Frederic Bechet

Christian Raymond

Achraf Hamane

Rim Abrougui

Gabriel Marzinotto

Géraldine Damnati

Can we predict how challenging Spoken Language Understanding corpora are across sources, languages and domains?

State-of-the art Spoken Language Understanding models of Spoken Dialog Systems achieve remarkable results on benchmark corpora thanks to the winning combination of pretraining on large collection of out-of-domain data with contextual Transformer representations and fine tuning on in-domain data. On average, performances are almost perfect on benchmark datasets such ATIS. However some phenomena can affect greatly these performance, like unseen events or ambiguities. They are the major sources of errors in real-life deployed systems although they are not necessarily equally represented in benchmark corpora. This paper aims to predict and characterize error-prone utterances and to explain what makes a given corpus more or less challenging. After training such a predictor on benchmark corpora from various languages and domains, we confront it to a new corpus collected from a French deployed vocal assistant with different distributional properties. We show that the predictor can highlight challenging utterances and explain the main complexity factors even though this corpus was collected in a completely different setting.

Introduction

In the Transformer era, Spoken Language Understanding models of Spoken Dialog Systems have achieved remarkable results on a wide range of benchmark tasks. State of the art models involve contextual embeddings trained on a very large quantity of out-of-domain text, usually with a Transformer approach, followed by a fine-tune training process on in-domain data to generate the semantic representation required, often made of intent+concept/value labels [START_REF] Louvan | Recent neural methods on slot filling and intent classification for task-oriented dialogue systems: A survey[END_REF].

This winning strategy gives a boost in performance compared to previous models, mostly because of the generalization power of pretrained contextual embeddings. However, if on some SLU benchmark corpora like ATIS, such models have reached almost perfect performance, other corpora remain challenging and performance can be greatly affected by the amount and the quality of data available for training or by the complexity and ambiguity of the semantic annotation scheme.

But how can we characterize how challenging a corpus is? What are the factors that explain why some utterances still resist to Transformer-based models? And can we predict automatically this complexity when dealing with a new corpora in order to partition data into several sets representing different sources and levels of difficulty?

Moreover, it was noticed in [START_REF] Bernier-Colborne | HardEval: Focusing on challenging tokens to assess robustness of NER[END_REF] and [START_REF] Lin | A rigorous study on named entity recognition: Can fine-tuning pretrained model lead to the promised land?[END_REF] that standard benchmark datasets don't contain enough difficult examples that can be found in real-life deployed services, giving a false impression that there are no margin of improvement in current models. Furthermore, the distribution of utterances in benchmark corpora doesn't necessarily reflect real-life usage. Distributions in corpora collected from deployed services are more likely to be imbalanced, with on one hand possibly more easy utterances that researchers may not consider interesting to integrate in benchmark corpora and on the other hand a larger variety of complex phenomena that are under-represented in benchmark corpora.

This paper aims to give some answers to these questions on benchmark SLU corpora as well as a new dataset collected from a deployed voice assistant in order to verify if knowledge extracted on artificial data can generalize to real humanmachine interactions.

Predicting corpus complexity

To predict corpus complexity we follow the approach proposed in [START_REF] Béchet | Is ATIS too shallow to go deeper for benchmarking Spoken Language Understanding models?[END_REF] and [START_REF] Béchet | Benchmarking benchmarks: introducing new automatic indicators for benchmarking Spoken Language Understanding corpora[END_REF] inspired by the NIST Recognizer output voting error reduction [START_REF] Fiscus | A post-processing system to yield reduced word error rates: Recognizer output voting error reduction (rover)[END_REF] method for scoring Automatic Speech Recognition (ASR) performance. In this method, multiple recognizers output are combined by voting on each decision, the most probable one being the output with most votes. This method acknowledges the fact that there is some kind of uncertainty in the output produced by statistically trained models, therefore using multiple decisions can help increasing robustness in the decision process. This phenomenon is particularly true for current deep learning models which involve some randomness in parameter initialization, leading to produced different performance on different runs of the same model.

In [START_REF] Béchet | Is ATIS too shallow to go deeper for benchmarking Spoken Language Understanding models?[END_REF] it was proposed to use a modified version of the ROVER method in order to qualify each utterance of an evaluation corpus for an SLU task of semantic concept recognition seen as a sequence labeling problem. By running multiple SLU models on the same data, we obtain several concept recognition hypotheses at the word level. According to the agreement between hypotheses, a cluster label is given to each word : AC means that all models agree, and the output is correct; AE means 1 Example of annotation of utterance u with two SLU models (m 1 , m 2 ) and the resulting cluster for each word that all models agree, and the output is incorrect; NC means that some models disagree but at least one of them is correct; NE means that some models disagree but none of them is correct. It was hypothesized in [START_REF] Béchet | Benchmarking benchmarks: introducing new automatic indicators for benchmarking Spoken Language Understanding corpora[END_REF] that cluster AC corresponds to the easy samples, NC to the difficult ones, NE to the very difficult ones, and finally AE to the problematic ones, often corresponding to annotation errors.

i word w i label(ref,u,i) label(m 1 ,u,i) label(m 2 ,u,i) cluster 1 find O O O AC 2 flights O O O AC 3 from O O O AC 4 new-york B-from-city B-from-city B-from-city AC 5 new-york O B-from-city B-to-city NE → NCE 6 next B-date-dep B-date-dep O NC → NCE 7 saturday I-date-dep I-date-dep B-date-arr NC → NCE Table
In this study we want to go further than just qualifying a sample as easy or difficult by understanding the reason behind this qualification. Moreover we want to uncover generic principles, that can be applied to any SLU task, independently from the language, the topic or the semantic model related to a given corpus. To this purpose we propose the following method based on a 2-step process: An example of such process is given in table 1 for two SLU concept taggers. Since this utterance contains at least one word labeled NCE, it will belong to the NCE cluster containing the difficult utterances. The second step of the process aims at understanding what makes a sample easy or difficult. AC samples stand for the easy one while labels AE, NC and NE are grouped into a new label NCE for difficult samples.

Second step:

1. Describe each word in the development and test corpora of each SLU corpus with language independent, topic independent and concept independent features (Generic Features -GF), such as syntactic features and features related to the coverage of the training corpus (e.g. how many times this word has been seen with this label in the training corpus?).

2. Train a glass-box classifier such as Adaboost on the union of the L development corpora described by GF features to predict the complexity labels AC and NCE and evaluate its performance on the SLU test corpora also labeled with AC and NCE labels as in step 1.4.

Analyze the classification model obtained by uncovering the rules and their

weights automatically learned on GF features to predict label NCE in order to qualify the major complexity factors on all the SLU corpora considered.

At the end of this 2-step process we obtain a complexity classifier that can process any new SLU corpus, regardless of its language, topic and semantic model, as long as each word is described by GF features, without the need to train and evaluate any SLU system. This classifier labels each word with a complexity label (AC or NCE), a score, and an explanation about this complexity, obtained by analyzing the NCE rules learned and their weights. This kind of explanation is obtained by characterizing each feature type in the GF set. This is presented in the next section.

Analyzing complexity factors

To analyze utterance complexity with respect to an SLU task such as concept tagging, we make the following assumption, following previous work done on Named Entity Recognition [START_REF] Bernier-Colborne | HardEval: Focusing on challenging tokens to assess robustness of NER[END_REF][START_REF] Lin | A rigorous study on named entity recognition: Can fine-tuning pretrained model lead to the promised land?[END_REF]: the two main sources of complexity that can affect an SLU model are ambiguity and lack of coverage of the training corpus.

• ambiguity: an utterance can be ambiguous if a word or a sequence of words can correspond to multiple labels in the semantic model and if either there is not enough context to help removing the ambiguity, or if the underlying structure of the utterance is complex (long utterance, multiple verbs, disfluencies, . . . ); • coverage: this source of complexity comes from a lack of coverage between the training and the evaluation data. The most obvious phenomenon is Out-Of-Vocabulary words, but it can also comes from a new or a rare association between a known word and a label, or a new n-gram of known words.

The features we use in the GF set to describe a word W with label l in a sentence S are either related to ambiguity or coverage. They are defined in table 2.

All the syntactic features are obtained through a parsing process on the train, dev and test partitions of each corpus. In order to be language independent, we use parsers [START_REF] Nasr | Annotation syntaxique automatique de la partie orale du C ÉFC[END_REF] based on the Universal Dependency syntactic model [START_REF] Nivre | Universal dependencies v1: A multilingual treebank collection[END_REF]. Hence syntactic features are shared across languages. Once a corpus is projected into the GF feature set, there is no lexical information and no semantic labels left, therefore corpora on different languages, topics and semantic models can be merged in order to train the complexity classifier for producing the AC or NCE labels.

