# Numerical study on the impact of Nanosecond Repetitively Pulsed discharges on the lean blowout limit for a hydrogen/air swirled flame

Boris Kruljevic, Stéphane Q.E. Wang, Nicolas Vaysse, Jean-Baptiste Perrin-Terrin, D. Durox, Antoine Renaud, Christophe O Laux, Benoît Fiorina

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Boris Kruljevic, Stéphane Q.E. Wang, Nicolas Vaysse, Jean-Baptiste Perrin-Terrin, D. Durox, et al. Numerical study on the impact of Nanosecond Repetitively Pulsed discharges on the lean blowout limit for a hydrogen/air swirled flame. Combustion and Flame, 2025, 277, pp.114149. 10.1016/j.combustflame.2025.114149. hal-05040022

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Graphical Abstract

Numerical study on the impact of Nanosecond Repetitively Pulsed
discharges on the lean blowout limit for a hydrogen/air swirled
flame

Boris Kruljevic, Stéphane Q.E. Wang, Nicolas Vaysse, Jean-Baptiste Perrin-Terrin, Daniel Durox, Antoine Renaud, Christophe O. Laux, Benoît Fiorina
Highlights

Numerical study on the impact of Nanosecond Repetitively Pulsed
discharges on the lean blowout limit for a hydrogen/air swirled
flame

Boris Kruljevic, Stéphane Q.E. Wang, Nicolas Vaysse, Jean-Baptiste Perrin-Terrin, Daniel Durox, Antoine Renaud, Christophe O. Laux, Benoît Fiorina

* The impact of plasma on the extension of the Lean Blowout (LBO) limit in a hydrogen-air flame is analyzed numerically for the first time.

* The LBO of a plasma-assisted partially-premixed hydrogen-air flame is correctly predicted by a phenomenological model.

* Plasma is able to extend the LBO limit by producing heat and radicals inside the recirculation zone.
Numerical study on the impact of Nanosecond
Repetitively Pulsed discharges on the lean blowout
limit for a hydrogen/air swirled flame

Boris Kruljevic<sup>a,*</sup>, Stéphane Q.E. Wang<sup>a</sup>, Nicolas Vaysse<sup>a</sup>, Jean-Baptiste Perrin-Terrin<sup>a</sup>, Daniel Durox<sup>a</sup>, Antoine Renaud<sup>a</sup>, Christophe O. Laux<sup>a</sup>, Benoît Fiorina<sup>a</sup>

<sup>a</sup>Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C, Gif-sur-Yvette
91190, France

**Abstract**

Plasma-assisted combustion (PAC) using Nanosecond Repetitively Pulsed (NRP) discharges is an efficient method to extend the lean blowout limit of flames, as shown in numerous experiments. In this study, the underlying mechanisms by which NRP discharges extend the lean blowout limit in hydrogen-air flames are analyzed numerically for the first time. The computations are performed using Large Eddy Simulations (LES) coupled with a semi-empirical model for the NRP discharges. The blowout is triggered at constant hydrogen mass flow rate (i.e., constant flame thermal power) through a very slow increase of the injected air mass flow rate, resulting in a decrease of the global equivalence ratio. A PAC configuration featuring NRP discharges at a frequency of 15 kHz and a 1.5 mJ deposited energy per pulse is computed, for which the experiments have shown a 20% reduction of the lean blowout equivalence ratio, by using NRP discharges. The case without

Email address: boris.kruljevic@gmail.com (Boris Kruljevic)

<footnote>*Corresponding author</footnote>
plasma is also computed. These two configurations are first compared in
terms of combustion efficiency. Next, results of blowout simulations are pre-
sented. The LES is able to predict the blowout equivalence ratios accurately
for both the case without plasma (0.9% error) and with the NRP discharges
(2.8% error). In the case without plasma, blowout is triggered through the di-
lution of burnt gases by fresh gases, which penetrated the inner recirculation
zone at sufficiently low global equivalence ratios. Plasma triggers the oxida-
tion of these pockets of fresh gases, resulting in the production of radicals
and heat, which stabilizes the flame.

***Keywords:*** Hydrogen; Plasma-assisted combustion; Blowout; Partially premixed flames.

**Novelty and Significance Statement**

This is the first time that simulations are performed of a plasma-assisted
combustion (PAC) experiment in pure hydrogen flames. Also, for the first
time, a PAC phenomenological model [1] is used to predict the lean blowout
(LBO) limit of a flame assisted by plasma and the results are evaluated
through comparisons with experimental data. The interactions between the
flame and the Nanosecond Repetitively Pulsed (NRP) discharges at the LBO
limit are studied numerically. The NRP discharges promote the oxidation of
pockets of fresh gases, resulting in the production of radicals and heat, which
stabilizes the flame and extends the LBO limit.

**Author Contributions**

* BK performed the LES, analyzed the results, wrote the paper

* SW set up the numerical framework, analyzed the results, edited the
paper

* NV provided experimental data, analyzed the results, edited the paper

* JP provided experimental data, analyzed the results, edited the paper

* DD supervised the research, obtained funding, analyzed the results, edited the paper

* AR supervised the research, obtained funding, edited the paper

* CL supervised the research, obtained funding, edited the paper

* BF analyzed the data, supervised the research, obtained funding, edited the paper

# 1. Introduction

Hydrogen has been gaining increasing attention in recent decades as an alternative to carbon-based fuels. Indeed, the major advantage of hydrogen combustion is the suppression of CO2 emissions, identified as the principal contributor to climate change. However, high temperatures that are characteristic of hydrogen flames may result in significant production of toxic NOx. To mitigate this, modern combustors are operating under increasingly leaner regimes, which can drastically lower the flame temperature. However, lean flames are prone to instabilities and ignition issues. Many strategies have been attempted to address these challenges, such as the use of bluff-bodies, swirlers, backward facing steps and trapped vortex combustors to create re-circulation zones of combustion products, stabilizing the flame. Although
these technologies have been successful in extending the lean blowout limit and ensuring the stabilization of lean flames, increasingly stringent emissions regulations require new approaches to make combustors operate under even leaner conditions and further reduce harmful emissions.

