M Guillaume Dayma

Natalia Mme

D R Titova

Christine Mme

Mounaïm-Rousselle

M Pierre-Alexandre

Glaude D R Au Lrgp

M Denis

Membres du

Acknowledgement

I want to express my deep gratitude to my supervisors, Pierre-Alexandre Glaude and Denis Anatolevich Knyazkov. Thanks to these people I got the opportunity to get in touch with a real scientific activity. They taught me how to perform an experiment or modeling, they taught me to formulate my ideas. My supervisors have introduced me to the scientific community and came up with the greatest adventure of my life, a joint French-Russian PhD program. At the same time I am very grateful to them for the fact that they have always provided freedom of my scientific thought.

I also want to say "merci beaucoup" to Valérie Warth, Juan Carlos Lizardo-Huerta, René Fournet, Frédérique Battin-Leclerc, Hervé LeGall and the entire KinCom team (now CiTherE) who welcomed me warmly in Nancy, shared their knowledge and helped me in my work.

I say "большое спасибо" to Andrey Gennadevich Shmakov, Tatyana Anatolevna Bolshova, Kseniya Nikolaevna Osipova, Ilya Evgenevich Gerasimov and the entire laboratory of Kinetics of Combustion Processes in Novosibirsk for their everyday help and support in the work on the thesis.

In conclusion, I want to thank all my family and friends for their patience and understanding. Special thanks to my grandfather, who gave me so much and who has always been an example of fortitude for me.

Table of contents

INTRODUCTION 1.1. FATTY ACID ESTERS AS A RENEWABLE BIOFUEL

The continuously growing consumption of energy resources and the struggle for the ecological safety of the energy sector are forcing researchers all over the world to develop new energy sources. One of the key topics is looking for renewable fuels as alternative to the fossil fuels. Special attention is paid to alternative fuels for the transportation sector, since such fuels must correspond to a variety of physical, chemical and economic factors straight away. At the same time liquid hydrocarbon fuels remain to be the best solution for long-distance transportation due to its high energy density [START_REF] Yu | Suitability of energy sources for automotive application -A review[END_REF]. In this regard, internal combustion engines (ICE) will remain the main driving force of the transportation for a long time despite the rapid development of electric vehicles.

[2], [START_REF] Reitz | IJER editorial: The future of the internal combustion engine[END_REF]. In such circumstances searching for the environmental friendly alternative fuels for ICE is an urgent task which is being solved in developed countries all over the world.

Liquid biofuels based on fatty acid esters appeared to be one of the possible solutions to this problem. Such fuels are renewable, as they are produced from biomass, they have a fairly high energy density and ester biofuels almost do not form soot and polyaromatic hydrocarbons during combustion [START_REF] Bergthorson | A review of the combustion and emissions properties of advanced transportation biofuels and their impact on existing and future engines[END_REF]. Also, bioderived fuels considered as carbon-neutral since carbon dioxide produced in combustion was previously captured in the biomass from the atmosphere. At the same time, such a fuel has physical characteristics close to conventional gasoline or diesel fuel which allows it to be used either in pure form or in a mixture with traditional fuel without significant modification of engines [START_REF] Agarwal | Biofuels (alcohols and biodiesel) applications as fuels for internal combustion engines[END_REF], [START_REF] Hossain | Plant oils as fuels for compression ignition engines: A technical review and life-cycle analysis[END_REF]. Fatty acid esters could be roughly divided into light (C2-C8) and heavy (C9 and heavier).

According to boiling points and viscosity, light fatty acid esters are considered as fuel additives to gasoline to reduce the consumption of conventional petroleum gasoline. At the same time, it is noted in several works that the addition of light esters increases the octane number of the fuel mixture [START_REF] Lange | Valeric Biofuels: A Platform of Cellulosic Transportation Fuels[END_REF]- [START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF]. Physical properties of heavier esters are close to those of the diesel oil fractions [START_REF] Atabani | A comprehensive review on biodiesel as an alternative energy resource and its characteristics[END_REF]- [START_REF] Mofijur | Chapter Fourteen -Assessment of Physical, Chemical, and Tribological Properties of Different Biodiesel Fuels[END_REF], therefore mixtures of heavy fatty acid esters are called biodiesel. Biodiesel and ethanol are the most common alternative liquid fuels for internal combustion engines, which already exist on the fuel market and actively used in a number of countries [START_REF] Agarwal | Biofuels (alcohols and biodiesel) applications as fuels for internal combustion engines[END_REF], [START_REF] Chauhan | Practice of diesel fuel blends using alternative fuels: A review[END_REF]. In particular, there are technological standards for the biodiesels and it mixtures with conventional fuels in the European Union (EN 14214) [START_REF]Liquid petroleum productsfatty acid methyl esters (FAME) for use in diesel engines and heating applications -requirements and testmethods[END_REF], USA (D6751-02, D7467 -20a) [START_REF]Specification for Biodiesel Fuel Blend Stock (B100) for Middle Distillate Fuels[END_REF], [START_REF]Specification for Diesel Fuel Oil, Biodiesel Blend (B6[END_REF], Canada (CAN/CGSB-3.524) [START_REF]SCC Standard CAN/CGSB-3.524-2017[END_REF] etc. At the moment, the main problem of introducing such types of fuel remains the higher production costs compared to the traditional gasoline and diesel [START_REF] Bergthorson | A review of the combustion and emissions properties of advanced transportation biofuels and their impact on existing and future engines[END_REF]. Nevertheless, in many countries there are government programs for the development of the biofuel industry which stimulates development of new cost-effective technologies for the biomass refinery and biofuel production from a variety of raw materials [START_REF] Bozbas | Biodiesel as an alternative motor fuel: Production and policies in the European Union[END_REF]- [START_REF] Joo | World Biodiesel Policies and Production[END_REF]. By itself the biodiesel is a mixture of fatty acid esters which is most often produced during the transesterification reaction of fats (triglycerides) with light alcohols [START_REF] Bozbas | Biodiesel as an alternative motor fuel: Production and policies in the European Union[END_REF][START_REF] Кугучин | Мировая индустрия биотоплива: общая характеристика, история и факторы развития отрасли[END_REF]. As usual the cheapest and commercially available alcohols are used for these purposes, such as methanol (CH3OH) and ethanol (C2H5OH). In the case of transesterification with methanol fatty acid methyl esters (FAME) are formed, and in the case of the reaction with ethanol fatty acid ethyl esters (FAEE) are formed. The by-product of the transesterification is glycerin which is a useful product in itself. The general reaction scheme is shown in Figure 1. 1. The choice between methanol and ethanol is determined by a number of factors since both alcohols have their own advantages and disadvantages.

Methanol has a higher reactivity in the transesterification process in comparison with ethanol. Also, methanol is easier to remove at the stage of the final product cleaning [START_REF] Yusoff | Comparison of Fatty Acid Methyl and Ethyl Esters as Biodiesel Base Stock: a Review on Processing and Production Requirements[END_REF]. In industry methanol is mainly obtained from the synthesis gas which makes methanol quite cheap. The last factor is decisive in the choice of alcohol for the industrial production of biodiesel at the moment. However, such fuel is not fully renewable, since methanol for its production is obtained from the non-renewable sources (natural gas and coal). Also, high toxicity and corrosive effects on metals are the significant disadvantages of methanol. Unlike methanol, ethanol is significantly less toxic making production much safer. Moreover, production of ethanol from the renewable sources is already well established and is constantly evolving towards lower prices. [START_REF] Gutiérrez | Process integration possibilities for biodiesel production from palm oil using ethanol obtained from lignocellulosic residues of oil palm industry[END_REF]- [START_REF] Verma | Review of process parameters for biodiesel production from different feedstocks[END_REF]. The use of bioethanol makes biodiesel a completely renewable energy source. The advantages of ethanol also include a higher reaction yield in terms of the mass ratio of FAEE/triglyceride and better solubility of fats in ethanol [START_REF] Encinar | Ethanolysis of used frying oil. Biodiesel preparation and characterization[END_REF]- [START_REF] Li | Ethanol as the acyl acceptor for biodiesel production[END_REF]. In addition, many studies have noted that biodiesel based on FAEE has better fuel characteristics than those of FAME-mixtures [START_REF] Makareviciene | Environmental effect of rapeseed oil ethyl ester[END_REF]- [START_REF] Reyero | Kinetics of the NaOHcatalyzed transesterification of sunflower oil with ethanol to produce biodiesel[END_REF]. This is also an argument in favor of using ethanol for the transesterification. The main disadvantage of ethanol is its higher cost compared to methanol. It should be noted that using methanol and ethanol simultaneously is also considered as an effective approach in biodiesel production [START_REF] Yusoff | Comparison of Fatty Acid Methyl and Ethyl Esters as Biodiesel Base Stock: a Review on Processing and Production Requirements[END_REF], [START_REF] Kim | The synergistic effect of alcohol mixtures on transesterification of soybean oil using homogeneous and heterogeneous catalysts[END_REF].

Almost any kind of biomass with a high fat content can be used as a feedstock. The main requirements for are low price and high production volumes of the feedstock. In the last decade a huge number of possible raw materials have been proposed for the production of biodiesel. On the one hand, a lot of possible resources have expanded the possibilities of biofuel production, but on the other hand, such diversity has complicated the technical verification and standardization of the fuels. At the moment, various kinds of oilseeds are the main sources from which vegetable oil can be extracted for the further transesterification [START_REF] Knothe | Biodiesel fuels[END_REF], [START_REF] Santori | A review analyzing the industrial biodiesel production practice starting from vegetable oil refining[END_REF]. More than 350 types of crops have been proposed as potential raw materials for biodiesel production [START_REF] Atabani | A comprehensive review on biodiesel as an alternative energy resource and its characteristics[END_REF]. However biodiesel production technologies from other types of raw materials have been actively developed in recent years. Let's consider in more detail the classification and types of the raw materials for the biodiesel production.

It is customary to classify biodiesels in literature by generations depending on the feedstock. However, the number of generations in different sources varies from three [START_REF]The current status of biofuels in the European Union, their environmental impacts and future prospects[END_REF] to four [START_REF] Singh | A review on feedstocks, production processes, and yield for different generations of biodiesel[END_REF] or five [START_REF] Hajjari | A review on the prospects of sustainable biodiesel production: A global scenario with an emphasis on waste-oil biodiesel utilization[END_REF]. It seems most logical to consider four generations of biodiesel fuels according to the classification from the work [START_REF] Singh | A review on feedstocks, production processes, and yield for different generations of biodiesel[END_REF].

First of all biodiesels are distinguished as the fuel from edible or inedible plant materials, the so-called first and the second generation of biodiesels. Edible crops such as soybeans, sunflowers, rapeseed, peanuts and others contain a lot of vegetable oil and are grown in large quantities in many countries. Agrarian production of these plants is well established. Therefore edible oilseeds were the first one feedstock proposed for the biodiesel production. However, the use of edible plants for the fuel production poses a number of serious problems. First of all it is a lack of arable lands, high production costs and conflicts with the food industry. Moreover, the use of edible crops is unsustainable in the long term, since the increasing fuel demands will not be covered by the production of edible crops [START_REF] Hill | Environmental, economic, and energetic costs and benefits of biodiesel and ethanol biofuels[END_REF], [START_REF] Chapagain | Desert date (Balanites aegyptiaca) as an arid lands sustainable bioresource for biodiesel[END_REF]. In view of the problems discussed the attention of researchers and producers has turned to inedible oilseeds such as oil palm, jatropha, karanja and many others [START_REF] Atabani | Non-edible vegetable oils: A critical evaluation of oil extraction, fatty acid compositions, biodiesel production, characteristics, engine performance and emissions production[END_REF]. As a rule industrial oilseeds are less demanding on agricultural technologies and soil quality, therefore they can be grown in more difficult conditions and at a lower cost. The use of inedible crops allows biomass production to be adapted to the geographic characteristics of the region that significantly increases the availability and economic attractiveness of the biodiesels. Another major advantage of these raw materials is the lower content of sulfur and aromatic substances that significantly improves the quality of the resulting fuel. The main disadvantages are the need to collect raw materials from large territories and the insufficient development of technologies for processing various types of crops [START_REF] Atabani | Non-edible vegetable oils: A critical evaluation of oil extraction, fatty acid compositions, biodiesel production, characteristics, engine performance and emissions production[END_REF].

