# Design of a plasma-assisted injector: Principle, characterization and application to supersonic combustion of hydrogen

Axel Vincent, Nathan Mallart Martinez, Julien Labaune

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Axel Vincent, Nathan Mallart Martinez, Julien Labaune. Design of a plasma-assisted injector: Principle, characterization and application to supersonic combustion of hydrogen. International Journal of Hydrogen Energy, 2024, 88, pp.1410-1421. 10.1016/j.ijhydene.2024.09.214. hal-04752569

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# Design of a plasma-assisted injector: Principle, characterization and application to supersonic combustion of hydrogen

Axel Vincent-Randonnier<sup>a,b,*</sup>, Nathan Mallart-Martinez<sup>a</sup>, Julien Labaune<sup>a</sup>

## ARTICLE INFO

Handling Editor: Dr M Djukic

### Keywords:

Plasma assisted combustion

Quasi-DC discharge

Supersonic combustion

Hydrogen

Injection

Jet in crossflow

## ABSTRACT

A new design of plasma-assisted injector to ignite or stabilize combustion is presented. This design is intended to produce discharges that penetrate the combustion chamber instead of staying at the wall. This plasma-assisted injector, simple and robust, allows compact designs for a weakly intrusive implementation in engines, and is compatible with either air or fuel, depending on the process or application. A prototype was manufactured, implemented and tested with quasi-DC discharges on the LAPCAT2 Dual Mode Ramjet combustor at LAERTE facility in ONERA. Combustion tests showed earlier ignition and increased pressure when the plasma was turned on with a measured plasma power of 1.4 kW.

## 1. Introduction

Air-breathing engines require stable combustion to be operated safely and efficiently, and their design is a trade-off between multiple parameters. Increasing performance or reducing the emission of greenhouse gases (CO₂, H₂O), pollutant species (NO, NO₂, CO, Volatile Organic Compounds) and soot particles can therefore impact high altitude relight capabilities or lead to the rise of combustion instabilities. In this context, the plasma assistance is a promising technique to stabilize combustion or improve ignition. Many experimental and numerical investigations dealing with the effects of plasmas on subsonic [1–9] or supersonic [10–14] combustion can be found in the literature.

In the case of jet-engines extinction at cruise altitude, the pressure and temperature in the combustion chamber fall dramatically with ambient pressure and temperature around 25 kPa and 220 K respectively. At the same time, the kinematic viscosity of kerosene strongly increases, resulting in a deteriorated spraying and thus lowered ignition efficiency. Ignition is generally achieved by using flush mounted spark igniters. The energy of a spark (a few joules) is deposited at the vicinity of the wall in about 100 µs at a repetition rate of a few hertz. Higher frequency or continuous discharges penetrating in the chamber could likely improve ignition efficiency.

In the case of high-speed air-breathing propulsion [15,16], specific combustion regimes such as transition from ramjet to scramjet modes

around Mach = 5 to 6 can also be prone to extinction phenomena. In particular, flow acceleration from subsonic to supersonic speed in the combustor leads to a significant decrease of the static temperature (below 1000 K) and the air/fuel mixing efficiency. As mixing is challenging in high-speed flows, considerable efforts are made to address this issue by using passive or active techniques [17,18]. Among passive techniques, the most common means of stabilization consists in introducing cavities [19–25], struts [26–28], or hypermixer struts [29,30] in the combustor to generate recirculation regions in their wake. In these regions, the flow generally slows to the subsonic regime, drastically increasing the static temperature and residence time, and therefore improving combustion at the cost of increased drag. Many experiments or numerical simulations also investigated the role of the shape and/or the arrangement of the injection orifices to improve mixing and combustion [20,31,32]. In the case of plasma assistance, combustion may be stabilized [33–35] while preventing the unneeded drag.

In the European project STRATOFLY, plasma assisted combustion was investigated as a way to extend the altitude of hypersonic flight, thereby reducing the environmental footprint of stratospheric emission of water (the photochemical lifetime of water is reduced by a factor of 3 between altitudes of 30,000 m and 35,000 m [36]).

The aim of this study is to apply plasma assistance to supersonic combustion in order to extend the operating range of hydrogen-fueled scramjet propulsion for high-speed and long-range civil transportation [37]. Plasma assistance was chosen for its ability to improve mixing,

<footnote><sup>a</sup> ONERA, Multi-physics Department for Energy, Palaiseau, France</footnote>

<footnote><sup>b</sup> ONERA, Multi-physics Department for Energy, Toulouse, France</footnote>

<footnote>* Corresponding author. ONERA, Multi-physics Department for Energy, Palaiseau, France.</footnote>

<footnote>E-mail address: axel.vincent@onera.fr (A. Vincent-Randonnier).</footnote>
**Nomenclature**

**Quantities**

d inter-electrodes distance (gap)

