The Radio-Frequency Corona Ignition System is characterised by a wide initial combustion volume and precursors production, via radical insemination by the streamers, in addition to high released thermal energy. These features lead to faster combustion, a higher tolerance for lean mixtures and EGR dilutions and, in general, more adaptability. The thermal energy released by the igniter to the surrounding medium can help to understand the performance, the behaviour and the application range. This paper proposes a systematic experimental analysis of the thermal energy released by the igniter at room temperature, via pressure-based calorimetry. This analysis, carried out at di erent pressures (up to 10 bar) and medium type (air or nitrogen), is extended to the whole range of the corona igniter control parameters, namely streamer duration and driving voltage. The latter is proportional to the maximum electrode voltage, as shown in the model here presented, and as con rmed by experiments. The results show, for all the vessel pressures, the high energetic eciency of the ignition system and the high amount of the released energy. The latter is found to increase linearly with the corona streamers duration and quickly with the driving voltage up to the streamer-to-arc transition threshold. The eciency tends to reach a de ned upper limit. For each tested point, the energy released to pure nitrogen is higher than to air, which evidences the impact of the oxygen presence under streamer exposure. Keywords: Corona streamer, Discharge thermal energy, Thermal eciency, Plasma assisted ignition, Pressure-based calorimetry 1. Introduction The pressing request, in term of pollutant emissions and carbon footprint, forces the automotive in- dustries to introduce and develop innovative technologies to allow the internal combustion engine to be competitive in the modern world market for the next years. The need for exhaust gas recirculation ( EGR ) [1] or ultra-lean combustion [2] requires the development of advanced and innovative ignition systems and strategies, by enhancing the thermal energy conversion eciency, that increases quite linearly with [3], and allowing operating conditions characterised by poor pollutant emissions [4, 5]. The water injection is also an advanced technology able to improve the combustion in the modern engines for the general performance enhancement [6, 7] as well as the thermal eciency improvement [8, 9] or the knocking control strategies [10]. All these new working conditions demand high ignition energy not available for the conventional inductive Corresponding author. E-mail address: gabriele.discepoli@unipg.it; Tel./fax: +39 075.585.3749 Universit a degli Studi di Perugia, Department of Engineering, Via Duranti 67, 06125 Perugia, Italy c 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/ licenses/by-nc-nd/4.0/ Preprint submitted to Applied Energy; https://doi.org/10.1016/j.apenergy.2020.114617 February 12, 2020ACCEPTED MANUSCRIPT 1 INTRODUCTION Nomenclature ACIS Advanced Corona Ignition System BDV Breakdown Voltage CIV Corona Inception Voltage E Electric eld EGR Exhaust Gas Recirculation Er Energy released to the medium Es Energy supplied to the igniter coil FM Federal-Mogul Powertrain Italy a Tenneco Group Company Is Igniter coil current N Concentration of the gas particles pch Bomb chamber inner pressure pmax ch Chamber pressure just after a streamer event pmin ch Chamber pressure just before a streamer event Ton Duration of corona discharge UniPG University of Perugia vion drift Ion drift velocity vel drift Electron drift velocity Vd Driving voltage V0 d Maximum driving voltage before corona inception VBDV d Driving voltage at breakdown VCIV d Driving voltage at corona inception Vmax d Maximum driving voltage before breakdown Ve Electrode voltage amplitude VBDV e Electrode voltage amplitude at breakdown VCIV e Electrode voltage amplitude at corona inception Vs Voltage amplitude applied to the igniter coil Vch Bomb chamber inner volume Heat speci c ratio pch Pressure gradient due to a streamer event  Thermal eciency of the igniter i Frequency of the igniter current spark plug [11]. The increase of eciency to transfer the primary energy (i.e. the energy supplied to the igniter primary circuit) to the air{to{fuel mix is critical [12] and, at present, it is widely below the 3% [13]. The conventional spark ignition systems have limitations in obtaining a robust ignition in high pressure (boosted engine), lean or EGR-diluted environment [14]. Therefore, the rising of the energy transferred to the mix is mandatory for the spark plug system, in particular for high turbulence intensity [15, 16]. This improvement is reached, for example, through the implementation of high-energy inductive ignition systems [3, 17, 18, 19]. Unfortunately, this technology shows electrode ablation/erosion/fouling [11, 20, 21, 22] where the plug electrodes widely a ect the ame kernel development [23]. Furthermore, when the lean limit is extended, then the cycle-to-cycle variability increases. The reduction of the latter condition requires even higher released energy that consequently produces a sudden drop of the eciency [19, 3]. The early uctuations of the thermodynamics and uid-dynamics operating conditions around the spark region are the main causes of the cycle-to-cycle variation [24] while large ame kernels are less subject to conditioning [25]. Furthermore, dielectric insulation becomes an issue once higher discharge voltage is required to achieve the breakdown conditions, as in the modern engines for the high levels of boosting [5]. The plasma assisted ignition is based on the non-equilibrium low-temperature plasma and is characterised 2ACCEPTED MANUSCRIPT 2 EXPERIMENTAL LAYOUT by streamers emission. Under this regime the heat loss to the electrodes is negligible [26], contrary to standard spark igniter. The energy is moved eciently to the rotational, vibrational and electronic excited states of the medium molecules [27, 28, 29]. The excited species production and their following quenching by the molecular oxygen make the gas heating fast while the oxygen is consequently dissociated in atomic oxygen [30]. This is the main mechanism for the Oproduction together with the direct electron impact on theO2[27]. TheOdensity is however reduced by the strong interaction with the water dissociation productsOHandHO2, capable to capture the O[30], of a particular