Thomas Panaget

Pierre Bragança

Bertrand Lecordier

Amaury Lahccen

Christophe Cuvier

Sébastien Batut

Yann Fenard

Guillaume Vanhove

Laure Pillier
email: laure.pillier@univ-lille.fr

Deriving cool

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

est destinée au dépôt

INTRODUCTION

From their discovery two centuries ago [START_REF] Davy | Some new experiments and observations on the combustion of gaseous mixtures, with an account of a method of preserving a continued light in mixtures of inflammable gases and air without flame[END_REF] to their recent observation under micro-gravity conditions [START_REF] Nayagam | Can cool flames support quasi-steady alkane droplet burning?[END_REF], cool flames raised a number of issues throughout the years [START_REF] Ju | Understanding cool flames and warm flames[END_REF][START_REF] Ju | Dynamics of cool flame[END_REF]. They are known to play a critical role in advanced combustion technologies [START_REF] Bhagatwala | Direct numerical simulations of HCCI/SACI with ethanol[END_REF] 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. [START_REF] Ju | Numerical simulations of premixed cool flames of dimethyl ether/oxygen mixtures[END_REF][START_REF] Ju | On the propagation limits and speeds of premixed cool flames at elevated pressures[END_REF] and by Zhao et al. [START_REF] Zhao | Initiation and propagation of laminar premixed cool flames[END_REF]. Using dimethyl ether (DME)/O2 mixtures in both freelypropagating 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 [START_REF] Gao | The effect of ozone addition on laminar flame speed[END_REF][START_REF] Ombrello | Flame propagation enhancement by plasma excitation of oxygen. Part I: Effects of O3[END_REF].

To the best of our knowledge, experimental cool flame propagation speeds were only reported under microgravity conditions [START_REF] Foster | Cool Flame Propagation Speeds[END_REF] or at sub-atmospheric pressure by the Belmont group [START_REF] Brown | Effects of ozone on n-heptane low temperature chemistry and premixed cool flames[END_REF][START_REF] Hajilou | Investigation of the structure and propagation speeds of n-heptane cool flames[END_REF][START_REF] Hajilou | Characterization of ozone-enhanced propane cool flames at subatmospheric pressures[END_REF][START_REF] Hajilou | Experimental and numerical characterization of freely propagating ozone-activated dimethyl ether cool flames[END_REF][START_REF] Belmont | Experimental and numerical investigation of freely propagating flames stabilized on a Hencken Burner[END_REF]. Foster and Pearlman [START_REF] Foster | Cool Flame Propagation Speeds[END_REF] measured the speed of a propane/O2 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 [START_REF] Brown | Effects of ozone on n-heptane low temperature chemistry and premixed cool flames[END_REF][START_REF] Hajilou | Investigation of the structure and propagation speeds of n-heptane cool flames[END_REF][START_REF] Hajilou | Characterization of ozone-enhanced propane cool flames at subatmospheric pressures[END_REF][START_REF] Hajilou | Experimental and numerical characterization of freely propagating ozone-activated dimethyl ether cool flames[END_REF][START_REF] Belmont | Experimental and numerical investigation of freely propagating flames stabilized on a Hencken Burner[END_REF] 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) [START_REF] Belmont | Experimental and numerical investigation of freely propagating flames stabilized on a Hencken Burner[END_REF][START_REF] Ombrello | Burner platform for sub-atmospheric pressure flame studies[END_REF] and data from the literature and simulations. The cool flame speeds obtained experimentally by Hajilou et al. were simulated with different kinetic models [START_REF] Hajilou | Investigation of the structure and propagation speeds of n-heptane cool flames[END_REF][START_REF] Hajilou | Characterization of ozone-enhanced propane cool flames at subatmospheric pressures[END_REF][START_REF] Hajilou | Experimental and numerical characterization of freely propagating ozone-activated dimethyl ether cool flames[END_REF] using freely-propagating flame simulations.

