Surface morphology and inner fractal cutoff scale of spherical turbulent premixed flames in decaying isotropic turbulence

Embargo End Date
2022-09-03

Type
Article

Authors
Kulkarni, Tejas
Bisetti, Fabrizio

Online Publication Date
2020-09-03

Print Publication Date
2020-09

Date
2020-09-03

Abstract
The surface of turbulent premixed flames is fractal within a finite range of scales and the fractal dimension and inner cutoff scale are key components of fractal turbulent combustion closures. In such closures, the estimate for the surface area is sensitive to the value of the inner fractal cutoff scale, whose modeling remains unclear and for which both experimental and numerical contradictory evidence exists. In this work, we analyze data from six direct numerical simulations of spherically expanding turbulent premixed flames at varying Reynolds and Karlovitz numbers. The flames propagate in decaying isotropic turbulence and fall in the flamelet regime. Past an initial transient, we find that the fractal dimension reaches an asymptotic value between 2.3 and 2.4 in good agreement with previous results at similar conditions. A minor dependence of the fractal dimension on the Reynolds and Karlovitz numbers is observed and explained by the relatively low values of the Reynolds number and narrow inertial and fractal ranges. The inner fractal cutoff scale Δ* is found to scale as where l is the integral scale of turbulence and Reλ is the Reynolds number based on the Taylor micro-scale computed in the turbulence on the reactants’ side. The scaling is robust and insensitive to the Karlovitz number over the range of values considered in this study. An important implication is that the ratio Δ*/η grows with Reynolds number (η is the Kolmogorov scale), albeit at a rather slow rate that may explain the widespread observation that 4 ≤ Δ*/η ≤ 10. This suggests that Δ*, although smaller than λ, is not a dissipative length scale for the flame surface and scaled solely by η. Finally, a dissipative threshold scale that remains constant once normalized by η is identified.

Citation
Kulkarni, T., & Bisetti, F. (2020). Surface morphology and inner fractal cutoff scale of spherical turbulent premixed flames in decaying isotropic turbulence. Proceedings of the Combustion Institute. doi:10.1016/j.proci.2020.06.117

Acknowledgements
The authors are sponsored in part by NSF grant #1805921. Numerical simulations were carried out on the “Shaheen” supercomputer at King Abdullah University of Science and Technology and on the “Stampede2” supercomputer at the Texas Advanced Computing Center with allocation TG-CTS180002 under the Extreme Science and Engineering Discovery Environment.

Publisher
Elsevier BV

Journal
Proceedings of the Combustion Institute

DOI
10.1016/j.proci.2020.06.117

Additional Links
https://linkinghub.elsevier.com/retrieve/pii/S1540748920301838

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