Conventional spark versus nanosecond repetitively pulsed discharge for a turbulence facilitated ignition phenomenon

Abstract This work applies both conventional-single-spark-discharge (CSSD) at 500-µs pulse duration time and nanosecond-repetitively-pulsed-discharge (NRPD) at various pulsed-repetitive-frequency PRF = 5–70 kHz to explore a turbulence facilitated ignition (TFI) phenomenon using a pair of pin-to-pin electrodes at an inter-electrode gap of 0.8 mm in randomly-stirred lean n-butane/air mixture with Lewis number ≫ 1. For CSSD, measured laminar and turbulent minimum ignition energies (MIEL and MIET) at 50% ignitability show that MIEL≈ 23 mJ > the smallest MIET≈ 19.7 mJ at u′ = 0.9 m/s (TFI) and then MIET≈ 28.6/30.8/36.8 mJ at u′ = 1.4/2.1/2.8 m/s (no TFI), where u′ is the r.m.s turbulent fluctuating velocity. For comparison, all NRPD experiments apply the same total ignition energy Etot≈ 23 mJ via a fixed train of 11 pulses, each pulse with 2.2 mJ except for the first pulse with 1 mJ. NRPD results show a cumulatively synergistic effect depending on the coherence between PRF and an inward reactant flow recirculation frequency (fRC) inside the torus-like kernel induced by the discharge that could enhance ignition. When PRF is approximately synchronizing with fRC, the synergistic effect is most profound at PRF = 20-kHz/40-kHz with very high ignition probability Pig = 90%/85% > 50% in quiescence, whereas lower values of Pig = 42%/34% are found at PRF = 10-kHz/60-kHz. Further, Pig = 0 at PRF = 5-kHz even when 5000 pulses (Etot≈ 10 J) are applied. We discover that Pig decreases significantly with increasing u′ for most PRFs (no TFI) except at higher PRF ≥ 60 kHz showing possible TFI. These results are attributed to the interactions between turbulent dissipation, differential diffusion, and synergistic influence, which are substantiated by Schlieren images of initial kernel development and the ignition time determined at one half of the flame critical radius that leads to a self-sustained spherical flame propagation.

1. For CSSD, measured laminar and turbulent minimum ignition energies (MIE L and MIE T ) at 50% ignitability show that MIE L ≈ 23 mJ > the smallest MIE T ≈ 19.7 mJ at u = 0.9 m/s ( TFI ) and then MIE T ≈ 28.6/30.8/36.8 mJ at u = 1.4/2.1/2.8 m/s (no TFI ), where u is the r.m.s turbulent fluctuating velocity. For comparison, all NRPD experiments apply the same total ignition energy E tot ≈ 23 mJ via a fixed train of 11 pulses, each pulse with 2.2 mJ except for the first pulse with 1 mJ. NRPD results show a cumulatively synergistic effect depending on the coherence between PRF and an inward reactant flow recirculation frequency ( f RC ) inside the toruslike kernel induced by the discharge that could enhance ignition. When PRF is approximately synchronizing with f RC , the synergistic effect is most profound at PRF = 20-kHz/40-kHz with very high ignition probability P ig = 90%/85% > 50% in quiescence, whereas lower values of P ig = 42%/34% are found at PRF = 10-kHz/60-kHz. Further, P ig = 0 at PRF = 5-kHz even when 5000 pulses (E tot ≈ 10 J) are applied. We discover that P ig decreases significantly with increasing u for most PRFs (no TFI ) except at higher PRF ≥ 60 kHz showing possible TFI . These results are attributed to the interactions between turbulent dissipation, differential diffusion, and synergistic influence, which are substantiated by Schlieren images of initial kernel development and

Introduction
How to develop reliable ignition sources for lean-burn devices with low emission is an important issue [1][2][3] . When using the conventionalsingle-spark-discharge (CSSD) ignition system (e.g., [3][4][5][6][7][8][9] among many others), there is a serious misfire problem in internal combustion engines under lean operating conditions. As noted by Ju and Sun [1] , one of plasma-assisted discharges, namely the nanosecond-repetitively-pulsed-discharge (NRPD), is a very promising energy deposition technique for the enhancement of ignition and combustion. Recently, the NRPD technique has attracted great attention for investigation of the ignition enhancement using a pair of pin-to-pin electrodes in flows that are either in quiescence or with large mean velocity (e.g., pulsed detonation engine [10] , flowing methane/air mixtures [11] , 3-D DNS quiescent lean methane/air mixture [12] , quiescent lean propane/air mixture using a constant-volume combustion chamber [13][14][15][16] ). Based on the best knowledge of the authors, the NRPD study in near-isotropic turbulence characterized by an energy-weighted r.m.s. turbulent fluctuating velocity ( u ) with negligible mean velocities is still not available. This motivates the present study to explore the effect of u on the ignition probability (P ig ) of NRPD over a range of pulsed repetitive frequency (PRF = 5-70 kHz). Hence, we investigate how exactly a turbulence facilitated ignition ( TFI ) phenomenon found by the CSSD ignition system using a pair of pin-topin electrodes would vary with a change of PRF and u .
