A Transition of Ignition Kernel Delay Time at the Early Stages of Lean Premixed n-Butane/Air Turbulent Spherical Flame Propagation

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A transition of ignition kernel delay time at the early stages of lean premixed n-butane/air turbulent expanding flame propagation is found, which may be relevant to spark ignition engines operated at lean-burn turbulent conditions.

Abstract

This paper explores the effects of root-mean-square turbulence fluctuation velocity (u′) and ignition energy (E_ig) on an ignition kernel delay time (τ_delay) of lean premixed n-butane/air spherical flames with an effective Lewis number Le ≈ 2.1 >> 1. Experiments are conducted in a dual-chamber, fan-stirred cruciform burner capable of generating near-isotropic turbulence with negligible mean velocities using a pair of cantilevered electrodes with sharp ends at a fixed spark gap of 2 mm. τ_delay is determined at a critical flame radius with a minimum flame speed during the early stages of laminar and turbulent flame propagation. Laminar and turbulent minimum ignition energies (MIE_L and MIE_T) are measured at 50% ignitability, where MIE_L = 3.4 mJ and the increasing slopes of MIE_T with u′ change from gradual to drastic when u′ > 0.92 m/s (MIE transition). In quiescence, a transition of τ_delay is observed, where the decrement of τ_delay becomes rapid (modest) when E_ig is less (greater) than MIE_L. For turbulent cases, when applying E_ig ≈ MIE_T, the reverse trend of MIE transition is found for τ_delay versus u′ results with the same critical u′ ≈ 0.92 m/s. These results indicated that the increasing u′ could reduce τ_delay on the one hand, but require higher E_ig (or MIE_T) on the other hand. Moreover, the rising of E_ig in a specific range, where E_ig ≤ MIE, could shorten τ_delay, but less contribution as E_ig > MIE. These results may play an important role to achieve optimal combustion phases and design an effective ignition system on spark ignition engines operated under lean-burn turbulent conditions.

1. Introduction

It is known that lean premixed turbulent combustion can enhance the thermal efficiency of spark ignition (SI) engines through the increase of the specific heat ratio [1] and the reduction of heat-transfer losses due to smaller adiabatic flame temperature with lower NO_x emissions [2,3]. However, one of the challenges to apply lean burn technology is the misfire problem that often relates to a longer ignition kernel delay time (τ_delay) [1,4,5,6] or a slower development of initial flame kernel at the early stage of combustion, which may worsen cycle-to-cycle variations in SI engines. A higher root-mean-square (r.m.s.) turbulence fluctuation velocity (u′) could be useful in accelerating the initial flame kernel development and thus shortening τ_delay. However, the increase of u′ usually requires a higher ignition energy (E_ig) or minimum ignition energy (MIE) for successful ignition [7]. As such, a clear understanding of the relations among τ_delay, MIE, and u′ during the combustion process is essential to the further development of high-thermal efficiency SI engines operated at lean-burn turbulent conditions. This motivates the present study.

To achieve a self-sustained flame propagation, many researchers have investigated a critical flame radius (R_c) for spherical flames (e.g., [8,9,10]) or for spray combustion flames [11]. When the heat release from chemical reaction is greater than the heat dissipation, the initial kernel radius could develop and grow beyond the required R_c, and then successful ignition with self-sustained flame propagation could occur [11]. Therefore, the ignition kernel delay time, which is determined as the time interval from the spark initiation to the time required to reach R_c, is an effective means to evaluate the physicochemical properties of combustible mixtures [11,12,13,14]. Although many ignition studies are available in the literature (e.g., Refs. [15,16,17]), most of these studies are for the autoignition delay time. Hence, τ_delay data at the early stage of flame propagation are still sparse. Based on both experimental and numerical studies of laminar spherical flames, Kelley et al. [8] and Chen et al. [9,10] reported that an increase of E_ig could enhance the early flame propagation speed, resulting in a shorter τ_delay. The larger E_ig, the higher concentration of active radicals inside the spark gap [18] and/or the higher chemical power release [19]. Further, using two-dimensional direct numerical simulation, Saito et al. [13] investigated the influence of turbulent strain rate (u′/l) on τ_delay of the lean n-C₇H₁₆/air mixture at an equivalence ratio of ϕ = 0.5, where u′ and l were the r.m.s. turbulent fluctuating velocity and the integral length scale of turbulence. By assuming the initial peak temperature T_peak,ini = 1500 K and R_c = 0.5 mm for all turbulent cases, they predicted an increase of τ_delay of proportional to (u′/l)². However, the engine result [20] indicated that the combination of the increase of E_ig and the enhancement of in-cylinder turbulence level can lead to a shorter inflammation time from the spark timing to a crank angle of 5%-mass fraction burnt (CA5) and a shorter main combustion duration time (CA10 to CA90), allowing SI engines to be operated at an extra-lean flammability limit. The result in [20] suggested that the determination of τ_delay at various E_ig (or MIE) and u′ may be important for a better design of SI engines.

