Deriving Cool Flame Propagation Speeds by Means of an
Ozone-Seeded, Stagnation Plate Burner Configuration

Thomas Panaget<sup>a,b,e</sup>, Pierre Bragança<sup>c</sup>, Bertrand Lecordier<sup>d</sup>, Amaury Lahccen<sup>e</sup>,
Christophe Cuvier<sup>c</sup>, Sébastien Batut<sup>e</sup>, Yann Fenard<sup>e</sup>, Guillaume Vanhove<sup>e</sup> and
Laure Pillier<sup>e,*</sup>

<sup>a</sup> Univ. Lille, Inserm, CHU Lille, Institut Pasteur Lille, U1167 - RID-AGE - Facteurs de risque et déterminants moléculaires des maladies liées au vieillissement, F-59000 Lille, France

<sup>b</sup>Junia, Health and Environment, Laboratory of Sustainable Chemistry and Health, F-59000 Lille, France

<sup>c</sup>Univ. Lille, CNRS, ONERA, Arts et Métiers Institute of Technology, Centrale Lille, UMR 9014 - LMFL - Laboratoire de Mécanique des Fluides de Lille - Kampé de Fériet, F-59000 Lille, France

<sup>d</sup>Normandie Univ., UNIROUEN, INSA Rouen, CNRS, CORIA, 76000 Rouen, France

<sup>e</sup>Univ. Lille, CNRS, UMR 8522 - PC2A - Physicochimie des Processus de Combustion et de l'Atmosphère, F-59000 Lille, France

Full length article

Abstract

This study aims to investigate the feasibility of experimental determination of DME/O₂/O₃ cool flame propagation speeds using Particle Image Velocimetry (PIV) in a stagnation plate burner operated at atmospheric pressure. A specific PIV data analysis procedure was developed in order to improve the accuracy of the measurements in this particular configuration. Five flame conditions, with equivalence ratio varying from 0.3 to 0.5 and ozone mole fraction varying from 1.5 to 2% were investigated to compare experimental results with kinetic modeling. Three ozone-submechanisms, respectively from Jian et al. (Jian et al., 2022), Halter et al. (Halter et al., 2011) and Zhao et al. (Zhao et al., 2016), were coupled with our previously developed DME mechanism (Panaget et al., 2021) and used to compare experimental and simulated axial velocity profiles. Results show that a thoughtful choice of the ozone-submechanism is of particular importance in predicting an accurate cool flame velocity in these conditions. A numerically assisted non-linear extrapolation method is proposed for the determination of the unstrained cool flame speed S<sub>u,0</sub>. Additionally, simulations for which the plate temperature reaches the maximal flame temperature (adiabatic conditions) were performed, demonstrating a negligible effect of the plate temperature on the determined S<sub>u,0</sub>. A kinetic analysis is also presented to highlight the most sensitive chemical reactions influencing the reference cool flame speed S<sub>u,ref</sub>, showing the preponderant role of the fuel low temperature chemistry.

Keywords: Cool flame, Propagation speed, Low temperature combustion, Particle Image Velocimetry, Ozone assisted combustion

*Corresponding author: laure.pillier@univ-lille.fr
# 1. INTRODUCTION

From their discovery two centuries ago [1] to their recent observation under micro-gravity conditions [2], cool flames raised a number of issues throughout the years [3,4]. They are known to play a critical role in advanced combustion technologies [5] as they control both autoignition and assisted-ignition processes in the low-temperature combustion regime. Flame propagation speeds are fundamental parameters in combustion due to their influence on the rate of heat release within the reaction zone of flames. Cool flame speeds were numerically investigated by Ju et al. [6,7] and by Zhao et al. [8]. Using dimethyl ether (DME)/$O_2$ mixtures in both freely-propagating and counter-flow conditions, it was reported that cool flame speeds typically range from 6 to 20 cm.s$^{-1}$, depending on the experimental conditions. Interestingly, they are almost insensitive to the equivalence ratio within their stability range, while their hot flames counterparts are known to be highly dependent on this parameter. Numerical investigations of the effect of ozone on the cool flame speed have shown that it increases as the ozone concentration increases, as in the case of hot flames [9,10].