We use a glass-box classifier called Bonzaiboost1 [START_REF] Laurent | Boosting bonsai trees for efficient features combination : application to speaker role identification[END_REF] based on boosting [START_REF] Schapire | Boostexter: A boosting-based system for text categorization[END_REF] where a set of weak classifiers made of small decision trees on the features of GF Ambiguity # of semantic labels acceptable for W # of Part-Of-Speech (POS) acceptable for W + POS label # of possible syntactic dependency for W + dependency label distance between W and the sentence syntactic root. utterance length (in words) % of words in S belonging to a concept Coverage # of occurrences of W in train # of occurrences of (W, l) in train is bigrams (W -1,W ) and (W,W + 1) occurring in train? are weighted in order to predict the output labels. When processing a sentence, the set of rules matching the input features are selected and the label chosen is the one maximizing the score according to the rules weights. When the NCE label is predicted, we can check in the selected rules which ones have contributed positively to predict the difficult label. Since each rule belongs either to the ambiguity or coverage set, we can estimate the % of weight in the NCE score that belongs to either set, and thus explain if this difficulty comes from an ambiguity issue or lack of coverage in the training data.

The classifier outputs decision at the word level, however they can be projected at the sentence level with this simple rule: the easy utterances are those where all words have been labeled as AC; the difficult utterances are those containing at least one word labeled as NCE. Therefore we can use the complexity classifier output in order to select utterances with a certain level of difficulty, expressed by the NCE score, and belonging either to the ambiguity or coverage category.

Experiments on benchmark corpora

The method presented in the two previous sections has been implemented on 4 SLU benchmark corpora described in table 3 split into train, dev and test partitions: 1. M2M: this corpus is a fusion of two datasets containing dialogues for restaurant and movie ticket booking. It has been released by [START_REF] Shah | Building a conversational agent overnight with dialogue self-play[END_REF] and collected using their M2M framework (Machines Talking To Machines) that combines dialogue selfplay and crowd sourcing to generate dialogues. 2. ATIS: The Air Travel Information System (ATIS) task [START_REF] Dahl | Expanding the scope of the ATIS task: the ATIS-3 corpus[END_REF] is dedicated to provide flight information. 3. MEDIA: this corpus is made of 1250 French dialogue, dedicated to provide tourist information. It has been collected by ELDA, following a Wizard of Oz protocol: 250 speakers have followed 5 hotel reservation scenarios. This corpus has been transcribed manually and annotated with concepts from a rich semantic ontology [START_REF] Bonneau-Maynard | Semantic Annotation of the French Media Dialog Corpus[END_REF]. 4. SNIPS: this corpus has been collected by the SNIPS company. It is dedicated to 7 in-house tasks, SearchCreativeWork, GetWeather, BookRestaurant,PlayMusic, AddToPlaylist,RateBook, SearchScreeningEvent [START_REF] Coucke | Snips voice platform: an embedded spoken language understanding system for private-by-design voice interfaces[END_REF].

pretraining bigru gru self attention BERT M1 M3 M5 random M2 M4 M6
In order to obtain the complexity labels AC and NCE, we developed 6 SLU sequence tagger models (M1. . . M6) in order to predict concept labels at the word level on our 4 corpora. These 6 systems differ either by the pretraining condition (BERT or random initialization) and the DNN architecture (GRU, BIGRU or selfattention) as described in table 4 . These systems follow state-of-the-art architectures for SLU concept tagging [START_REF] Louvan | Recent neural methods on slot filling and intent classification for task-oriented dialogue systems: A survey[END_REF]. If BERT pretraining outperforms by a large margin random initialization, it is interesting to keep this option for detecting easy utterance that does not need any generalization capabilities outside the training data. Table 5 shows F-measure results obtained by all systems on the four corpora.

As we can see models without pretraining (M2, M4 and M6) obtain much worst performance on all corpora except M2M, first indication that this corpus does not need generalization capabilities.

From the automatic labelling with models M1 to M6, we can compute labels AC and NCE at the word and sentence levels as presented in section 2. The repartition between easy (AC) and difficult (NCE) utterances is presented in table 6 Following the method presented in section 3, we trained a Bonzaiboost classifier to predict the complexity labels AC and NCE on the union of the 4 development corpora. The results are presented in table 8. As we can see, if the classification results vary according to the corpus considered, we obtain an F-mesure over 93% for label AC and almost 60% on label NCE. These are encouraging results considering that no lexical nor semantic labels are used as features to predict utterance complexity and that we mix in the training and test conditions very different SLU corpora on different languages, topics and semantic models.

Table 9 shows the analysis of the NCE decisions in terms of the respective weights of the ambiguity and coverage features as described in section 3. As we can see it is interesting to notice that, depending on the corpus considered, the complexity can come mostly because of coverage issues (ATIS and M2M), ambiguity issues (MEDIA) or a mixt of both (SNIPS). The distribution obtained on partitions obtained with predicted labels, rather than reference ones are very similar. This is also encouraging showing that even if the complexity classifier makes errors (60% Fmeasure), it can still be used to accurately partition a corpus according to criteria linked to the utterance complexity and the sources of this complexity.

Application to deployed SLU system data

In addition to the previous experiments on benchmark corpora obtained either through a Wizard-Of-Oz paradigm (ATIS, MEDIA), or through an automatic process with human supervision (SNIPS, M2M), we decided to test the genericity of our approach on a corpus collected through a deployed service by Orange in France.

Orange, the French telco company, has experimented towards the general public the Djingo vocal domestic assistant with a set of skills centred on interactions with corporate services (Orange TV, music with its partner Deezer, Orange Radio, telephony), general services (weather, shopping, calendar, news) and general interaction with the speaker (small talks, global commands). According to the customer agreement, and in respect of the French GDPR law, log data have been anonymously collected and annotated in terms of intents and concept slots. The annotated corpus is built on a weekly basis, and corresponds to a random sub sampling of a whole week logs. The sub-sampling strategy is guided by the annotation capacity for a given week (the average amount of annotations produced by annotators, denoted N a ) and is motivated by the objective of preserving the original distribution of utterances in the test set. Note that the annotations are not produced by crowd sourcing but by expert annotators. Let L be the set of logs gathered during a week, L can be divided into L s , the subset of already seen utterances, present in the annotation database and L u =L s , the subset of unseen utterances that constitute the pool of candidates for annotation. In a first step, L u is randomly down-sampled to N a samples, and the corresponding random sampling probability is applied to L s in order to derive a down-sampled subset from already annotated samples. The corpus also contains out of domain utterances that are labelled as "NoIntent". The data distribution strategy and the presence of out of domain utterances constitute the most significant differences between this data-set and public benchmark datasets.

Semantic annotations are directly performed on ASR transcriptions and annotated automatic transcriptions are used both for training and testing the NLU model.

For these experiments, the test set is composed of 9984 utterances randomly sub-sampled from a full week of logs. The training corpus is composed of a set of anterior utterances, respecting the usage distribution except that the number of duplicate occurrences for a given utterance is notched to a maximum value of 50 in order to avoid over representation of some very common commands. Overall, the training corpus contains 279375 utterances (with 52132 different utterances). The model ontology is composed of 233 intents and 42 concepts. As can be seen in table 3, the characteristics of the Djingo corpus are different from benchmark corpora from several perspectives.

The distribution of utterances reflects the usage and we observe for instance a larger proportion of utterances that are observed in the training corpus, but also a set of out-of-domain utterances and a significant amount of utterances without any concepts.

The SLU model used for this study is a Camembert Transformer [START_REF] Martin | CamemBERT: a tasty French language model[END_REF] fine-tuned on the task of jointly predicting the concept slots with a BIO encoding and the sample's intent, with the intent label set on the [CLS] first token, as in the example below.

[CLS] put france info Set Radio Channel O B-channel I-channel

In early experiments we tested different pretrained models and different output layer configurations. As they had similar performances we settle for the fine-tuned Camembert baseline with a simple linear output layer. The model was trained using Pytorch and hyper parameters were chosen using an internal architecture hyper parameter completion toolbox (batch size of 10, learning rate of 5.0e-05, samples padded to a maximum of 50 word pieces, Adam optimizer and 5 epochs). The evaluation of this SLU model on the Djingo corpus is given in the last column of table 10. We show 3 metrics: token accuracy, F-measure on concepts and sentence accuracy where a sentence is correct only if both the intent and the concept sequence are correct. As can be seen, the performance are in line with those obtained in table 5 We applied our complexity classifier on the Djingo corpus without any retraining or adaptation. We partitioned the corpus into an easy set and a difficult one according to the label predicted by the classifier. As we can see in table 10, 86.5% of the sentences were labeled as AC sentences are 13.5% as NCE. By measuring the SLU performance on these 2 subsets, we can check if the AC/NCE prediction are indeed predicting sentence complexity. Results in 10 show that the predicted labels are meaningful since there is a drop of an absolute 16% between results on partition AC (95.7) compared to the NCE (79.7) partition.

By looking at the distribution of the weights between the ambiguity rules and the coverage ones, we observed that if issues linked to a lack of coverage in the training date represent 71.1% of the weights, nearly 30% come from ambiguity issues, making this corpus more challenging than ATIS or M2M where a very large majority of rules came from a lack in the training data.

