Investigation of the E ﬀ ects of Plasma Discharges on Methane Decomposition for Combustion Enhancement of a Lean Flame

: The present work focuses on the impact of dielectric barrier discharge (DBD) plasma actuators (PAs) on non-premixed lifted ﬂame stabilization in a methane CH 4 -air Bunsen burner. Two coaxial DBD-PA conﬁgurations are considered. They are composed of a copper corona, installed on the outer surface of a quartz tube and powered with a high voltage sinusoidal signal, and a grounded needle installed along the burner axis. The two conﬁgurations di ﬀ er in the stando ﬀ distance value, which indicates the positioning of the high frequency / high voltage (HV) electrode’s upper edge with respect to the needle tip. Experimental results highlight that ﬂame reattachment is obtained at a lower dissipated power when using a negative stando ﬀ distance (i.e., placing the needle upstream with respect to the corona). At 11 kV peak-to-peak voltage and 20 kHz frequency, plasma actuation allowed for reattaching the ﬂame with a very low dissipated power (of about 0.05 W). Numerical simulations of the electrostatic ﬁeld conﬁrmed that this negative stando ﬀ conﬁguration has a beneﬁcial e ﬀ ect on the momentum sources, which oppose the ﬂow and show that the highest electric ﬁeld extends into the inner quartz tube, as conﬁrmed by experimental visualization close to the needle tip. The modeling predicted an increase in the gas temperature of about 21.8 ◦ C and a slight modiﬁcation of the fuel composition at the burner exit. This impacts the ﬂame speed with a 10% increase close to the stoichiometric conditions with respect to the clean conﬁguration.


Introduction
Nowadays, the aeroengine industries have addressed the development of low NO x combustion technologies in many ambitious national and international research programs. Along these research paths, the "lean burn" has been considered for mid-to long-term targets, pointing to the design of new low NO x emission combustors. Lean burning combustors include low-temperature flames of lean fuel mixture as one of the most promising solutions [1,2]. However, lean flames are usually affected by efficiency penalty as well as strong flame instabilities that increase the risk of flame quenching (i.e., the flame blow-off, as leaner conditions are approached). The incipience of the blow-off condition is usually anticipated by the lifting of the flame, whose behavior has not been deeply understood yet. It is worth underlining that the lean burn is defined by the lean flammability limit (LFL) expressed as percentage by volume of the fuel into the mixture; lean combustion usually occurs below the LFL [3].
In cases concerning premixed or partially premixed flames, the conventional way to address flame stabilization involves adding a pilot flame for safe operation [4]. However, this pilot flame may generate a significant level of unwanted NO x emissions. In addition to a pilot flame, passive control systems are of common use in the field of aeroengine combustor design. They are based on the modification of the air injection geometry (such as swirlers) and flame holders, which promote the flame stability by means of the establishment of large-scale vortexes. These flow structures permit turbulent mixing with recirculation of hot gases and extend the mixture flammability range. In this regard, an experimental investigation concerning the stabilization of turbulent non-premixed flames was presented by Cha and Chung [5], Fokaides et al. [6] provided, instead, an experimental characterization of the mixing evolution, the flow pattern, and the temperature distribution of a lifted-stabilized swirl flame near lean blowout conditions.
In the case of non-premixed diffusive lifted flames, flame stabilization is strongly affected by the velocity gradient and the burnt gas expansion on edge flame propagation, as determined by Chen [7]. In a different study, Chen and colleagues [8] also found that in presence of lifted diffusion jet, the flame stability is influenced by local flame extinction in the flame area where the outer mixing layer merges with the central flame front.
A different and complementary active control approach is the use of plasma assisted combustion (PAC) technology [9]. PAC has the potential to enhance combustion by acting as a source of heat, radicals, excited species, electrons/ions, and fuel fragments, simultaneously [10,11]. Furthermore, plasma actuators also produce strong electric fields; they introduce significant electro-hydrodynamic momentum sources which affect the electrically charged flow (ion wind) resulting from both combustion and plasma ionization reactions. Recently, several experimental investigations were conducted to evaluate the impact of an external electric field into the combustion region on non-premixed methane-air diffusive flames by means of an ion current [12][13][14][15]. Based on the experimental observation that chemi-ions modify flame behavior in the presence of an applied electric field, Lopez-Camara et al. [16] performed a numerical investigation on the potential relationship between peak location and magnitude of ions and excited species. Previously, Belhi et al. [17] carried out numerical simulations which demonstrated the capability of both direct current (DC) and alternating current (AC) external electric fields in stabilizing a lifted diffusion methane-air flame. In particular, plasma actuators are active, electrically-driven devices able to provide a high frequency/high voltage (HV) signal. When applied to combustion enhancement, they provide high flexibility since they can be combined with other passive control devices such as swirlers. Furthermore, they are characterized by an extremely short response time when compared to other active control systems, which allows for a rapid adjustment of control parameters according to real-time operation conditions.
