Tristan Ferry
email: tristan.ferry@univ-lyon1.fr

Piseth Seng

Didier Mainard

Jean-Yves Jenny

Frédéric Laurent

Eric Senneville

Marion Grare

Anne Jolivet-Gougeon

Louis Bernard

Simon Marmor

Pr T Ferry

The CRIOAc healthcare network in France: a nationwide Health Ministry program to improve the management of bone and joint infection

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

possible to build at a national level, a network involving orthopaedic surgeons, infectiologists and microbiologists performing locally multidisciplinary meetings to facilitate the recruitment and the management of patients with complex bone and joint infection in regional centers?

Hypothesis:

A national healthcare network with regional labeled centers creates a dynamic that improves the recruitment, the management, the education, and the clinical research in the field of complex BJI Patients and Methods:

We describe the history of this unique national healthcare network and how it works, specify the missions confided to the CRIOAcs, evaluate the activity of the network over the first decade, and finally discuss perspectives.

Results:

The labelling of 24 centers in the CRIOAc network allowed for a meshing of the territory, with the possibility of management of complex BJI in each region of France. A dedicated secure national online information system was designed and used to facilitate decision-making during multidisciplinary consultation meetings. Since October 2012 to June 2017, 4,553 multidisciplinary consultation meetings have been performed in the structures belonging to the network, with 34,607 cases discussed in 19,961 individual. Prosthetic joint infections represented 38% (7,585/19,961) of all BJIs. Among all the cases discussed, the rate of complexity was of 61% (21,110/34,607) (related

4
to antibiotic resistance, infection recurrence, patient co morbidities). A national scientific meeting was created and a national postgraduate diploma in the field of BJI was launched in 2014. The promotion of education, clinical research and interactivity between each academic discipline and between each labeled centers across the country has synergized the strengths and have greatly facilitated the management of patients with BJI.

Discussion:

The setting up of the CRIOAc network in France took time, and has a cost for the French Ministry of Health. However, this network has greatly facilitated the management of BJI in France, and allowed to concentrate the management of complex BJI in centers that have significantly gained skills. There is, to our knowledge, no other exemple of such nation-wide network in the field of BJI.

Level of Evidence : IV, case series without control group Key Words: Bone and joint infection; Osteomyelitis; Reference center; Network; Antibiotherapy 5

Introduction

Different kinds of bone and joint infection (BJI) have been described, with correspondingly different therapeutic strategies and prognoses. Some of them, such as uncomplicated childhood osteomyelitis, are easy to treat, requiring short-course antimicrobial therapy without surgery.

Others, such as implant-associated BJI, a very heterogeneous group of BJIs, are more complex to treat, as eradication of the pathogen is challenging [START_REF] Lew | Osteomyelitis[END_REF][START_REF] Pääkkönen | Acute osteomyelitis in children[END_REF][START_REF] Bauer | Arthroplasty following a septic arthritis history: a 53 cases series[END_REF][START_REF] Lazennec | Infections in the operated spine: update on risk management and therapeutic strategies[END_REF][START_REF] Joulie | Factors governing the healing of Staphylococcus aureus infections following hip and knee prosthesis implantation: a retrospective study of 95 patients[END_REF][START_REF] Klouche | Infected total hip arthroplasty revision: one-or two-stage procedure?[END_REF]. It has been proven that the implementation of a surgical site infection surveillance protocol reduces the incidence of surgical site infection such as post-operative prosthetic joint infections [START_REF]Recommandation de Bonne Pratique de la Haute Autorité de Santé[END_REF]. However, the risk of post-operative infection still persist, especially in patients that cumulate several risks factors for infection such as age, obesity, diabetes, smoking and iterative prosthesis replacement [START_REF] Baker | Patient-adapted treatment for prosthetic hip joint infection[END_REF]. In such infected patients, it is widely recognized in the literature that team-work is required to personalize disease management, determine optimal medico-surgical strategy, and limit treatment failure, motor disability and amputation risk [9]. Several multidisciplinary groups have formed in the major hospital-university hospitals in Europe, but no national network structuring has been implemented, except in France.

As a result, the management of BJI was included in the 2 "corresponding centers" (CCs), in order to provide the most appropriate care possible throughout the national territory.

The aims of the article were: 1) to describe the history of this unique national network and how it works; 2) to specify the missions confided to the CRIOAcs; 3) to evaluate the activity of the network over the first decade; 4) to discuss perspectives; to finally answer the question: is it possible to build at a national level, a network involving orthopaedic surgeons, infectiologists and microbiologists performing locally multidisciplinary meetings to facilitate the recruitment and the management of patients with complex bone and joint infection in regional centers?

Patients and Methods

Burden of BJI

A national study using the national health administration data-base (Programme de Médicalisation des Systèmes d'Information: PMSI) demonstrated that BJIs have a major clinical and economic impact in France. There was overall prevalence of 54 cases per 100000, which is in the range of other studies performed in Europe and in the USA. BJI prevalence was age-and sex-dependent, increasing 6-fold between age <50 years and age >70 years. Most patients had underlying diseases, especially diabetes, and related comorbidities, including ulcer sores and vascular disorders. In 2008, the total direct cost of BJI-related care in France was of €259 million (€7,178 per hospital stay); one of the main contributors to this cost was the rate of hospital readmission (19%). Of note, these figures do not take account of the cost of long-term care and rehabilitation, or the vast array of indirect costs. The authors estimated that only 10% of the total costs were healthcare-related, the remainder being social and occupational costs [START_REF] Grammatico-Guillon | Bone and joint infections in hospitalized patients in France, 2008: clinical and economic outcomes[END_REF]. Implant-associated BJI, corresponding to onethird of all BJI patients in France, is frequently postoperative and more costly than native BJI: at least one surgery is always required, the prevalence of bacterial resistance is higher, the use of expensive antibiotics greater, the overall length of stay longer, and the rate of relapse higher. For instance, in the USA in 2009, the estimated mean cost associated with methicillin-susceptible S.

7 aureus prosthetic joint infection (PJI) was of $68,053, whereas methicillin-resistant S. aureus BJI costs were significantly higher, at a mean $107,264 per case [START_REF] Parvizi | Periprosthetic joint infection: the economic impact of methicillin-resistant infections[END_REF]. In Australia, the median cost per patient of treating PJI was of AU$34,800 ($26,000), with a 156% increment in case of treatment failure [START_REF] Peel | Factors influencing the cost of prosthetic joint infection treatment[END_REF]. Finally, the global cost of BJI will increase in coming decades, especially due an increase in the absolute number of PJI cases, as the need for joint arthroplasty is expected to increase substantially with population demographic ageing. In the USA, the annual cost to hospitals of revision surgery for infection increased from $320 million in 2001 to $566 million in 2009, and is projected to exceed $1.62 billion by 2020 [START_REF] Kurtz | Economic burden of periprosthetic joint infection in the United States[END_REF].

First step: 2008-2009

In Tourcoing (north of France), Reims (north-east), Lyon (east), Marseille, (south-east), Toulouse (south-west), and Tours (center) [START_REF]2010 relative au dispositif de prise en charge des infections ostéo-articulaires complexes[END_REF].

Second step: national coordination 2009-2010

A first national coordination meeting of the 8 CRIOAcs was held in June 2009, and a national coordinator (Pr. Alain Lortat-Jacob) was appointed by the Ministry of Health to ensure that its implementation matched the original orientation, notably as concerns perceived stakes, internal organization, and inter-regional coordination with other health-care establishments. To optimize geographic coverage, a 9 th CRIOAc was designated in early 2011 (Rennes, west of France). A funding plan for the centers was drawn up, with an already set annual budget plus activitydependent budget. The budget is of about €150,000 per CRIOAc, for financing 2 officers to facilitate events organization, information and inter-regional coordination. The activity-dependent budget is based on the PMSI data-base, for which a specific code (08C56x) was created and used for each hospital admission for complex BJI. For each surgical stay with this code, the hospital receives an extra 12% funding from the national health insurance system. Criteria for complex BJI were detailed in the "Journal Officiel de la République Française" that publishes Laws and Decrees, and are summarized in Table 1 [START_REF]2010 relative au dispositif de prise en charge des infections ostéo-articulaires complexes[END_REF].

Third step: Network finalization, including corresponding centers (CCs), and implementation of an online information system (2011-2016)

To finalize the network, 15 "corresponding centers" (CCs) were labeled in 2011 (1 or 2 per CRIOAc), totaling 24 CRIOAcs and CCs (figure 1). In 2012, the Nancy university hospital replaced Reims, as the CRIOAc of the north-east region. Missions attributed to CRIOAc and CCs were clarified at this step. CRIOAcs and CCs share certain missions: (1) information and orientation: organization of response to calls from health-care professionals and also patients; (2) referral:

responses to requests for advice on treatment for patients with easy-to-treat or complex BJI; (3)

9
organization and centralization of multidisciplinary consultation meetings with quorum (at least one infectious disease physician, one orthopedic surgeon, and one microbiologist), to determine the optimal medico-surgical strategy for each patient, and determine whether the BJI is complex or not.

CRIOAcs have national, regional and local level teaching missions, and also promote clinical

Results

The labelling of 24 centers in the CRIOAc network allowed for a meshing of the territory, with the possibility of management of complex BJI in each region of France. Since October 2012 to June This scientific meeting brings together 300 to 500 professionals involved in the management of BJI.

