Use of Fractal Geometry to Model Turbulent Combustion in SI Engines

REFERENCES

• Abraham , J. , Williams , F. A. , and Bracco , F. V. ( 1985 a). A discussion of turbulent flame structure inpremixed charges . SAE Technical Paper 850345 .
   Google Scholar
• Abraham , J. , Bracco , F. V. , and Reitz , R. D. ( 1985 b). Comparisons of computed and measured premixedcharge engine combustion . Combustion and Flame , 60 , 309 – 322 .
   Web of Science ®Google Scholar
• Ahmadi-Befrui , B. , Gosman , A. D. , Lockwood, F. C, and Watkins , A. P. ( 1981 ). Multidimensionalcalculation of combustion in an idealized homogeneous charge engine a progress report. SAE Technical Paper 810151 .
   Google Scholar
• Ball , W. F. , Pettifer , H. F. and Waterhouse , C. N. F. ( 1983 ). Laser Doppler velocimeter measurements of turbulence in a direct-injection diesel combustion chamber . Proc, Int. Symposium on Combustion in Engineering ,Vol. 1 , I. Mech. E. Paper C52/83, 163 – 174 .
   Google Scholar
• Barilaud , T. A. and Green , R. M. ( 1986 ). A 2D flame visualization technique applied to the IC engine. SAETechnical Paper 860025 .
   Google Scholar
• Barilaud , T. A. ( 1989 ). Combustion and fluid dynamic measurements in a spark ignition engine effects ofthermochemistry , velocity field; turbulent flame speeds. SAE Technical Paper 892098 .
   Google Scholar
• Barr , P. K. and Witze , P. O. ( 1988 ). Some limitations to the spherical flame assumption used inphenomenological engine models . SAE Technical Paper 880129 .
   Google Scholar
• Bcretta , G. P. , Rashidi , M. and Keck , J. C. ( 1983 ). Turbulent flame propagation and combustion in sparkignition engines . Combustion and Flame . 52 , 217 – 245 .
   Google Scholar
• Blizzard , N. C. and Keck , J. C. ( 1974 ). Experimental and theoretical investigation of turbulent burningmodel for internal combustion engines . SAE Technical Paper 740191 .
   Google Scholar
• Blumbcrg , P. N. , Lavoie , G. A. and Tabaczynski , R. J. ( 1979 ). Phenomenological models for reciprocatinginternal combustion engines . Progress in Energy and Combustion Science . 5 , 123 – 167 .
   Google Scholar
• Bopp , S. , Vafidis , C. and Whitelaw , J. H. ( 1986 ). The effect of engine speed on the TDC flow field in amotored reciprocating engine . SAE Technical Paper 860023 .
   Google Scholar
• Borgnakke , C. , Arpaci , V. and Tabaczynski , R. J. ( 1980 ) A model for the instantaneous heat transfer andturbulence in a spark ignition engine . SAE Technical Paper 800287 .
   Google Scholar
• Borgnakke , C. , Davis , G. C. and Tabaczynski , R. J. ( 1981 ). Predictions of in-cylinder swirl velocity andturbulence intensity for an open chamber cup-in-piston engine . SAE Technical Paper 810224 .
   Google Scholar
• Chung , S. H. and Law , C. K. ( 1984 ). An invariant derivation of flame stretch . Combustion and Flame . 55 , 123 – 125 .
   Web of Science ®Google Scholar
• Chung , S. H. and Law , C. K. ( 1988 ). An integral analysis of the structure and propagation of stretchedpremixed flames . Combustion and Flame . 12 , 325 – 336 .
   Google Scholar
• Cole , J. B. and Swords , M. D. ( 1978 ). Optical studies of turbulence in an internal combustion engine . 17th Symposium (International) on Combustion , The Combustion Institute , Pittsburgh , pp. 1295 – 1303 .
   Google Scholar
• Daneshyar . H. and Fuller , D. E. ( 1986 ). Definition and measurement of turbulence parameters inreciprocating I.C. engines . SAE Technical Paper 861529 .
   Google Scholar
• Daneshyar , H. and Hill , P. G. ( 1987 ). The structure of small-scale turbulence and its effect on combustionin spark ignition engines . Progress in Energy and Combustion Science , 13 , 47 – 73 .
   Web of Science ®Google Scholar
• Davis , G. C. and Borgnakke , C. ( 1982 ). The effect of in-cylinder flow processes (swirl, squish, andturbulence intensity) on engine efficiency model predictions . SAE Technical Paper 820045 .