What is TFI ? TFI means that the required ignition energy (E ig ) for successful ignition in turbulent conditions is smaller than that in quiescence through differential diffusion if the effective Lewis number ( Le ) of mixtures is sufficiently larger than unity, as first observed by Wu et al. [17] using CSSD with small inter-electrode gaps ( d gap ≤ 0.8 mm) in near-isotropic turbulence. Further, Saha et al. [18] reported a competing role of turbulence and differential diffusion for the occurrence and disappearance of TFI using CSSD at d gap = 0.8 mm in randomly stirred n-butane/air mixture ( Ø = 0.7, Le ≈ 2.2 1). They revealed that such TFI phe-nomenon only occurs in weak and/or moderate turbulence, because strong turbulence re-asserts its dominant role and renders ignition more difficult. Note that TFI is very sensitive to d gap . Recently, Shy et al. [3 , 19] measured the effect of d gap on TFI by applying the same rich hydrogen/air mixture at ϕ = 5.1 with Le ≈ 2.3 1 as in [17] in a large fanstirred cruciform bomb capable of generating nearisotropic turbulence. Based on measured laminar and turbulent minimum ignition energies (MIE L and MIE T ), Shy et al. [19] discovered that TFI only occurs at sufficiently small d gap (typically < 1 mm) and at sufficiently large Le 1, whereas TFI disappears when d gap > 1 mm. Moreover, Shy et al. [3] substantiated that the occurrence of TFI is due to a ball-like embryonic kernel at sufficiently small d gap having large positive curvature that weakens reaction rate through differential diffusion for Le 1 making ignition much more difficult to occur in quiescence than in turbulence. No TFI when d gap > 1 mm, because the embryonic kernel is rod-like with small or negligible positive curvature (see Fig. 4 c in [3] ). It is thus interesting to apply the most promising NRPD ignition system [1] for investigating the aforesaid TFI phenomenon.
Previous NRPD studies (e.g., [10][11][12][13][14][15][16] ) have provided important knowledge and information on the cumulative effect of successive NRPD at some certain PRFs, typically around 10-40 kHz depending on various parameters such as d gap , the total deposited energy (E tot ), and flow conditions, showing a significant enhancement of P ig . Such cumulative effect can be called as the synergistic effect, which might be attributed to the coherence between characteristic recirculation time ( τ RC ) from the discharge-induced flow field and the inter-pulse time (PRF −1 ) (e.g., [12][13][14][15][16] ). In short, the present work has three objectives: (1) to explore for the first time the interactions among effects of the NRPD synergy, differential diffusion, and turbulent dissipation for possible TFI and ignition enhancement using the lean n-butane/air mixture at ϕ = 0.7 with Le ≈ 2.2 1 and d gap = 0.8 mm as that used in [18] ; (2) to measure MIE L and MIE T over a range of u for the same mixture and d gap as in (1) using CSSD; and (3) to gain a better understanding of laminar and turbulent ignition characteristics between NRPD and CSSD.