The main objective in this study is to gain a better understanding of the influences of E_ig and turbulence level on τ_delay for lean premixed turbulent combustion, which may be relevant to lean-burn SI engines with high thermal efficiency. To the first level approximation, this study measures MIE_L and MIE_T of a lean n-butane/air mixture with an effective Lewis number Le ≈ 2.1 >> 1 using pin-to-pin electrodes at a fixed spark gap of d_gap = 2 mm in a large dual-chamber, fan-stirred cruciform burner capable of generating near-isotropic turbulence with negligible mean velocities. Here, MIE is the measured value of E_ig determined at 50% ignitability, the subscripts L and T represent laminar and turbulent conditions, and Le is defined as the ratio of thermal diffusivity and mass diffusivity with the mass diffusivity being that of the deficient reactant and the abundant inert. Near-isotropic turbulence was generated by a pair of counter-rotating fans and perforated plates in the central uniform region of the cruciform burner measured by high-speed PIV, detailed in Refs. [21,22]. Furthermore, as will be shown later, τ_delay is determined at a minimum critical radius (R_min) having a minimum flame speed (dR/dt)_min during the early stage of flame kernel development. Hence, the effects of E_ig or measured MIE_L and MIE_T, as well as the r.m.s turbulence fluctuation velocity (u′) on τ_delay, can be scrutinized.

Moreover, two ignition transition (IT) modes at d_gap = 0.8 mm and 2.0 mm, based on MIE as a function of u′ for the present lean n-C₄H₁₀/air mixture, similar to that recently reported in Ref. [23] using a lean primary reference fuel (PRF) with Le ≈ 2.98 >> 1, are also discussed. At small d_gap = 0.8 mm, an irregular IT is observed, where MIE_T decreases first with increasing u′ (turbulence facilitated ignition, TFI) and then MIE_T increases drastically when u′ is greater than some critical value (u′_c) [24]. The phenomenon of TFI was first observed by Wu et al. [25]. At large d_gap = 2.0 mm, a regular IT is found by which the increasing slopes of MIE_T with u′ change from modestly to exponentially when u′ > u′_c. Finally, we discuss the relationship between the regular IT and the ignition kernel delay time, as well as their implication to the potential application in SI engines operated at turbulent lean-burn conditions.