Ozone has been widely used in experimental cool flames studies [START_REF] Hajilou | Experimental and numerical characterization of freely propagating ozone-activated dimethyl ether cool flames[END_REF][START_REF] Reuter | Cool Flames Activated by Ozone Addition[END_REF] 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 [START_REF] Liao | Influence of ozone addition on the lowtemperature oxidation of dimethyl ether in a jet-stirred reactor[END_REF]. 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 [START_REF] Jian | A reaction mechanism for ozone dissociation and reaction with hydrogen at elevated temperature[END_REF][START_REF] Zhao | Kinetic studies of ozone assisted low temperature oxidation of dimethyl ether in a flow reactor using molecular-beam mass spectrometry[END_REF][START_REF] Halter | Experimental and Detailed Kinetic Modeling Study of the Effect of Ozone on the Combustion of Methane[END_REF]. 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 [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF]. 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-submechanims from the literature [START_REF] Jian | A reaction mechanism for ozone dissociation and reaction with hydrogen at elevated temperature[END_REF][START_REF] Zhao | Kinetic studies of ozone assisted low temperature oxidation of dimethyl ether in a flow reactor using molecular-beam mass spectrometry[END_REF][START_REF] Halter | Experimental and Detailed Kinetic Modeling Study of the Effect of Ozone on the Combustion of Methane[END_REF] coupled to a detailed kinetic mechanism recently developed in our group [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF] 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.

EXPERIMENTAL AND NUMERICAL METHODS

Experimental setup for PIV measurements

The stagnation plate burner used in the present study has already been extensively described in a previous study [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF], 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 [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF]. The particle diameter is estimated to be in the range 1 -5 µm, as usually met for this kind of atomizer [START_REF] Kähler | Generation and control of tracer particles for optical flow investigations in air[END_REF].

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. 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 mm 2 ), which leads in our conditions to an insufficient spatial resolution for accurate measurements. To tackle this difficulty, a more advanced and adapted post-processing approach has been specifically developed at the CORIA laboratory, and is detailed below.

Particle Image Velocimetry (PIV) images post-processing

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 3 rd 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 [START_REF] Lecordier | Estimation of the accuracy of PIV treatments for turbulent flow studies by direct numerical simulation of multi-phase flow[END_REF][START_REF] Balusamy | Direct measurement of local instantaneous laminar burning velocity by a new PIV algorithm[END_REF], 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 mm 2 ) 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 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 (ur) distribution of the velocities is axisymmetric, and that the axial velocity (ua) 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 Su,ref (minimum velocity upstream of the flame front, as shown in Figure 3), which has been averaged at ± 1 cm.s -1 .

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 (uin) 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).

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 Su,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 [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF] and showed an excellent agreement.

A detailed kinetic mechanism recently developed in our group [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF] has been used, it is based on the AramcoMech1.3 mechanism [START_REF] Metcalfe | A Hierarchical and Comparative Kinetic Modeling Study of C1 -C2 Hydrocarbon and Oxygenated Fuels[END_REF] 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 O3submechanims from the literature, respectively from Jian et al. [START_REF] Jian | A reaction mechanism for ozone dissociation and reaction with hydrogen at elevated temperature[END_REF], Zhao et al. [START_REF] Zhao | Kinetic studies of ozone assisted low temperature oxidation of dimethyl ether in a flow reactor using molecular-beam mass spectrometry[END_REF] and Halter et al. [START_REF] Halter | Experimental and Detailed Kinetic Modeling Study of the Effect of Ozone on the Combustion of Methane[END_REF], were coupled to the aforementioned mechanism [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF]. 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 [START_REF] Jian | A reaction mechanism for ozone dissociation and reaction with hydrogen at elevated temperature[END_REF] 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.

