# Experimental Comparison of Diesel and Crude Rapeseed Oil Combustion in a Swirl Burner
## 3 Results and Discussion
### Spectral Analysis of Diesel Oil Combustion  
All practical signals contain stochastic and deterministic parts. An efficient control system requires the proper filtering of the deterministic part, i.e., feeding it with a high signal-to-noise ratio. For this purpose, the probability of the measured temporal pressure signal is analyzed in this subsection. Figure 6 shows the histogram of the pressure signal of \(2^{14}\) datapoints of D combustion at the observed three flame shapes and right before the blowout, corresponding to Cases 2-5. Note that the latter state was also characterized by a V-shaped flame. All the histograms of the pressure signal follow a normal distribution, hence, a normal probability density function (PDF) was fitted to all subplots in Figure 6a by using the fitdist function of Matlab. This algorithm estimates the standard deviation through the unbiased estimate of the variance. A PDF is added to all further 1D histograms of the pressure signal, which follows a normal distribution as well. The straight flame was dominated by higher frequencies, and its overall sound pressure level was also higher, as discussed in a previous work [46]. The noise emission of the transitory flame was similar, however, the V-shaped flame was characterized by lower noise, which decreased until blowout. This finding is also supported by the histograms as they became narrower as the blowout is approached. Figure 6b shows the joint histogram of the CWT coefficients at \(f_{1}\) and \(f_{2}\). The dominance of \(f_{1}\) over \(f_{2}\) is apparent in both the straight and V-shaped flames, as the distribution of the joint histogram is flatter in the horizontal direction. However, the CWT coefficients at \(f_{1}\) and \(f_{2}\) are closely equal in both the transitory and the V-shaped regime. A similar result was reached in cases where the flame blowout occurred in the straight flame shape with the modification in the characteristic frequencies, which were \(f_{3}=1600\) Hz and \(f_{4}=3200\) Hz. Figure 5: CWT (continuous wavelet transform) of the CWT coefficients at \(f_{1}=230\) Hz. The flame blowout occurred in the transitory regime in Case 1, which was shown in Figure 4 in detail. For comparison, the results of BL-D and Q15-D (Case 6) are shown in Figure 7, as the latter setup belongs to a stable flame, well below the blowout limitation. The difference is only the presence of a quarl. The histogram of the pressure signal is similar, however, Q15-D is flatter, and the large amplitude fluctuations drive the microphone electronics to saturation more often. This phenomenon is interesting since the microphone is capable of detecting 140 dB overall sound pressure level, \(L_{p}\), while this value was only 97 dB in the present case, which is enormous as the scale is logarithmic. Moreover, the measurement series included straight flames with \(L_{p}>100\) dB without observing the saturation of the noise analyzer. The answer is the sudden change in flame shapes, occurring as a hammer blow, which is a subcritical Hopf bifurcation [58, 66, 67]. Hence, the change requires the passing of a certain threshold with hysteresis; then, there is a sudden jump in the mathematical characteristics. The axis limits of the joint histograms in Figure 7 were doubled compared to those of Figure 6, while the number of bins was similarly 30 in both axes to cover a broader range in CWT magnitudes. In Case 1, the similar amplitudes of \(f_{1}\) and \(f_{2}\), which were observed previously, do not characterize the pre-blowout phase, as the joint histogram is not confined to lower amplitudes. Nevertheless, Case 6 shows a slightly more stochastic behavior with the dominance of \(f_{1}\), similar to BL-D. Consequently, flame blowout detection requires a deeper understanding of the signal structure of the given flame. Figure 6: (a) Histograms of the pressure signal at characteristic flame shapes. (b) Joint histograms of CWT coefficients at \(f_{1}\) and \(f_{2}\) of Cases 2–5.