interest in the water injection case. Fundamentally, the oxygen in atomic, ionic or excited state seems to be the key chemical species for the plasma ignition [31, 32, 33], in particular in the atomic state, to increase the ame's propagation velocity [27, 34]. By means of several production mechanisms of ions and excited species [35], in particular of the highly reactiveOHradical [36, 37], the plasma-based igniters add new paths to start a reaction chain that leads to combustion [38]. As a consequence, these igniters are characterised by the reduction of the ignition time up to two orders of magnitude [39] and the decrease of the ignition temperature [27] with respect to conventional spark igniters. More in general, this family of technologies improves the ame stability [40] and the engine performance [41, 42] thanks to the multiple spreading ignition locations of the areas of greatest active species production [43, 44, 45]. In addition, plasma-based ignition enhances the reaction kinetic due to the high electron energies [31] and to the e ect on the fuel reactivity and di usivity [46]. At present, the state-of-art plasma-assisted ignition models are lacking of accurate prevision of the released thermal energy. They have to face challenging issues [47, 48, 49] as, for example the di erent magnitudes order of the timescale between the plasma formation and the ignition process [48, 50]. The same streamers phenomenon is hard to model due to the complexity of the involved physics mechanisms [51, 52]. In this work, the subject of investigation is the Radio-Frequency Advanced Corona Ignition System ( RF ACIS ), based on low temperature plasma and characterised by a single electrode, fed by a 1 MHz AC current. It has been proved that the RF corona discharge extends the lean air{to{fuel mix combustion limit with respect to the conventional spark igniter [53, 54, 55, 56] and, as other low temperature plasma igniters, the EGR dilution tolerance [57, 58, 59]. This is possible by stabilising the combustion ignition with a large area ame kernel [60, 61] and by reducing the cycle-to-cycle variability for a given EGR rate with bigger impact on naturally aspirated loads than on boosted ones [62]. These result in an overall advantage in terms of fuel consumption and exhaust raw emissions [63]. Generally speaking, the thermal energy delivered to the charge mix is a key parameter since it heavily a ects the ame kernel formation and then a proper ignition [13], as the ame kernel growth leads an essential role [64]. Indeed, the chemical activity cannot be separated from the thermal phase, even if the radicals production is supposed to be the main feature of the plasma assisted igniter. The thermal phase is spatially distributed, enhancing the chemical kinetics of the exothermic fuel oxidation, resulting in the combustion initiation [43]. Therefore, the aim of the present work is to generalise the preliminary test described in [65], on a pre-production Corona igniter element, supplied by Federal-Mogul Powertrain Italy a Tenneco Group Company (FMfrom now on). We adopted a systematic approach to assess the thermal energy released by the streamers to the medium (pure nitrogen, used as baseline characterisation, and air, the oxidising uid in real working conditions). The thermal energy is measured in a simpli ed and controllable environment, i.e. a constant volume vessel, operated at di erent pressures for both the gases. The study is extended from the Corona inception voltage until the breakdown and for di erent duration of the discharge. 2. Experimental Layout 2.1. Advanced Corona Ignition System The ignition system studied in this work is a pre-series model of Advanced Corona Ignition System (ACIS) fed by an alternating current with a frequency of about 1 :04MHz (RF Corona). Inside the combustion chamber, the igniter generates a strong alternating electric eld magni ed by the igniter tip, characterised by a small curvature radius and sharp edge [66, 67]. The electric eld induces, from the four-point electrode, 3ACCEPTED MANUSCRIPT 3 METHODOLOGY 2.2 Experimental setup of the released thermal energy measurement the production of the streamers (normally, one streamer for each electrode-point), plasma channels free to propagate inside the chamber. The streamers activate a large volume of air{fuel mixture and release a considerable amount of energy, essential for ignition in lean conditions [18, 68, 65]. The igniter is controlled by a dedicated electronic system that works as a high frequency ampli er. This system allows to set the time duration of the streamers activity Tonand the driving voltage Vd, the input voltage of the high frequency ampli er, to control the electric potential at the ring tip electrode. Details of the ACIS are available in our previous publications [55, 69]. 2.2. Experimental setup of the released thermal energy measurement A constant volume vessel, the bomb , in Plexiglas (low thermal conductivity, 0 :187Wm1K1), accom- modates the igniter tip for the released energy measurement at room temperature. The inner chamber has cylindrical geometry with a volume Vch= 22:5cm3and allows the management of the operating conditions, i.e. temperature, pressure and gas type (air or nitrogen, 5 :0 purity, Linde ). The measurement of the inner pressure variation  pch, generated by the streamer discharge, is obtained by the piezoelectric low-pressure sensor Kistler Type 7261 , with 2200 pCbar1of sensitivity and 105bar of resolution. The pressure sensor is installed at the opposite side of the igniter in the chamber and works as a ground electrode. It produces a charge signal collected by the charge ampli er Kistler Type 5011 and converted in a proportional voltage signal. Current and voltage supplied to the igniter coil are collected by, respectively, the current probe Teledyne LeCroy CP030 (sensitivity of 10 mAdiv1) and the passive probe Teledyne LeCroy PP020 . A thermocouple records the temperature in the inner bomb chamber. A piezoresistive pressure transmitters Keller PA-22S (accuracy1%FS), once calibrated by a Scandura Pascal 100 system, measures the initial pressure inside the chamber. All these quantities are acquired by a fast oscilloscope Teledyne LeCroy Wavesurfer 3000 with a sampling frequency of 10 MHz , about ten times bigger than ACIS AC supply frequency. A pneumatic system (valves, precision pressure reducer Festo LRP, one-way ow controllers Festo GR ) allows to properly control the gas pressure and the (intensive) replacement in the chamber. The medium renewal is needed before/after any test sequence as it seems the streamers products impact the igniter performance, in particular when highly electronegative and reactive species, as the oxygen, are included [70, 71], arguably due to the electrode erosion/fouling [28]. Each single discharge event is triggered by the Arbitrary Wave Generator HP 33120A . 