Aside from the plant crops, food by-products such as beef, lard, used frying oil, fish or poultry oil can be also used as raw materials for the biodiesel production [START_REF] Öner | Biodiesel production from inedible animal tallow and an experimental investigation of its use as alternative fuel in a direct injection diesel engine[END_REF], [START_REF] Montefrio | Recovery and pre-treatment of fats, oil and grease from grease interceptors for biodiesel production[END_REF]. This group of biofuel feedstock is considered as the third generation of biodiesels, but sometimes it is also referred to the second generation. Such fats are produced in large quantities all over the year, they do not require special production and agricultural territories. Besides, the use of waste oils as the raw materials helps to solve the problem of waste disposal. Since 70-80% of the biodiesel production costs is determined by the price of the raw materials [START_REF] Gebremariam | Economics of biodiesel production: Review[END_REF] the use of waste oils can significantly reduce the total cost of the final product. It is noted that processing fatty waste is more profitable than growing special crops for some countries with arid climates [START_REF] Hajjari | A review on the prospects of sustainable biodiesel production: A global scenario with an emphasis on waste-oil biodiesel utilization[END_REF]. The use of fatty food waste is considered as the most profitable strategy for the production of biofuels at the moment by a number of experts. [START_REF] Riazi | Renewable diesel from oils and animal fat waste: implications of feedstock, technology, co-products and ILUC on life cycle GWP[END_REF], [START_REF] -F. Abomohra | Potential of fat, oil and grease (FOG) for biodiesel production: A critical review on the recent progress and future perspectives[END_REF]. The key disadvantages of these raw materials are the food impurities and high water content which reduce the useful product yield during transesterification. In this regard the raw materials from wastes require serious preliminary treatment that consequently complicates production and ultimately affects the biofuel price [START_REF] Atabani | A comprehensive review on biodiesel as an alternative energy resource and its characteristics[END_REF], [START_REF] -F. Abomohra | Potential of fat, oil and grease (FOG) for biodiesel production: A critical review on the recent progress and future perspectives[END_REF], [START_REF] Talebian-Kiakalaieh | A review on novel processes of biodiesel production from waste cooking oil[END_REF].

According to many scientists the most promising raw material for the biodiesel production are microalgae. The microalgae biofuels are often called the fourth generation of biodiesels [START_REF] Chisti | Chapter 1 -Introduction to algal fuels[END_REF]- [START_REF] Suganya | Macroalgae and microalgae as a potential source for commercial applications along with biofuels production: A biorefinery approach[END_REF]. Microalgae number tens of thousands of naturally and artificially bred cultures. During the photosynthesis process they absorb carbon dioxide and sunlight increasing their biomass, and the efficiency of this process is much higher than that of terrestrial plants. Dry microalgae can be used as a fuel directly or can be converted into the feedstock for a variety of biofuels, including triglycerides [START_REF] Chisti | Fuels from microalgae[END_REF]. Some types of microalgae can produce and store fat in their cells up to 70% of their dry weight. For comparison, in ordinary plants this value is about 5% [START_REF] Malcata | Microalgae and biofuels: A promising partnership?[END_REF]. During mechanical or chemical processing triglycerides can be extracted from the microalgae [START_REF] Mubarak | A review on the extraction of lipid from microalgae for biodiesel production[END_REF]. The large yield per unit mass, rapid growth and relatively small production areas make microalgae potentially the most efficient and sustainable feedstock for the biofuel industry in the long term. Despite the already existing startups of microalgae biofuel production, the large-scale production does not seem to be profitable yet due to a number of serious technological difficulties. [START_REF] Chisti | Constraints to commercialization of algal fuels[END_REF]. The key problems are the lack of sunlight and carbon dioxide when algae are grown in large vessels. Because of this, the yield of a useful product drops significantly. Also, microalgae require phosphorus, nitrogen and other inorganic additives for active growth. Together with the energy consumption for the full cycle of the fuel production that makes this approach quite expensive on a large scale [START_REF] Rawat | Biodiesel from microalgae: A critical evaluation from laboratory to large scale production[END_REF]. Nevertheless, the development of bioengineering technologies and new approaches to the industrial production organization leave microalgae in the list of the most promising bioenergy resources for the near future [START_REF] Kumar | Algae as potential feedstock for the production of biofuels and value-added products: Opportunities and challenges[END_REF].

The feedstock and its availability mostly determine the cost of the final biofuel, so the search for new sources of feedstock does not stop. As the new raw materials appeared, parallelly new technologies for their processing and production of the final product are developing. Particular attention is paid to the search for catalysts and optimization of conditions for the processing of different types of feedstock [START_REF] Aransiola | A review of current technology for biodiesel production: State of the art[END_REF]- [START_REF] Tabatabaei | Reactor technologies for biodiesel production and processing: A review[END_REF]. It is worth to know that the classification of biodiesel by generation does not mean that the third generation biodiesel will be more profitable than the second generation biodiesel. Moreover, the combined production of biodiesel of different generations can be an effective strategy in future. [START_REF] Knothe | Biodiesel and renewable diesel: A comparison[END_REF].

Regardless the types of feedstock and alcohol for the transesterification, basing on the literature review the general advantages and disadvantages of biodiesels can be identified.

Benefits of ester biofuels:

 Mixture of fatty acid esters is a renewable, non-toxic, environmentally friendly fuel  It could be easily used as a single fuel or in blends with traditional fossil fuels  Esters does not contain sulfur, practically does not form soot and produces less carbon monoxide, polyaromatic and hydrocarbon compounds during combustion in comparison with traditional diesel  The use of ester biofuel reduces net life cycle carbon dioxide emissions by about 80% compared to conventional diesel  Fatty acid ester is a biodegradable fuel, so its leakage does not pose a serious environmental hazard  Ester production, particularly, biodiesel production is well localized because of the availability of different raw materials, each country has the ability to produce biodiesel as a locally produced fuel  Light esters have a high octane number, so can be used as the octane boosters to the gasoline blends  Biodiesels have a higher cetane number than conventional diesel, that increases engine efficiency  Biodiesel has additional lubricating properties that reduces engine wear  The use of biodiesel does not require significant engine modifications

Disadvantages of ester biofuels:

 Biofuel production is more expensive today than production of fossil fuels  Ester biofuels have a slightly lower energy density than fossil fuels resulting in an increase in fuel consumption of about 2-10%  Biodiesel has a higher viscosity, cloud point and pour point than traditional diesel, making cold start difficult  Several studies point out slightly higher NOx emissions compared to conventional fuels [START_REF] Coniglio | Combustion chemical kinetics of biodiesel and related compounds (methyl and ethyl esters): Experiments and modeling -Advances and future refinements[END_REF]  Biofuel can oxidize and change its properties during long-term storage and decompose in the absence of stabilizers

SPECIFICS OF OXIDATION AND COMBUSTION OF FATTY ACID ESTERS

First of all, ester based biofuels are considered as a biodiesel. Biodiesel is defined as a mixture of long alkyl chain fatty acid methyl or ethyl esters. A typical set of fatty acids which esters are most often found in the biodiesel production is shown in Table 1.

After the transesterification of these acids with methanol or ethanol Table 1. Chemical structure of typical fatty acids for biodiesel production [START_REF] Atabani | A comprehensive review on biodiesel as an alternative energy resource and its characteristics[END_REF], [START_REF] Lin | Opportunities and challenges for biodiesel fuel[END_REF].

Another class of ester oxidation reactions corresponds to the ester group which contains two oxygen atoms. This class of reactions has been studied much less. For this reason the transformation kinetics of the ester group is of greatest interest when the oxidation chemistry of fatty esters is studied. It is important to note that the presence of oxygen atoms in the ester group changes the bond energy of neighboring C-C and C-H groups. This inductive effect can influence the reaction rates at the α and β carbons of the alkyl group, in particular, it can change the activation energy of the H-abstraction reactions [START_REF] Cavallotti | Analysis of acetic acid gas phase reactivity: Rate constant estimation and kinetic simulations[END_REF]. To obtain the information on the ester group reactions systematic experimental and theoretical studies are required. Usually light esters with an alkyl chain up to three carbon atoms are used as research objects, since they are quite simple and the most convenient for experimental studies. It is assumed that the length of the ester alkyl chain does not significantly affect reactions of the ester group.

However, it is noted in many works that light esters with a short alkyl group are poorly suited as the model surrogates of a real biodiesel [START_REF] Dagaut | Methyl Acetate Oxidation in a JSR: Experimental and Detailed Kinetic Modeling Study[END_REF]- [START_REF] Westbrook | A detailed chemical kinetic reaction mechanism for oxidation of four small alkyl esters in laminar premixed flames[END_REF]. The reason is that they have a much higher reactivity and do not exhibit a negative temperature coefficient which is characteristic for the heavier esters. In this regard kinetic studies of oxidation and combustion of esters with long alkyl groups are in demand. Formation of an intermediate cycle is caused by the interaction of the terminal hydrogen atom with the oxygen atom in the ester group due to the deformation of the ethyl group. In the case of methyl esters such interaction is less possible due to another number of atoms in the group and, thus, another electronic structure. The reaction of six-center unimolecular decomposition is a distinctive feature of FAEEs. As it mentioned in literature the decomposition can occur at lower temperatures than radical initiation, therefor oxidation reactivity of ethyl ester can be higher than that of corresponding methyl ester.

CHAPTER 1. LITERATURE REVIEW. EXPERIMENTAL AND NUMERICAL STUDY OF THE OXIDATION KINETICS

This reaction pathway was introduced by Metcalfe et al. [START_REF] Metcalfe | Experimental and Modeling Study of C5H10O2 Ethyl and Methyl Esters[END_REF], [START_REF] Metcalfe | A jetstirred reactor and kinetic modeling study of ethyl propanoate oxidation[END_REF] in their detailed mechanism of oxidation of small esters with the general formula C5H10O2. [START_REF] Akih-Kumgeh | Experimental and Modeling Study of Trends in the High-Temperature Ignition of Methyl and Ethyl Esters[END_REF] have confirmed this trend.

In their work they have investigated the ignition behavior of various methyl and ethyl esters in shock tube experiments and also they have carried out numerical simulations. The authors have analyzed isomerization effects and the influence of different alkyl groups on the ignition delay times of the esters. As in the work of Metcalfe, a more rapid ignition of isomeric ethyl esters was observed. The homologous sequence of three small ethyl esters, ethyl formate (EF), ethyl acetate (EA) and ethyl propanoate (EP), was investigated by Ren et al. [START_REF] Ren | Experimental and Modeling Study of the Thermal Decomposition of C3-C5 Ethyl Esters Behind Reflected Shock Waves[END_REF]. Using nearinfrared laser spectroscopy they tracked the time evolution of the concentration of H2O, CO2 and CO molecules behind reflected shock waves. The experimental results showed a significant difference in the pyrolysis rates of the three esters.

To simulate the experimental results the authors have used the improved Metcalfe's mechanism [START_REF] Metcalfe | A jetstirred reactor and kinetic modeling study of ethyl propanoate oxidation[END_REF]. Concentration profiles of reactants, stable intermediates and final products were identified and measured using a coupled gas chromatography-mass spectrometry (GC/MS). Thanks to the data obtained the authors have managed to improve and confirm the above-mentioned mechanism [START_REF] Hakka | Oxidation of methyl and ethyl butanoates[END_REF].

The laminar flame speed of fuel is one of the most important global parameters, but only a few papers cover this topic in the case of FAEEs. Laminar burning velocities of the mixtures of air with small esters were measured by Wang et al. [START_REF] Wang | Oxidation of small alkyl esters in flames[END_REF]. Seven methyl and ethyl esters, including ethyl formate (EF), ethyl acetate (EA) and ethyl propionate (EP), were investigated in flames by the particle image velocimetry (PIV) in a counterflow burner. The speeds were measured over a wide range of equivalence ratios, at atmospheric pressure and at elevated fresh mixture temperatures. In addition the authors carried out numerical simulations of the experimental data based on several literature known mechanisms. The calculated laminar velocities turned out to be overestimated in comparison with the experiments for almost all compounds.

After the kinetic schemes analysis the authors came to the conclusion that it is necessary to determine more accurately the rate constants for the reactions of primary esters destruction, in particular, reactions of the fuel radicals' decomposition. In the work Dayma et al. [START_REF] Dayma | Laminar Burning Velocities of C4-C7 Ethyl Esters in a Spherical Combustion Chamber: Experimental and Detailed Kinetic Modeling[END_REF] the laminar combustion velocities of mixtures of several ethyl esters with air were measured in a spherical chamber. In this work the flame propagation velocities were measured at different initial temperatures, equivalence ratios and pressures. To describe the results obtained a new kinetic mechanism was proposed which was obtained by reducing the detailed mechanism of ethyl pentanoate oxidation [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF] developed by the same group. As the result a good agreement was achieved between the experimental values of the burning rates and the model predictions for all esters.

