Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-01T21:44:51.360Z Has data issue: false hasContentIssue false
  • English
  • Français

Measurements of Fractal Properties of Premixed Turbulent Flames and Their Relation to Turbulent Burning Velocities

Published online by Cambridge University Press:  05 May 2011

S. I. Yang  and
S. S. Shy
S. I. Yang*
Affiliation:
Department of Mechanical Engineering, National Central University, Chung-Li, Taiwan 32054, R.O.C.
S. S. Shy*
Affiliation:
Department of Mechanical Engineering, National Central University, Chung-Li, Taiwan 32054, R.O.C.
*
*Graduate student
**Professor
Get access

Abstract

The fractal properties of premixed transient flames propagating downwards through a near-isotropic turbulent flow field in a fan-stirred cruciform burner were investigated. The long vertical section of the cruciform burner was used to provide a downward propagating premixed flame at 1 atm. The large horizontal vessel equipped with a pair of counter-rotating fans and perforated plates at each end was used to generate near-isotropic turbulence. Turbulent flame front images were obtained using high-speed laser sheet imaging for both methane-air and propane-air mixtures. The nondimensional turbulent intensity (u′/SL), Reynolds number based on the integral length scale, and turbulent Karlovitz number were varied from 1 to 10, from 698 to 6032, and from 0.05 to 1.43, respectively. Hundreds of runs for each experimental condition were carried out to obtain sufficient images of these turbulent transient flame fronts just in the central uniform region. These images were then processed to extract fractal dimension, inner and outer cutoffs using both the circle and the caliper methods. It was found that the mean fractal dimension is only 2.18, nearly independent of u′/SL, in support of recent Bunsen-flame results found by Gülder and his co-workers. This contradicts the findings of many previous studies in which the fractal dimension may approach asymptotically to a value of 2.33 when u′/SL > 3. The inner (εi) and outer (ε0) cutoffs are found to be nearly constant for all flames studied, where ε0 is an order of magnitude greater than εi and it is smaller than the integral length scale of unreacted turbulence. Finally, the present fractal characteristics cannot predict turbulent burning velocities correctly when the available fractal closure model was used, indicating a limit of the fractal analysis on prediction of turbulent burning velocities.