2.3. Experimental setup of the igniter electric characterisation Performance of the overall system has been evaluated analysing input and output electrical parameters. Using nitrogen (UN1066 99 ;9% of nitrogen) at 20 barpressure, the system was stressed to simulate the operating conditions running inside an engine combustion chamber. A cylindrical constant volume vessel, made in steel AISI 316 with a tempered glass inspecting window, is used as test bench environment for system characterisation. The chamber has a constant volume of 20 mm3. Test is performed at constant room temperature and the system, consisting of a pressure valve Tartarini PS90A and a pressure controller, allows to maintain the 20 barduring the overall test. No gas recirculation is requested during the characterisation test. A high voltage probe Tektronix P6030A (capacitance 3 :0pF, accuracy3%) is mounted on the other side of the chamber, in physical contact with the electrode tip centre by means of a pin extender RS 434-790 . A current probe Tektronix TCP0030A (accuracy1:5%) and a voltage probe Tektronix P6015A (capacitance 3:0pF, accuracy3%) acquire current and voltage supplied to the igniter. The probes are connected to an RF cable bridge before the input coil connector. The oscilloscope Tektronix MS056 , with a bandwidth of 350MHz , acquires input and output current and voltage. 3. Methodology 3.1. Electrode voltage assessment The analysis of the igniter electrode voltage Veis led, along with the coil input voltage Vsand current Is, by varying the duration Tonand driving voltage Vd. Actually, Ve,VsandIsrepresent the amplitude of the corresponding alternating quantity. The power input Psis evaluated using VsandIs, functions of the duty 4ACCEPTED MANUSCRIPT 3 METHODOLOGY 3.2 Thermal energy assessment cycle. Once the igniter is mounted on the pressure bomb, pressurised at 20 barin nitrogen, the oscilloscope is set with a sample rate of 1 :25GS=s to reach the accuracy on acquiring the 1MHz ACIS signal. Test is divided in two phases: -phase 1 . ShorterTonand continuous trigger impulse, necessary to analyse the power input in the igniter coil. -phase 2 . LongerTonbut a single pulse trigger to provide a more stable output voltage. During the phase 1 ,Tonis set at 500 s, the trigger input signal has a frequency ftrof 25HzandVd changes from 20 Vto 50Vwith steps of 10 V. Data were acquired after 5 son each point to have a stable result. Phase 2 has aTonof 1000s, single pulse as trigger input signal and Vdsweep from 20 Vto 50V with 10Vstep. Also in this case data is acquired after 5 s. The results are pretty well described by a linear regression ( g. 4). Once the data are acquired, the power supplied to the igniter coil Psis calculated considering the duty cycle acquired during the rst test phase, the current Isand the voltage Vsaccording to: Ps=ftrTonVsIs (1) 3.2. Thermal energy assessment Once the external trigger starts an event, the ACcurrent amplitude begins to rise from zero to the target level with a certain rate ( g. 1, top), not dependent on the particular duration selected. The streamer discharge is active as soon as the amplitude reaches a de ned threshold ( CIV, the Corona Inception Voltage ), depending on the bomb chamber inner pressure Pch, the gas type and the driving voltage Vd (and consequently the electrode voltage Ve). Correspondingly, the pressure signal shows a current{induced electromagnetic noise with an overall rise characterised by di erent local maxima and minima ( g. 1, bottom ), after some tens of microseconds. This shape is consistent with the mutual interaction of sound waves propagating in the bomb chamber medium. Finally, the current falls quickly (a few tens of s) as soon as the discharge duration reaches the assigned value. Likewise, the streamer ends once the current amplitude decreases under the CIV threshold. Then, the pressure signal is not a ected by electromagnetic noise anymore and continues the oscillations around a well-de ned average value. The raw data of a streamer event are acquired and then processed to nd the corresponding  pch: - a 2kHzlow-pass lter is applied to smooth the signal (red solid line in g. 1, bottom ) and remove all the noise components (well visible in the frequency domain and already described in our preliminary work [65]). - the sections before and after the streamer event are identi ed to calculate, respectively, pmin chandpmax ch as the average of the corresponding pressure measurement data. Note that the proper identi cation of the time domain section relative to pmax chis critical since the pressure signal has strong oscillations and tends to decrease quickly. The nal  pchis obtained as the mean value of 20 consecutive streamer events, produced with a frequency of 10Hz, for each parameters con guration. The number of the consecutive recorded events and the streamers generation frequency are chosen as a compromise to collect as much data as possible with no visible e ect on the igniter performance. If the bomb chamber is assumed as adiabatic [13] suitable as a rst approximation for few milliseconds after the streamer event), the thermal energy Er, delivered to the chamber medium by the igniter, is given by the rst law of the thermodynamics: Er=1 1Vchpch (2) 5ACCEPTED MANUSCRIPT 3 METHODOLOGY 3.3 Test Campaign -2024Current, A 0100200300400500Time, s-20246Pressure, mbar-404 Figure 1: ( Top) Sinusoidal current of 1MHz produced by the ACIS igniter in a 300 sshot and ( top right corner ) its magni cation along two periods ( 2s.) (Bottom ) Pressure waves induced by the current in the bomb chamber. The solid red line represents the smoothed pressure signal once the 2 kHzlow-pass lter is applied. where is the speci c heat ratio, Vchis the chamber volume and  p=pmax chpmin ch, the pressure di erence before and after the streamer event, respectively. The energy Essupplied to the coil, or primary energy, is a function of the driving voltage Vdand of the corona duration