In the field of electrical discharge plasmas, non-thermal plasmas (NTPs), sometimes called non-equilibrium or 'cold' plasmas, were recently investigated. As underlined by Rosocha, Kim, and Stange [18], in NTPs, electrons and ions/neutral gas are not in thermal equilibrium: the former have high energy and "hot" temperature, whereas the latter are near ambient temperature ("cool"). This results in little waste enthalpy (heat) deposited in a process gas. Consequently, NTPs provide a small gas temperature rise in combination with high electrical-to-fluidic energy conversion efficiency, namely the ratio between the power delivered to the fluid and the electrical power consumption. One of the most promising non-thermal plasma devices is the dielectric barrier discharge plasma actuator (DBD-PA). As demonstrated by Kim and colleagues [19] and Rosocha and co-workers [20], in such plasmas, electron temperatures lower than 12 eV can break down the fuel species producing free radicals. To date, several DBD-PAs have been investigated to improve the fuel/air mixtures ignition [21][22][23], increase flame propagation [24,25], or enhance flame stabilization by extending flammability limits [26][27][28][29][30][31]. Concerning this last aspect, combustion enhancement has been observed when applying a DBD-PA for fuel/oxidizer decomposition [32,33]. Among all configurations, coaxial DBD-PAs have been widely investigated as fuel reforming reactors with promising results when applied to combustion systems [34][35][36].
In this context, the present work provides an investigation of plasma actuation in a coaxial DBD configuration for a non-premixed lean lifted flame stabilization. Experiments were carried out in a Bunsen-type burner with an inner methane jet surrounded by an outer air jet (LFL equal to 0.05, Energies 2020, 13, 1452 3 of 19 corresponding to a lean burn equivalence ratio Φ of about 0.485), confined by two coaxial quartz tubes. The coaxial DBD was composed of a high-voltage corona electrode mounted on an outer quartz tube, coupled with an axially-placed grounded needle electrode. Based on the relative position of the needle electrode with respect to the corona electrode, two coaxial DBD configurations were investigated. Hence, the analysis of the experimental results is supported by simulations of the electrostatic field, in combination with a one-dimensional spatio-temporal analysis of the plasma chemistry inside the methane tube, aiming to decouple thermal and kinetics effects.

Experimental Set-Up and Methods
The experimental setup consisted of a coaxial Bunsen burner equipped with a plasma actuator in a ring-needle configuration, as shown in Figure 1. Dedicated gas lines fed air and methane into two coaxial quartz tubes, the inner one for CH 4 and the outer one for air. The inner quartz tube (methane line) had an external diameter of 10 mm and a thickness of 1 mm, while the coaxial outer tube (air line) had an external diameter of 30 mm and a thickness of 2 mm.  The final coaxial flow configuration resulted in a normal diffusive flame (NDF), which was characterized by an inner fuel jet surrounded by an outer oxidizer jet. The top ends of the two coaxial quartz tubes were aligned as shown in Figure 2; thus, the flame established at the exit of the burner.
The air and methane flow rates were recorded using flow meters, with an accuracy of ±3% of reading and ±0.3% full scale value for the air flow, and ±0.8% of reading and ±0.2% full scale value for the methane flow.
The electrical setup was composed of a HV generator, a HV probe, and a current transformer, which allowed for the measurement of the electrical power. A copper ring 30 mm in length, 1 mm in thickness, and 30 mm in inner diameter, was fastened by screws onto the external surface of the outer quartz tube and connected to the HV (herein referred as HV electrode). The grounded electrode consisted of a copper needle having a blunt tip with a 90 • angle, and a diameter of 1 mm, which Energies 2020, 13, 1452 4 of 19 was axially placed into the inner quartz tube. Concerning the electrical feeding, a sinusoidal high frequency/HV signal was provided to the HV electrode by means of a HV generator (the PVM500 Plasma Resonant and Dielectric Barrier Corona Driver). The applied voltage signal was acquired using the HV probe Tektronix P6015A (accuracy of ±3% of reading). The current transformer Bergoz mod. CT-C1.0-BNC was used, instead, to measure the current flowing in the circuit with an accuracy of ±0.5% of reading.  Both the HV probe and the current transformer signals were simultaneously acquired by means of the oscilloscope model Tektronix TDS2024C (accuracy of ±3% of reading). The acquisition sample rate was set to 25 MHz and each measurement point was given by the average of 128 samples. Based on voltage and current measurements, the electrical power consumption of the DBD was computed as follows: Both the HV probe and the current transformer signals were simultaneously acquired by means of the oscilloscope model Tektronix TDS2024C (accuracy of ±3% of reading). The acquisition sample rate was set to 25 MHz and each measurement point was given by the average of 128 samples. Based on voltage and current measurements, the electrical power consumption of the DBD was computed as follows: where ∆t V is the period of the applied voltage and I(t) and V(t) are the acquired current and