To test the new mechanism the authors simulated literature known experimental data on the ignition delays and oxidation in a jet-stirred reactor of the esters studied. The proposed mechanism described most of the experimental data quite satisfactorily. The work [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF] Ethyl pentanoate oxidation mechanism [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF] was examined on the new experimental data by Knyazkov et al. [START_REF] Knyazkov | Photoionization mass spectrometry and modeling study of a low-pressure premixed flame of ethyl pentanoate (ethyl valerate)[END_REF]. Using the same experimental setup as in the works [START_REF] Osswald | Isomer-Specific Fuel Destruction Pathways in Rich Flames of Methyl Acetate and Ethyl Formate and Consequences for the Combustion Chemistry of Esters[END_REF], [START_REF] Westbrook | A detailed chemical kinetic reaction mechanism for oxidation of four small alkyl esters in laminar premixed flames[END_REF], [START_REF] Yang | Fuel-specific influences on the composition of reaction intermediates in premixed flames of three C5H10O2 ester isomers[END_REF], [START_REF] Yang | Photoionization mass spectrometry and modeling study of premixed flames of three unsaturated C5H8O2 esters[END_REF] It is worth to note that pentanoic (valerate) esters are of great interest themselves [START_REF] Boot | Biofuels from Lignocellulosic Biomass[END_REF]. The reason is that this type of esters can be easily obtained from lignocellulose which is one of the main components of wood. [START_REF] Lange | Valeric Biofuels: A Platform of Cellulosic Transportation Fuels[END_REF], [START_REF] Zhou | Preparation of valeric acid and valerate esters from biomass-derived levulinic acid using metal triflates + Pd/C[END_REF]. Therefore woody residuals can be effectively used as a raw material for the production of the ester-based biofuels. In the work of Contino et al. [START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF] the efficiency of a gasoline internal combustion engine (PSA EP6 engine) was tested running on several fuel mixtures: pure methyl pentanoate, pure ethyl pentanoate, a mixture of 20% ester with reference fuel PRF95 and pure PRF95. In addition, the researchers have monitored the composition of the exhaust gases in different engine operating regimes. The authors did not find any significant deterioration in engine performance when using valerates compared to the reference fuel. In the work of Lange et al. [START_REF] Lange | Valeric Biofuels: A Platform of Cellulosic Transportation Fuels[END_REF] a long-term test was carried out on ten gasoline engines that had been run for four months on a EPe(15%)/gasoline mixture. The engine power, its wear, composition of exhaust gases, fuel consumption and stability were monitored during machine exploitation. No operational problems were identified with the exception of a slight increase in consumption. A slightly higher engine performance was also noted that was associated by the authors with a high octane number (~100) of the ester. Thus, due to the high octane number and higher energy density than ethanol, methyl pentanoate and ethyl pentanoate are considered as effective additives or even an alternative to traditional fossil gasoline [START_REF] Lange | Valeric Biofuels: A Platform of Cellulosic Transportation Fuels[END_REF], [START_REF] Contino | Engine Performances and Emissions of Second-Generation Biofuels in Spark Ignition Engines: The Case of Methyl and Ethyl Valerates[END_REF]. T -mixture temperature, p -pressure in reactor, φ -equivalence ratio, X -mole fraction.

THE MAIN OBJECTIVES OF THE WORK

Analyzing the literature review it can be concluded that there is a fairly good understanding of the kinetics of oxidation and combustion of small ethyl esters such as ethyl acetate and ethyl propanoate.

Description of the Botha-Spalding burner and the fuel supply system

Atmospheric flames of the investigated substances were stabilized on a flat burner of the Botha-Spalding type [START_REF] Botha | The laminar flame speed of propane/air mixtures with heat extraction from the flame[END_REF] shown in 4. Here X is the mole fraction of a substance in the mixture, Qv is the total volumetric flow rate of the fuel mixture under standard conditions (25 °C), Qm is the total mass flow rate of the mixture, φ is the equivalence ratio.

Fuel X (ester) X (O2) X (Ar)

Qv , cm 3

Description of the MBMS-setup for studying the chemical flame structure at atmospheric pressure

The analysis of the chemical composition of the flames was carried out using a molecular-beam mass-spectrometric setup (MBMS) with soft ionization by electron impact. This setup was constructed in the Laboratory of Kinetics of combustion processes to analyze the chemical structure of flames in a wide range of pressures. The experience of successful operations of this setup is reflected in many publications of the laboratory staff [START_REF] Korobeinichev | The destruction chemistry of organophosphorus compounds in flames-I: quantitative determination of final phosphorus-containing species in hydrogen-oxygen flames[END_REF]- [START_REF] Knyazkov | The effect of methyl pentanoate addition on the structure of a non-premixed counterflow n-heptane/O2 flame[END_REF].

The general scheme of the MBMS-setup is shown in Figure 2.2. This experimental setup consists of three series-connected vacuum chambers with constant evacuation. The analyzed gas volume enters the first chamber through the sampler. After sampling the gas volume moves forward in the form of a molecular beam into the third chamber with a quadrupole mass spectrometer installed in it. The signal from the mass spectrometer is processed by the data acquisition system and output to the computer. The sampling process and the technical details of the installation are described in more detail below. The manufacture of such a probe is tailored manually and is an extremely demanding process since the quality and accuracy of manufacturing of the probe affects directly the gas sampling from the flame. For the experiments described a standard probe for this setup was prepared. The geometric parameters of the probe were selected on the basis of theoretical justifications and the previous experience of the laboratory staff of KCP [START_REF] Korobeinichev | Substantiation of the probe mass-spectrometric method for studying the structure of flames with narrow combustion zones[END_REF], [START_REF] Korobeinichev | Dynamic flame probe mass spectrometry and condensed-system decomposition[END_REF]: the inner opening angle of the cone is 40 o , the outer angle is 50 o , the size of the hole at the tшp is 0.08 mm, the wall thickness near the hole is about 0.08 mm, the total height of the cone is 25 mm. The probe is glued with epoxy resin to a watercooled metal flange which in turn is rigidly attached to the 1st chamber. Pressure in the 1st chamber is maintained at the level of 10 -2 -10 -3 Torr using a diffusion steam-oil pump with a pumping capacity of 1100 l/s. Due to the created pressure difference outside and inside the probe a portion of gas is sucked from the flame.

During sampling the gas reaches supersonic speed at the nozzle inlet. Rapid expansion into vacuum leads to the "freezing" of the degrees of freedom and then the gas moves in the form of a non-reacting molecular beam. Measurement unit: mm.

Molecular beam enters the 2 nd chamber through a skimmer which is presented as a stainless steel cone with an internal angle of 40 o , an external angle of 60 o and a hole in the tip with a diameter of 0.64 mm. The distance between the tip of the sampling probe and the skimmer is 20 mm. This distance is chosen so that the top of the skimmer is placed closer to the probe than the theoretical position of the Mach disk in the gas flow (~25 mm for this system). The skimmer cuts out the central unperturbed part of the molecular beam and passes it into the 2nd chamber. Operating pressure in the 2nd chamber is maintained at a level of 10 -5 Torr using a turbomolecular pump with a capacity of 500 l/s. The second chamber contains a modulator which is performed as a rotating disc with three slots. The modulator alternately overlaps and then passes the molecular beam into the 3rd chamber. Presence of the modulator in the system makes it possible to distinguish between the "background" and "beam + background" signals.

The beam passes from the 2 nd chamber to the 3 rd chamber through a collimator orifice with a diameter of 4 mm and then enters to the ion source. The distance between the holes "skimmer -collimator" is 350 mm and "collimatorion source" is 50 mm. Normal pressure in the 3 rd chamber is about 10 -7 -10 -8 Torr, and it is maintained using a turbomolecular pump with a pumping capacity of 500 l/s. This setup is equipped by a modified ion source in the form of a filament cathode with a voltage drop compensation system and ion optics developed at the

Institute of Energy Problems of Chemical Physics, Russian Academy of Sciences

[106]. The source creates a beam of ionizing electrons with a narrow energy spread (±0.25 eV) that allows operating in the "soft" ionization mode at energies close to the ionization potential of particular atoms and molecules in a flame (~8-16 eV). This ionization method reduces fragmentation and overlapping of mass peaks from different substances that greatly simplifies the mass spectra interpretations.

Separation by the masses of the resulting ions occurs in an EZAN MS-7302 quadrupole mass-spectrometer. The signal from the secondary electron multiplier VEU-6, which acts as a detector, is guided through the shaping amplifier to the pulse counter. Herewith the background signal determined by the molecular beam modulation is automatically subtracted. Each signal value of a particular mass peak is formed from averaging over three detector measurements. The entire data acquisition and synchronization system of the modulator is based on the CAMAC standard and is controlled from a computer.

Setting the ionizing energy of the ion source and adjusting the quadrupole to mass are also made from a computer through digital-to-analog converters (DAC).

Measurement of mass spectra and identification of compounds

Moving the burner vertically by a screw mechanism we measured the dependence of the mass peak intensities on the distance "probe -burner" at a given ionization energy for each mass. The distance "probe -burner" was controlled using a cathetometer with an accuracy of ±0.05 mm. The list of measured mass peaks was compiled individually for each flame based on a literature analysis and the assumed paths of the corresponding fuel destruction.

For each compound the parent peak or the most intense fragmentation peak (or both) was chosen as the measured mass. The database of the National Institute for Standards and Technology (NIST) was used as a database of mass spectra Therefore F(T,p) is a unique function of the apparatus and it has the same value for all the species detected on the same setup.

Si(E) coefficients for most of the stable compounds were determined in direct calibrations using the gas mixtures of known composition. For the calibrations the flow of calibration gases was injected directly to the probe through a burner with a quartz tube attached to it. The tube was heated by an external source to 453-473 K in order to avoid formation of gas clusters at the probe entrance.

Writing equation 2.1 and taking into account 2.2 for two compounds i and j in a molecular beam we can obtain the relation:

(2.4) 𝐼 𝑖 /𝐼 𝑗 = 𝜎 𝑖 (𝐸 𝑖 )/𝜎 𝑗 (𝐸 𝑗 ) • 𝐷(𝑚 𝑖 )/𝐷(𝑚 𝑗 ) • 𝑋 𝑖 /𝑋 𝑗
The ratio 𝐷(𝑚 𝑖 )/𝐷(𝑚 𝑗 ) can be determined experimentally. For that the measurements were carried out using the calibration mixtures of known composition consisting of gases with different molecular weights. It was shown that for compounds with close molecular weights the ratio 𝐷(𝑚 𝑖 )/𝐷(𝑚 𝑗 ) ≈ 1.

These value also corresponds to the theoretical substantiation of this effect [START_REF] Springer | Engine Emissions: Pollutant Formation and Measurement[END_REF]. Equation 2.4 shows that determining the signal intensities of the two compounds, the corresponding ionization cross sections and the mole fraction of one of the compounds, the mole fraction of the second compound can be calculated. This method for the mole fraction determining is called the method of relative ionization cross-section (RICS) [START_REF] Cool | Studies of a fuel-rich propane flame with photoionization mass spectrometry[END_REF]. This approach was applied in the case of impossibility of direct calibration for any compound. The electron impact ionization cross-sections for a given ionizing electron energy were taken from the NIST database [START_REF] Kim | Electron-Impact Cross Sections for Ionization and Excitation Database[END_REF]. Unfortunately, the error this method is quite high, by the order of 20%, since the theoretical calculations of the effective ionization crosssections at low electron energies is a complex physical problem. In this regard the general accuracy of determining the molar fraction according to the RICS method was noticeably lower than that according to the direct calibrations.

The total statistical uncertainty of determining the mole fractions of reactants and stable products (Esters, O2, CO, CO2, H2O) was about ±15%. The measurement accuracy of molecular hydrogen was approximately ±30% due to the difficulties with it pumping out of the vacuum system. The mole fractions of the remaining compounds were determined with an accuracy of ±50%. All Engineering CNRS (LRGP) in Nancy, France. The measurements were carried out on a combustion facility with probe sampling from a flame front in a low-pressure chamber with further analysis on a gas chromatograph. This setup was constructed by the collective of the LRGP and it has been successfully applied for the combustion kinetics studies in previous works [START_REF] Gueniche | Rich methane premixed laminar flames doped with light unsaturated hydrocarbons: I. Allene and propyne[END_REF]- [START_REF] Tran | An experimental and modeling study of the combustion of tetrahydrofuran[END_REF].

Description of the fueling and vacuum pumping systems

The general scheme of the experimental stand is shown in Since the experiments were carried out in a low-pressure chamber, the flame was ignited by an electric discharge created between an electrode in the chamber and the burner surface. It was not always possible to ignite the investigated combustible mixture with such approach. To solve this problem a stoichiometric flame of methane was ignited first. An additional methane line was connected to the general mixture supply system through its own MFC. After methane had been ignited, the ester supply was switched on and the methane flow rate was gradually decreased to zero until the combustible mixture composition completely reached the required values.

During the experiments pressure in the chamber was maintained at 50

Torr due to a constant evacuation by two vane pumps. The pumping rate was regulated by a pressure regulator (12 in Figure 2.4). Since a combustion process generates a large amount of water, two nitrogen traps and a cooling thermostat were installed on the pumping line in front of the pumps. This allowed us to minimize the amount of water entering the pumps.

Description of the McKenna burner

The flame was stabilized on a McKenna burner mounted in a metal combustion chamber (8-10 in Figure 2.4). The burner was mounted on a metal rod and could be moved vertically with a screw mechanism under the chamber.

The position of the burner surface was controlled using a cathetometer with an accuracy of ±0.05 mm.