In addition to the use of the AC/NCE prediction, we wanted also to check if the confidence scores given by Bonzaiboost on the NCE label predictions, could be use to partition further this corpus into sets of different complexity. To this purpose we tested a very simple approach consisting of fixing a threshold δ , then selecting all sentences containing at least one word labeled NCE with a score above threshold δ .

By varying δ we obtain the curve of figure 1 which plots the F-measure on concept with respect to the coverage of the corresponding partition. This curve clearly indicates that the NCE label scores are meaningfull as they allow to select sentences of various complexity.

Conclusion

We have shown in this study that it was possible to predict sentence complexity without running an SLU system on the data. Just by defining very generic features that could be related either to ambiguity issues, or lack of coverage in the training data, we can process corpora in different languages, topics and semantic models without adaptation. Furthermore the complexity classification model can be analyzed to explain the major complexity factors on the corpus considered, leading to a better characterisation of corpora. Finally, the model was successfully applied on a new corpus collected from a deployed vocal assistant with real-usage distributions, enabling to predict and explain complex utterances.

First step: 1 .

 1 Select a set of L SLU corpora, with concept annotation at the word level (with B,I,O info if multi-word concepts), partitioned into train, development and test. 2. Select a set of N Deep Neural Network (DNN) sequence tagger implementing different DNN architectures and using different kinds of word pretraining. 3. Train the N sequence taggers separately on each train partition of the L corpora, and evaluate the performance on their corresponding development and test sets. 4. Label each word in the development and test corpora with the AC, AE, NC and NE labels according to the agreement and the correctness of the concept label predicted by the N concept sequence taggers;

Fig. 1 F

 1 Fig.1F-measure vs. coverage for different partitions of the eval corpus according to thresholds applied on the predicted difficulty (NCE) score

Table 2

 2 The Generic Feature (GF) set

	corpora	ATIS MEDIA SNIPS Djingo Spk
	#word	8333 25977 6595	34938
	#sent	893	3005	700	9984
	vocabulary	485	1219 1752	2637
	#concept	84	70	39	34
	#intent	-	-	7	109
	%OOD sentences	0	0	0	6.6%
	%sent ∈ train ∩ test	1.9 44.6% 0.9%	76.9%
	%sent+concept	99.3% 86.5% 100%	59.3%
	av. sent length	10.3	7.6 9.16	4.2

Table 3

 3 Corpora characteristics

Table 4

 4 Description of models M1 to M6 in terms of pretraining conditions and DNN architecture

	Model/F-measure ATIS MEDIA SNIPS M2M
	M1	94.6	85.7 95.4 91.5
	M2	93.8	81.7 69.6 91.7
	M3	94.7	85.8 95.2 93.6
	M4	79.0	60.1 69.0 91.0
	M5	94.8	85.3 95.9 93.0
	M6	77.4	59.8 68.9 91.0

Table 5

 5 Concept detection performance (F-measure) for models M1. . . M6 on the 4 benchmark corpora

Table 6

 6 . We can Repartition into easy (AC) and difficult (NCE) samples at the word and sentence levels

	label/%	ATIS MEDIA SNIPS M2M
	AC (word) 89.8% 70.1% 83.1% 96.1%
	NCE (word) 10.2% 29.9% 16.9% 3.9%
	AC (sent) 46.2% 54.3% 35.1% 84.2%
	NCE (sent) 53.8% 45.7% 64.9% 15.8%
	label/Fmes ATIS MEDIA SNIPS M2M
	AC	98.7	98.5 99.7 99.0
	NCE)	91.7	82.3 93.1 68.6

Table 7

 7 Performance of model M1 on AC and NCE sentences see that the amount of difficult tokens and sentences differ greatly from one corpus to another, giving more insights about the complexity of a given corpus than just looking at the average SLU performance. For example, although the M2M corpus seems more challenging that ATIS and SNIPS according to the best model (M1) in table[START_REF] Coucke | Snips voice platform: an embedded spoken language understanding system for private-by-design voice interfaces[END_REF], we can see in table 6 that it contains a lot more of easy tokens and sentences than the other corpora.Table7clearly indicates the relevance of the AC/NCE clustering since performance obtained with a state-of-the-art model such as M1 obtain much worse results on NCE utterances compared to AC utterances.

Table 8

 8 Classification performance on AC/NCE labels with the GF feature set. Training on the union of all corpora.

	ATIS	Precision Recall F-measure
	AC		91.75 98.26	94.89
	NCE	60.61 23.26	33.61
	MEDIA Precision Recall F-measure
	AC		82.55 87.82	85.11
	NCE	63.03 52.80	57.46
	SNIPS Precision Recall F-measure
	AC		92.54 96.04	94.26
	NCE	58.93 42.31	49.25
	M2M Precision Recall F-measure
	AC		98.08 99.89	98.98
	NCE	97.00 65.10	77.91
			All corpora
	all		Precision Recall F-measure
	AC		91.58 95.57	93.53
	NCE	68.42 52.21	59.23
	All		88.83 88.83	88.83
	ATIS	weight(NCE,AMBIG) weight(NCE,COVER)
	reference		13.1%	86.9%
	prediction		19.9%	80.1%
	MEDIA weight(NCE,AMBIG) weight(NCE,COVER)
	reference		84.4%	15.6%
	prediction		84.3%	15.7%
	SNIPS	weight(NCE,AMBIG) weight(NCE,COVER)
	reference		37.2%	62.8%
	prediction		23.5%	76.5%
	M2M	weight(NCE,AMBIG) weight(NCE,COVER)
	reference		4.1%	95.9%
	prediction		2.3%	97.7%
	all	weight(NCE,AMBIG) weight(NCE,COVER)
	reference		65.8%	34.2%
	prediction		68.0%	32.0%

Table 9

 9

% of weight for boosting rules belonging to the ambiguity (AMBIG) category vs. the coverage (COVER) category.

Table 10

 10 Evaluation of easy (AC) and difficult (NCE) partitions of the Djingo corpus thanks to the AC/NCE labels predicted by the complexity classifier

	partition	AC NCE all
	coverage	86.5% 13.5% 100%
	token accuracy	98.6 92.4 97.3
	F1 concepts	95.6 83.8 92.2
	intent+concepts OK 95.7 79.7 93.5
	weight(AMBIG)	-	28.9	-
	weight(COVER)	-	71.1	-

Aix Marseille University, CNRS, LIS UMR 7020 -e-mail: frederic.bechet@lis-lab.f, achraf.hamane@etu.univ-amu.fr

INSA Rennes -IRISA -Rennes -e-mail: christian.raymond@irisa.fr

Orange Labs, Lannion -e-mail: firstname.lastname@orange.com

http://bonzaiboost.gforge.inria.fr/


Thomas Panaget

Nabil Mokrani

Sébastien Batut

Amaury Lahccen

Yann Fenard

Laure Pillier

Guillaume Vanhove
email: guillaume.vanhove@univ-lille.fr

Insight into the Ozone-Assisted Low-Temperature Combustion of Dimethyl Ether by Means of Stabilized Cool Flames

Keywords: Low-temperature combustion, Cool flame, Ozone, Formaldehyde PLIF, Kinetic modeling

The low-temperature combustion kinetics of dimethyl ether (DME) were studied by means of stabilized cool flames in a heated stagnation plate burner configuration, using ozone-seeded premixed flows of DME/O 2 . Direct imaging of CH 2 O* chemiluminescence and Laser Induced Fluorescence of CH 2 O were used to determine flame front positions in a wide range of lean and ultra-lean equivalence ratios and ozone concentrations, for two strain rates. Temperature and species mole fraction profiles along the flame were measured coupling thermocouples, gas chromatography, micro-chromatography and quadrupole mass spectrometry analysis. A new kinetic model was built on the basis of the Aramco 1.3 model, coupled with a validated submechanism of O 3 chemistry, and was updated to improve the agreement with the obtained experimental results and experimental data available in the literature. Main results show the efficiency of the tested model to predict the flame front position and temperature in every tested condition, as well as the importance of reactions typical of atmospheric chemistry in the prediction of cool flame occurrence. The agreement on the fuel and major products is overall good, except for methanol, highlighting some missing kinetic pathways for the DME/O 2 /O 3 system, possibly linked to the direct addition of atomic oxygen on the fuel radical, modifying the products distribution after the cool flame.