the voltage signals, respectively. Table 1 shows the experimental test matrix, where S SO is the standoff distance defined as the axial distance between the HV electrode upper edge and the needle tip (see Figure 2a). All experiments were conducted by fixing both the air and the fuel flow rates at 1.12 ± 0.04 g/s and 0.0023 ± 0.0002 g/s respectively, which corresponded to the characteristic axial velocities of fuel and air flows at the burner exit of about u f = 0.074 ms −1 and u a = 2.3 ms −1 , and a global equivalence ratio [36] of 0.035, which is defined as Φ = ( m is the mass flow rate, the subscripts f and a denote the fuel and the air respectively, while the subscript st refers to the stoichiometric conditions with a stoichiometric fuel-to-air ratio equal to 0.0559. It is worth observing that the local equivalence ratio differs from the global one: it varies into the flame region due to the diffusive nature of the flame, approaching unity in the proximity of the flame surface [36]. The LFL was equal to 0.05, corresponding to a lean burn equivalence ratio Φ LFL = 0.485. Regarding the plasma actuation, the peak-to-peak (V pp ) value of the sinusoidal HV was changed at a fixed actuation frequency of about 20 kHz. For each test case, several snapshots of the flame appearance were captured using a Canon EOS 700D camera, equipped with a Canon EFS 55-250 mm lens with resolution of 2912 pixels × 5184 pixels. The image pixel gray level value was discretized using 8 bits, ranging from 0 to 255; they defined the full dark condition (ultra-low luminosity) and the full bright condition (ultra-high luminosity). The toolbox Matlab®was used to process the flame images, which were cropped in order to select the region of interest (ROI). Then, the image grayscale was converted to the image luminance I ranging between 0 and 1. Finally, a proper false-color map ranging between 0 and 0.7 was chosen in order to highlight the flame structure depicted into each raw image.

Electrostatic Field Simulation
In order to provide further insights for the analysis of the experimental findings, two-dimensional axisymmetric numerical computations of the electric field → E inside the burner were performed. The prediction of the electric field aims to identify the ionization area, where the presence of body force induced by the plasma discharge would be relevant. Furthermore, it also permits the evaluation of the direction of this body force. Due to the negligible influence of the magnetic induction and the absence of a relevant external magnetic field, electric field simulations were performed using the electric potential method provided by the magnetohydrodynamic (MHD) module of the toolbox Ansys®Fluent 2019 R1. This allowed to solve the electric field into the computational domain without further addition of user-defined functions and scalars. The set of the governing equations was thus defined as follows: where ϕ represents the electric potential, σ is the electric conductivity in a solid zone or the ionic conductivity in a fluid zone, and → j is the electric current density. Equations (2)-(4) are reduced to the Laplacian of the electric potential, namely: Both coaxial DBD configurations were investigated, as reported in Table 2. A suitable computational grid was defined for each based on the same geometrical domain (see Figure 3a), but different location of the axial needle. The geometrical domain extended about 0.16 mm along the burner tubes, while the external region extended 3R oqt along the axial direction and 2R oqt along the radial direction, where R oqt is the outer radius of the outer quartz tube. The resulting mesh had 125,280 cells. Dielectric surfaces, such as the quartz tubes, were treated as an insulating boundary, and a zero flux of electrons was set on them, as well as the far-field external boundaries. A zero-voltage condition was set instead on the conductive walls of the grounded electrode, and a specific fixed voltage was imposed on the conductive walls of the HV electrode. Coupled walls defined the interfaces between fluid and solid. Both air and methane temperatures were set at 300 K. Based on the experimental mass flow rates, the methane jet velocity at the inner quartz tube inlet was fixed at 0.074 ms −1 , while the air velocity at the entrance of the outer quartz tube was set at 2.3 ms −1 .

Plasma Modeling of the Methane Kinetics and Reactor
By coupling electrostatic field computation insights with experimental observations, ionization was supposed to occur only in the methane tube meant to work as a plasma reactor, while negligible ionization was considered to occur in the air coaxial tube. Therefore, a numerical analysis of the methane plasma chemistry was performed in order to evaluate the thermo-chemistry effect of plasma actuation on the flame behavior which was experimentally observed. To this purpose, the configuration with SSO = −40 mm was considered (test case 2), since it resulted as the most performing.
The electron-impact excitation, dissociation, and ionization reactions were integrated into the reduced gas-phase radicals reaction scheme shown in Table 3. Similar to a study by Poinsot and Veynante [37], the zero-dimensional plasma kinetics solver ZDPlasKin [38] was coupled with the Chemkin-Pro [39] package for the spatial solution of the plasma chemistry along the methane quartz tube and for the flame analysis.