RESULTS AND DISCUSSION

Axial velocity profiles

The axial velocity profile measured for the strained cool flame at  = 0.5, xO3 = 1.5% is pictured for five different inlet velocities uin (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. 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 [START_REF] Durocher | Measurements of the laminar flame speed of premixed, hydrogen-air-argon stagnation flames[END_REF][START_REF] Munzar | An experimental and reduced modeling study of the laminar flame speed of jet fuel surrogate components[END_REF][START_REF] Bergthorson | Experiments and modelling of premixed laminar stagnation flame hydrodynamics[END_REF]. 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 [START_REF] Sung | Further studies on effects of thermophoresis on seeding particles in LDV measurements of strained flames[END_REF] and that 1D approaches typically fail in providing accurate prediction of the corresponding velocity profile [START_REF] Bouvet | On the simulation of laminar strained flames in stagnation flows: 1D and 2D approaches versus experiments[END_REF]. 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 Su,ref).

HAB / m

Plate

Experimental strain rates K and inlet velocities were inferred from the axial velocity profile 2 mm upstream from Su,ref, as pictured in Figure 3. The effect of the domain size on the accuracy of the velocity profile, targeting both the reference velocity Su,ref and its position above the burner, was studied and the results are pictured in Figures S3 andS4 of the Supplementary Material. Results showed that the simulated Su,ref were similar within 1% for domain sizes below 8 mm, but that selecting a too small domain size, here less than 3.2 mm, led to a greater deviation. The computational domain length therefore lies between 3.05 and 4.45 mm, depending on the flame conditions. To ensure reproducible determination of the experimental K, the experimental axial velocity profile was fitted using a 2 nd -order polynomial function beforehand.

The axial velocity profiles simulated using the three aforementioned ozonesubmechanisms [START_REF] Jian | A reaction mechanism for ozone dissociation and reaction with hydrogen at elevated temperature[END_REF][START_REF] Zhao | Kinetic studies of ozone assisted low temperature oxidation of dimethyl ether in a flow reactor using molecular-beam mass spectrometry[END_REF][START_REF] Halter | Experimental and Detailed Kinetic Modeling Study of the Effect of Ozone on the Combustion of Methane[END_REF] were compared to the experimental ones. Two flame conditions at  = 0.5, xO3 = 1.5% and  = 0.3, xO3 = 2.0% are presented in Figure 5 and Figure 6 respectively. In order to evaluate the capabilities of these models to predict cool flame speeds, the Root-Mean-Square Error (RMSE) between experimental and simulated Su,ref was calculated over the investigated strain rate range, for the five flames conditions. 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 Su,ref .

Determination of the unstrained cool flame speed Su,0

A well-established method [START_REF] Vagelopoulos | Direct experimental determination of laminar flame speeds[END_REF] has been widely used to derive the unstrained flame speed Su,0 of hot flames. It consists of measuring the axial velocity profiles for different strain rates (K) and determining the reference velocity (Su,ref) as represented in Figure 3. From the plot of Su,ref = f(K), the extrapolation to strain rate K = 0 returns the unstrained laminar flame speed Su,0.

Both linear [START_REF] Davis | Determination of and Fuel Structure Effects on Laminar Flame Speeds of C 1 to C 8 Hydrocarbons[END_REF] and non-linear [START_REF] Tien | On the burning velocity of stretched flames[END_REF] extrapolation methods have been used in the past.

Vagelopoulos et al. [START_REF] Vagelopoulos | Direct experimental determination of laminar flame speeds[END_REF] and Chong and Hochgreb [START_REF] Chong | Measurements of laminar flame speeds of acetone/methane/air mixtures[END_REF] 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 nonlinear extrapolation was revisited by Egolfopoulos et al. [START_REF] Veloo | A comparative experimental and computational study of methanol, ethanol, and n-butanol flames[END_REF][START_REF] Ji | Propagation and extinction of premixed C5-C12 n-alkane flames[END_REF][START_REF] Wang | Propagation and extinction of premixed dimethyl-ether/air flames[END_REF][START_REF] Egolfopoulos | Advances and challenges in laminar flame experiments and implications for combustion chemistry[END_REF] with a computational approach, where the simulated Su,ref at various K (using a counter-flow flame code) and the simulated Su,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 [START_REF] Wang | Propagation and extinction of premixed dimethyl-ether/air flames[END_REF]. This method however requires using a kinetic mechanism that yields an accurate value of Su,0.

