Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.

Figure 1

Instantaneous flow velocity field on the $x\text{−}z$ plane at $y=0\mathrm{mm}$ in two coupled turbulent diffusion flames under normal gravity.

Figure 2

Time variations in the second-order moment of flow velocity fluctuations along $z$ axis $M_{w1}$ and $M_{w2}$ at different locations $z$ under (A) low gravity ($G=0.7$) and (B) high gravity ($G=1.5$). (a) $z=0.1\mathrm{m}$, (b) $z=0.2\mathrm{m}$, and (c) $z=0.3\mathrm{m}$.

Figure 3

(a) Variation in the recurrence rate $R_R$ of the CRPs at different locations $z$ for gravity levels $G=0.7$, 1, and 1.5. (b) Surface plot of $R_R$ as a function of $G$ at different $z$.

Figure 4

(a) Variation in the maximal information coefficient $C_M$ at different locations $z$ for gravity levels $G=0.7$, 1, and 1.5. (b) Surface plot of $C_M$ as a function of $G$ at different $z$.

Figure 5

Variation in the recurrence rate $S_R$ of the SRPs as a function of the delay time ${\tau }_a$ at different locations $z$. (a) $G=0.7$, (b) $G=1$, and (c) $G=1.5$.

Figure 6

Variation in the recurrence rate $S_R$ of the SRPs as a function of gravity level $G$ at different locations $z$. Here, ${\tau }_a=0$.

Figure 7

Variation in the correlation coefficient $C$ between the predicted values and the corresponding reference values of the second-order moment of flow velocity fluctuations $M_{w2}$ at different locations $z$. (a) $G=0.7$, (b) $G=1$, and (c) $G=1.5$.

Figure 8

Temporal evolution of the vorticity field on the $x\text{−}z$ plane at $y=0\mathrm{mm}$ under (A) low gravity ($G=0.7$) and (B) high gravity ($G=1.5$). (a) $t=2\mathrm{s}$, (b) $t=2.025\mathrm{s}$, (c) $t=2.05\mathrm{s}$, and (d) $t=2.075\mathrm{s}$.

Figure 9

Variation in the fraction $F_N$ of false nearest neighbors of the trajectories in phase space as a function of the embedding dimension $D$.

Figure 10

Variations in the recurrence rate $R_R$ of the CRPs as functions of vertical location $z$ and gravitational level $G$ at different recurrence point densities $r_d$. (a) $r_d=0.01$, (b) $r_d=0.05$, and (c) $r_d=0.1$.

Figure 11

Variations in the recurrence rate $S_R$ of the SRPs as functions of vertical location $z$ and gravitational level $G$ at different embedding delay times $\tau$. (a) $\tau =1$, (b) $\tau =5$, and (c) $\tau =10$.