The McKenna burner itself consists of a round metal housing with a diameter of 120 mm. Connections for the inlet of gases and water are mounted in the burner body (Figure 2.5 (a)). A porous sintered bronze disc is pressed into the central part of the body (60 mm in diameter) and a spiral copper tube of water cooling is pressed inside the disk. The burner temperature was maintained during the experiments at 333 K using a water thermostat. Around the central disc there is a porous ring also made of sintered bronze. A gas flow can be supplied separately from the main combustible mixture through this ring that makes it possible to stabilize the flame additionally. However, this opportunity was not used in our experiments. (b) (a)

Description of sampling system

Sampling from the flame was carried out using a thin quartz capillary probe with a conical narrowing and a hole in the tip ( This type of probe has a narrower shape compared to the probe for MBMS experiments that makes it possible to reduce gas-dynamic and thermal disturbances of the flame. However, due to the small opening angle a molecular beam is not formed in a narrow probe and highly reactive compounds, such as radicals, recombine on the inner surface of the walls.

The probe was fixed in the cap of the vacuum chamber in such a way that the sampling part was in the chamber and the outer part was stuck out of the chamber. Moving the burner inside the chamber it was possible to take a gas sample from different flame zones and to obtain a profile of the species mole fractions as the function of distance above the burner.

On the open side the probe was connected to an evacuated and heated sampling line leading to the vacuum system and GC analyzers. A valve was installed on the line near the capillary to cut it off from the chamber. Vacuum in the sampling line and in the later volumes was maintained using a turbomolecular pump (TMP) connected to the system with a shut-off valve.

The sampling process at each point of the flame was carried out according to the following algorithm: first, the vacuum system and the sampling line were pumped out to a pressure of 10 -2 -10 -3 Torr. At this time the burner with flame was installed at the required height relative to the probe. Then the valve on the line was opened and the residual gas was pumped out in the capillary for several minutes. After that the valve in front of the TMP was closed, and sampling into the vacuum system began. Since pressure in the combustion chamber is low, the process of sampling leakage took about 1-2 minutes until pressure in the sampling system reached 10-12 Torr. Then the valve on the sampling line was closed stopping the sampling. The gas portion sampled was compressed up to 20-25 Torr using a mercury piston. This manipulation was done in order to increase the concentration of the investigated substances at the inlet to the chromatographs. After compression by mercury the gas portion entered two GC analyzers and the chemical analysis process was started.

Chromatographic analysis

Online gas chromatography was used to obtain isomer-specific information for stable flame intermediates. Two standard GC analyzers were exploited for the sample analysis: ■ Agilent 7890A equipped with HP-PlotQ and HP-Molesieve columns for separation of hydrocarbons, oxygenates and argon. Helium was used as a carrier gas. A flame ionization detector (FID) with a methanizer and a thermal conductivity detector (TCD) provided identification of the compounds. The methanizer provided conversion of CO, CO2 and oxygenated compounds into methane that made it possible to record their signals on the FID, which allow a better precision and a much lower detection threshold.

■ HP 5890 Series II with Carbosphere column and TCD was used only for H2 and O2 detection. Argon was used as a carrier gas in this apparatus.

Retention times of the species were determined from the calibration mixtures and the previous works on this setup. The duration time of one sample analysis was mostly determined by the retention time of the corresponding fatty acid formed during ester combustion. For the flame of EPe the time of a single measurement reached 90 minutes. Detailed list of GC-analyses parameters is provided in Appendix 2. The list of the species detected in GC-analyses is provided in Appendix 3.

Calibration and data processing

GC-signal from the i-th compound (Ii) is defined as the area under the peak corresponding to the given compound on the chromatogram. The signal Ii is proportional to the concentration ni and, therefore, to the partial pressure of the given compound in the gas sample pi. The proportionality coefficient between the peak area of the i-th substance in the chromatogram and its partial pressure is called calibration coefficient Si. When we know the coefficient Si mole fraction of a compound (Xi) can be easily found by the formula:

(2.1)

𝑋 𝑖 = 𝑝 𝑖 𝑃 = 𝐼 𝑖 𝑆 𝑖 ×𝑃 ,
where P -pressure of the taken sample at the inlet to the chromatograph.

To determine the calibration coefficients Si direct calibrations were carried out with gas mixtures of known composition. For the calibrations the cylinders installed on a vacuum system were filled with a calibration mixture, then known amount of gas was let from the cylinder into the system and analyzed on GC. Most of the compounds measured in these experiments were calibrated directly.

When it was impossible to calibrate directly any species, the corresponding coefficient Si was estimated indirectly by the number of carbon atoms in the molecule. Such estimation is possible due to the fact, that the molecule is converted into methane passing through the methanizer which performs as a catalytic converter. The number of methane molecules formed corresponds to the number of carbon atoms in the starting compound. Thus the calibration coefficient of a substance of n carbon atoms can be estimated by the formula:

(2.1)

𝑆 𝑖 = 𝑆 𝐶𝐻 4 × 𝑛 ,
where 𝑆 𝐶𝐻 4 -calibration coefficient for methane determined precisely from the direct calibrations.

It has been verified on many species that estimated calibration coefficients agree with coefficients of the direct calibrations with acceptable accuracy. For example, direct calibrations with C2-compounds (C2H2, C2H4, C2H6) provided coefficients Si in the range of 13906-15562, whereas the coefficient calculated by the number of carbons is 15614. As it seen, the greatest deviation from the direct calibrations does not exceed 10%. The same situation was observed for the heavier compounds. Depending on the concentration of the component in a flame the uncertainty of the mole fraction determination was about 5% for the main components and about 10% for intermediate products (Xi <10 -4 ) that corresponds to the accuracy of the devices used. Since the thermocouple in a flame front heats up to temperatures of 1300-1500 K, the thermocouple wire begins to glow strongly thereby cooling and lowering the gas temperature readings. Therefore it is necessary to correct thermocouple measurements for radiation during experimental data processing.

Temperature measurements at atmospheric pressure

For the temperature measurements at atmospheric pressure thin S-type thermocouples made of Pt-Pt10%Rh wire of 0.03 mm thickness were used. The thermocouples were hand made for each experiment. Prepared thermocouple wire with thermojunction has been attached to the thermocouple body (Figure 2.8). For that platinum and platinum-rhodium wires were spot-welded under a microscope control. Then they were welded to the mustaches of a V-shaped holder made of thicker (0.2 mm) wires of the same metals. The mustaches were additionally stretched on the sides with springs to avoid sagging of the thermocouple in a flame because of heating. To prevent catalytic reactions on the wire surface the thermocouple was covered with a thin layer of silicon oxide SiO2.

Together with the coating the thickness of the thermocouples was about 0.05-0.07 mm. The thermocouple thickness was controlled before and after each measurement. To take into account radiation heat losses the temperature correction was calculated using the formula proposed earlier in the work [START_REF] Kaskan | The dependence of flame temperature on mass burning velocity[END_REF]:

(2.2) ∆𝑇 = 𝑇 𝑔 -𝑇 𝑐 = 1 𝜆 [1.25 • 𝜀 • 𝜎 • 𝑑 3 4 • (𝑇 𝑐 4 -𝑇 𝑤 4 ) • ( 𝜂 𝜌𝑣 ⁄ ) 1 4 ] ,
where Tg is the gas temperature, Tc is the temperature of thermojunction, Tw is ambient temperature, d is thermocouple diameter, ε is the emissivity factor, σ is the Stefan-Boltzmann constant, λ, η are the coefficients of gas thermal conductivity and viscosity, ρ, v are the gas density and velocity. This formula is an analytical solution of heat balance between a hot gas flow and a cylinder.

Since argon was the main component of gas mixtures (70-80%), the coefficients of viscosity and thermal conductivity in the above formula were taken for argon taking into account their dependence on temperature. The temperature dependence of ε was taken into account according to the formula proposed in the work [START_REF] Tereshchenko | Perturbations of the flame structure due to a thermocouple. I. Experiment[END_REF]. The resulting profile was obtained by averaging over several measurements. The absolute uncertainty of temperature measurements did not exceed ±50 K.

Temperature measurements at low pressure

In experiments at low pressure the temperature profiles were measured using a thin B-type thermocouple. This type of thermocouples is made of platinum-rhodium wires with different ratios of platinum and rhodium:

Pt30%Rh-Pt6%Rh by weight. In this work wires of 0.1 mm thickness were used.

The flame zone at low pressure is much wider compared to the experiments at atmospheric pressure. Therefore a good spatial resolution can be achieved with thicker wire that greatly simplifies the manufacture and operation with such a thermocouple.

The thermocouple was spot-welded of corresponding wires and then welded to a U-shaped holder made of wires of larger diameter (0.5 mm) made of the same alloys. The general construction of the thermocouple body is shown in Figure 2.9. To avoid catalytic reactions on the surface of the thermocouple a ceramic coating of BeO-Y2O3 ceramics was applied to the wire. The use of BeO-Y2O3 as a protective coating for thermocouples is described in the work [START_REF] Kint | A noncatalytic coating for platinum-rhodium thermocouples[END_REF]. Measurement unit: mm.

Low pressure thermocouple measurements were also corrected during data processing to take into account radiative heat loss from the thermocouple.

The method of electrical compensation was used for this purpose [START_REF] Bonne | Messungen in der Reaktionszone von Wasserstoff-Sauerstoff-und Methan-Sauerstoff-Flammen[END_REF]. This method is based on the compensation of radiation heat losses by forced electric heating of the thermocouple. For the thermocouple with electrical compensation in a flame we can write the heat balance equation:

(2.3) ℎ • (𝑇 𝑔 -𝑇 𝑐 ) + 𝑅 • 𝐼 2 = 𝜀 • 𝜎 • (𝑇 𝑐 4 -𝑇 0 4 ) ,
where Tg is the gas temperature, Tc is the thermocouple temperature, T0 is temperature of the chamber walls which absorb radiation, h is convective heat transfer coefficient, R is the thermocouple resistance, I is the current through the thermocouple, ε is the emissivity factor, σ is the Stefan-Boltzmann constant For calibration the thermocouple has been placed in a vacuum chamber and was heated by electric current. In this case the convective term in the heat balance equation is equal to zero that makes it possible to construct a dependence curve of radiation heat loss on the current passed.

Next, the temperature was measured in the flame with the heating system connected to the thermocouple. Increasing the amperage passed through the thermocouple, the thermocouple reading increased linearly. These reading can be approximated by a straight line. For the measurements at different distances from the burner a set of lines could be plotted. The point of intersection of the straight line with the calibration curve corresponds to the current at which electrical heating completely compensates radiation heat loss at a given temperature. Thus the temperature of the intersection of the straight line with the calibration curve corresponds to the actual gas temperature Tg. This method is applicable in the linear thermocouple region and not too high temperatures since the thermocouple can burn out from additional current heating. According to the estimations the total uncertainty did not exceed ±100 K.

The largest measurement uncertainties correspond to the zone of final products,

where the flame temperature is the highest. So, in the main flame zone the uncertainty was even lower. gradients for all components is required. Boundary conditions for temperature are set either in a similar way or as a defined temperature profile T(x) measured in the experiment. In the latter case the heat balance equation in the system (2.4) -(2.7) is not solved and the temperature from the input file is used. Thus, the solution to the complete system of equations (2.4) -(2.7) corresponds to a freely propagating flame, and the solution to the system with a given profile T(x)

NUMERICAL SIMULATIONS

Theoretical problem description

corresponds to a real flame with heat losses to the burner and probe.

In addition to the initial composition, pressure, mass flow rate and temperature profile, the chemical-kinetic mechanism is loaded to CHEMKIN.

Chemical kinetic mechanisms usually have a form of three text files with input data but sometimes it could be just a one file.

The first file contains a list of all compounds considered in the system and all chemical reactions in which they are involved. Parameter values Ai, ni and Ei are given for reaction rate constant ki for each reaction in the modified Arrhenius form:

(2.8)

𝑘 𝑖 = 𝐴 𝑖 𝑇 𝑛 𝑖 𝑒 -𝐸 𝑖 𝑅𝑇 ,
where Ai is the pre-exponential factor, ni is the power of the temperature multiplier and Ei is the activation energy. Pressure dependence of each ki could be additionally specified in the file. The reverse reaction rate is calculated from thermodynamic data, if it is not explicitly defined.

The second file contains information on the thermodynamic characteristics of all substances. The file looks like a set of coefficients a 0 p,1 -a 0 p,7 which describe heat capacity C 0 p, enthalpy H 0 T and entropy S 0 T of a molecule in the polynomial form:

(2.9) .

С 𝑝 0 𝑅 = 𝑎 𝑝,1 0 +
To enhance the accuracy of the polynomial approximation the coefficients This assumption is partially confirmed by calculations in several works [START_REF] Wang | Theoretical and kinetic study of the hydrogen atom abstraction reactions of ethyl esters with hydrogen radicals[END_REF], [START_REF] Mendes | Theoretical Study of the Rate Constants for the Hydrogen Atom Abstraction Reactions of Esters with •OH Radicals[END_REF].

c 0 p,1 -c 0 p,
In the mechanism of Dayma the rate constants for the H-abstraction reactions by radicals in the 2nd, 3rd and 4th positions are taken to be the same.