Plasma has been used to promote combustion for a long time, such as in spark ignition. However, sparks correspond to an equilibrium (or thermal) type of plasma, which is characterized by very high gas temperatures (20,000-50,000 K). For steady operation, such as flame stabilization for example, high temperatures may result in significant production of NOx and significant energy losses due to production of acoustic waves and turbulence as a consequence of a fast increase in temperature [2]. The so-called non-equilibrium plasmas constitute an alternative to previous plasma regimes, in which the temperatures of the neutral gas molecules are much lower (300-4,000 K). Amongst the numerous non-equilibrium plasma-assisted combustion (PAC) technologies [3, 4, 5], the Nanosecond Repetitively Pulsed (NRP) discharges [6] have gained popularity due to their high efficiency and ability to control the plasma process, namely promoting either the thermal or the kinetic effect.

Numerous experiments of NRP discharges have been conducted for different purposes. NRP discharges have been successfully applied to improve ignition characteristics [7], to extend the lean blowout (LBO) limit of gaseous [8, 9, 10, 11, 12, 13, 14] and spray flames [15]. For example, Barbosa et al. [16] showed that NRP discharges extended the LBO limit of a lean propane-air flame from a global equivalence ratio of $\phi_g = 0.41$ to $\phi_g = 0.11$. Similarly, Perrin-Terrin et al. [14] reported that plasma pulses significantly reduced the
LBO limit of a hydrogen-air flame. These studies consistently highlight the
significant influence of discharge parameters on flame dynamics, such as pulse
frequency and energy per pulse. It was also found that the positioning of the
electrodes in the combustion chamber played a critical role. For example,
Lacoste et al. [13] observed that a 15 kHz discharge frequency was sufficient
to extend the LBO limit when discharges are performed in the burnt gases.
Sabatino et al. [17] showed that higher frequencies are required if discharges
are performed in fresh gases. The cumulative effect of the NRP discharges is
strongly related to the flow residence time, in the region where the pulses are
deposited. Despite these results, research remains largely observational, with
limited exploration of the physical mechanisms underlying the role of plasma
interactions with the flame in LBO limit extension. A promising approach
to uncovering these mechanisms is to exploit data from detailed numerical
simulations.

Different modelling approaches have been used to simulate NRP dis-
charges, with varying levels of complexity. Detailed models have been used
for 0D [18, 19, 20], 1D [21, 22] and 2D [23, 24] configurations. In these works,
the reactions include electrons, excited and charged species, which makes
them very computationally expensive. 3D computations such as [1, 25] are
carried out using phenomenological models [1] to avoid very high compu-
tational costs, providing very good results compared to experiments. The
model from [1] has been validated against experimental measurements in
terms of temperature, flame shape and OH number density in [26]. In these
approaches, reactions only include ground state species and the main plasma
effects, such as the production of O radicals and heat, are accounted for
through source terms in the governing equations, based on numerical and
experimental observations. To the best knowledge of the authors, the 3D
simulations have been performed only for premixed methane/air flames. Yet
it is crucial to fully understand the mechanisms by which plasma affects
the combustion process, whether through chemical, thermal or transport ef-
fects. For example, in [27], the recirculation of reactive species produced by
the plasma was found to be the key mechanism that enhances the combus-
tion process. In [28], a phenomenological PAC model, coupled with Large
Eddy Simulations (LES), was used to explain the stabilization process of
a methane-air premixed swirled flame, where the flame would periodically
detach without PAC effects.

Recently at the EM2C laboratory, LBO experiments have been carried
out on the SICCA hydrogen/air burner, with a swirl-stabilized partially pre-
mixed flame assisted by NRP discharges [14]. This work represents the first
experimental study on the extension of the lean blowout limit of a plasma-
assisted hydrogen flame. The NRP discharges are able to significantly extend
the LBO limit, compared to a case without plasma. The extent to which
plasma can delay blowout depends on the input parameters of the NRP dis-
charges. In the present study, this swirl-stabilized hydrogen/air configuration
is retained to numerically investigate the impact of NRP on the LBO. LES
results of a plasma-assisted case are compared to that without plasma, in
order to gain a better understanding in the underlying mechanisms that al-
lows the NRP discharges to extend the LBO limit. This is the first numerical
study on the impact of NRP discharges on the LBO limit. The objective of
this work is also to evaluate whether the model of [1] is able to predict the
extension of the LBO limit by plasma assistance.

The paper is organized as follows : first, the experimental configuration
is described, followed by the modeling and numerical details. Then, the LES
results are analyzed for the cases with and without NRP discharges. Results
are presented for a stable condition, followed by the simulations of the LBO.
Finally, conclusions are summarized.

## 2. Experimental setup

The SICCA-H2 is a partially-premixed hydrogen/air swirl-stabilized burner,
featuring a crossflow injection of gaseous hydrogen. The setup is derived
from the configuration presented in [29] and studied numerically in [30], the
only differences being a longer hydrogen injection head and truncated conical
shape [14]. The schematic is shown in Fig. 1. The cylindrical combustion
chamber has a length $l = 150$ mm and a diameter $d_c = 70$ mm.

Hydrogen is injected through 6 radial holes, which have a diameter of $d_{h2} = 1.2$ mm. The hydrogen mass flow rate is kept constant at 12.4 NL/min, which corresponds to a flame thermal power of $P = 2.2$ kW. Air is introduced through the air plenum. In this study, the global equivalence ratio is modified by varying the air mass flow rate. The swirl number, measured by laser Doppler velocimetry, is kept constant at $S = 0.60$.