To the best of our knowledge, experimental cool flame propagation speeds were only reported under microgravity conditions [11] or at sub-atmospheric pressure by the Belmont group [12–16]. Foster and Pearlman [11] measured the speed of a propane/$O_2$ cool flame at low-pressure and microgravity conditions, using the spherically-propagating flame method. It was however observed that heat was released by pre-ignition of the mixture, prior to the cool flame formation. Thus, the measurement could not be used to determine the propagation speed of the propane cool flame. Recent work from Belmont group at the University of Wyoming [12–16] showed the feasibility of measuring cool flame speeds using a Hencken Burner operated at sub-atmospheric pressure. They reported low pressure data for ozone-seeded cool flames of dimethyl ether, propane and *n*-heptane. This method consists of varying the gas inlet flow rate while keeping the equivalence ratio fixed, and measuring the position of the flame
above the burner by excited formaldehyde chemiluminescence or formaldehyde planar laser induced fluorescence (PLIF). Two distinct regimes are then identified: a/ a first regime where the flame remains anchored to the burner by the heat losses, and where the variation of the inlet flow rate causes only a minimal variation of the flame position; b/ a second regime, where the flame detaches from the burner surface and is considered freely-propagating and nearly adiabatic, the heat transfer being considered negligible. In this case, the flame position varies linearly with the inlet flow rate. The transition between these two regimes was suggested to provide a reasonable estimate of the cool flame speed. This method was validated for hot flames by comparing flame speeds measured by Particle Image Velocimetry (PIV) [16,17] and data from the literature and simulations. The cool flame speeds obtained experimentally by Hajilou et al. were simulated with different kinetic models [13-15] using freely-propagating flame simulations.

Ozone has been widely used in experimental cool flames studies [15,18] as its thermal decomposition releases highly reactive oxygen atoms at temperatures close to 450 K at the atmospheric pressure, facilitating the initiation of low-temperature reactivity [19]. Several ozone specific submechanisms have been developed in the past years, and are commonly coupled with hydrocarbon mechanisms to describe the decomposition of ozone and its impact on combustion [20–22]. Knowing the important influence of ozone on the combustion process, it is important to wisely choose the ozone submechanism when simulating the behaviour of ozone-seeded cool flames.

In this work, we investigated the feasibility of measuring atmospheric pressure lean DME/O₂/O₃ cool flames propagation speeds from the measurements of the axial velocity profiles using PIV in a newly implemented stagnation plate burner [23]. A specific PIV data analysis procedure, developed in order to improve the accuracy of the measurements, is presented. Five different flames conditions have been studied with equivalence ratio varying
from 0.3 to 0.5 and O₃ mole fraction from 1.5 to 2%. Comparison with simulations is performed using three different O₃-submechanisms from the literature [20–22] coupled to a detailed kinetic mechanism recently developed in our group [23] for DME low temperature combustion. The performance of the coupled mechanisms is first assessed in predicting experimental axial velocity profiles in the strained cool flames, then a method to extract the unstrained propagation speed is proposed. Finally, a kinetic analysis is performed to highlight the most sensitive chemical reactions influencing the cool flame speed.

## 2. EXPERIMENTAL AND NUMERICAL METHODS

### 2.1. Experimental setup for PIV measurements

The stagnation plate burner used in the present study has already been extensively described in a previous study [23], and will therefore only briefly be presented in the present work (Figure 1). It consists of a stainless-steel body, with a coaxial converging nozzle of an inner diameter of 10 mm for the DME/O₂/O₃ mixture. This mixture is injected through four orthogonal inlets and flows through a stainless-steel porous disc before entering the convergent section of the burner. This geometry is chosen as it provides a laminar and uniform flow at the burner exit. A N₂ co-flow exits through a 20 mm internal diameter co-axial nozzle also equipped with a stainless-steel porous section to protect the cool flames from external perturbations. The burner body is kept at a constant temperature of 300 K by a temperature-regulated water circulation system, and is operated at atmospheric pressure. A cylindrical heated plate, with a diameter of 65 mm and a thickness of 8 mm, is placed at 13 mm from the burner nozzle, with a strictly parallel geometry, and is heated at 600 ± 0.1 K. Gas flow rates are controlled by Bronkhorst mass flow controllers, whose calibration was performed using DryCal DC-Lite Primary Flow Meters. Part of the O₂ flows through two ozone generators (BMT Messtechnik GMBH) arranged in parallel. The ozone mole fraction is measured at the entrance of the burner
with a Teledyne API 452 ozone analyser, the relative uncertainty on the reported ozone
concentrations being ± 0.02% for every studied condition. The ozone mole fraction at the burner
outlet has been measured both in reactive and non-reactive conditions using an Omnistar GSD
301 O₂ Pfeiffer Vacuum mass spectrometer, showing no ozone reactivity or decomposition
before the burner outlet.

Measurements of the axial velocity profiles between the burner and the plate are
performed using the PIV technique which is based on the diffusion of illuminated particles
seeded in the flow. In our case, part of the oxygen flows through a liquid atomizer, allowing
the seeding of small particles in the flow. Silicon oil, provided by Chem-Lab, is chosen for its
well-defined properties (viscosity, surface tension, etc.) and its high vaporization temperature,
around 600 K. In the studied conditions, the temperature does not exceed 900 K downstream
from the flame, and the temperature in the flame front is around 600 K [23]. The particle
diameter is estimated to be in the range 1 – 5 µm, as usually met for this kind of atomizer [24].
The flame position did not change with the addition of particles, demonstrating that the seeding
by silicon oil droplets does not affect the cool flame speed. The use of silicon oil is therefore
well adapted for such PIV measurements, as will be demonstrated further later in this
manuscript.