In particular, the ZDPlasKin model implemented a Boltzmann equation solver [40] for the electron-impact reactions, and computed the corresponding reaction rate constants, based on the input list of collision cross sections. The last one was built using the database LXCat [41]. A nonequilibrium system with an electron temperature much higher than gas temperature was set, whereas Computations were performed using a pressure-based steady-state solver in combination with the coupled scheme for the pressure-velocity coupling, a Green-Gauss cell-based scheme for the gradient operator, a second-order scheme for the pressure, and a second-order upwind scheme for all the rest of the spatial discretization variables. Simulations were stopped when all residuals were below 10 −6 .

Plasma Modeling of the Methane Kinetics and Reactor
By coupling electrostatic field computation insights with experimental observations, ionization was supposed to occur only in the methane tube meant to work as a plasma reactor, while negligible ionization was considered to occur in the air coaxial tube. Therefore, a numerical analysis of the methane plasma chemistry was performed in order to evaluate the thermo-chemistry effect of plasma actuation on the flame behavior which was experimentally observed. To this purpose, the configuration with S SO = −40 mm was considered (test case 2), since it resulted as the most performing. The electron-impact excitation, dissociation, and ionization reactions were integrated into the reduced gas-phase radicals reaction scheme shown in Table 3. Similar to a study by Poinsot and Veynante [37], the zero-dimensional plasma kinetics solver ZDPlasKin [38] was coupled with the Chemkin-Pro [39] package for the spatial solution of the plasma chemistry along the methane quartz tube and for the flame analysis. Table 3. Overall reactions scheme. Electron-impact reaction rates were calculated at T elec = 1.7 eV. Reaction rate coefficients k r = A r T β r exp(−E r /T). Units: A r , cm·molecules·s·K; β r , dimensionless;

Reactions
A r β r E r CH

Electron-Impact Ionization
In particular, the ZDPlasKin model implemented a Boltzmann equation solver [40] for the electron-impact reactions, and computed the corresponding reaction rate constants, based on the input list of collision cross sections. The last one was built using the database LXCat [41]. A non-equilibrium system with an electron temperature much higher than gas temperature was set, whereas ion temperature was not considered. During the discharge process, the time evolution of each species was computed using the following equation: where the subscripts i and j refer to the species i and the reaction j, respectively, N represents the species number density, Q ij is the source rates of the species i corresponding to the reaction j, and i max and j max are the total number of species and reactions considered in the model. ZDPlasKin computations were performed at constant atmospheric pressure and gas temperature of 300 K. The gap length was set equal to the inner radius of the methane tube, while the ionization region was supposed to be semi-spherical with the same radius. A constant applied voltage equal to the root mean square of the experimental voltage signal (i.e., V app = (V pp /2)/ √ 2 = 3.76 kV), was used for the estimation of the average reduced electric field established in the ionization region. The time step was set to 10 −5 s, and computations were stopped after 300 s, which ensured the steady-state solution. The electrical behavior of the plasma discharge was considered by tuning a resistance R based on comparison between the experimental current peak with the one predicted by the ZDPlasKin model. As a result, R was set at 1000 kΩ.
Computations estimated a reduced electric field E/N of about 30 Td in accordance with Pitchford and colleagues [42]. Concerning the plasma kinetics, in accordance with Sun and co-workers [43], the electron-impact reaction scheme involved 11 species (CH 4 , CH 3 , CH 2 , CH, H 2 , H, CH + 4 , CH + 3 , CH + 2 , CH + , and the electron e), and consisted in three electron-impact reaction groups, namely the ionization reactions (Equations (E1)-(E9) in Table 3), the recombination reactions (Equations (E10)-(E13) in Table 3), and the dissociation reactions (Equations (E14)-(E18) in Table 3). The solution provided by ZDPlasKin estimated the reaction rate constants of all electron-impact reactions, corresponding to an electron temperature T elec = 1.7 eV.
Therefore, based on the reaction path analysis provided by Masi and colleagues [44], underlining that the plasma zone would mainly consist of hydrogen radicals with trace amounts of CH x radicals, the reaction scheme was enlarged. In particular, 12 more reversible gas-phase reactions (Equations (R1)-(R13) in Table 3) involving five new species (i.e., C 2 H 2 , C 2 H 3 , C 2 H 4 , C 2 H 5 , and C 2 H 6 ) were considered. The reaction rate constants of the gas-phase reactions were taken from the GRI-Mech 3.0 kinetic scheme [45] and the thermodynamic properties of all 16 species were retrieved from the Burcat database [46].
The overall plasma kinetics were then spatially solved by means of Chemkin-Pro. To this purpose, the plasma plug flow reactor (PFR) model was used.
The chemical reactor is represented in the model as a long tube with a constant cross section. Standard assumption of the plug flow model is that the fluid is perfectly mixed in the direction perpendicular to the axis. Furthermore, it is assumed that radial and angular variations of the flow variables (as species fraction, axial velocity, and temperature) are negligible. Perfect mixing also implies strong friction between species, such that they all have the same axial velocity.