Ton, in rst approximation. Experimentally, the supply current Isand voltage Vsare simultaneously measured to determine an Es(Vd;Ton) parametrization curve to simplify the experimental layout: once VdandTonare speci ed, Es is indeed a constant of the system. The trend of the parametrization curve, as a function of Vdat xed Ton= 300s, is shown in g. 2, while the dependence on Tonis just linear. Finally, the thermal eciency characterises the capability of the igniter to transfer the primary energy to the inner chamber medium as thermal energy and is de ned as the ratio between the released (thermal) energyErand the supplied (electric) energy Es: =Er Es(3) 3.3. Test Campaign The test campaign is built by varying each operating parameter, one at a time, starting from a de ned set of values, addressed as standard conditions (tab. 1). Table 1: Standard conditions of the operating parameters for the thermal released energy measurement. Bomb Chamber Igniter Gas type Pressure Driving voltage Corona duration N2 5:5 bar 40 V 300 s The corona duration has an important role in ignition strategy since it could act as a reducer for the high cycle-to-cycle variability, characteristic of the ultra lean blends or high EGR levels [56]. This is possible at the cost of some extra energy in more stressing conditions. The operating interval of Tonincludes values from 100sto 500s, sampled in steps of 100 s, with the remaining parameter set as in tab. 1. 6ACCEPTED MANUSCRIPT 4 ACIS MODEL 05001000150020002500 020406080100120Supplied Energy, mJDriving Voltage, V Figure 2: Parametrization curve of Es, the energy supplied to the igniter, as a function of the driving voltage, at xed corona duration (300 s). The dependence on the driving voltage Vdneeds more care because it is strictly connected with the bomb chamber inner pressure pch. Indeed, the same test modality used for Tonis applied to Vdfor four di erent chamber pressures, from 3 :25barto 10barabsolute, to obtain a matrix of 5 4 points. The 1 barpoint, initially expected, was rejected because the low pressure moves up the arc event at very low Vdand directly to the igniter external metallic shell (not towards the pressure sensor). Therefore, it loses comparability with the remaining cases. The driving voltage operating interval strongly depends on the chamber pressure pch. It has to be deter- mined experimentally for each tested pressure, point by point, by looking for the opposite working conditions of breakdown voltage ( streamer-to-arc transition) and corona inception voltage (minimum required for the transition to the streamer), respectively BDV and CIV, according to the nomenclature used in [72]. 4. ACIS model 4.1. Model Generally, resonant ignition systems are con gured as a series-resonant RLC circuit but these simpli ed circuit models do not show a good prediction on the voltage output assessment. The reason is attributed to the stray electrical parameters in the igniter assembly. The circuit of g. 3 represents this igniter assembly as lumped-parameter circuit and comprises: -a coil . The inductance L1can be measured from prototypes at reasonable low frequency where capac- itive e ect has not contributes (normally, the impedance analyser instruments have a good electrical parameters prediction for simple LRcircuits instead of more complicated circuit models which involve also the capacitance). The component L1is not purely inductive but it has some resistance, modelled separately as R1. This value must be assessed under operating conditions where it will be many times higher than the value measured using a DC source. R1includes resistance representing ohmic loss, skin and proximity e ects in the winding and tan losses in all dielectrics. Moreover, the inductor includes the C1parasitic capacitance between the turns. Values of R1andC1can be estimated by FEM analysis. -a ring end . It is installed into the head of the combustion chamber and generates the corona streamers. Typically, it contributes to most of the capacitance CLof the igniter assembly. Any 7ACCEPTED MANUSCRIPT 4 ACIS MODEL 4.1 Model Figure 3: Scheme of the ACIS igniter assembly lumped-parameter circuit model. component and connection between the inductor and the ring end must be considered since they can contribute signi cantly to the system performance. Any connection component provides additional capacitance and, consequently, as for the inductor case, an additional resistance RLto take into account the ohmic resistance of air and bulk insulation. The RLand theCL, connected in parallel, represent mostly the tan losses in all dielectrics and the stored electrostatic energy. Note that the lumped parameters described above may be subject to change for signi cantly di erent temperature operations. Based on such circuit, the analytic model predicts the electrode voltage Veas a function of the driving voltageVd, given that Vsis proportional to Vdthrough the coecient k(eq. 4). In the following, we use the complex phasor notation. Vs=kVd (4) Since Vs=V12+Ve (5) where V12=Z1I Ve=Z2I(6) then Ve=Vs2 6641 1 +1 Y1Z23 775(7) Introducing the angular frequency at the resonant condition !0, the electrode voltage can be expressed as 8ACCEPTED MANUSCRIPT 4 ACIS MODEL 4.2 Calibration Vef!0g=Vs2 6641 1 +1 Y1f!0gZ2f!0g3 775(8) where Y1=j!C 1+1 R1+j!L 1=1!2C1L1+j!R 1C1 R1+j!L 1 Z1=R1+j!L 1 1!2C1L1+j!R 1C1 Z2=RL 1 +j!R LCL(9) 4.2. Calibration During the calibration stage, the load capacitance CLwas considered as sum of the intrinsic capacitance in the igniter assembly, of the HV probe Tektronix P6015A capacitance (3 pF2%) and of the estimated stray capacitance introduced by the pressure chamber. The calibration was conducted at room temperature and nominal power absorption. Pressure chamber capacitance assessment The pressure chamber stray capacitance contributes signi cantly to the system performance and be- haviour. Its calibration was performed on Federal-Mogul Powertrain setup and then estimated by matching the analytic result and the measured resonance frequency (setup shown on section 2.3). The iterative process is based on the frequency resonant criterion (detailed mathematical proof in Appendix): Bp C2+D2+C Dp A2+B2+A= 1 (10) where A=R1+RL!2RLL1(CL+C1) B=!