In the field of the clinical research, several regional and national projects have been completed and the French guidelines hosted by the "Haute Autorité de Santé" (HAS) for the management of prosthetic joint infection occurring during the month following the implantation. The methodology used followed the "best practice recommendations" of the HAS. Accordingly, the first step was a review of the literature and a critical analysis of the data. Once enough evidence was gathered, an evidence report was drafted. Secondly a multidisciplinary and multiprofessional group, of 15 to 20 professionals and representatives of patients and users of the Healthcare system, drafted the recommendations that were submitted to a peer review group, before publication of the guidelines.

Discussion

The management of BJIs requires a multidisciplinary approach, and a great experience for the most complicated cases to limit treatment failure, motor disability and amputation risk. The French Health Ministry hypothesized that a nationwide healthcare network with regional labeled centers could create a dynamic that improves the recruitment, the management, the education, and the clinical research in the field of complex BJI. The setting up of the CRIOAc network in France took time, and has a cost for the French Ministry of Health. However, this network has greatly facilitated the management of BJI in France, and allowed to concentrate the management of complex BJI in centers that have significantly gained skills. There is, to our knowledge, no other example of such nation-wide network in the field of BJI. This dynamic is the first step to obtain a reduction of the burden of CRIOAc in France. To drive this effort, the health ministry has to continue to support the network, and the CRIOAc scientific committee has to identify and support key thematic research for complex BJIs in the following domains: prevention; pathophysiology, diagnosis, biomarker development and monitoring; dedicated pharmacological agents and medical device; quality of care; public awareness and understanding. To evaluate and perpetuate the network, as for all certified and funded structures, and in addition to the annual reports produced, conformity to the specifications is reassessed periodically [START_REF]2016 relative au renouvellement du dispositif des structures labellisées pour la prise en charge des infections ostéoarticulaires complexes[END_REF], and CRIOAc certification will be re-assessed for a 5year period starting in 2017. A national jury representing the CRIOAcs, the patient association "Le 12

Lien" and BIJ experts from the regional health agencies will advise the DGOS health-care supply office on the selection of candidates put forward by the regional health agencies, and the DGOS will decide in the light of this advice. The specifications have been updated, and now encourage taking into account activity in terms of hospital stays and number of multidisciplinary consultation meetings, with thresholds being set such as (i) effective patient satisfaction assessment; (ii) effective geographic coverage, without blank areas; and (iii) effective implementation of CRIOAc missions in terms of coordinating the expertise, orientation and information of other agents (community practices, patients, private-sector structures, etc.). During the 5-year period aforementioned, the national database collecting the data of each multidisciplinary consultation meetings will be used for epidemiological studies and report purposes. A national website for patients and the various health professionals will be created to publicize the system, and optimize referrals and timely treatment before simple situations become complex. As this networking structure greatly facilitates the synergy between the representatives of each academic disciplines involved, it will also continue to promote research, with clinical trials assessing new diagnostic tools, surgical procedures for a given BJI, specific antibiotics, or overall medical/surgical strategy. Epidemiological data will allow feasibility studies and also partnerships with the industry, in the fields of diagnostic, implants, bone cements, bone substitutes, antibiotics and all the various therapeutic alternatives such as bacteriophages. To answer the question, it was possible to build at a national level in France, a network involving orthopaedic surgeons, infectiologists and microbiologists performing locally multidisciplinary meetings. This dynamic facilitates the recruitment and the management of patients with complex bone and joint infection in regional centers. The promotion of education, clinical research and interactivity between each academic discipline and between each labeled centers across the country has synergized the strengths and optimized the management of patients with BJI.

By drawing upon the strengths of academic and health ministry expertise, the CRIOAc network represents a potential new model at a national level, for filling knowledge gaps, and enhancing management and innovation in complex diseases.

13

Our study has some limitations: 1) we are not aware of BJI not implemented in the database and the extra cost related when those patients are managed in centers outside the CRIOAc network.

However, every cases discussed in multidisciplinary meetings are recorded in the system, centers outside the network more and more facilitate the recruitment of their patients by centers belonging the network, and based on the PMSI database, most of BJI in France are managed in the CRIOAc network; 2) we did not compare the cost and rate of success of BJI managed inside vs. outside this network, but the patients outside the network probably have the most easy-to-treat BJI. Finally comparison of BJI healing of patients inside the network could be monitored over the time in future dedicated investigation. 20 Table 1. Criteria for complexity (summarized from the 2010 publication in "Journal Officiel de la République Française"). The presence of at least one criterion provides to the labeled center an extra 12% funding for surgical stays.

Host criteria

Patient with severe comorbidity limiting treatment options Patient with severe allergy

Microbiological criteria

Difficult-to-treat micro-organism(s) with or without multidrug resistance

Surgical criteria

BJI requiring bone resection and bone and/or soft-tissue reconstruction

Relapse

Relapse of a previous episode of BJI

The

  CRIOAc healthcare network in France: A nationwide Health Ministry program to improve the management of bone and joint infection Tristan Ferry, Piseth Seng, Didier Mainard, Jean-Yves Jenny, Frédéric Laurent, Eric Senneville, Marion Grare, Anne Jolivet-Gougeon, Louis Bernard, Simon Marmor To cite this version: Tristan Ferry, Piseth Seng, Didier Mainard, Jean-Yves Jenny, Frédéric Laurent, et al.. The CRIOAc healthcare network in France: A nationwide Health Ministry program to improve the management of bone and joint infection. Orthopaedics & Traumatology: Surgery & Research, 2019, 105 (1), pp.185-190. 10.1016/j.otsr.2018.09.016. hal-02871359

  research in BJI. All of the CRIOAc and CC have to draft an annual report describing their activities, the reports are yearly presented by the General Directorate for Provision of healthcare to the community and discussed. For use by all of the labeled centers, a dedicated secure national online information system was designed to collect several data such as medical history, clinical characteristics, the type of BJI, pathogen and surgery and antibiotics proposed. The objectives of this online information system are to: (1) facilitate decision-making during multidisciplinary consultation meetings; (2) draw up a summary of the patient's clinical history, the BJI's complexity status, and decisions taken; (3) share the medical synthesis in pdf format within the approved structures and with the concerned physicians; (4) facilitate patient follow-up; (5) produce activity data for assessment of the centers' missions; and (6) undertake epidemiological research. The system allows for real-time knowledge of the activity of the centers (number of multidisciplinary consultation meetings, number of cases discussed, complexity rate, etc.). In 2011, it has been proposed that the CRIOAc should alternatively organize national scientific meeting on BJI every 2 years. In 2014, the Société de Pathologie Infectieuse de Langue Française (SPILF), and the Société Française de Chirurgie Orthopédique et Traumatologique (SOFCOT) decided to create a postgraduate national diploma in the field of BJI in which residents in medicine or surgery can be enrolled every 2 years. In 2016, a scientific committee was set up among health professionals from the CRIOAc to organize access to and use of medical data for epidemiological studies.

  published. Of note, some national projects were funded or supported by the Health Ministry such as DATIPO in 2009 (comparison of different duration of antibiotics in patients with PJI; Prospective open randomized multicentre non-inferiority phase 3 trial NCT01816009), EVRIOS in 2015 (comparison of different dosages of rifampin; Prospective open randomized multicentre noninferiority phase 3 trial; NCT02599493), and PHAGOS and PHAGOPIED in 2016 (safety of bacteriophages targeting S. aureus in patients with PJI and diabetic foot osteomyelitis; NCT02664740). Indeed, these multiple interactions in the CRIOAc network facilitate the emergence and the feasibility of multicentric studies with high level of evidence. Finally, to optimize the management of acute prosthetic joint infection, and to avoid its complication, some experts from the CRIOAc network directly participated to the literature review and the drafting of 11

Figure 1 .Figure 1 .

 11 Figure 1. Distribution of CRIOAcs (orange) and their CCs (yellow) in the various regions of France in 2011-2016. CRIOAc: Complex Bone and Joint Infection reference Center (Centre de Référence des Infections Ostéoarticulaires complexes); CC: Corresponding Center

Figure 2 .

 2 Figure 2. Cumulative number of multidisciplinar consultation meetings, cumulative number of patients and cumulative number of case discussions performed by the 24 centres belonging to the CRIOAc network since the use of the secure national online information system in 2012.

Figure 2 .

 2 Figure 2. Nombre cumulé de Réunion de Concertations Pluridisciplinaires (RCP), nombre cumulé

Figure 1 .

 1 Figure 1.

Figure 2 .