To provide NRP discharges, a 1-mm diameter tungsten electrode (anode) is utilized. The injector tip serves as the cathode, as shown in Fig. 1. The pulses are obtained by a FPG 30-100MC4K pulse generator (FID Technology). The retained electrode position presented in this paper and in the experimental paper was the only one leading to an LBO extension. Notably,
<figure><img src="image_2.png" /><figcaption>Figure 1: Schematics of the SICCA-H2 burner, taken with permission from [14].</figcaption></figure>

the authors of [14] tested generating the plasma on the burner backplane, as
done in a previous PAC study on the same burner but with a spray flame
[15], without observing any effect on LBO extension.

OH* chemiluminescence flame images are captured by a Princeton Instru-
ments PI-MAX4 intensified camera with an Asahi Spectra XBPA310 optical
bandpass filter centered at 310 nm. In Fig. 2, a line-of-sight integrated OH*
chemiluminescence image of the flame (without plasma) at an equivalence
ratio φ = 0.231 is shown in false colors. The flame presents a V-shape, not
significantly affected by the electrode.
<figure><img src="image_3.png" /><figcaption>Figure 2: Line-of-sight integrated OH* chemiluminescence images of the flame, in false colors, from [14], without (left) and with (right) the electrode, which is represented by a white dashed line. The equivalence ratio is $\phi = 0.231$.</figcaption></figure>

# 3. Modelling for plasma-assisted turbulent combustion

## 3.1. Nanosecond Repetitively Pulsed discharge model

The phenomenological model of Castela et al. [1] is applied in this study, coupled with LES. This is a semi-empirical model that aims to capture the thermal and chemistry effects of NRP. The model assumes that: (i) nitrogen molecules are electronically excited through electron collisions and subsequently relaxed, resulting in ultra-fast heating of the gas and ultra-fast dissociation of O₂ into atomic O, and (ii) nitrogen molecules are vibrationally excited and their relaxation results also in gas heating, however on a much longer time scale. In [31], it was observed that the effects of NRP discharges located in burnt gases, for a lean flame, are very similar. Additionally, a comparison between a detailed plasma-combustion model [32], the Castela model and experimental data was done by Malé et al. in [33], with a very good agreement.

Radical production and heating are closely linked due to the ultra-fast mechanism: O₂ dissociation requires less energy than the energy in N₂*;
the surplus of energy goes into heating [34]. Therefore, if we increase the deposited energy, both contributions will increase until we reach full O₂ dissociation. Beyond this threshold, additional energy goes into N₂ ionization, joule heating, nitrogen dissociation.

Based on the above analysis, the energy input $\dot{E}^p$ from the NRP discharges is broken down into three components, namely the ultra-fast heating $\dot{E}_{heat}^p$, chemistry effects (ultra-fast production of atomic O) $\dot{E}_{chem}^p$, and vibrational excitation of nitrogen molecules $\dot{E}_{vib}^p$:

$$ \dot{E}^p = \dot{E}_{chem}^p + \dot{E}_{heat}^p + \dot{E}_{vib}^p $$

where the chemistry effects are modeled as $\dot{E}_{chem}^p = \eta_c \frac{Y_{O_2}}{Y_{O_2}^f} \left(1 - \frac{e_{O_2}}{e_O}\right) \dot{E}^p$, the ultra-fast heating as $\dot{E}_{heat}^p = \left[\alpha - \eta_c \frac{Y_{O_2}}{Y_{O_2}^f} \left(1 - \frac{e_{O_2}}{e_O}\right)\right] \dot{E}^p$, and the vibrational excitation as $\dot{E}_{vib}^p = (1 - \alpha) \dot{E}^p$. Here, $Y_{O_2}^f$ represents the mass fraction of oxygen in the fresh gases and $e_k$ is the internal energy of species k.

The coefficient $\alpha$ represents the fraction of energy that leads to the electronic excitation of nitrogen molecules, which results in ultra-fast heating and dissociation. The coefficient $\eta_c$ is the fraction of energy that results in ultra-fast O₂ dissociation. The fraction of energy that goes into ultra-fast heating is $(\alpha - \eta)$. According to simulations [35] and experiments [34] of the impact of NRP discharges in air, as well as theory [36], $\alpha = 55\%$ and $\eta_c = 35\%$.

This two-step model is coupled to the LES balance equations, as described in the following section.
## 3.2. Balance equations for Large-Eddy Simulation

The filtered balance equations for the total energy $\tilde{e}_{tot}$, vibrational energy $\tilde{e}_{vib}$ and species mass fractions $\tilde{Y}_k$ are:

$$ \frac{\partial (\bar{\rho} \tilde{e}_{tot})}{\partial t} + \frac{\partial (\bar{\rho} \tilde{u}_i \tilde{e}_{tot})}{\partial x_i} = \frac{\partial}{\partial x_i} \left( \left[ F \Xi \frac{\bar{\mu}}{Pr} + (1-S) \frac{\mu_t}{Pr^t} \right] \frac{\partial \tilde{T}}{\partial x_i} \right) \\ + \frac{\partial}{\partial x_i} \left( \sum_{k=1}^{N_{sp}} \left[ F \Xi \frac{\bar{\mu}}{Sc_k} + (1-S) \frac{\mu_t}{Sc_k^t} \right] \frac{\partial \tilde{Y}_k}{\partial x_i} \tilde{h}_k \right) \quad (1) \\ + \frac{\partial (\bar{\sigma}_{ij} \tilde{u}_i)}{\partial x_i} + \dot{E}_{chem}^p + \dot{E}_{heat}^p + \dot{R}_{VT}^p $$

