Pair dispersion of turbulent premixed flame elements

Flame particles are mathematical points comoving with a reacting isoscalar surface in a premixed flame. In this Rapid Communication, we investigate mean square pair separation of flame particles as a function of time from their positions tracked in two sets of direct numerical simulation solutions of ${\mathrm{H}}_2$-air turbulent premixed flames with detailed chemistry. We find that, despite flame particles and fluid particles being very different concepts, a modified Batchelor's scaling of the form $\langle {|{\mathit{\Delta }}^F\left(t\right)-{\mathit{\Delta }}^F\left(0\right)|}^2\rangle =C_F{\left({\langle \varepsilon \rangle }_0^F{\Delta }_0^F\right)}^{2/3}{t}^2$ holds for flame particle pair dispersion. The proportionality constant, however, is not universal and depends on the isosurface temperature value on which the flame particles reside. Following this, we attempt to analytically investigate the rationale behind such an observation.

Figure 1

Scaled, mean squared flame particle pair separation vs time in seconds for flame particles belonging to the isosurface (a) $T=500\mathrm{K}$ and (b) $T=1000\mathrm{K}$ for case A. Compensated mean squared flame particle pair separation vs time normalized with Kolmogorov time scale for flame particles belonging to the isosurface (c) $T=500\mathrm{K}$ and (d) $T=1000\mathrm{K}$ for case A.

Figure 2

Scaled, mean squared flame particle pair separation vs time in seconds for flame particles belonging to the isosurface (a) $T=500\mathrm{K}$ and (b) $T=1000\mathrm{K}$ for case B. Compensated mean squared flame particle pair separation vs time normalized with Kolmogorov time scale for flame particles belonging to the isosurface (c) $T=500\mathrm{K}$ and (d) $T=1000\mathrm{K}$ for case B.

Figure 3

Compensated structure functions for case A corresponding to different terms of Eq. (15) at $t=0$ for (a) $T=500\mathrm{K}$ and (b) $T=1000\mathrm{K}$. The symbols represent the range of $50\eta \le {\Delta }_0^F\le 242\eta$ which was used for flame particle pair dispersion (PD) scaling reported in Figs. 1–1.

Figure 4

Compensated structure functions for case B corresponding to different terms of Eq. (15) at $t=0$ for (a) $T=500\mathrm{K}$ and (b) $T=1000\mathrm{K}$. The symbols represent the range of $50\eta \le {\Delta }_0^F\le 200\eta$ which was used for flame particle pair dispersion (PD) scaling reported in Figs. 2–2.