 2 Figure 2.

de Clermont-Ferrand, Clermont-Ferrand; Pr

  All authors did not receive any industrial grant regarding the current study.The network presented in the study is funded by the Direction Général de l'Offre de Soin (DGOS), that belongs to the French Health Ministry. No author has conflict related to the current study.Outside the current study TF has consultancy for Pfizer, Debiopharma, MaaT Pharma, Sanofi R&D and received travel grant from Pfizer. ES has consultancy for Novartis, Pfizer and MSD, is a Speaker for Sanofi-Aventis, AstraZeneca, Zimmer and Gilead. JYJ has royalties from B-Braun Aesculap, declare consultancy from Exactech, and has support for travel from FH Orthopedics. Funding sources: DGOS Authors'contribution: TF wrote the first draft of the article; all other authors contributed to the involvement of the final manuscript

	coordinator), Pr. Philippe Rosset (Orthopedic surgeon), Dr. Anne-Sophie Valentin (Microbiologist);
	CHU de Rennes, Rennes; Dr. Cédric Arvieux (Infectiologist, coordinator), Dr. Jean Christophe
	Lambotte (Orthopedic surgeon), Pr. Anne Jolivet-Gougeon (Microbiologist). Corresponding
	Centers: Centre Hospitalier de Versailles André Mignot, Le Chesnay; Dr. Philippe Boisrenoult
	(Orthopedic surgeon, coordinator), Dr. Audrey Therby (Infectiologist), Dr. Béatrice Pangon
	(Microbiologist); AP-HP Hôpital Lariboisière, Paris; Pr. Rémy Nizard (Orthopedic surgeon,
	coordinator), Dr. Véronique Delcey (Infectiologist), Dr. Béatrice Bercot (Microbiologist); CHU
	Amiens Picardie, Amiens; Dr. Benoit Brunschweiler (Orthopedic surgeon, coordinator), Dr.
	Cédric Joseph (Infectiologist), Dr. Florence Rousseau (Microbiologist); CHU de Caen, Caen; Pr.
	Christophe Hulet (Orthopedic surgeon, coordinator), Dr. Jocelyn Michon (Infectiologist), Dr.
	. Olivier Lesens
	(Infectiologist, coordinator), Pr. Stéphane Descamps (Orthopedic surgeon), Dr. Frédéric Robin
	(Microbiologist); CHU de Nice, Nice; Pr. Christophe Trojani (Orthopedic surgeon, coordinator),
	Dr. Evelyne Bernard (Infectiologist), Pr. Raymond Ruimy (Microbiologist); CHU de Bordeaux,
	Bordeaux; Pr. Michel Dupon (Infectiologist, coordinator), Pr. Thierry Fabre (Orthopedic surgeon),
	Pr. Francis Megraud (Microbiologist); CHU de Limoges, Limoges; Dr. Fabrice Florenza
	(Orthopedic surgeon, coordinator), Dr. Éric Denès (Infectiologist), Dr. Christian Martin
	(Microbiologist); CHU de Brest, Brest; Pr. Eric Stindel (Orthopedic surgeon, coordinator), Pr.
	14 17

Francois Guerin (Microbiologist); CHU de Besançon, Besançon; Pr. Catherine Chirouze (Infectiologist, coordinator), Dr. Grégoire Leclerc (Orthopedic surgeon), Dr. Isabelle Patry (Microbiologist); Hôpitaux Universitaires de Strasbourg, Illkirch Graffenstaden; Dr. Jeannot Gaudias (Infectiologist, coordinator), Pr. Jean-Yves Jenny (Orthopedic surgeon); Dr. Philippe Riegel (Microbiologist); CHU de Grenoble, Grenoble; Pr. Jean-Paul Stahl (Infectiologist, coordinator), Pr. Dominique Saragaglia (Orthopedic surgeon), Dr. Sandrine Boisset (Microbiologist); CHU Séverine Ansart (Infectiologist), Dr. Didier Tande (Microbiologist); CHU d'Angers, Angers; Dr. Pierre Abgueguen (Infectiologist, coordinator), Pr. Pascal Bizot (Orthopedic surgeon), Dr. Carole 16 Conflict of interest:

Acknowledgments

We thank all physicians involved in the network. CRIOAc network collaborators: CRIOAc: Groupe Hospitalier Diaconesses-Croix Saint Simon, Paris; Dr. Simon Marmor (Orthopedic surgeon, coordinator), Dr. Valérie Zeller (Infectiologist), Dr. Nicole Desplaces (Microbiologist);


Alexandre Jean

Jacques Rouden

Jacques Maddaluno

Michaël De Paolis

Jérôme Blanchet

Catalytic and Metal-Free Cyclizing Hydroalkoxylation of Alkynes

Keywords:

Benzyltrimethylammonium hydroxide act as an efficient metal-free catalyst for the intramolecular hydroalkoxylation of alkynes. Notably, the use of microwave irradiation allowed reaction to operate in only two minutes. Under optimized reaction conditions, linear alkynes bearing aryl and heteroaryl substituents were successfully cyclized with good level of stereoselectivity.

Introduction

Exocyclic enol ethers are a class of heterocycle present in a range of natural or pharmacology active molecules [1]. (Figure 1). Moreover, they are useful intermediates for the synthesis of important biomolecules subunits such as C-glycosides [2a,b] or spirodiketal [2c]. In the context of our recent study regarding selective pyrrolidine and pyrrole synthesis [9] we recently discovered that linear alkynes substituted with an appropriate alcohol moiety could be rapidly cyclized through a specific combination of a small amount of Triton B (benzyltrimethylammonium hydroxide) and microwave irradiations. The overall process conveniently yielded the corresponding 5-membered exocyclic enol ethers in a catalytic and metal-free manner.

Results and discussion

Our investigations started with the attempted cyclization of inactivated alcohol 1a under moderate microwave irradiations. Using catalytic amount of cesium or potassium hydroxide as base in highly polar solvents such as N-methylpyrrolidone (NMP) or dimethylsulfoxyde (DMSO), no conversion to the desired cyclic enol ethers 2a was observed (Table 1, Entry 1 and2). Switching to tetrabutylammonium fluoride in dimethylformamide (DMF) did not promote the reaction. Surprisingly, when using the strong organic bases tetrabutyl ammonium hydroxide (TBAH), a clean 5-exo-dig cyclisation of alcohol 1a was observed in very short reaction time and expected selectivity favouring isomer (Z)-2a. [8b] Moreover, Triton B gave a slightly improved selectivity with a (Z)-2a:(E)-2a ratio of 88:12 (Table 1,Entry 6). Thus, nonactivated alkyne 1a was efficiently cyclized upon a catalytic and metal-free process.

Table 1

Optimization of 1a 5-exo-dig cyclization.

Entry

Conditions Yield (%) (Z):(E)-2a [a] 1

CsOH ( 20 Triton B (10 mol%), 1,4-dioxane [b] 0 10 Triton B (10 mol%), toluene [b] 0 11 Triton B (10 mol%), THF [b] 0 11 Triton B (10 mol%), CH 3 CN [b] >95 (65/35) 12 Triton B (10 mol%), DMSO [b] >85 (88/12)

[a] Isolated as a (Z/E) mixture, yield and ratio determined by 1 H NMR. [b] 60 °C, 3,5 min.

The amount of Triton B could be decreased to 5 mol% (Table 1, Entry 7). When 1 mol% Triton B was used, no conversion was observed after 2 minutes. Increased concentration gave a complex mixture of unidentified products while decreasing the temperature at 40 °C led to reproducibility problems.

The nature of the solvent has a decisive influence on the result of the reaction: dioxane, toluene or THF gave no conversion, in line with known ineffective microwave heating in solvents with low dielectric constant [START_REF]For a discussion on microwave activation[END_REF]. More polar solvent such as acetonitrile gave complete conversion with a lower (Z)-2a selectivity and dimethyl sulfoxide (DMSO) provided similar selectivity as DMF, although inseparable side products (< 10%) were detected in the crude reaction mixture (Table 1, Entries 11 and 12).

To assess the critical effect of microwave irradiations, control experiments with one equivalent of Triton B at room temperature or at 100 °C using a conventional oil bath heating were performed. After a prolonged period (3-12 hours), no conversion was observed. However, increasing the temperature to 120 °C during 10 hours finally gave a lower 84% conversion and no selectivity (Z/E 55:45).

With optimized conditions in hand, the scope of the catalytic reaction was explored with various alcohols (Table 2).

Table 2

Scope of Triton B-mediated cyclization of arylalkynyl alcohols.

Entry

Yield %) [a] (Z):(E) [a] 1 [b] 7 2h 86 63:37, 98:2 [b] 8 2i 87 88:12, 98:2 [b] 9 2j 90 96:4

Isolated yields; Z/E ratio determined by 1 H NMR of crude mixture;

[a] Over 2 steps after hydrogenation using Pd/C, see SI for details; [b] After treatment with CF 3 CO 2 H, see SI for details.

Thus electron-rich arenes connected to alkynyl alcohols were successfully reacted and converted into cycloethers 2b-2d with moderate (Z)-selectivity. Those heterocycles displayed poor stability and required an additional reduction step (Pd/C, AcOEt, H 2 ) to be isolated, providing 2-substituted tetrahydrofurans in 81-40% yield over 2 steps.

Having a lower LUMO, electron-poor alkynes gave better results leading to stable cyclic ethers 2e and 2f in excellent yields (> 98%). Furthermore, pyridine, pyrazine, quinoline and pyrimidine substituted alkynes were similarly cyclized in 2h-j with excellent yields (86-90%). In some instances, moderate stereoselectivities were enhanced by isomerisation upon work-up with trifluoroacetic acid in dichloromethane (2h-i). This was rationalized in terms of increased stabilization of (Z)-2g-i through intramolecular hydrogen bonding between the oxygen atom and the protonated heterocycle. The substitution of the alkyne with electron depleted heterocycles facilitated considerably the cyclization process. Hence, a control experiment showed that 1g (Ar = 2-pyridyl) cyclized into 2g in 93% yield (Z/E 66:34) at room temperature, but at a much slower pace over 5 hours. Replacing the ammonium hydroxide with catalytic 1,8diazabicyclo-[5.4.0]undec-7-ene or 1,1,3,3-tetramethylguanidine failed to promote the cyclization of 1g at room temperature.

The possibility to obtain cyclic enol ethers substituted with Lewis basic nitrogen heterocycles further illustrate the versatility of this metal-free process. However, some limitations were noted: no cyclization occurred with 4-pentyn-1-ol and trimethylsilyl-substituted alkyne led only to clean desilylation. With more robust triisopropylsilyl group, only degradation compounds were observed.