   Google Scholar
• Foster , D. E. and Witze , P. O. ( 1988 ). Two-component laser velocimeter measurements in a spark ignitionengine . Combustion Science and Technology , 59 , v85 .
   Web of Science ®Google Scholar
• Fraser , R. A. and Bracco , F. V. ( 1988 ). Cycle-resolved LDV integral length scale measurments in an ICengine . SAE Technical Paper 880381 .
   Google Scholar
• Fraser , R. A. Bracco , F. V. ( 1989 ). Cycle-resolved LDV integral length scale measurementsinvestigating clearance height scaling , isotropy, and homogeneity in an IC engine. SAE TechnicalPaper 890615 .
   Google Scholar
• Fraser , R. A. , Felton , P. G. , Bracco , F. V. , and Santavicca , D. A. ( 1986 ). Preliminary turbulence lengthscale in a motored engine . SAE Technical Paper 860021 .
   Google Scholar
• Glover , A. R. , Hundleby , G. E. and Hadded , O. ( 1988 ). An investigation into turbulence in engines usingscanning LDA . SAE Technical Paper 880379 .
   Google Scholar
• Gokalp , L. ( 1987 ). An evaluation of the Klimov-Williams criterion . Combustion and Flame , 67 , 111 – 119 .
   Web of Science ®Google Scholar
• Gouldin , F. C. , ( 1987 ). An application of fractals to modeling premixed turbulent flames . Combustion and Flame . 68 ( 3 ), 249 – 266 .
   Web of Science ®Google Scholar
• Gouldin , F. C. , Hilton , S. M. and Lamb , T. ( 1988 ). Experimental evaluation of the fractal geometry offlamelets . 22nd Symposium (International) on Combustion , The Combustion Institute , Pittsburgh ,pp. 541 – 550 .
   Google Scholar
• Groff , E. G. , Alkidas , A. C. and Myers , J. P. ( 1981 ). General Motors Research Laboratories Report No.3577 .
   Google Scholar
• Hall , M.J. ( 1989 ). The influence of fluid motion on flame kernel development and cyclic variation in a sparkignition engine . SAE Technical Paper 890991 .
   Google Scholar
• Hall , M. J. and Bracco , F. V. ( 1987 ). A study of velocities and turbulence intensities measured in firing andmotored engines . SAE Technical Paper 870453 .
   Google Scholar
• Herweg , R. and Ziegler , G. F. W. ( 1990 ). Flame kernel development in a spark-ignition engine . Diagnostics and Modeling of Combustion in Internal Combustion Engines (International Symposium COMOD1A90), SAEJJSME , Tokyo , pp. 173 – 178 .
   Google Scholar
• Herweg , R. , Begleris , P. , Zeittliz , A. , and Ziegler , G. F. W. ( 1988 ). Flow field effects on flame kernelformation in a spark-ignition engine . SAE Technical Paper 881639 .
   Google Scholar
• Hindmarsh , A. C. ( 1980 ). LSODE and LSOD1 Two new initial value ordinary differential equationsolvers . SIGNUM Newletter , 15 ( 4 ), 10 – 11 .
   Google Scholar
• Hires , S. D. , Tabaczynski , R. J. and Novak , J. M. ( 1978 ). The prediction of ignition delay and combustionintervals for a homogeneous charge spark ignition engine . SAE Technical Paper 780232 .
   Google Scholar
• Kalghatgi , B. T. ( 1987 ). Spark ignition, early flame development, and cyclic variation in l.C. engines . SAETechnical Paper 870163 .
   Google Scholar
• Keck , J. C. , Heywood , J. B. and Noske , G. ( 1987 ). Early flame development and burning rates in sparkignition engines and their cyclic variability . SAE Technical Paper 870164 .
   Google Scholar
• Kee , R. J. , Miller , J. A. and Jefferson , T. H. ( 1980 ). CHEMKIN A General-Purpose, Problem-Independent, Transportable Fortran Chemical Kinetics Code Package . Sandia National LaboratoriesReport SAND - 80 – 8003 .
   Google Scholar
• Kee , R. J. Warnatz , J. and Miller , J. A. ( 1983 ). A FORTRAN Computer Code Package for the Evaluationof Gas-Phase Viscosities, Conductivities , and Diffusion Coefficients. Sandia National LaboratoriesReport SAND 83 – 8209 .