(L1+R1RL(CL+C1)) C= 1!2C1(R1RLCL+L1) D=! RLCL+R1C1!2C1L1RLCL(11) Electrode voltage calibration SinceR1is the electrical parameter most a ected by the operating condition, the model was calibrated basing on experimental data (par. 4.3), by tuning R1. After the calibration, the analytic model allows to estimate Veby adjusting the stray capacitance for each setup. The stray capacitance assessment was performed on both FM and UniPG setup. 4.3. Experimental Fig. 4 shows the measured data of the electrode voltage Ve(black crosses) as a function of the driving voltageVd, according to the methodology explained in section 3.1. The small dispersion of each of the four 9ACCEPTED MANUSCRIPT 5 EXPERIMENTAL RESULTS 051015202530 01020304050Electrode Voltage, kVDriving Voltage, VExperimental (Federal Mogul setup)Model (UniPG setup) Figure 4: Experimental Veas a function of Vd, for di erent Tonandpch(black crosses). The solid line is a linear regression. FMelectric model of the corona igniter adapted to the UniPG test case to predict Veas a function of Vdfor di erent gas type andpch(white- lled squares). data clouds is due to the performance variation between the di erent igniters used for the test more than to a presumed dependence of Veon pressure pchor on discharge duration Ton, thereforeVeis constant at xed Vd. The linear regression (black solid line) highlights the strict linearity of the dependence Ve=f(Vd). Even if such dependence is clear, it cannot be exported as it is to the UniPG data collection. In fact, the experimental tool used to measure the electrode voltage (i.e. the voltage probe) involves a high stray capacitance that a ects the data systematically as a bias (gap between crosses and squares in g. 4). The developed model of the igniter allows to assess the stray capacitance of the measurement system. 5. Experimental results 5.1. Stray Capacitance assessment and Electrode Voltage range The FM model can be adapted and extended to the UniPG case to calculate Ve, by evaluating the di erent stray capacitance given by the UniPG system igniter-pressure sensor . The measurement of the feeding current frequency of the coil iis required because the stray capacitance a ects it (the higher the stray capacitance, the lower the i). This allows to compare its value with the theoretical one and then to derive the estimated stray capacitance. The result shows a current frequency i= 1:029MHz (compared with a theoretical value of 1 :04MHz ) therefore the UniPG system is a ected by a stray capacitance of about 2:56pFon average and with a standard deviation of 0 :2pF, rather independent on the applied driving voltage in this range ( g. 5). Therefore, Veis describable as a linear function of Vdas in g. 4. 5.2. Corona Duration This test is led in pure nitrogen starting from the standard conditions (Vd= 40VandTon= 300s) by varying the corona duration parameter Ton. Between the rise and the fall, the current has a pretty constant behaviour characterised by a di erent duration consistently with the assigned setup: in g. 6 is well visible how the subsequent Tonincrease ( g. 6 top, from 100sto 500sby 100sstep) implies a wider pressure gradient pch( g. 6 bottom ).The corresponding released thermal energy Eris a linear function of the corona duration Ton( g. 7) in this range of pressure. Therefore, the power supply system and the coil fully support the energy demand and the streamers production rate. 10ACCEPTED MANUSCRIPT 5 EXPERIMENTAL RESULTS 5.3 Released energy as a function of the applied electrode voltage 00.511.522.533.5 0204060CstaryCapacitance, pFDriving Voltage, V02468102.02.22.42.62.83.03.23.4No. of EventsCstrayCapacitance, pF Figure 5: ( Main )Cstray capacitance distribution as a function of Vd. (Inner ) Occurrence frequency of the same Cstray distribution. Since the energy supplied to the coil Esis linearly dependent on Ton, the eciency of the igniter is pretty constant in the range 100 500s,= 11:8% on average. This value is about an half of the maximum observed (beyond 20%, see section 5.3, g. 10), due to the selected operating conditions. 5.3. Released energy as a function of the applied electrode voltage BDV andCIV are transition phases where the igniter ACIS emission is characterised by an intrinsically stochastic behaviour. It is possible to de ne a driving voltage VCIV d, and consequently an electrode voltage VCIV e, under which there is no streamer production at all. Similarly, it is possible to de ne VBDV d , and soVBDV e , over which the igniter system works in arc conditions constantly. Both VBDV d andVCIV d are functions of the bomb chamber inner pressure pchand of the lling gas type. For intermediate Vdvalues (or ratherVe), the igniter generally produces streamers, i.e. the corona e ect is active. On the other hand, when Vdapproaches VCIV d orVBDV d , the igniter shows the mix of behaviours: succes- sion of corona/failure events ( failure event is that one with no released energy associated) and corona/spark events, respectively. The more Vdis close toVCIV d, orVBDV d , the more is the probability to have null, or spark, events. As a consequence, this aleatory behaviour produces a certain degree of randomness and of arbitrariness in identifying VBDV d andVCIV d and, then, in the de nition of V0 dandVmax d. These are the corresponding operating values for VBDV d andVCIV d: the maximum Vdallowed before, respectively, the corona inception and the breakdown. Note that the electronic control system accepts integer values only forVd(not designed for this ne tuning application). A brief description of the stochastic behaviour of the ACIS system near VCIV d is given in section 6.2. Fig. 8 shows the found operating range in terms of electrode voltage Ve, according to the adopted de nition of CIV and BDV , for the di erent tested pressures pch. As the de nition consequence, the BDV points fall on a Paschen curve [73] obtained by a tting procedure for the speci c gap between the electrodes. Nitrogen Nitrogen is used as a medium reference case for the pure thermal e ect, being almost inert and with a lower radicals production than oxygen [31, 50]. Furthermore, nitrogen is also used for the igniter electrical characterisation by FM, allowing a more e ective comparison between results. 11ACCEPTED MANUSCRIPT 5 EXPERIMENTAL RESULTS 5.3 Released energy as a function of the applied electrode voltage -0.200.20.40.6Time, s-4-3-2-101234Current, A500 s400 s300 s200 s100 s -20246Time, s-4-2024681012Pressure, mbar500 s400 s300 s200 s100 s Figure 6: ( Top) Current produced by the ACIS igniter when the activity duration goes from 100 sto 500s. (Bottom ) Correspondingly, the measured pressure of the bomb inner chamber increases proportionally. 