Intramolecular hydroalkoxylation of alkyne leading to a 6membered heterocycle is considerably less documented than 5membered counterpart. Therefore cyclization of homologous phenylhexynol 3 was attempted. Upon treatment with Triton B, a 6-exo-dig cyclization took place followed by an isomerization, providing dihydropyran 4 with >90% NMR purity (Scheme 2) [11].

Scheme 2. 6-exo-dig cycloisomerization of phenylhexynol 3

Poor stability of compound 4 prevented further purification by flash chromatography and subsequent hydrogenation afforded tetrahydropyran 5 in 65% yield over 2 steps.

Conclusion

In summary, we have developed 5-exo-dig cyclizations of arylalkynyl alcohols under unprecedented tetraalkylammonium hydroxide catalysis. One example of 6-exo-dig cyclization is also reported. Without favorable bias such as present in benzylic alcohol derived alkynes, the chemistry is compatible with alkynyl connected to electron-rich or electron-poor aryl groups with similar efficiency. In all cases, good to excellent stereoselectivities in favour of the (Z)-enol ethers were obtained. The base used in this reaction, Triton B, is readily available, easy to handle and was used in catalytic amount. Further studies to clarify the reaction mechanism, in particular the contribution of the counter cation are currently in progress in our laboratory.

Figure 1 .

 1 Figure 1. Naturally occurring and biologically active exocyclic enol ethers.

Figure 2 .

 2 Figure 2. Context of base mediated hydroalkoxylation of alkynes.

Acknowledgments

The authors thank the CNRS, Normandie université, Labex Synorg (ANR-11-LABX-0029) and and the CRUNCh network for a fellowship to A.J. The Conseil Régional de Normandie and the European FEDER fundings are also acknowledged for financial support.


Y Fenard

H Song

R Dauphin

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

An engine-relevant kinetic investigation into the anti-knock effect of organometallics through the example of ferrocene

Keywords: Phase Reaction Kinetics ignition delay, rapid compression machine, kinetics, ferrocene, anti-knock octane boosters

A detailed study on the ignition of ferrocene-containing mixtures has been undertaken in a Rapid Compression Machine (RCM). Two hydrocarbon fuels, isooctane and 3-hexene, were investigated in order to assess the hypothesis of an inhibiting effect of iron oxide particles on HO2 radicals and H2O2. Ignition delays were measured at core gas temperatures of 700 K and 850 K, pressures from 6 to 20 bar, and ferrocene mole fractions in the original fuel from 0 to 900 ppm. These experiments provide insight into the kinetics of the antiknock effect of ferrocene on both the non-octane sensitive (isooctane) and octane sensitive (3-hexene) fuels.

Experimental results show that doping reactive mixtures with ferrocene always lengthens the total ignition delay. Also, the increment in auto-ignition delay is monotonic with increasing amount of ferrocene while no loss of effectiveness was noticed, even at the highest mole fractions. On the other hand, in the event of two stage ignition, the first stage delay is not affected by any doping with ferrocene. The kinetic mode of action of ferrocene is investigated, based on these statements, in an effort to better understand the impact of organometallic octane boosters on the combustion of fuels.

A kinetic short sub-mechanism was built in order to describe the influence of ferrocene on the reactivity of isooctane and 3-hexene in a RCM, yielding qualitative agreement.

Introduction

The use of organometallics as anti-knock agent goes back to the 1920s, when it was pointed out that TetraEthyl Lead (TEL) had a beneficial effect on preventing knock in Spark Ignition (SI) engines. With the emergence of three-way exhaust catalyst, TEL has been gradually banned from commercial petrol fuels due to its poisoning effect on catalysts, but remains at use for limited applications, such as aviation [1]. As an effort to replace this anti-knock agent, several organometallic octane boosters were used, among which are methylcyclopentadienyl manganese tricarbonyl and ferrocene.

Ferrocene is an organometallic molecule, synthesized for the first time in the 1950's. Ferrocene, or bis(η 5 cyclopentadienyl)iron, also draws its name from its structure: an iron atom between two cyclopentadienyl groups. Ferrocene is an efficient anti-knock octane booster which is cost-competitive and miscible in gasoline but not in water. However, its extensive use in SI engines causes an iron deposit on the spark plug, thus decreasing the insulation resistance of spark plugs which causes spark plug dysfunction, leading to increased fuel consumption and exhaust emissions. Nevertheless, ferrocene is still being used in several countries, and might be used in high-performance engines. Moreover, the mechanism responsible for its octane-boosting effect can also be relevant for other organometallic additives.

Most experimental studies on the effect of ferrocene on combustion relate to flame studies. For example, the soot-inhibiting characteristics of ferrocene have been demonstrated in several conditions. Bonczyk [2] noticed that the doping of isooctane/air diffusion flames with ferrocene enhances the soot burn out, without affecting the flame temperature. This was confirmed by several studies, with various fuels and experimental setups: Crude oil pool fires [3], laminar, coannular, ethylene/air non-premixed flames [4,5], heavy-duty diesel engines [6], acetylene diffusion flames [7], and ethylene diffusion flames [8]. All conclude that carbonaceous compounds condense at the surface of iron oxide nuclei formed during the early stage of the flame, followed by burn out during the last stage of combustion. The critical sooting C/O ratio was measured by Hirasawa et al. [9] for laminar premixed ethylene flames, concluding in a marked increase in the sooting tendency for flames doped with ferrocene. A five-step reaction mechanism of ferrocene decomposition, leading to the formation of the cyclopentadienyl, was proposed, suggesting that the contribution to aromatics formation and growth of the cyclopentadienyl groups in the ferrocene molecule is insignificant. Linteris et al. [START_REF] Linteris | Proc. Combust. Inst[END_REF][START_REF] Linteris | [END_REF][12] studied the catalytic inhibition of laminar flames by organometallic compounds through several studies, complemented by a review of the literature. These works point out the reduction of the burning velocity of premixed methane flames with addition of ferrocene or iron pentacarbonyl, with a reduced effect at mole fractions above a few hundred ppm. From these studies, a detailed kinetic submechanism for the oxidation of ferrocene was suggested, based on the previous modeling work of Rumminger et al. [13] on iron pentacarbonyl. The chemical structure of a premixed propene/air flame was investigated by Tian et al. [14]. The influence of iron-containing additives on the measured hydrocarbon intermediates concentrations is small, but a decrease of the flame temperature by 40 K was observed. These experimental results were simulated using the model built by Linteris et al. [START_REF] Linteris | Proc. Combust. Inst[END_REF] with reasonable success. Recently, Zhu et al. [15] studied the kinetic effect of gaseous iron atoms on the ignition and combustion of n-heptane with a detailed model based on the work by Linteris et al. [START_REF] Linteris | Proc. Combust. Inst[END_REF], at T = 800K and p = 50 bar. Their work was a modeling effort, with no experimental data available to evaluate the effect of iron on the ignition delay of heptane/O2/inert mixtures, and predicted a reduction of the ignition delay time when a concentration of 100 ppm of gaseous iron atom is added. This conclusion is however surprising, given the well-known effect of ferrocene on knock resistance of fuels. A widely accepted hypothesis suggests that metallic oxides particles formed from organometallics act as scavengers for HO2 and H2O2 (see, for example, [16]). This has however never been experimentally demonstrated. Considering the relevance of Low Temperature Combustion (LTC) mechanisms to the knock phenomenon in Spark-Ignition engines, a kinetic study of the effect of ferrocene on ignition in low temperature and high pressure conditions has therefore the potential to provide insight into the mechanisms of knock inhibition by organometallic octane boosters.

In this study, ignition delay times of fuel/air mixtures doped with ferrocene have therefore been measured, using two fuels with differing ignition kinetics. Isooctane is a non octane-sensitive, branched alkane primary reference fuel, with important LTC reactivity and two-stage ignition [START_REF] Minetti | Symp. Int. Combust[END_REF][START_REF] Curran | [END_REF]. 3-Hexene is an octane-sensitive fuel (RON = 94, MON = 80 [19]) representative of olefin reactivity in gasolines. HO2 radicals have an increased importance in its limited LTC reactivity, mostly because of the additional reaction pathways associated with the C=C double bond [19,20]. The target mole fraction of ferrocene was from 0 to 900 ppm in the fuel. The temperatures, 700 K and 850 K, are representative respectively of the low temperature and the negative temperature coefficient region. The pressure ranged from 6 to 20 bar.

Experimental section

The ULille rapid compression machine, extensively described in the past [START_REF] Minetti | Symp. Int. Combust[END_REF]21,22], has a right angle configuration. A translating cam transmits the movement of the driving piston to the compression piston which compresses the gaseous mixture in the combustion chamber. At the end of the compression, the cam profile prevents the compression piston from bouncing backwards. Furthermore, this design ensures strict control over the piston velocity history during compression.

