991b ). A simple recipe for modeling reaction-rates in flows with turbulent-combustion . AIAA paper AIAA-91-1792 .
   Google Scholar
• Girimaji , S. S. ( 1992 ). Towards understanding turbulent scalar mixing . NASA CR 4446 s.
   Google Scholar
• Givi , P. and McMurtry , P. A. ( 1988 ). Non-premixed reaction in homogeneous turbulence Direct numerical simulations . AIChE J. 34 , 1039 – 1042 .
   Web of Science ®Google Scholar
• Givi , P. ( 1989 ). Model free simulations of turbulent reactive flows . Prog. Energy Combust. Sci. 15 , 1 – 107 .
   Web of Science ®Google Scholar
• Hawthorne , W. R. , Wedell , D. S. , and Hottel , H. C. ( 1949 ). Mixing and combustion in turbulent gas jets . In 3rd Symp. on Combustion, Flames and Explosion Phenomena , pages 266 – 288 . The Combustion Institute , Pittsburgh , PA .
   Google Scholar
• Hussaini , M. Y. , Speziale , C. G. , and Zang , T. A. ( 1990 ). The potential and limitations of direct and large eddy simulations . In Lumley, J. L., editor , Whither Turbulence? Turbulence at the Crossroads , volume 357 of Lecture Notes in Physics , pages 354 – 368 . Springer .
   Google Scholar
• Janicka , J. and Peters , N. ( 1982 ). Prediction of turbulent jet diffusion flame lift-off using a pdf transport equation . In Proceedings of 19th Symp. (Int.) on Combustion pages 367 – 374 . The Combustion Institute , Pittsburgh , PA .
   Google Scholar
• Janicka , J. , Kolbe , W. , and Kollmann , W. ( 1979 ). Closure of the transport equation for the probability density function of turbulent scalar field . J. Nonequil. Thermodyn. 4 , 47 – 66 .
   Web of Science ®Google Scholar
• Jiang , T.-L. , Givi , P. , and Gao , F. ( 1992 ). Binary and trinary scalar mixing by Fickian diffusion-some mapping closure results . Phys. Fluids A 4 , 1028 – 1035 .
   Web of Science ®Google Scholar
• Johnson , N. L. and Kotz , S. ( 1972 ). Distributions in Statistics Continuous Multivariate Distributions , John Wiley and Sons , New York , NY .
   Google Scholar
• Johnson , N. L. ( 1949a ). Systems of frequency curves generated by methods of translation . Biometrika 36 , 149 – 176 .
   PubMed Web of Science ®Google Scholar
• Johnson , N. L. ( 1949b ). Bivariate distributions based on simple translation systems . Biometrika 36 , 297 – 304 .
   PubMed Web of Science ®Google Scholar
• Johnson , M. E. ( 1987 ). Multivariate Statistical Simulation . John Wiley and Sons , New York , NY .
   Google Scholar
• Jones , W. P. and Priddin , C. H. ( 1978 ). Predictions of the flowfield and local gas composition in gas turbine combustors . In 17th Symp. (Int.) on Combustion , pages 399 – 409 . The Combustion Institute , Pittsburgh , PA .
   Google Scholar
• Kollmann , W. ( 1990 ). The pdf approach to turbulent flow . Theoret. Comput. Fluid Dynamics 1 , 249 – 285 .
   Google Scholar
• Kosaly , G. and Givi , P. ( 1987 ). Modeling of turbulent molecular mixing . Combust. Flame 70 , 101 – 118 .
   Web of Science ®Google Scholar
• Kosaly , G. ( 1986 ). Theoretical remarks on a phenomenological model of turbulent mixing . Combust. Sci. and Tech. 49 , 227 – 234 .
   Web of Science ®Google Scholar
• Kraichnan , R. H. ( 1989 ). Closures for probability distributions . Bull. Amer. Phys. Soc. 34 , 2298 .
   Google Scholar
• Linan , A. ( 1974 ). The asymptotic structure of counterflow diffusion flames for large activation energies . Acta Astronautica 1 , 1007 – 1039 .
   Web of Science ®Google Scholar
• Lockwood , F. C. and Moneib , H. A. ( 1980 ). Fluctuating temperature measurement in a heated round free jet . Combust. Sci. and Tech. 22 , 63 – 81 .
   Web of Science ®Google Scholar
• Madnia , C. K. and Givi , P. ( 1992 ). On DNS and LES of homogeneous reacting turbulence . In Galperin, B. and Orszag, S. A., editors , Large Eddy Simulations of Complex Engineering and Geophysical Flows . Cambridge University Press , Cambridge , U.K . in press .
   Google Scholar
• Madnia , C. K. , Frankel , S. H. , and Givi , P. ( 1991 ). Mathematical modeling of the reactant conversion rate by single-point pdf methods . In Proc Fall Technical Meeting of the Combustion Institute, Eastern Section , Ithaca , NY .
   Google Scholar
• Madnia , C. K. , Frankel , S. H. , and Givi , P. ( 1992 ). Reactant conversion in homogeneous turbulence Mathematical modeling, computational validations and practical applications , Theoret. Comput. Fluid Dynamics , 4 , 79 – 93 .
   Google Scholar
• McMurtry , P. A. and Givi , P. ( 1989 ). Direct numerical simulations of mixing and reaction in a nonpremixed homogeneous turbulent flow . Combust. Flame 77 , 171 – 185 .