E electric field

I current

J jet-to-crossflow momentum flux ratio

L streamwise length of the discharge

ṁ mass flow rate

Mach Mach number

p pressure

P power

R resistance

t<sub>run</sub> test run time

T temperature

U voltage

γ<sub>SE</sub> secondary electron emission coefficient

Φ equivalence ratio

**Subscripts**

0 total conditions

air air

air* vitiated air

inj injector

S static conditions

**Acronyms**

DC Direct Current

DMScr Dual Mode Scramjet

HV High Voltage

NRPD Nanosecond Repetitive Pulsed Discharges

stabilize or enable combustion while minimizing the induced drag when compared with passive techniques such as struts or cavities. The selected approach consists in coupling the plasma assistance with a classical transverse injection of fuel in a supersonic crossflow of hot air [38,39]. For this setup, a dedicated module was designed to be flush-mounted to the wall of the LAPCAT2 combustor at the LAERTE facility (ONERA – Palaiseau center). Contrary to the design proposed by Bianchi et al. [40] where DC arc discharges are used to control supersonic flows, the module described in the present study do not contain protruding parts prone to induce shocks in the supersonic flow. The present design generates quasi-DC discharges [41,42] (similar to gliding arcs discharge [43–46]) and offers improvements to a former plasma module tested at ONERA [14] by moving the dielectric material far from the hot parts of the combustor. The main advantages are a gain of compactness at the injection side of the module and the possibility to use cheaper, easier to machine and less fragile dielectric materials than ceramics, even for “long” lasting tests.

## 2. Principle of the coaxial plasma-assisted injector

This new design of a plasma-assisted injection module is based on a coaxial configuration of the electrodes (Fig. 1a). The body of the nozzle-shaped injector is metallic and connected to the ground. Along its centerline, a high-voltage rod electrode is mounted, and the tip of the rod is located at the exit of the nozzle, as shown in Fig. 1a. The setup has been designed to place the shortest inter-electrodes distance at the exit

of the injector’s nozzle. When pressurizing the injector with air or fuel, the flow accelerates and pressure decreases along the converging section of the nozzle. As a result, and in accordance with Paschen’s law [47,48], the breakdown voltage will be minimal at the nozzle outlet: discharges only start at this point, which prevents breakdown inside the injector. An example of an HV and ground electrodes arrangement is shown in Fig. 1b, and the related profiles of Mach number, static pressure and breakdown voltage in air or hydrogen along the nozzle are shown in Fig. 1c.

Breakdown voltage was calculated from Equation (1) [49] for a fluid inlet temperature of 290 K. The constant C was added to consider the non-plane-to-plane geometry of the electrodes.

$$U_b = C \cdot \frac{B \cdot p \cdot d}{\ln(A \cdot p \cdot d) - \ln\left[\ln\left(1 + \frac{1}{\gamma_{SE}}\right)\right]} \quad \text{Equation 1}$$

where $U_b$ is the breakdown voltage in volts, $p$ is the pressure in MPa, $d$ is the gap distance in meters, $γ_{SE}$ is the secondary-electron-emission coefficient ($γ_{SE}$ for electrodes made of stainless steel was estimated from Ref. [50]), A is the saturation ionization in the gas at a particular $E/p$ (electric field/pressure), and B is related to the excitation and ionization energies. The A and B values for air and hydrogen are indicated in Table 1.

Fig. 1c shows that breakdown voltage is minimal at the exit of the nozzle, and its value in air (solid orange line) is more than twice the

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Schematic cross view of the plasma injector (a), dimensions (b) and Mach number, pressure and breakdown voltage profiles along the choked nozzle with $p_0$ = 0.61 MPa (c).</figcaption></figure>
<table><caption>**Table 1**
Values of A and B constants used in Equation (1).</caption><thead><tr><th>Gas</th><th>A (MPa<sup>-1</sup>·m<sup>-1</sup>)</th><th>B (V·MPa<sup>-1</sup>·m<sup>-1</sup>)</th><th>Range of E/p<br>(V·MPa<sup>-1</sup>·m<sup>-1</sup>)</th><th>Ref.</th></tr></thead><tbody><tr><td>Air</td><td>1.125E+07</td><td>2.738E+08</td><td>4.500E+07</td><td>[51]</td></tr><tr><td>H<sub>2</sub></td><td>3.600E+06</td><td>1.020E+08</td><td>1.125E+07</td><td>[49]</td></tr></tbody></table>

value found in hydrogen (dashed orange line). As the radius of curvature of the high voltage electrode is small, the reduced electric field will be higher than for plane-to-plane electrodes thus leading Equation (1), which applies to plane-to-plane geometries, to overestimate the actual breakdown voltage.

For long-lasting discharges (like DC-discharges) in high-speed flows, the hot filament is convected, extending as a U-shaped plasma channel outside of the inter-electrode area to penetrate inside the combustor. The present design seeks to harness this effect. The maximum length of the discharge filament thus depends on the applied current as discharge lengthening increases both its electrical resistance and cooling by the fresh gas blowing on it.

The current study will focus on experiments achieved with this new design of plasma-injector for combustion application with the DC generated discharges. The application of Nanosecond Repetitive Pulsed Discharges will not be addressed, although similar behavior (i.e. extension of the plasma discharges into the combustor) was observed at high repetition rate (i.e. at least tens of kHz).