This is a logical assumption, however, it can be assumed that the ester group should influence the rate of reactions in the 2nd position due to the inductive effect of oxygen. This hypothesis is supported by Sun et al. [START_REF] Sun | Experimental and modeling efforts towards a better understanding of the high-temperature combustion kinetics of C3C5 ethyl esters[END_REF], which calculations for EA and EP predicted a larger value of the rate constants of the Habstraction reactions with radicals in the 2nd position. Also, in the mechanism of A complete list of reactions with modified rate constants in the new mechanism is shown in Table 5. The resulting developed mechanism contains 320 compounds participating in 2027 reactions. Thermochemical and transport data were taken from the mechanism [START_REF] Sun | Experimental and modeling efforts towards a better understanding of the high-temperature combustion kinetics of C3C5 ethyl esters[END_REF] and extended with data from the mechanism [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF].

To describe the chemical structure of ethyl acetate flames the mechanism from the work of Ahmed et al. [START_REF] Ahmed | Small ester combustion chemistry: Computational kinetics and experimental study of methyl acetate and ethyl acetate[END_REF] was used in addition to the Dayma mechanism and the mechanism proposed in the thesis. This mechanism is the most recent published mechanism of methyl acetate and ethyl acetate oxidation.

Mechanism analysis methods

As can be seen from the previous section, detailed kinetic mechanisms include hundreds of compounds and thousands of reactions that makes an analysis of kinetic schemes rather difficult. Methods of numerical analysis of kinetic mechanisms are widely used for a deep understanding of the relationship between the global parameters of a system and specific reaction pathways. The most widely used methods are the sensitivity analyses and the rate of production analyses.

The sensitivity analysis quantifies how the solution of the equation system describing the reactor depends on changes in specific model parameters.

Actually, the sensitivity analysis is a calculation of partial derivatives of some global parameter X (temperature, compound concentration, ignition delay time, etc.) using a set of reaction rate constants k, included in the model. If the value of the derivative 𝜕𝑋 𝜕𝑘 𝑖 comes to zero, then the variation of ki has a little effect on the solution vector. This result means that there is no need for a high accuracy of ki determining to estimate the parameter X at these conditions. Otherwise, the rate constants of reactions with high sensitivity should be determined as accurately as possible, since they strongly affect the final solution. In this work we analyzed the sensitivity of the laminar burning velocities to the reaction rate constants.

The rate of production analyses allows us to determine the percentage contribution of individual reactions to the total formation or consumption of any compound in the reactor. There are two main approaches in this way: a single point analysis and an integral analysis. The single point analysis provides determination of the instantaneous contribution of all formation/consumption reactions of a component under specific conditions (temperature, composition, pressure) corresponding to only one spatial or temporal point of the reactor. On the contrary the integral analysis implies the sum of contributions from all spatial or temporal points of the reactor. For the one-dimensional flame model the integral analysis is reduced to the calculation of the integral:

(2.12)

𝜔 𝑖 = ∫ 𝜔 𝑖 ′ 𝑑𝑡 = ∞ 0 ∫ 𝜔 𝑖 ′ 𝑣 𝑑𝑥 ∞ 0
, where ωi is a local volumetric rate of compound production in the i-th reaction, v is a local gas velocity and x corresponds to the distance from the burner. The integral analyses approach was used in the presented work. Discussion is performed to reveal and explain the major inaccuracies of the models. Special attention is paid to the new mechanism.

CHAPTER 3. RESULTS. EXPERIMENTAL STUDY AND NUMERICAL SIMULATION OF THE FLAMES OF FATTY ACID ETHYL ESTERS

EXPERIMENTAL MEASUREMENTS OF ETHYL ESTER FLAME STRUCTURES

Ethyl acetate

Ethyl acetate is one of the most studied ethyl esters. A lot of works were dedicated to the combustion studies of that ester including chemical flame structure at low pressures. However, there is still no experimental data in the literature on the chemical structure of EA flames at atmospheric pressure. In this regard, the results and discussion of the EA flames at atmospheric pressure presented in this part. Kinetic simulation of EA flames was carried out using three kinetic schemes: the mechanism of Dayma et al. [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF], the mechanism of Ahmed et al.

[134] and the newly developed mechanism proposed in this thesis. But it is worth to note that in the case of EA the latter mechanism completely matches the mechanism of Sun et al. [START_REF] Sun | Experimental and modeling efforts towards a better understanding of the high-temperature combustion kinetics of C3C5 ethyl esters[END_REF]. Therefore, the Sun mechanism will be referred in the discussion. Calculations using all three mechanisms gave almost the same distribution of reactants and main products. Thus, Figure 3.1 shows only the simulation results obtained with the Sun mechanism. We have detected a peak signal corresponding to the ions with mass 42 u.

Propene (C3H6) and ketene (CH2CO) which are often formed in flames of heavy hydrocarbons [START_REF] Sarathy | An experimental and kinetic modeling study of methyl decanoate combustion[END_REF], [START_REF] Tian | An experimental and kinetic investigation of premixed furan/oxygen/argon flames[END_REF] contribute to this peak. Unfortunately, the MBMS setup used does not allow the separation of these two compounds. However, the simulations with all three mechanisms predicted similar peak values for propene mole fraction but different for ketene. Moreover, the mole fraction of ketene is several times higher (about 10 -4 in stoichiometric flame and 10 -3 in the rich one) than that of propene (about 3⨯10 -5 ). In this regard the mass-peak 42 can be analyzed in terms of ketene formation. However, a noticeable discrepancy between the measured and simulated profiles of oxygen can be observed. The reason is, that in this experiment there was a small air leakage in the sampling line. The amount of additional oxygen was estimated and subtracted from the final oxygen profile, but the accuracy of this profile has become less. Nonetheless, the product composition demonstrates almost full oxidation of the fuel (stoichiometric mixture), while the simulations predicts slightly more CO and non-zero fraction of O2. In this regard, the shape of the oxygen profile is looking reasonable. predict two and three times lower values, respectively. However, as it seen, the acid profile is shifted toward the burner as it is with the ethylene mole fraction profile. Since both these compounds are the products of the EA unimolecular decomposition, earlier fuel decomposition in the flame can be considered.

Simulations based on the

Compared to the atmospheric pressure results, simulations at lowpressure conditions differ noticeably. The mechanisms, which were adequate in predictions of some species at 760 Torr, appeared to be incorrect at 50 Torr. Such differences could be attributed to the different pressure-dependent parameters in the mechanisms. Unfortunately, the mole fraction determination of atomic oxygen O, which is also an essential radical in combustion, is practically impossible in hydrocarbon flames due to the presence of large amounts of methane with the same molar weight (m/z=16). As can be seen from the figure the experimental values and calculations are in good agreement taking into account the relatively high measurement uncertainty of the radicals. However, there are some discrepancies between the experimental and calculated profiles near the burner surface. This effect could be caused by the probe perturbations. Also, it could be attributed to the incorrect chemistry of H and OH formation in vicinity of the burner. The experimentally measured mole fractions of butanoic acid (C3H7COOH)

Ethyl butanoate

have been described with acceptable accuracy by both models. However, as in the case of EA, a better agreement of the Dayma model with experiment under stoichiometric conditions can be noticed. At the same time, in the rich flame both models have overestimated the maximum mole fraction of acid again. Thus, some systematic inaccuracy in the description of the primary destruction pathways can be mentioned. Also, as it discussed in the case of EA, the problem could lay in the relationship between the unimolecular decomposition and the radical destruction reactions.

Dayma. However, for individual species, such as ethane and butylene, significant discrepancies have been observed. It indicates the need for the rate of production analysis for these compounds in the mechanisms. In the case of 1,3-butadiene, its experimental peak mole fraction has landed exactly in the middle between the corresponding model predictions. Herein the Dayma mechanism has overestimated the peak mole fraction of C4H6 by a factor of two, and the new mechanism has predicted exactly two times less value than the experiment. Thus, both the models have described the experimental profile with the equal accuracy. However, the peak mole fraction of butadiene is only about 10 -5 . Thus, the accuracy of its determination does not play a significant role in comparison with acetylene, for example.

Ethyl pentanoate

In contrast to the stoichiometric flames of EA and EB, in the EPе flame the calculated mole fraction profiles of oxygenated species have appeared in a good agreement with the experimental results (Fig. 3.15.). The maximum mole fractions of formaldehyde (CH2O) and acetaldehyde (CH3CHO) were adequately predicted by both the models within the experimental uncertainty. The similar situation has been observed with the total peak mole fraction of ketene (CH2CO) and propene (C3H6). It should be noted that the mechanism of Dayma has predicted more propene (~10 -3 ) than ketene (~10 -4 ) in this flame, whereas the new mechanism has predicted very close maximum mole fractions of these compounds: ~6.5×10 -4 for propene and ~1.5×10 -4 for ketene. accurately by both the models. Propene, which has not been separated from ketene in the atmospheric pressure experiment, was very well described by the mechanisms at low pressure. At the same time, in the experiment at atmospheric pressure a good agreement was observed between the models and experiment for the total propene+ketene profile. So, it can be assumed that kinetics of these compounds in EPe flames is described a fairly well in the mechanisms. In general, positions of the peak mole fractions of the other compounds were reproduced well in the simulations, but there are noticeable discrepancies in absolute values between the model predictions and the experiment. The new mechanism has described very well again the mole fraction profiles of acetylene (C2H2), allene and propyne (a-C3H4 and p-C3H4), while the mechanism of Dayma has underestimated the maximum mole fractions of these compounds by 3-5 times. The peak mole fractions of methane and ethane, on the contrary, were calculated a slightly better by the Dayma model, whereas in the new mechanism the peak mole fractions of these species were underestimated by 1.5-2 times.

The experimental maximum mole fractions of ethylene (C2H4), isobutane (i-C4H10) and 1,3-butadiene (1,3-C4H6) differ markedly from the calculated ones.

As it seen, the measured mole fraction of ethylene appeared to be quite high and its position is shifted toward the burner relative to the calculated profiles. In this case, the models predict one and a half time lower value of the peak ethylene mole fraction than it was measured. We assumed that such a high ethylene mole fraction has appeared due to the additional unimolecular decomposition of EPe during the sampling process, since the small angle of the probe does not allow a molecular beam formation. To check this hypothesis we have estimated the possible amount of ethylene that could be formed in the probe at its temperature and have received a slight correction to the measured data. However, that estimation was not yet enough to match the modeling peaks. Thus, despite the obvious experimental issue, it can be still argued that both the models underestimate the maximum mole fraction of ethylene in the low-pressure EPe flame. It points again the possible inaccuracies in the ethylene formation chemistry used in the models.

As it seen from the experiment isobutane was formed less than n-butane in an order of magnitude. This is probably the reason why isobutane has not been incorporated into the mechanism of Dayma. However, isobutane was included to the AramcoMech 1.3 mechanism which was used as a sub-mechanism in the new model. Thus, the isobutane mole fraction profile was calculated using the new mechanism. The mechanism has reproduced well the shape and position of the experimental isobutane profile but overestimated its maximum by a factor of 3.

The calculated peak mole fraction profiles of 1,3-butadiene were shifted far from the burner than the experimental maximum. Even so, the absolute maximum mole fraction of 1,3-C4H6 was very well described by the Dayma model and was 2 times underestimated by the new model. As it seen, nonzero concentrations were observed close to the burner for a number of compounds in the experiment, for example, 1-butene or propene.

However, the models have predicted a zero mole fraction of these compounds near the burner. We suggested two explanations for this effect. The first is associated with the complexity of the probe measurements in vicinity of the burner surface. Since the probe takes a gas sample in a certain volume in front of it, sampling close the very surface might be distorted.

Another explanation is associated with a really faster formation of these substances than it is assumed in the models. This hypothesis is partially confirmed by the fact that nonzero concentrations near the burner surface were observed for ethylene and C4-hydrocarbons which, most likely, are formed at the early stages of the fuel destruction. It is worth noting that the similar problem was discussed in the work [START_REF] Knyazkov | Photoionization mass spectrometry and modeling study of a low-pressure premixed flame of ethyl pentanoate (ethyl valerate)[END_REF]. In the case of valeric acid, its maximum mole fraction in the experiment has been overestimated and shifted towards the burner, as in the case of ethylene. This is consistent with the assumption that some decomposition of EPe has been gone in the probe due to insufficient sample cooling (if the temperature drop in the probe is not fast enough). It should be noted that the heated sample line from the probe to the GC analysers does not change the composition of the sample. We have check this possibility with calibration measurements using a gas mixture of known composition (EPe/Ar). However, even taking into account the excess acid formation in the probe, both models have underpredicted the maximum mole fraction of valeric acid.

In general, a satisfactory description of the mole fraction profiles of most of the hydrocarbons measured can be observed. The model oа Dayma and the new model have demonstrated a different predictive accuracy for individual compounds. Unfortunately, the probe effect did not allow us to determine with acceptable accuracy the ethylene and valeric acid mole fractions, which are the products of unimolecular decomposition. Nevertheless, from the data obtained it could be concluded that both models still underestimate the mole fractions of these compounds.