12ACCEPTED MANUSCRIPT 5 EXPERIMENTAL RESULTS 5.3 Released energy as a function of the applied electrode voltage 0100200300400Supplied Energy, mJ 05101520253035404550 0100200300400500600Released Energy, mJCorona Duration, μsN2 Figure 7: Corona duration test in standard conditions (nitrogen, 5 :5bar,Vd= 40V). EachToncorresponds to a certain supplied energy Es(top axis ) to the igniter coil. With good approximation, Eris a linear function of Ton(the solid line is a linear regression). 110100 110Electrode Voltage, kVpch, barN2 CIVN2 BDVAir CIVAir BDV Figure 8: Operating area of the igniter in terms of Veas a function of pch(nitrogen : transparent blue, white- lled symbols; air: transparent red, black- lled symbols). The triangles are the lower limit ( CIV condition) while the squares specify the upper extremes ( BDV condition) that fall on the relative Paschen curve (obtained by a tting procedure, dashed line for nitrogen and solid line for air). 13ACCEPTED MANUSCRIPT 5 EXPERIMENTAL RESULTS 5.3 Released energy as a function of the applied electrode voltage 0102030405060708090100 051015202530Released Energy, mJElectrode Voltage, kV3.25 bar5.5 bar7.75 bar10 bar N2 Figure 9: ( Nitrogen )Eras a function of Vefor di erent pch. The trends are well described by a second order polynomial (solid lines). The corona inception voltage VCIV e increases with the applied pressure. Once pchis set,Ergrows from zero (corresponding to V0 das an increasing function of the electrode potential. The relation can be pretty well described by a second order polynomial (solid lines in g. 9). Thus, Er, as a function of Ve, results in a set of parabolas that move towards Veby increasing pch. The parabolas bundle seems to be quite tight, gathering towards higher pressure. The maximum of Ercan be found for BDV conditions and, therefore, depends on the Paschen curve of g. 8. It is about 70 mJ, quite constant, except the 10 barcase (88mJ). As a result, higher pressure means lower energy released to the gas medium for the same potential Veapplied to the electrode, in agreement with [31, 74]. This behaviour is the opposite of what seen and expected for the spark case [13, 65], where a pressure increase pushes the released energy and the system eciency to higher values. Fig. 10 shows the corresponding eciency , de ned as in eq. 3, plotted versus Es. The eciency quickly increases with Vefrom 0% to beyond 20%, independently of pch, at least four times more than the best eciency showed by the spark [13, 65]. The starting point and the particular trend instead, are functions of the pressure, according to the behaviour showed in g. 2 and g. 9. At 3 :25barthe eciency highlights a strong decrease of the growth rate. This feature becomes lighter with continuity at higher pressures, where the growth rate is already lower from the beginning. It should be noted that the relative pressure gap between 3 :25barand 5:5baris higher then the one between 7 :75barand 10bar, so that, trivially, we should expect bigger changes. Likewise Er, also the eciency trend has a fast drop by increasing the pressure, at xed Es. Air The partial replacement of nitrogen with oxygen changes quantitatively the bunch of curves showed in g. 9 with no sensitive behaviour twisting ( g. 11): the fast energy fall with the pressure increase and Er growth with Veare still well highlighted. Finally, the maximum Er, just before the breakdown, is quite constant (with the exception of 5 :5bar), included between 70 mJand 80mJ: as for the nitrogen case, this trend re ects the impact of the BDV behaviour described by the Paschen curve. On the other hand, compared to the nitrogen case, the bunch is not so tight. Furthermore, the curves move to higher Vealmost linearly with the increase of pchstarting from the zero-point (that re ects the CIV trend of g. 8). These di erences seem to widen at high pressure. The bunch broadening and the higher requested potential for the CIV are probably due to the quenching e ect of the oxygen component of the air, as observed in [75]: since the oxygen easily captures a fraction 14ACCEPTED MANUSCRIPT 6 DISCUSSION 0%5%10%15%20%25% 0100200300400500Efficiency η, %SuppliedEnergy, mJ3.25 bar5.5 bar7.75 bar10 barN2 Figure 10: ( Nitrogen ) Eciency of the corona igniter as a function of the coil Es, for di erent pch. The solid lines are drawn only for sake of plot legibility. of the emitted electrons, it limits and prevents the corona e ect occurrence. The wide multiplicity of the produced oxygen states, molecular or atomic ionised, excited and metastable states [76], generates a variety of di erent available channels to degrade the energy absorbed by the chamber medium. Not all the energy referred to these channels is, nally, measurable as thermal energy. Furthermore, the oxygen presence highlights a feature that the nitrogen case just hinted: the theoretical possibility of having an intersection between consecutive curves (in particular, the 3 :25barand the 5:5bar curves). This would mean a radically new, opposite, behaviour: after the crossing of the curves, Erwould increases with the pressure instead of decreasing (see deeper analysis in sec. 6). The high voltage zone, here not reachable because of the arc onset, could be explored in future work in di erent operating conditions to experimentally con rm this supposed inversion. The igniter eciency con rms what seen in the nitrogen case, stressing some features as the tendency to sharply increase to reach a plateau, clear at 3 :25barwhile more inde nite at higher pressure ( g. 12). The eciency reaches its maximum value around 20% at the lower pressure (3 :25bar) for the higher electrode potential available. Anyway, at the applied operating conditions with air, the eciency is generally lower than the nitrogen case since it needs higher value of the Esto release a comparable amount of thermal energy. Generally, the air data su ers of a larger uncertainty (compare g. 10 and 12): this could be related to the aggressive byproducts of the oxygen chemistry that a ect somehow the performances, increasing the measurement dispersion. 