Analysis of flame-flame interactions in premixed hydrocarbon and hydrogen flames

Flame-flame interactions are analyzed in twin hydrocarbon and hydrogen turbulent premixed flames. The interactions are identified with the help of Morse theory for critical points. Flame topology in the vicinity of critical points is analyzed and is categorized into four main groups, namely tunnel formation, tunnel closure, reactant pockets, and product pockets. The number of flame-flame interactions is presented in the form of histograms for the different flame cases. The relative frequency of occurrence of each type of topology changes with the turbulence intensity. In hydrocarbon flames, the fraction of product pockets and tunnel formation events increases with turbulence intensity, whereas the fraction of reactant pockets and tunnel closure events decreases. The results for hydrocarbon flames are compared with those for hydrogen flames and the differences are explained both qualitatively and quantitatively. An additional comparison is made between the number of flame-flame interactions observed for a single hydrocarbon flame against the number of interactions for twin hydrocarbon flames. It is found that having two flames in the domain does not significantly alter the number of interactions per flame, therefore indicating that the observed interactions are mainly self-interactions within individual flames.

Figure 1

The set of all possible flame–flame interaction topologies as determined by the shape factors [31].

Figure 2

Schematic diagram of the twin hydrocarbon flame configuration. Outflow boundary conditions are set on the end faces of the domain, with periodic boundary conditions on all other faces. Blue contours in the middle represent the turbulent eddies.

Figure 3

Slices through the 3D domain of twin hydrocarbon flames at $t=0,4\tau ,8\tau$ in the left, middle, and right panels, respectively, for $u^{\prime }/s_L=10,20$, and 40 cases (top to bottom). The flames are seen to become wrinkled and eventually collide with each other.

Figure 4

Temperature field from a subset of the $\mathrm{Da}+$ dataset from Hawkes et al. [43].

Figure 5

Contour slices of subsets of the $\mathrm{Da}+$ (top) and $\mathrm{Da}-$ (bottom) cases showing various isosurfaces of progress variable $c$ ranging from the leading edge represented by blue lines to the trailing edge represented by red lines.

Figure 6

Histograms for the frequency of occurrence of different topologies in the hydrocarbon-air dataset represented by different colors. The left column shows the results for $0.01<c<0.99$, whereas the right column shows the results for $0.3<c<0.99$. The turbulence intensity is increased from $u^{\prime }=10s_L$ (top row) to $u^{\prime }=20s_L$ (middle row) to $u^{\prime }=40s_L$ (bottom row).

Figure 7

Histograms showing the number of flame-flame interactions in the hydrogen-air dataset for $\mathrm{Da}+$ (top) and $\mathrm{Da}-$ (bottom) cases.

Figure 8

Histograms showing the number of flame-flame interactions normalized by the surface area in the hydrogen-air dataset at $c=0.5$ for $\mathrm{Da}+$ (top) and $\mathrm{Da}-$ (bottom) cases.

Figure 9

Mean turbulent kinetic energy averaged over surfaces of progress variable $c$ for the hydrocarbon flames and normalized by its values in the unburnt mixture. The KE decays as $c$ increases through the flame.

Figure 10

(a) Contours of progress variable at $c=0.1$ representing the leading edge (blue) and at $c=0.9$ representing the trailing edge (red) of the flame; (b) absolute value of the mean curvature surface averaged over the isosurfaces of progress variable $c$ normalized by unstrained laminar flame thickness ${\delta }_L$, plotted against $c$ for the hydrocarbon flame cases.

Figure 11

Reaction rate for a 1D laminar hydrocarbon flame plotted against progress variable $c$ showing the rise in reaction rates and the subsequent drop in the number of interactions represented by the shaded background.

Figure 12

Slices of the mass fraction profile showing a pair of isosurfaces separated by $c=0.02$ at four different locations of the flame for $u^{\prime }=20s_L$ case.

Figure 13

Surface averaged absolute value of the mean curvature $\overline{\left|\kappa \right|}$ normalized by the unstrained laminar flame thickness ${\delta }_L$, plotted against the progress variable $c$ for the hydrogen-air dataset. In this figure, the blue line represents $\overline{\left|\kappa \right|}$ for the $\mathrm{Da}+$ case and the red line represents $\overline{\left|\kappa \right|}$ for the $\mathrm{Da}-$ case.

Figure 14

Variation of Lewis number with $c$ in a 1D laminar hydrogen flame.

Figure 15

Results showing the effects of thermodiffusive instabilities caused by $\mathrm{Le}<1$ on the statistics of flame-flame interactions. (a) Surface averaged absolute mean curvature $\overline{\left|\kappa \right|}$ normalized by the unstrained laminar flame thickness ${\delta }_L$ plotted against $c$ for three-dimensional hydrogen-air flame in low-intensity turbulence. (b) Histogram showing frequency of occurrence of flame-flame interactions for three-dimensional hydrogen-air flame in low-intensity turbulence.

Figure 16

Reaction rate profile for a 1D laminar hydrogen flame (blue line) plotted against $c$. The shaded red background represents the general shape of the histograms of frequency of flame-flame interactions for the $\mathrm{Da}+$ case.

Figure 17

Fractions of RP and PP (top) and fractions of TF and TC (bottom) for the twin flame dataset.

Figure 18

Histograms showing the number of interactions in a single flame (left) vs. twin flames (right). The number of interactions for the twin flame configuration is approximately twice as that of the single flame.