ANALYSIS OF DETAILED COMBUSTION MECHANISMS USED

This section provides a detailed discussion of the mechanisms used basing on the integral analysis of the fuel conversion pathways in the flames. The mechanisms are discussed in the context of the accuracy of the experimental data description presented in the previous section. Particular attention is paid to the discussion of the new mechanism proposed in the thesis. The analyses performed allows to draw specific conclusions about the advantages and disadvantages of the mechanisms and to identify reaction pathways, which kinetic parameters require additional clarification.

Analyses of the primary decomposition pathways of esters in flames

Ethyl acetate

As a rule, the general scheme of species oxidation in flames presents a destruction of parent fuel molecules to lighter compounds, which form stable products depending on the conditions. The specific ratio of quasi-stationary concentrations of intermediate species in a flame under given conditions depends on the reaction pathways in which the fuel predominantly decomposes. In this regard, the initial fuel oxidation stages are of particular interest for the analyses of detailed kinetic mechanisms. Hereby, the ROP analysis of the primary transformation pathways made it possible to explain in detail the reasons of discrepancies between experimental data and predictions of the models in EA flames. The above analysis clearly indicates the need for a more correct account of the isomerization reactions of fuel radicals. Also, revision of the kinetic parameters of the acid formation reactions from the fuel radicals in the Sun model is needed. These observations correspond automatically to the new mechanism presented in the thesis.

Ethyl butanoate

ROP analysis of the primary oxidation pathways of ethyl butanoate in stoichiometric atmospheric flame is shown in Ethyl butanoate has a longer alkyl chain unlike ethyl acetate. That leads to an increase in the number of C-H bonds that can be attacked by radicals. At the same time, rate of reactions for different carbons of the alkyl group is different, that leads to a certain distribution of fuel radicals. For ethyl butanoate there can be five fuel radicals in total. For the convenience of the reader they are signed in pressure, so it can be assumed that the pressure effect on the rate constant of this reaction is taken into account more correctly in the AramcoMech 1.3 mechanism.

However, that is not enough as can be seen from the profile comparisons.

Propane mole fraction is closely related to the concentrations of ethane and methyl radical. The analysis has shown that the main reaction of C3H8 formation in the mechanisms is the recombination of methyl and ethyl (C2H5) radicals. The latter, in turn, is mainly formed from ethane and the decomposition products of fuel radicals. In the Dayma mechanism C2H5 is mainly formed from the C3H7CO radical which appears together with acetaldehyde during the EBEJ decomposition. In the new mechanism, the main ethyl radical source is the C2H5OCO radical, which is a decomposition product of the EB3J radical. Also, a significant contribution to the C2H5 production in the rich flame is provided by unimolecular decomposition of butanoic acid. So, the accuracy of the simulations of the propane mole fraction profiles is linked to the prediction accuracy of the short radicals.

Another minor compound whose mole fraction profile has been poorly described by the models is 1-butene (C4H8). The discrepancy between the maximum mole fraction of butene according to calculations and experiments was observed not only in the rich, but also in the stoichiometric flame (see Figure 3.10). Butene is mainly formed in recombination of methyl radical with allyl radical (C3H5), which is a product of the H-abstraction from propene. Therefore, the accuracy of butene mole fraction predictions is directly related to the accuracy of the methyl radical quantifications and the rate of destruction of the EB3J fuel radical.

In general we can conclude that it is necessary to refine the kinetics of radical formation in fuel-rich flames to improve the accuracy of the models. As can be seen from the analysis, the refinement of the formation and consumption of methyl radical can significantly improve the description of the concentration of light hydrocarbons in ethyl butanoate flames.

Ethyl pentanoate

IROP analysis of oxidation pathways of ethyl pentanoate was carried out in the greatest detail since this ester is the most complex of those investigated in this work and is also of the greatest practical interest. In the Dayma model, the total contribution of the H-abstraction reactions in positions 2, 3 and 4 is the same (20.3%), since the same rate constants were used for these reactions in all positions. However, as already discussed in Section 2.2.2, the new mechanism uses the refined rate constants of the H atom abstraction in position 2. That is why the total contribution of the EPE2J formation reactions in the new mechanism appeared to be higher than the contribution of the reactions leading to the formation of EPE3J and EPE4J: 26, 7% (2) and 13.4% (3 and 4).

Further decomposition of the EPE2J radical leads to the formation of ethyl acrylate (C5H8O2) which was measured at low pressure. Apparently, the increase of the EPE2J production explains the overestimation of the ethyl acrylate mole fraction profile in calculations with the new mechanism. It indicates the necessity to improve H-abstraction constant and especially their relative ratios between the different radical formed. Also, we suppose that it is important to carry out a precise quantum-chemical calculation of the H-abstraction rate constants for the EPе molecule at position 2.

In addition to decomposition reaction, the EPE2J radical can isomerize into the other fuel radicals:

(1) EPE2J  EPEEJ

(2) EPE2J  EPE5J

(3) EPE2J  EPEMJ Herein, the contribution of the isomerization (2) is the same in both mechanisms (24-25%), but the contributions of reactions (1) and (3) are slightly different: 44% (1) and 14.3% (3) according to the mechanism of Dayma, and 65%

(1) and 1.8% (3) in the new mechanism.

The IROP analysis of EPe conversion in the flame at 1 atm (Figure 3.25)

demonstrates generally the same trends in the distribution of the H-abstraction reaction contributions for both mechanisms. This is quite natural, since the rate constants of these reactions do not depend on pressure. In this case, the contribution of the EPe unimolecular decomposition in the Dayma mechanism is slightly increased in comparison with the flame at 50 Torr. In the new mechanism, on the contrary, it is slightly decreased. Nevertheless, the contribution of the fuel unimolecular decomposition in the atmospheric flame is also rather low in comparison with the radical abstraction of hydrogen.

It can be seen from Figure 3.25 that the pressure increase affects the percentage distribution of isomerization reactions. According to the Dayma mechanism, the contribution of reaction ( 1) is increased from 44% to 63%, and according to the new mechanism it is increased from 65% at 50 Torr to 69.9% at atmospheric pressure. Also, the contribution of reaction (2) in the Dayma mechanism decreased by 7.5%, and in the new mechanism it is only by 2.7%. The reaction (3) in the Dayma mechanism has changed direction at atmospheric pressure, and its contribution is turned out to be quite insignificant. It is important to note that the contribution of reaction (3) according to the Dayma mechanism was quite noticeable and amounted to 14.3% under the low pressure conditions. According to the analysis of the new mechanism, the contribution of reaction (3), on the contrary, is increased by 5% and the direction of isomerization remain the same as at low pressure.

Thus, the use of the refined rate constants for the H-abstractions at positions 2 and M significantly influenced the contribution of these reactions to the complete consumption of EPe in comparison with the Dayma mechanism. It can be seen from the analysis that the pressure change has the greatest effect on the isomerization reactions (1) -(3). As it shown, the isomerizations play a significant role in the redistribution of the fuel consumption pathways and, as a consequence, affect the resulting pool of shorter intermediate compounds. To solve this problem, it was necessary to identify the most important chemical reactions in the mechanisms that effect the velocity calculations.

Therefore, an analysis of the sensitivity coefficients of burning velocity to the reaction rate constants in the new mechanism was carried out. For ease of comparison, the analysis was performed in the same way as it was done in the work of Dayma [START_REF] Dayma | Experimental and Detailed Kinetic Modeling Study of Ethyl Pentanoate (Ethyl Valerate) Oxidation in a Jet Stirred Reactor and Laminar Burning Velocities in a Spherical Combustion Chamber[END_REF]: for lean (φ=0. Cette décomposition se produit à des températures plus basses que l'initiation Ester X (ester) X (O2) X (Ar) Qv , cm 3 Étude cinétique de la combustion en flammes laminaires de biocarburants de type ester Le progrès partout dans le monde nécessite une variété de sources d'énergie propre. Les biocarburants liquides de type ester semblent être très efficaces dans ce contexte, car ils sont faciles à utiliser dans les véhicules modernes, ils peuvent être produits à partir de diverses ressources renouvelables et ils offrent des caractéristiques de combustion respectueuses de l'environnement. À cet égard, les esters éthyliques d'acides gras (EEAG) sont considérés comme une classe prometteuse de biocarburants.

APPENDIX 1

L'objectif principal de cette thèse était de développer un mécanisme cinétique chimique actualisé de la combustion des EEAG légers jusqu'au pentanoate d'éthyle et de le valider par rapport aux nouvelles données expérimentales sur la structure de flammes laminaires prémélangées à basse pression et pression atmosphérique. Les flammes alimentées par trois EEAG, l'acétate d'éthyle, le butanoate d'éthyle et le pentanoate d'éthyle, ont été étudiées au moyen de la spectrométrie de masse avec faisceau moléculaire et de la chromatographie en phase gazeuse. Plus de 40 espèces stables et intermédiaires comprenant des radicaux ont été détectées et quantifiées dans les flammes. Une analyse complète du mécanisme développé a été réalisée.

La thèse se compose de 3 chapitres. Le premier chapitre présente une revue bibliographique. Les études expérimentales et théoriques les plus importantes sur la combustion des EEAG sont discutées. Le deuxième chapitre présente un aperçu des méthodes expérimentales et de simulation utilisées dans la thèse. Des détails sur le développement du mécanisme sont également fournis dans cette partie. Le dernier chapitre présente des résultats expérimentaux et de modélisation sur les esters étudiés en comparaison avec les mécanismes cinétiques de la littérature.

Mots clés: Combustion, Biocarburant, Chromatographie en phase gazeuse, Spectrométrie de masse à faisceau moléculaire, Flamme prémélangée, Modélisation cinétique chimique, Mécanisme cinétique chimique détaillé

Kinetic study of ester biofuels in flames

Global progress all over the world requires a variety of clean energy sources. Liquid esterbased biofuels seem to be very effective in this context since they are easy to use in modern vehicles, they can be produced from a variety of renewable resources, and they provide environmentally friendly combustion characteristics. In this regard, fatty acid ethyl esters (FAEEs) are considered as a promising class of biofuels.

The main goal of this thesis was to develop an updated chemical kinetic mechanism of combustion of light FAEEs up to ethyl pentanoate and validate it against the new experimental data on chemical speciation in low and atmospheric pressure premixed laminar flames. The flames fueled by three FAEEs, ethyl acetate, ethyl butanoate and ethyl pentanoate, were investigated by means of molecular-beam mass-spectrometry and gas-chromatography. More than 40 stable and intermediate species including radicals were detected and quantified in the flames. A comprehensive analysis of the developed mechanism was performed.

The thesis consists of 3 chapters. In the first chapter a review of literature is presented. The most important experimental and theoretic studies on FAEEs are discussed. The second chapter presents an overview of experimental and simulation methods used in the work. Details on the mechanism development are also provided in this part. The last chapter present experimental and modeling results on the esters studied in comparison with the literature kinetic mechanisms. Keywords: Combustion, Biofuel, Gas chromatography, Molecular beam mass spectrometry, Premixed flame, Chemical kinetic modeling, Detailed chemical kinetic mechanism

3. 2 . 2 .

 22 Calculation of the ethyl pentanoate laminar burning velocity ................. MAIN RESULTS AND CONCLUSIONS ........................................................................................ APPENDIX 1 ......................................................................................................................................... APPENDIX 2 ......................................................................................................................................... APPENDIX 3 ......................................................................................................................................... LIST OF REFERENCES .....................................................................................................................

Figure 1 . 1 .

 11 Figure 1.1. Transesterification reaction of triglyceride with alcohol. It is the main industrial method of fatty acid ester production.

  corresponding FAME and FAEE are formed. Until the XXI century chemical kinetics of esters' oxidation and combustion was not of particular interest since esters are not the main components of traditional hydrocarbon fuels. However, with the development of the biofuel industry chemical kinetics of the oxidation of ethers and esters began to be studied more widely and in detail. The key motivation was in the need for thorough understanding of the oxidation chemistry of new classes of compounds both in the pure form and in the mixtures with traditional fuels for the practical applications. Experimental and numerical studies of the oxidation and combustion kinetics of real biodiesel components are extremely complex due to the large sizes of the molecules. To solve this problem a hierarchical approach is used at which construction of a kinetic mechanism for the oxidation of a heavy compound is based on the kinetic submechanisms of lighter intermediate components. In this way the systematic studies of the oxidation chemistry of shorter model molecules allow us to describe the kinetics of intermediate stages of heavy fuel oxidation. At the same time, it can provide important information on the characteristics of the main reaction classes of a real fuel.The reaction pathways of a molecule oxidation are determined by its structure and external conditions. Due to the long alkyl groups fatty acid esters can participate in the same transformation chains as normal hydrocarbons of the same length[START_REF] Coniglio | Combustion chemical kinetics of biodiesel and related compounds (methyl and ethyl esters): Experiments and modeling -Advances and future refinements[END_REF]. At the combustion conditions these are mainly reactions of the abstraction of a hydrogen atom (H-abstraction) when a molecule is attacked by a free flame radical. Nowadays the chemistry of hydrocarbon oxidation has been studied quite deeply, therefore to describe this class of ester oxidation reactions existing kinetic schemes for the hydrocarbon oxidation can be exploited[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],

1. 1 .