In the present work, a similar approach has been applied but without using the Su,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 Su,ref = f(K) was extracted, as shown in Figure 7. The simulated curve Su,ref = f(K) is then fitted using a 2 nd order polynomial and vertically translated to best fit the experimental results [START_REF] Chong | Measurements of laminar flame speeds of acetone/methane/air mixtures[END_REF][START_REF] Veloo | A comparative experimental and computational study of methanol, ethanol, and n-butanol flames[END_REF][START_REF] Ji | Propagation and extinction of premixed C5-C12 n-alkane flames[END_REF][START_REF] Wang | Propagation and extinction of premixed dimethyl-ether/air flames[END_REF]. The experimental unstrained cool flame speed Su,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 Su,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 [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF], such flames are not adiabatic. To assess the effect of this non-adiabaticity on the determined unstrained cool flame speeds Su,0, additional simulations were carried out. The stagnation plate module of Cantera 2.6 [START_REF] Goodwin | Cantera: An Object-oriented Software Toolkit for Chemical Kinetics[END_REF] was used in the same domain width and input compositions as in the simulations of Figures 56, 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 Su,ref = f(K) results

were fitted to a 2 nd order polynomial leading to Su,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 [START_REF] Bosschaart | The laminar burning velocity of flames propagating in mixtures of hydrocarbons and air measured with the heat flux method[END_REF]. The adiabatic Su,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.

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.

Kinetic analysis

A brute-force sensitivity analysis was performed on the experimental reference axial velocity Su,ref, using the Jian et al. O3-submechanism [START_REF] Jian | A reaction mechanism for ozone dissociation and reaction with hydrogen at elevated temperature[END_REF] in conjunction with our previously published DME sub-mechanism [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF], with the stagnation flame module of the Cantera 2.6 solver [START_REF] Goodwin | Cantera: An Object-oriented Software Toolkit for Chemical Kinetics[END_REF]. To do so, the domain size and input conditions were chosen as in the experiments and simulations of Figures 56, 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 Su,ref, and vice versa. The two most extreme conditions were selected for the sensitivity analyses, respectively the flame at  = 0.3, xO3 = 2.0%, which contains the highest ozone mole fraction in this study, and the flame at  = 0.5, xO3 = 1.5%, which contains the lowest. The results are displayed for the 16 reactions with the highest absolute sensitivity coefficients in Figure 9.

In both conditions, it is observed that the simulated Su,ref is strongly dependent on the branching between the decomposition of the Q ̇OOH into two molecules of formaldehyde and an O ̇H radical, which tends to decrease the cool flame velocity, and the addition of Q ̇OOH to O2, which will lead to indirect chain-branching. Among the other important features is the competition between the ROO ̇  Q ̇OOH pathway, and the 2 ROO ̇  2 RO ̇ + O2 route. The latter is traditionally associated with atmospheric conditions, but was previously observed to be significant in our conditions [START_REF] Panaget | Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames[END_REF]. 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 O ̇H. 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.

CONCLUSIONS

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

Figure 1 .

 1 Figure 1. Schematic diagram of the experimental setup.

Fuel

Figure 2 .

 2 Figure 2. Radial velocity streamlines (top) and axial velocity profile (bottom) of a DME/O2/O3 cool flame at  = 0.4 and xO3 = 1.9%. ur represents the radial velocity, ua the axial velocity, y the Height Above the Burner (HAB) and x the burner radius.

Figure 3 .

 3 Figure 3. Simulated temperature (red) and axial velocity (black) profiles of a cool flame. Determination of the couple (Su,ref, K) is also shown.

