# Influence of plasma parameters on the lean blow-off limit of a model aeronautical combustor

Jean-Baptiste Perrin-Terrin, Hugo Veran, Philippe Scouflaire, Christophe O Laux, Sébastien Ducruix

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Jean-Baptiste Perrin-Terrin, Hugo Veran, Philippe Scouflaire, Christophe O Laux, Sébastien Ducruix. Influence of plasma parameters on the lean blow-off limit of a model aeronautical combustor. 12th European Combustion Meeting, Apr 2025, Edinburgh, United Kingdom. hal-05076071

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Distributed under a Creative Commons Attribution 4.0 International License
Influence of plasma parameters on the lean blow-off
limit of a model aeronautical combustor

Jean-Baptiste Perrin-Terrin<sup>a,*</sup>, Hugo Veran<sup>a</sup>, Philippe Scouflaire<sup>a</sup>,
Christophe O. Laux<sup>a</sup>, Sébastien Ducruix<sup>a</sup>

<sup>a</sup>Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C

Abstract

This work presents an experimental investigation of the plasma-assisted staged combustor BIMER-PAC. Previous studies of this facility have proven the capability of Nanosecond Repetitively Pulsed (NRP) discharges to significantly extend (by up to 40%) the Lean Blow-off (LBO) limit of a 100-kW methane-air flame with a plasma power less than 0.25% of the flame thermal power. This extension is made possible thanks to a change of the flame shape: without plasma, the V-shaped flame extinguishes during the oscillations caused by a change in the flow topology; when the plasma is applied, the flame survives the oscillation phase and becomes a tulip flame. The present work focuses on the flame shape transition mechanism and the influence of the plasma parameters on the LBO extension with NRP discharges. A parametric study is conducted in a 50-kW CH<sub>4</sub>/air flame with a staging ratio of 40%. First, the V-to-tulip transition and the LBO are studied with decreasing ramps of equivalence ratios. The effects of the applied voltage and Pulse Repetition Frequency (PRF) are studied. A non-linear dependence of the LBO equivalence ratio with plasma power is observed. This is explained by the existence of a minimum threshold voltage required to obtain a V-to-tulip transition. When the transition is obtained, the LBO equivalence ratio scales linearly with plasma power. The influence of the PRF on this threshold voltage is also determined. Between 20 and 30 kHz, increasing the PRF lowers the threshold voltage, yet for higher PRF no variations are observed. The tulip-to-V shape transition is also studied with ramps of increasing equivalence ratios. The effect of the PRF on the stability of the transition is measured. At 50 kHz, a stable branch-shaped flame is observed during the transition. When the PRF is decreased, flame-shape fluctuations are observed near the transition limit. These observations lead to the formulation and testing of a flame shape control strategy based on the PRF.

Keywords: Plasma-Assisted Combustion; Lean Blow-off Limit; Nanosecond Repetitively Pulsed discharges; Partially premixed combustion; swirled-stabilized combustion.

<footnote>*Corresponding author.</footnote>
## 1. Introduction

Plasma-assisted combustion (PAC) is a novel and promising technology for meeting the challenges of lean-flame stabilization [1–3]. Among the many nonequilibrium plasma sources used in the literature, the nanosecond repetitively pulsed (NRP) discharge stands out as an energy efficient and versatile source, and experimental demonstrations in many burner configurations and fuels have been made [4,5]. Alongside these demonstrations, fundamental studies were conducted to understand the effects of the plasma created by NRP discharges [6,7]. These studies have revealed that the plasma contributions are chemical (mainly) and thermal. Additionally, they showed that the chemical contribution is mostly driven by dissociation of molecular oxygen into atomic oxygen and the thermal effect consists in an ultra-fast heating (~1000 K in 50 ns). Based on these findings and theoretical data from Popov [8], a phenomenological model was developed by Castela et. al. [9] to include plasma effects in large eddy simulation (LES) of turbulent flames. This model was validated against experimental data obtained in a canonical burner stabilized by bluff-body [10]. Simulations and experiments agreed on the stabilizing mechanisms: thanks to repetitive pulses, cumulative chemical and thermal effects build up within the recirculation zone of the bluff-body. Then, the radicals and heat produced are convected to the flame front where they locally increase the heat release rate and stabilize the lean flame [11,12].