Introduction

In the current context -where a growing energy demand meets decreasing fossil fuel stocks and a need to decrease greenhouse gases, nitrogen oxides and soot emissions -alternative energy carriers are seen as a sustainable solution for combustion applications. These last years, oxygenated biofuels and e-fuels have attracted attention because of their ability to reduce pollutant emissions on the full well-to-wheel cycle [START_REF] Agarwal | Biofuels (Alcohols and Biodiesel) Applications as Fuels for Internal Combustion Engines[END_REF] . Especially Poly(oxymethylene) dimethyl ethers (POMDMEs), also called Oxymethylene ethers (OMEs), with the general structure CH 3 -O-(CH 2 -O) n -CH 3 , have the potential to reduce soot production during combustion processes due to their high oxygen content and the absence of C-C bond [START_REF] Iannuzzi | Combustion Behavior and Soot Formation/Oxidation of Oxygenated Fuels in a Cylindrical Constant Volume Chamber[END_REF][START_REF] Iannuzzi | POMDME-Diesel Blends: Evaluation of Performance and Exhaust Emissions in a Single Cylinder Heavy-Duty Diesel Engine[END_REF] in the fuel structure. Their production also presents great interest in reducing global carbon footprint: The smallest OME, OME 0 or dimethyl ether (DME), can be directly produced from recycled CO 2 [START_REF] Olah | Chemical Recycling of Carbon Dioxide to Methanol and Dimethyl Ether: From Greenhouse Gas to Renewable, Environmentally Carbon Neutral Fuels and Synthetic Hydrocarbons[END_REF][START_REF] Centi | Catalysis for CO 2 Conversion: A Key Technology for Rapid Introduction of Renewable Energy in the Value Chain of Chemical Industries[END_REF] . Larger OMEs can also be produced from methanol and formaldehyde [START_REF] Burger | Poly(Oxymethylene) Dimethyl Ethers as Components of Tailored Diesel Fuel: Properties, Synthesis and Purification Concepts[END_REF] with a competitive price compared to conventional diesel fuel production [START_REF] Schmitz | From Methanol to the Oxygenated Diesel Fuel Poly(Oxymethylene) Dimethyl Ether: An Assessment of the Production Costs[END_REF] , reinforcing their position as diesel fuel alternative.

In parallel, recent research has been focused on new combustion concepts to reconcile high thermal efficiency and low pollutant emissions. Technologies such as HCCI (Homogeneous Charge Compression Ignition) [START_REF] Musculus | Conceptual Models for Partially Premixed Low-Temperature Diesel Combustion[END_REF] or SACI (Spark Assisted Compression Ignition) [START_REF] Zhou | Effects of Applying EGR with Split Injection Strategy on Combustion Performance and Knock Resistance in a Spark Assisted Compression Ignition (SACI) Engine[END_REF] could help reach these goals inside internal combustion engines. These concepts depend strongly on Low Temperature Combustion (LTC) kinetics [START_REF] Battin-Leclerc | Detailed Chemical Kinetic Models for the Low-Temperature Combustion of Hydrocarbons with Application to Gasoline and Diesel Fuel Surrogates[END_REF] , governing the auto-ignition of the fuel. They result in a phenomenon, called cool flame, which is generally studied in Jet-Stirred Reactors (JSR) [START_REF] Herbinet | Experimental and Modeling Investigation of the Low-Temperature Oxidation of n-Heptane[END_REF] or Rapid Compression Machines (RCM) [START_REF] Vanhove | Experimental Study of Tetrahydrofuran Oxidation and Ignition in Low-Temperature Conditions[END_REF] . However, quantification of the heat release is typically difficult using such devices, as JSR operate in highly-diluted and isothermal conditions, and RCM use creviced pistons to mitigate fluid motion after compression, allowing part of the mixture to transfer to the crevice during the first-stage ignition, and therefore reducing the relevant pressure increase. Facilities in which the study of the low temperature combustion of fuels can be operated in permanent, non-diluted regime, such as burner-stabilized cool flames, are therefore useful to quantify the heat release of cool flames, which is in turn correlated to second-stage ignition in RCMs [START_REF] Song | A Kinetic Investigation on the Synergistic Low-Temperature Reactivity, Antagonistic RON Blending of High-Octane Fuels: Diisobutylene and Cyclopentane[END_REF][START_REF] Cheng | Autoignition and Preliminary Heat Release of Gasoline Surrogates and Their Blends with Ethanol at Engine-Relevant Conditions: Experiments and Comprehensive Kinetic Modeling[END_REF] .

First observations of cool flames were achieved two centuries ago [START_REF] Humphry | 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] by igniting gaseous diethyl ether over a heated platinum wire. Few studies on stabilized double flames of n-butane were realized some decades ago [START_REF] Minetti | On the Reactivity of Hydroperoxy Radicals and Hydrogen Peroxide in a Two-Stage Butane-Air Flame[END_REF][START_REF] Carlier | Autoignition of Butane: A Burner and a Rapid Compression Machine Study[END_REF] , but this research field gained a renewed interest in the context of plasma-assisted ignition [START_REF] Ombrello | Flame Propagation Enhancement by Plasma Excitation of Oxygen. Part I: Effects of O 3[END_REF] and ozone-assisted ignition [START_REF] Reuter | Cool Flames Activated by Ozone Addition[END_REF] . To this day, studies have been performed to stabilize cool flames in different configurations and for different fuels, however we will mainly focus here on studies using dimethyl ether as the fuel. Lee et al. [START_REF] Lee | DME/Oxygen Wall-Stabilized Premixed Cool Flame[END_REF] [START_REF] Reuter | Flame Structure and Ignition Limit of Partially Premixed Cool Flames in a Counterflow Burner[END_REF] in a counterflow burner working at atmospheric pressure, with an ozone concentration in the oxidizer ranging from 2.9 to 3.7%. Their studies were mainly based on the comparison of hot and cool flames extinction strain rates in a wide range of conditions. Hajilou et al. studied premixed DME/O 2 /O 3 cool flames in a Hencken burner working at low pressure [START_REF] Hajilou | Experimental and Numerical Characterization of Freely Propagating Ozone-Activated Dimethyl Ether Cool Flames[END_REF] , with an ozone concentration in the oxidizer of 6.1%, reporting for the first time an estimation of the propagation speed of the cool flame. Zhao et al. succeeded at stabilizing a cool flame of DME/O 2 without O 3 addition, working in a counterflow burner, but in a rich mixture configuration of  = 1.5 [START_REF] Zhao | Initiation and Propagation of Laminar Premixed Cool Flames[END_REF] . Planar Laser Induced Fluorescence of formaldehyde [START_REF] Klein-Douwel | Laser-Induced Fluorescence of Formaldehyde Hot Bands in Flames[END_REF] (CH 2 O-PLIF) proved to be an efficient tool in characterizing such flames, allowing a clear distinction between cool and hot flames. These studies highlighted the impact of ozone in promoting the low temperature combustion of the fuel in ultra-lean conditions, as also observed at lower concentrations in Jet-Stirred Reactor [START_REF] Liao | Influence of Ozone Addition on the Low-Temperature Oxidation of Dimethyl Ether in a Jet-Stirred Reactor[END_REF] and Flow Reactor [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] or Rapid Compression Machine 29 configurations, confirming its potential for the control or enhancement of combustion in ultralean conditions. The aim of this study is to present a newly developed burner dedicated to the investigation of such flames, resulting from the low temperature oxidation of the fuel. Cool flames were stabilized by ozone-seeding a DME/O 2 flow under a heated plate. This setup allowed the stabilization of lean and ultra-lean cool flames, with equivalence ratios ranging from 0.2 to 0.5, and with ozone mole fractions in the mixture varying from 1.2% to 2.4%. CH 2 O*-Chemiluminescence and CH 2 O-PLIF permitted the measurement of flame front positions in a wide range of experimental conditions. Temperature and major stable species profiles were established for two different conditions, i.e. at equivalence ratio of 0.3 and 0.5. These experimental results were used as validation target for a kinetic model developed on the basis of the Aramco 1.3 [START_REF] Metcalfe | A Hierarchical and Comparative Kinetic Modeling Study of C 1 -C 2 Hydrocarbon and Oxygenated Fuels[END_REF] kinetic model, which was further updated to include pathways missing from the original model.

Experimental method

The burner developed and used for this study is presented in Figure 1. It consists of a stainlesssteel body, with a coaxial nozzle of an inner diameter of 10 mm for the DME/O 2 /O 3 mixture. The mixture was injected through 4 orthogonal inlets and flows through a steel porous disc, shown as a yellow disc in Figure 1, before entering the convergent section of the burner. This geometry was established following the work of Rolon et al. [START_REF] Rolon | Etude theorique et expérimentale de la flamme de diffusion à contre-courant[END_REF] , ensuring laminar and uniform flow at the burner exit. A neat N 2 co-flow was injected via the co-axial nozzle, also equipped with a stainless steel porous section with a 20 mm internal diameter, to isolate the flame from external perturbations. The burner body was kept at 300 K by cool water circulation. Experiments were operated at atmospheric pressure. A cylindrical heated plate, with a diameter of 65 mm and a thickness of 8 mm, was placed at 13 mm above the burner nozzle, with a strictly parallel geometry, and was heated at 600 ± 0.1 K. Gas flow rates were controlled by Bronkhorst mass flow controllers. The oxygen flow was directed to a BMT 803N ozone generator, the ozone mole fraction in the oxygen flow being measured at the entrance of the burner with a Teledyne API 452 ozone analyzer. The relative uncertainty on the ozone measurement is ± 0.02% on the reported values.

