**1. Introduction**

Combustion is a crucial factor in air transportation due to the high energy density of liquid fuels. However, the low efficiency of current aeroengines and the production of harmful emissions contributing to climate change are pressing issues. To comply with strict emission regulations set by CAEP (Committee on Aviation Environmental Protection) and improve fuel efficiency, various international organizations are exploring the concept of lean combustors.

Lean fuel burning is an effective solution for reducing NOx emissions by lowering flame temperature. However, these low temperature flames are prone to critical instabilities that can lead to re-ignition and flame blowout issues [1,2]. To address issues with methane combustion, the addition of a more reactive and cleaner fuel such as hydrogen could be a practical solution [3]. Blending methane with hydrogen has been shown to enhance performance and reduce emissions without modifying existing combustors [4]. Hydrogen is a carbon-free fuel with low ignition energy, a wide flammability range, fast flame propagation, and high reactivity [3]. Several studies in the past [3–6] have focused on the impact of hydrogen on the flame speed of CH4/H2 mixtures. Halter et al. [5] studied the effect of hydrogen content and inlet pressure on the laminar flame speed of CH4/H2 flames, with results indicating that the laminar flame speed improved with increasing hydrogen content and decreased with increasing inlet pressure.

Mandilas et al. [6] studied the impact of hydrogen on iso-octane-air and methane mixtures in both laminar and turbulent conditions. They found that using hydrogen led to earlier flame instabilities but improved laminar flame speed at lean limits in turbulent

**Citation:** Mehdi, G.; De Giorgi, M.G.; Bonuso, S.; Shah, Z.A.; Cinieri, G.; Ficarella, A. Comparative Analysis of Flame Propagation and Flammability Limits of CH4/H2/Air Mixture with or without Nanosecond Plasma Discharges. *Aerospace* **2023**, *10*, 224. https://doi.org/10.3390/ aerospace10030224

Academic Editors: Spiros Pantelakis, Andreas Strohmayer and Jordi Pons-Prats

Received: 31 January 2023 Revised: 19 February 2023 Accepted: 23 February 2023 Published: 25 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

combustion. Adding hydrogen to methane slightly improved reactivity at lean conditions, but also increased complexities, safety issues, and thermoacoustic instabilities [3–6]. Flame speed was slightly better at lean compared to rich conditions [4]. Non-thermal plasma combustion can improve flame stability, flame speed, and lean blowout limits. NTP enhances combustion through kinetic, thermal and momentum effects [7]. NTP improves combustion through three mechanisms: kinetic (creation of active particles from fuel decomposition), thermal (increased fuel/air mixture temperature), and momentum (ionic wind and flow motion from electro-hydrodynamic forces) [8].

Among NTP technologies, nanosecond plasma discharge (NSPD) has gained attention due to its ability to effectively produce excited states and active particles [9,10]. NSPD also rapidly heats the gas, which accelerates combustion [11,12]. Despite numerous research studies on NTP combustion [1], commercialization is only possible with the development of accurate numerical models for plasma chemistry in combustion. Our group [12–15] has studied CH4/air mixtures with NSPD for flame propagation and ignition enhancement. We compared ignition delay, flame speed, and flammability limits under different conditions and found that NSPD improved ignition, flame propagation, and flammability limits due to the production of neutral radicals and increased mixture temperature. The improvements were primarily due to NSPD's kinetic effects. Prior studies on NSPD have individually considered H2/air and CH4/air mixtures.

While initial studies have explored the kinetics of NSPD, a comprehensive understanding of plasma mechanisms for CH4/H2/air mixtures is still lacking. It has been shown that the evolution of active particles over time provides the most accurate analysis of plasma kinetics [16,17].

This paper presents a study of CH4/H2/air with nanosecond plasma discharge. There is currently no numerical study available on methane blended hydrogen plasma-assisted combustion. Both plasma and combustion kinetics were analyzed using validated mechanisms and compared to previously published experimental data. The impact of NSPD and hydrogen content on flame propagation and flammability limits in methane/air mixtures was studied. A comparative analysis of flame speed enhancement with and without plasma actuation was performed using different methane blended hydrogen ratios.

