# Modeling turbulent flame enhancement by Nanosecond Repetitively Pulsed discharges using a low-order model

Stéphane Q.E. Wang, Nasser Darabiha, Benoît Fiorina

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Stéphane Q.E. Wang, Nasser Darabiha, Benoît Fiorina. Modeling turbulent flame enhancement by Nanosecond Repetitively Pulsed discharges using a low-order model. 12th European Combustion Meeting, Apr 2025, Edinburgh, United Kingdom. hal-05109899

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# Modeling turbulent flame enhancement by Nanosecond Repetitively Pulsed discharges using a low-order model

Stéphane Q. E. Wang, Nasser Darabiha and Benoît Fiorina

Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire EM2C - France

## Mechanism of flame stabilization by NRP discharges

Plasma-Assisted Combustion (PAC) with Nanosecond Repetitively Pulsed (NRP) discharges can [1]:

* promote ignition,

* extend flammability domain,

* stabilize lean flames.

<figure><img src="image_4.png" /></figure>

Complex interactions between plasma, turbulence and combustion can be captured by LES [2] with a phenomenological modeling of NRP discharges [3]

NRP discharges enhance the local reactivity by:

* increasing the gas temperature,

* producing active radicals, such as atomic O.

At post-discharge, **OH** is produced and convected to the flame front, improving the flame stabilization.

However, the **CPU** cost remains relatively high, due to:

* response time of the flame,

* resolution of the discharge region.

A low-order approach is required for engineering design!

**How to model the impact of NRP discharges on the heat release rate (HRR)?**

## Reduced-Order Modeling

PHYSICS

<figure><img src="image_5.png" /></figure>

SUB-MODELING

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

## Model application: Mini-PAC burner [5]

NUM. SET-UP

**PSR Inlet and Initial:**
* T<sup>BG</sup> = 2000 K
* r<sub>d</sub> = 0.6 mm
* L<sub>d</sub> = 5 mm

**NRPD model:** Castela's [3]
* E<sub>p</sub> = 1.00 mJ
* f<sub>p</sub> = 20 kHz

**Residence time***: τ<sub>res</sub> = 0.165 ms

**Length***: L<sub>RZ</sub> = 5 mm

**Velocity***: u<sub>flow</sub> = 7.3 m.s<sup>-1</sup>

**Dilution***: β = 0.30

**PFR inlet:**
Y<sub>k</sub><sup>in</sup> = βY<sub>k</sub><sup>A</sup> + [1 - β] Y<sub>k</sub><sup>BG</sup>
h<sup>in</sup> = βh<sup>A</sup> + [1 - β] h<sup>BG</sup>

Performed with REGATH solver [6].
CH<sub>4</sub>-Air mixture at φ = 0.80 and P<sub>atm</sub>.
Combustion kinetics: ARC Lu19 [7].
*Parameters estimated from LES [8].

**PMX-CF**
right inlet:
T<sup>FG</sup> = 300 K

**Strain rate***: ε = 1000 s<sup>-1</sup>

ZONE A : PSR

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

ZONE B : PFR

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

ZONE C : PMX-CF

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

### In zone A

* Comparison with OES measurements by [5].

* Lower envelope of temperature increase recovered: ~1250 K (from 2000 to 3250 K).

### In zone C

* Diluted plasma-impacted burnt gases have an influence on the flame reactive layer.

* increase heat release rate (HRR)

### In zone B

* Between Inlet and Outlet: temperature increases.
  * recombination of atomic O into O<sub>2</sub>

* No much change of OH mass fraction. So, OH plays an important role in flame enhancement.

* Moderate amplitude of variations at outlet.

* unsteady part not considered for zone C

## Validation & Parametric study

<figure><img src="image_11.png" /></figure>

Flame thickness and maximum HRR captured.
Max. non-assisted to plasma-assisted HRR ratio:
→ 1.64 (LES) and 1.59 (ROM).

<figure><img src="image_12.png" /></figure>

No effects at low strain rate ε values.
From ε ≥ 350 s<sup>-1</sup>, more pronounced as ε increases.
Similar trend for the model sensitivity to dilution β.

## Conclusions

Flame stabilization by NRPD in a recirculation zone.

* Decomposition into three zones of the flow dynamics around the near-electrode regions:

(A) a **plasma** region, modeled by PSR;

(B) a **recirculation** region, modeled by PFR;

(C) a **flame front** region, modeled by PMX-CF.

* Increase of HRR in LES captured by ROM.
  → Validation of the low-order approach.

* Pronounced effects and high sensitivity to dilution at high strain rate values.

* Possibility to use non-assisted cold flow RANS or LES to compute model parameters.

## Acknowledgment & References

This research was supported by the ERC under EU's H2020 program (GREENBLUE project, grant #101021538).

[1] A. Starikovskiy and N. Aleksandrov, **PECS 39** (2013)

[2] Y. Bechane and B. Fiorina, **PROCI 39** (2023)

[3] M. Castela et al., **CNF 166** (2016)

[4] S.Q.E. Wang et al., **AECS 15** (2023)

[5] V.P. Blanchard et al., **CNF 270** (2024)

[6] N. Darabiha, **CST 86** (1992)

[7] T. Lu and C.K. Law, **CNF 154** (2008)

[8] S.Q.E. Wang et al., in: **MCS13** (2025)