$$ \frac{\partial (\bar{\rho} \tilde{e}_{vib})}{\partial t} + \frac{\partial (\bar{\rho} \tilde{u}_i \tilde{e}_{vib})}{\partial x_i} = \frac{\partial}{\partial x_i} \left( \left[ \frac{\bar{\mu}}{Sc_{N_2}} + \frac{\mu_t}{Sc_{N_2}^t} \right] \frac{\partial \tilde{e}_{vib}}{\partial x_i} \right) + \dot{E}_{vib}^p - \dot{R}_{VT}^p \quad (2) $$

$$ \frac{\partial (\bar{\rho} \tilde{Y}_k)}{\partial t} + \frac{\partial (\bar{\rho} \tilde{u}_i \tilde{Y}_k)}{\partial x_i} = \frac{\partial}{\partial x_i} \left( \left[ F \Xi \frac{\bar{\mu}}{Sc_k} + (1-S) \frac{\mu_t}{Sc_k^t} \right] \frac{\partial \tilde{Y}_k}{\partial x_i} \right) + \frac{\Xi}{F} W_k \dot{\bar{\omega}}_k^c + W_k \dot{\bar{\omega}}_k^p \quad (3) $$

where $Pr$ and $Sc_k$ are the Prandtl and Schmidt numbers respectively. $\Xi$ is the sub-grid scale wrinkling and $F$ is the thickening factor defined as $F = 1 + (F_{max} - 1)S$. The flame sensor $S$ is defined as 1 in the reactive layer and 0 outside. These $\Xi, F, S$ parameters come from the use of the thickened flame model, described in more detail in the next section. The source terms $\dot{\bar{\omega}}_k^p$ correspond to the production/consumption of species $k$ due to plasma, while $\dot{\bar{\omega}}_k^c$ is due to chemical reactions not directly related to plasma. The source terms added to the $O_2$ and O transport equations from the plasma
effects are closed by:

$$ \dot{\bar{\omega}}_O^p = \eta_c \frac{\tilde{Y}_{O_2}}{Y_{O_2}^f} \frac{\dot{E}^p}{e_O W_O} \qquad (4) $$

$$ \dot{\bar{\omega}}_{O_2}^p = -\frac{W_O}{W_{O_2}} \dot{\bar{\omega}}_O^p \qquad (5) $$

$$ \dot{\bar{\omega}}_k^p = 0 \quad \text{if } k \neq \{O, O_2\} \qquad (6) $$

The filtered terms $\dot{\bar{E}}_{chem}^p$, $\dot{\bar{E}}_{heat}^p$ and $\dot{\bar{E}}_{vib}^p$ are closed as described in section 3.1, and by neglecting sub-grid scale contributions, i.e. by assuming that $\dot{\bar{E}}_y^p = \dot{\bar{E}}_y^p(\tilde{Y}_{O_2}, \dot{E}p)$. The relaxation rate of the vibrational energy into slow gas heating $\dot{\bar{R}}_{VT}^p$, is defined through the Landau-Teller harmonic oscillator approach as

$$ \dot{\bar{R}}_{VT}^p = \bar{\rho} \frac{\tilde{e}_{vib} - e_{vib}^{eq}(\tilde{T})}{\tau_{VT}} \qquad (7) $$

where $\tau_{VT}$ is computed as a function of the vibrational-translational relaxation time of N$_2$ [37]. The equilibrium value of the vibrational energy is $e_{vib}^{eq}(T) = r\Theta_1/(\exp(\Theta_1/T) - 1)$, where $\Theta_1 = 3396K$ and $r = R/W_{N_2}$. R is the gas constant and $W_{N_2}$ is the molar mass of nitrogen.

## 4. Numerical set-up

The numerical simulations are carried out with the variable-density solver (VDS) from the YALES2 code [38], which solves low-Mach number Navier-Stokes equations with a variable density. The temporal evolution is performed using a fourth-order scheme, while the spatial terms are discretized with a fourth-order central scheme.

The chemical kinetics are calculated with the latest UCSD chemical reaction scheme [39], which includes 9 species and 23 elementary reactions. The
UCSD mechanism is commonly used to represent hydrogen-air combustion [40, 41, 42].

The flame front is artificially thickened to ensure sufficient resolution, by the dynamic thickened flame model for LES (DTFLES) [43]. The thickening is adapted according to the local grid size and the laminar flame thickness estimated from 1-D freely propagating laminar flamelets. Turbulence-chemistry interactions are accounted for by the Charlette's subgrid-scale flame wrinkling model [44].

The mesh consists of about 10 M elements. The cell size is refined in the plasma region ($\Delta_x \approx 0.05$ mm) in order to resolve the reactive layers on the grid. The largest cell size in the flame region is $\Delta_x \approx 0.2$ mm, resulting in a maximum thickening factor below 6. The computational domain is the same for both unassisted and assisted simulations. Grid convergence has been performed on both cases.

The discharge zone, assumed cylindrical, is filtered by the spatial function $\mathcal{F}(r) = \text{erfc}[(r^2/a)^b]$ to avoid numerical discontinuities as

$$ \dot{E}^p(t) = \begin{cases} \frac{\sigma_{pulse}}{\tau_{pulse}} \mathcal{F}(r) & \text{if } t_{per} \le \tau_{pulse} \\ 0 & \text{if } t_{per} > \tau_{pulse} \end{cases} \qquad (8) $$

where $\sigma_{pulse} = E_p/(\pi r_d^2 L_d)$, with $r_d$ and $L_d$ being the characteristic radius and length of the discharge channel, respectively. The pulse duration is denoted by $\tau_{pulse}$. The radius of the discharge zone is 0.4 mm and the length is 2.3 mm, stretching from the tip of the injector cone to the tip of the electrode (see Fig. 1). The radius was determined from experimental direct visualization of the discharges in the UV range. The geometric filter parameters a and b are
adjusted to ensure that the radius and volume are correctly reproduced and that the discharge surface has enough points to avoid numerical problems due to strong gradients. The deposited plasma energy is $E_p = 1.5$ mJ per pulse, constant in time during the pulse, with a repetition frequency $f = 15$ kHz. Because just one PAC LBO simulation requires around 80 000 CPU hours, only these operating conditions are simulated in this study, due to high computational costs.