# 3. Experimental setup

## 3.1. The LAERTE facility

The LAERTE facility is used to feed the LAPCAT2 Dual Mode Scramjet (DMScr) combustor [14,52,53] with hot vitiated-air (heating by H₂/air combustion and O₂ replenishment to maintain O₂ molar fraction to 0.21). Total temperature ($T_0$) and pressure ($p_0$) can reach up to 1800–1900 K and 1.0–1.2 MPa, respectively. They are measured in a 105 mm inner diameter pipe 220 mm upstream from the throat of the LAPCAT2 de Laval nozzle. Although measured at the wall, pressure is assumed to equal the total pressure as the local Mach number is 0.054 ($p_s/p_0 = 0.998$). The total temperature is calculated from measurements at different radial positions in the pipe (one at the center, the second one at $r = 0.5 R_{pipe}$ and the last one at $r = 0.75 R_{pipe}$), based on the assumption of a parabolic temperature profile across the pipe diameter [53]. This non-uniform temperature profile influences the ignition delay, depending on whether the fuel is injected at the wall (local air temperature below the average value of $T_0$) or in the centerline of the air flow (local air temperature over the average value of $T_0$).

Embedded instrumentation includes static pressure measurements along the combustor, with up to 128 wall pressure transducers scanned at 10 Hz. The sensors are calibrated before each test campaign, according to ONERA's quality procedures (ISO 9001 certification). A computer-based system controls the reproducibility and the stability of the operating conditions.

The outlet of the combustor is connected to a 400 mm diameter exhaust pipe where the pressure is around 0.1 MPa (ambient pressure).

## 3.2. The LAPCAT2 combustor

The combustor inlet is connected to the hot air supply line of the LAERTE facility by a round-to-rectangular cross-section transformation duct followed by a Mach = 2 de Laval nozzle (rectangular cross-section). The LAPCAT2 combustor can be used to investigate supersonic combustion of gaseous [53] or liquid fuels [52]. This combustor consists of four flanged sections: the first one (55 mm < $x_1$ < 280 mm) has a constant cross-section, while the following sections (280 mm < $x_2$ < 598 mm < $x_3$ < 952 mm < $x_4$ < 1257 mm) have respectively 1°, 3° and 1°

diverging half angles to prevent/stunt thermal choking. The reference position ($x = 0$ mm) corresponds to the throat of the de Laval nozzle. The combustor width is constant (40 mm) and inlet height is 35.4 mm. Due to the 0.1 MPa back pressure in the exhaust pipe, the combustor is over-expanded for total pressure below 0.9 MPa: the boundary layer detaches in the combustor at a position depending on the total pressure. In the test conditions of this study ($p_0 = 0.4$ MPa), the flow separation from the walls occurs around $x = 750–850$ mm.

Fuel is injected at $x = 200$ mm (upper wall at $y = 17.7$ mm) by a flush-mounted injector.

Large fused silica windows placed at the locations shown in Fig. 2d allow visualization and optical diagnostics. The combustion chamber is made of a copper alloy. The inner walls are coated with a 0.3 mm thick YSZ (Yttria-Stabilized Zirconia) thermal barrier.

As the combustor is not water cooled, the overall duration of a combustion test run is limited to approximately 1 min but the useful duration, i.e. at the required temperature, lasts between 5 s and 15 s, depending on the test conditions. Up to 20 runs can be achieved during a test session.

## 3.3. Plasma-assisted injector

A prototype of the plasma/injection module was manufactured for proof of concept. Compared to the former module [14] that generated a surface discharge that was mainly manufactured from a large and expensive block of ceramic, the new module is much simpler, compact and robust using FR4 (a cheap fiberglass/epoxy resin compound) as its dielectric material. The HV electrode has a diameter of 2 mm and is coaxially placed in the injector's nozzle. The inner diameter of the injector ranges between 8 mm and 3.2 mm (0.6 mm gap at the throat of the nozzle). The injector includes pressure and temperature measurements upstream of the nozzle exit ($y = y_{inj} + 138$ mm), as well as a static pressure port at $x = x_{inj} - 5.5$ mm.

The plasma-assisted injector was implemented on the LAPCAT2 combustor [53] at the LAERTE facility (ONERA – Palaiseau Center), by being flush-mounted to the combustor's upper wall. Fig. 2 presents a diagram of the test sequence, the corresponding systems on the schematic of the facility, and a photograph of this setup.

## 3.4. Electrical setup and measurements

The plasma/injection module is powered by a –5 kV and 3.4 A DC power supply set to “current regulation” mode, the output of the generator being stabilized by a 1430 Ω ballast resistor (Fig. 3). The HV output is in the negative polarity.

Electric measurements were recorded using a Tektronix P6015A high voltage probe to measure U2 and a Lecroy PPE20kV high voltage probe to measure U1 (1000:1 attenuation for both probes). The signal is recorded by a fast digital oscilloscope (LeCroy 6050–1 GHz bandwidth, 4 channels, 12.5 Msamples/channel), instantaneous and averaged estimate of the electrical power being obtained by post-processing these measurements.