6. Discussion The collected data establish some evidences here summarised: - the electrode voltage is linearly proportional to the driving voltage ( Ve/Vd); - the released energy, at xed chamber pressure and driving voltage, is linearly proportional to the streamers time of activity, the corona duration (Er/Ton); -Er, at xedpchandVd, is experimentally proportional to the square of the driving voltage ( Er/V2 d) and thus to the square of the electrode voltage ( Er/V2 e); - the same Erdrops quickly by increasing pch, at xedVd; 15ACCEPTED MANUSCRIPT 6 DISCUSSION 020406080100 051015202530Released Energy, mJElectrode Voltage, kV3.25 bar5.5 bar7.75 bar10 bar Air Figure 11: ( Air)Eras a function of Vefor di erent pch. Also for the air case, the trends are well described by a second order polynomial (solid lines). 0%5%10%15%20%25% 0200400600Efficiency η, %Supplied Energy, mJAir3.25 bar5.5 bar7.75 bar10 bar Figure 12: ( Air) Eciency of the corona igniter as a function of the coil Esfor di erent pch. The solid lines are drawn only for sake of plot legibility. 16ACCEPTED MANUSCRIPT 6 DISCUSSION 6.1 Released Energy Parametrization - it is expected that the trend is reversed at high Veand lowpch. Generally speaking, Veestablishes on the bomb chamber medium an electric eld that, by means of intermediate stochastic processes as ionisation or photo-ionisation, produces free electrons and accelerates them, activating the avalanche production mechanism [35, 67]. Once electrons and positive ions are created, the latter move towards the negative electrode with a drift velocity vion drift. For low ratio between the electric eldEand the pressure pch(i.e. the reduced electric eld E=pch, or more accurately E=N, whereNis the gas particle concentration, proportional to the medium density), vion drift is proportional to the reduced electric eld: vion drift/E pch; (low E=pch) (12) For high values of the ratio E=pch, the ions drift velocity is proportional to the square root of the reduced electric eld [66]: vion drift/s E pch; (high E=pch) (13) The drift velocity is the main ionic velocity component, once averaged. Ions' kinetic energy, proportional to the square of the gained drift velocity, is then transferred to the medium during the thermalization process. Therefore, the experimental data imply a linear dependence between the electrode voltage and the ions drift velocity. Intuitively, it can be assumed that the dependence described by eq. 13 could a ect the lower pressure test (3 :25bar) at higher electrode voltage (10 15kV), recognisable in a linear trend (in particular for the air case). Of course, this hypothesis should be conveniently veri ed. Electron drift velocity vel drift follows as well a relation similar to eq. 13 at ionising energies [66]: vel drift/s E pch(14) Since the curves of g. 9 and 11 do not show linear behaviour, we should conclude that the electrons contribution to the thermal energy is lower than the ions' one as long as the eq. 12 is true. Furthermore, not the whole electron kinetic energy is degraded into thermal energy since it is also employed in radicals production and photons emission. 6.1. Released Energy Parametrization This kind of considerations let us expect the behaviour showed in g. 9-11 and, therefore, it allows to use a second order polynomial as a model, according to the expression Er=aV2 e+bVe+c (15) and to nd the best tting curves (namely, a,bandc) to represent the collected data. Fig. 13 ( top) compares the trends of the acoecients for nitrogen ( aN2) and air (aAir). Theacoecient is an estimator of how quickly Ergrows with Ve. Both trends increase until the coecients reach a plateau at high pressure values. The nitrogen case ( dashed line ) is much more stable and the growth is small. The air coecient aAirstarts from a lower value, compared to aN2, and quickly increases. Probably, this is due to the availability of higher Ve(VBDV ejairis higher than VBDV ejN2see g. 8), corresponding to higher Es(and power). aAirtends towards very low values at low pch. Consequently, the relation Er=Er(Ve) approaches a transition to a linear behaviour. The coecients bandcare less meaningful, even if both monotonic: they contribute with ato determine VejEr=0, the electrode tension value such that Eris null, i.e. the abscissa intercept. The latter corresponds to the experimental value found for VCIV e and therefore shows analogous monotonic increasing trend. 17ACCEPTED MANUSCRIPT 6 DISCUSSION 6.1 Released Energy Parametrization 00.10.20.30.40.50.60.7 024681012𝑎, mJ·kV-2 pch, bar𝑎 N2AIR-20-15-10-505 024681012b, mJ·kV-1 pch, barb N2AIR -40-20020406080100120140160 024681012c, mJpch, barc N2AIR024681012141618 024681012Ve, kVpch, barVe|Er=0 N2AIR Figure 13: Trend of the second order polynomial coecients as a function of pchfor the nitrogen ( dashed line ) and air ( solid line) cases, according to the expression Er=aV2 e+bVe+c. (Bottom right ) Trend of the abscissa intercept VejEr=0(the tension value such that Eriszero) of the same function, corresponding to VCIV e . The description of Er=Er(Ve), via a second order polynomial, allows to build a map of the released energy as a function of pch( g. 14) for arbitrary values (in the tested range) of Es, thanks to the parametriza- tion showed in g. 2. The map is built by linearly increasing Es(evenly spaced steps of  Es= 26:8mJfor both gases) from 105:2mJto 346:4mJfor the nitrogen (dotted lines) and from 105 :2mJto 373:2mJfor the Air case (solid lines).Esincreases according to the black arrow in g. 14, where only the two highest Eslevels are pointed out (for both gases). The released energy behaviour showed in the map is not trivial. The iso-energy curves Esestablish a tight bundle for low and high pressure while it is wide in the middle range of pch. This happens for both pure nitrogen and air. A tight bundle means that a lot of Esis needed to reach relatively high value of Er. This is particularly true for air at highest pressure and it is related to the igniter diculty to quickly reach high eciency in such operating conditions ( g. 12). Nitrogen is much more stable, with no dramatic fall at high pressure. The area around 5 :5barin g. 14 is of a certain interest, since the density reduction of the iso- energy curves denotes an easier condition to reach high eciency. In addition, for the air case this area is featured with a maximum for the highest iso-energy curves. The remaining ones, instead, are monotonic decreasing. The decreasing trend with pchis the typical behaviour observed in g. 11. A maximum means that the released energy, locally, does not depend on the chamber pressure. As a consequence, there is an Er=Er(pch) trend transition from decreasing (at higher