A Direct Numerical Simulation Investigation of Spherically Expanding Flames Propagating in Fuel Droplet-Mists for Different Droplet Diameters and Overall Equivalence Ratios

ABSTRACT

Laminar and turbulent spherically expanding n-heptane flames in mono-sized fuel droplet-mists have been simulated for a range of different overall equivalence ratios and droplet diameters using three-dimensional Direct Numerical Simulations (DNS). Flame wrinkling and the evolutions of flame surface area and burned gas volume have been investigated for spherically expanding spray and gaseous premixed flames with the same initial burned gas radius and overall equivalence ratios. It has been found that droplet-induced wrinkling for laminar flame kernels strengthens with increasing overall equivalence ratio and droplet diameter. However, the effects of droplet-induced flame wrinkling are masked by wrinkling induced by fluid motion in turbulent spherically expanding spray flames. The gaseous phase mixture within the flame has been found to have smaller equivalence ratios (predominantly fuel-lean) in comparison to the overall equivalence ratio for globally stoichiometric and fuel-rich droplet cases and this tendency strengthens with increasing droplet diameter. By contrast, it is possible to obtain higher local equivalence ratio values than the overall equivalence ratio in globally fuel-lean spray flames. The presence of droplets in the globally fuel-lean cases enhances the growth of flame surface area under laminar and turbulent conditions. However, for the laminar globally stoichiometric spray flame, flame surface area for small droplets grows faster than the corresponding laminar premixed flame and this tendency is observed also for turbulent globally fuel-rich spray flames. It has been found that the burned gas mass increases for large (small) droplets for overall fuel-lean (fuel-rich) mixtures for flame propagation in droplet-laden mixtures, which is in qualitative agreement with previous experimental findings.

KEY WORDS:

• Droplet combustion
• Spherically expanding flame
• Direct Numerical Simulations

Acknowledgments

We gratefully acknowledge Rocket and ARCHER for their computational support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ It is worth noting that in order to ensure that all cases are subjected to same initial turbulence both $u^{\prime }$ and $L_{11}$ are kept unchanged. This means that $u^{\prime }/S_{b\left({\varphi }_g\right)}$ and $L_{11}/{\delta }_{\left({\varphi }_g\right)}$ values are different for ${\varphi }_{ov}=0.8$ (i.e., $u^{\prime }/S_{b\left({\varphi }_g=0.8\right)}=6.66$ and $L_{11}/{\delta }_{\left({\varphi }_g=0.8\right)}=1.47$) and 1.2 (i.e., $u^{\prime }/S_{b\left({\varphi }_g=1.2\right)}=4.76$ and $L_{11}/{\delta }_{\left({\varphi }_g=1.2\right)}=2.77$) cases where ${\delta }_{\left({\varphi }_g\right)}$ is the thermal flame thickness for the equivalence ratio ${\varphi }_g$.

² $T_b\left(\xi \right)=T_{F\mathrm{\infty }}\xi +T_{O\mathrm{\infty }}\left(1-\xi \right)+\left(1-\xi \right)/\left(1-{\xi }_{st}\right)$ for $\xi >{\xi }_{st}$ and $T_b=T_{F\mathrm{\infty }}\xi +T_{O\mathrm{\infty }}\left(1-\xi \right)+\xi /{\xi }_{st}$ for $\xi \le {\xi }_{st}$ where $T_b$, $T_{F\mathrm{\infty }}$, and $T_{O\mathrm{\infty }}$ are non-dimensional burned gas temperature, pure fuel stream temperature, and pure air stream temperature, respectively.

³ ${\dot{\omega }}_c$ is the reaction rate of progress variable, which is given by ${\dot{\omega }}_c=-{\xi }_{st}{\dot{\omega }}_O/\left[\xi \left(1-{\xi }_{st}\right)Y_{O\mathrm{\infty }}\right]$ (${\dot{\omega }}_c=-{\dot{\omega }}_O/\left[\left(1-\xi \right)Y_{O\mathrm{\infty }}\right]$) for $\xi \le {\xi }_{st}$ ($\xi >{\xi }_{st}$) (Wacks et al., 2016).

⁴ The temporal evolutions of ${\mathrm{\Omega }}_c=\underset{V}{\int }{\dot{\omega }}_{c}dV$ and ${\mathrm{\Omega }}_c/{\mathrm{\Omega }}_{c0}$ are qualitatively similar to ${\mathrm{\Omega }}_F$ and ${\mathrm{\Omega }}_F/{\mathrm{\Omega }}_{F0}$, respectively.

Additional information

Funding

The financial support of the Republic of Turkey Ministry of National Education and EPSRC (EP/K025163/1) is gratefully acknowledged.