Experimental methods
Both CSSD and NRPD ignition experiments of the n-butane/air mixture at ϕ = 0.7 with Le ≈ 2. 1 1 were conducted in a large dualchamber fan-stirred cruciform explosion facility using the same 2-mm stainless steel electrodes with sharp ends at a fixed d gap = 0.8 mm which are cantilevered at an angle of 45 °to the horizon and positioned at the center of the experimentation domain. The averaged minimum diameter inside the large fan-stirred cruciform burner was about 30 cm. The burner was equipped with a pair of counter-rotating fans and perforated plates capable of generating near-isotropic turbulence within a region of 15 × 15 × 15 cm 3 . The reader is directed to Ref. [3] and references therein for detailed information on the explosion facility, associated turbulence properties, and mixture preparation before ignition, so they are not elaborated upon here. The followings are the descriptions on how to measure CSSD and NRPD ignition energies (E ig ) in the present study.
Since the spark breakdown is statistical in nature, it is necessary to measure E ig in situ directly from the discharged electrodes. For CSSD, we apply a precision high-voltage pulse generator with a maximum breakdown voltage of 25 kV (HV-M25K) together with adjustable loading resistances and a small damping resistor of 100 in a home-made ignition circuit to create near-square voltage and current waveforms within the selected pulse duration time varying from 1 μs to a few milliseconds, same as that used in our previous MIE transition studies [20] . As shown in Fig. 1 (a) as a typical example, accurate E ig = 23.2 mJ can be measured by the integration of the product of the discharged current I ( t ) and the voltage difference [ V 1 ( t ) -V 2 ( t )] across the spark gap between electrodes within τ p = t 2 -t 1 ( = 500 μs), where the breakdown voltage used is 15 kV and the discharged voltages and current are measured by two high-voltage Tektronix probes and the Pearson current probe [20] . In an attempt to make a comparison between CSSD and NRPD ignition characteristics, we first measure the value of MIE L for the lean n-butane/air mixture ( ϕ = 0.7) at d gap = 0.8 mm and τ p = 500 μs in quiescence. MIE is a statistical property, not a threshold value, because there is an overlapping regime of E ig within which "Go" and "No Go" ignition events coexist at the same E ig . In the Supplemental Materials, Fig.  S1 shows that MIE L = 22.7 mJ at 50% ignitability using the logistic regression method. Each value of MIE L and MIE T determined at 50% ignitability is obtained from 20 ∼40 trials over a range of well-controlled E ig . Note that the same cantilevered electrodes with sharp ends, as indicated in Fig. 1 (a), are applied for both CSSD and NRPD experiments.
As to the NRPD study, the power supply (FID GmbH FPG 20-100NK) produces peak pulse amplitudes up to 30 kV, pulse durations of 3-5 ns FWHM, and pulsed repetitive frequencies up to 100 kHz. A delay/pulse function generator (GW INSTEK AFG-2225) is used to control the NRPD power supply via external trigger signals. For all NRPD ignition experiments, we apply a fixed peak open-circuit voltage of 28 kV over a range of PRF = 5-70 kHz with a burst of 11 pulses having a constant total ignition energy E tot ≈ 23 mJ which is almost the same as MIE L = 22.7 mJ measured by CSSD. The NRPD voltage and current signals are respectively measured by high voltage probe (Tektronix P6015A) and Pearson coil (model 6585), which are recorded by a 500 MHz oscilloscope (Tektronix MD03054). Fig. 1 (b) shows voltage, current, and energy waveforms of the second pulse from a burst of 11 pulses at PRF = 20 kHz, as a typical example for single nanosecond-pulse discharge. As seen from Fig. 1 (b), after the first major voltage/current peak, oscillating voltage/current waves can be observed which contribute to a small portion of the integrated discharge energy. Note that the wave profile remains roughly the same for each nanosecond-pulse. Fig. 1 (c) displays all 11 NRPD voltage and current signals at PRF = 20 kHz with E tot ≈ 23 mJ. Fig. 1 (d) presents the accumulated energy depositions plotted against the pulse number from the burst of 11 pulses which are nearly the same at different PRFs = 10-60 kHz. The individual energy of each pulse from the burst of 11 pulses is about 2.2 mJ, independent of the PRF, except for the first pulse having a lower E ig of about 1 mJ, similar to that reported in [11] . Moreover, Schlieren images of initial kernel development for both CSSD and NRPD are recorded by a highspeed, high-resolution camera (Phantom V711) at 10,000 frames/s with 800 × 800 pixels.