It is worth observing that some discrepancies between numerical predictions and experimental data can be retrieved, owing to the simplified treatment of the heat transfer inside the reactor body, the simplified treatment of the heat and mass transfer in the radial direction (due to averaging) and the lack of heat and mass transfer (plug flow assumption) in the axial direction (due to the Lagrangian approach). Despite these limitations, the implemented two-step modeling approach is valuable for process engineering applications involving design, optimization, and verification of plasma reactors by using much less computational resources than a two-dimensional model.
Based on one-dimensional (1D) approximation in relation to the axisymmetric geometry of the reactor, it solved the following species, momentum, and energy balance equations: where A represents the cross-sectional area of the reactor, F is the drag force, P is pressure, T is the temperature, h is the specific enthalpy, u is axial velocity, and ρ is density. Also, W is the molecular weight, Y is the molar fraction, . ω i is molar production rate, c p is the mean heat capacity per mass, . q plasma is the plasma power deposition per unit length, a e is the inner surface area per unit length, and . q ext is the heat flux from the surroundings to the reactor tube. PFR computations estimated the plasma-induced modification of the fuel composition at the methane tube exit section. The zero axial position was set at the tip of the needle and the reactor diameter was set equal to the inner diameter of the methane quartz tube. A pressure value equal to 101,325 Pa was set at the inlet section, together with a 0.99 molar fraction of CH 4 , a 0.001 molar fraction of H 2 , and an electron number density of about 10 8 molecules/cm 3 . Computations were performed by fixing the gas temperature at 300 K. The plasma power deposition profile, shown in Figure 4, was provided in order to reproduce the plasma reactor behavior.  The amplitude of the plasma power was set equal to the experimental dissipated power (i.e., 0.05 W). The heat exchange between the gas and the surroundings was neglected based on coldplasma assumption.
Finally, the modification of the flame speed as a function of the local equivalence ratio Φ value in the presence of plasma actuation was analyzed using the laminar premixed flame speed (LPFS) model. It solves the mass, momentum, species, and energy balance equations of a premixed flow based on on*10-dimensional approximation. The temperature and the modified fuel composition (estimated at the exit of the burner by means of PFR computations) were used for flame speed predictions, which were then compared with the ones predicted in the absence of plasma actuation, namely at ambient temperature and pure methane. Figure 5 shows the effect of the standoff distance on the flame anchoring. When applying a peakto-peak voltage of about 11 kV, the effectiveness of the coaxial DBD configuration is estimated. In particular, the flame reattached to the lips of the inner quartz tube when SSO = −40 mm (test case 2), while for SSO = 20 mm (test case 3), flame reattachment was not experienced, and no differences were The amplitude of the plasma power was set equal to the experimental dissipated power (i.e., 0.05 W). The heat exchange between the gas and the surroundings was neglected based on cold-plasma assumption.

Results
Finally, the modification of the flame speed as a function of the local equivalence ratio Φ value in the presence of plasma actuation was analyzed using the laminar premixed flame speed (LPFS) model. It solves the mass, momentum, species, and energy balance equations of a premixed flow based on on*10-dimensional approximation. The temperature and the modified fuel composition (estimated at the exit of the burner by means of PFR computations) were used for flame speed predictions, which were then compared with the ones predicted in the absence of plasma actuation, namely at ambient temperature and pure methane. Figure 5 shows the effect of the standoff distance on the flame anchoring. When applying a peak-to-peak voltage of about 11 kV, the effectiveness of the coaxial DBD configuration is estimated. In particular, the flame reattached to the lips of the inner quartz tube when S SO = −40 mm (test case 2), while for S SO = 20 mm (test case 3), flame reattachment was not experienced, and no differences were exhibited with respect to the clean case (test case 1). This result increased its relevance when the dissipated power results were taken in consideration: its value for S SO = −40 mm was about 18% less than the one measured for S SO = 20 mm. When using the actuator configuration with S SO = 20 mm, a partially reattached flame condition was observed when increasing the supplied voltage, and the complete flame reattachment was obtained for V pp = 18.4 kV (test case 4). As a result, when considering the plasma power required for flame reattachment, the DBD configuration with S SO = 20 mm revealed to be less efficient since it was 23 times more power-consuming than the configuration with S SO = −40 mm. model. It solves the mass, momentum, species, and energy balance equations of a premixed flow based on on*10-dimensional approximation. The temperature and the modified fuel composition (estimated at the exit of the burner by means of PFR computations) were used for flame speed predictions, which were then compared with the ones predicted in the absence of plasma actuation, namely at ambient temperature and pure methane. Figure 5 shows the effect of the standoff distance on the flame anchoring. When applying a peakto-peak voltage of about 11 kV, the effectiveness of the coaxial DBD configuration is estimated. In particular, the flame reattached to the lips of the inner quartz tube when SSO = −40 mm (test case 2), while for SSO = 20 mm (test case 3), flame reattachment was not experienced, and no differences were exhibited with respect to the clean case (test case 1). This result increased its relevance when the dissipated power results were taken in consideration: its value for SSO = −40 mm was about 18% less than the one measured for SSO = 20 mm. When using the actuator configuration with SSO = 20 mm, a partially reattached flame condition was observed when increasing the supplied voltage, and the complete flame reattachment was obtained for Vpp = 18.4 kV (test case 4). As