Current I(t) and power P(t) applied to the discharges were calculated according to $(U2(t)-U1(t))/R$ and $U1(t)·(U2(t)-U1(t))/R$ relations respectively.

## 3.5. High-speed schlieren and discharge imaging

High-speed imaging of the discharge and flow structure were recorded using a Vision Research Phantom V711 camera. The framerate ranged from 26 kfps to 390 kfps, depending on the size of the images (between 800 × 256 pixels and 128 × 64 pixels respectively). The images resolution is around 0.16 mm·px⁻¹.

The Schlieren setup (Fig. 4) consists in a light source (300 W xenon arc lamp Oriel Xe,OF Model 6258), a diaphragm to make the light source punctual (300 mm away from the lamp condenser), two Clairaut
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Main characteristics of the LAERTE facility equipped with the LAPCAT2 combustor: time sequence of a test (a) and related items on the schematic of the facility (b), 3D view and photograph of the combustor with the plasma-assisted injector (c) and geometry of the combustor showing the position of pressure ports and side windows (d).</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Principle layout of the electrical circuit (U1 and U2 correspond to high-voltage measurement probes).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Schematic of the Schlieren setup implemented in the LAERTE facility.</figcaption></figure>
objectives (diameter = 120 mm; focal length = 800 mm), a knife-edge, and the high speed camera equipped with a Nikon 80–200 mm f/4 zoom.

# 4. Experimental results

The operating conditions corresponding to the tests achieved in this study are summarized in Table 2.

## 4.1. Discharges characterization

### 4.1.1. Discharges in air jet without crossflow

A first set of experiments was achieved for a sonic injection of air ($p_{inj}$ = 0.61 MPa, related air mass flow around $7.4 \text{ g s}^{-1}$) without crossflow to characterize the discharges. Two cyclic discharge regimes were identified, depending on the applied current: Fig. 5a for a 0.65 A setting and Fig. 5b for a 1.7 A setting. These figures show schematics of the related mechanisms (upper line) and electrical measurements with global (center line) and zoomed (lower line) views. The numbering of the different steps of the mechanisms appear at the corresponding place in the underneath measurement graphs.

With the current regulation set to 0.65 A (Fig. 5a), the behavior can be described and explained as follow. Before $t = 0$ s, no power is applied to the gas (air) flowing through the injector (i.e. in the gap between HV and ground electrodes). At $t = 0$ s, the power is switched on and the applied voltage gradually decreases, generating a growing electric field between the electrodes. At low voltage the dielectric properties of air electrically insulate the gap between the HV electrode and the grounded metallic body of the injector: $I = 0$. When the electric field reaches breakdown conditions ($t = 0.0316$ s, $U1 = -4.86$ kV; Fig. 5a-marker #1), a filamentary discharge establishes in the gap between the tip of the HV electrode and the edge of the injector’s outlet (i.e. the throat of the nozzle), connecting them by a conductive plasma channel. The resulting short-circuit leads to the abrupt drop of $U1$. At the same time, the current increases over 3 A. As this value exceeds the required setting (0.65 A), the power generator starts regulating and the current gradually decreases (Fig. 5a-marker #2). Simultaneously, the arc discharge is subject to the convection of the gas flowing in the injector, thus convecting the

hot species generated by the plasma. While each extremity of the discharge remains anchored to an electrode (one on the cathode and one on the anode), the filament takes a U-shape and expands in the direction of the flow. Since arc discharges are resistive, their resistance increases with their length. When below 1 A (i.e. over the current regulation setting of 0.65 A), the excessive resistance of the discharge combined with the –5 kV limit of the generator do not allow the discharge to be sustained by the current anymore: the discharge extinguishes (Fig. 5a-marker #3) and the insulating properties of air are recovered. The voltage can decrease again (Fig. 5a-marker #4) to generate a new discharge. For these operating conditions, average current and power are 0.62 A and 0.60 kW respectively. A discharge cycle lasts between 11 ms (1st cycle) and 3 ms ($t > 0.42$ s). At the same time, the absolute value of the breakdown voltage gradually decreases from 4.86 kV (first breakdown event) to 3.35 kV, probably due to the electrodes heating.

With the current regulation set to 1.7 A (Fig. 5b), steps #1 and #2 are common with the 0.65 A case. However, the higher current setting allows greater expansion of the discharge. Now, the discharge extends far enough to be 3-dimensionally twisted by the local electro-magnetic field (Fig. 5b-marker #3), and restrike phenomena occur between both legs of the filament (Fig. 5b-marker #4). The new conductive channel is shorter and due to its lower resistance, its geometry allows to by-pass the downstream part of the discharge which vanishes. The shortened discharge can extend again, starting a new cycle. With these expansion and restrike cycles, the discharge self-sustains without extinction, as visible in Fig. 5b (the current never drops to 0). During plasma application, the voltage mainly varies between –300 V and –1500 V (average voltage, current, and power around –710 V, 1.74 A, and 1.21 kW respectively). The amplitude of variations of $U1(t)$ is large with a standard deviation corresponding to almost 90% of the average value. Two series of images showing the initiation/convection of the discharge by the flow and a restrike event are presented in Fig. 6. The U-shape of the discharge appears when its extension is below 10 mm. At larger extension the discharge takes a more chaotic and likely 3-dimensional shape. These images were recorded at 110,000 frames per second with a Phantom V711 camera (0.16 mm/pixel) during the same run as results in Fig. 5b. On Fig. 6b, at $t_1 + 27$ µs, a restrike event is observed and the