Ignition probability and kernel development in quiescence
Ignition is statistical in nature. A successful ignition event (Go) must include all three stages from the breakdown and the formation of flame kernel to the self-sustained propagation flame. If only the breakdown and the kernel formation occur without the development of self-sustained propagation flame, this event belongs to failure ignition (No Go). The NRPD ignition probability (P ig ) is defined as the ratio of the number of successful ignitions to the total number of ignition trials. Thus, many ignition trials are required to obtain an accurate P ig . Fig. 2 shows laminar P ig,L versus the number of cumulative trials for six different PRFs = 5-kHz/10-kHz/20-kHz/40-kHz/60-kHz/70-kHz corresponding to P ig, L = 0%/42%/90%/85%/34%/27%, using a fixed train of 11 pulses with E tot ≈ 23 mJ ≈ MIE L . In this study, 60 trials are used to obtain a reliable value of P ig at each of different PRFs ( Fig. 2 ). At d gap = 0.8 mm, the highest P ig, L = 90% occurs at PRF = 20 kHz. If the smaller number of pulse than 11 pulses is used, P ig,L decreases. On the other hand, P ig,L increases if the pulse number increases. Please see Fig. S2 in the Supplemental Materials, where the effect of pulse number on P ig is demonstrated using PRF = 20 kHz, as a typical example. To better explain and understand why the non-monotonic increase and decrease of P ig with the maximum P ig = 90% at PRF = 20 kHz happen, we examine the early development of the embryonic kernel at various PRFs. Fig. 3 shows Schlieren images of ignition kernel structures and their subsequent flame develop-ment in quiescence for four different cases, including (a) a CSSD case at τ p = 0.5 ms and (b) three NRPD cases at PRF = 5 kHz, 20 kHz, and 60 kHz, respectively. These four different cases apply the same E ig ≈ 23 mJ ( ≈ E tot ), lean n-butane/air with Le ≈ 2.2 1, and d gap = 0.8 mm < 1 mm. In Fig. 3 , the first four columns have a smaller view field of 16 × 16 mm 2 to see the embryonic kernel, while the fifth column has a larger view field of 42 × 42 mm 2 to view self-sustained flame propagation. There are three key points. First, the CSSD case ( Fig. 3 a) has a P ig = 50%, where MIE L ≈ 22.7 mJ when using Le ≈ 2. 2 1 mixture at d gap = 0.8 mm. This is due to the fact that the large positive curvature of the embryonical kernel at 0.1 ms (the first image of Fig. 3 a having a torus-like shape) weakens reaction rate through differential diffusion (also see   [3] ). Note that there is no wrinkling inside the single-shot CSSD torus-like (elliptic) embryonic kernel at 0.1 ms and 0.5 ms. Second, at PRF = 5 kHz (the first row of Fig. 3 b), all 60 ignition trials never ignite successfully at E tot ≈ 23 mJ (see also Fig. 2 ). Although the first embryonic hot kernel ignited by the first pulse of only about 1 mJ (the first image at 0.1 ms) looks just like the CSSD kernel at 0.1 ms ( Fig. 3 a), it is cooled down by the inward recirculation flow induced by the discharge. This is because the interpulse time of 200 μs (PRF = 5 kHz) is too long as compared to the typical timescale of flow recirculation, resulting in a fade-out before the arrival of the second pulse at 0.5 ms (no synergistic effect). Such cool-down and fade-out processes continue to the tenth pulse at 2 ms and to the last pulse at 2.2 ms (not shown), leading to failure ignition (No Go). Could an increase of pulses (more than 11 pulses) at PRF = 5 kHz result in a successful ignition? The answer is no. We discover that even applying 5000 pulses with E tot = 10 J, P ig remains zero at PRF = 5 kHz. Third, at PRF = 20 kHz (the second row of Fig. 3 b), P ig = 90% P ig = 50% for the CSSD case. There are strong wrinkling structures inside the embryonic torus-like hot kernel due to the superadded multiple pulses, as can be clearly seen from the first and second images at 0.1 ms and 0.5 ms, showing the strongest synergistic effect that enhances significantly the P ig when using the present electrode configuration. It is anticipated that the synergistic effect is most profound when the inter-pulse time is approximately synchronizing with τ RC , implying that τ RC is roughly on the order of 50 μs ( ∼ 20 kHz) in the present setup. The early developing stage of the aforesaid strongest synergistic kernel is accelerated by superadded mul-  where two kinds of τ delay at R min and R c are estimated from (a). Also plotted is the ignition probability (P ig ) as a function of PRF using the same E tot ≈ 23 mJ ≈ MIE L (E ig at 50% ignitability for the CSSD case).