2. Experimental Methods

Ignition experiments of the n-butane/air mixture at ϕ = 0.7 with Le ≈ 2.1 >> 1 are conducted in the central uniform region of the large dual-chamber, constant-temperature/pressure, fan-stirred cruciform explosion facility using a pair of stainless-steel electrodes of 2 mm in diameter with sharp ends over a range of u′ = 0~2.1 m/s and at atmospheric pressure and room temperature conditions. The selection of lean n-C₄H₁₀ at ϕ = 0.7 as a fuel is because of its possible relevance to lean-burn combustion in SI engines having a sufficiently large Le ≈ 2.1 >> 1, closely matching that of lean gasoline fuel. Such dual-chamber, fan-stirred cruciform burner has been used to measure laminar and turbulent burning velocities of expanding spherical flames at various gaseous and liquid fuel/air mixtures with different values of Le under high-temperature and high-pressure conditions [26,27], as well as MIE_L and MIE_T of the lean iso-octane/air mixture [7] and the lean PRF95/air mixture [23]. Details of the explosion facility and its associated turbulence properties can be found in [21,22,24,28] and references therein. For completeness, a simplified sketch version of the dual-chamber cruciform explosion facility is presented in Figure 1. Moreover, also plotted in Figure 1 is the ignition circuit for generating near-square voltage and current waveforms to measure E_ig of high accuracy [7], and the high-speed schlieren imaging arrangement for recording the early development of flame kernels over a range of u′ varying from 0 to 2.1 m/s.

The experimental procedure used in the present work is the same as our previous studies; this will not be elaborated upon here, so the reader is directed to Refs. [23,27,28] for details. The outer safety chamber is pressurized with the dehumidified air at a pressure slightly higher than the initially selected pressure inside the inner cruciform burner. The inner cruciform burner is first vacuumed and then the appropriate mole fractions of n-butane and air are sequentially injected into the inner cruciform burner to 1 atm in this study using the partial pressure method. Next is the mixing of the lean n-butane/air mixture by counter-rotating two specially-designed fans and perforated plates (see Figure 1), where the two fans are rotated at a fixed fan frequency f = 30 Hz for at least 1.5 min to ensure the well mixing of fuel and air. For the laminar case, the two fans are turned off right after the mixing, and then we wait for about 10 s to let turbulence completely dissipate, allowing a quiescent mixture before ignition. As to turbulent cases, after the well mixing of fuel and air, the fan frequency is set to the desired value for the wanted u′ ≈ 0.0462f (ms⁻¹), measured by high-speed particle image velocimetry (PIV) [22,26,29]. Additionally, the integral length scale of turbulence L_I ≈ 10.7f^0.34 (mm), leveled off to about 45 mm at high values of f ≥ 70 Hz [22,26,29].

A pair of 2-mm stainless-steel electrodes with sharp ends at a constant d_gap = 2.0 mm are used to centrally ignite the lean n-butane/air mixture under quiescent and turbulent conditions at various values of E_ig controlled by the loading resistors (R_Ω) in the ignition circuit (see the top left inset of Figure 1). The higher the value of R_Ω is, the smaller the value of E_ig is. An accurate E_ig measurement is vital to determine the ignition probability, as well as MIE_L and MIE_T. The present work applies the same ignition methodology as used in [7] to measure E_ig of high accuracy with near-square current and voltage waveforms. Note that E_ig is determined by the integration of the product of I(t) and [V₁(t) − V₂(t)] across the spark gap (see Figure 1) within a fixed pulse duration time of τ_p = 100 μs. Schlieren images of the ignition kernel and its subsequent flame development under various experimental conditions are recorded by a high-speed, high-resolution CMOS camcorder (Phantom V711), operated at 25,000 frames per second.

3. Results and Discussion

3.1. Laminar and Turbulent Minimum Ignition Energies of Lean n-Butane/Air Mixture

Figure 2a shows the ignition probability versus ignition trials with various values of E_ig of the lean n-butane/air mixture at ϕ = 0.7 in quiescence, as a typical example for demonstrating the statistical determination of MIE at 50% ignitability. Each datum of MIE_L and MIE_T is determined by more than 30 runs over a range of E_ig with either “Go” (open circle symbols) or “No Go” (cross symbols), as indicated in Figure 2a. There is an overlapping regime within which “Go” and “No Go” co-exist. As indicated in Figure 2a, the newly obtained datum of MIE_L for the present lean n-C₄H₁₀/air mixture at d_gap = 2.0 mm is 3.4 mJ. The reader is directed to Ref. [7] for a detailed methodology on MIE determination using the logistic regression method.