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<figure><img src="image_1.png" /><figcaption>**Figure 1.** Schematic diagram of the experimental setup.</figcaption></figure>

Particles are illuminated by a dual cavity Nd:YAG Splitlight Compact laser from Innolas, delivering a 50 mJ pulse at 532 nm, at a frequency of 10 Hz. The laser sheet, centred on the burner, is generated using spherical (f# 550 mm) and cylindrical (f# - 80 mm) lenses. The laser sheet dimensions are ~ 12 mm height x 600 µm thick. The particles displacement between two laser pulses is captured using a LaVision Scmos camera of 2560 by 2160 pixels, equipped with a 105 mm Nikkor lens at an aperture of f#8, the resulting magnification being equal to 20 µm per pixel. The time between two pulses (Δt) was fixed to 220 µs, in order to record a 10-pixel displacement between the pulses at the lowest flow rate. A total of 1000 images were recorded for each condition.

In the vicinity of the flame, the particle concentration is estimated to 0.005 particle per pixel. Such a low concentration is caused by the difficulties of effectively seeding the flow, as the oxygen flow rate had to be split between the ozone generators and the atomizer. For conventional PIV, this very low concentration requires a minimum interrogation window size (IWS) of 32 x 32 pixels (0.64 x 0.64 mm²), which leads in our conditions to an insufficient spatial resolution for accurate measurements. To tackle this difficulty, a more advanced and
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adapted post-processing approach has been specifically developed at the CORIA laboratory,
and is detailed below.

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## 2.2. Particle Image Velocimetry (PIV) images post-processing

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Before applying the PIV image processing, an advanced background correction is
performed from conditioned averaged images, one at t and one at t + Δt. A standard background
correction is not adapted in the case of low-densities due to the difficulty to remove the
individual particle signal on averaged images, even when 1000 images are considered. In our
approach, the conditioned background images are then obtained by averaging all the
instantaneous images but without integrating the signal of particles in the process using a
Kuwahara filter. This specific image processing improves the estimation of background images
in particular in low density regions. Following the background correction, only the particle
signal remains on the corrected images. Then, the spatial calibration is done with a well-defined
target (0.977 x 0.977 mm), and is used to estimate a polynomial camera model of 3rd order used
to dewarp each image, ensuring a perfect alignment of both wall and burner axes within the (x,
y) frame. This step also corrects any image distortion induced by the camera lens. From this
step, PIV processing starts by an extraction of the particles position in the images using a 2D
correlation pattern recognizing technique. Between 1500 and 3500 particles are detected on
each image, depending on the experimental conditions. The vector calculation is then initiated
at the particle location, and not on a regular mesh as it is usually performed when the particles
density is higher. This calculation is based on an iterative continuous window shift technique
[25,26], starting with an interrogation window size (IWS) of 64 x 64, and reaching an IWS of
8 x 8 pixels (0.16 x 0.16 mm²) in the final pass. This results in a series of non-regular velocity
fields which are validated with a rate higher than 85%. The scaling in the real coordinated
system is realized with the burner plate as reference, with an accuracy of ± 20 µm. The final
step consists in computing a mean velocity field on a regular mesh by averaging every

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instantaneous vector in small cells at each mesh node, the cell size being compatible with the
PIV resolution of 8 x 8 pixels. This processing method allows a significant improvement in the
particle detection in the area close to the flame front. A comparison of the axial velocity profiles
determined using a conventional image processing method, i.e., with an IWS of 32 x 32 pixels,
and the present one is presented in Figure S1 of the Supplementary Material.

Axial velocity profiles are finally extracted from the mean velocity field by averaging
on a radial width of ± 1 mm around the centre of the burner. A two-dimensional velocity field
in reactive conditions is shown in Figure 2. It demonstrates that the radial (u_r) distribution of
the velocities is axisymmetric, and that the axial velocity (u_a) profile at the burner exit is almost
uniform over the entire diameter of the burner (10 mm). The flat cool flame front, stabilized
two millimetres under the heated plate, can be distinguished on the axial velocity profile. This
confirms the efficiency of the converging nozzle geometry, and constitutes further justification
of the averaging process over a region of ± 1 mm used in the image post-processing, as the axial
velocity can be considered constant over a significant portion of the burner diameter. From
Root Mean Square (RMS) analysis, the uncertainty on the determination of the axial velocity
with the PIV technique is estimated to be ± 5%. This lead to an uncertainty in the flame speed
determination lying between 0.83 and 1.05 cm.s⁻¹, depending on the value of the reference axial
velocity S_u,ref (minimum velocity upstream of the flame front, as shown in Figure 3), which has
been averaged at ± 1 cm.s⁻¹.
<figure><img src="image_2.png" /><figcaption>**Figure 2.** Radial velocity streamlines (top) and axial velocity profile (bottom) of a DME/O₂/O₃ cool flame at φ = 0.4 and xO₃ = 1.9%. u_r represents the radial velocity, u_a the axial velocity, y the Height Above the Burner (HAB) and x the burner radius.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 3.** Simulated temperature (red) and axial velocity (black) profiles of a cool flame. Determination of the couple (S<sub>u,ref</sub>, K) is also shown.</figcaption></figure>
## 2.3. Flame conditions