a result, when considering the plasma power required for flame reattachment, the DBD configuration with SSO = 20 mm revealed to be less efficient since it was 23 times more power-consuming than the configuration with SSO = −40 mm. In particular, the comparison between the clean case (test case 1) and the plasma actuated case with negative stand-off (test case 2) figured out that the overall plasma-induced combustion enhancement allowed to overcome the strong confinement effect produced by the outer air flow, In particular, the comparison between the clean case (test case 1) and the plasma actuated case with negative stand-off (test case 2) figured out that the overall plasma-induced combustion enhancement allowed to overcome the strong confinement effect produced by the outer air flow, which caused a lifted flame when in the absence of plasma actuation. To this regard, the rate of flame propagation, or burning velocity, is of primary importance in determining the flame stability, which occurs when the burning velocity balances the local fuel-air mixture velocity at the flame surface. Figure 6 shows the comparison between two experimental snapshots of the flame appearance, as previously described in Section 2: on the left side the flame is lifting, as observed when operating without plasma actuation (test case 1); on the right side, the flame is anchored to the Bunsen lips as a consequence of the plasma-induced flame reattachment (test case 2). The black dashed curves represent the iso-line of the image luminance at I = 0.4, and they qualitatively denote the flame surface, along which the stabilization point is located at the most upstream point. As a result, the plasma actuation modified the local flow structure close to the stabilization point that moved towards the burner exit. This allowed for the extension of the flame region until complete flame reattachment was achieved, owing to the flame propagation rate enhancement. This could be due to three main coupled effects:

Results
• momentum effect which led to the slowing down of the flow into the quartz tube; • plasma chemistry effect with fuel conversion; • thermal effects with gas temperature rise.
Therefore, a numerical investigation was performed in order to decouple these effects. As first, it was considered that the DBD configuration with S SO = −40 mm mostly differs from the one with S SO = 20 mm due to the presence of stronger electric field edge effects at the needle tip. Consequently, Energies 2020, 13, 1452 11 of 19 simulations of the electrostatic field under steady-state conditions were performed in order to estimate the electric field strength in both DBD configurations. Results are shown in Figure 7, where the contour plot of the electric field in the radial direction (E x ) and the axial direction (E y ) are compared. It is worth mentioning that the color map has been properly scaled in order to better figure out the extension and the shape of the electric field. Furthermore, a negative value of E y represents a negative component of the axial-induced body force on the flow, pointing towards the inlets of the Bunsen. As expected, simulations determined that the maxima of the electric field were placed in the region of the electrode corners. In particular, when considering the axial electric field, the extension of the negative E y for S SO = −40 mm was larger than the one computed for S SO = 20 mm. Conversely, a strong positive electric field was established just above the needle tip when S SO = 20 mm. Consequently, the DBD configuration with S SO = −40 mm introduced momentum sources opposed to the flow, slowing it down with the consequent reduction of the mean residence times. On the contrary, the DBD configuration with S SO = 20 mm led to a momentum increase in the direction of the flow, and the flow velocity rose in such a way that the flame reattachment effect was damped. Moreover, when S SO = 20 mm, the positive and the negative maxima of E y were of the same order of magnitude while, for S SO = −40 mm, the negative part was highly prevailing on the positive one.

Methane Plasma-Reactor Model Results
Numerical simulations showed that when using the DBD configuration with S SO = −40 mm, the highest electric field extended into the inner quartz tube, as confirmed by experimental visualization close to the needle tip, as shown in Figure 7a. This impacted the plasma chemistry and methane dissociation, leading to the activation of electron-impact and radical reactions, as confirmed by the reaction rates shown in Figure 8 resulting from the zero-dimensional chemistry analysis on ZDPlasKin.
Energies 2020, 13, x FOR PEER REVIEW 11 of 19 which caused a lifted flame when in the absence of plasma actuation. To this regard, the rate of flame propagation, or burning velocity, is of primary importance in determining the flame stability, which occurs when the burning velocity balances the local fuel-air mixture velocity at the flame surface. Figure 6 shows the comparison between two experimental snapshots of the flame appearance, as previously described in Section 2: on the left side the flame is lifting, as observed when operating without plasma actuation (test case 1); on the right side, the flame is anchored to the Bunsen lips as a consequence of the plasma-induced flame reattachment (test case 2). The black dashed curves represent the iso-line of the image luminance at I = 0.4, and they qualitatively denote the flame surface, along which the stabilization point is located at the most upstream point. As a result, the plasma actuation modified the local flow structure close to the stabilization point that moved towards the burner exit. This allowed for the extension of the flame region until complete flame reattachment was achieved, owing to the flame propagation rate enhancement. This could be due to three main coupled effects: • momentum effect which led to the slowing down of the flow into the quartz tube; • plasma chemistry effect with fuel conversion; • thermal effects with gas temperature rise. Consequently, the DBD configuration with SSO = −40 mm introduced momentum sources opposed to the flow, slowing it down with the consequent reduction of the mean residence times. On the contrary, the DBD configuration with SSO = 20 mm led to a momentum increase in the direction of the flow, and the flow velocity rose in such a way that the flame reattachment effect was damped.