 1 EXPERIMENTAL STUDY AND NUMERICAL SIMULATION OF OXIDATION OF FATTY ACID ETHYL ESTERS1.1.1. Chemical-kinetic studies of small FAEEs as model components of biodiesel For the beginning of this section it is important to note that there is a large number of technical and motor tests of various biodiesel fuels and their components in literature. Most of these works are purely descriptive and do not delve into the physical chemistry of the processes. Therefore, in this review we will discuss only works devoted to the study of the chemical kinetics of ethyl esters' oxidation.Fatty acid methyl esters have been studied much more intensively than similar ethyl esters due to their prevalence and applied value. However, the increased interest to the FAEE-based biofuels has motivated researchers to study the kinetics of oxidation and combustion of ethyl esters in more detail. Also, a certain interest to the oxidation chemistry of FAEEs arose from a purely academic point of view. This is due to the fact that FAEEs are characterized by a unimolecular pericyclic decomposition through a six-centered transition state with the formation of ethylene and the corresponding carboxylic acid (Fig.1.2).

Figure 1 . 2 .

 12 Figure 1.2. Unimolecular decomposition of an ethyl ester through the intermediate six-centered ring complex [70].

  scheme in the studied range of conditions and parameters.Experimental data on the spatial distribution of species concentrations in flames (i.e. the chemical structure of a flame) under various conditions provides important information about the oxidation mechanism of a particular fuel. In addition, the flame structure measurements make it possible to check kinetic submechanisms in more detail in contrast to the global parameters (burning velocity, ignition delay time). Gasnot et al.[START_REF] Gasnot | Ethyl acetate oxidation in flame condition: an experimental study[END_REF] has conducted the first experimental study of the chemical composition of a flame with the addition of

Figure 2 .

 2 1 (a). A flame ignited on the given burner is quasi-one-dimensional that means the concentration of substances and the flame temperature at any point in a plane parallel to the burner surface are constant and depend only on the coordinate along the normal to the burner surface. The one-dimensionality is violated only at the edges of the flame where significant heat losses and convective flows appeared. Therefore all measurements were carried out in the central part of the flame. The burner itself is a brass disc with a radius of 16 mm and a thickness of 3 mm with holes 0.5 mm in diameter and a distance of 0.7 mm between them. The disc is mounted in a water-cooled brass body controlled by a Termex VT4-1 thermostat. The burner temperature was maintained at 95 °C. Oxygen and argon flows were manually set with an accuracy of ±1% using a calibrated mass-flow controller (MKS) MKS System Inc.Liquid fuel was supplied from a syringe to evaporator through a metal capillary (Figure2.1 (b)). The syringe plunger was driven by a stepper motor operating at a given frequency corresponding to the required volumetric flow rate. A stream of argon and oxygen was passed through the evaporator carrying along the vapors of the liquid fuel. The vaporizer was made of a pyrex vessel filled with steel balls and equipped with an electric heater. The evaporator was maintained at a temperature of 10-15 °C below the boiling point of the particular ester studied. The choice of such a temperature regime ensured a complete evaporation of liquid ester continuously supplied to the evaporator. At the same time the temperature lower the boiling point did not lead to ester boiling that can cause instabilities in the fuel vapor supply to the burner.

Figure 2 . 1 .

 21 Figure 2.1. Botha-Spalding burner device (a) and the system of the fuel mixture supply to the burner (b).

Figure 2 . 2 .

 22 Figure 2.2. General scheme of the MBMS-setup for the measurements of the chemical flame structures.

Figure 2 . 3 .

 23 Figure 2.3. Schematic drawing of the probe with a mounting flange and the real photograph of the probe above the thermocouple and burner.

[

  107]. Since argon is the main component (70-80%) of the fuel mixture in all flames, the initial signals of the measured mass peaks (𝐼 𝑖 0 ) were normalized to the intensity of the signal of the 40th mass (𝐼 𝐴𝑟 0 ) and the mole fraction of argon (XAr): Such normalization makes it possible to compare flames with different argon dilutions and to avoid the scatter of measured signals associated with possible fluctuations in the gas flow. Further data processing is carried out with normalized signals. The signal intensity of the i-th component (Ii) is related to its mole fraction (Xi) by a simple ratio: (2.2) 𝐼 𝑖 = 𝑆 𝑖 (𝐸) • 𝑋 𝑖 , where Si(E) is a calibration factor for a given substance at the fixed ionizing electron energy E. The calibration factor depends on many parameters and can generally be represented by the following expression [108]: (2.3) 𝑆 𝑖 (𝐸) = 𝐴 • 𝜎 𝑖 (𝐸) • 𝐷(𝑚 𝑖 ) • 𝐹(𝑇, 𝑝), where A is a numerical coefficient of proportionality, σi(E) is an effective ionization cross-section of the i-th compound at the energy of ionizing electrons E, D(mi) is a coefficient that characterizes the dependence of the sensitivity of the MBMS-setup on the mass of detected ions; the mass-discrimination factor appears due to the fact that the central part of the molecular beam can be enriched with the heavier particles because of barodiffusion, F(T,p) is an empirical function that establishes the dependence of the molecular beam density in the ionization region on the flame pressure p and local temperature T. The F(T,p) function is an instrumental function, so it is determined by the geometry (probe, skimmer, collimator) and gas-dynamic characteristics of the system.

2 . 1 . 3 .

 213 profiles below are obtained by averaging over several measurements. A complete list of compounds measured in the flames at atmospheric pressure is given in Appendix 1. The Appendix also contains the values of the ionization potentials (PI), the energy of ionizing electrons (EIE) at which each compound was measured, the calibration method and the accuracy of the mole fraction determination. Online sampling gas chromatographic setup for studying the chemical flame structure at low pressure Experimental measurements of the chemical flame structure of esters at low pressure were performed at the Laboratory of Reactions and Process

Figure 2 . 4 .

 24 figure. The fueling line was additionally heated to avoid condensation of heavy ester vapors. The mass flow of each gas was controlled by a corresponding massflow controller (Bronkhorst) connected to a computer. The liquid fuel was supplied from a metal vessel which was pressurized by argon injected through the special channel. The fuel portion pressed out of the vessel entered the fuel supply line. The exact ester flow rate was controlled by a Coriolis-type mass-flow controller (Bronkhorst Cori-Tech) installed at the outlet of the ester vessel. After the MFC the liquid entered an evaporator-mixer (Bronkhorst) where it was evaporated and mixed with argon. The resulting fuel mixture entered the burner along with the other gases. All the controllers were calibrated before the experiments. Then the flow control manipulations were carried out from the computer only.

Figure 2 . 4 .

 24 Figure 2.4. General scheme of the experimental facility for studying the chemical flame structure at low pressure. 1 -metal vessel with a liquid fuel 2 -evaporator 3 -filter/flow stabilizer 4 -burner cooling thermostat 5 -water condensing system with a cooling thermostat 6 -water condensation system with liquid nitrogen traps 7 -rotary vane pump 8 -low pressure chamber 9 -McKenna burner 10 -flame 11 -sampling probe 12 -pressure regulator 13 -mercury piston for the gas pressurizing 14 -inlet for the calibration mixture 15 -turbomolecular pump V1-V17 -valves GC1-GC2 -gas chromatographs MFC1-MFC5 -mass-flow controllers P1-P3 -pressure gauge V1-V2 -free vessels for the calibration mixtures

Fuel

  gas entered the burner mixes uniformly in the housing and exits through the porous disk as a laminar flow. This flow after ignition forms a flat quasi-one-dimensional flame (Figure 2.5 (b)).

Figure 2 . 5 .

 25 Figure 2.5. McKenna burner device (a) and real photograph of the flame stabilized on the burner in the low pressure chamber (b).

  Figure 2.5 (b)). The geometric characteristics of the probe are shown in Figure 2.6.

Figure 2 . 6 .

 26 Figure 2.6. Geometry of the sampling probe used in experiments at low pressure. Measurement unit: mm.

2. 1 . 4 .

 14 Flame temperature measurements 2.1.4.1. Thermocouple temperature measurements Temperature is the most important parameter in a reacting system. Accurate numerical simulation of the chemical flame structures requires information on the actual flame temperature in experiments. In this regard the profile of the temperature dependence on the height above the burner was measured in all flames. Temperature measurements in flames are rather complicated since the profiles are characterized by sharp gradients and high absolute values of temperature on the scales of several millimeters. In this regard the micro-thermocouple method was chosen for temperature measurements in both atmospheric and low pressure flames. One important specific of temperature measurements in experiments with sampling is the necessity of taking into account thermal disturbances of the flame by the probe. To account for these disturbances temperature is measured in a flame in the presence of a probe. Such approach provides a real temperature information as it is during the sampling. Thermocouple junction is placed near the probe orifice (~0.1 mm) measuring the gas temperature at the inlet of the sampling probe. Thermocouple position relative to the probe and the burner surface during temperature measurements are shown in Figure 2.7. For these measurements the thermocouple should be as thin as possible in order to obtain sufficient spatial resolution and minimize flow deceleration in front of the probe.

Figure 2 . 7 .

 27 Figure 2.7. Thermocouple position relative to the probe and the burner surface during temperature measurements.

Figure 2 . 8 .

 28 Figure 2.8. Schematic of the thermocouple in experiments at atmospheric pressure. Measurement unit: mm.

Figure 2 . 9 .

 29 Figure 2.9. Schematic of the thermocouple in experiments at low pressure.

Figure 2 . 10 .

 210 Figure 2.10. Thermocouple calibration curve and electro-compensated temperature measurements in EPe flame at different distances from the burner.

Figure 2 . 10 shows

 210 the calibration curve of the thermocouple and the temperature measurements in the EPe flame at low pressure.

  Numerical modeling is an essential part of a detailed analysis of combustion processes. It allows us to highlight and understand the most important aspects of the complex physicochemical processes independently complementing experimental investigations. Numerical simulation of chemical kinetics in reacting systems (including flames) makes it possible to calculate practically important global parameters, such as laminar flame speeds, ignition delay times, chemical composition of pyrolysis and combustion products (presence of harmful emissions), ignition conditions, flame stability and so on. In addition numerical simulations are extremely useful for purely research purposes greatly speeding up and simplifying the analysis processes.There is a number of specialized software packages for such calculations developed both by individual research groups and by large commercial companies. The most popular ones are CHEMKIN[START_REF] Kee | Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics[END_REF], [119], Cantera [120], OpenSMOKE [121]-[123], Chemical Workbench [124], FlameMaster [125], Cosilab [126]. In this work, the CHEMKIN II and CHEMKIN-Pro software package were used. In fact, CHEMKIN-Pro is an extended and more convenient version of CHEMKIN II. The CHEMKIN program is a set of numerical models of various typical reactors for solving the problems of reacting flows. It can take into account the gas-phase and surface kinetics, thermochemical and physical properties of substances. The "Premixed Laminar Burner-Stabilized Flame" reactor was used to simulate the chemical structure of the flames studied. This reactor is a mathematical model of a premixed laminar one-dimensional flame stabilized on a flat burner at a constant pressure. The model is described by the following system of equations: (2.4) ideal gas equation of state 𝑆) Here R -the universal gas constant, x -spatial coordinate, t -time, Ttemperature, P -pressure, ρ -mass flow density, v -gas velocity, ср, λ -heat capacity at constant pressure and thermal conductivity of the gas mixture, Maverage molecular weight of the mixture, S -cross-sectional area of the flow tube (the area of the flow tube is assumed constant as default), qr -heat flow, Yi -mass fraction of the i-th component of the mixture (there are I components in total), cpi -heat capacity at constant pressure of the i-th component, hi -specific enthalpy of the i-th component, ji = ρYiVi -diffusion flux of the i-th component, where Vidiffusion velocity of the i-th component, wi -mass rate of formation of the i-th component in a chemical reaction per unit volume. This system of equations consists of I+3 equations for I+3 variables: 𝜌, v, T, Y1,…, YI. To solve it boundary conditions are set on the left (x=0, burner surface) and right border of the flame (x=h, where h is the maximum calculated distance from the burner, it corresponds to the zone of flame products). In the flame front the total mass flow rate Vm=ρv is conserved. On the left boundary Vm is defined from the initial conditions and on the right boundary vanishing of concentration

2 . 2 . 2 .