The mechanisms of lean flame stabilization with NRP discharges applied in a recirculation zone are now well in hand. However, in different configurations, especially in swirled-stabilized burners, the effects of NRP discharges on combustion stability are not yet fully understood, especially because of the stronger influence of flow dynamics on the plasma. This is well illustrated in the literature, notably with the work of Shanbhogue et al. [13] who successfully implemented an open-loop flame control strategy using plasma actuation. To do so, they adopted a “black-box” approach, assuming that the

flame responded linearly to the plasma repetition frequency and calibrating beforehand the model on the experiment. However, Pavan et al. showed that a certain threshold voltage must be exceeded to reach the high energy deposition plasma mode where this linear behavior is observed. Therefore, there is a coupled effect of the various plasma parameters. Similarly, Di Sabatino et. al. [14] suggested that applying NRP discharges with low voltage and high repetition frequency leads to higher energy efficiency. A different observation was made by Aravind et al. [15] who, using the same burner with similar plasma integration, suggested that high voltage and low frequency were more energy efficient. There is therefore a need for a better understanding of the plasma effect in swirled stabilized burners, especially on understanding the separate influences of the applied voltage and pulse repetition frequency.

Recently, Blanchard et al. [16] demonstrated a significant LBO extension using PAC in a staged swirled-stabilized combustor, BIMER-PAC. They successfully extended the LBO limit by 50%, with a plasma power less than 0.25% of the flame thermal power. The authors attributed this large extension to a change in the flame shape: without plasma, the flame extinguished during oscillations caused by the change in the flow topology. When plasma was applied, the flame is sustained through the oscillations, and after the stabilization of the flow topology, the flame is stabilized in a tulip shape. They called it a V-to-tulip transition. In this work, we study the effect of the repetition frequency and applied voltage of NRP discharges on the LBO limit and the V-to-tulip transition in the BIMER-PAC combustor.

## 2. Experimental Setup

### 2.1. BIMER-PAC

The BIMER-PAC experiment was previously studied by Blanchard et al. [16]. This facility is dedicated to the study of PAC using a fuel injector representative of aeronautical systems at semi-industrial thermal power ~100 kW. The facility is

<figure><img src="image_3.png" /><figcaption>Fig. 1: (a) Schematic of the BIMER-PAC experiment. (b) Schematic of the two-stage injector with the high voltage electrode.</figcaption></figure>

<figure><img src="image_4.png" /></figure>
1 composed of an air plenum, a two-stage injector and

2 a combustion chamber, as depicted in Fig. 1 (a). The

3 combustion chamber has a 15-cm square section, and

4 the side walls are made of silica for flame imaging.

5 The upper and lower walls are water-cooled. At the

6 injector side, two small silica windows are inserted in

7 the lower and upper wall, initially designed for laser

8 diagnostics and used in this study to place the

9 electrode mounting system. Two type-K

10 thermocouples are inserted into blind holes in the

11 upper wall. Additional thermocouples are inserted

12 into the water-cooling system to measure the

13 extracted heat flux.

14 A close-up view of the two-stage injector is shown

15 in Fig. 1 (b). In the *pilot* stage, the fuel is injected

16 axially through a 4-mm diameter tube. In the

17 multipoint stage, the fuel is injected in a crossflow

18 configuration through a multipoint crown comprising

19 15 holes, each 700 µm in diameter. This staged

20 injection is representative of new low emissions

21 injection systems [17]: the multipoint stage generates

22 a lean and well premixed flame providing most of the

23 thermal power; yet, this lean and well-premixed flame

24 is prone to instabilities, thus a stable fuel-rich flame

25 created by the pilot stage is added to stabilize the

26 whole. The methane mass flow rates of both stages are

27 independently controlled by two mass flow

28 controllers (Bronkhorst EL-Flow F-203AC-AAD-44-

29 V for the pilot stage and Bronkhorst Cori-Flow M15-

30 RAD-44-0-S for the multipoint stage).

31 The staging ratio noted $\alpha_p$ is used to characterize

32 the injection. It is defined as follows:

$$ \alpha_p = \frac{\dot{m}_{CH_4,pilot}}{\dot{m}_{CH_4,pilot} + \dot{m}_{CH_4,multi}} \quad (1) $$

33 where $\dot{m}_{CH_4,pilot}$ and $\dot{m}_{CH_4,multi}$ are the mass flow

34 rates of the pilot and multipoint stage, respectively.

35 When $\alpha_p = 0\%$, all fuel is injected into the multipoint

36 stage, and conversely, when $\alpha_p = 100\%$ all fuel flows

37 through the pilot stage. In this study, only a staging

38 ratio of $\alpha_p = 40\%$ is studied.