Solutions were prepared by dissolving a mass of solid ferrocene in the investigated liquid fuels (isooctane, and trans-3-hexene, >99.8%, Sigma Aldrich). The said solutions were then fully evaporated in heated glass vessels (90°C), and high purity oxygen, nitrogen and argon (>99.99%, Air Liquide) were added to form the gaseous mixtures with an inert-to-oxygen ratio of 3.78. Dissolution of ferrocene into liquid isooctane or 3hexene, and successive dilutions, results in an actual concentration of 322, 632 and 924 ppm for isooctane/O2/inert mixtures and 306, 607 and 909 ppm for 3-hexene/O2/inert mixtures. We report an uncertainty of 1% on the mole fraction of ferrocene in those mixtures. The partial pressures of each component are measured by heated pressure gauges (0-100 and 1000 torr, MKS Baratron), avoiding condensation on their surface. Pure nitrogen and argon are used as inert gases to reach core gas temperatures Tc of 700 and 850 K respectively. Minor adjustments to the initial temperature of the combustion chamber were made to reach the target compressed temperatures. Tc is calculated from the initial and compressed pressures and initial temperature using the isentropic law, showing a deviation from the target temperatures inferior to 5 K. The mixture is introduced into the combustion chamber through a heated line (90°C) in order to avoid condensation. The combustion chamber is surrounded by temperature-controlled heating elements, ensuring a 1 K deviation along the axial dimension. The RCM, mixture preparation facility and gas lines temperatures were chosen so that the ferrocene partial pressure was inferior to its vapor pressure by a factor of two in all cases [23]. The volumetric compression ratio is 9.65, the compression time being set to 60 ms to minimize fluid motion and mechanical vibration after compression [21]. Following the suggestion by Lee and Hochgreb [24], a creviced piston head is used to limit the formation of the piston corner vortex. Pressure profiles in the chamber are recorded with a piezoelectric transducer protected from thermal shock (Kistler 6052). The piston position and pressure are recorded with a 40 µs time step using a National Instruments acquisition card and LabView. The first stage and total ignition delays are defined as the time elapsed between the top dead center time and the maximum of the time derivative of the pressure associated with firststage ignition and final ignition, respectively. Only ignition delays between 2 and 200 ms are reported here, to accommodate with the measurable test times in this experimental device. All reactive shots are reported to provide information on the reproducibility of the experimental data. To control for possible surface contamination by iron oxides, the ignition delays of isooctane were measured before, after the ferrocene experiments, and finally after a thorough cleaning of the chamber walls, yielding similar results. The results for pure isooctane and 3-hexene were compared to previous data [20,25] obtained with the same RCM, using a flat piston, yielding comparable results.

Results and discussion

Isooctane

Ignition delays of stoichiometric isooctane/O2/inert mixtures, with various amounts of added ferrocene, were obtained for pressure ranging from 10 to 20 bar at TC = 700 K and 850 K. First stage ignition is observed at TC = 700 K, as presented in Fig. 1 with typical two-stage ignition behavior. The first stage ignition delay, in Fig. 1, decreases very slightly, but in a reproducible way, as the mole fraction of ferrocene increases. It is accompanied with a reduction of the amplitude of the pressure jump associated with first-stage ignition. Figure 2a illustrates the modification of the ignition delays over the whole pressure range.

Simultaneously, the second stage -or time period between first stage and final ignition-increases. Overall, the total ignition delay therefore increases as the ferrocene content increases. The competition between chain-propagating and chain-branching pathways determines the timing of ignition [26]. Low temperature chain-branching results from the formation and thermal decomposition of ketohydroperoxides, which causes the formation of two OH radicals that promote the reactivity. This in turn leads to a cool flame or first-stage ignition. The fact that ferrocene has little to no effect on the first-stage ignition delay could result from the absence of iron oxide particles before the cool flame, as well as limited activity of these particles on OH radicals. However, possible OH formation pathways involved in the conversion of ferrocene to iron oxides could explain the slight reduction of the first stage ignition delay. Ignition delays obtained at 700 K and 850 K are shown in Fig. 2a and 2b respectively at all investigated ferrocene compositions. The increase of the ignition delay by ferrocene addition is visible for all pressure conditions, but more intense at the lowest pressures at 700 K. In RCM experiments, second-stage ignition is related to the temperature history of the mixture during the ignition delay, and is therefore caused by intermediate temperature radical branching. In a simplified approach, the ignition event can be correlated with the brutal consumption of H2O2 giving two OH radicals through reaction (R1):

H2O2 (+M) = OH+OH (+M) (R1)
The duration of the second stage is thus affected by the concentration of HO2 radicals, an important source of H2O2, as well as the temperature and pressure after first stage ignition. It is also true for single-stage ignition at 850 K, where ignition depends solely on intermediate temperature branching. Any source of consumption of HO2 and H2O2 will then increase the second stage of the ignition delay. These experimental results therefore are in agreement with the description of the anti-knock effect of TEL by Pitz and Westbrook [16],

through consumption of HO2 radical and H2O2 onto the surface of lead oxides particles. Indeed, ferrocene will rapidly produce iron oxide particles following attack by the radical pool, with diameters in the order of magnitude of the nanometer [27]. In Fig. 3, the evolution of relative ignition delay variation with ferrocene addition is presented. A monotonic increment of the ignition delay can be observed. When pTDC decreases, the duration of the second stage increases as the reaction rate of (R1) decreases. This could explain the superior effect of ferrocene observed at the lowest investigated pressures.

3-hexene

In order to evaluate the accepted mechanism of the anti-knock effect of organometallics, a similar study was undertaken using 3-hexene. This fuel has higher octane sensitivity than isooctane, very different phenomenology of ignition, associated with additional reaction pathways specific to the double bond. These pathways include addition reactions of radicals to the double bond [19,28], of which HO2 reactions have been identified as particularly important in the low temperature, high pressure oxidation of short alkenes in RCMs [29]. Because of the central position of the double bond in the 3-hexene molecule, it is expected that these pathways are also of great importance in this case.

Figure 4 shows a comparison of the pressure profile at TC = 700 K for all ferrocene compositions. Limited pressure increase is observable right before ignition, due to limited heat release from LTC reactivity, as previously experimentally observed and predicted from kinetic modeling [19,20]. As for isooctane, ferrocene addition increases the ignition delay of 3-hexene. The effect of ferrocene is visible at all pressures for both TC = 700 and 850 K, as shown in Figs. 5a andb.

The increase of ignition delay is monotonic with ferrocene addition without any evidence of saturation (Figs. 6a and6b). The relative increase of the ignition delay is visible at both investigated temperatures and superior than in the case of isooctane, reaching values of about 200% at 20 bar. The increased effect of ferrocene in the case of 3-hexene can originate from the additional pathways of radical addition to the double bond. The addition of OH is usually followed by the addition of the resulting hydroxyalkyl radical to O2, yielding two aldehydes and an OH radical through the so-called Waddington mechanism [30]. The addition of HO2 to the double bond in turn yields a hydroperoxyalkyl radical that can undergo fast decomposition to an oxirane and an OH radical as previously observed in RCM sampling studies [20,[START_REF] Baldwin | Eighteenth Symp. Int. Combust[END_REF]. The addition of HO2 to an allylic radical will result in the formation of a carbonyl and OH, or an unsaturated alkoxy radical and H2O. These pathways are particularly important to predict the global reactivity of the fuel [29], as they form a reactive OH radical from a relatively unreactive radical HO2. Moreover, the branching pathways described for alkanes are globally less effective for alkenes because of the overall inferior reactivity of allylic radicals towards O2 addition and following indirect branching. In the case of 3-hexene, the allylic 3-hexen-2-yl radical will be readily formed. This is true to some extent for all species that are likely to form resonance stabilized radicals, e.g. aromatics. Finally, because of the prominence of HO2 radicals and the easy formation of allylic radicals, the formation of alkadienes through second hydrogen abstraction is easy for 3-hexene and represents a vast proportion of the reactivity [20]. This reaction is exothermic and will therefore facilitate intermediate temperature branching through Reaction (R1). Again, HO2-inhibiting pathways are likely to postpone ignition. These results therefore further confirm the hypothesis of HO2 and H2O2 inhibition by iron oxide particles when ferrocene is added to the fuel.

Simulations

In order to provide further insight into these results and allow qualitative description of the effect of ferrocene, a submechanism describing the decomposition of ferrocene and reactivity of iron oxides particles was built, and added to the LLNL kinetic mechanism of gasoline surrogate fuels [START_REF] Mehl | [END_REF], which contains submechanisms for isooctane and 3-hexene. The ferrocene submechanism consists of the ferrocene thermal decomposition pathway, adopting the rate constant suggested by Lewis et al. [33], as well as addition reactions of OH, HO2, O and H on ferrocene, since the cyclopentadienyl groups are sensitive to radical addition on double bonds. Rate constants for the addition reaction of O and H were proposed by Hirasawa et al. [9], with reaction rates close to the ones observed for alkenes [34], while the reaction rate for the addition of OH is adopted from Tsang [34]. For the addition of HO2, the reaction rate published by Stark [35] was used. These addition reactions on one of the cyclopentadienyl groups of ferrocene lead to the formation of iron cyclopentadienyl (FeC5H5) and another product. The rate constant for the thermal decomposition of FeC5H5 was also given by Hirasawa et al. [9]. The addition reaction rates used for ferrocene were applied in the case of FeC5H5, reduced by a factor of two. A cyclopentadienyl submechanism was already included in the LLNL model. The oxidation of iron atoms, as described by Hirasawa et al. [9], was included with four reactions leading to iron oxide formation. However, the reaction rate for the reaction + + = + exceeded the limit calculated from the collision theory [36], and was therefore reduced to its collision limit, without modification of the performance of the model. Finally, with respect to the simulation work of Pitz and Westbrook [16] for TEL, two reactions of HO2 radical and H2O2 on the surface of iron oxide particles were added. Reaction rates are estimated from the kinetic theory of gases:

= Γ ⁄ 2 ⁄
Where is the surface efficiency; surf/vol is the developed surface of particle per unit of gas volume; m is the mass of the interacting gaseous species. Several assumptions were made in order to simplify the calculation of ksurf: The rate of diffusion of gaseous species through the surrounding gases is not limiting. Also, the particles are supposed to be spherical with a constant diameter during the range of time of the simulation. For HO2 and H2O2, Γ, the surface efficiency, is taken to be unity, as was estimated by Pitz and Westbrook [16] in the case of TEL. The diameter of iron oxide particles was estimated to be 2 nm [27].

