# Hydrodynamic Recirculation Induced by Nanosecond Discharges: A Strategy to Mitigate Cumulative Heating

Renaud Gablier, C.O. Laux

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Renaud Gablier, C.O. Laux. Hydrodynamic Recirculation Induced by Nanosecond Discharges: A Strategy to Mitigate Cumulative Heating. AIAA SCITECH 2025 Forum, Jan 2025, Orlando, United States. 10.2514/6.2025-0397. hal-04954834

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Distributed under a Creative Commons Attribution 4.0 International License
Hydrodynamic Recirculation
Induced by Nanosecond Discharges:
A Strategy to Mitigate Cumulative Heating

Renaud Gablier<fnref n="1" /> and Christophe O. Laux<fnref n="2" />

Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C,
Gif-sur-Yvette, 91190, France

This work studies the impact on flames of the toroidal hydrodynamic regime induced by Nanosecond Repetitively Pulsed discharges. Thanks to OH Planar Laser-Induced Fluorescence, experimental images of toroidal recirculation cells are observed for the first time in a plasma-assisted combustion experiment. In addition, the gas temperature between the electrodes is measured by optical emission spectroscopy of the (0,2) and (1,3) vibrational bands of N₂(C³Πu-B³Πg). The temperature in the inter-electrode gap is below 2500 K in the experimental conditions for which recirculation cells are observed. This level of cumulative heating by the repetitive discharges is far below previous experimental and numerical literature results reporting values around 3500 K for the same pulsing frequency and energy per pulse. The lower temperature is beneficial for NOx emissions as it reduces the production of NOx via the thermal Zeldovich reactions. The total NOx emissions due to the thermal and chemical effects induced by the plasma increase slower with the pulse energy than the traditionally observed linear dependence. This work shows that exploiting the hydrodynamic recirculation effects induced by nanosecond spark discharges is an effective way to deposit more plasma power, increasing the reactivity, with lower NOx emissions.

I. Introduction

Plasma-Assisted Combustion (PAC) has proven to be an effective method to extend the Lean Blow Out (LBO) limit [1,2], enhance flame ignition [3,4], and control thermo-acoustic instabilities [5,6]. Successful demonstrations have been made with a wide variety of fuels, including methane and heavier hydrocarbons, hydrogen, and ammonia. The combustion enhancement is due to the chemical, heating, and hydrodynamic effects of plasma. One of the most efficient ways to generate nonequilibrium plasmas for PAC applications is with Nanosecond Repetitively Pulsed (NRP) discharges [7]. However, several studies [8–10] have shown a linear increase in nitrogen oxide (NOx) emissions with the plasma power.

In PAC, NOₓ are produced by thermal effects, mainly via the Zeldovich reactions [11], whose rate constants increase exponentially with the temperature, and by plasma-induced chemical reactions. The mechanisms of NOₓ formation by plasma-induced reactions are not fully established. Still, some reaction pathways have been suggested [12,13] that involve excited electronic states of N or N₂ reacting with O or O₂ to form NO. When applied at high pulse repetition frequencies (tens of kilohertz), NRP spark discharges can generate a cumulative gas heating effect on the order of 1000 K between the electrodes [14]. Hence, the plasma kernel potentially becomes an important source of thermal NOₓ via the Zeldovich reactions. Fig. 1 shows the local temperature increase between the electrodes when starting to apply NRP discharges in a lean flame. Recently, Ref. [15] showed that the main effect of NRP discharges enhancing combustion comes from the chemical effects rather than the heating and hydrodynamic ones. Thus, reducing the temperature in the hot kernel zone by preventing the cumulative heating effect might reduce the Zeldovich NOₓ production without impacting the performance of the plasma on combustion.

<footnote n="1">¹ Ph.D. student.</footnote>

<footnote n="2">² Professor, AIAA Fellow.</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Cumulative heating effect of repetitive discharges between the electrodes in a 2000 K, CH₄/Air-premixed flame [16]. Pulses start at 0 ms and are repeated every 50 µs (i.e., at 20 kHz). An increase of more than 1000 K is observed in the first ten pulses, and a steady-state temperature is reached after about 20 pulses (1 ms). P<sub>name</sub> = 13.3 kW, φ = 0.8, Inter-electrode gap = 5 mm, Energy per pulse = 1.8 mJ, Pulse frequency = 20 kHz.</figcaption></figure>