In the presence of turbulence at large d_gap = 2.0 mm, as shown in Figure 2b, newly measured values of MIE_T are respectively 3.96 mJ/9.37 mJ/17.3 mJ/30.5 mJ at u′ ≈ 0.46 m/s/0.92 m/s/1.4 m/s/2.1 m/s, where values of MIE_T are all larger than MIE_L = 3.4 mJ. This confirms that that there is no TFI at d_gap = 2.0 mm, even when the mixture’s Lewis number is sufficiently greater than unity (Le ≈ 2.1 >> 1). At large d_gap = 2.0 mm, turbulence always renders ignition more difficult. A sufficiently large E_ig is required to overcome heat losses induced by electrodes and turbulence for successful ignition. In the pre-transition when u′ < u′_c, MIE_T increases modestly with increasing u′, while such increase becomes much more drastic when in the post-transition u′ > u′_c. As previously shown on the inset of Figure 5 in Ref. [24], at small d_gap = 0.8 mm, it was found that MIE_T first decreases with increasing u′ where MIE_T < MIE_L ≈ 23 mJ, showing TFI with the minimum value of MIE_T ≈ 19.8 mJ occurring also at u′_c ≈ 0.92 m/s. When u′ > u′_c, turbulence re-claims its totally dominating role where MIE_T increases rapidly to be greater than MIE_L ≈ 23 mJ. Again, the phenomenon of TFI only occurs at sufficiently large Le >> 1 and at sufficiently small d_gap = 0.8 mm. This is attributed to the competition between differential diffusion (the effect of Le) and turbulent dissipation (the effect of u′), similar to that discussed in our previous studies for lean PRF95/air mixture with Le ≈ 2.95 >> 1 [23] or rich hydrogen/air mixture at ϕ = 5.1 with Le ≈ 2.3 >> 1 [28]. In the present study, except at the largest u′ = 2.1 m/s, where almost the same value of MIE_T ≈ 31 mJ is found for both small and large d_gap, all other values of MIE_L and MIE_T at d_gap = 2.0 mm are smaller than those of d_gap = 0.8 mm (Figure 2b). As such, the use of large d_gap = 2.0 mm is better than small d_gap = 0.8 mm because the former can have a higher ignition probability than the latter at the same u′ up to 2 m/s.

3.2. Flame Kernel Development in Quiescent and Turbulent Conditions

Figure 3 presents high-speed schlieren images for time evolutions of the early flame kernel development under laminar and turbulent conditions at five different values of u′ varying from 0 to 2.1 m/s, all for successful ignition events. The first four columns have a 24 × 24 mm² view field to see the embryonic kernel development after the spark discharge; the fifth column has a larger view field of 42 × 42 mm² for the observation of self-sustained flame propagation.

For the laminar case, the initial rod-like kernel at t = 0.04 ms develops into an oval flame kernel and continuously propagates to form a laminar self-sustained spherical flame at t = 20 ms (the last image of the first row in Figure 3). For the turbulent cases at u′ = 0.46 m/s (the 2nd row) and u′ = 0.92 m/s (the 3rd row), the initial spark kernels at t = 0.04 ms and their subsequent development of flame kernels at t = 1.2 ms are very similar to that of the laminar case, indicating that weak and/or modest turbulence have almost nearly negligible effect on the embryonic kernel development at least up to 1.2 ms. This is possibly due to the suppression effect by the emitted shock wave [30]. However, such a shock wave suppression effect seems to become unimportant, as the kernel is wrinkled earlier by stronger turbulence. This is evidenced by the schlieren images shown in the 4th and 5th rows of Figure 3 at u′ = 1.4 m/s and 2.1 m/s, where the flame kernels at t = 1.2 ms have largely wrinkled by turbulence with higher values of u′. For the early development of the flame kernel, the higher the value of u′ is, the larger the wrinkled flame kernel area is, and the higher the flame kernel speed is. Furthermore, the wrinkled flame kernel with negative curvature segments could be induced by turbulence that can enhance reaction rate of Le >> 1 mixtures through differential diffusion [25]. We observe that turbulence can enhance the flame kernel speed to be much greater than its laminar flame speed for successful ignition events, resulting in a shorter τ_delay for the present Le >> 1 flames, as seen by comparing the lapsed times indicated in the last column of Figure 3.