It results a succinct sub-mechanism of 16 reactions involving 6 iron-containing species, which is included as supplementary material. Simulations were performed with the sub-routine SENKIN from the Chemkin II package in constant volume conditions, as in the original validation of the LLNL model. It should be pointed out here that this modeling does not aim at providing an in length description of ferrocene reactivity in other conditions than those reached in this study, but rather to further test the hypothesis of an effect on HO2 and H2O2 with help from kinetic modeling. A more detailed study would require state-of-the-art calculation of reaction rate constants, as well as proper description of the particulate matter, and is beyond the scope of this study. Figures 7a andb depict the performance of the model. However, this effect is significantly under-estimated in the case of the 3-hexene experiments. Nevertheless, it is worth emphasizing that the model provides qualitative agreement on the effect of ferrocene in both cases (Fig. 7); the addition of ferrocene always increases the ignition delays, and this increase is monotonic with the mole fraction of ferrocene. The observed disagreement in the case of 3-hexene could result from missing reaction pathways involving HO2 or H2O2 in the ferrocene decomposition mechanism. The hereby developed mechanism was also tested in conditions relevant to a previous study [15], where atomic iron was added to nheptane/air mixtures. The model predicts a reduction of the ignition delay when iron atoms are added, as suggested in [15]. This could be a consequence of the highest extent of Low Temperature reactivity in the case of n-heptane, in comparison with isooctane and 3-hexene.

Conclusions

The effect of ferrocene on the ignition delays of stoichiometric fuel/O2/inert mixtures was experimentally investigated with the ULille RCM, at pressures from 6 to 20 bar, core gas temperatures of 700 and 850 K, and mole fractions of ferrocene up to 900 ppm. Fuels selected were isooctane and 3-hexene, in order to investigate the effect of this octane booster in the case of fuels with significantly different reactivity patterns.

From the experimental results, the addition of ferrocene shows:

-A clear increase of the ignition delay in all conditions. In the case of two-stage ignition, the effect on the first stage ignition delay is limited, and lies mostly in an increase of the second stage of the ignition delay.

-No loss of effectiveness while increasing the mole fraction of ferrocene up to 900 ppm.

-Highest effect in the case of fuels with limited negative temperature coefficient behavior, where HO2 addition reactions are of importance.

These experimental observations concur with the suggestion from Pitz and Westbrook [16] that the mode of action of organometallics on ignition delays lies in an inhibition of HO2 and H2O2, with little to no effect on OH radicals. The oxidation of ferrocene yields gaseous iron that rapidly oxidizes into gaseous iron oxides, which aggregate into particles. On the surface of iron oxide particles, HO2 and H2O2 are converted onto unreactive species.

With respect to this kinetic insight, a 16-reactions kinetic sub-mechanism of the oxidation of ferrocene in the low temperature combustion range of temperature was developed. This sub-mechanism was coupled with a gasoline surrogate model, and yielded qualitative description of the anti-knock effect of ferrocene. While it would be risky to extrapolate on other organometallic octane boosters, the present results suggest that the ability of such molecules to lose their organic moiety, and form oxide particles is one of their most important features. This correlates with the fact that the nature of the metallic atom in such molecules has larger influence on their antiknock properties than the structure of their organic part. This work could therefore be extended to other organo-metallic octane boosters, provided that their decomposition mechanisms are understood.

.

Figure captions

Figure 1 :

 1 Figure 1: Pressure profiles during the two-stage ignition of isooctane/ferrocene/synthetic air mixtures and

Figure 2 :

 2 Figure 2: Evolution of total ignition delays as a function of pressure for isooctane/ferrocene/O2/Ar mixtures.

Figure 3 :

 3 Figure 3: Relative variation of the ignition delay due to ferrocene addition to isooctane as a function of the

Figure 4 :

 4 Figure 4: Pressure profiles during the ignition of 3-hexene/ferrocene/synthetic air mixtures. Φ = 1, pTDC =

Figure 5 :

 5 Figure 5: Evolution of total ignition delays as a function of pressure for 3-hexene/ferrocene/O2/Ar mixtures.

Figure 6 :

 6 Figure 6: Relative variation of the ignition delay due to ferrocene addition to 3-hexene as a function of the

Figure 7 :

 7 Figure 7: Comparison between simulated (lines) and experimental (symbols) relative variation of the total

Figure 7

 7 Figure 7 presents the experimental and modeled relative variations of the ignition delay with ferrocene

Figure 1 :

 1 Figure 1: Pressure profiles during the two-stage ignition of isooctane/ferrocene/synthetic air mixtures and

Figure 2 :

 2 Figure 2: Evolution of total ignition delays as a function of pressure for isooctane/ferrocene/O2/Ar mixtures.

Figure 3 :

 3 Figure 3: Relative variation of the ignition delay due to ferrocene addition to isooctane as a function of the

Figure 4 :

 4 Figure 4: Pressure profiles during the ignition of 3-hexene/ferrocene/synthetic air mixtures. Φ = 1, pTDC =

Figure 5 :

 5 Figure 5: Evolution of total ignition delays as a function of pressure for 3-hexene/ferrocene/O2/Ar mixtures.

Figure 6 :

 6 Figure 6: Relative variation of the ignition delay due to ferrocene addition to 3-hexene as a function of the

Figure 7 :

 7 Figure 7: Comparison between simulated (lines) and experimental (symbols) relative variation of the total

Acknowledgements

This work has been funded by Total Marketing Services.

Supplementary Material

Ferrocene sub-mechanism, in Chemkin format. Table of the measured and simulated ignition delays.


Romain Grosseuvres
email: romain.grosseuvres@cnrs-orleans.fr

A Comandini

A Bentaib

N Chaumeix

Combustion properties of H2/N2/O2/Steam mixtures

Keywords: Laminar Flames, Detonations, Explosions, and Supersonic Combustion nuclear safety, combustion parameters, laminar flame speed, hydrogen

Word equivalent length of main text:

3562 words equations:

Eq(1) : 8 words references:

822 words figures + captions: Supplemental material available

Introduction

During severe accident in Pressurized Water Reactor (PWR), the interaction between the fuel rod and steam leads to the build-up of an explosive atmosphere inside the containment building [2]. This atmosphere is mainly composed of hydrogen, oxygen, nitrogen and water vapor. In case of an ignition by an energy source (electrical discharge spark, hot surface, etc.), a flame occurs and is capable to threaten the containment building. To assess such scenario, CFD codes permit to model flame propagation in equivalent environment [2][3]. Furthermore, under certain conditions the flame which is propagating in the containment building can accelerate and undergo transition to detonation [4][5]. For these reasons it is a need to determine the laminar flame speed of H2/N2/O2 mixtures. First because the laminar flame speed is one of the fundamental input data to the CFD codes. Then it permits to evaluate fundamental parameters (laminar flame thickness δ, effective Lewis number Leeff, overall activation energy Ea, Zel'dovich number β) which are directly involved in the criterion of flame acceleration permitting to distinguish fast flames from slow flames [2,5]. Substantial work has been conducted to determine laminar flame speed of hydrogen/air mixtures in ambient conditions (Tini=296-300K; Pini= 100-101.3kPa) [6][7][8][9][10][11][12][13][14][15][16]. Fewer experiments were performed at high temperature with or without steam. Some of them were directly addressed to the hydrogen/air mixtures [16][17][18][19] while some others concerned mixtures of syngas (H2/CO) on restricted equivalence ratio domain [20,21] or stoichiometric hydrogen/oxygen mixture [22]. Then, also a limited number of studies have been conducted on the dilution with nitrogen [6,9,19,23].

In the present investigation, new experimental data on the laminar flame speed were obtained using the spherical bomb method of H2/N2/O2/Steam mixtures over a wide range of initial conditions (Tini= 296, 363, 413 K; Pini= 100kPa; N2/O2=3.76, 5.67, 9; %mol.Steam=0, 20, 30). The fundamental parameters mentioned above were calculated from numerical simulations using the Mével mechanism [1] and some of them were derived from the experimental data. For H2/Air mixtures at 296 K and H2/Air mixtures diluted with 20%mol.Steam at 363K several kinetic models (the model of Li [24] and the GRI-Mech 3.0 mechanism [25]) were used in order to compare their impact on these combustion parameters and on SL 0 .

Material and method

The experiments leading to the laminar flame speeds measurements were conducted in two different stainless steel spherical bombs. The first one [26] was used for ambient temperature studies (296K), and the second one [27] for high temperatures studies (363, 413K). These two vessels are similar, they differs only by their volume: 93L and 56L. Both vessels are made of two concentric spheres permitting the circulation of a heat transfer fluid in order to regulate the inside temperature. For the high temperatures studies, a septum injector nut is directly connected to the vessel for the liquid water injection. For both devices, two opposite quartz windows for optical observations are mounted. The spark-ignition of the mixture is realized by two thin tungsten electrodes located along a diameter of the sphere which are linked to a high voltage and adapted probes to monitor the input power. High frequency pressures transducers (Kistler 601A/6001) are mounted flush with the inner wall to measure the pressure during the combustion. To observe the flame propagation and measure the laminar burning velocity, a Z-type Schlieren arrangement and high-speed camera are employed.