Some of the energy released by the discharge is converted into acoustic waves, causing locally a decrease in temperature [1]. Because the acoustic waves cannot be captured by the low-Mach number formulation, the fraction of energy leaving the domain in the form of acoustic waves has been evaluated in DNS computations [1], which amounts to about 10%. This fraction is deducted from the deposited discharge energy in the low-Mach LES solver.

# 5. Results

## 5.1. Stable configuration simulation with constant global equivalence ratio

The simulated configuration corresponds to a global equivalence ratio of $\phi_G = 0.231$. According to experiments [14], this is a stable condition, 5% above the LBO limit for the non-assisted case by the NRP discharges. The combustion efficiency as a function of time is plotted in Fig. 3 for both non-assisted and assisted cases and for a global equivalence ratio $\phi_G = 0.231$. The numerical instantaneous combustion efficiency $\eta$ is computed as follows:

$$ \eta = \frac{P^{LES}}{P^{th}} \qquad (9) $$

$P^{LES} = \int_V (\Xi/F) \bar{\omega}_H dV$ is the instantaneous flame power computed from
the LES results, where $\bar{\omega}_H$ is the flame heat release rate. $P^{th}$, the theoretical
flame power that would have been released by complete burning of the whole
hydrogen injected in the combustion chamber is expressed as $P^{th} = NCV_{H_2} \times$
$\dot{m}_{H_2}^{in}$, where $NCV_{H_2}$ is the net calorific value of hydrogen and $\dot{m}_{H_2}^{in}$ corresponds
to the mass flow rate of hydrogen injected at the inlet. For the investigated
cases, the theoretical flame power is $P^{th} = 2.2$ kW. For the global equivalence
ratio of $\phi_G = 0.231$, the combustion efficiency obtained from experiments is
$0.40 \pm 0.15$, which corresponds to a flame power of $880 \pm 330$W.

Based on simulation results in Fig. 3, the average combustion efficiency
for NP (no plasma) is 0.266 and for PAC is 0.281, which corresponds to
an increase of heat release due to plasma limited to 5%. This is consistent
with experiments showing no significant effect on the flame structure under
these operating conditions. The computed combustion efficiency retrieves
the value of 0.40 ± 0.15 measured experimentally for this operating condition
without plasma using exhaust gas analysis in Fig. 9 of [14].
<figure><img src="image_4.png" /><figcaption>Figure 3: Comparison of combustion efficiencies from the NP and PAC cases. The global equivalence ratio is $\phi_G = 0.231$. The instantaneous flame power of the NP and PAC configurations are denoted by the green and blue lines respectively. The '-.' show the mean efficiency calculated from simulations.</figcaption></figure>

To understand this moderate effect of plasma on the flame, the temperature and mass fractions of OH radicals are shown at four time instants between the 72nd and 73rd discharges in Fig. 4. The four time instants are uniformly distributed over the time T between two pulses. At the beginning of the cycle (t=0), there is a sharp rise in temperature inside of the discharge region, produced by the plasma pulse. These hot gases are then transported towards the flame, as observed in the figure, for t= T/4 and t=T/2. The white isoline indicates the reaction zone that corresponds to the region where the heat release rate is above 10% of the maximum encountered in the domain. The OH radicals (bottom row) follow the same trend as the temperature and are also transported towards the flame during the NRPD cycle.
<figure><img src="image_5.png" /><figcaption>Figure 4: The instantaneous temperature (top) and OH mass fraction (bottom) during one NRPD cycle. The reaction zone is represented by the white isoline.</figcaption></figure>

The temporal evolution of the OH radicals distribution between two plasma pulses is qualitatively similar to that observed experimentally using phase-averaged OH* images as shown in Fig. 5, obtained from [14].

This mechanism causes a limited increase of heat release, which does not significantly affect the overall flame stabilization. The effect of the plasma is investigated in the following section when the operating conditions get closer to the LBO.
<figure><img src="image_6.png" /><figcaption>Figure 5: Phase-averaged OH* chemiluminescence images of the flame between two plasma pulses. The line-of-sight integrated images of the flame are shown on the top figure. The difference between these phase-averaged images and the image of the flame without plasma, shown at the bottom. The image is from ref. [14].</figcaption></figure>

