Spatiotemporal dynamics and early detection of thermoacoustic combustion instability in a model rocket combustor

We numerically study the spatiotemporal dynamics and early detection of thermoacoustic combustion instability in a model rocket combustor using the theories of complex networks and synchronization. The turbulence network, which consists of nodes and vertexes in weighted networks between vortices, can characterize the complex spatiotemporal structure of a flow field during thermoacoustic combustion instability. The transfer entropy allows us to identify the driving region of thermoacoustic combustion instability. In addition to the order parameter, a phase parameter newly proposed in this study is useful for capturing the precursor of thermoacoustic combustion instability.

Figure 1

(a) Instantaneous configuration of ${\mathrm{H}}_2/{\mathrm{O}}_2$ flame in the combustion chamber. (b) Temporal evolution of pressure fluctuations during the transition and the subsequent well-developed thermoacoustic instability, together with the extracted instantaneous flame configuration of lifted flame near the injector rim at $t=17.5\mathrm{ms}$.

Figure 2

(a) Instantaneous vertex strength field in turbulence network and (b) probability distribution of the vertex strength $P\left(s\right)$ in the turbulence network during well-developed thermoacoustic combustion instability.

Figure 3

Temporal evolution of the average vertex strength $\overline{s}$ with respect to $y$ and extracted representative vorticity fields.

Figure 4

Temporal evolution of the turbulence network entropy $S_t$ during well-developed combustion instability.

Figure 5

(A) Temporal evolutions of the spatially averaged pressure fluctuations $\overline{p}$, heat release fluctuations $\overline{q}$, and their variances ${\sigma }^2$. (B) Temporal evolutions of the order parameter $K$, the variance ${\sigma }_K^2$, and the phase parameter $M$, together with the extracted phase fields. $K$ and $M$ are obtained for the ranges of 54 mm $\le y\le$ 90 mm and 0 mm $<z\le$ 50 mm, respectively. (a) $t=15.24\mathrm{ms}$ and (b) $t=15.65\mathrm{ms}$.

Figure 6

Temporal evolutions of the edge position of the ${\mathrm{H}}_2/{\mathrm{O}}_2$ flame $Z_{\mathrm{edge}}$ and the order parameter $K$ during well-developed thermoacoustic combustion instability. $K$ is obtained for the ranges of 65 mm $\le y\le$ 79 mm and 30 mm $\le z\le$ 50 mm.

Figure 7

Spatial distributions of the transfer entropy $S_T$ during the transition to thermoacoustic combustion instability for (a) 14 ms $\le t\le$ 15 ms and (b) 19 ms $\le t\le$ 20 ms. (A) $S_{T{p}^{\prime }\to q^{\prime }}$ for the direction from pressure fluctuations $p^{\prime }$ to heat release fluctuations $q^{\prime }$. (B) $S_{T{q}^{\prime }\to p^{\prime }}$ for the direction from heat release fluctuations $q^{\prime }$ to pressure fluctuations $p^{\prime }$.

Figure 8

Temporal evolution of the entropy difference $\mathrm{\Delta }S$ during the transition and the subsequent well-developed thermoacoustic combustion instability.

Figure 9

Spatial distributions of the Rayleigh index $RI$ during the transition to thermoacoustic combustion instability for (a) 14 ms $\le t\le$ 15 ms and (b) 15 ms $\le t\le$ 16 ms.