Flow, Turbulence and Combustion

, Volume 103, Issue 4, pp 913–941 | Cite as

Propagation of Spherically Expanding Turbulent Flames into Fuel Droplet-Mists

  • Gulcan Ozel ErolEmail author
  • Josef Hasslberger
  • Markus Klein
  • Nilanjan Chakraborty
SI: THMT-2018


The effects of droplet diameter and the overall (liquid+gas) equivalence ratio on flame topology and propagation statistics in spherically expanding turbulent n-heptane spray flames have been analysed based on three-dimensional Direct Numerical Simulations (DNS) data. It has been found that the range of both mean and Gauss curvatures of the flame surface, and the probability of finding saddle topologies increase with increasing droplet diameter and overall equivalence ratio. The presence of droplets affects the displacement speed and consumption speed statistics principally through the reaction rate of the mixture composition in the reaction zone. The magnitudes of the components of density-weighted displacement speed arising from mixture inhomogeneity and droplet evaporation remain small in comparison to the magnitudes of the reaction rate and molecular diffusion rate components. The presence of large droplets decreases the mean density-weighted displacement speed \( {S}_d^{\ast } \) and increases the probability of finding negative \( {S}_d^{\ast } \) values, except for overall fuel-lean equivalence ratios. The mean consumption speed shows an increasing trend with increasing droplet diameter for fuel-lean overall equivalence ratios, whereas the mean consumption speed decreases with increasing droplet diameter for overall stoichiometric and fuel-rich mixtures. The mean consumption speed remains greater than the mean density-weighted displacement speed for all cases considered here. An alternative flame speed, which represents the growth rate of the flame surface area, has been found to provide an approximate measure of mean consumption flame speed. By contrast, an alternative flame speed, which represents the growth rate of burned gas volume, has been found to approximate the mean density-weighted displacement speed for large droplets in the case of stoichiometric and fuel-rich overall equivalence ratios.


Droplet combustion Spherically expanding flame Displacement speed Consumption speed Direct numerical simulations 



The financial support of the Republic of Turkey Ministry of National Education and EPSRC (EP/K025163/1, EP/R029369/1) and the computational support of Rocket and ARCHER are gratefully acknowledged.

Compliance with Ethical Standards

This work did not involve any active collection of human data.

Competing Interests

We have no competing interests.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Gulcan Ozel Erol
    • 1
    Email author
  • Josef Hasslberger
    • 2
  • Markus Klein
    • 2
  • Nilanjan Chakraborty
    • 1
  1. 1.School of Engineering, Newcastle UniversityNewcastle-Upon-TyneUK
  2. 2.Bundeswehr University MunichNeubibergGermany

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