5.2. Blowout simulations

Transient numerical simulations are performed to replicate the blowout phenomenon under lean combustion conditions. The simulation is initialized by a steady-state solution obtained with a starting global equivalence ratio $\phi_G = 0.240$, significantly above the lean global equivalence ratio limit observed experimentally, which is $\phi_G^{LeanExp} = 0.220$, for the case without plasma [14]. To characterize the LBO simulations, the equivalence ratio at the inlet $\phi_{in}$ is used instead of the global equivalence ratio $\phi_G$, because the air mass flow is continuously changing and $\phi_G$ is used for steady-state conditions. The inlet equivalence ratio is defined as $\phi_{in} = s\dot{m}_{in}^{H_2}/\dot{m}_{in}^{air}$, where s is the mass stoichiometric coefficient, while $\dot{m}_{in}^{H_2}$ and $\dot{m}_{in}^{air}$ are the injected mass flow rate of hydrogen and air, respectively. $\phi_{in}$ is then continuously reduced by increasing the air intake mass flow rate. In steady state, $\phi_{in}$ and $\phi_G$ are equal and can be used indifferently. In the experiments, the temporal variation of the air mass flow rate $d\dot{m}_{in}^{air}/dt$ is constant and approximately
equal to 0.1 (NL/min)/s. Flame extinction occurs after a couple of minutes.
The LES computation of this configuration over such a physical time is con-
siderably too expensive to be considered. To speed up the computation, the
temporal decay of the air inlet mass flow rate at the inlet boundary condi-
tion is artificially increased by four orders of magnitude (10⁴). The temporal
variations of $d\dot{m}_{in}^{air}/dt$ should be much slower than the rate of the flame's re-
sponse to these variations. Due to the complexities of the case under study,
defining the proper times scales of the flame's response is not so evident. It is
assumed that increasing $d\dot{m}_{in}^{air}/dt$ does not affect the flame dynamics, which
continuously reach a quasi-stationary state. So to verify this hypothesis,
three calculations were carried out for the plasma-assisted case with different
values of $d\dot{m}_{in}^{air}/dt$, namely TE1 with $d\dot{m}_{in}^{air}/dt = 3.35 \cdot 10^3$ (NL/min)/s, TE2
with $d\dot{m}_{in}^{air}/dt = 6.7 \cdot 10^3$ (NL/min)/s and TE3 with $d\dot{m}_{in}^{air}/dt = 13.4 \cdot 10^3$
(NL/min)/s. Figure 6 plots the transient flame power in terms of the inlet
equivalence ratio for TE1, TE2 and TE3 with the NRP discharges activated.
Extinction occurs around the same equivalence ratio $\phi_{in}^{LBO,LES} \approx 0.172$, in
the case of the two slowest temporal variations (TE1 and TE2), as shown
in Fig. 6 for the plasma-assisted case. This value is close to the experimen-
tal measurement $\phi_{in}^{LBO,EXP} \approx 0.177$, while TE3 tends to underestimate the
LBO limit. The numerical methodology for mimicking the lean blowout is
therefore validated for TE1 and TE2. For the remainder of the study, the
TE2 value $d\dot{m}_{in}^{air}/dt = 6.7 \cdot 10^3$ (NL/min)/s is retained.

Transient simulations are analyzed for both unassisted and plasma-assisted
cases. To verify the repeatability of the numerical experiments, each case is
computed twice, differing only in the initial conditions, which correspond
<figure><img src="image_7.png" /><figcaption>Figure 6: The flame power with respect to the equivalence ratio at the inlet $\phi_{in}$, for the three time evolutions of the air flow rate, namely TE1, TE2 and TE3.</figcaption></figure>

to two specific time-instant solutions for a fixed starting equivalence ratio $\phi_G = 0.240$. Figure 7 illustrates the evolution of the flame power as a function of the inlet equivalence ratio for both the non-assisted and plasma-assisted cases. The lean blowout equivalence ratios measured experimentally for both configurations are indicated by the vertical dashed red arrows.

For the unassisted cases, the flame power drops to zero for a mean inlet equivalence ratio $\phi_{in}^{LBO,LES,NP} = 0.222$, consistent with the experimentally observed equivalence ratio at extinction, which is at 0.220. As expected, plasma activation enables combustion to be sustained at lower inlet equivalence ratios, with the numerically predicted flame power reaching zero at $\phi_{in}^{LBO,LES,PAC} = 0.172$, very close to the experimental value of $\phi_{in}^{LBO,EXP,PAC} = 0.177$. Table 1 quantitatively compares the LBO limits pre-
<figure><img src="image_8.png" /><figcaption>Figure 7: The flame power with respect to the equivalence ratio at the inlet $\phi_{in}$, for a case with no plasma (NP), for a case with plasma-assisted combustion (PAC), and for 2 initial conditions (IC).</figcaption></figure>

dicted by the LES $\phi_{LBO,LES}$ to experimental values $\phi_{LBO,Exp}$. The errors, calculated using the formula $\epsilon = (\phi_{LBO,Exp} - \phi_{LBO,LES})/\phi_{LBO,Exp}$, are small, showing the ability of the numerical code to reproduce the lean blowout, even for the case with plasma.

<table><caption>Table 1: The predicted LBO limits from experiments and LES, with the relative error.</caption><thead><tr><th>Case</th><th>φ<sub>LBO,Exp</sub></th><th>φ<sub>LBO,LES</sub></th><th>Error (ε)</th></tr></thead><tbody><tr><td>NP</td><td>0.220</td><td>0.222</td><td>0.9 %</td></tr><tr><td>PAC</td><td>0.177</td><td>0.172</td><td>2.8 %</td></tr></tbody></table>
<figure><img src="image_9.png" /><figcaption>Figure 8: Non-assisted case LES. The instantaneous heat release rate (left), local equivalence ratio (middle) and progress variable (right) are shown at three different $\phi_{in}$. $\phi_{in} = 0.225$ (upper), $\phi_{in} = 0.220$ (center) and $\phi_{in} = 0.219$ (bottom).</figcaption></figure>