Five stable cool flame conditions were selected for the measurement of cool flame speeds, and are summarized in Table 1. Note that the inlet velocity ($u_{in}$) range is limited as it is constrained by the stability domain of the cool flames, which is known to be narrower than for hot flames. Furthermore, at high inlet velocity (and strain rate, usually calculated as the ratio between the flow velocity and the burner/plate distance), the cool flames tend to stabilize closer to the stagnation plate, leading to difficulties in resolving the entire velocity profile. On the contrary, at low inlet velocity, the particle seeding is not sufficient to provide accurate measurement of the velocity field in the burner.

The detailed flames conditions are provided in the Supplementary Material (Table T1).

<table><thead><tr><td>φ</td><td>x<sub>O3</sub>*/%</td><td>u<sub>in</sub> / cm.s<sup>-1</sup></td></tr></thead><tbody><tr><td>0.5</td><td>1.5</td><td>65 – 80</td></tr><tr><td>0.45</td><td>1.7</td><td>75 – 110</td></tr><tr><td>0.4</td><td>1.7</td><td>65 – 85</td></tr><tr><td>0.4</td><td>1.9</td><td>75 – 110</td></tr><tr><td>0.3</td><td>2.0</td><td>65 – 95</td></tr></tbody></table>

*The indicated values correspond to the ozone mole fraction in the DME/O₂/O₃ mixture

<caption>**Table 1.** Experimental conditions for the investigated DME/O₂/O₃ cool flames.</caption>

## 2.4. Flame simulations

The axial velocity profiles for all flames conditions were simulated with multicomponent transport using the Pre-Mixed Burner Stagnation Flame module of Chemkin-Pro 2021 [27]. The size of the simulation domain (see Table T1 in Supplementary Material) was varied depending on the studied conditions, as detailed later. The GRAD and CURV parameters were fixed at 0.03 each, resulting in ~ 450 points per simulation, which is sufficient
to ensure accurate simulations of the reference axial velocity $S_{u,ref}$ within a 1% uncertainty, as demonstrated in the Supplementary Material (Figure S2). The Soret effect option was disabled for the axial velocity profiles simulations as it did not significantly modify the reference axial velocity and allowed a drastic reduction of the computational time. The energy equation was solved for simulation; hence the experimental temperature profile was not used as an input. The experimental and simulated temperature profiles of lean DME/O₂/O₃ cool flames were compared in our previous study [23] and showed an excellent agreement.

A detailed kinetic mechanism recently developed in our group [23] has been used, it is based on the AramcoMech1.3 mechanism [28] with reassessed reaction pathways and modified Arrhenius parameters. It was validated on the prediction of the mole fraction profiles of intermediates species above the burner for DME/O₂/O₃ cool flames. Three different O₃-submechanisms from the literature, respectively from Jian et al. [20], Zhao et al. [21] and Halter et al. [22], were coupled to the aforementioned mechanism [23]. A summary of the different reactions and their associated modified Arrhenius reaction rate coefficients is given in the Table T2 of the Supplementary Material. Note that these three O₃-submechanisms have been very recently [20] compared to experimental data on O₃ decomposition, O₃/O₂ flame speeds and H₂/O₂/O₃ reaction in a flow reactor, showing satisfactory predictions in these experimental conditions.

# 3. RESULTS AND DISCUSSION

## 3.1. Axial velocity profiles

The axial velocity profile measured for the strained cool flame at $\phi = 0.5$, $x_{O3} = 1.5\%$ is pictured for five different inlet velocities $u_{in}$ (and strain rates) as an example of the obtained results in Figure 4. The increase of velocity upstream of the flame front due to thermal expansion is less pronounced than in hot flame cases since the heat release of cool flames is
significantly lower. The entire velocity profile is well defined in each condition supporting the use of silicon oil droplets and the applied PIV image processing. As the inlet velocity (and strain rate) increases, the flame moves towards the stagnation plate and the acceleration observed in the flame front is reduced in accordance with a decrease of the maximum flame temperature.