tiple pulses, where the wrinkled flame kernel with locally negative and positive curvature stretch can be observed at 2 ms and 6 ms images in the second row of Fig. 3 b. Such wrinkled kernel soon develops into a self-sustained propagating spherical flame (see the image at 21 ms). The situation at PRF = 60 kHz (the third row of Fig. 3 b) is similar to that at PRF = 20 kHz, but having a much weaker synergistic effect where P ig = 34% < P ig = 50% for the CSSD case.

Ignition delay time as a function of PRF
To quantify the ignition delay time as a function of pulsed repetitive frequency for successful ignition, we record the time evolutions of flame kernel radii ( R ) using high-speed Schlieren imaging (see Fig. 3 b), where R = ( A / π ) 0.5 and A is the area enclosed by the flame front. As such, flame speeds (d R /d t ) versus R can be obtained. Fig. 4 (a) presents fiv e data sets of d R /d t vs . R at five different PRFs = 10, 20, 40, 60, 70 kHz. All fiv e flame speeds on the burned side ( S L b ) first decrease drastically and then reach their minimum ( S L b min ) at corresponding radii ( R min ) depending on PRF for the lean n-butane/air mixture with Le ≈ 2. Then all fiv e d R /d t data increase and merge together at a critical flame radius R c ≈ 12 mm to approach the planar value which is independent of PRF. The inset in Fig. 4 (a) presents the raw data of R ( t ) vs. t at fiv e PRFs varying from 10 kHz to 70 kHz, demonstrating again that the times required to reach R c from the fastest to the slowest are in sequence of 20 kHz, 40 kHz, 10 kHz, 60 kHz, and 70 kHz. Also, the slopes of these fiv e PRF data beyond R c are the same, indicating the flame speed is constant, regardless of PRF at least within the range of 10-70 kHz. Two ignition delay times are estimated, one located at 0.5 R c ( τ delay,50% R c ) and the other located at R min ( τ delay, R min ) where the flame speed is the lowest. As shown on the top of Fig. 4 (b), we find that τ delay,50% R c is only slightly higher than τ delay, R min within 10-40 kHz, but τ delay,50% R c is much higher than τ delay, R min at 60 kHz and 70 kHz. Since the ignition delay time is inversely proportional to the ignition probability, the ignition delay time determined at one half of the flame critical radius should be a better representing parameter as its non-monotonic curve fits inversely better with that of P ig,L (see the bottom of Fig. 4 b). Specifically, τ delay,50% R c = 5.2 ms (20 kHz) and 6.4 ms (40 kHz) corresponding to P ig, L = 90% and 85%, whereas τ delay,50% R c = 7.2 ms (10 kHz), 12.6 ms (60 kHz), and 13.8 ms (70 kHz) corresponding to P ig, L = 42%, 34%, and 27%. Based on the results of τ delay,50% R c using the same E tot ≈ 23 mJ, it is concluded that the synergistic effect is most obvious at 20-40 kHz having very high P ig, L 50%, while lower and higher PRFs become detrimental for ignition having lower P ig, L < 50%. the CSSD case, in which all MIE data (black circle symbol) are measured at τ p = 500 μs and determined at 50% ignitability with successful ignition (open circle symbol) and failure ignition (cross symbol). A non-monotonic decrease and increase of MIE with increasing u is found in support of the finding of Saha et al. [18] , although the present values of MIE L and MIE T are much smaller than that reported in [18] who measured MIE at an ignition probability higher than 50%. Note that the lowest MIE ≈ 19 mJ occurs at u ≈ 0.9 m/s, suggesting that there is TFI when u < 0.9 m/s where MIE T < MIE L = 22.7 mJ. However, when u > 0.9 m/s, turbulence regains its dominance where MIE T ( > MIE L ) increases with increasing