To investigate the mechanism by which the NP flame is extinguished, the local heat release rate, equivalence ratio, and progress variable (PV) are presented in Fig. 8 for three inlet equivalence ratios: $\phi_{in} = 0.225$ (top figures),
$\phi_{in} = 0.220$ (center figures), and $\phi_{in} = 0.219$ (bottom figures). As $\phi_{in}$ decreases in Fig. 8, the flame shortens, and PV distributions for $\phi_{in} = 0.220$ and $\phi_{in} = 0.219$ show that fresh gases penetrate the recirculation region, diluting the burnt gases. The progress variable definition is based on elements according to the formula $PV = 1.0 - Y_{H_2}/Y_H$, where $Y_{H_2}$ is the mass fraction of H$_2$ and $Y_H$ is the mass fraction of the element H. The recirculation zone is identified in the images of the middle $\phi_{in} = 0.220$ row by the axial velocity isoline $U_y = 0$ (white line). In premixed flames, combustion is sustained by the diffusion of radicals and heat from the burnt gases into the reaction zone. However, the intrusion of leaner fresh gases disrupts this process, leading to flame quenching. For $\phi_{in} = 0.219$, the yellow isoline indicates the $\phi = 0.11$ isoline. Values of the local equivalence ratio $\phi$ are getting lower downstream from the injector, which is due to the mixing with the air flow. For sufficiently low values of $\phi$, the mixture does not ignite and fresh gases then enter the recirculation zone and dilute the combustion products. These values of $\phi$ are higher than the unstrained theoretical lean flammability limit of H$_2$/air flames $\phi = 0.11$, which was determined from the 4.2 vol% of H$_2$ lean flammability limit [45], because the strain rate easily induces extinction for lean flames [46]. The maximum strain rate values observed in the flame region are about 1000 s$^{-1}$. In Fig. 8, the local equivalence ratio distribution for $\phi_{in} = 0.219$ at extinction is between $0.3<\phi<0.5$ in the flame region (this was verified from the PDF of $\phi$ in the flame, not shown here), which are significantly higher than the theoretical value of $\phi = 0.11$.

To investigate the role of the NRP discharge in the re-ignition mechanism, three time instants, labeled A, B, and C, are selected in Fig. 9. A zoomed-in
view is provided for better clarity. Instantaneous views of the heat release
rate (HRR), progress variable (PV), and local equivalence ratio are presented
in Fig. 11 for these three time instants.

<figure><img src="image_10.png" /><figcaption>Figure 9: Evolution of flame power as a function of the inlet equivalence ratio for the plasma-assisted simulation at IC 1. A re-ignition event is highlighted with a red square box (left) and presented in a zoomed-in view where three time instants, labeled A, B, and C, are identified (right).</figcaption></figure>

First, the conditions at point A ($\phi_{in} = 0.2065$, see Fig. 9) are examined both before and during a plasma pulse. The top row of Fig. 10 shows the instantaneous progress variable (PV), hydrogen production, and heat release rate (HRR) prior to the pulse, while the bottom row displays these variables during the pulse.

Before the pulse, the flame exhibits a behavior similar to the NP case (Fig. 8), where fresh gases penetrate the recirculation region and mix with burnt gases. During the plasma pulse, hydrogen is consumed faster (as seen in the bottom row), which is accompanied by a significant increase in HRR and reaction products, as reflected in the PV distributions.

The plasma enhances the recirculation zone by introducing radical species
<figure><img src="image_11.png" /><figcaption>Figure 10: Plasma-assisted case. The instantaneous progress variable (left), the production of H₂ (middle) and heat release rate (right) are shown just before the plasma pulse (upper) and after the pulse (bottom), at time instant A ($\phi_{in} = 0.2065$, see Fig. 9).</figcaption></figure>

and heat, which help to sustain the flame. These radicals and heat are transported towards the flame, as illustrated in Fig. 4. As noted in [18], the production of radicals - critical for igniting H₂/air flames - is primarily driven by the chemical effects of NRP discharges, particularly the generation of O radicals. The cumulative effects of plasma, i.e. due to production of heat and O radicals according to the Castela model, are strongly related to the flow residence time. So placing the discharges in the recirculation region would enhance these cumulative effects.
In contrast to the non-assisted case, which exhibits a continuous decrease
in flame power with the inlet equivalence ratio, the plasma-assisted case
shows re-ignition events. Figure 9 illustrates the evolution of flame power as
a function of the inlet equivalence ratio, highlighting one such event.

<figure><img src="image_12.png" /><figcaption>Figure 11: Plasma-assisted case. The instantaneous heat release rate HRR (left), progress variable PV (center) and local equivalence ratio $\phi$, at points A, B and C indicated in Fig. 9.</figcaption></figure>

In Fig. 11, at time instant A the flame is nearly extinguished due to
the penetration of a fresh gas pocket into the internal recirculation zone,
as depicted in Fig. 10. The plasma discharges promote the consumption of
hydrogen which brings combustion products inside the recirculation zone, keeping the flame from extinguishing.

At time instant B, the local equivalence ratio values in the inter-electrode region increase due to turbulent fluctuations. The progress variable field in the recirculation zone shows the presence of burnt gases, which is the result of higher values of local $\phi$ distributions.

By time instant C, this flame kernel propagates, leading to the enhancement of the flame and a significant increase in the heat release rate. The internal recirculation zone is subsequently filled with burnt gases, enabling the flame to stabilize under steady conditions.

The NRP discharges sustain the flame at low local $\phi$ values. When turbulence causes the local $\phi$ values in the flame region to increase, the flame intensifies and grows again.

As previously shown in Fig. 10, there is a negative reaction rate of $H_2$ just after a pulse, which means that the NRP discharges will promote the $H_2$ consumption. A chemical pathway analysis was conducted, which indeed showed that the dissociation of $O_2$ into O radicals by the NRP discharges promotes the hydrogen consumption through the following reactions :

$$O + H_2 \rightarrow H + OH \quad (R_1)$$

$$OH + H_2 \rightarrow H + H_2O \quad (R_2)$$

$$O + OH \rightarrow H + O_2 \quad (R_3)$$

where $R_1$ is significantly more dominant, due to the production of O radicals by the NRP discharges. A considerable amount of H radicals are
produced by reaction $R_3$, through the reaction of OH with O. The instantaneous mass fractions of O, H, OH, $H_2$ and $H_2O$ during two pulses are shown in Fig. 12, at the center of the discharge zone. At the top figure where the discharges act on the fresh gases, during the pulse, there is consumption of $H_2$ shown by the decrease in the mass fraction of $H_2$.