<figure><img src="image_4.png" /><figcaption>**Figure 4.** Axial velocity profiles as a function of the Height Above the Burner (HAB) of a DME/O₂/O₃ cool flame at φ = 0.5, xO₃ = 1.5%, for five different inlet velocities uᵢₙ.</figcaption></figure>

The measured axial velocity profiles in the strained cool flames were compared with simulations performed with the Pre-Mixed Burner Stagnation Flame module of Chemkin-Pro, following the methodology proposed in [29–31]. It consists in imposing the exact boundary conditions inferred from the PIV experiments, as it is recognized that the experimental flow field in stagnation plate burner configuration is usually neither a plug flow nor a potential flow [32] and that 1D approaches typically fail in providing accurate prediction of the corresponding velocity profile [33]. In this work, the inlet position of the simulation domain was fixed two millimetres before the minimum velocity upstream of the flame front position (defined as S<sub>u,ref</sub>).
Experimental strain rates $K$ and inlet velocities were inferred from the axial velocity profile 281 mm upstream from $S_{u,ref}$, as pictured in Figure 3. The effect of the domain size on the accuracy 282 of the velocity profile, targeting both the reference velocity $S_{u,ref}$ and its position above the 283 burner, was studied and the results are pictured in Figures S3 and S4 of the Supplementary 284 Material. Results showed that the simulated $S_{u,ref}$ were similar within 1% for domain sizes 285 below 8 mm, but that selecting a too small domain size, here less than 3.2 mm, led to a greater 286 deviation. The computational domain length therefore lies between 3.05 and 4.45 mm, 287 depending on the flame conditions. To ensure reproducible determination of the experimental 288 $K$, the experimental axial velocity profile was fitted using a 2^nd^-order polynomial function 289 beforehand. 290

The axial velocity profiles simulated using the three aforementioned ozone-submechanisms [20–22] were compared to the experimental ones. Two flame conditions at $\phi = 0.5$, $x_{O3} = 1.5\%$ and $\phi = 0.3$, $x_{O3} = 2.0\%$ are presented in Figure 5 and Figure 6 respectively. 291 For the sake of brevity, the same comparisons for other flame conditions are presented in 292 Figures S5 to S7 in the Supplementary Material, and the exact boundary conditions used for the 293 simulation are given in the Table T1 of the Supplementary Material. Comparing the three 294 different $O_3$-submechanisms, large variations in the prediction of the velocity profile can be 295 observed between the Halter et al. model and the two other models, with an important 296 underprediction of the minimum velocity $S_{u,ref}$ for the Halter et al. model. It should be noted 297 that in the case $\phi = 0.3$, $x_{O3} = 2\%$ (Figure 6), the Halter et al. model predicts almost no minimum 298 velocity for higher strain rates, but only an inflection of the axial velocity curve upstream of the 299 flame front. The predictions from the Jian et al. and Zhao et al. models are comparable, as both 300 models accurately describe the overall velocity profile. 301

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<figure><img src="image_5.png" /><figcaption>**Figure 5.** Comparison between experimental axial velocity profiles measured by PIV (□) and simulated ones with different $O_3$-submechanisms, respectively from Jian et al., Halter et al. and Zhao et al., for the cool flame at $\phi = 0.5$, $x_{O3} = 1.5\%$, at different strain rates.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 6.** Comparison between experimental axial velocity profiles measured by PIV (□) and simulated ones with different $O_3$-submechanisms, respectively from Jian et al., Halter et al. and Zhao et al., for the cool flame at $\phi = 0.3$, $x_{O3} = 2.0\%$, at different strain rates.</figcaption></figure>

In order to evaluate the capabilities of these models to predict cool flame speeds, the Root-Mean-Square Error (RMSE) between experimental and simulated $S_{u,ref}$ was calculated over the investigated strain rate range, for the five flames conditions.
The RMSE data are summed up in the Table 2, for each O<sub>3</sub>-submechanism. One can see that the Halter et al. submechanism constantly underestimates the value of S<sub>u,ref</sub>, while the two other models yield similar performance.