3.3. Effect of Ignition Energy on Ignition Kernel Delay Time in Quiescence

To quantify the ignition kernel delay time as a function of ignition energy during the early development of flame kernel for successful ignition, the time evolutions of flame kernel radii (R) are recorded by using high-speed schlieren imaging (Figure 3). R = (A/π)^0.5 and A is the area enclosed by the developing flame kernel front. As such, flame speeds (dR/dt) of the developing flame kernels versus R can be obtained. Figure 4a presents six data sets of (dR/dt) versus R at different E_ig varied from one half to twice of MIE_L (½MIE_L ≤ E_ig ≤ 2MIE_L, where MIE_L = 3.4 mJ) for successful ignition cases. After the discharge, all six laminar flame speeds (dR/dt) first decrease drastically to a minimum value of (dR/dt)_min corresponding to a critical flame radius, which is termed as R_Lmin (see Figure 4a). If the kernel’s heat release generated by chemical reaction can be sustained to be greater than heat losses to electrodes and ambient after τ_delay determined at R_Lmin with the minimum (dR/dt), successful ignition should occur. As such, the self-sustained laminar flame propagation becomes possible, by which dR/dt starts to increase and then the flame speed asymptotically approximates to its laminar burning velocity when R > 15 mm in the present lean n-butane/air flames (Figure 4a). Therefore, τ_delay is the time interval from the initiation of the spark to the time that the flame speed reaches its minimum at R_Lmin. R_Lmin is found to be about 5 mm in the present study, regardless of different values of E_ig applied (Figure 4a). As shown in the inset of Figure 4a, an increase of E_ig from 0.5 MIE_L to 2 MIE_L promotes the early development of the flame kernel growth rate with an increase of (dR/dt)_min, resulting in a reduction of τ_delay.

Figure 4b shows the ignition kernel delay time measured at R_Lmin ≈ 5 mm that is plotted against a normalized ignition energy (E_ig/MIE_L), revealing a transition of τ_delay by which the decreasing slope of τ_delay with E_ig/MIE_L changes from rapid to gradual when E_ig/MIE_L reaches its critical value of unity. Note that the reverse result is found for that of (dR/dt)_min. In the pre-transition, when 0.6 < E_ig/MIE_L < 1, values of τ_delay decrease from 7.5 ms to 5 ms, but a much smaller decrease of τ_delay from about 4.6 ms to 4.2 ms is observed when 1 < E_ig/MIE_L ≤ 2.15 in the post-transition. This is attributed to the reverse behavior of the drastic and modest increase of (dR/dt)_min before and after the transition occurring at the same critical value of (E_ig/MIE_L)_c ≈ 1.1. The marginal effect of higher E_ig/MIE_L > 1 on (dR/dt)_min and τ_delay is probably due to the saturation of the refreshed mixture induced by recirculation vortices inside the initial kernel [31,32] that may limit the increase of active radicals for the laminar case; the increase of heat conduction losses to electrodes with increasing E_ig [19] could be another possible factor.