39 The plenum feeds the air in the injector for

40 subsequent mixing with the fuel. Thanks to head

41 losses, the air is split between the two stages (80% on

42 the multipoint, 20% on the pilot stage). The air mass

43 flow rate is controlled by a single controller

44 (Bronkhorst EL-Flow F-206BI-FA-00-V). We define

45 three equivalence ratios: global $\Phi_g$, pilot $\Phi_p$, and

46 multipoint $\Phi_m$. They are calculated as follows:

$$ \Phi_g = s \times \dot{m}_{CH_4,tot} / \dot{m}_{air,tot} $$

$$ \Phi_p = 5\alpha_p \times \Phi_g \quad (2) $$

$$ \Phi_m = 1.25(1 - \alpha_p) \times \Phi_g $$

47 where s is the mass stoichiometric ratio.

48 Finally, the water-cooled electrode is inserted in

49 the chamber through the top small silica window. The

50 window is adapted and fitted with a clamping flange

51 to ensure airtightness. The plasma is formed between

52 the tip of the electrode and the divergent nozzle of the

53 pilot stage. The plasma is generated with NRP

54 discharges delivered by an FID-FPG 15-100NM10

55 pulser with negative polarity. The setpoint voltage V

56 can be adjusted between 3 and 15 kV. The Pulse

57 Repetition Frequency (PRF) is adjusted by a gate-and-

58 delay generator (BNC model 575) used to trigger the

59 pulser. The PRF varies between 20 and 50 kHz in this

60 study.

## 2.2. Diagnostics

62 Waveforms of voltage and current are acquired

63 with fast probes (a Lecroy PPE-20 kV, 100-MHz

64 bandwidth voltage probe, and a 200-MHz bandwidth

65 current monitor, Pearson model 6585) connected to an

66 oscilloscope (TeledyneLecroy HDO 6104B). The

67 probes are placed 2-m away of the pulser in a 8-m long

68 cable, in the remote configuration described in the

69 appendix of [18]. Typical measurements are shown in

70 Fig. 2. The energy is obtained by integrating over time

71 the product of current and voltage. The energy

72 deposited in the plasma, noted $E_p$, corresponds to the

73 end value of the energy curve, in this case $E_p = 8$ mJ.

74 Plasma power is given by $P_{plasma} = E_p \times f_{rep}$.

75 Flame imaging is performed with an ICCD camera

76 (Princeton Instruments, PI-MAX 4) equipped with a

77 50-mm lens (Nikon, AF Nikkor f/1.4) and a bandpass

78 filter (Asahi spectra, F0101, center

79 wavelength = 430 nm, spectral FWHM = 10 nm)

80 centered on the CH* chemiluminescent emission.

<figure><img src="image_5.png" /><figcaption>Fig. 2. Voltage and current traces measured in the middle of an 8-m coaxial cable (top). Energy deposited by the</figcaption></figure>

85 discharge (bottom). Here, the setpoint voltage is 13 kV and

86 the deposited energy is 8 mJ. The setpoint voltage is the

87 voltage difference across the electrodes: it corresponds to

88 the sum of the incident and reflected pulses.

89 The LBO limit is determined experimentally by

90 slowly increasing the air flowrate until the flame

91 extinguishes. The rate of increase is such that the

92 equivalence ratio is decreased by 0.01 every 5

93 seconds. When the flame extinguishes, the air mass

94 flow rate is recorded to infer the equivalence ratio. For
1 each experimental conditions, the measurement is
2 repeated at least three times.

3

## 3. Results and discussions

### 3.1. Effect of voltage on LBO limit

6 shows the effect of applied voltage on the LBO limit
7 at three different PRF. Individual measurements are
8 plotted. For all three PRF, an abrupt decrease in the
9 LBO equivalence ratio is observed above a certain
10 voltage value: 12.25 kV for 20 kHz and 10.75 kV for
11 both 30 and 50 kHz. This sudden decrease
12 corresponds to the transition to a tulip flame. For
13 voltages below the threshold value, no V-to-tulip
14 flame shape transition is observed. At 13 kV, $\Phi_{LBO}$
15 decreases with the PRF, from 0.36 at 20 kHz to 0.295
16 at 50 kHz.

17 The dependence of the equivalence ratio on both
18 the applied voltage and the PRF could be attributed to
19 the total plasma power. This is usually the case in the
20 literature. In Fig. 4, the equivalence ratios at LBO are
21 plotted against the plasma power. The plasma power
22 ranges from 80 W to 360 W, corresponding to 0.16%
23 to 0.72% of the flame thermal power. Remarkably, the
24 equivalence at LBO does not scale linearly with
25 plasma power. For instance, at 225 W, for a PRF of
26 50 kHz, extinction is at 0.44 whereas for 30 kHz the
27 extinction is much leaner, in tulip flame at 0.33.
28 However, for extinction in the same flame shape (V
29 or tulip), linear trends are observed.