   Web of Science ®Google Scholar
• Miyawaki , O. , Tsujikawa , H. , and Uraguchi , Y. ( 1974 ). Turbulent mixing in multi-nozzle injector tubular mixers . J. Chem. Eng. Japan 7 , 52 – 74 .
   Google Scholar
• Narumi , S. ( 1923 ). On the general form of bivariate frequency distributions which are mathematically possible when regression and variation are subjected to limiting conditions, I . Biometrika 15 , 77 – 88 .
   Google Scholar
• Nomura , K. K. and Elgobashi , S. E. ( 1992 ). Mixing characteristics of an inhomogeneous scalar in isotropic and homogeneous sheared turbulence . Phys. Fluids A 4 , 606 – 625 .
   Web of Science ®Google Scholar
• Norris , A. T. and Pope , S. B. ( 1991 ). Turbulent mixing model based on ordered pairing . Combust. Flame 83 , 27 .
   Web of Science ®Google Scholar
• O'Brien , E. E. and Jiang , T.-L. ( 1991 ). The conditional dissipation rate of an initially binary scalar in homogeneous turbulence . Phys. Fluids A 3 , 3121 – 3123 .
   Web of Science ®Google Scholar
• O'Brien , E. E. ( 1980 ). The probability density function (PDF( approach to reacting turbulent flows . In Libby, P. A. and Williams, F. A., editors , Turbulent Reacting Flows , chapter 5 , pages 185 – 218 . Springer-Verlag , Heidelberg .
   Google Scholar
• Passot , T. and Pouquet , A. ( 1987 ). Numerical simulation of compressible homogeneous flows in the turbulent regime . J. Fluid Mech. 181 , 441 – 466 .
   Web of Science ®Google Scholar
• Pearson , K. ( 1895 ). Contributions to the mathematical theory of evolution II. skew variations in homogeneous material . Philos. Trans, of the Royal Soc. of London , Series A . 186 , 343 – 414 .
   Google Scholar
• Peters , N. ( 1984 ). Laminar diffusion flamelet models in non-premixed turbulent combustion . Prog. Energy Combust. Sci. 10 , 319 – 339 .
   Web of Science ®Google Scholar
• Pope , S. B. ( 1976 ). The probability approach to modelling of turbulent reacting flows . Combust. Flame 27 , 299 – 312 .
   Web of Science ®Google Scholar
• Pope , S. B. ( 1979 ). The statistical theory of turbulent flames . Phil. Trans. Royal Soc. London 291 , 529 – 568 .
   Web of Science ®Google Scholar
• Pope , S. B. ( 1981 ). A Monte Carlo method for the pdf equations of turbulent reactive flow . Combust. Sci. and Tech. 25 , 159 – 174 .
   Web of Science ®Google Scholar
• Pope , S. B. ( 1982 ). An improved turbulent mixing model . Combust. Sci. and Tech. 28 , 131 – 145 .
   Web of Science ®Google Scholar
• Pope , S. B. ( 1985 ). PDF methods for turbulent reacting flows . Prog. Energy Combust. Sci. 11 , 119 – 192 .
   Web of Science ®Google Scholar
• Pope , S. B. ( 1990 ). Computations of turbulent combustion: Progress and challenges . In Proceedings of 23rd Symp. (Int.) on Combustion , pages 591 – 612 . The Combustion Institute , Pittsburgh , PA .
   Google Scholar
• Pope , S. B. ( 1991 ). Mapping closures for turbulent mixing and reaction . Theoret. Comput. Fluid Dynamics 2 , 255 – 270 .
   Google Scholar
• Priddin , C. H. ( 1991 ). Turbulent combustion modelling-A review . In Johansson, A. V. and Alfredsson, P. H., editors . Advances in Turbulence 3 , pages 279 – 299 . Springer-Verlag , Berlin .
   Google Scholar
• Rhodes , P. R. ( 1975 ). A probability distribution function for turbulent flows . In Murthy, S. N. B., editor , Turbulent Mixing in Non-Reactive and Reactive Mixing , pages 235 – 241 . Plenum Press , New York , NY .
   Google Scholar
• Spalding , S. B. ( 1961 ). Theory of mixing and chemical reaction in the opposed-jet diffusion flame . Journal of the American Rocket Society 31 , 763 – 771 .
   Google Scholar
• Toor , H. L. ( 1962 ). Mass transfer in dilute turbulent and nonturbulent systems with rapid irreversible reactions and equal diffusivities . AIChE J. 8 , 70 – 78 .
   Web of Science ®Google Scholar
• Toor , H. L. ( 1975 ). The non-premixed reaction A ° B → Products . In Brodkey, R. S., editor , Turbulence in Mixing Operations , pages 123 – 166 . Academic Press , New York , NY .
   Google Scholar
• Vblino , L. and Gao , F. ( 1991 ). Monte Carlo implementation of the mapping closure for turbulent reacting flows . In Fluid Dynamics Division Meeting of the American Physical Society , Phoenix , Arizona .
   Google Scholar
• Williams , F. A. ( 1985 ). Combustion Theory . The Benjamin/Cummings Publishing Company , Menlo Park , CA , |ot2nd edition|ost.
   Google Scholar