u . As to the NRPD case, four data sets of P ig,L and P ig,T at PRF = 5, 10, 20 and 60 kHz are plotted against u for clarity, where the subscripts L and T represent laminar and turbulent conditions. We discover that P ig,T decreases significantly with increasing u for most PRFs (no TFI ), except at higher PRF = 60 kHz where P ig, T = 37% at u = 0.5 m/ s > P ig, L = 34% at u = 0 showing TFI . At any given u , P ig,T at 20 kHz is always the highest among all PRFs studied in the present work. This is again attributed to the synergistic effect when the inter-pulse time is approximately synchronizing with the inward reactant flow recirculation time. At PRF = 60 kHz, the inter-pulse time is only 17 μs which is much shorter than the inward reactant flow recirculation time (assuming on the order of 50 μs for PRF = 20 kHz). As such, only a small amount of fresh reactant enters the inter-electrode gap between two consecutive pulses and thus the subsequent pulses mainly add ignition energy into radicals or possibly other active species, revealing a rather weak synergistic effect with a lower P ig, L = 34% in quiescence (see the first column images in Fig. 5 ). When u = 0.5 m/s, the weak and/or modest turbulence wrinkles the kernel, as seen in the second column image at 0.5 ms, generating locally negative curvature stretch that can enhance reaction rate through differential diffusion and increase P ig, T = 37% ( TFI ). When u = 0.9 m/s, local quench can occur, as seen by comparing the third column images at 2 ms and 3 ms, resulting in a significant drop of P ig, T = 20%. When u = 2.1 m/s, P ig,T is nearly zero, showing a dominating influence of intense turbulence that renders ignition much more difficult to occur.

Conclusions
Using the lean n-butane/air mixture with Le 1 and d gap = 0.8 mm, we apply both CSSD and NRPD to explore how exactly P ig and TFI would vary with changes of u and PRF. For CSSD results, a non-monotonic decrease and increase of MIE with increasing u is found, of which MIE L ≈ 23 mJ > MIE T ≈ 19 mJ at u = 0.9 m/s, showing TFI . But turbulence re-claims its dominating role when u > 0.9 m/s where MIE T > MIE L .
As to NRPD studies using a fixed train of 11 pulses with E tot ≈ 23 mJ, we discover that P ig,L and P ig,T remain zero at 5 kHz, regardless of the pulse number (up to 5000 pulses) and u . This is attributed to lack of synergistic effect at 5 kHz, large heat losses to electrodes at d gap = 0.8 mm, and differential diffusion effect (positive curvature weakens reaction rate for Le 1). The highest values of P ig, L = 90%/85% occur at PRFs = 20/40 kHz, respectively. Outside this PRF range, P ig,L is smaller than 50%. Such nonmonotonic increase and decrease of P ig,L with increasing PRF is attributed to the cumulatively synergistic effect, which is most profound when the inter-pulse time (PRF −1 = 50 μs at 20 kHz) is approximately synchronizing with the inward reactant flow recirculation time. The ignition delay time determined at one half of the flame critical radius should be a better representing parameter as its non-monotonic curve fits inversely better with that of P ig,L. Finally, P ig,T decreases significantly with increasing u for most PRFs (no TFI ), except at higher PRF ≥ 60 kHz showing possible TFI .
These results are important to turbulent premixed ignition, which should deserve to disseminate in our combustion community for stimulating further research. For future NRPD studies, we will measure the effect of d gap on turbulent ignition characteristics as well as turbulent flame propagation behavior for Le 1 flames.

Declaration of Competing Interest
None.