<figure><img src="image_6.png" /></figure>

30

31 Fig. 3: Effect of applied voltage on the LBO limit at
32 different PRF (green: 20 kHz, blue: 30 kHz, red: 50 kHz).
33 Plotted values correspond to individual measurements of
34 LBO, i.e. without averaging. The error bar corresponds to
35 the B-type error of the three mass flow controllers. The
36 dispersion of the values is typically lower than 0.015.

37 It is important to note that plasma power is
38 computed using a deposited energy averaged over the
39 whole LBO sequence. However, it has been reported
40 in several studies of PAC in swirled flows [15,19] that
41 because of the flame dynamic, different energy modes
42 could be reached for the same plasma conditions.
43 Therefore, the effective plasma power at LBO might
44 be different. Measurements of the energy per pulse

45 synchronized with the flame shape could answer this
46 question.

47

<figure><img src="image_7.png" /></figure>

48

<caption>Fig. 4: Equivalence ratio at LBO plotted against plasma power.</caption>

50

### 3.2. Detailed study of transition to tulip flame

52 The LBO limit is highly dependent on the V-to-
53 tulip transition, and that transition does not depend
54 solely on the plasma power. In this part, the transition
55 is studied in detail. To do so, the combustor is
56 stabilized with plasma at $\phi = 0.53$ to get a stable V-
57 shaped flame and reach a stable temperature in the
58 upper wall thermocouples. Then, the air mass flow
59 rate is first increased up to approximatively 130
60 $Nm^2/h$, corresponding to $\phi = 0.36$. Immediately after
61 reaching this value, the air mass flow rate is decreased
62 back to its initial value. Typical traces of the output
63 signals of the mass flow controllers are given in Fig.
64 5, where the procedure is repeated three times. The
65 computed equivalence ratio is also plotted. During
66 this sequence, the flame topology is monitored with
67 CH\* chemiluminescence images. The resulting
68 images are shown in Fig. 6 for $V = 13$ kV and $f_{rep} =$
69 30 kHz.

70

<figure><img src="image_8.png" /></figure>

71

<caption>Fig. 5: Top: traces of measured mass flow rates of air (black line), CH₄ on the multipoint stage (blue line) and on the pilot stage (red line). Bottom: global equivalence ratio.</caption>
<figure><img src="image_9.png" /><figcaption>Fig. 6: Images of the flame shape transition at P<sub>th</sub> = 50 kW, α<sub>p</sub> = 40%, V = 13 kV and f<sub>rep</sub> = 30 kHz. Top row is the V-to-tulip transition, bottom is the tulip-to-V transition. In each condition, 100 frames are acquired. The plotted image is the standard deviation of the 100 samples. The pictograms in the top right corner of the images describe the flame shape; white color corresponds to stable shapes, whereas grey stands for alternating shapes.</figcaption></figure>

1

2 During the transition from V to tulip, an

3 intermediate stable flame shape is observed. It looks

4 like a branch of the V flame, but smaller and located

5 at the top of the injector, hence called a *branch* flame.

6 In this state, the flame surface is lower, suggesting a

7 lower combustion efficiency. As shown in Fig. 6, a

8 transition develops as follows: as the air flow is

9 increased, first the V flame is destabilized and

10 oscillates between V and branch. Next, the flame

11 stabilizes only in branch shape. Then, oscillations

12 between branch and tulip appear, until finally a stable

13 tulip is obtained. The inverted transition follows the
14 same steps, without any hysteresis phenomenon.

15 **3.3. Effect of frequency on tulip transition**

16 To assess the effect of the frequency, the

17 transitions are studied for the three PRF already

18 presented earlier (20, 30 and 50 kHz) and at 13 kV.