A promising way to prevent cumulative heating is to use the properties of a post-discharge hydrodynamic regime observed in Refs. [17,18], shown in Fig. 2, and explained in Refs. [19–21]. Indeed, in specific discharge configurations (gap length, pulse energy), recirculation cells may appear, bringing colder surrounding gases inside the inter-electrode gap and expelling the hot core created by the previous discharge [22]. By continuously replacing hot gases with cooler ones before the subsequent discharge, the cumulative heating effect might be reduced, thus limiting thermal NOₓ production. Our goal in this study is to use the recirculation cells induced by NRP discharges in plasma-assisted flames to limit the thermal NOₓ emissions while providing the same quality of flame stabilization.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** OH PLIF observation of the OH distribution created by a nanosecond discharge in ambient humid air. For a large gap (top), OH and the hot kernel cool down by thermal diffusion after the pulse, while for a short gap (bottom), the kernel is expelled outwards and is replaced by fresh ambient gas.</figcaption></figure>

## II. Experimental setup and diagnostics

All experiments presented here were conducted with the Mini-PAC burner, the same facility as in Ref. [23]. Mini-PAC is a laboratory-scale, bluff-body-stabilized, methane/air, premixed burner at atmospheric pressure. A schematic of the burner is shown in Fig. 3. The premixed gases are injected through a Macor tube of 16-mm in internal diameter in which the bluff-body is inserted. The bluff-body is a 10-mm diameter stainless steel cylinder that creates a recirculation zone downstream where combustion reactions preferentially occur. The flow rates of
air and methane are controlled using mass flow controllers (Bronkhorst EL-FLOW F-203AV-M50-RAD-44-V for air and Bronkhorst EL-FLOW F-201AV-50K-RAD-33-V for methane). The air injected in the burner is dried out and filtered upstream of the flow meter. For the experiments presented in this paper, the air flow rate is set to 16.0 Nm³/h (5.72 g/s) and the methane flow rate to 1.35 Nm³/h (0.27 g/s), giving an equivalence ratio of $\phi = 0.8$ and a theoretical flame power of 13.3 kW, corresponding to the reference condition defined in Ref. [23].

The plasma discharges are NRP sparks of duration 10 ns. They are generated using a high-voltage pulse generator (FID Technology model FPG 10-30NM10). Voltage and current traces are measured using a Lecroy PPE 20kV probe and a Pearson current monitor model 6585, respectively. The probes are connected to an oscilloscope (Teledyne Lecroy HDO 6104) and allow the control of the deposited energy in the inter-electrode gap. In this study, the pulses are applied at a constant Pulse Repetition Frequency (PRF) of 20 kHz, and the deposited energy per pulse ranges up to 5 mJ. Thus, the plasma average power can reach 100 W, and the ratio between the plasma electrical power and the flame thermal power is below 1%. A grounded tungsten cathode with a diameter of 1 mm and a height of 2 mm is embedded on top of the bluff-body. The anode is a 1-mm-diameter tungsten rod set on a vertical translation stage to allow for various inter-electrode gaps.

<figure><img src="image_4.png" /><figcaption>Fig. 3 Mini-PAC schematic with a close-up view of the recirculation zone where the flame anchors and NRP discharges are applied.</figcaption></figure>

Gas analysis is performed using an ECOM J2KN that continuously monitors $O_2$, unburnt hydrocarbons, CO, $H_2$, and $NO_x$ concentrations. A probe collects a fraction of the burnt gases and feeds them into the gas analyzer, where the water vapor is condensed, and the dried gases are fed into electrochemical cells. Therefore, the measurements are volumetric concentrations in the dried gases, denoted as %vd or ppmvd.

The experimental setups for optical diagnostics are presented in Fig. 4. The OH PLIF setup used to image the recirculation cells consists of a 10-ns, 10-Hz pulsed Nd:YAG Continuum Precision laser pumping a dye laser. The second harmonic of the Nd:YAG at 532 nm pumps Rhodamine 590 to produce a 563 nm laser beam. The output beam of the dye laser is doubled at 281.4 nm to excite the $R_1(9)$ line of the $X^2\Pi \rightarrow A^2\Sigma^+$ (0,1) vibrational band of OH. We measure a beam energy of 27 ± 3 mJ per pulse using an Ophir Nova II power meter. The laser-induced fluorescence is then collected using a Princeton Instruments PI-MAX 2 ICCD camera with a 310 nm bandpass filter of FWHM 10 nm (Asahi Spectra ZBPA310). The laser beam is shaped to form a 0.5 mm x 8 mm laser sheet using a UVFS cylindrical lens (Thorlabs LK4385RM, $f = -75.0$ mm) and a UVFS spherical lens of focal length $f = 150$ mm.