As cool flames are characterized by very low light emission, mostly due to the chemiluminescence of excited formaldehyde CH 2 O*, they require adaptation to be observed with the naked eye and therefore the cool flame emission was recorded using an ICCD Princeton PIMAX3 camera. A bandpass filter (396-450 nm) was used to suppress stray light from other species. The obtained images were further treated with three-point Abel inversion [START_REF] Cormack | Representation of a Function by Its Line Integrals, with Some Radiological Applications[END_REF] to extract axial CH 2 O* profiles and determine cool flame positions, defined as the position above the burner at which the emission of CH 2 O* is maximal.

CH 2 O-PLIF was used to measure the 2D spatial distribution of ground-level formaldehyde above the burner, and permitted the measurement of the flame front position through another technique. Formaldehyde excitation was performed at 355 nm using the third harmonic of a Qswitched Quantel Brilliant B Nd:YAG laser. The laser beam was converted into a laser sheet of ~ 300 µm thickness and ~ 12.2 mm height. The laser pulse duration was 15 ns at a 20 Hz repetition rate. In this configuration, the laser delivered a 50 mJ/pulse energy intensity. The vertical energy distribution was measured by collecting the Raman signal from a quartz cell filled with ultrapure water, and was used to correct the PLIF signal after acquisition. Semi-automated treatment of the PLIF images was used to infer cool flame positions, which were then defined in the experiments and simulations as the position of the maximum of the derivative of the CH 2 O signal. The signal was averaged on 40 pixels centered on the burner axis. Details on the comparison between these two techniques (CH 2 O*-chemiluminescence and CH 2 O-PLIF) will be discussed later. The uncertainty on the cool flame position with the PLIF method was estimated to ± 150 µm, while the uncertainty on the same measurement with the chemiluminescence method can be roughly estimated to ± 250 µm.

Temperature profiles inside the flame were measured with a 250 µm diameter type K thermocouple. Measurements were performed from the side, the tip of the thermocouple lying along the axis of the burner. Repeatability and the absence of catalytic effects due to the presence of the thermocouple were ensured by performing two runs, one starting the measurement from the burner towards the plate and one in the opposite direction, yielding nearly identical temperature profiles, as demonstrated in the Supplementary Material. The global uncertainty on the flame temperature was estimated to ± 25 K, corresponding to the maximum observed deviation between the two runs described above. The uncertainty on the measurement position was considered equal to the thermocouple radius, ± 125 µm, as the position of the thermocouple was periodically verified using a scope. Radiative heat losses were neglected in this study since the experimental and simulated maximal cool flame temperatures typically do not exceed 900 K, which is below the frequently accepted limit of 1000 K for such an assumption [START_REF] Lamoureux | Experimental and Numerical Study of the Role of NCN in Prompt-NO Formation in Low-Pressure CH 4 -O 2 -N 2 and C 2 H 2 -O 2 -N 2 Flames[END_REF] . Since perturbation of the flame front can be expected from such an intrusive measurement, temperature profiles were performed with different thermocouples with diameters ranging from 250 µm to 1 mm. It was observed that while the temperature gradient was strongly affected at the largest thermocouple diameters, the maximum temperature downstream from the flame front was identical (within the experimental uncertainty) whatever the thermocouple diameter, as demonstrated in the Figure S1 in the Supplementary Material. The primary objective of these measurements was the determination of the maximum temperatures after the flame front, and the reported post-flame temperatures can therefore be trusted as not being affected by the intrusion of the thermocouple into the gases.

Major species mole fraction profiles were established with a conjunction of micro-Gas Chromatography (µGC), Gas Chromatography (GC) and Quadrupole Mass Spectrometry (QMS) techniques. Sampling was operated using a 250 µm external diameter, 150 µm internal diameter capillary. The ozone mole fractions were measured with an Omnistar GSD 301 O2 Pfeiffer Vacuum mass spectrometer, using a quadrupole mass analyser. Calibration was performed using O 2 /O 3 mixtures using the same sampling procedure and on the same day as the flame experiments. The measurement of DME, CH 2 O, CO 2 , CH 3 OH and CH 3 OCHO mole fractions was performed using an Agilent 490 µGC, equipped with a HP-PLOT U PT column and a TCD detector. The signal from DME was calibrated using DME/O 2 mixtures directly sampled at the burner exit. This method was initially validated by comparing the calibration factor obtained using this method with the one obtained from in-house prepared mixtures of DME. CO 2 , CH 3 OH, CH 2 O and CH 3 OCHO signals were calibrated using in-house prepared gas mixtures. Finally, CO mole fractions were measured with an Agilent 6890 GC, the permanent gases being separated on a CP-Molsieve 5A column and analyzed via TCD, and calibration being performed using a standard mixture. The relative uncertainty on species mole fraction measurements was estimated to ± 5% for DME, CO 2 and CH 3 OCHO, ± 10% for O 3 , CH 2 O and CH 3 OH, and ± 20% for CO. The carbon balance was evaluated, and yielded maximal deviation of ± 3% in the postflame region.

Computational methods

The Aramco 1.3 mechanism 30 coupled with the ozone submechanism from Foucher et al. [START_REF] Foucher | Influence of Ozone on the Combustion of N-Heptane in a HCCI Engine[END_REF] was used to simulate the experimental results, resulting in a 254 species mechanism, including 1559 elementary reactions. The choice of version 1.3 of AramcoMech was motivated by an initial comparison of the performance of all published versions of this mechanism, demonstrating superior performance of this version in the prediction of cool flame occurrence and stabilization in comparison with later ones. In the light of the remaining discrepancies observed between the experimental and calculated intermediate species mole fractions, the mechanism was further updated. The modified or added reactions to the mechanism are summarized in Table 1. Details about the reasons behind such modifications will be discussed in the section dedicated to the results and discussion. The modified model was then tested against data from the literature to ensure its validity, showing similar to better performance against the validation targets, most notably in the low-temperature range, as demonstrated in the Figures S2,S3 and S4 of the Supplementary Material. Burning velocities were calculated using LOGEsoft [START_REF] Logesoft | [END_REF] , and ignition delay times were calculated using a constant volume adiabatic reactor with Cantera

] c a High pressure limit, b analogy from dimethoxymethane, c full submechanism modified, d calculated at 600K for comparison between the old and revised Arrhenius parameters. Units for A and E a : cm 3 , mole, s, cal•mol -1 . AM1.3 stands for "AramcoMech 1.3", p.w. stands for "present work".

All flames were simulated with multicomponent transport using the impinging jet reactor class from Cantera [START_REF] Goodwin | An Object-Oriented Software Toolkit for Chemical Kinetics[END_REF] . In order to ensure the initiation of a cool flame in the simulations, the heated plate temperature was initially set to 700 K, then progressively reduced in cases where a 'hot' flame condition was predicted, and finally set at the experimental value of 600 K before grid refinement. Cases of hot flames in the simulations were identified by maximal flame temperatures greater than 1000 K. It should be stressed that since one of the purposes of this work is to enable a correct prediction of the heat release during the cool flame event, the measured temperature profiles were not used as input for the simulations, and the energy equation was solved during the computation.

Lefkowitz et al. [START_REF] Lefkowitz | Uncertainty Assessment of Species Measurements in Acetone Counterflow Diffusion Flames[END_REF] compared PLIF and probe measurement of acetone in a diffusion flame, and showed that the effect of the probe on the spatial distribution of the species could not be neglected. Similarly, Lamoureux et al. [START_REF] Lamoureux | In Situ Laser-Induced Fluorescence and Ex Situ Cavity Ring-Down Spectroscopy Applied to NO Measurement in Flames: Microprobe Perturbation and Absolute Quantification[END_REF] conducted measurements of NO by LIF and in-situ probe sampling in a methane premixed flame, and observed a discrepancy in the species profiles between both techniques. The influence of the probe sampling on the species profiles could be important in our case, as ozone is known to be a species that can quickly decompose at temperatures greater than 400 K [START_REF] Liao | Influence of Ozone Addition on the Low-Temperature Oxidation of Dimethyl Ether in a Jet-Stirred Reactor[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] . In order to evaluate the possibility of reactivity inside the sampling capillary, especially in the ozone-rich samples, additional simulations were performed, and will be referred to as 'facility effect' simulations later in this manuscript. For these simulations, a bidimensional temperature map of the flame was acquired using the same thermocouple as described in the experimental section, an example of such a map being presented in the Figure S5 in the Supplementary Material. For selected heights above the burner, the capillary was modeled as a plug-flow reactor (PFR) with an imposed temperature profile corresponding to the radial distribution of temperature inferred from the bidimensional temperature map, and inlet conditions corresponding to those calculated using the impinging jet approach described above. The flow rate inside the PFR was calculated at each height above the burner using the correlation given for a turbulent flow inside the capillary given in Wißdorf et al. [START_REF] Wißdorf | Gas Flow Dynamics in Inlet Capillaries: Evidence for Non Laminar Conditions[END_REF] .