Moreover, when SSO = 20 mm, the positive and the negative maxima of Ey were of the same order of magnitude while, for SSO = −40 mm, the negative part was highly prevailing on the positive one.

Methane Plasma-Reactor Model Results
Numerical simulations showed that when using the DBD configuration with SSO = −40 mm, the highest electric field extended into the inner quartz tube, as confirmed by experimental visualization close to the needle tip, as shown in Figure 7a. This impacted the plasma chemistry and methane dissociation, leading to the activation of electron-impact and radical reactions, as confirmed by the reaction rates shown in Figure 8 resulting from the zero-dimensional chemistry analysis on ZDPlasKin. Therefore, based on experimental conditions of test 2, the solution of the plasma flow into the inner quartz tube, modeled as a PFR, predicted both the fuel composition and gas temperature at the entrance of the flame region. Figure 9 shows the axial profiles of the concentration of the main species in terms of number density. Results indicate that at the burner exit, CH4 consumption, due to plasmainduced dissociation, was about 6%. On the other hand, plasma discharge promoted the production Therefore, based on experimental conditions of test 2, the solution of the plasma flow into the inner quartz tube, modeled as a PFR, predicted both the fuel composition and gas temperature at the entrance of the flame region. Figure 9 shows the axial profiles of the concentration of the main species in terms of number density. Results indicate that at the burner exit, CH 4 consumption, due to plasma-induced dissociation, was about 6%. On the other hand, plasma discharge promoted the production of new species (hydrocarbons like ethane C 2 H 6 and ethylene C 2 H 4 ), radicals (e.g., methyl), and ions. It is worth underlining the prevailing production of the methyl radical CH 3 , which plays a crucial role in DBD and low-energy density discharges. As experimentally retrieved in studies by Burcat and Ruscic [47] and Nozaki and Okazaki [48], electron impact reactions drive the reactivity in such systems, leading to CH 3 radical formation in the discharge and, consequently, to ethane and ethylene production owing to CH 3 radical recombination reactions at low temperatures. Therefore, based on experimental conditions of test 2, the solution of the plasma flow into the inner quartz tube, modeled as a PFR, predicted both the fuel composition and gas temperature at the entrance of the flame region. Figure 9 shows the axial profiles of the concentration of the main species in terms of number density. Results indicate that at the burner exit, CH4 consumption, due to plasmainduced dissociation, was about 6%. On the other hand, plasma discharge promoted the production of new species (hydrocarbons like ethane C2H6 and ethylene C2H4), radicals (e.g., methyl), and ions. It is worth underlining the prevailing production of the methyl radical CH3, which plays a crucial role in DBD and low-energy density discharges. As experimentally retrieved in studies by Burcat and Ruscic [47] and Nozaki and Okazaki [48], electron impact reactions drive the reactivity in such systems, leading to CH3 radical formation in the discharge and, consequently, to ethane and ethylene production owing to CH3 radical recombination reactions at low temperatures.  Plasma actuation also led to a slight increase of gas temperature at about 21.8 • C, as highlighted in Figure 10.
Therefore, the analysis of the effect of the plasma discharge was extended to the flame region. To this purpose, the comparison between the clean configuration (test case 1) and the plasma actuated one (test case 2) was performed in terms of flame speed and neat heat production, which were estimated by means of LPFS computations. The clean configuration was set at ambient temperature and pure methane, while the plasma actuated case was initialized using the fuel composition and temperature at the burner exit predicted by PFR computations. Figure 11 shows the comparison of the predicted flame speed as a function of the local equivalence ratio.