pressure) to increasing (at lower pressure): a real behaviour inversion. The local maximum of g. 14 is related to the intersection, experimentally still not reached , in g. 11 between the 3 :25barand 5:5barcurves at the higher value of Ve. Such inversion is only inferred since the breakdown occurs and prevents to achieve the corresponding operating conditions. On the other hand, the breakdown is due only to the geometrical features of inner chamber (gap between the electrodes). The monotonic trends of the polynomial coecients ( g. 13) imply that the curves intersection eventually occurs. Under this assumption, at higher Ve, i.e. at higher free electron energy, a pressure increase, that means 18ACCEPTED MANUSCRIPT 6 DISCUSSION 6.2 Stochastic Behaviour Description 0102030405060708090 3579Released Energy, mJPch, barN2AirES346.4 mJ319.6 mJ346.4 mJ373.2 mJ Figure 14: Map of the inferred trend of the released energy Erto the bomb chamber medium as a function of the inner pressure pchand for various level of energy supplied to the coil Es, for both tested gas types, nitrogen ( dotted lines ) and air ( solid lines ). a particle density increment and a mean free path decrease, would produce: - a growth of the scattering occurrences; - an improvement of the energy transfer eciency in the medium. Anyway, the change of behaviour at low pressure is not completely unexpected since many variables a ect the system. For example, the low pressure supports the atomic oxygen excited state production [31]. As already reported in the introduction, this is an ecient channel to heat the gas: Erdi erences between air and nitrogen are smaller at the lowest pressure, where the maximum of g. 14 takes place. Furthermore, we already saw that the ions' kinetic energy is heavily a ected from the E=pchratio and therefore the trend change may suggest a slow transition from the eq. 12 regime description towards the eq. 13 one, by lowering pch. Finally, high pressure produces a change in the streamer propagation [31] due to a change in the ionisation-recombination balance [77] and in mechanisms as photoionisation by the excited-state quenching of molecular nitrogen [78]. 6.2. Stochastic Behaviour Description The nitrogen 7 :75bardata explain the typical stochastic behaviour of the Corona e ect just over the CIV condition. To each Vecorresponds a series of raw measurements of Erversus time, each one characterised by a small dispersion ( g. 15). On the contrary, the 12 kVseries (black cross) shows a particularly uctuating trend, with many zeros too. This data collection can be gathered as in the histogram of g. 16 ( white- lled bars) where it is easy to distinguish ve di erent energy values around which the data are concentrated. Therefore, we can rearrange consequently the histogram with just ve groups as in g. 16 ( black- lled bars ) and nd the corresponding ve energy levels (included the 0 mJlevel). The energy of each group is simply de ned as the energy average of the corona events belonging to the same group. Fig. 17 reports the ve energy levels relative to the 12 kVseries compared to the whole sequence of 7:75bardata collection, included the corresponding tting curve. The series is distributed from 0 mJup to the tting curve, that corresponds to the higher energy level ( 9:9mJ). This unpredictable behaviour was clari ed by a previous test led on the optical engine and reported in [56]: indeed, approaching the VCIV e 19ACCEPTED MANUSCRIPT 6 DISCUSSION 6.2 Stochastic Behaviour Description Figure 15: Nitrogen case at pch= 7:75bar,Erdistributions corresponding to the various level of Ve, whole data series. The distribution of 12 kVdata series is distinctly the widest. 0246810121416 01234567891011Number of EventsEvents Energy, mJ12 kV - Released energyoccurrencesFive energy levelsrearrangement Figure 16: Nitrogen case at pch= 7:75bar, detail of the 12 kVdata series. The Erdistribution of the occurred events ( white- lled bars ) suggests a regular structure attributable to di erent igniter emission modes. The distribution can be correspondingly rearranged according to the assumption of an emission characterised by a di erent number of streamers ( black- lled bars ). 20ACCEPTED MANUSCRIPT 7 CONCLUSIONS 01020304050607080 05101520Released Energy, mJElectrode Voltage, kVE [mJ]Ev2_0Ev2_1Ev2_2Ev2_3Ev2_4051015 8101214 Figure 17: Erdistribution of the nitrogen sub-cases atVe= 12kV, compared to the whole tested sequence of 7 :75bar. The sub-plot contains a zoom of the area including the 12 kVpoints. conditions from higher voltage, Veis not high enough to generate all the four standard streamers for every shot, so we can obtain from four to no streamers at all for each shot. As observed, the behaviour is strongly stochastic and suggests that, under a certain threshold of Veand aboveVCIV e, the production of a particular number of streamers has its own probability, depending on how close Veis toVCIV e. 7. Conclusions In this work, we tested a radio-frequency igniter based on the corona e ect (ACIS) to have a systematic characterisation of the thermal energy released by the igniter in a constant volume vessel both in pure nitrogen and pure air. The inner pressure of the vessel, the type of medium (nitrogen or air) and the operating parameters of the igniter (driving voltage and the corona discharge duration) are all settable and matter of analysis. We can summarise the main results as follow: - A lumped-parameter circuit model of the igniter was developed and calibrated with experimental data to determine the stray capacitance of the calorimeter and to foresee the electrode voltage of the igniter, depending on the control parameters. - The thermal energy released to the medium from the igniter is linearly proportional to the duration of the corona discharge. - The thermal energy released to the medium grows proportionally to the square of the electrode voltage (or, operatively, of the driving voltage). - In general, higher pressures of the medium need higher electrode voltage values to release the same amount of thermal energy. - Air, as vessel medium, brings a lower value of thermal energy released compared to nitrogen in similar operating conditions. It is worth noticing that air is much more aggressive towards the electrode and needs special care to guarantee a reliable measurement process. - Both in nitrogen and air, the igniter is able to reach more than 20% of eciency. 21ACCEPTED MANUSCRIPT