#### **2. Numerical Procedure and Kinetic Modelling**

### *2.1. Numerical Procedure*

Numerical analyses were conducted using two solvers: ZDPlasKin (0D Plasma kinetic solver) [18] and CHEMKIN (Chemical kinetic solver) [19]. The methodology is shown in Figure 1 and explained in [13]. ZDPlasKin was used to analyze the kinetic and thermal effects of NSPD in CH4/H2/Air mixture. BOLSIG+ was linked to ZDPlasKin to predict the temporal evolution of excitation states and the reactions producing free radicals/active particles. It has been assumed that the non-equilibrium plasma created from a CH4/H2/air mixture at atmospheric pressure is uniformly distributed, which is a similar assumption to what was previously executed in [13]. Although the nanosecond pulsed plasma combustion process is three-dimensional and not homogeneous, we used a simplified homogeneous model. To investigate the effects of plasma CH4/H2/air products on flame speed and flammability limits, we used the plasma products of CH4/H2/air as the inlet domain of the reactor.

**Figure 1.** Flowchart for numerical analysis.

ZDPlasKin boundary conditions were set as ambient temperature and pressure, fixed EN and electron number density, and initial CH4/H2/Air composition. The simplified homogeneous model was used as in [20]. ZDPlasKin simulation was performed using the integral mean value of EN obtained from experiments, about 200 Td over 10−<sup>6</sup> s, as shown in Figure 2. Experimental setup and EN estimation are described in [13]. The gas temperature was predicted using equations from [18]. The adiabatic gas temperature was calculated from the energy conservation equation and reallocation of electrical power *Pext* to electron translational degree *Pelec*, gas internal degree *Pchem*, and gas *Pgas*:

$$Pext = Pgas + Plecc + Pchem\tag{1}$$

**Figure 2.** Experimental EN value used for numerical analysis [13].

The above equation can be described below.

$$Pext = e[Ne]veE\tag{2}$$

$$Pgas = \frac{1}{\gamma - 1} + \frac{d(NTgas)}{dt} \tag{3}$$

$$Pelocity = \frac{3}{2} + \frac{d([\text{Ne}]\,\text{Te})}{dt} \tag{4}$$

$$Pchem = \sum\_{i}^{n} Qi + \frac{d\left[Ni\right]}{dt} \tag{5}$$

where *E* is the reduced field, *e* is the elementary charge, *Te* is the electron temperature, *ve* is the drift velocity of electrons [*Ne*] is the electron density, *N* is the total gas density, *γ* = 1.2 is the specific gas heat ratio and *Qi* is the potential energy of species *i*.

The results gained from the ZDPlaskin solver in terms of neutral and excited species (at a time of 0.5 ms because the residence time is too short that autoignition chemistry does not significantly influence the reactants compositions), and the gas temperature of the activated region were introduced into the CHEMKIN solver to investigate the combustion process.

A 1-D premixed laminar flame speed reactor was employed to analyze combustion characteristics, considering thermal diffusion and multicomponent diffusion options. The adaptive mesh parameters were set as CURV = 0.5 and GRAD = 0.05, with absolute and relative error criteria of ATOL = 1 × <sup>10</sup>−<sup>9</sup> and RTOL = 1 × <sup>10</sup>−5, respectively. The total number of grid points used was typically 350–400. In this study, we have established that the calculation domain of the CHEMKIN reactor ranges from −2.0 cm upstream to 4.0 cm downstream with respect to the reactor and is sufficient to attain adiabatic equilibrium. Numerical analyses were performed at various fueling conditions based on H2/CH4 ratio (xH2) with or without plasma actuation. Table 1 shows the mole fraction of CH4, and H2 reactants at equivalence ratio of 1.


**Table 1.** Reactants mole fraction of CH4/H2/Air flames at plasma on and off conditions.
