Vectorial structure of the near-wall premixed flame

The turbulent premixed flame-wall interaction (FWI) has been numerically analyzed in a head-on quenching configuration at statistically stationary state under different boundary conditions. When the wall temperature is not high enough, the near wall flame isosurfaces become broken because of local flame extinction within the quenching and influence zones of FWI. According to the relative orientation of the flame normal and the wall normal, the flame can be either head-on or entrained. Outside of the influence zone the head-on flame elements are predominant, while inside the quenching zone flames are more likely to be entrained. The alignment relations among important vectors, including the principal axes of the strain rate tensor, the flame normal vector and vorticity have been investigated. Outside of the influence zone the normal vector of the progress variable isosurfaces aligns with the most extensive principle axis in the reaction zone and with the most compressive axis in the unburned and burned gas regions. Within the quenching zone, the preferential orientation with the most extensive principal axis disappears, once the flame dilatation and flame-normal strain rate decrease. Conditional alignment statistics demonstrate the distinctly different properties between the entrained flame and the head-on flame parts. In summary, the alignment relations are primarily determined by the relative strengths of chemical heat release, turbulent staining, and wall heat flux.

Figure 1

The statistically stationary FWI configuration. The streamlines are colored with the velocity magnitude.

Figure 2

Comparison of the flow and flame structure: (a) case 6A, (b) case 8A, (c) case 10A, (d) case 8T5, and (e) case 8T0. The flame is presented by the $c=0.85$ isosurface colored by the local temperature. When the wall temperature decreases, the near-wall flame speed decreases and thus the flame front tends to be closer to the wall. Especially for the 8T0 case, the flame front breaks because of local quenching.

Figure 3

PDFs of the flame-wall distance along the wall normal direction for different cases, in accordance with the field visualization in Fig. 2.

Figure 4

Joint PDF between the flame-wall distance and the velocity component $u_1$ before the flame brush for (a) the entrained flame elements and (b) the head-on flame elements of case 8T0.

Figure 5

Variation of the temperature (on $c=0.85$) with the flame-wall distance for (a) the overall sample, (b) the entrained part, and (c) the head-on part of case 8T0.

Figure 6

PDFs in logarithmic scale of $\left|cos〈{\vec{\lambda }}_i,\vec{n}〉\right|$ from $c=0.05$ to $c=0.95$ for (a) case 6A, (b) case 8A, (c) case 10A, (d) case 8T5, and (e) case 8T0.

Figure 7

PDFs of $\left|cos〈\vec{n},\vec{\omega }〉\right|$ throughout the flame brush from $c=0.05$ to $c=0.95$ for (a) case 6A, (b) case 8A, (c) case 10A, (d) case 8T5, and (e) case 8T0.

Figure 8

Conditional mean dilatation $\mathrm{\Delta }$, flame-normal strain rate $s_n$ and flame-tangential strain rate $s_t$ on different $c$ isosurfaces from $c=0.05$ to $c=0.95$ for all cases.

Figure 9

For the cold wall case $8T0$ in the quenching zone, variation of the conditional mean dilatation $\mathrm{\Delta }$, flame-normal strain rate $s_n$, and flame-tangential strain rate $s_t$ on different $c$ isosurfaces from $c=0.05$ to $c=0.95$ for (a) the entire sample, (b) the sample beyond the influence zone, (c) the entrained elements in the quenching zone, and (d) the head-on elements in the quenching zone.

Figure 10

PDFs of $\left|cos〈{\vec{\lambda }}_i,\vec{n}〉\right|$ on flame isosurface of $c=0.1, c=0.5$ and $c=0.9$ in case 8T0 for (a) the entrained part in the quenching zone and (b) the head-on part in the quenching zone.

Figure 11

PDFs of $\left|cos〈\vec{n},\vec{\omega }〉\right|$ for (a) the entrained parts and (b) the head-on parts of case 8T0 in the quenching zone of FWI.

Figure 12

PDFs of $\left|cos〈{\vec{\lambda }}_i,\vec{n}〉\right|$ conditioned on the different temperature ${\tilde{T}}_{c=0.85}$ of $c=0.85$ isosurfac for (a) the entire elements, (b) the entrained flame part, and (c) the head-on part of case 8T0.