At time instants B and C, the discharges, which occur in lean burnt gases, still promote the formation of O radicals which now react mainly with OH ($R_3$) and $H_2O$ ($R_4$) through the elementary reaction:

$$H_2O + O \rightarrow 2OH \quad (R_4)$$

Fig. 12 (bottom) shows the instantaneous mass fractions of O, H, OH, $H_2$ and $H_2O$ during two pulses at stable conditions for $\phi_G = 0.231$, when plasma is deposited in the burnt gases. The mass fraction of $H_2O$ is decreased when the discharges are deposited, shown in Fig. 12 (bottom), as it is consumed by reacting with the O radicals.

The highly reactive species produced by the plasma influence the combustion kinetics significantly. Similar chemical activities induced by bursts of NRP discharges were previously observed in the numerical investigations conducted by Bechane et al. [27] and Malé et al. [33]. However, the way this localized increase in chemical activity affects the turbulent flame dynamics is here different.

In the study by Bechane et al. [27], the plasma caused a generation of radical species within the recirculation zone, which continuously sustained the flame base. This led to a localized increase in the flame consumption speed at the flame base, consolidating the flame anchoring. Consequently, the over-
<figure><img src="image_13.png" /><figcaption>Figure 12: Top: The instantaneous mass fractions of O, H, OH, H₂ and H₂O during two pulses, in the case when fresh gases enter the discharge zone. Bottom: The instantaneous mass fractions of O, H, OH, H₂ and H₂O during two pulses at stable conditions for $\phi_G = 0.231$.</figcaption></figure>
all flame surface area increased, resulting in an enhanced total heat release
rate. In contrast, the mechanism observed in the present study shows that
LBO is extended through a different mechanism. Here, the NRP discharges
prevent flame quenching when fresh gases rapidly penetrate the stabilizing
internal recirculation zone by promoting the consumption of H₂. The flame
power is then able to increase once more as soon as local conditions, such as
strain rate and equivalence ratio, become favorable. This allows the turbu-
lent flame to stabilize effectively. Once the flame is stable, the role of plasma
in combustion enhancement remains limited.

In future work, it would be interesting to study numerically how differ-
ent levels of the deposited plasma energy impacts the LBO limit, which was
explored experimentally in [14]. Radical production and heating are closely
linked due to the ultra-fast mechanism: O₂ dissociation requires less energy
than the energy in N₂*; the surplus of energy goes into heating [34]. There-
fore, if we increase the deposited energy, both contributions will increase
until we reach full O₂ dissociation. Beyond this threshold, additional energy
goes into N₂ ionization, joule heating, nitrogen dissociation.

6. Conclusions

The lean blowout (LBO) of a partially-premixed swirled H2-air flame as-
sisted by Nanosecond Repetitively Pulsed (NRP) discharges was investigated
numerically. The simulations were performed using large eddy simulations
(LES) coupled with a phenomenological model that takes into account the
effects of the NRP discharges. Simulations of a plasma-assisted combustion
(PAC) configuration were performed along with a case with no-plasma (NP),
to better understand the effects of the NRP discharges. The LBO is triggered
by a decrease in the global equivalence ratio, achieved through an increase
of air flow into the domain while the injected mass flow rate of hydrogen is
kept constant.

The NP and PAC simulations were first validated in terms of combustion
efficiency for a stable condition at a global equivalence ratio φ<sub>G</sub> = 0.231. The
computed combustion efficiencies of the NP and PAC configurations are very
close to one another, which shows that the effects of the NRP discharges
for stable conditions are limited for this configuration. The impact of the
NRP discharges on the flame was then analyzed during one NRP cycle. The
simulation reveals that the heat and OH radicals produced by the plasma are
transported towards the flame; however, the increase in the maximum heat
release rate with respect to the NP case is not significant.

LBO simulations were performed next. As turbulence was observed to
have a strong impact on the flame power, just before the LBO, simulations
were performed under two initial conditions to verify that these initial con-
ditions do not influence the predicted LBO limit. The LES was able to
correctly predict the LBO limit for both the NP and PAC cases, at the two
initial conditions.

During the blowout mechanism, the flame, which is stabilized at the in-
jector outlet, becomes shorter as the inlet equivalence ratio is reduced. The
turbulence is responsible for local equivalence ratio fluctuations that can lead
to flame extinction. Indeed, lean pockets of fresh gases may be able to pen-
etrate the recirculation zone induced by the swirling flow, diluting the burnt
gases and leading to the flame extinction. This blowout occurs at local values
of the equivalence ratio between $\phi = 0.3$ and $\phi = 0.5$, which is far from the
unstrained theoretical maximum lean flammability limit of the hydrogen/air
flame ($\phi = 0.11$), meaning that blowout is due to the strong flame stretching
with the type of burner used.

The NRP discharges prevent the local extinction by generating a pool of active species (mainly H and OH), which allows the flame to become stable when the local equivalence ratio within the internal recirculation and the local stretch are more favorable. Due to this mechanism, the LBO limit decreases from 0.22 to 0.17.

Acknowledgments

This research was funded by the Fondation Simone and Cino Del Duca
through a scientific grant attributed to the project PLATHON, by the FlyHy
project of the Agence Nationale de la Recherche (ANR-21-CE05-0008) and by
the European Research Council (ERC) under the European Union's Horizon
2020 research and innovation programme (GreenBlue project, Grant Agree-
ment No.101021538). A CC-BY 4.0 public copyright license has been applied
by the authors to the present document and will be applied to all subsequent
versions up to the Author Accepted Manuscript arising from this submission
in accordance with the grants' open access conditions. This research was
conducted using HPC resources from IDRIS, TGCC, and CINES under the
allocation A0152B10253 by GENCI (Grand Equipement National de-Calcul
Intensif). The code YALES2 was used. Vincent Moureau and co-workers
from CORIA are acknowledged for providing the YALES2 code and their
technical support.
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