3.4. Effect of Turbulence on Ignition Kernel Delay Time

Figure 5 presents the effect of u′ on τ_delay for the early flame kernel development at d_gap = 2.0 mm, in which there are five averaged data sets of (dR/dt) versus R at five different values of u′ varying from 0 to 2.1 m/s, similar to the five cases presented in Figure 3. Each datum is averaged from at least three repeated successful ignition runs using the same E_ig, where E_ig,L ≈ MIE_L for the laminar case and E_ig,T ≈ MIE_T at corresponding vlues of u′ for turbulent cases from Figure 2b are applied. As seen, dR/dt increases with increasing u′ that leads to a decrease of τ_delay, as indicated in the inset of Figure 5a. These measured (dR/dt)_min and τ_delay are then plotted in Figure 5b against u′. The result seems to indicate a transition of τ_delay that occurs at a critical u′_c ≈ 0.92 m/s. When u′ < u′_c, τ_delay decreases slightly from 4.8 ms at u′ = 0 to 4.3 ms at u′ ≈ 0.92 m/s (only about 8% decrement). However, when u′ > u′_c, a more rapid decrease of τ_delay is found, where τ_delay ≈ 4.3/3.7/2.8 ms at u′ = 0.92/1.4/2.1 m/s, respectively. The decrease of τ_delay with increasing u′ is attributed to the flame kernel speed enhancement by turbulence, where corresponding values (dR/dt)_min increase with u′. These results in Figure 5b reveal that turbulence in the pre-transition has a small influence on the early flame kernel development, as can be also seen from these sequential schlieren images in the 2nd and 3rd rows of Figure 3. In the post-transition at higher u′ > u′_c, turbulence can facilitate the growth rate of the early flame kernels (see the 4th and 5th rows in Figure 3), resulting in a more rapid reduction of τ_delay. By comparing Figure 2b for the regular MIE transition with Figure 5b for the τ_delay transition, it is found that both transitions are reversely dependent on each other. An increase of u′ accelerates the early flame kernel development with a shorter τ_delay that requires a sufficiently high MIE_T to overcome the turbulent convection heat losses; such a trend is even more profound when u′ > u′_c in the post-transition.

4. Conclusions

Laminar and turbulent minimum ignition energies of a lean n-butane/air mixture with Le ≈ 2.1 >> 1 at a fixed 2-mm inter-electrode gap are statistically measured by the logistic regression method in a dual-chamber, fan-stirred cruciform burner capable of generating near-isotropic turbulence with negligible mean velocities. Using measured values of MIE_L and MIE_T, the effects of the ignition energy and the r.m.s turbulence fluctuation velocity on the early flame kernel speed dR/dt and its associated ignition kernel delay time determined at (dR/dt)_min were then investigated. These measurements reveal the following points.

(1) When d_gap = 2 mm, it is found that turbulence always renders ignition more difficult; there is no turbulence facilitation ignition which only occurs at small d_gap = 0.8 mm (Figure 2b). A regular MIE transition is found, where the increasing slopes of MIE with increasing u′ changes from gradual to rapid when u′ is greater than a critical value of u′_c ≈ 0.92 m/s for the present study.

(2) In quiescence, the early development of flame kernel speed increases with increasing E_ig, resulting in a reduction of the ignition kernel delay time. Specifically, when E_ig/MIE_L is increased from 0.67 to about 1, values of τ_delay decrease drastically from 7.5 ms to 5 ms, but a much more modest decrease of τ_delay from about 4.6 ms to 4.2 ms is observed within 1 < E_ig/MIE_L ≤ 2.15. This is attributed to the reverse behavior of the drastic and modest increase of (dR/dt)_min before and after E_ig/MIE_L ≈ 1.

(3) There is a τ_delay transition. In the pre-transition, when u′ < u′_c ≈ 0.92 m/s, τ_delay only decreases slightly from 4.8 ms at u′ = 0 to 4.3 ms at u′ = 0.92 m/s. However, the decrease of τ_delay becomes drastic in the post-transition when u′ > u′_c, where τ_delay ≈ 4.3/3.7/2.8 ms at u′ = 0.92/1.4/2.1 m/s, respectively. The decrease of τ_delay with increasing u′ is attributed to the flame kernel speed enhancement by turbulence, where corresponding values of (dR/dt)_min increase with u′. The increase of u′ promotes the early development of the flame kernel, which results in a smaller τ_delay and a higher MIE_T is required to overcome turbulent convection heat losses; such higher MIE_T and lower τ_delay with increasing u′ become profound when u′ > u′_c.

These results may be useful to our further understanding of lean premixed turbulent ignition and combustion with a potential application to lean-burn high-thermal efficiency SI engines. As a final remark, it should be interesting in modelling τ_delay of the present n-butane/air mixture using detailed chemical kinetics even under one-dimensional or homogeneous condition.