<table><caption>**Table 2**

Operating conditions of the different tests.</caption><thead><tr><th>Test condition</th><th>#1</th><th>#2</th><th>#3</th><th>#4</th><th>#5</th><th>#6</th><th>#7</th><th>#8</th><th>#9</th><th>#10</th></tr></thead><tbody><tr><td>Fluid<br>Mach</td><td></td><td></td><td></td><td></td><td>air</td><td></td><td></td><td>vitiated air</td><td></td><td></td></tr><tr><td>p<sub>o</sub> [MPa]</td><td></td><td></td><td></td><td></td><td>0.389 ± 0.005</td><td></td><td>2</td><td>0.414 ± 0.002</td><td></td><td>0.410</td></tr><tr><td>T<sub>o</sub> [K]</td><td></td><td></td><td></td><td></td><td>266 ± 5</td><td></td><td></td><td>1539 ± 4</td><td></td><td>1490</td></tr><tr><td>m&#775;<sub>air</sub> [g·s<sup>-1</sup>]</td><td></td><td></td><td></td><td></td><td>765 ± 1</td><td></td><td></td><td>253 ± 1</td><td></td><td>254</td></tr><tr><td>m&#775;<sub>O2</sub> [g·s<sup>-1</sup>]</td><td></td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>57.1 ± 0.1</td><td></td><td>57.1</td></tr><tr><td>m&#775;<sub>H2-heaters</sub><br>[g·s<sup>-1</sup>]</td><td></td><td></td><td></td><td></td><td>-</td><td></td><td></td><td>3.03 ± 0.01</td><td></td><td>4.65</td></tr><tr><td>Fluid<br>Mach</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Speed of<br>sound<br>[m·s<sup>-1</sup>]</td><td></td><td></td><td></td><td></td><td>340</td><td></td><td></td><td></td><td>1304</td><td>1292</td></tr><tr><td>p<sub>o-inj</sub> [MPa]</td><td></td><td></td><td></td><td></td><td>0.61</td><td></td><td></td><td></td><td>0.77</td><td>0.62</td></tr><tr><td>T<sub>O-inj</sub> [K]</td><td></td><td></td><td></td><td></td><td>287</td><td></td><td></td><td></td><td>290</td><td>285</td></tr><tr><td>m&#775;<sub>inj</sub> [g·s<sup>-1</sup>]</td><td></td><td></td><td></td><td></td><td>7.43</td><td></td><td></td><td></td><td>2.36</td><td>1.69</td></tr><tr><td>J</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.59</td><td></td><td>2.00</td><td></td></tr><tr><td>Current<br>setting [A]</td><td></td><td>0.65</td><td>1.7</td><td></td><td></td><td></td><td></td><td>1.7</td><td></td><td></td></tr><tr><td>U<sub>breakdown</sub><br>[kV]</td><td></td><td>-4.86</td><td>-5.21</td><td></td><td>-4.15</td><td>-4.56 ± 0.1</td><td></td><td>-3.16 ± 0.2</td><td></td><td>-3.72</td></tr><tr><td>U<sub>avg</sub> [kV]</td><td></td><td>-2.68</td><td>-1.04</td><td></td><td>-0.39</td><td>-0.42 ± 0.01</td><td></td><td>-0.87 ± 0.05</td><td></td><td>-0.80</td></tr><tr><td>I<sub>avg</sub> [A]</td><td></td><td>0.51</td><td>1.62</td><td></td><td>1.75</td><td>1.75 ± 0.01</td><td></td><td>1.76 ± 0.01</td><td></td><td>-1.78</td></tr><tr><td>P [kW]</td><td></td><td>1.36</td><td>1.69</td><td></td><td>0.69</td><td>0.75 ± 0.01</td><td></td><td>1.53 ± 0.09</td><td></td><td>1.41</td></tr><tr><td>Diagnostics</td><td>Schlieren<br>imaging</td><td></td><td>Schlieren<br>imaging</td><td>Discharge<br>imaging</td><td>Schlieren<br>imaging</td><td>Discharge<br>imaging</td><td>Schlieren<br>imaging</td><td>Discharge<br>imaging</td><td>Discharge<br>imaging</td><td>Schlieren<br>imaging</td><td></td></tr><tr><td>Diag. Framerate [fps]</td><td>25,885</td><td></td><td>25,885</td><td>110,000</td><td>150,000</td><td>150,000</td><td>390,000</td><td>390,000</td><td>390,000</td><td></td></tr><tr><td>Image size [px]</td><td>800 × 256</td><td></td><td>800 × 256</td><td>128 × 256</td><td>256 × 128</td><td>256 × 128</td><td>128 × 64</td><td>128 × 64</td><td>128 × 64</td><td></td></tr></tbody></table>
<figure><img src="image_8.png" /><figcaption>Fig. 5. Discharge evolution cycles in an air jet ($p_{inj}$ = 0.61 MPa) without cross-flow for current setting at $I$ = 0.65 A (a) and $I$ = 1.7 A (b): schematic sequence (top), global electrical measurements (center), and zoomed electrical measurements (bottom).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 6. Imaging at 110 kHz showing the initiation of the discharge followed by the extension of its U-shape (a) and a restrike event at $t_I$ + 27 µs (b).</figcaption></figure>
bypassed part of the discharge filament vanishes. Bourlet et al. presented numerical simulations of such a restrike mechanism applied to gliding DC arcs [54] or to the current experiments [55]. These non-reactive simulations are based on the coupling of the ONERA in-house CFD code CEDRE [56] with the MHD code TARANIS that includes a dedicated model for streamer discharges propagation. In Ref. [55], a new discharge takes the U-shape and reaches a 10–12 mm extension in about 25 µs thus satisfactorily agreeing with experiments (Fig. 6a). When the streamwise length of the discharge exceeds 10 mm, the furthest section of the filament also highlights a stronger stretching/twisting.

