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ABSTRACT
The dynamical responses of a small coflow diffusion flame to low-frequency alternating current (AC) were investigated under voltages (Vac) and frequencies (fac) in the range of 0–5 kV and of 0–200 Hz, respectively. As high voltages were applied to the fuel nozzle, a frequency-multiplication mode was identified from the flame oscillations at fac < 8 Hz using high-speed imaging. This mode was characterized by bulk flame oscillations at multiples of fac until fac = 12 Hz, close to the frequency of the natural buoyancy-driven oscillation with the burner configuration used in this study. As fac increased past 12 Hz, the bulk flame oscillated at fac, resulting in a ‘lock-in’ mode. The results of experiments using a counterflow diffusion flame configuration with negligible buoyancy confirmed that it was the coupling between buoyancy-driven flows and AC-driven ionic winds that caused the frequency-multiplication phenomenon. For fac > 32 Hz, the bulk flame ceased to oscillate, and a spectral analysis found that ionic winds dominated the dynamic flame responses. The distinctions between AC forcing and acoustic forcing were highlighted. Particle image velocimetry (PIV) experiments at a kHz repetition rate were conducted to reveal the time-resolved flow fields. Electrical diagnostics captured the electrical signals; the calculated power consumption of the applied AC, with respect to the flame-heating power, was about 10–6.
Nomenclature
| Vac: | = | applied voltage of the alternating current (kV) |
| Vp: | = | peak positive value of Vac (kV) |
| V′: | = | normalized applied voltage by peak value of Vac |
| Iac: | = | electric current from ac electric field (A) |
| Ip: | = | peak value of Iac (A) |
| I′: | = | normalized electric current by Ip |
| Pac: | = | instantaneous electric power from ac electric field (W) |
| Pp: | = | peak value of Pac (W) |
| Ph: | = | flame heat power (W) |
| P′: | = | normalized electric power by Pp |
| = | averaged power consumption | |
| = | averaged power consumption per ac frequency cycle | |
| fac: | = | applied frequency of the alternating current (Hz) |
| fcrest: | = | frequency of the crest appearing in the oscillatory trajectory of V′ and L′ |
| fbuoy: | = | frequency of the crest appearing buoyancy-driven flame flickers |
| fR: | = | responding frequency in the frequency domain after FFT |
| UF: | = | velocity of the fuel stream (cm/s) |
| Uco: | = | velocity of the coflow stream (cm/s) |
| UH=2 mm: | = | velocity of the fuel stream about 2 mm above the nozzle exit (cm/s) |
| Zst: | = | mixture fraction |
| L: | = | overall flame luminosity (counts) |
| L0: | = | flame luminosity at baseline condition (counts) |
| L′: | = | normalized flame luminosity by the value at the baseline condition |
| ∆L′: | = | difference between the high and low peak in the oscillatory trajectory of L′ |
| H: | = | flame height determined by the luminosity (cm) |
| H0: | = | flame height at baseline condition (cm) |
| H′: | = | normalized flame height by the value at the baseline condition |
| ∆H′: | = | difference between the high and low peak in the oscillatory trajectory of H′ |
| Ha: | = | amplitude of the response in the frequency domain |
| Hd: | = | flame height location for the counterflow flame |
| D: | = | gap distance of the counterflow burner |
| Hd′: | = | normalized flame height for the counterflow flames |
| t′: | = | normalized time by multiply applied ac frequency |
| tdelay: | = | time delay calculated based on the phase delay |
| θHV: | = | phase delay between the transient oscillations of H′ and V′ |
| θLV: | = | phase delay between the transient oscillations of L′ and V′ |
| θYV: | = | phase delay between the transient oscillations of Hd′ and V′ |
| θhu: | = | phase delay between the transient oscillations of heat release rate and velocity |
| θUV: | = | phase delay between the transient oscillations of UH=2 mm and voltage |
| θVI: | = | phase delay between the transient oscillations of V′ and I′ |
Acknowledgments
This study was supported by Competitive Research Funding from King Abdullah University of Science and Technology (KAUST).