Brute-force sensitivity analyses were performed on the cool flame delay, i.e. the first stage ignition delay, and the sensitivity coefficient on the reaction i, S i , was calculated as follows:

S i = ln ( i + / i -) / ln (2/0.5).  i
+ represents the first stage ignition delay time when the pre-exponential of the reaction i has been multiplied by a factor of two, and  i -represents the first stage ignition delay time when the pre-exponential of the reaction i has been divided by a factor of two. A positive value of S i indicates an inhibiting effect of the reaction on the reactivity at a given temperature, and vice versa.

Results and discussion

Figure 2 summarizes the stability limits of experimental cool flames observed for two strain rates, 40 and 50 s -1 . It is important to note that for the lowest equivalence ratio at each strain rate, the flashback could not be reached because the ozone production range of the generator was exceeded. The reported strain rates are calculated as the ratio between the flow velocity and the burner-plate distance. Formaldehyde is formed inside the flame front, and is present all the way to the heating plate, as expected in a cool flame case, as it is a stable oxidation product in this temperature range. In 'hot' or 'warm' flame cases, formaldehyde would indeed be fully converted in the flame front as a combustion intermediate. On the contrary, excited CH 2 O* is formed in the flame front but quickly transitions to its ground-state, permitting another visualization of the flame front. Figure 3 shows that both techniques evidence a flat and axisymmetric flame front along a significant distance from the burner axis. This allows precise flame front position determination using the procedures described in the experimental section. Figure 4 shows a comparison of the extracted axial profiles as a function of the Height Above Burner (HAB) for both techniques. It demonstrates that the position for the maximum of the CH 2 O* profile is close to the one of the 0 1 maximum derivative of the CH 2 O LIF signal, demonstrating that both techniques will yield similar flame front positions. However, uncertainties associated to the Abel inversion result in a slightly larger uncertainty using the chemiluminescence approach. This uncertainty can be roughly estimated to ± 250 µm, in comparison to the ± 150 µm associated to the PLIF measurement, that depend mostly on the resolution of the ICCD camera. The CH 2 O-PLIF method was therefore used for all the flame positions reported in this study.

Temperature profiles

Since one of the purposes of this study is the quantification of the heat release from the cool flame, temperature profiles were measured and compared to simulated profiles obtained with Aramco 1.3 and the current model, as pictured in Figure 5 for two conditions, at a fixed equivalence ratio of 0.3, strain rates of 40 and 50 s -1 , and a respective ozone mole fraction in the mixture of 1.8 and 2.0%. As mentioned in the computational methods section, the temperature profile was not used as input for the simulations, but calculated by solving the energy equation. The CH 2 O* chemiluminescence axial profile has been plotted in order to visualize the exact position of the flame without the perturbation induced by the thermocouple. Comparisons between simulated and experimental results show a close agreement on the maximal temperature of the cool flame, which does not exceed 900 K in both cases, as well as the height above the burner where this maximum is observed. Downstream the flame front, the decrease of the temperature under the plate is captured within the experimental uncertainty in the simulation. No significant change in the temperature profile can be observed between the Aramco 1.3 model and the current model, except that the temperature rise happens at a slightly lower HAB using the current model, which will be discussed in the next section. The largest discrepancy can be observed at the flame front and upstream, where perturbation of the flame by the thermocouple is evidenced by comparing the experimental temperature profile with the chemiluminescence signal. This results in a steeper temperature gradient in the simulation in comparison with the experiments. This phenomenon can be confirmed by increasing the diameter of the thermocouple, leading to a more and more deformed temperature gradient as the diameter increases, without affecting the maximal temperature of the flame, as shown in Fig. S1.

It is expected that in non-isothermal experiments, such as RCM or shock tube configurations, the increase of the temperature induces a loss of competitivity of the low temperature chain branching against propagation or termination reactions. As a consequence, the reactivity decreases, illustrated by the Negative Temperature Coefficient (NTC). In the current configuration, the same cause results in an interruption of the low-temperature reactivity downstream from the cool flame, where the temperature reaches a maximum between the flame front and the stagnation plate. In this context, it is of interest to note that the maximum measured temperatures for both flames presented here are very close, 877 K for the flame  = 0.3,  = 50 s - 1 and x O3 = 1.8% and 884 K for the flame  = 0.3,  = 50 s -1 and x O3 = 2.0%.

Flame stabilization

The influence of ozone on the flame front position is presented in Figure 6 for two different strain rates, 40 and 50 s -1 , and equivalence ratios varying from 0.2 to 0.5. A flashback limit is also represented, corresponding to the situation where ozone causes a transition towards a 'hot' flame. As the ozone concentration increases, the flame front position decreases in all cases. This behavior is well captured by both models, and the agreement between experimental and simulated flame front positions is overall good, with a maximum discrepancy of about 500 µm at the lowest ozone concentrations. As the equivalence ratio decreases, the required ozone mole fraction for flame stabilization and flashback increases, which is also very well predicted in the simulations. The flame front position is however slightly underestimated by the current model, which could be attributed to the modification of the rate constants for both isomerization reactions of the ROO• and •OOCH 2 OCH 2 O 2 H radicals [START_REF] Konnov | Combustion Chemistry of Methoxymethanol. Part II: Laminar Flames of Methanol+formaldehyde Fuel Mixtures[END_REF] , causing a rise of reactivity in the low temperature range. This modification was however conserved in the mechanism as it results in improved prediction of both first-stage and total IDT in the low-temperature range, as can be seen in the Supplementary Material (Figures S2-S4) for three different sets of data. Possible solutions to the discrepancy between the predictions of the current model and the experimental flame front positions include improvements in the physical model used in the simulations, as well as the identification of sensitive reactions with regards to the burning velocity of the cool flames.

 = 0.2  = 0.3  = 0.4  = 0.
Figure 7 shows the experimental and simulated effect of the ozone mole fraction on the maximal temperature downstream of the cool flame. As the mole fraction of ozone in the mixture is increased, this temperature increases, demonstrating the influence of ozone on the NTC behavior. This observation is well reproduced in the simulations, and agrees with the results from Foucher et al. [START_REF] Foucher | Influence of Ozone on the Combustion of N-Heptane in a HCCI Engine[END_REF] who described a reduction of the NTC intensity, coupled to an increase of the heat release of the cool flame, as the ozone concentration increases. As indicated before, if the O 3 concentration in the mixture was increased above the values presented here, it would result in a flashback, as represented with a dashed line in Figure 7. Finally, one can note that at  = 0.3,  = 40 s -1 , the simulated influence of O 3 on the flame temperature is less pronounced with the current model than with Aramco 1.3, leading to a divergence of 5 K at the highest ozone concentration in the mixture, which stays within the uncertainty limit of the experimental flame temperature measurement. Figure 8 presents the effect of the equivalence ratio on the flame front position at two strain rates, 40 and 50 s -1 , and for a constant ozone mole fraction of 1.9% in the mixture. The flame front tends to get closer to the burner as the equivalence ratio increases for both conditions, indicating an increase in the cool flame propagation speed, as demonstrated numerically by Ju et al. [START_REF] Ju | Numerical Simulations of Premixed Cool Flames of Dimethyl Ether/Oxygen Mixtures[END_REF] and Brown et al. [START_REF] Brown | Experimental Characterization of Ozone-Enhanced n-Decane Cool Flames and Numerical Investigation of Equivalence Ratio Dependence[END_REF] in ultra-lean conditions. This trend, as well as the flame front positions, is also captured in the simulations within the uncertainty limit, except at the lowest equivalence ratio of  = 0.2. As shown in the previous section, the different flame fronts simulated with the current model are located at a lower HAB than with the Aramco 1.3 model, the agreement remaining fair.