The streamwise length of the discharge (L) was estimated by applying a Python algorithm to a series of images. Based on this set of data, Fig. 7 presents the variations of L and the related PDFs (Probability Density Functions). The average value of L is around 12 mm with a maximal extension of 29 mm and a standard deviation of 3.4 mm. Additionally, the normalized PDF is non-Gaussian.

Based on this set of data and literature (numerical simulations from Bourlet et al. [55] or experimental work from Leonov et al. [57] and Efimov et al. [58]), the shape of the discharges can reasonably be assumed to be 3-dimensional (instead of only 2-dimensional), and cannot be considered as fully representative of the true length of the discharge. In all cases, crossing $U1(t)$ measurements with L estimated with the Python algorithm highlights the correlation between these parameters, as can be seen in the lower part of Fig. 7.

Schlieren and discharge imaging were achieved with the same operating conditions during two successive test runs to characterize the flow/plasma interaction (Fig. 8). From left to right, we can see.

* single-shot Schlieren images,

* averaged Schlieren images,

* an average image of the discharge,

* a stack of the average Schlieren image with a colored version of the average image of the discharge.

The single-shot Schlieren images show the strong influence of the plasma discharge on the flow pattern and the significant increase of the turbulence around the air jet. These flow phenomena probably promote the mixing of the jet flow with the surrounding fluid (static air in the present case). Additionally, diamond-like shock patterns can be observed on averaged Schlieren images, with or without plasma. The asymmetry and the non-verticality of the air jet is probably due to a misalignment of the HV electrode in the nozzle.

The right half of the discharge filament (ground electrode side) appears fuzzier than the left half (HV electrode side). Contrary to the HV electrode, the rim of the nozzle enables the mobility of the discharge anchoring point, thus blurring the related filament. The bright spot of light visible at its base is due to the intense heating of the metal by the arc discharge.

### 4.1.2. Discharges in air jet with a supersonic crossflow of hot air

A second set of experiments was achieved by adding a Mach = 2 crossflow of hot air ($p_0$ = 0.4 MPa, $T_0$ = 1541 K) to the test conditions of section 4.1.1. The static pressure of the supersonic crossflow around x = 200 mm (i.e. the position of the fuel injector) is about 0.06 MPa. Schlieren and discharge imaging were recorded during two successive test runs with the same operating conditions (Fig. 9). The discharge is significantly shortened and curved to follow the streamline of the air jet interacting with the supersonic crossflow.

Transverse jet injected in a supersonic crossflow is a fundamental canonical flow topology which was extensively investigated [59–62]. It presents 3D-flow patterns including separation and recirculation regions. For an underexpanded sonic injection, the typical structure observed in the wake of the injection orifice is a barrel shock which ends with a Mach disk (Fig. 10-left). The impact of the supersonic crossflow on this fluid obstacle creates a large structure named “bow-shock” (Fig. 10-left and right). The interaction of the supersonic crossflow with the transverse jet also generates vortical structures surrounding the barrel shock to take the shape of contra-rotating horse-shoe vortices in its wake (not visible in Fig. 10). The presence of a coaxial electrode in the injector significantly modifies the shape of the barrel shock and the Mach disk is no more visible (Fig. 10-right).

According to Schlieren and discharge images stack (Fig. 9), the size and shape of the discharge seems to be driven by the barrel shock. The value of the jet-to-crossflow momentum flux ratio J, which is calculated according to Refs. [52,59], is about 1.59. The corresponding electric measurements show much lower fluctuations of $U1(t)$ (and consequently of the correlated discharge’s length) than in absence of crossflow: the standard deviation of $U1(t)$ here only represents 15% of the average value.

Numerical analogs of the flow and the discharge patterns visible in Fig. 9 can be found in the simulation work from Bourlet et al. [55].

