Electrohydrodynamic instability of premixed flames under manipulations of dc electric fields

We report an electrohydrodynamic instability in a premixed stagnation flame under manipulations of a dc electric field. This instability occurs when the electric field strength is at a certain value below the breakdown threshold, which is 0.75 kV/cm in the experimental setup. Above this value the flame front suddenly transits from a substrate-stabilized near-flat shape to a nozzle-stabilized conical surface, accompanied by a jump in the electric current through the flame field. At the transition moment, the flame spontaneously propagates upstream to the nozzle while the flow velocity at the upstream of the flame front decreases to zero, as revealed by high-speed photographs and PIV measurements. These phenomena indicate a transient balance between the fluid inertia and the electric body force around the instability threshold. A quantitative model suggests that the flame instability can be explained by a positive feedback loop, where the electric field applies a nonuniform electric body force, pulling the flame front upstream, and the pulled flame front in turn enhances the local electric body force. The electrohydrodynamic instability occurs when the electric pulling is strong enough and both the growth rates and the magnitudes of the electric body force on flame exceed those of the fluid dynamic pressure.

Figure 1

Schematic of the stagnation flame setup, the electric circuit system, and cameras (a Nikon camera for static images and a high-speed camera for dynamic images). The premixed gas flows through the honeycomb nozzle and the flame is stabilized on the stagnation plate or the nozzle outlet. The negative high voltage is added on the plate while the honeycomb nozzle is grounded. The pseudocolor image in the schematic indicates the chemiluminescence of ${\mathrm{CH}}^{*}$.

Figure 2

(a) Electric current as a function of the applied voltage. Solid, dashed, and dotted lines stand for the first, second, and third cycles of changing voltages, respectively. The black (the dark line following points A-B-C-D-E) and blue (the dark gray line following points E-F-G-H) lines indicate the increasing and decreasing lines when the periodic time of applied voltages is 100 s, i.e., the maximum $|dU/dt|$ is $86.4\mathrm{V}/\mathrm{s}$; the red (the light gray line following points A-B-C-D-E) and green (the light gray line following points E-F-G-H) lines indicate the increasing and decreasing lines when the periodic time is 200 s, i.e., the maximum $|dU/dt|$ is 43.2 V/s. The consistence of these lines indicates that the F-C and C-F transitions are repeatable and do not depend on the increasing rate of the applied voltages. The inlet figure shows the double logarithm curves of the same $I-U$ curve; the purple dashed line indicates the fitting proportional and quadratic line. (b) Flame chemiluminescence at different voltages corresponding to the points A to H at the upper $I-U$ curves. The pseudocolor images indicate the intensities of the flame chemiluminescence.

Figure 3

PIV measured flow field at $U=0$ (a), 1.2 kV (b), and 1.65 kV (c). Electric body forces [red (dark gray) arrows in the left half], current densities (white arrows in the right half), and the electric potentials at $U=1.2\mathrm{kV}$ (d) and 1.65 kV (e). Lengths of the arrows are proportional to magnitudes of the vectors. The maximum electric body force is $19.3{\mathrm{N}/\mathrm{m}}^3$ at $U=1.2\mathrm{kV}$ and $770.2{\mathrm{N}/\mathrm{m}}^3$ at $U=1.65\mathrm{kV}$; the maximum current density is $0.012{\mathrm{A}/\mathrm{m}}^2$ at $U=1.2\mathrm{kV}$ and $0.67{\mathrm{A}/\mathrm{m}}^2$ at $U=1.65\mathrm{kV}$. The flame fronts obtained from the chemiluminescence are plotted by black and white lines.

Figure 4

Transition process of flame structure. (a) Position of the flame front in the center (black squares and line) and the current response [blue (dark gray) squares and line] during a typical F–C transition. The current responses from 235 to 257 ms are zoomed in at the inset figure. (b) Flame front structure imaged by a high-speed camera.

Figure 5

Normalized electric pressure differences based on the simulated electric body forces (blue squares) and fluid dynamic pressure based on the PIV velocities (red triangles) at positions of the flame wrinkle during the F–C transition. The blue (dark gray) dotted line and red (light gray) dotted line represent the analytic results based on Eq. (3) and the square of an error function, respectively. The electric pressure difference and the fluid dynamic pressure are normalized by their respective pressures at the flashback point [namely the ${\mathrm{c}}_1$ point with $z\approx 6$ mm in Fig. 4]. Two arrays point to the two critical positions of the F–C transition, i.e., the first and secon necessary conditions for the electrohydrodynamic instability.

Figure 6

Measured critical currents at the F–C transition point with different inlet flow velocities.

Figure 7

Concentrations of CH, O, temperatures, and the chem-ionization rate of the reaction CH + O $\to {\mathrm{CHO}}^{+}+e^{-}$.

Figure 8

Concentrations of ${\mathrm{O}}_2$, ${\mathrm{N}}_2$, temperatures, and the reaction coefficient of the attachment reactions $e^{-}+{\mathrm{O}}_2+{\mathrm{O}}_2\to {\mathrm{O}}_2^{-}+{\mathrm{O}}_2$ and $e^{-}+{\mathrm{O}}_2+{\mathrm{N}}_2\to {\mathrm{O}}_2^{-}+{\mathrm{N}}_2$.