<table><caption>**Table 2.** Root Mean-Square Error (RMSE) calculated for each flame condition with the different O<sub>3</sub>-submechanisms</caption><thead><tr><th rowspan="2">Condition</th><th colspan="3">Root-Mean-Square Error (RMSE)</th></tr><tr><th>Jian et al.</th><th>Halter et al.</th><th>Zhao et al.</th></tr></thead><tbody><tr><td>φ = 0.3, x<sub>O3</sub> = 2.0%</td><td>0.5</td><td>4.7</td><td>0.5</td></tr><tr><td>φ = 0.4, x<sub>O3</sub> = 1.9%</td><td>1.2</td><td>5.9</td><td>0.7</td></tr><tr><td>φ = 0.4, x<sub>O3</sub> = 1.7%</td><td>0.2</td><td>3.8</td><td>0.3</td></tr><tr><td>φ = 0.45, x<sub>O3</sub> = 1.7%</td><td>0.2</td><td>4.5</td><td>0.4</td></tr><tr><td>φ = 0.5, x<sub>O3</sub> = 1.5%</td><td>0.2</td><td>3.1</td><td>0.2</td></tr></tbody></table>

A possible explanation for the constant underestimation of the flame speed by the model of Halter et al. is the definition of the ozone decomposition within the model, where only N<sub>2</sub>, O<sub>2</sub> and O<sub>3</sub> are declared as collision partners in the O<sub>3</sub> + M ⇌ O<sub>2</sub> + O̅ + M reaction, in contrast with the other two mechanisms (for which all species are considered with a collision efficiency of 1, except if specified). In our experimental conditions, the fuel mole fraction lies between 10 and 15% of the mixture. The absence of DME as a third-body in the ozone decomposition reaction can therefore lead to a lowered reactivity of the Halter et al. model (see Table T2 in the Supplementary Material). This aspect has been tested by replacing the O<sub>3</sub>+M decomposition reactions of the model of Jian et al. by the O<sub>3</sub>+M reactions of Halter et al., showing a deterioration in the prediction of the axial velocity profile, as seen in Figure S8 in the Supplementary Material.

For the following sections, the Jian et al. submechanism will be used solely, because of its more recent rate constants data and its good performance in predicting S<sub>u,ref</sub>.
## 3.2. Determination of the unstrained cool flame speed $S_{u,0}$

A well-established method [34] has been widely used to derive the unstrained flame speed $S_{u,0}$ of hot flames. It consists of measuring the axial velocity profiles for different strain rates (K) and determining the reference velocity ($S_{u,ref}$) as represented in Figure 3. From the plot of $S_{u,ref}$ = f(K), the extrapolation to strain rate K = 0 returns the unstrained laminar flame speed $S_{u,0}$.

Both linear [35] and non-linear [36] extrapolation methods have been used in the past. Vagelopoulos et al. [34] and Chong and Hochgreb [37] have demonstrated that for low-strain rate hot flames (50 - 250 s⁻¹), the linear extrapolation method yields accurate results within a reported uncertainty of ~ 1-2 cm.s⁻¹. In the case of cool flames, for which the speed is significantly smaller, this added uncertainty might however be problematic. The issue of non-linear extrapolation was revisited by Egolfopoulos et al. [38–41] with a computational approach, where the simulated $S_{u,ref}$ at various K (using a counter-flow flame code) and the simulated $S_{u,0}$ at K = 0 (using the freely propagating flame module of the PREMIX code) are fitted using a polynomial function. This computed curve is vertically translated to best fit the experimental data and the experimental flame speeds are derived from this non-linear extrapolation [40]. This method however requires using a kinetic mechanism that yields an accurate value of $S_{u,0}$.

In the present work, a similar approach has been applied but without using the $S_{u,0}$ calculated from a freely-propagating flame module. Axial velocity profiles were simulated using the Pre-Mixed Burner Stagnation Flame module of Chemkin-Pro by progressively decreasing the strain rate, from which a numerical curve $S_{u,ref}$ = f(K) was extracted, as shown in Figure 7. The simulated curve $S_{u,ref}$ = f(K) is then fitted using a 2nd order polynomial and vertically translated to best fit the experimental results [37-40]. The experimental unstrained cool flame speed $S_{u,0}$ is then considered at K = 0. Figure 7 shows the application of this method
for the five DME/O₂/O₃ cool flames conditions. As seen in Figure 7, the numerical and experimental Sₐ,₀ lie very close to each other (those values are given in Table 3 for the five flames studied, columns 2 and 3).