Two different cameras were used: for SL 0 higher than 3m/s we used Phantom V2520 up to 39 000 image/s and for SL 0 lower than 3m/s we used Phantom V1610 up to 25 000 image/s. The flame radius is extracted from the images via a home-made code based on Matlab® [START_REF] Matlab | The Matworks Incorporated, Version[END_REF] which detects the position of the flame front [27] with an uncertainty of ±1pixel. The spark triggers the camera recording, the measurement of the pressure and the input power via a TTL generator connected to the electrodes.

The mixtures were prepared directly in the bomb using the partial pressure method. All the gas components were supplied by Air Liquide (purity>99.9999%). The air is composed of 20.9% O2 + 79.1% N2. For experiments with steam, water vapor was obtained by the vaporization of liquid water (distilled water). Each time, the water vapor partial pressure was checked to be less than the saturated value in order to make sure that all the liquid phase has evaporated. The partial pressures and the initial total pressure were measured using different capacitance manometers: MKS 690A Baratron and MKS 631. The uncertainties on the equivalence ratio and on the steam molar fraction are respectively ±0.8% and ±0.15%. For experiments conducted in the 93L bomb, considering the large vessel volume the 8 fans were used in order to mix the mixture during 2 minutes. After this time, fans were stopped and the mixture was resting during 5 minutes before the ignition in order to dissipate the turbulence induced by this mixing process. This time was considered to be sufficient since there was no significant difference in the measured laminar flame speed over 20 minutes of resting is reported in the Fig. S1 in the Supplemental material. In the same way for experiments conducted in the 56L bomb, mixtures were also resting during 5 minutes after the filling process to remove any turbulence [27]. The initial temperature was checked prior to the ignition. Experiments were conducted at initial pressure of 100 kPa and initial temperatures of 296, 363, 413 K.

The laminar flame speed is defined as the unburned gases velocity in a normal direction relative to the flame front. Considering an outwardly expanding flame, curvature and strain rate have to be considered to determine this velocity. Indeed, local stretch induces a modification of the flame front upstream flow [START_REF] Mével | [END_REF]. From the flame front images obtained in the spherical bomb ((Fig. 1(a)) the flame radius is deduced from which one can easily calculate a burning speed VS = dRf/dt. Unstretched velocity VS 0 are determined considering a non-linear variation of the flame speed with the stretch rate. Several relations can be used [30][31]. In the present study, the non-linear equation proposed by Ronney and Sivashinsky 6 [32] and modified later by Kelley and Law [33] (noted NQ for Quasi-steady Nonlinear model in [31])

was used. The laminar flame speed SL° and the Markstein length are derived from the solution of the following equation [27,34]: An example of the unstretched velocity extraction is given in Fig. 1(c). The range of experimental radius used in this data processing was from 10 to 70 mm in the 93L vessel and from 10 to 46 mm in the 56L vessel. The minimum radius was defined in order to remove the influence of the ignition energy while the maximum radius was chosen to avoid pressure effect on the laminar flame speed [35] (Fig. 1(b)).

V S V S 0 2 • ln V S V S 0 2 =- 2L b •κ V S 0 (1)
Since the pressure remains constant during the observation time, the laminar flame speed, SL° is determined by the ratio VS°/σ, σ being the expansion ratio (=ρu/ρb). The densities of the unburned and burned gases (respectively ρu and ρb) are calculated by using the equilibrium code of COSILAB® [START_REF] Cosilab | The Combustion Simulation Laboratory[END_REF].

Numerical calculations

To establish criterion of flame acceleration for the safety analysis, the combustion parameters (δ, Leeff, Ea, β) of H2/N2/O2/Steam mixtures have to be determined by the laminar flame speeds simulations.

Therefore, the detailed kinetic mechanism which should be used has to be selected based on his capability to reproduce experimental results for H2/N2/O2 mixtures over a wide range of initial conditions. For the present study, the Mével mechanism was used [1] because of its validation against a variety of experimental results for H2/N2/O2 mixtures [START_REF] Mével | [END_REF] (laminar flame speeds, ignition delay times, detonation velocities and detonation cells widths). These simulations were conducted by using the one dimensional freely propagating flame code of COSILAB® [START_REF] Cosilab | The Combustion Simulation Laboratory[END_REF].

Following the Zel'dovich analysis [START_REF] Zel | The mathematical theory of combustion and explosions[END_REF], The activation energy is the slope of the plot of 2*lnSL 0 = f(1/Tb).

To calculate the Lewis number of our mixtures, the definition corresponding of a weighted average of the reactants Lewis number was used [START_REF] Addabbo | [END_REF].

Results and discussion

Laminar flame speed uncertainties

Many parameters can be potential uncertainties on the laminar flame speed determination from a spherical expanding flame [31,[40][41]. These parameters were carefully taken into account in the present study: experimental conditions, radiative heat losses and extrapolation process. This section presents how these uncertainties sources were fixed in order to assess the accuracy of the experimental results.

Experimental conditions

For each experiment, the initial conditions were well-known (∆Pini = ±0.5kPa, ∆Tini = ±1K, ∆φ = ±0.8%). The ignition energy for each test was measured (10mJ maximum). There had been very careful consideration of the electrodes implementation (alignment, gap between the tips, diameters) in order to reduce flame-electrodes interactions.

Radiative heat losses

Radiative heat losses can lead to a decrease of the flame speed [42]. In the present study, in order to verify that flames were not greatly influenced by radiation, the equation proposed in [43] was used to calculate the radiation-corrected flame speed. Results are presented in Fig. 2. One can see that differences between laminar flame speed experimentally obtained and radiation-corrected flame speed varies from 0.37 to 0.67 cm/s leading to a maximum uncertainty of 2%. Furthermore it was also checked that any bending was observed on flame speed profiles (Fig. 1(c)). Indeed as investigated in [44],

bending on the flame speed profiles is a characteristic of flames which are greatly affected by the radiation effects.

Extrapolation process

As aforementioned in the previous section, different relations can be used to extract the unstretched velocity VS 0 using the spherical expanding flame method [30][31]. To verify that the present data are not impacted by the extrapolation method, the four extrapolation methods have been used to derive VS° and Quasi-steady nonlinear model (NQ) (notations based on the one used in [31]). The results obtained with these different models are presented in Fig. 3. It is visible that all the models give very close results on the entire equivalence ratio domain, with a maximum standard deviation (9.65cm/s) obtained at φ=2.11. We can also notice that the uncertainties of the results obtained with the model used in the present study (NQ) encompass the results obtained from the other results. This good agreement is due to the large radii used here to derive the laminar flame speed [30]. The impact of the extrapolation process can also be studied by using the relation proposed in [31] which corresponds to the product between the Markstein number (obtained using the LS model) and the Karlovitz number calculated at the middle radius for each experiment. Wu et al. [31] showed that to minimize extrapolation uncertainties, experiments should be conducted in the range of -0.05<Malinear.Kamiddle<0.15. The product Malinear.Kamiddle was calculated for all experiments conducted in the present study and reported with these limits in Fig. 3. One can see that only few experiments in lean and rich conditions may be slightly less accurate due to non-unity values of the Lewis number [31].

Laminar flame speed and Markstein lengths

The laminar flame speeds obtained from the spherical bomb method are reported in Fig. 4 for the three initial temperatures and the three ratios N2/O2 investigated. Results obtained for H2/Air mixtures at 363K and 413K with 20 and 30%mol. of steam are also reported. It has to be noted that for N2/O2=9 at Tini=296K and for N2/O2=3.76 at Tini=363 and 413K, investigated domain of φ was reduced due to nonignitable mixtures in rich conditions. Results obtained for H2/Air mixtures at 296K were compared with the literature ones. This comparison is reported in the Supplemental material, Fig. S2. In each case, the maximum of the laminar flame speed is obtained for equivalence ratio between 1.6 and 1.8. As expected, the flame speed increases with increasing the initial temperature and decreasing ratio N2/O2

(nitrogen playing the role of diluent). For a fix ratio N2/O2=3.76 the steam dilution presents also a strong impact on the speed profile. In average SL 0 decreases of 41-42% or 62-65% when 20%mol. or 30%mol.

of steam is added to the H2/Air mixtures at 363K and 413K. Fig. 4 also contains the simulated SL° obtained with Mével mechanism [1]. Overall the simulation results follow the same trend as the experimental results. They are in very good agreement for lean and stoichiometric mixtures in dry conditions, and for ultra-rich mixtures with steam. Nevertheless, two other kinetic mechanisms [24][25] were used in order to operate a comparison on the laminar flame speed for H2/Air mixtures at 296K and H2/Air mixtures diluted with 20%mol.Steam at 363K. The comparison between the results from these numerical calculations is reported in the Supplemental material, Fig. S3. For dry and wet cases, the models results are quite in agreement with SL 0 obtained experimentally. For H2/Air mixtures at 296K large discrepancies can be observed for lean mixtures between experimental and numerical results.