Species mole fraction profiles

In order to improve the understanding of the mechanisms governing the occurrence and stabilization of cool flames, the mole fraction profiles of the reactants and major stable species formed in the flame were established using the procedure described previously. The comparison between the experimental and simulated results are presented in Figure 9 and Figure 10, for two selected flames with a strain rate  = 50 s -1 , at a respective equivalence ratio  = 0.3 and  = 0.5, and ozone mole fraction x O3 = 2.0% and x O3 = 1.7%. The corresponding CH 2 O* chemiluminescence profile for each case is also plotted in order to visualize the flame front position. As described in the computational methods section, two different simulation approaches were used, and the results for the simulations with facility effects (simulated with the current model) are also plotted in the figures for the fuel and the O 3 case. One can first note that the mole fraction profiles of the intermediates show a plateau downstream from the flame front, demonstrating that at this position the reactivity is globally halted and the mixture has reached the negative temperature coefficient domain. The experimental mole fraction profiles demonstrate significant reactivity upstream from the flame front, motivating the "facility effect" modeling procedure described in the computational methods section, which simulates the sampling capillary as a PFR with a fixed temperature profile. The modeling results including facility effects demonstrate the conversion of ozone in the pre-flame region with excellent agreement. However, in the upstream region where reactivity is observed (grey points on graphs), agreement on the other species mole fractions cannot be expected because surface deactivation of ozone is probably an important process inside the capillary [START_REF] Ouederni | Ozone Decomposition on Glass and Silica[END_REF] , and is not considered in the "facility effect" simulations. This modeling procedure therefore presents a worst-case scenario, where the reactivity inside the capillary is largely overestimated, as can be witnessed on the overestimated conversion of DME by this procedure in the pre-flame region. Considering the reactivity inside the capillary however allows to demonstrate:

-that the reactivity observed upstream from the flame is due to the presence of ozone-rich mixtures inside the capillary, as reported by Hajilou et al. for dimethyl ether [START_REF] Hajilou | Experimental and Numerical Characterization of Freely Propagating Ozone-Activated Dimethyl Ether Cool Flames[END_REF] and propane [START_REF] Hajilou | Characterization of Ozone-Enhanced Propane Cool Flames at Sub-Atmospheric Pressures[END_REF] ozone-assisted cool flames, -that since both simulation approaches lead to comparable results, i.e. within the experimental uncertainty limits, in the post-flame region, the post-flame mole fractions can be trusted to build useful kinetic analysis. The discussion will thus focus on the post-flame region, i.e. at HAB greater than 11 mm, where ozone has been fully converted in the flame. The fuel, CH 3 OCH 3 , is partially consumed through the flame, resulting in a 30-40% conversion of the fuel into low temperature oxidation products for both flames. Both models slightly over-predict the DME conversion. This partial conversion of the fuel is typical of the cool flame process. Ozone is totally decomposed downstream of the flame front, forming atomic oxygen, O:, and molecular oxygen. The O: atom will then further react with the fuel molecule, giving •OH and radicals, yielding CH 3 O• or CH 3 OCH 2 O• by addition reactions, and therefore enabling the initiation of the reactivity in our conditions. The fuel radical will then undergo several O 2 additions, leading to the formation of products characteristics of its low temperature oxidation.

On the products side, CH 2 O presents a profile showing a decrease of the mole fraction in the post-flame region, which is consistent with the obtained PLIF results, as shown in Figure 11 for the flame at  = 0.5. A deviation exists when comparing the intrusive and non-intrusive method in the pre-flame region, which can be directly related to the perturbation of the flame by the sampling capillary. The important production of formaldehyde is typical of a cool flame, which can be produced from the decomposition of the hydroperoxymethoxymethyl radical, •CH 2 OCH 2 OOH, formed after oxygen addition on the fuel radical and isomerization. The modifications made to the model allowed to improve the performance of the model in the prediction of the CH 2 O profile in both flames. CH 2 O can be produced by the fuel radical betascission and the decomposition of •QOOH. The update of the kinetic parameters of formation of •QOOH [START_REF] Konnov | Combustion Chemistry of Methoxymethanol. Part II: Laminar Flames of Methanol+formaldehyde Fuel Mixtures[END_REF] by internal H-atom migration have the effect of decreasing the reaction rate constant of this reaction for temperatures higher than 700 K in comparison to Aramco 1.3. Moreover, the consumption of methoxymethoxyl radical takes place by C-C and C-H beta-scissions in Aramco 1.3, the first one being favored. However, an experimental and theoretical study of these reactions showed that more than 95% of the consumption of CH 3 OCH 2 O• happens by β-CH bond cleavage [START_REF] Song | Mechanistic and Kinetic Study of the O + CH 3 OCH 2 Reaction and the Unimolecular Decomposition of CH 3 OCH 2 O[END_REF] . Finally, the addition reaction CH 3 OCH 2 • + O: = CH 3 OCH 2 O• was added to the model [START_REF] Song | Mechanistic and Kinetic Study of the O + CH 3 OCH 2 Reaction and the Unimolecular Decomposition of CH 3 OCH 2 O[END_REF] . The formation of the methoxymethoxy radical will compete with fuel radical addition on O 2 , explaining the improvement in the prediction of the mole fraction of CH 2 O by the current model.

Using the work of Song. et al. [START_REF] Song | Mechanistic and Kinetic Study of the O + CH 3 OCH 2 Reaction and the Unimolecular Decomposition of CH 3 OCH 2 O[END_REF] , combined with the utilization of the methyl formate submechanism from Minwegen et al. [START_REF] Minwegen | Experimental and Theoretical Investigations of Methyl Formate Oxidation Including Hot β-Scission[END_REF] led to significant improvement of the prediction of the formation of methyl formate by the current model. This improvement is also observable for the CO 2 profile, where the current model shows better performance in comparison with Aramco 1.3. It can be noted that this high CO/CO 2 ratio is typical of the low temperature combustion of the fuel, as the thermal conversion of CO to CO 2 is not effective given the limited maximal temperature of the flame [START_REF] Vandooren | Rate Constant of the Elementary Reaction of Carbon Monoxide with Hydroxyl Radical[END_REF] . Finally, methanol was also measured as a minor product of the low temperature combustion of dimethyl ether. Both models underestimate the formation of this species by about a factor 3 in both flames, demonstrating the need for further improvement of the submechanism for this species. One can note that the rate constants used in Aramco 1. A brute-force sensitivity analysis on the first stage ignition delay was performed using the current model, and is presented on Figure 12. As one can see, the DME/O 2 /O 3 system is particularly sensitive to the O 3 submechanism, containing the three most sensitive reactions (R1, R2, R3) at 600 K, as its decomposition is crucial in the initiation of combustion in this temperature range. Interestingly, the ROO• isomerization into •QOOH (R9) has a negative effect on the first stage ignition delay at 450 K, but a positive one at 600 K, suggesting that the most important contribution to the reactivity at the lowest temperatures among fuel-specific reactions comes from the 2 CH 3 OCH 2 OO• = 2 CH 3 OCH 2 O• + O 2 reaction (R4) as will be highlighted below. In parallel a reaction pathway analysis was performed for the  = 0.3,  = 50 s -1 , x O3 = 2.0% flame case at 5% and 20% fuel conversion, corresponding respectively to HAB = 10.44 mm and 10.71 mm and temperatures of 412 K and 612 K. The main pathways of DME conversion in these conditions are shown in Figure 13. For a comprehensive reading of the figure, the normalized flux is not indicated for values lower than 0.1%. Observed and quantified species in this study are highlighted by black rectangles.

As explained above, the initiation of the reactivity takes place through H-atom abstraction on the fuel molecule, assisted by the decomposition of O 3 above the burner, and followed by addition to O 2 . At 5% fuel conversion, it is noticed that the most influential reaction of consumption of ROO• is not the H-atom migration as expected from the low temperature combustion of DME 56 , but a reaction typical of atmospheric chemistry: Two ROO representative of atmospheric chemistry, this confirms the recently pointed out link between kinetic studies of low temperature combustion and atmospheric chemistry 57 . A change in the branching ratio is observed when the temperature has increased, at 20% fuel conversion, where the ROO• isomerization into •QOOH becomes more predominant, as commonly observed in LTC studies 56 .

As an overall conclusion on the performance of the modified model, one can observe that it predicts a slightly higher reactivity at low temperature, illustrated by a lower position of the flame in the burner compared to Aramco 1.3, and a lower first stage ignition delay time as shown in the Supplementary Material (Figure S2). However, the changes permitted to better predict the composition of the post-flame area, especially for the methyl formate, which is highly underpredicted by the original model.

+ - + - - - - + + / - • • • / / / + - • • • • • • • • • • • • • -• • • • •

Conclusions

Stabilized ozone-seeded lean cool flames of dimethyl ether/O 2 were studied in a stagnation plate burner. Two strain rates were fixed, 40 and 50 s -1 , the equivalence ratio being varied between 0.2 and 0.5, and the ozone mole fraction being varied between 1.2 and 2.4% in the mixture. CH 2 O-PLIF was used to measure the formaldehyde distribution in the burner, and flame front positions were inferred from the maximum of its derivative in the center of the burner, providing global validation data. Temperature and stables species profiles were measured by coupling thermocouple, gas chromatography, micro-gas chromatography and quadrupole mass spectrometry, thereby allowing detailed validation of kinetic models on the majority of the species formed in such flames. Simulations from the Aramco 1.3 model, coupled to an O 3submechanism, were compared to the experimental data, yielding satisfactory agreement on the global validation targets, and the model was further updated to better reproduce the measured distribution of products in the post-flame region.

Ozone has a strong promoting effect on the low temperature combustion of dimethyl ether, and its mole fraction is directly correlated to the position of the flame in the burner. These results highlight the fact that ozone can not only be considered as a provider of radicals facilitating the initiation of low temperature combustion, but also strongly affects the species distribution. Such initiation of reactivity at very low temperatures strengthens the contribution to radical chainbranching of reactions usually associated to atmospheric chemistry conditions.