*

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

Figure 4 .

 4 Figure 4. Axial velocity profiles as a function of the Height Above the Burner (HAB) of a DME/O2/O3 cool flame at  = 0.5, xO3 = 1.5%, for five different inlet velocities uin.

For

  Figures S5 to S7 in the Supplementary Material, and the exact boundary conditions used for the

Figure 5 .

 5 Figure 5. Comparison between experimental axial velocity profiles measured by PIV (□) and simulated ones with different O3-submechanisms, respectively from Jian et al., Halter et al. and Zhao et al., for the cool flame at  = 0.5, xO3 = 1.5%, at different strain rates.

Figure 6 .

 6 Figure 6. Comparison between experimental axial velocity profiles measured by PIV (□) and simulated ones with different O3-submechanisms, respectively from Jian et al., Halter et al. and Zhao et al., for the cool flame at  = 0.3, xO3 = 2.0%, at different strain rates.

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 N2, O2 and O3 are declared as collision partners in the O3 + M  O2 + O ̈ + 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 O3+M decomposition reactions of the model of Jian et al. by the O3+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.

Figure 7 .

 7 Figure 7. Variations of Su,ref with K and determination of Su,0 using a numerically assisted non-linear extrapolation. Flame conditions:  = 0.5, xO3 = 1.5% (a),  = 0.45, xO3 = 1.7% (b),  = 0.4, xO3 = 1.7% (c),  = 0.4, xO3 = 1.9% (d) and  = 0.3, xO3 = 2.0% (e).

Figure 8 .

 8 Figure 8. Simulated variations of Su,ref with K using a non-linear extrapolation in adiabatic and nonadiabatic conditions. Flames conditions:  = 0.5, xO3 = 1.5% (a),  = 0.45, xO3 = 1.7% (b),  = 0.4, xO3 = 1.7% (c),  = 0.4, xO3 = 1.9% (d) and  = 0.3, xO3 = 2.0% (e).

Figure 9 .

 9 Figure 9. Brute-force sensitivity analysis performed on the reference cool flame Su,ref, at  = 0.5, xO3 = 1.5% and at  = 0.3, xO3 = 2.0%.

from 1 .

 1 5 to 2% were used to compare experimental results with kinetic modeling. Three ozonesubmechanisms, 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 O3submechanism. The Jian et al. submechanism was selected because of its good predictive abilityfor axial velocity profiles and was used to determine the unstrained cool flame speed Su,0 for each tested condition. A numerical assisted non-linear extrapolation method is proposed for the determination of Su,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 Su,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 Su,ref in two flame conditions emphasize the importance of the fuel low-temperature chain-branching pathways, over the ozone submechanism.

Table 1 .

 1 Experimental conditions for the investigated DME/O2/O3 cool flames.

  The RMSE data are summed up in the Table 2, for each O3-submechanism. One can see that the Halter et al. submechanism constantly underestimates the value of Su,ref, while the two other models yield similar performance.