Keywords

Fractal dimensionInner and outer cutoffsPremixed turbulent combustionTurbulent burning velocities
Type
Articles
Information
Journal of Mechanics , Volume 17 , Issue 2 , June 2001 , pp. 93 - 101
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Williams, F. A., Combustion Theory, 2nd Edition., Addison-Wesley, Redwood City (1985).Google Scholar
2Peters, N., “Laminar Flamelet Concepts in Turbulent Combustion,” Proc. Combust. Inst., Vol. 21, pp. 1231–1250 (1986).Google Scholar
3Bray, K. N. C., in Complex Chemical Reactive System, Warnatz, J. and Jäger, W., eds., Springer-Verlag, pp. 356–375 (1987).Google Scholar
4Damköhler, G., “The Effect of Turbulence on the Flame Velocity in Gas Mixtures,” Z. Elektrochem, Vol. 46, pp. 601–652 (1940) [English transl., NACA Tech. Mem., 1112, 1947].Google Scholar
5Gouldin, F., “An Application of Fractals to Modeling Premixed Turbulent Flames,” Combust. Flame, Vol. 68, pp. 249–266 (1987).CrossRefGoogle Scholar
6Gülder, Ö. L. and Smallwood, G. J., “Characterization of Flame Front Surfaces in Turbulent Premixed Methane/Air Combustion,” Combust. Flame, Vol. 103, pp. 107–114 (1995).Google Scholar
7Anand, M. S. and Pope, S. B., “Calculations of Premixed Turbulent Flames by PDF Methods,” Combust. Flame, Vol. 67, pp. 127–142 (1987).Google Scholar
8Yakhot, V., “Propagation Velocity of Premixed Turbulent Flames,” Combust. Sci. Tech., Vol. 60, pp. 191–214 (1988).Google Scholar
9Bray, K. N. C., “Studies of the Turbulent Burning Velocity,” Proc. Roy. Soc. (London) A, Vol. 431, pp. 315–335 (1990).Google Scholar
10Bray, K. N. C., Moss, J. B. and Libby, P. A., “Unified Modelling Approach for Premixed Turbulent Combustion — Part 1: General Formulation,” Combust. Flame, Vol. 61, pp. 87–102 (1985).Google Scholar
11Marble, F. E. and Broadwell, J. E., “The Coherent Flame Model for Turbulent Chemical Reactions,” Project Squid Technical Report TRW-9-PU, USA (1977).Google Scholar
12Pope, S. B., “Evolution of Surface in Turbulence,” Int. J. Eng. Sci., Vol. 26, pp. 445–469 (1988).Google Scholar
13Candel, S. and Poinsot, T., “Flame Stretch and the Balance Equation for the Flame Surface Area,” Combust. Sci. Tech., Vol. 70, pp. 1–15 (1990).Google Scholar
14Trouvé, A. and Poinsot, T., “The Evolution Equation for the Flame Surface Density in Turbulent Premixed Combustion,” J. Fluid Mech., Vol. 278, pp. 1–31 (1994).CrossRefGoogle Scholar
15Kerstein, A. R., “Fractal Dimension of Turbulent Premixed Flames,” Combust. Sci. Tech., Vol. 60, pp. 441–445 (1988).Google Scholar
16Hentschel, H. G. E. and Procaccia, I., “Intermittency Exponent in Fractally Homogeneous Turbulence,” Phys. Rev. Lett., Vol. 49, pp. 1158–1161 (1982).Google Scholar
17Dandekar, K. V. and Gouldin, F. C., “Temperature and Velocity Measurements in Premixed Turbulent Flames,” AIAA Journal, Vol. 20, p. 652 (1982).Google Scholar
18Cho, P., Law, C. K., Hertzberg, J. R. and Cheng, R. K., “Structure and Propagation of Turbulent Premixed Flames Stabilized in a Stagnation Flow,” Proc. Combust. Inst., Vol. 21, pp. 1493–1499 (1986).CrossRefGoogle Scholar
19Gulati, A. and Driscoll, T. F., “Velocity-Density Correlations and Favre Averages Measured in a Premixed Turbulent Flame,” Combust. Sci. Tech., Vol. 48, p. 285 (1986).Google Scholar
20Murayama, M. and Takeno, T., “Fractal-Like Character of Flamelets in Turbulent Combustion,” Proc. Combust. Inst., Vol. 22, pp. 551–559 (1988).Google Scholar
21Mantzaras, J., Felton, P. G. and Bracco, F. V., “Three-Dimensional Visualization of Premixed- Charge Engine Flames: Islands of Reactants and Products; Fractal Dimensions; and Homogeneity,” SAE Paper No. 881635 (1988).Google Scholar
22North, G. L. and Santavicca, D. A., “The Fractal Nature of Premixed Turbulent Flames,” Combust. Sci. Tech., Vol. 72, pp. 215–232 (1990).Google Scholar
23Gülder, Ö. L. and Smallwood, G. J., Wong, R., Snelling, D. R., Smith, R., Deschamps, B. M. and Sautet, J. C., “Flame Front Surface Characteristics in Turbulent Premixed Propane/Air Combustion,” Combust. Flame, Vol. 120, pp. 407–416 (2000).CrossRefGoogle Scholar
24ShyS. S., I, W. K. S. S., I, W. K. and Lin, M. L., “A New Cruciform Burner and Its Turbulence Measurements for Premixed Turbulent Combustion Study,” Exp. Thermal Fluid Sci., Vol. 20, pp. 105–114 (2000).Google Scholar
25Abdel-Gayed, R., Bradley, D. and Lawes, M., “Turbulent Burning Velocities: a General Correlation in Terms of Straining Rates,” Proc. R. Soc. (London) A, Vol. 414, pp. 389–413 (1987).Google Scholar
26Mandelbrot, B. B., “On the Geometry of Homogeneous Turbulence, with Stress on the Fractal Dimension of the Iso-Surfaces of Scalars,” J. Fluid Mech., Vol. 72, pp. 401–416 (1975).Google Scholar
27Sreenivasan, K. R. and Meneveau, C., “The Fractal Facets of Turbulence,” J. Fluid Mech., Vol. 173, pp. 357–386 (1986).Google Scholar
28Mantzaras, J., Felton, P. G. and Bracco, F. V., “Fractal and Turbulent Premixed Engine Flames,” Combust. Flame, Vol. 77, pp. 295–307 (1989).Google Scholar
29Mandelbrot, B. B., The Fractal Geometry of Nature, Freeman, New York (1983).CrossRefGoogle Scholar
30Chen, Y. C., Private Communication (1996).Google Scholar
31Shy, S. S., Lin, W. J. and Wei, J. C., “An Eexperimental Correlation of Turbulent Burning Velocities for Premixed Turbulent Methane-Air Combustion,” Proc. R. Soc. (London) A, Vol. 456, pp. 1997–2019 (2000).CrossRefGoogle Scholar
32Gouldin, F. C., Bray, K. N. C. and Chen, J. C., Combust. Flame, Vol. 77, pp. 241–259 (1989).Google Scholar
33Ronney, P. D. and Yakhot, V., Combust. Sci. Tech., Vol. 86, pp. 31–43 (1992).CrossRefGoogle Scholar