### 4.1.3. Hydrogen injection in a supersonic crossflow of hot air

As this plasma/injection module was primarily designed for

<figure><img src="image_10.png" /><figcaption>Fig. 7. Time-evolution of the streamwise length of the discharge (upper left), related PDF (upper center), and normalized PDF (upper right). Correlation between $U1$ and the streamwise length of the discharge (down).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 8. Characterization of the discharge/flow interaction (the black horizontal stripes are due to dirt deposit on the windows).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 9. Images of the flow (left column), the discharge (central column) and their stack (right column) for an air jet ($p_0$ = 0.611 MPa, $T_0$ = 289 K, $J$ = 1.59) in a supersonic crossflow ($p_0$ = 0.414 MPa, $T_0$ = 1541 K) and related electric measurements.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 10. Comparison of the hydrogen jet pattern highlighting the effect of the electrode wake on the flow: 2 mm injection orifice without electrode (left) and 3.2 mm injection orifice with electrode (right).</figcaption></figure>
combustion and propulsion applications, the present investigation will conclude its characterization with the plasma-assisted injection of hydrogen. In general, the flow structure with hydrogen (Figs. 11 and 12) is very similar to the one with air. Nevertheless, the hydrogen flow penetrates slightly deeper in the combustor. This agrees with the higher value of the jet-to-crossflow flux momentum ratio (J = 2.00). In particular, the higher speed of sound in hydrogen (around 1300 m s⁻¹ instead of 340 m s⁻¹ in air) over-compensates its low molar mass. This higher speed also induces a motion blur that lowers the sharpness of the single-shot schlieren image in hydrogen. A bright spot can be seen at the right-sided discharge anchoring point. In air, the (slightly) brighter spot is at the HV electrode connection point instead. This is probably due to the electronegativity of air and the electropositivity of hydrogen (the effect of the fluid electronegativity/positivity on the discharges electrical measurements is mentioned in Ref. [63]). The breakdown voltage is lower in hydrogen (−3.0 kV) than in air (−4.2 kV). Once the arc regime established, the voltage stabilizes at a higher level in hydrogen (−830 V with a standard deviation of 108 V) than in air (−430 V with a standard deviation of 63 V). The average power is also higher in hydrogen with 1.46 kW instead of 0.68 kW in air.

## 4.2. Application to supersonic combustion

For the combustion tests, the fuel used is pure gaseous hydrogen. The injection orifice is centered at $x = 200$ mm. The supersonic crossflow stabilizes at the required conditions around $t_{run} = 27$ s–28 s while fuel injection starts at $t_{run} = 28$ s and stabilizes at $t_{run} = 29$ s. Fuel injection, air heating and oxygen replenishment are switched off at $t_{run} = 35$ s. Until the run sequence ends (around $t_{run} = 65$ s), cold air flows to cool the combustor. The selected test conditions are close to the self-ignition temperature threshold ($T_0 = 1450–1500$ K at $p_0 = 0.4$ MPa). Hydrogen mass flow is about $1.7 \text{ g s}^{-1}$ and the plasma discharge is activated during 0.88 s at an average power of 1.41 kW. No electromagnetic disturbance of the facility equipment is observed during the tests. The effect of the plasma on combustion is mainly visible in the pressure profile along the combustor (Fig. 13) which shows a pressure rise for $300 \text{ mm} < x < 600 \text{ mm}$ from $t_{run} = 30.2 \text{ s}$ to $t_{run} = 30.9 \text{ s}$, thus demonstrating the ability of penetrating quasi-DC discharge to improve combustion.

Fig. 13 shows the average pressure profiles for fuel-off (black) or fuel-on conditions before (blue), during (red) and after plasma application (green). The colored areas surrounding each curve correspond to the range of measurements fluctuation during the related interval of time. The non-overlapping of the red line/area with the blue or green ones for $300 \text{ mm} < x < 600 \text{ mm}$ indicates that the increase of pressure during the plasma activation is not due to unsteady flow fluctuations. From $x = 600$ mm, the higher divergence of the combustor (3° half-angle instead of 1°) accelerates the flow until the supersonic-to-subsonic transition region is reached (around $x = 780$ mm). When the plasma is on (red curve), the supersonic-to-subsonic transition occurs slightly

later than when plasma is off (blue and green curves), probably due to the higher flow enthalpy and therefore temperature. In particular, a pressure increase induced by a flow detachment in the combustor would have led to an earlier supersonic-to-subsonic transition.

The quasi-overlap of the green and blue curves indicate the stability and accuracy of the flow control and the pressure measurements, as well as the absence of hysteresis with the plasma switching on or off (reversible process). At the injection point ($x = 200$ mm), the shock-induced pressure peak slightly increases during the plasma activation, probably due to the local heating of the flow.

At $x = 240$ mm, the pressure does not vary when the plasma is on, indicating that the penetrating discharge do not induce a downstream detachment of the flow. Combustion starts slightly earlier when the plasma is on ($300 \text{ mm} < x < 350 \text{ mm}$) and is followed by a pressure increase up to $x \approx 600$ mm. Numerical simulations by Dong et al. [5] show a reduction of the ignition distance by plasma induced $O_3$ supplementation.