					PIV measurement
		0.5			sim. Jian et al.		0.5							0.5
					sim. Halter et al.
	-1	0.4			sim. Zhao et al.	-1	0.4						-1	0.4
	Axial velocity / m.s	0.1 0.2 0.3	K = 101 s -1				Axial velocity / m.s	0.1 0.2 0.3	K = 111 s -1				Axial velocity / m.s	0.2 0.3 0.1	K = 119 s -1
		0.008	0.009	0.010 HAB / m 0.011	0.012	0.013	0.008		0.009	0.010 HAB / m 0.011 Root-Mean-Square Error (RMSE) 0.012 0.013 0.008 0.009	0.010 HAB / m 0.011	0.012	0.013
		0.5				0.5 Condition		Jian et al. Halter et al. Zhao et al.
	-1	0.4					-1	0.4
	Axial velocity / m.s	0.1 0.2 0.3	K = 124 s -1			K = 127 s -1  = 0.3, xO3 = 2.0% 0.1 0.2 0.3 Axial velocity / m.s  = 0.4, xO3 = 1.9%	0.5 1.2		4.7 5.9		0.5 0.7
		0.008	0.009	0.010	0.011	0.012  = 0.4, xO3 = 1.7% 0.013 0.008	0.009	0.010 0.2	0.011	0.012 3.8	0.013	0.3
				HAB / m						HAB / m
						 = 0.45, xO3 = 1.7%		0.2		4.5		0.4
						 = 0.5, xO3 = 1.5%		0.2		3.1		0.2
					PIV measurement
		0.7			sim. Jian et al.		0.7							0.7
		0.6			sim. Halter et al. sim. Zhao et al.	0.6							0.6
	Axial velocity / m.s -1	0.2 0.3 0.4 0.5					Axial velocity / m.s -1	0.2 0.3 0.4 0.5						Axial velocity / m.s -1	0.2 0.3 0.4 0.5
		0.1	K = 103 s -1					0.1	K = 114 s -1					0.1	K = 124 s -1
		0.008	0.009	0.010	0.011	0.012	0.013	0.008		0.009	0.010	0.011	0.012	0.013	0.008	0.009	0.010	0.011	0.012	0.013
				HAB / m						HAB / m					HAB / m
		0.7						0.7							0.7
		0.6						0.6							0.6
	Axial velocity / m.s -1	0.2 0.3 0.4 0.5					Axial velocity / m.s -1	0.2 0.3 0.4 0.5						Axial velocity / m.s -1	0.2 0.3 0.4 0.5
		0.1	K = 146 s -1					0.1	K = 165 s -1					0.1	K = 170 s -1
		0.008	0.009	0.010	0.011	0.012	0.013	0.008		0.009	0.010	0.011	0.012	0.013	0.008	0.009	0.010	0.011	0.012	0.013
				HAB / m						HAB / m					HAB / m

Table 2 .

 2 Root Mean-Square Error (RMSE) calculated for each flame condition with the different O3submechanisms

Flame conditions Su,0 / cm.s -1

		Experimental	Simulated	Simulated Adiabatic
	 = 0.5, xO3 = 1.5%	14.5  1 cm•s -1	14.7	14.8
	 = 0.45, xO3 = 1.7%	15.8	16.1	16.1
	 = 0.4, xO3 = 1.7%	15.4	15.6	15.8
	 = 0.4, xO3 = 1.9%	17.3	16.7	16.6
	 = 0.3, xO3 = 2.0%	16.8	16.9	16.6

Table 3 .

 3 Experimental and simulated unstrained cool flame speeds Su,0 for all the cool flames conditions.

	By comparing both flames at xO3 = 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  = 0.4 (xO3 = 1.7% and 1.9%) demonstrates the

  3, x O3 = 2.0%

	H 2 OCH 2 O 2 H + O 2	OCH 2 OCH 2 O 2 H
	CH 3 OCH 3 + H CH 3 O H 2 + H 2 O
	CH 3 OCH 2 O	H 2 OCH 2 O 2 H
	+ O 2 + M O 3 + M
		+ HO	2 H
	HO 2 CH 2 OCHO	CH 2 OCHO + H
	CH 3 O H 2 + O 2 CH 3 OCH 2 O
	HO + O 3	2 O 2 + H
			CH 2 O +	H 2 + HC
			2 HO	H 2 O 2 + O 2
			HO + H	H 2 O + O 2
			2 CH 3 OCH 2 O	2 CH 3 OCH 2 + O 2
			CH 3 O H 2	CH 2 O + H 3
			+ O 2 (+M)	HO (+M)
			CH 2 O + H H 2 O + HC
			H 2 OCH 2 O 2 H 2 CH 2 O + H

Acknowledgements

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

Supplementary material

Supplementary Material can be found in the attached file.

Authors contributions

Conceptualization