Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Experimental criteria for the determination of fractal parameters of premixed turbulent flames

Abstract

The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 μm/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.

This is a preview of subscription content, log in to check access.

References

  1. Boyer, L. 1980: Laser tomographic method for flame front movement studies. Combust. Flame 39, 321–323

  2. Cheng, R. K.; Shepherd, I. G. 1991: The influence of Burner geometry on premixed turbulent flame propagation. Combust. Flame 85, 7–26

  3. Cho, P.; Law, C. K.; Cheng, R. K.; Shepherd, I. G 1988: Velocity and scalar fields of turbulent premixed flame in stagnation flow. 22nd Int. Symp. Combust., 739–745

  4. Goix, P. J.; Shepherd, L. G.; Trinite, M. 1987: A fractal study of premixed V-shaped H2/air flames. Combust. Sci. Technol. 63, 273–287

  5. Gouldin, F. C. 1987: An application of fractals to modeling premixed turbulent flames. Combust. Flame 68, 249–266

  6. Gouldin, F. C.; Bray, K. N. C.; Chen, J.-Y. 1989: A chemical closure model for fractal flamelets. Combust. Flame 77, 241–259

  7. Hertzberg, J. R.; Namazian, M.; Talbot, L. 1984: A laser tomographic study of a laminar flame in a Karman street. Combust. Sci. Technol. 38, 205–216

  8. Mandelbrot, B. B. 1982: The fractal geometry of nature. San Francisco: W. H. Freeman

  9. Mantzaras, J.; Felton, P. G.; Bracco, F. V. 1989: Fractals and turbulent premixed engine flames. Combust. Flame 77, 295–310

  10. Murayama, M.; Takeno, T. 1988: Fractal-like character of flamelets in turbulent premixed combustion. 22nd Int. Symp. Combust., 551–559

  11. Peters, N. 1986: Laminar flamelet concepts in turbulent combustion. 21st Int. Symp. Combust., 1231–1250

  12. Prasad, R. R.; Sreenivasan, K. R. 1990: The measurement and interpretation of fractal dimensions of surfaces in turbulent flows. Phys. Fluids A 2, 792–807

  13. Shepherd, I. G.; Cheng, R. K.; Goix, P. J. 1991: The spatial scalar structure of premixed turbulent stagnation point flames. 23rd. Int. Symp. Combust., 781–788

  14. Sreenivasan, K. R. 1991: Fractals and multifractals in fluid turbulence. Annu. Rev. Fluid Mech. 23, 539–600

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shepherd, I.G., Cheng, R.K. & Talbot, L. Experimental criteria for the determination of fractal parameters of premixed turbulent flames. Experiments in Fluids 13, 386–392 (1992). https://doi.org/10.1007/BF00223246

Download citation

Keywords

  • Fractal Parameter
  • Turbulent Flame
  • Flame Surface
  • Flame Length
  • Copper Vapor Laser