Limitations of this method should however be considered. First, unlike hot flames, the fuel conversion is only partial in a cool flame. Therefore, thermochemical equilibrium is not reached in the post flame region. This causes non-zero temperature and velocity gradients in the downstream area of the flame. Such results can therefore not be considered as laminar burning velocities, nor modelled using a freely propagating flame module. Secondly, since the stagnation plate temperature (600 K) is below the measured flame peak temperatures of about 900 K [23], such flames are not adiabatic. To assess the effect of this non-adiabaticity on the determined unstrained cool flame speeds Sₐ,₀, additional simulations were carried out. The stagnation plate module of Cantera 2.6 [42] was used in the same domain width and input compositions as in the simulations of Figures 5-6, and the stagnation plate temperature was progressively increased until it reached a temperature identical to the maximal flame temperature within a 0.01% tolerance. The strain rate was varied, and the Sₐ,₀ = f(K) results were fitted to a 2nd order polynomial leading to Sₐ,₀ values at K=0 reported in Figure 8 and Table 3 (column 4). Because these cool flames are below 1000 K and sufficiently lifted to neglect heat losses to the exit burner nozzle, they can be considered adiabatic, as for example in the well-known heat flux method [43]. The adiabatic Sₐ,₀ results (Table 3) are identical within the uncertainty of the experiments to the simulated values at a plate temperature of 600 K, demonstrating a negligible effect of the plate temperature on the measured unstrained cool flame velocities.
<figure><img src="image_7.png" /><figcaption>**Figure 7.** Variations of S<sub>u,ref</sub> with K and determination of S<sub>u,0</sub> using a numerically assisted non-linear extrapolation. Flame conditions: φ = 0.5, x<sub>O3</sub> = 1.5% (a), φ = 0.45, x<sub>O3</sub> = 1.7% (b), φ = 0.4, x<sub>O3</sub> = 1.7% (c), φ = 0.4, x<sub>O3</sub> = 1.9% (d) and φ = 0.3, x<sub>O3</sub> = 2.0% (e).</figcaption></figure>

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<figure><img src="image_8.png" /><figcaption>**Figure 8.** Simulated variations of $S_{u,ref}$ with K using a non-linear extrapolation in adiabatic and non-adiabatic conditions. Flames conditions: $\phi = 0.5$, $x_{O3} = 1.5\%$ (a), $\phi = 0.45$, $x_{O3} = 1.7\%$ (b), $\phi = 0.4$, $x_{O3} = 1.7\%$ (c), $\phi = 0.4$, $x_{O3} = 1.9\%$ (d) and $\phi = 0.3$, $x_{O3} = 2.0\%$ (e).</figcaption></figure>

<table><caption>**Table 3.** Experimental and simulated unstrained cool flame speeds $S_{u,0}$ for all the cool flames conditions.</caption><thead><tr><th rowspan="2">Flame conditions</th><th colspan="3">S<sub>u,0</sub> / cm.s<sup>-1</sup></th></tr><tr><th>Experimental</th><th>Simulated</th><th>Simulated Adiabatic</th></tr></thead><tbody><tr><td>φ = 0.5, x<sub>O3</sub> = 1.5%</td><td>14.5 ± 1 cm·s<sup>-1</sup></td><td>14.7</td><td>14.8</td></tr><tr><td>φ = 0.45, x<sub>O3</sub> = 1.7%</td><td>15.8</td><td>16.1</td><td>16.1</td></tr><tr><td>φ = 0.4, x<sub>O3</sub> = 1.7%</td><td>15.4</td><td>15.6</td><td>15.8</td></tr><tr><td>φ = 0.4, x<sub>O3</sub> = 1.9%</td><td>17.3</td><td>16.7</td><td>16.6</td></tr><tr><td>φ = 0.3, x<sub>O3</sub> = 2.0%</td><td>16.8</td><td>16.9</td><td>16.6</td></tr></tbody></table>

By comparing both flames at $x_{O3} = 1.7\%$, one can see that the cool flame speed increases moderately as the equivalence ratio increases from 0.4 to 0.45. This effect is captured by the simulation. A comparison of both flames at $\phi = 0.4$ ($x_{O3} = 1.7\%$ and $1.9\%$) demonstrates the
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important effect of ozone addition on the cool flame speed, which increases by about 2 cm.s⁻¹
(experimentally) when the ozone mole fraction increases only from 1.7% to 1.9%. This effect
is also captured in the simulation, yet underestimated.

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**3.3. Kinetic analysis**

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A brute-force sensitivity analysis was performed on the experimental reference axial velocity $S_{u,ref}$, using the Jian et al. $O_3$-submechanism [20] in conjunction with our previously published DME sub-mechanism [23], with the stagnation flame module of the Cantera 2.6 solver [42]. To do so, the domain size and input conditions were chosen as in the experiments and simulations of Figures 5-6, and the sensitivity coefficients of the reactions on the minimum of axial velocity associated with the cool flame were evaluated from a positive and negative variation of the frequency factor of each reaction by 5%. A positive sensitivity coefficient therefore means that increasing the reaction rate constant for the associated reaction increases the reference cool flame velocity $S_{u,ref}$, and vice versa. The two most extreme conditions were selected for the sensitivity analyses, respectively the flame at $\phi = 0.3$, $x_{O3} = 2.0\%$, which contains the highest ozone mole fraction in this study, and the flame at $\phi = 0.5$, $x_{O3} = 1.5\%$, which contains the lowest. The results are displayed for the 16 reactions with the highest absolute sensitivity coefficients in Figure 9.