Indeed for all the reaction models these differences oscillate between 8.9 and 11.8%. Better agreements are obtained for the largest laminar flame speeds (1.4≤φ≤1.8) while divergences increase for ultra-rich mixtures except with the GRI kinetic mechanism at φ=2.4 and φ=2.9 where the differences are lower than 4.5cm/s. Considering the experimental errors, the Li model presents the best predictions with an average error around 3%. For H2/Air/Steam mixtures at 363K, all the reaction models underestimate the laminar flame speeds although they present the same trend as the experimental results. This can be explained by the fact that radiations effect is not taking into account in the simulations. Indeed, radiations absorption by fresh gases plays an important role in enhancing SL 0 especially with three atomic molecules like water vapor which heat capacity is important. However, it appears that the Mével reaction model permits to present the best predictions on the entire equivalence ratio domain with an average error of 7.1%.

Eq(1) permits also to obtain the burned gases Markstein length LB and consequently the unburned gases Markstein length L' (L'=LB/σ). For the experimental sets in Fig. 4, L' are reported in Fig. 5. Except for certain flames in lean mixtures (especially for mixtures diluted with steam), one can see that for each initial condition on almost the entire range of equivalence ratio studied flames are stable (L'>0). While the initial temperature does not affect the response of the flame to the stretch, it appears that increasing the nitrogen dilution (increasing ratio N2/O2) leads to an increase of the instabilities for lean and stoichiometric mixtures. As an example, for stoichiometric mixtures L' is becoming negative when N2/O2 is increasing from 3.76 to 9. For N2/O2=3.76, the steam dilution appears to have a stronger impact on the Markstein length, making unstable flame from lean mixtures and more stable flame from ultrarich (φ>2) mixtures. As mentioned previously, combustion parameters for safety analyses are inferred from laminar flame speeds such as the laminar flame, the thickness δ, the effective Lewis number Leeff, the overall activation energy Ea and consequently the Zel'dovich number β.

Laminar flame thickness

The definition of the flame thickness can be based on the thermal diffusivity (δtherm=λ/ρ.Cp.SL 0 ) or on gradient of temperature (δgradT=(Tburned gases-Tunburned gases)/(dT/dx)max)). 1-D simulation was operated in order to obtain the flame temperature profile and the other thermal parameters. Fig. 6 reports the values of δgradT for the mixtures considered in the present study while δtherm is reported in the Supplemental material, Fig. S4. The results from the two methods can present important differences. Indeed, the calculation using the temperature gradient leads to thicknesses higher than the ones calculated from the thermal diffusivity by a factor between 4.17 to 19.64. It can be noted for both flame thickness calculations the ratio N2/O2 is the parameter which has the most influence. For the calculation based on thermal diffusivity, the temperature appears to have a minor impact except for the ratio N2/O2=9 where the lowest temperature leads to have the thicker flame. On contrary, for the calculation based on gradient of temperature a measurable variation is observed when the initial temperature is varied and the maximum flame thickness is obtained at 413K.

As for SL 0 , laminar flame thicknesses were also calculated with two others kinetic mechanisms for H2/Air mixtures at 296K and H2/Air mixtures diluted with 20%mol.Steam at 363K in order to study the impact of the kinetic model. A comparison between the numerical results is presented in the Supplemental material, Fig. S5. One can see as in the previous results that for each reaction model, δgradT always gives much larger values than δtherm. For dry and wet mixtures all the mechanisms present very similar δtherm excepted for lean and ultra-rich mixtures while noticeable differences can be noted on δgradT. For H2/Air mixtures at 296K, the models of Mével and Li provide comparable results whereas the GRI mechanism gives always lower values excepted at φ=3.5 and 4. For H2/Air/Steam mixtures at 363K, δgradT can present large variations (from 29.5 to 90.4µm) according to the kinetic mechanism used.

Effective Lewis number

Fig. 7 reports the values of Effective Lewis numbers for the mixtures considered in the present study.

The Lewis numbers of the reactants (H2 and O2) are also figuring in order to illustrate that the Leeff of the mixture is driven by LeH2 in lean conditions and by LeO2 in rich conditions [START_REF] Addabbo | [END_REF]. Following the trend of L' (Fig. 5), it has to be noted that the majority of the studied flames are stable (Leeff>1) except for some conditions (φ=1 at N2/O2=3.76 with 20%mol.Steam, φ=1 at N2/O2=9 and also for lean mixtures in every conditions). It is also visible that the dilution by N2 (increasing ratio N2/O2) or by steam leads to a decrease of the Leeff. In particular we can notice stoichiometric mixtures which are becoming unstables (Leff<1) when the ratio N2/O2 increases from 5.67 to 9 or when the steam is added.

Overall activation energy and Zel'dovich number

Calculation results of the Overall Activation Energy are reported in the Supplemental material, Fig. S6.

The evolution of β with the equivalence ratio is presented in Fig. 8. In each case, the minimum of β is obtained at the equivalence ratio for which the laminar flame speed is the highest one. As it could be intuitively predicted, the reactivity of the mixtures of interest increases with the temperature and decreases with the dilution by nitrogen or steam. The decrease of β with the initial temperature increases when the dilution by N2 increases. The average decreasing at N2/O2=3.76 is around 13.1% while it is approximately 22.6% at N2/O2=9. For dry mixtures β was also derived from SL 0 obtained experimentally. A comparison between the β derived from experiments and the one obtained numerically with Mével model is reported in the Supplemental material, Fig. S8. In order to increase the number of data, a fit was applied on the experimental curve SL 0 =f(φ) as reported in the Supplemental material, Fig. S9. As one can see, trends are very well reproduced with the mechanism for ratios N2/O2=5.67 and 9. Furthermore, an excellent agreement can be observed at 363 and 413K for N2/O2=5.67 while for N2/O2=9, β is always slightly overpredicted. For N2/O2=3.76 and Tini=296K, results from simulation are shifted toward the richer mixtures, whereas at 363 and 413K large discrepancies and an excellent agreement can be noticed respectively for φ<2 and φ≥2.

Conclusions

Expanding spherical flames of H2/N2/O2 mixtures have been studied for a wide range of equivalence ratios φ (0.8 ≤ φ ≤ 4), initial temperatures (296, 363 and 413K) and N2/O2 ratios (3.76, 5.67, 9) at 100 kPa. From these experiments, SL°, L' have been determined. Moreover, the effect of steam addition to the mixtures was also investigated (20, 30%mol of steam). Higher temperatures and ratio N2/O2 promote faster flame propagation while steam addition has a suppressing effect. Mével chemical kinetic model was used in order to simulate laminar flame speeds in the same initial conditions and was compared to the results. Good agreements between experimental and simulated results were observed. This validation demonstrates that this model can be used to simulate premixed flame properties relevant to combustion hazard evaluation in NPP [START_REF] Breitung | Flame Acceleration and Deflagration-to-Detonation Transition in Nuclear Safety[END_REF]. Moreover, SL 0 is also important for the use of CFD codes where it is used as a normalizing parameter for the determination of the turbulent flame speed. The model was

List of Figures

Fig. 1

 1 Total Length of Paper: 6156 words (Method 1)

Fig. 1 .

 1 Fig. 1. Example of results for a H2/air flame at φ=3.6, Tini=296K, Pini=100kPa. (a): flame images, (b): recorded pressure profile, (c) flame speed versus stretch rate.

Fig. 2 .

 2 Fig. 2. Evaluation of the radiation-corrected flame speed according to [43].

  obtained at 413K for H2/Air mixture: Linear model based on curvature (LC), Linear model based on stretch (LS), Nonlinear model with 3 fitting parameters (N3P), Nonlinear model in expansion form (NE)

Fig. 3 .

 3 Fig. 3. Extrapolation models on SL 0 (a) and {MalinearxKamiddle} parameter (b) for H2/Air mixtures, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 4 .

 4 Fig. 4. Laminar flame speeds of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K, Pini=100kPa. Symbols: experiments; Lines: simulations.

Fig. 5 .

 5 Fig. 5. Markstein lengths L' of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 6 .

 6 Fig. 6. Calculated δgradT of H2/N2/O2/Steam mixtures with the Mével model, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 7 .

 7 Fig. 7. Effective Lewis numbers of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 8 .

 8 Fig. 8. Calculated Zel'dovich numbers of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 1 .

 1 Fig. 1. Example of results for a H2/air flame at φ=3.6, Tini=296K, Pini=100kPa. (a): flame images, (b):

Fig. 2 .

 2 Fig.2. Evaluation of the radiation-corrected flame speed according to[43].

Fig. 3 .

 3 Fig. 3. Extrapolation models on SL 0 (a) and {MalinearxKamiddle} parameter (b) for H2/Air mixtures,

Fig. 4 .

 4 Fig. 4. Laminar flame speeds of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 5 .

 5 Fig. 5. Markstein lengths L' of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K, Pini=100kPa.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Calculated δgradT of H2/N2/O2/Steam mixtures with the Mével model, Tini=296K, 363K, 413K,

Fig. 8 .

 8 Fig. 8. Calculated Zel'dovich numbers of H2/N2/O2/Steam mixtures, Tini=296K, 363K, 413K,

subsequently used to perform calculations of the following parameters: laminar flame, thickness δ, effective Lewis number Leeff, overall activation energy Ea, Zel'dovich number β. These new data permit to estimate the flame acceleration criterion in case of mixtures diluted with water vapor.

Acknowledgements

The present study was funded by Programme Investissement d'Avenir-MITHYGENE Grant agreement n°ANR 11-RSNR-0015.

List of supplemental material

• Supplemental_Material_Combustion properties of H2 N2 O2 Steam mixtures.pdf