For optical emission spectroscopy (OES), two off-axis parabola mirrors (reflective focal length of 250 mm on the Mini-PAC side and 200 mm on the spectrometer side) collect the light from the discharge and send it onto the entrance slit of a spectrometer (Teledyne Princeton Instruments SpectraPro HRS-500-MS) in Czerny-Turner configuration. The slit width is 150 µm. The light is diffracted on a 1200 gr/mm grating, blazed at 300 nm, and collected on an ICCD camera (Teledyne Princeton Instruments PI-MAX 3) with a 3 ns gate width. Experimental spectra of the $N_2$ C-B (0,2) and (1,3) vibrational bands are fitted using the radiative code Specair [24] to determine the temperature of the gas using the relation given in Ref. [25] between the rotational temperature of $N_2(C^3\Pi_u)$ and the gas temperature.

A pulse delay generator (Berkeley Nucleonics Corporation model 575) synchronizes all devices with sub-nanosecond precision.
<figure><img src="image_5.png" /><figcaption>Fig. 4 Experimental setup for (left) OH PLIF and (right) optical emission spectroscopy.</figcaption></figure>

### III. Results

#### A. Imaging of post-discharge recirculation cells using OH PLIF

Recirculation cells induced by nanosecond discharges were previously observed in ambient air with single-shot discharges [21]. In this study, we observed these recirculation cells in the 13-kW methane-air flame of the Mini-PAC burner. An example obtained with pulses of energy 3 mJ applied at 10 Hz across a 2-mm gap is shown in Fig. 5.

<figure><img src="image_6.png" /><figcaption>Fig. 5 OH PLIF imaging of post-discharge recirculation cells in a plasma-assisted methane-air flame. The laser sheet is slightly offset in depth from the electrodes to avoid laser reflections. P<sub>flame</sub> = 13.3 kW, φ = 0.8, PRF = 10 Hz (quasi single pulse), gap = 2 mm, Energy per pulse = 3 mJ.</figcaption></figure>

#### B. Inter-electrode translational temperature measurements

To investigate the effect of the deposited energy and the inter-electrode gap on the cumulative heating effect through the possible presence of recirculation cells, we perform a parametric study of the rotational temperature profile along the inter-electrode gap. Gaps of 1 and 5 mm are studied with a discharge energy ranging from 0 to 5 mJ.

We measure the emission spectra during the first three nanoseconds of the discharge, and we fit with Specair the spectra emitted in a region of height 250 µm in the middle of the gap. An example of such spectrum and fit is given in Fig. 6.
<figure><img src="image_7.png" /><figcaption>**Fig. 6** Emission spectrum of the first three ns of the plasma discharge. Focus on the center of the discharge. Experimental spectrum of N₂ C-B (top left). Fit of the rotational temperature using Specair (top right). Zoom on the (1,3) vibrational band (bottom left). Zoom on the (0,2) vibrational band (bottom right). The vibrational population is not at equilibrium in these conditions, hence the spectrum-fit error for the (2,4), (3,5), and (4,6) bands. The vibrational temperature has been chosen to fit the (0,2) and (1,3) bands.</figcaption></figure>

Fig. 7 presents the parametric study on the rotational temperature for steady-state conditions. For 5 mm, temperature increases above 3000 K between the electrodes, while the temperature remains below 2500 K for any pulse energy conditions when the gap is set to 1 mm. Since the adiabatic methane-air flame temperature at $\phi = 0.8$ is about 2000 K, the temperature increase in the gap is less than 500 K, much lower than the gas temperature increase of 1500 K measured for the 5-mm gap with the same pulse energy.

Fig. 8 illustrates the temporal establishment of the cumulative heating effect for different gap conditions but for the same plasma energy when starting from a non-assisted flame and switching the plasma on at $t = 0$ ms. With a 5 mm gap, conditions correspond to the one from Fig. 1 and accurately reproduce the temperature increase of 1500 K. With a 1-mm gap, we also observe a temperature increase pulse to pulse, but it stabilizes faster and at a much lower temperature, only 250 K above the adiabatic flame temperature. Steady-state measurements in the graph would correspond to conditions presented in Fig. 7.