Images of the supersonic combustion without and with plasma are visible in Fig. 13. These images were extracted from a video recording of a camcorder. The plasma-off image (top) was recorded about 1 s before the plasma on image (bottom). The plasma-on image shows the strong light emission from the discharge at the injection point ($x = 200$ mm) which visibly do not overlap the flame area. The emission of the flame seems slightly brighter and starts earlier when the plasma is on but the brighter background due to the Mie scattering of the plasma emission on the rear wall hinders a quantitative comparison between images.

## 5. Conclusion

This paper presents a new design of a plasma-assisted injector based on the coaxial geometry of a central high-voltage needle electrode surrounded by a grounded metallic nozzle. This injector is relatively simple to manufacture, and robust by not requiring ceramic as a dielectric material (electric insulation can be placed far enough from the hot elements of the combustor to warrant the use of plastics or composites). The present design can also be as compact as usual spark igniters (easy and less intrusive to implement) and when operated with a DC power supply, the electromagnetic emissions are too weak to interfere with the surrounding electronics. The discharges generated with this module penetrate inside the combustor due to the high speed of the fluid injection (air or hydrogen). For an applied current exceeding 1 A, restrike mechanism was identified, which can be described as follows. First, an arc discharge initiates in the gap between electrodes when the growing applied voltage reaches breakdown conditions (i). The fast fluid flow escaping from the injector through this gap curves and blows the discharge, resulting a U-shape discharge (ii). Past a certain length, the discharge is stretched and twisted by the local electromagnetic field, leading to a restrike (with the appearance of a new plasma channel between both legs of the U-shaped filamentary discharge thus by-

<figure><img src="image_14.png" /><figcaption>Fig. 11. Images of the flow (left column), the discharge (central column) and their stack (right column) for a hydrogen jet ($p_0 = 0.760$ MPa, $T_0 = 303$ K, $J = 2.00$) in a supersonic crossflow ($p_0 = 0.413$ MPa, $T_0 = 1538$ K) and related electric measurements.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Fig. 12. Photomontage to compare air vs hydrogen injection, discharges, and flow patterns.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Fig. 13. Pressure profile along the combustor before fuel injection (black line at $t_{run} = 27.8$ s) or at $\Phi = 0.18$ before (blue), during (red) and after (green) plasma activation. Photographs were added with respect to x-axis scale and position, showing the supersonic combustion without plasma (top) and with plasma (bottom). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

passing the downstream part of the discharge) (iii). The shortened discharge is then convected until a new restrike event occurs, starting a new cycle. The fluctuations of the discharge length are strongly correlated with voltage fluctuations as shown by the cross-analysis of electrical measurements and high-speed visualization. When the discharge is produced in the air jet without crossflow, its length can reach 28 mm. In the presence of a supersonic crossflow of air, the discharge propagates in the barrel shock, which controls its shape and maximum extension (around 10 mm).

In the case of the self-ignition of hydrogen injected in a supersonic cross-flow of hot air ($p_0 = 0.4$ MPa; $T_0 = 1490$ K; $\Phi = 0.18$; $P = 1.4$ kW), plasma assistance leads to a slightly earlier ignition (i.e. closer to the injection point) and an increased static pressure 100 mm after injection. At present, the authors do not know if the observed effect is due to the improved mixing, the stimulation of the combustion by the local heating or the production of radicals/excited species by the plasma. Numerical simulations coupling CFD and MHD are in progress to identify and quantify the dominant contributor to the observed effect. We also expect to clarify the plasma/combustion interaction by achieving coupled high-speed Schlieren and OH imaging in the combustion region. These additional tests would enable the accurate measurement/

characterization of the ignition distance, flame dynamics, and size of the boundary layers with and without plasma assistance. Further experiments will also be carried out to investigate plasma assisted staged injection and to find test conditions where supersonic combustion could be triggered by plasma in air below the self-ignition temperature threshold.

**Aknowledgment:** The authors are grateful to Nicolas Fdida for the implementation and the tuning of the Schlieren setup, Jeanne Methel for the improvement of English language, Laurent Jacquin, Head of ONERA's Scientific Directorate of the Fluid Mechanics and Energetics for the funding of design, manufacturing and preliminary tests of the plasma module and the European Union's Horizon 2020 research and innovation program (STRATOFLY project, Grant Agreement No. 769246) for the funding of the supersonic combustion tests.

CRediT authorship contribution statement

**Axel Vincent-Randonnier:** Writing – original draft, Visualization, Validation, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Nathan Mallart-Martinez:** Visualization, Investigation. **Julien Labaune:** Writing – review & editing, Investigation, Formal analysis.
Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Axel Vincent-Randonnier, Nathan Mallart-Martinez and Julien Lab-
aune, authors of the submitted paper entitled “Design of a plasma-
assisted injector: principle, characterization and application to super-
sonic combustion of hydrogen” declare that they do not have identified
conflict of interest.

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