   Google Scholar
• Kiehne , T. M. , Matthews , R. D. and Wilson , D. E. ( 1987 ). An eight-step kinetics mechanism for hightemperature propane flames . Combustion Science and Technology . 54 , 1 – 23 .
   Web of Science ®Google Scholar
• Klimov , A. M. ( 1983 ). Premixed turbulent flames-interplay of hydrodynamic and chemical phenomena .In Flames, Lasers, and Reactive Systems Progress in Astronautics and Aeronautics . 88 , 133 – 146 .
   Google Scholar
• Kocroghlian , M. M. , Chin , Y-W. and Matthews , R. D. ( 1988 ). Development of a computationally fastequilibrium-equivalent 4-stroke SI engine model . SAE Technical Paper 880130 .
   Google Scholar
• Kuo , T-W. and Reitz , R.D. ( 1989 ). Computation of premixed-charge combustion in pancake and pent-roofengines . SAE Technical Paper 890670 .
   Google Scholar
• Lancaster , D. R. ( 1976 ). Effects of engine variables on turbulence in a spark ignition engine . SAE TechnicalPaper 760159 .
   Google Scholar
• Lancaster , D. R. , Krieger , R. B. , Sorenson, S. C, and Hull , W. L. ( 1976 ). Effects of turbulence on sparkignition engine combustion . SAE Technical Paper 760160 .
   Google Scholar
• Law , C. K. ( 1988 ). Dynamics of stretched flames . 22nd Symposium (International) on Combustion , TheCombustion Institute , Pittsburgh , pp. 1381 – 1402 .
   Google Scholar
• Lewis , B. von Elbe , G. ( 1961 ). Combustion, Flumes, and Explosions of Cases , 2nd Edition . Academic Press , New York .
   Google Scholar
• Liou , T-M. and Santavicca , D. A. ( 1983 ). Cycle resolved turbulence measurements in a ported engine withand without swirl . SAE Technical Paper 830419 .
   Google Scholar
• Liou , T-M. , Hall, M., Santavicca, D. A., Bracco, F. V. ( 1984 ). Laser Doppler velocimctrymeasurements in valved and ported engines . SAE Technical Paper 840375 .
   Google Scholar
• Liou , D. , North , G. L. and Santavicca , D. A. ( 1990 ). A fractal model of turbulent flame kernel growth.SAE Technical Paper 900024 .
   Google Scholar
• Mantzaras , J. , Felton , P. G. and Bracco , F. V. ( 1988 ). Three-dimensional visualization of premixed-chargeengine flames islands of reactants and products; fractal dimension; and homogeneity . SAE TechnicalPaper 881635, SAE Special Publication SP-759 .
   Google Scholar
• McCuiston , F. D. , Lavoic , G. A. and Kauffman , C. W. ( 1977 ). Validation of a turbulent flame propagationmodel for a spark ignition engine . SAE Technical Paper 770045 .
   Google Scholar
• Mctghalchi , M. and Keck , J. C. ( 1982 ). Burning velocities of mixtures of air with methanol, iso-octane, andindolene at high pressure and temperature . Combustion and Flame , 48 , 191 – 210 .
   Google Scholar
• Miao , S. and Matthews , R. D. ( 1987 ). Combustion efficiency of spark ignition engines . Int. J. of Vehicle Design . 8 ( 3 ), 345 – 354 .
   Web of Science ®Google Scholar
• Murayama , M. Takeno , T. ( 1988 ). Fractal-like character of flamelets in turbulent premixedcombustion . 22nd Symposium (International) on Combustion , The Combustion Institute , Pittsburgh ,pp. 551 – 559
   Google Scholar
• North , G. L. and Santavicca , D. A. ( 1986 ). Fractal analysis of premixed turbulent flame structure . Paperpresented at the Fall technical Meeting of the Eastern Stales Section of the Combustion Institute , SanJuan, Puerto Rico , Dec.
   Google Scholar
• North , G. L. and Santavicca , D. A. ( 1988 ). Fractal analysis of premixed turbulent flame structure andisovelocity surfaces. Poster paper P80 presented at the 22nd International Symposium on Combustion , Seattle, August .
