## 3 Results and Discussion
### Flame Height  
To quantitatively evaluate the flame appearances of the three NC samples, the MATLAB-based binarization method developed by [PERSON] et al. [35] is employed to acquire the flame height data in current study. Be more specified, the video records are firstly converted into gray images frame by frame, and then binarized to obtain flame envelopes. The flame heights of the three samples with \(L=8\) cm during the whole combustion process are plotted in Figure 5 together with their corresponding histories of MLR. Previous research demonstrates that the flame height can be correlated with the \(2/5\) power of HRR or MLR [36; 37]. Thus, the variation range of flame height is not as much as that of MLR, as shown in Figure 5.  
In a very short time after ignition, MLR curves of NC-I and NC-E rapidly reach to a plateau, reflecting as the relatively stable combustion illustrated in Figure 4, which is defined as quasi-steady burning stage for further discussion. Meanwhile, it should be noticed that the flame heights in Figure 5 are remarkably decentralized, i.e., the flame heights exhibit regular and reproducible intense oscillations. The flame oscillation frequency, \(f\), can be roughly estimated as \(1.5D^{-1/2}\), where \(D\) is the hydraulic diameter of the burner [38]. Hence, the oscillation frequencies for \(L=8\) cm and \(10\) cm pool dimensions in the current study are \(4.99\) and \(4.46\) Hz, respectively. The luminous time-sequenced images are analyzed via a fast Fourier transform method to obtain the oscillation frequency, and the ultimate results in the quasi-steady burning stage are listed in Table 3, all of which are close to the predicted values, indicating that the current image recording speed is acceptable.  
Figure 4: Flame appearances of tests with \(L=8\) cm at typical moments of \(2\), \(6\), \(10\), \(18\), \(26\) s after ignition:  
(a) NC-I; (b) NC-E; and (c) NC-D, where the reference value \(H=76\) cm.  
Figure 5: \(Cont.\)  
To further assess the oscillation amplitudes of flame heights, the flame oscillation intensity, \(I_{f}\), defined as the ratio of the half of difference between the highest (\(z_{f-max}\)) and lowest (\(z_{f-min}\)) heights to the mean flame length (\(z_{f-m}\)), is introduced here, i.e., \(I_{f}=\left(z_{f-max}-z_{f-min}\right)/\left(2z_{f-m}\right)\)[39]. For the convenience of comparison, only the results in the quasi-steady burning stage are calculated for NC-I and NC-E, and the flame heights in the vicinity of maximum MLR (\(\pm\)2 s) are also used to give the values of \(f\), \(z_{f-m}\), and \(I_{f}\) for NC-D. As presented in Table 3, \(I_{f}\) values for NC-I and NC-E are in close proximity to each other, regardless of the pool dimensions, while they are distinctly larger than that for NC-D, indicating that the flocculent NC samples with alcohol humectants exhibit more drastic flame oscillation amplitude than NC-D with strip structure. In spite of that, \(I_{f}\) values for current NC samples are still larger than that for n-heptane pool fire with similar dimension (\(I_{f}\) = 0.22) [37] and for gaseous methane flame (\(I_{f}\) = 0.14) under atmospheric pressure [39]. To quantify the flame heights, the average flame height in each second, i.e., 25 frames, is calculated for further discussion, as shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \(L\) **(cm)** & **Ave./Max. MLR (g/s)** & \(f\) **(Hz)** & \(z_{f-m}\) **(m)** & \(I_{f}\) \\ \hline \multirow{2}{*}{NC-I} & 8 & 0.52 & 5.13 & 0.35 & 0.77 \\  & 10 & 1.03 & 4.55 & 0.50 & 0.64 \\ \hline \multirow{2}{*}{NC-E} & 8 & 0.51 & 5.02 & 0.33 & 0.72 \\  & 10 & 0.95 & 4.52 & 0.42 & 0.71 \\ \hline \multirow{2}{*}{NC-D} & 8 & 1.14 & 4.42 & 0.53 & 0.44 \\  & 10 & 1.79 & 4.93 & 0.70 & 0.36 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of key information from MLR and flame height.  
Figure 5: Variation of flame height together with corresponding MLR for cases with \(L\) = 8 cm: (**a**) NC-I; (**b**) NC-E; and (**c**) NC-D.