Ethylene–air detonation in water spray

Abstract

Detonation experiments are conducted in a 52 $\hbox {mm}$ square channel with an ethylene–air gaseous mixture with dispersed liquid water droplets. The tests were conducted with a fuel–air equivalence ratio ranging from 0.9 to 1.1 at atmospheric pressure. An ultrasonic atomizer generates a polydisperse liquid water spray with droplet diameters of 8.5–12 $\upmu \hbox {m}$, yielding an effective density of 100–120 $\hbox {g}/\hbox {m}^{3}$. Pressure signals from seven transducers and cellular structure are recorded for each test. The detonation structure in the two-phase mixture exhibits a gaseous-like behaviour. The pressure profile in the expansion fan is not affected by the addition of water. A small detonation velocity deficit of up to 5 % was measured. However, the investigation highlights a dramatic increase in the cell size ($\lambda$) associated with the increase in the liquid water mass fraction in the two-phase mixture. The detonation structure evolves from a multi-cell to a half-cell mode. The analysis of the decay of the post-shock pressure fluctuations reveals that the ratio of the hydrodynamic thickness over the cell size ($x_{{\mathrm {HT}}}/{\lambda }$) remains quite constant, between 5 and 7. A slight decrease of this ratio is observed as the liquid water mass fraction is increased, or the ethylene–air mixture is made leaner.

Appendix

This appendix highlights the process involved in filtering the raw pressure signals to estimate the experimental detonation pressure and the hydrodynamic thickness ratio. The timescale chosen is lower than 1 $\hbox {ms}$ after the shock front arrival, to ensure a close-up selection on the post-shock zone pressure decay. The following filtering operations are applied to each pressure signal independently:

• 1. A signal selection is first proceeded by removing the front shock to filter the post-shock signal.

• 2. A fast Fourier transformation (FFT) is then applied on each pressure signal. To analyse and extract worthy information from the pressure signals, several considerations need to be kept in mind.

  As suggested by Boeck [42], a natural mechanical influence generated by the pressure transducer itself generates pressure oscillations not related to the observed phenomenon. To remove this influence, a low-pass filtering with a cutoff frequency lower than 30 % of the natural transducer frequency was applied to the raw pressure signals. This implies a maximum frequency choice of 100 $\hbox {kHz}$.

  Frequencies larger than 20 $\hbox {kHz}$ can be selected as they catch fluctuations related to phenomena smaller than a cell size. Indeed, the greatest detonation cell size obtained reaches approximately 80 $\hbox {mm}$, therefore considering the associated detonation velocity of $\approx$1700 $\hbox {m}/\hbox {s}$, a detonation characteristic frequency $D/{\lambda }$ can be assessed, yielding approximately 21 $\hbox {kHz}$.

  Low frequencies ( $20~\hbox {kHz}$) are processed independently, as they capture the expansion wave characteristic frequencies.

• 3. Considering the above analysis, a low-pass filter with a cutoff frequency of 5 $\hbox {kHz}$ was used to estimate the experimental detonation pressure, as it is more suitable to select the expansion wave evolution in comparison with a 0–20 $\hbox {kHz}$ low-pass filter.

  A 20–100 $\hbox {kHz}$ band-pass filter is applied to the decay of the pressure fluctuations behind the front shock to estimate the hydrodynamic thickness ratio. In both cases, the selected frequency bandwidths avoid the 12–14 $\hbox {kHz}$ range containing frequencies inherent to the experimental setup visible on transducers C2–C4, as discussed in Sect. 3.3. This frequency range was also observed on the latter pressure transducers when the experimental apparatus was used in a shock tube configuration.

• 4. An inverse Fourier transformation is applied on the filtered pressure signal, and a superimposition is performed for the same initial condition tests.