Abstract
The fractal properties of premixed turbulent flames are analysed. First, the regimes of turbulent combustion are defined. Fractal analysis is found only to be meaningful in the regime of corrugated flamelets. Experimental data of flame contours measured with decreasing length scales are presented. A simple model is derived to explain the dependence of the measured fractal dimension on the ratio of the turbulence intensity to the laminar burning velocity. It is concluded that the ratio of the actual flame surface to the cross-sectional area — a quantity that should be proportional to the ratio of the turbulent to the laminar burning velocity — is independent of the results of fractal analysis.
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References
Damköhler, G.: Der Einfluß der Turbulenz auf die Flammengeschwindigkeii in Gasgemischen, Z. f. Elektroch. 46, No. 11, 601–652 (1940).
Peters, N.: Laminar Flamelet Concepts in Turbulent Combustion, 21st Symposium on Combustion, The Combustion Institute, Pittsburgh, 1231–1250 (1987).
Richardson, L.F.: Atmospheric Diffusion Shown on a Distance-Neighbour Graph, Proc. of the Royal Society, A110, 709–737 (1926).
Kolmogorov, A.N.: The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers C.R. Acad.Sci.USSR 30, 301–305 (1941).
Peters, N.: Length Scales in Laminar and Turbulent Flames, to be published.
Peters, N.; Williams, F.A.: Asymptotic Structure of Methane Flames, Complex Chemical Reaction Systems, Springer Series in Chemical Physics 47, 310–317 (1987).
Clavin, P.: Dynamic Behavior of Premized Flame Fronts in Laminar and Turbulent Flows, Prog. Energy Combust. Sci. 11, 1–59 (1985).
Williams, F.A.: Combustion Theory, 2nd edition, The Benjamin/Cummings Publishing Company, Menlo Park (1985).
Oboukhov, A.M.: Some Specific Features of Atmospheric Turbulence, J. Fluid Mech. 13, 77–81 (1962).
Kolmogorov, N.A.: 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 (1962).
Mandelbrot, B.B.: On the Geometry of Homogeneous Turbulence, with Stress on the Fractal Dimension of Iso-Surfaces of Scalars, J. Fluid Mech. 72, 401–416 (1975).
Gouldin, F.C.; Hilton, S.M.; Lamb, T.: Experimental Evaluation of the Fractal Geometry of Flamelets, 22nd Symposium on Combustion, The Combustion Institute, 541-550 (1988).
Lovejoy, S.: Area-Perimeter Relation for Rain and Clouds Areas, Science 216, 185–187 (1982).
Gouldin, F.C.: An Application of Fractals to Modeling Premized Turbulent Flames, Comb, and Flame 68, 249–266 (1987).
Mantzaras, J.;Felton, P.G.; Bracco, F.V.: Three-Dimensional Visualization of Premized Charged Engine Flames: Islands of Reactanis and Products; Fractal Dimensions and Homogeneity, SAE-Paper 881635.
Ziegler, G.F.W.; Zettlitz, A.; Meinhardt, P.; Herweg, R.; Maly, R. Pfister, W.: Cycle-Resolved Two-Dimensional Flame-Visualization in a SI-Engine, SAE-Paper 881634.
Holtorf, J.: Bestimmung und Charakterisierung der Flammcnfront in einem Ottomotor, Diplomarbeit at the Lehrstuhl für Technische Thermodynamik, RWTH Aachen (1988).
Murayama, M.; Takeno, T.: Fractal-Like Character of Flamelets in Turbulent Premized Combustion, 22nd Symposium on Combustion, The Combustion Institute, 551-559 (1988).
Strahle, W.C.: Fractal Geometry Applications in Turbulent Combustion Data Analysis, 22nd Symposium on Combustion, The Combustion Institute, 561-568 (1988).
Chew, T.C.: Aspects of Premized Turbulent Combustion, Thesis at Cambridge University (1988).
Franke, Ch.; Peters, N.: Flammenoberfläche und Brenngeschwindigkeit von turbulenten Vormischflammen Kolloquium des SFB 224 “Motorische Verbrennung”, RWTH Aachen, F. Pischinger (Ed.), 126-147 (1988).
Screenivasan, K.R.; Ramshankar, R.; Meneveau, C.: Mixing, Entrainmcnt and Fractal Dimension of Surfaces in Turbulent Flows, Proc. R. Soc. Lond. A421, 79–108 (1989).
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Peters, N., Franke, C. (1990). The Fractal Concept of Turbulent Flames. In: Meinköhn, D. (eds) Dissipative Structures in Transport Processes and Combustion. Springer Series in Synergetics, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84230-6_5
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DOI: https://doi.org/10.1007/978-3-642-84230-6_5
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