Thus, by changing the gap length, we decrease the inter-electrode temperature by more than 1000 K. This result suggests that the NOₓ production via the thermal pathways is likely to be reduced in the 1-mm gap case compared to the 5-mm gap case.
<figure><img src="image_8.png" /><figcaption>Fig. 7 Rotational temperature at the center of the discharge as a function of the deposited energy for two inter-electrode gap lengths. P<sub>flame</sub> = 13.3 kW, φ = 0.8, PRF = 20 kHz.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8 Temporal evolution of the gas temperature at the center of the inter-electrode gap measured by OES in a lean flame for two gap distances. Pulses start at t = 0 ms and are repeated at 20 kHz. Steady-state measurement is added to represent long timescales. P<sub>th</sub> = 13.3 kW, φ = 0.8, PRF = 20 kHz.</figcaption></figure>

### C. NOₓ emissions of the plasma-assisted flame

Along with the parametric study on temperature, we measure the NOₓ emissions of the plasma-assisted flame for the two gap distance conditions and for the same energy per pulse as in the previous section. The results are shown in Fig. 9. Without plasma, the NOₓ emissions of the flame are about 8 ppmvd. With plasma assistance, the NOₓ emissions increase linearly with the energy per pulse (or plasma power), and the slope of the increase is independent of the gap distance up to an energy per pulse of about 1-2 mJ/pulse. Above this energy threshold, we observe an interesting behavior: a break in slope, which depends on the gap distance. The NOₓ emissions increase more slowly than at low energies. The smaller the gap distance, the smaller the slope. This observation contrasts with previous studies where the NOₓ production was always shown to increase linearly with the pulse energy [26–28]. This is mainly because previous studies were performed at large gaps, where the slope break is less noticeable.

Finally, we compare NOₓ concentration and temperature evolution with energy. With a 1-mm gap, even though the rotational temperature, thus the gas temperature, is constant with energies above 2 mJ (see Fig. 7), the NOₓ emissions still increase with the discharge energy (see Fig. 9). This behavior illustrates that, apart from the plasma-related Zeldovich mechanism, other mechanisms become predominant in these conditions.
<figure><img src="image_10.png" /><figcaption>Fig. 9 Variation of NOₓ emissions in a plasma-assisted flame as a function of the deposited pulse energy for different inter-electrode gaps. The solid black line represents the linear, gap-independent variation of the NOₓ emissions for small energies per pulse. Pflame = 13.3 kW, φ = 0.8, PRF = 20 kHz.</figcaption></figure>

## IV. Conclusions

Enhancing the hydrodynamic recirculation induced by NRP discharges is proposed to reduce the cumulative heating effect caused by plasma discharges in flames. This would be useful in limiting the formation of NOₓ via the thermal Zeldovich reactions.

For the first time in our knowledge, using OH PLIF imaging, we evidenced recirculation cells induced by the hydrodynamics of the discharge in a flame. These recirculation cells were observed for low interelectrode gap distances below 2 mm. We also measured the gas temperature in the electrode gap as a function of the gap distance for the same energy deposited per pulse. The gas temperature increase produced by a train of nanosecond pulses through cumulative heating is found to be smaller when the gap distance is low. We also showed that NOₓ emissions increase linearly with the plasma power at all gap distances for an energy per pulse less than 1-2 mJ. However, above these values, the NOₓ emissions increase much less with the pulse energy for the small gap distances. This observation, along with the measured temperature dependence on the pulse energy, suggests that one way to limit the NOₓ emissions of NRP discharges is to operate in regimes where hydrodynamic recirculation entrains fresh gases into the discharge gap, thus limiting the formation of NOₓ via the Zeldovich processes. To fully understand this behavior, an extensive kinetic study must be performed to better compare the relative production of NOₓ via the thermal Zeldovich reactions and the dissociative quenching reactions.

## Acknowledgments

This work is part of the GREENBLUE project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 101021538). The authors thank Erika Jean-Bart, Yannick Le Teno, Jérôme Bonnety, Koro Sokhona, and Hubert Jubeau for their technical support on the Mini-PAC burner.

The authors have applied a CC-BY public copyright license to the present document, which will be applied to all subsequent versions up to the Author Accepted Manuscript arising from this submission, in accordance with the grant's open access conditions.

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