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In both conditions, it is observed that the simulated $S_{u,ref}$ is strongly dependent on the branching between the decomposition of the $\dot{Q}OOH$ into two molecules of formaldehyde and an $\dot{O}H$ radical, which tends to decrease the cool flame velocity, and the addition of $\dot{Q}OOH$ to $O_2$, which will lead to indirect chain-branching. Among the other important features is the competition between the $RO\ddot{O} \Leftrightarrow \dot{Q}OOH$ pathway, and the $2RO\ddot{O} \Leftrightarrow 2R\ddot{O} + O_2$ route. The latter is traditionally associated with atmospheric conditions, but was previously observed to be
significant in our conditions [23]. To a more reduced extent, the branching of R radical between
addition to O₂ or direct scission into formaldehyde and a methyl radical is also of importance.
One can however note the large sensitivity coefficient of the H-atom abstraction reaction on
DME by OH. A striking feature of these results is that, in contrast with hot flames burning
velocities, the most sensitive reactions are all directly part of the fuel submechanism, the O₃ +
M ⇔ O₂ + O + M reaction only ranking as the fourth most sensitive reaction. This is a strong
argument in favour of these experimental data as potential targets for the validation of kinetic
models in the low-temperature domain.

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

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Figure 9. Brute-force sensitivity analysis performed on the reference cool flame $S_{u,ref}$, at $\phi = 0.5$, $x_{O3} = 1.5\%$ and at $\phi = 0.3$, $x_{O3} = 2.0\%$.

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## 4. CONCLUSIONS

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The measurement of ozone-seeded dimethyl ether cool flame speeds was successfully realized in a stagnation plate burner for the first time. The PIV technique was used to measure the 2-D velocity profiles, from which axial velocity profiles were inferred to measure the unstrained cool flame speeds. For this purpose, an in-house PIV image processing method has been developed and used in order to improve the accuracy of the measurement. Five flame conditions, with equivalence ratios varying from 0.3 to 0.5 and ozone mole fraction varying from 1.5 to 2% were used to compare experimental results with kinetic modeling. Three ozone-submechanisms, namely from Jian et al., Zhao et al. and Halter et al., were coupled with our previous mechanism validated in DME/O₂/O₃ cool flames and used to compare experimental and simulated axial velocity profiles, emphasizing the importance of the choice of the O₃-submechanism. The Jian et al. submechanism was selected because of its good predictive ability for axial velocity profiles and was used to determine the unstrained cool flame speed Sₐ,₀ for each tested condition. A numerical assisted non-linear extrapolation method is proposed for the determination of Sₐ,₀. Additionally, simulations for which the plate temperature reaches the maximal flame temperature (i.e., adiabatic conditions) were performed, demonstrating a negligible effect of the plate temperature on the unstrained cool flame velocity. However, for the purpose of mechanism validation, the direct comparison with the experimental axial velocity profiles should be preferred as it requires no numerical assisted method. Values of Sₐ,₀ were found to lie between ~14 and 17 cm·s⁻¹ within the range of flame conditions studied here, showing a limited effect of the equivalence ratio variations, and a more striking effect of the ozone concentration. Finally, sensitivity analyses performed on the reference axial velocity Sₐ,ref in two flame conditions emphasize the importance of the fuel low-temperature chain-branching pathways, over the ozone submechanism.
462 Acknowledgements

463 This work is a contribution to the LabEx CaPPA project funded by the French National Agency
464 under contract « ANR-11-LABX-0005-01 », the CPER research project CLIMIBIO funded by
465 the French Ministère de l'Enseignement Supérieur et de la Recherche and the MéOL
466 (Métrologie Optique de Lille) platform. The authors thank the Regional Council « Hauts-de-
467 France » and the « European Regional Development Fund » for their financial support to these
468 projects.

469

470 Supplementary material

471 Supplementary Material can be found in the attached file.

472

473 Authors contributions

474 Conceptualization: **L. Pillier, G. Vanhove**; Data curation: **All authors**; Formal analysis: **T. Panaget, B. Lecordier, Y. Fenard, G. Vanhove, L. Pillier, P. Bragança, C. Cuvier**; Funding acquisition: **L. Pillier, G. Vanhove**; Investigation: **T. Panaget, P. Bragança, L. Pillier, C. Cuvier**; Methodology: **All authors**; Project administration: **L. Pillier, G. Vanhove**; Resources: **L. Pillier, G. Vanhove, B. Lecordier, C. Cuvier**; Software: **T. Panaget, Y. Fenard, G. Vanhove, B. Lecordier, P. Bragança, C. Cuvier**; Supervision: **L. Pillier, G. Vanhove, Y. Fenard**; Validation: **All authors**; Visualization: **All authors**; Roles/Writing - original draft: **T. Panaget, L. Pillier, G. Vanhove**; and Writing - review & editing: **All authors**

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