The newly developed experimental setup, as well as the associated numerical methods therefore constitute an efficient tool for the kinetic study of cool flames. Table 1. Modifications operated on the Aramco 1.3 (+ O 3 submechanism) model.

TOC Graphic

Figure 1 .

 1 Figure 1. Stagnation plate burner setup used in this study.

Figure 2 .

 2 Figure 2. Stabilization map. Stability limits are represented by continuous lines at 40 s -1 , and dashed lines at 50 s -1 .

Figure 3 .

 3 Figure 3. Raw CH 2 O* chemiluminescence (left) and CH 2 O-PLIF (right).  = 40 s -1 ,  = 0.4, x O3 = 1.6%. The dashed lines represent the burner (bottom) and plate (top) positions, the solid line represents the top of the laser sheet. The color bar on the right indicates the relative intensity of each image, between 0 and 1.

Figure 4 .

 4 Figure 4. Extracted CH 2 O* and CH 2 O-PLIF profiles from Fig. 3,  = 40 s -1 ,  = 0.4, x O3 = 1.6%.

Figure 5 .

 5 Figure 5. Temperature profiles, (a)  = 40 s -1 ,  = 0.3, 1.8% O 3 , (b)  = 50 s -1 ,  = 0.3, 2.0% O 3 .

Figure 6 .

 6 Figure 6. Evolution of the flame front position as a function of the ozone mole fraction.a = 40 s -1 (left), (b)  = 50 s -1 (right).

Figure 7 .

 7 Figure 7. Effect of the ozone mole fraction on the maximal cool flame temperature at  = 0.3 and α = 40 s -1 (black) and 50 s -1 (red). Experiments are represented with symbols, simulations with lines.

Figure 8 .

 8 Figure 8. Effect of the equivalence ratio on the flame front position at fixed strain rates α = 40 s -1 (black) and 50 s -1 (red) and ozone mole fraction x O3 = 1.9%.

Figure 9 .

 9 Figure 9. Experimental and simulated species mole fractions profiles,  = 0.3,  = 50 s -1 , x O3 = 2.0%. Grey points represent the perturbated zone where in-capillary reactivity takes place.

Figure 10 .

 10 Figure 10. Experimental and simulated species mole fractions profiles,  = 0.5,  = 50 s -1 , x O3 = 1.7%. Grey points represent the perturbated zone where in-capillary reactivity takes place.

Figure 11 .

 11 Figure 11. Comparison between CH 2 O profiles obtained by PLIF and µGC,  = 0.5,  = 50 s -1 , x O3 = 1.7%. Grey points represent the perturbated zone where in-capillary reactivity takes place.

  3 for the CH 3 OCH 3 + CH 3 O• reaction, forming CH 3 OCH 2 • and CH 3 OH, are taken by analogy with the CH 3 OH + CH 3 O• reaction 55 , and are unchanged in the current model. This reaction being very sensitive for the production of methanol in our conditions, further investigation of the CH 3 OCH 3 + CH 3 O• reaction is recommended.

Figure 12 .

 12 Figure 12. Brute force sensitivity analysis of the first stage ignition delay, modified model.  = 0.3, x O3 = 2.0%.

Figure 13 .

 13 Figure 13. Reaction pathway analysis in the cool flame with the current model at 5%, T flame = 412 K (bold, red) and 20%, T flame = 612 K (italic, black) fuel conversion,  = 0.3,  = 50 s -1 , x O3 = 2.0%. Empty arrows represent added reactions, dashed arrows represent modified reactions in the current model, squared species were experimentally observed and quantified.

( 56 )Figure 1 .

 561 Figure 1. Stagnation plate burner setup used in this study.

Figure 2 .

 2 Figure 2. Stabilization map. Stability limits are represented by continuous lines at 40 s -1 , and dashed lines at 50 s -1 .

Figure 3 .

 3 Figure 3. Raw CH 2 O* chemiluminescence (left) and CH 2 O-PLIF (right).  = 40 s -1 ,  = 0.4, x O3 = 1.6%. The dashed lines represent the burner (bottom) and plate (top) positions, the solid line represents the top of the laser sheet. The color bar on the right indicates the relative intensity of each image, between 0 and 1.

Figure 4 .

 4 Figure 4. Extracted CH 2 O* and CH 2 O-PLIF profiles from Fig. 3,  = 40 s -1 ,  = 0.4, x O3 = 1.6%.

Figure 5 .

 5 Figure 5. Temperature profiles, (a)  = 40 s -1 , Φ = 0.3, 1.8% O 3 , (b)  = 50 s -1 , Φ = 0.3, 2.0% O 3 .

Figure 6 .

 6 Figure 6. Evolution of the flame front position as a function of the ozone mole fraction.a = 40 s -1 (left), (b)  = 50 s -1 (right).

Figure 7 .

 7 Figure 7. Effect of the ozone mole fraction on the maximal cool flame temperature at  = 0.3 and α = 40 s -1 (black) and 50 s -1 (red). Experiments are represented with symbols, simulations with lines.

Figure 8 .

 8 Figure 8. Effect of the equivalence ratio on the flame front position at fixed strain rates α = 40 s -1 (black) and 50 s -1 (red) and ozone mole fraction x O3 = 1.9%.

Figure 9 .

 9 Figure 9. Experimental and simulated species mole fractions profiles,  = 0.3,  = 50 s -1 , x O3 = 2.0%.

Figure 10 .

 10 Figure 10. Experimental and simulated species mole fractions profiles,  = 0.5,  = 50 s -1 , x O3 = 1.7%. Grey points represent the perturbated zone where in-capillary reactivity takes place.

Figure 11 .

 11 Figure 11. Comparison between CH 2 O profiles obtained by PLIF and µGC,  = 0.5,  = 50 s -1 , x O3 = 1.7%. Grey points represent the perturbated zone where in-capillary reactivity takes place.

Figure 12 .

 12 Figure 12. Brute force sensitivity analysis of the first stage ignition delay, modified model.  = 0.3, x O3 = 2.0%.

Figure 13 .

 13 Figure 13. Reaction pathway analysis in the cool flame with the current model at 5%, T flame = 412 K (bold, red) and 20%, T flame = 612 K (italic, black) fuel conversion,  = 0.3,  = 50 s -1 , x O3 = 2.0%. Empty arrows represent added reactions, dashed arrows represent modified reactions in the current model, squared species were experimentally observed and quantified.

  studied wallstabilized premixed DME/O 2 cool flames using a heated plate at 700K, observing the formaldehyde distribution by Planar Laser Induced Fluorescence (CH 2 O-PLIF). Reuter et al. studied DME/O 2 /O 3 21 and DME/CH 4 /O 2 /O 3 22 premixed cool flames, partially premixed DME/O 2 /O 3 cool flames

Table 1 .

 1 [START_REF] Goodwin | An Object-Oriented Software Toolkit for Chemical Kinetics[END_REF] . Modifications operated on the Aramco 1.3 (+ O 3 submechanism) model.

	Reactions

CH 3 OCH 3 (+M) = •CH 3 + CH 3 O• (+M) p.

w. 2.33•10 19 -0.661 84139 7.60•10 -14 [44] a

  • radicals forming 2 CH 3 OCH 2 O• radicals and an O 2 molecule. The decomposition of these radicals into methyl formate, CH 3 OCHO, plays an important role in the improvement of the prediction of this species by the current model. Bimolecular reactions of peroxy radicals being usually

	R11. + O 2 (+M) <=> HO (+M)
	R10. 2 HO <=> H 2 O 2 + O 2
	R9. CH 3 OCH 2 O <=> H 2 OCH 2 O 2 H
	R8.	+ 2 O 2 <=> O 2 + O 3
	R7. CH 3 OCH 3 + O <=> CH 3 O H 2 + H
	R6.	+ O 3 <=> HO +			Decrease reactivity
	R5. OCH 2 OCH 2 O 2 H <=> HO 2 CH 2 OCHO + H
	R4. 2 CH 3 OCH 2 O <=> 2 CH 3 OCH 2 + O 2
	R3.	+ O 3 <=> O 2 + H
	R2. HO + O 3 <=> 2 O 2 + H				450K
	R1. O 2 + O 3 <=> + 2 O 2				600K
		-0.6	-0.4	-0.2	0.0	0.2	0.4
				Sensitivity Coefficient

ACKNOWLEDGMENTS

This work is a contribution to the LabEx CaPPA project funded by the French National Agency under contract « ANR-11-LABX-0005-01 » and to the CPER research project CLIMIBIO funded by the French Ministère de l'Enseignement Supérieur et de la Recherche. The authors thank the Regional Council « Hauts-de-France » and the « European Regional Development Fund » for their financial support to these projects. The authors would also like to thank the technical staff from PC2A laboratory for the help in the construction of the burner.

SUPPORTING INFORMATION

Supplementary experimental data and validation of the proposed model on experimental data from the literature are provided in the Supplementary Material.