As a result, the establishment of weak ionization process into the burner was estimated with no relevant modification of the fuel composition. However, it coupled with the temperature rise of 21.8 • C which significantly impacted the laminar flame speed. In fact, an increase of about 10% was retrieved near stoichiometric conditions. This implies that the chemical characteristic time reduced, and the combustion process became faster in the presence of plasma actuation with respect to the clean configuration. Plasma actuation also led to a slight increase of gas temperature at about 21.8 °C, as highlighted in Figure 10. Therefore, the analysis of the effect of the plasma discharge was extended to the flame region. To this purpose, the comparison between the clean configuration (test case 1) and the plasma actuated one (test case 2) was performed in terms of flame speed and neat heat production, which were estimated by means of LPFS computations. The clean configuration was set at ambient temperature and pure methane, while the plasma actuated case was initialized using the fuel composition and temperature at the burner exit predicted by PFR computations. Figure 11 shows the comparison of the predicted flame speed as a function of the local equivalence ratio. As a result, the establishment of weak ionization process into the burner was estimated with no relevant modification of the fuel composition. However, it coupled with the temperature rise of 21.8 °C which significantly impacted the laminar flame speed. In fact, an increase of about 10% was retrieved near stoichiometric conditions. This implies that the chemical characteristic time reduced, and the combustion process became faster in the presence of plasma actuation with respect to the clean configuration. This finding is confirmed by the chemical heat release versus gas temperature plot shown in Figure 12. In particular, the comparison highlights that when in presence of plasma actuation, the chemical heat release increased at lower temperature because of the additional energy that was coupled into the system by the plasma. Consequently, the elevated level of heat release in the flame  Therefore, the analysis of the effect of the plasma discharge was extended to the flame region. To this purpose, the comparison between the clean configuration (test case 1) and the plasma actuated one (test case 2) was performed in terms of flame speed and neat heat production, which were estimated by means of LPFS computations. The clean configuration was set at ambient temperature and pure methane, while the plasma actuated case was initialized using the fuel composition and temperature at the burner exit predicted by PFR computations. Figure 11 shows the comparison of the predicted flame speed as a function of the local equivalence ratio. As a result, the establishment of weak ionization process into the burner was estimated with no relevant modification of the fuel composition. However, it coupled with the temperature rise of 21.8 °C which significantly impacted the laminar flame speed. In fact, an increase of about 10% was retrieved near stoichiometric conditions. This implies that the chemical characteristic time reduced, and the combustion process became faster in the presence of plasma actuation with respect to the clean configuration. This finding is confirmed by the chemical heat release versus gas temperature plot shown in Figure 12. In particular, the comparison highlights that when in presence of plasma actuation, the chemical heat release increased at lower temperature because of the additional energy that was coupled into the system by the plasma. Consequently, the elevated level of heat release in the flame This finding is confirmed by the chemical heat release versus gas temperature plot shown in Figure 12. In particular, the comparison highlights that when in presence of plasma actuation, the chemical heat release increased at lower temperature because of the additional energy that was coupled into the system by the plasma. Consequently, the elevated level of heat release in the flame accelerated all reactions, which impacted the structure of the flame and enhanced its propagation rate.  In conclusion, the plasma reactor/laminar premixed flame analysis demonstrated that the flame reattachment experimentally observed could be related to flame speed enhancement due to plasma actuation.  In conclusion, the plasma reactor/laminar premixed flame analysis demonstrated that the flame reattachment experimentally observed could be related to flame speed enhancement due to plasma actuation.

Conclusions
In the present work, the effect of a sinusoidal plasma actuation on lifted flames was investigated. At this purpose, a lean non-premixed CH 4 /air flame in a non-premixed Bunsen-type burner with annular fuel jet was considered. Experiments focused on investigating the effect of the actuator standoff distance S SO on the flame lift-off. To this purpose, two different coaxial DBD configurations were considered, namely S SO = −40 mm and S SO = 20 mm.
Experimental results showed that the flame reattached to the burner lips when operating at V pp voltage of about 11 kV and using the configuration with S SO = −40 mm. On the contrary, the configuration with S SO = 20 mm did not work for flame reattachment. Moreover, a reduction of the dissipated power of about 18% was also retrieved when using the configuration with S SO = −40 mm. In order to reattach the flame with S SO = 20 mm configuration, the applied voltage had to increase up to V pp = 18 kV, with a power consumption about 23 times higher than the one measured with S SO = −40 mm at V pp = 11 kV.
Furthermore, in order to decouple the effect of the plasma actuation in terms of momentum, plasma chemistry, and thermal effects, a numerical analysis was performed. Steady-state electrostatic field simulations were combined with computations of the plasma-chemistry into the methane quartz tube modeled as a plasma reactor. Finally, the impact of the predicted fuel composition and temperature when in the presence of plasma actuation was investigated in terms of flame speed modification.
As predicted by the electric field computations, the DBD configuration with S SO = −40 mm exhibited an electric field opposed to the flow. Therefore, due to the proportional relation between the electric field and the plasma-induced body forces, the DBD configuration with a negative S SO value allowed to introduce momentum sources, with the consequent reduction of the mean residence times. Furthermore, the highest electric field extended into the inner quartz tube, as confirmed by experimental visualization close to the needle tip.
The methane plasma reactor model predicted the activation of the electron-impact reactions which led to the production of CH 3 ; this enabled the gas-phase reaction for C 2 H 6 production and, hence, C 2 H 4 production by ethane dehydrogenation. The plasma discharge also led to the increase of gas temperature of about 21.8 • C. Consequently, the flame speed increased in the measure of about 10% when close to the stoichiometric conditions, in comparison with the absence of plasma actuation. Therefore, the flame reattachment experimentally observed can be related to the enhancement of the flame speed due to reduced chemical characteristic times and a faster combustion process when in the presence of plasma actuation.