Effect of gravity on nonlinear dynamics of the flow velocity field in turbulent fire

We numerically study the effect of gravity on the dynamic behavior of flow velocity field in a turbulent fire from the viewpoints of symbolic dynamics, statistical complexity, and complex networks. The randomness of streamwise flow velocity fluctuations significantly increases with increasing gravity, which is found to be correlated with the mean permutation entropy and the Froude number. The multiscale complexity-entropy causality plane clearly shows that under high gravity, high-dimensional deterministic chaos starts to be formed in the near field. We observe the appearance, disappearance, and reappearance of a scale-free structure in weighted networks between vortices under high gravity, clearly showing the presence of power-law decay in the lifetime of the scale-free structure.

Figure 1

Instantaneous flow velocity field on the $x-z$ plane and temporal evolutions of streamwise flow velocity $w$ along the centerline of the fire source at different heights $z$ [(a) $z=0.5\mathrm{m}$, (b) $z=1.0\mathrm{m}$, and (c) $z=3.0\mathrm{m}$] in enhanced gravity. (A) $G=3$, (B) $G=3$, and (C) $G=10$.

Figure 2

Spatial distribution of the permutation entropy $S_p$ for the temporal evolution of streamwise flow velocity fluctuations $w^{\prime }$ on the $x-z$ plane in enhanced gravity. (A) $G=3$ and (B) $G=10$.

Figure 3

Variation in the mean permutation entropy $\langle S_p\rangle$ as a function of the Froude number $F_r$ for (a) the near field and (b) far field. (a) $-0.5\mathrm{m}\le x\le 0.5\mathrm{m}$, $0.3\mathrm{m}\le z\le 0.5\mathrm{m}$, and (b) $-0.5\mathrm{m}\le x\le 0.5\mathrm{m}$, $3.0\mathrm{m}\le z\le 3.6\mathrm{m}$.

Figure 4

Complexity-entropy causality planes of streamwise flow velocity fluctuations $w^{\prime }$ along the centerline of the fire source at different heights $z$ [(a) $z=0.5\mathrm{m}$ and (b) $z=3.0\mathrm{m}$] in enhanced gravity $G=3$ and 10.

Figure 5

Variation in the delay time ${\tau }_{C_{JS,max}}$ as a function of the Froude number $F_r$ for the near field ($z=0.5\mathrm{m}$).

Figure 6

(A) Instantaneous vorticity field and the corresponding spatial distribution of the vertex strength $s$ in enhanced gravity $G=10$. (B) Probability density function of the vertex strength in the turbulence networks $p\left(s\right)$ in enhanced gravity $G=10$.

Figure 7

Probability density function of the lifetime $p\left({\tau }_d\right)$ of the scale-free structure in enhanced gravity $G=10$.

Figure 8

Variations in the existence probability of scale-free structure $P_e$ and absolute value of mean scaling exponent of vertex strength distribution $|\langle \gamma \rangle |$ as a function of the Froude number $F_r$.