19 Table 1 shows the different sequences of transitions.

20 Several observations can be made.

21 First, as the PRF increases, the V-flame stability

22 domain is increased. Second, at 20 kHz flame shape

23 oscillations are much more pronounced than at

<table><caption>Table 1: Equivalence ratios of flame shape transitions during the sequence described in Fig. 5 (from left to right: V-to-tulip then tulip-to-V transition). The flame shapes are represented by their pictogram defined in Fig. 6. Black pictograms stand for stable flame whereas grey is for alternating shapes. The equivalence ratios correspond to an average over three samples.</caption><thead><tr><th></th><th colspan="12">20 kHz</th></tr><tr><th>Flame shape:</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th></tr></thead><tbody><tr><th>φ:</th><td>0.50</td><td>0.49</td><td>0.47</td><td>0.44</td><td>0.42</td><td>0.36</td><td>0.43</td><td>0.46</td><td>0.49</td><td>0.49*</td><td></td><td></td></tr></tbody><thead><tr><th></th><th colspan="12">30 kHz</th></tr><tr><th>Flame shape:</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th></tr></thead><tbody><tr><th>φ:</th><td></td><td>0.47</td><td>0.44</td><td>0.43</td><td>0.41</td><td>0.36</td><td>0.42</td><td>0.44</td><td>0.45</td><td>0.47</td><td></td><td></td></tr></tbody><thead><tr><th></th><th colspan="12">50 kHz</th></tr><tr><th>Flame shape:</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th><th>∠</th></tr></thead><tbody><tr><th>φ:</th><td></td><td>0.45</td><td>0.37</td><td>0.36</td><td>0.40</td><td>0.44</td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>
1 30 kHz, and even short extinction (< 0.1 s) are

2 observed. At 50 kHz, the branch flame is more stable

3 and no oscillations with other shapes are reported.

4 Third, the equivalence ratio of the branch-to-tulip

5 transition decreases with the PRF.

6 This shows that the higher the PRF, the more stable

7 the combustion during the transitions. It is probably

8 linked to the increased stability of the branch flame,

9 which prevents extinction and flame shape

10 oscillations. However, as the stability domain of the

11 branch flame increases, the branch-to-tulip transition

12 is delayed. This effect could be detrimental to the

13 overall combustion efficiency, as the flame surface of

14 the branch flame is smaller than the tulip flame. A

15 trade-off on the PRF should be found to ensure a

16 stable transition but also transitioning as soon as

17 possible in tulip shape.

18 Finally, it is noted that the equivalence ratio of the

19 branch-to-tulip transition is slightly lower than for the

20 tulip-to-branch transition. This might suggest a

21 hysteresis phenomenon, but further work is needed to

22 properly assess this claim.

### 3.4. Flame shape control

24 It can be seen in Table 1 that for a given

25 equivalence ratio, several flame shapes can be

26 obtained. For instance, at $\phi = 0.41$, during the

27 transition at 20 kHz, the flame is in tulip shape

28 whereas in the transition at 50 kHz it is in branch

29 shape. However, these flame shapes were obtained

30 dynamically by varying the equivalence ratio. It is

31 interesting to test whether the flame shape can be

32 controlled statically by varying the PRF instead. This

33 is successfully demonstrated experimentally: at $\phi = $

34 0.41, a tulip flame is stabilized at a PRF of 20 kHz.

35 Then, the PRF is progressively increased and at

36 approximatively 45 kHz, the flame stabilizes in a

37 branch shape.

38 This flame shape control could be useful to

39 overcome both the stability and the low efficiency

40 issues during a transition. The following strategy can

41 therefore be used: set a PRF of 50 kHz from $\phi = 0.53$

42 to $\phi = 0.41$ to ensure a stable branch flame, then at $\phi$

43 = 0.41, reduce the PRF down to 20 kHz to obtain a

44 stable tulip flame. This strategy was experimentally

45 tested and successfully demonstrated. In future work,

46 the effect of this strategy on NOₓ emissions and

47 combustion efficiency will be assessed.

48

### 4. Conclusion

50 In this work, we studied the LBO limit extension

51 of a swirled-stabilized staged combustor using PAC

52 with NRP discharges. The flame thermal power and

53 the staging ratio are kept constant at 50 kW and 40%

54 respectively. The effect of the applied voltage and the

55 PRF on the LBO limit and the V-to-tulip transition are

56 assessed. The main findings of this work are:

57 • The LBO limit does not scale linearly with plasma power.

59 • A threshold voltage must be exceeded to enable V-to-tulip transition. When this threshold is obtained, the LBO limit scales linearly with plasma power.

60 • During the transition, the flame takes the shape of a small branch of a V-flame. This branch flame helps reduce flame shape oscillations during the transition.

61 • High PRFs increase the stability of both the V and the branch flame.

62 • Adjusting the PRF allows controlling the flame shape. This could be used to increase combustion performance.

### Declaration of competing interest

74 The authors declare that they have no known

75 competing financial interests or personal relationships

76 that could have appeared to influence the work

77 reported in this paper.

78

### Acknowledgments

80 This work has received funding from the European

81 Research Council (ERC) under the European Union's

82 Horizon 2020 research and innovation program (ERC

83 GreenBlue grant agreement No.101021538). The

84 authors thank E. Jean-Bart, Y. Le Teno, J. Bonnety,

85 C. Mirat, H. Jubeau, and K. Sokhona for technical

86 assistance.

87

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