   Google Scholar
• Obokata , T. , Hanada , N. and Kurabayashi , T. ( 1987 ). Velocity and turbulence measurements in acombustion chamber of S.I. engine under motored and firing operations by L.D.A. with fiber-opticpick-up . SAE Technical Paper 870166 ,
   Google Scholar
• Olikara , C. and Borman , G. L. ( 1975 ). A computer program for calculating properties of equilibriumcombustion products with some applications to IC engines . SAE Technical Paper 750468 .
   Google Scholar
• Peters , N. ( 1986 ). Laminar flamelet concepts in turbulent combustion. Invited Lecture , 21st Symposium (International) on Combustion , The Combustion Institute , Pittsburgh , pp. 1231 – 1250 .
   Google Scholar
• Pischinger , S. and Heywood , J. B. ( 1990 ). A model for flame kernel development in a spark-ignition engine . Twenty-Third Symposium (International) on Combustion , The Combustion Institute , Pittsburgh ,pp. 1033 – 1040 .
   Google Scholar
• Poulos , S. G. and Heywood , J. B. ( 1983 ). The effect of chamber shape on spark ignition engine combustion . SAE Technical Paper 830334 .
   Google Scholar
• Rask , R. B. ( 1979 ). Laser Doppler anemometer measurements in an internal combustion engine . SAETechnical Paper 790094 .
   Google Scholar
• Reuss , D. L. , Adrian , R. J. , Landreth, C. C, French , D. T. , and Fansler , T. D. ( 1989 ) Instantaneous planarmeasurements of velocity and large scale vorticity and strain rate in an engine using particle-imagevclocimetry . SAE Technical Paper 890616 .
   Google Scholar
• Saxena , V. and Rask , R. B. ( 1987 ). Influence of inlet flows on the flow field in an engine . SAE TechnicalPaper 870369 .
   Google Scholar
• Schipperijn , F. W. , Nagasaka , R. and Sawyer , R. F. ( 1988 ). Imaging of engine flow and combustionprocesses . SAE Technical Paper 881631 .
   Google Scholar
• Sreenivasan, K. R. and Meneveau, C. ( 1986 ). The fractal facets of turbulence . J. Fluid Mech . 173 , 357 – 386 .
   Web of Science ®Google Scholar
• Tabaczynski , R. J. ( 1976 ). Turbulence and turbulent combustion in spark-ignition engines . Progress in Energy and Combustion Science . 2 , 143 – 165 .
   Web of Science ®Google Scholar
• Tabaczynski , R. J. , Ferguson , C. R. and Radhakrishnan , K. ( 1977 ). A turbulent entrainment model forspark ignition engine combustion . SAE Technical Paper 770647 .
   Google Scholar
• Tennekes , H. and Lumley , J. L. ( 1973 ). A First Course in Turbulence , MIT Press , Cambridge , MA .
   Google Scholar
• Tomita , E. and Hamamoto , Y. ( 1988 ). The effect of turbulence on combustion in cylinder of a sparkignition engine-evaluation of entrainment model . SAE Technical Paper 880128 .
   Google Scholar
• Winsor , R. E. and Patterson , D. J. ( 1983 ). Mixture turbulence-a key to cyclic combustion variations SAETechnical Paper 730086 .
   Google Scholar
• Witze , P. O. ( 1977 ). Measurements of the spatial distribution and engine speed dependence of turbulentair motion in an 1C engine . SAE Technical Paper 770220 .
   Google Scholar
• Witze , P. O. and Foster , D. E. ( 1988 ). Two-component velocity probability density measurments duringcombustion in a spark ignition engine . IMechE Paper C51/88 .
   Google Scholar
• Witze , P. O. , Hall , M. J. and Bennet , M. J. ( 1988 ). Are gas velocities in a motored piston enginerepresentative of the pre-ignition fluid motion in a fired engine ? Sandia National Laboratories ReportSAND - 88 – 8878 .
   Google Scholar
• Witze , P. O. Martin , J. K. and Borgnakke , C. ( 1983 ). Measurements and predictions of the precombustionfluid motion and combustion rates in a spark ignition engine . SAE Technical Paper 831697, SAE Transactions . 92 , 786 – 796 .
   Google Scholar
• Witze , P. O. Mendes-Lopes , J. M, C. ( 1986 ). Direct measurement of the turbulent burning velocity ina homogeneous-charge engine . SAE Technical Paper 861531 .
   Google Scholar
• zur Loye , A. O. and Bracco , F. V. ( 1987 ). Two-dimensional visualization of ignition kernels in an ICengine . Combustion and Flame . 69 , 59 – 69 .
   Google Scholar