 222 7 in the file are given for high and low temperatures. The third file describes physical properties of the substances. For each molecule the Lennard-Jones potential coefficients (collision diameter 𝜎 and potential well depth 𝜀), dipole moment, polarizability and rotational relaxation parameter are given. The equation system (2.4) -(2.7) can be solved using the parameter 𝜎 which is necessary for the diffusion coefficients calculations. Thus, the system of equations (2.4) -(2.7) together with the boundary conditions and the input data forms a complete boundary value problem which could be solved by the finite difference methods incorporated to the CHEMKIN package. As the solution the program generates a file with the spatial distribution of molar fractions of species, temperature and other parameters along the flame coordinate. Detailed kinetic mechanisms of oxidation and combustion To calculate the chemical flame structure of ethyl acetate, ethyl butanoate and ethyl pentanoate a detailed mechanism of EPe oxidation proposed by Dayma et al. [79] was used. This mechanism was the first detailed kinetic mechanism of EPe oxidation proposed in the literature. It is based on the chemical-kinetic mechanisms for the oxidation of C1-C5 species [127]-[129] developed to describe oxidation kinetics of various alcohols and their mixtures with small hydrocarbons. This mechanism was extended by Dayma and coauthors taking into account the corresponding oxidation chemistry of EPе and lighter ethyl ethers. This fact made it possible to use this mechanism for the flame simulations of EA and EB. Since only the flames were investigated in this work the lowtemperature chemistry associated with the formation of a large amount of peroxide compounds did not have a significant effect. Thereby this lowtemperature part was removed from the mechanism. The full version of the mechanism includes 522 compounds and 2719 reactions while the reduced version consists of 232 compounds and 1845 reactions. The last one was exploited for the calculations in the work. The mechanism of Dayma was published in 2012 and the kinetic parameters of specific reactions of FAEEs were poorly understood at that time. In this regard, the rate constants of the primary reaction pathways of FAEE destruction used in this mechanism were estimated only from the principles of structural analogy with other oxygenated compounds (alcohols and aldehydes). This fact has motivated us to create a new version of the EPe combustion mechanism based on recent studies of the combustion kinetics of ethyl esters.The mechanism of oxidation of small FAEEs proposed by Sun et al.[START_REF] Sun | Experimental and modeling efforts towards a better understanding of the high-temperature combustion kinetics of C3C5 ethyl esters[END_REF] was taken as a basement for the new mechanism. The mechanism of Sun was developed to describe high temperature oxidation of three light ethyl esters: ethyl formate, ethyl acetate and ethyl propanoate. The well-proven AramcoMech 1.3 mechanism[START_REF] Metcalfe | A Hierarchical and Comparative Kinetic Modeling Study of C1 -C2 Hydrocarbon and Oxygenated Fuels[END_REF] was used as the basic kinetic scheme for the oxidation of small C0-C4 compounds in the mechanism of Sun et al. To describe the main destruction pathways of ethyl esters the rate constants of the corresponding reactions were calculated by the quantum chemical methods or have been taken from the recent theoretical works.

Figure 2 . 11 .

 211 Figure 2.11. The structure of ethyl pentanoate molecule with carbon labeling.

  Dayma the H-abstraction reactions in positions 5 and M have the same rate constants taken as an analogy with terminal carbons in a linear alkane. In the new mechanism these constants are different since the proximity of oxygen in the ethyl group affects the energy of the C-H bond in position M.For better agreement of the model predictions and the experimental results on EPе flame at low pressure, the main reaction of ethanol formation C2H5OH (+M)  C2H5+OH (+M) was taken with the rate constant from the wellknown Marinov mechanism[START_REF] Marinov | A detailed chemical kinetic model for high temperature ethanol oxidation[END_REF]. The original rate constant of this reaction given in the mechanism of AramcoMech 1.3 led to a significant underestimation of the maximum mole fraction of ethanol. It should be noted that in the mechanism of Dayma the ethanol oxidation chemistry is fully described by the Marinov mechanism.

  This chapter presents the measured chemical flame structures of FAEEs in the experiments at atmospheric and low pressure. In addition to the mole fraction profiles in each flame a temperature profile was measured. The measured temperature profiles were used as the input for a numerical simulation of the corresponding flames. Experimental data in the chapter are presented together with the results of the numerical simulations. Discussion is provided in the context of description accuracy of experimental data by the models. In all figures in this chapter symbols represent the experimentally measured values and lines represent the results of numerical simulations by different mechanisms. In the second part of the chapter a numerical analysis of the models is provided.

Figure 3 .

 3 Figure 3.1 shows the mole fraction profiles of reactants (EA, O2) and the main products (H2O, CO2, CO) in near-stoichiometric (φ = 1.1) and fuel-rich (φ = 1.7) EA/O2/Ar flames. Black line with dots on the figure represents the experimentally measured temperature profiles; the corresponding values are shown on a separate scale on the right side.

Figure 3 . 1 .

 31 Figure 3.1. Temperature profiles and mole fraction profiles of reactants and main products in near-stoichiometric (top) and rich (below) flames of ethyl acetate at atmospheric pressure. Symbols: experimental data; dashed lines: numerical simulation with the model of Sun.

Figure 3 . 2 .Figures 3 . 2

 3232 Figure 3.2. Mole fraction profiles of intermediate hydrocarbon products in the near-stoichiometric (φ=1.1, left) and rich (φ=1.7, right) ethyl acetate flames at atmospheric pressure. Symbols: experimental data; solid lines: Dayma mechanism; dotted lines: Ahmed mechanism; dashed lines: Sun mechanism.

  Ahmed and Sun mechanisms have predicted an overestimated value of the maximum mole fractions of ketene especially under the rich flame conditions. On the contrary, the Dayma model has underestimated these values. However, we can conclude that the Sun and Dayma models are equally close to the experimental values in the near-stoichiometric flame taking into account the experimental uncertainty. In the rich flame the mechanism of Dayma has shown a complete agreement with the experiment, whereas the other two models overestimated the peak mole fraction of ketene by 3-4 times.According to the experiments the mole fraction of formaldehyde (CH2O) is insensitive to the equivalence ratio changes. This fact was confirmed in calculations by all three mechanisms. As it seen, the calculated values are almost two times higher than the experimental results. However the discrepancies between the simulations and experiments do not exceed the experimental uncertainty. Such result can be assumed as satisfactory, since the accuracy of formaldehyde quantification in the flame was rather low due to the impossibility of the direct calibration.

Figure 3 . 3 .

 33 Figure 3.3. Mole fraction profiles of intermediate oxygenates in the nearstoichiometric (left) and rich (right) ethyl acetate flames at atmospheric pressure. Symbols: experimental data; solid lines: Dayma mechanism; dotted lines: Ahmed mechanism; dashed lines: Sun mechanism.

Figure 3 . 4 .

 34 Figure 3.4. Temperature profile and mole fraction profiles of reactants and main products in the stoichiometric flame of ethyl acetate at 50 Torr. Symbols: experimental data; solid lines: Dayma mechanism; dotted lines: Ahmed mechanism; dashed lines: Sun mechanism.

Figure 3 . 5 .

 35 Figure 3.5. Mole fraction profiles of intermediate species in the stoichiometric flame of ethyl acetate at 50 Torr. Symbols: experimental data; solid lines: Dayma mechanism; dotted lines: Ahmed mechanism; dashed lines: Sun mechanism.

Figure 3 . 6 .

 36 Figure 3.6. Mole fraction profiles of intermediate species in the stoichiometric flame of ethyl acetate at 50 Torr. Symbols: experimental data; solid lines: Dayma mechanism; dotted lines: Ahmed mechanism; dashed lines: Sun mechanism.

Figure 3 .

 3 Figure 3.7 shows the mole fraction profiles of reactants (EB, O2) and the main products (H2O, CO2, CO) in stoichiometric (φ=1.0) and fuel rich (φ=1.5) EB/O2/Ar flames. Two mechanisms were used to simulate the chemical structure of EB flames: the mechanism of Dayma et al. [79] and the mechanism proposed in the thesis. The simulation results based on the Dayma mechanism are shown in

Figure 3 .

 3 Figure 3.7 by solid black lines and the calculations based on the new mechanism

Figure 3 . 7 .

 37 Figure 3.7. Temperature and mole fraction profiles of reactants and main products in stoichiometric (top) and rich (below) flames of ethyl butanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 .

 3 Figure 3.8 shows the experimentally measured and calculated mole fraction profiles of key radicals which are the main chain carriers in flames.

Figure 3 . 8 .

 38 Figure 3.8. Mole fraction profiles of H, OH and CH3 radicals in stoichiometric (φ=1.0, left) and rich (φ=1.5, right) flames of ethyl butanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 . 9 .

 39 Figure 3.9. Mole fraction profiles of intermediate hydrocarbons in stoichiometric (left) and rich (right) flames of ethyl butanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 . 10 .

 310 Figure 3.10. Mole fraction profiles of intermediate hydrocarbons in stoichiometric (left) and rich (right) flames of ethyl butanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 .

 3 Figure 3.11 shows comparison of the experimental and calculated mole fraction profiles of oxygenated compounds. The largest discrepancy between the experiment and modeling is observed in the case of formaldehyde (CH2O). Here, both models have predicted a twice higher mole fraction of CH2O than was observed experimentally. Despite that fact the calculated values still lie within the experimental accuracy range. The similar discrepancy between the model calculations and experimental data was observed in the EA flames. That indicates the general tendency of the mechanisms to overestimation of the CH2O concentration in the flames of these esters.

Figure 3 .

 3 Figure 3.12 shows the mole fraction profiles of reactants (EPe, O2) and main products (H2O, H2, CO2 and CO) in stoichiometric EPe/O2/Ar flame. The mechanism of Dayma and the new mechanism were also used to simulate the chemical structure of this flame.

Figure 3 . 12 .

 312 Figure 3.12. Temperature profile and mole fraction profiles of reactants and main products in the stoichiometric flame of ethyl pentanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 . 13 .

 313 Figure 3.13. Mole fraction profiles of major radicals in the stoichiometric flame of ethyl pentanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 . 14 .

 314 Figure 3.14. Mole fraction profiles of intermediate hydrocarbon products in the stoichiometric flame of ethyl pentanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 . 15 .

 315 Figure 3.15. Mole fraction profiles of oxygenated products in the stoichiometric flame of ethyl pentanoate at atmospheric pressure. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 .

 3 Figure 3.16 shows the mole fraction profiles of reactants (EPe, O2) and main products (H2O, H2, CO2, CO) in stoichiometric EPe/O2/Ar flame at pressure of 50 Torr. As expected, the simulated profiles agreed well with the experimental data. A slight discrepancy between the experimental and calculated oxygen profiles was found in the initial flame zone. This shortcoming could be associated with an older and less accurate chromatograph to determine oxygen mole fraction. As can be seen from the temperature profile, the EPe flame at low pressure was significantly hotter than the atmospheric pressure flame. This came from the lower argon dilution and other flame stabilization conditions: the flame at 50 Torr is farther from the burner and loses less heat. Also, the thinner and narrower probe in these experiments introduced less thermal disturbances of the flame compared to the sonic probe at the MBMS setup. One more reason was due to the higher radical concentrations which recombine less often at low pressure than at high.

Figure 3 . 16 .Figures 3 . 17

 316317 Figure 3.16. Temperature profile and mole fraction profiles of reactants and main products in the stoichiometric flame of ethyl pentanoate at 50 Torr. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

  Figures 3.17and 3.18 demonstrate the measured mole fraction profiles of intermediate C1-C4 hydrocarbons in comparison with modeling by two mechanisms. The measured mole fraction profiles of propene (C3H6), propane (C3H8), n-butane (n-C4H10) and 1-butene (1-C4H8) were reproduced fairly

Figure 3 . 17 .

 317 Figure 3.17. Mole fraction profiles of intermediate hydrocarbon products in the stoichiometric flame of ethyl pentanoate at 50 Torr. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 . 18 .

 318 Figure 3.18. Mole fraction profiles of intermediate hydrocarbon products in the stoichiometric flame of ethyl pentanoate at 50 Torr. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism.

Figure 3 .

 3 Figure 3.19 shows experimental and simulation results for oxygenated intermediates. As at atmospheric pressure, the mole fraction of acetaldehyde (CH3CHO) is higher than that of formaldehyde (CH2CO). It can be seen that the new model has predicted the peak mole fraction of acetaldehyde much better than the Dayma mechanism which has overestimated it by almost two times. The experimentally determined mole fraction of ethanol (C2H5OH) was quantitatively described by the models but the peak position in the experiment was shifted toward the burner surface similar to the above-described shifts of some hydrocarbons. The mole fraction profiles of acetone (CH3COCH3), ethyl acrylate (C5H8O2) and valeric acid (C4H9COOH) measured in the experiment are in much worse agreement with the simulation results. The maximum mole fraction of acetone was underestimated by 3 times in the Dayma model and almost by 5 times in the new mechanism. However, the mole fraction of CH3COCH3 has been only about 10 -5 , thus the description accuracy of this component was not of particular interest. In the low-pressure experiment we have measured the mole fraction profile of ethyl acrylate (C5H8O2) which should be formed at the early stages of EPe oxidation. As can be seen from the figure the peak mole fraction of C5H8O2 was predicted by the mechanism of Dayma quite well. According to the new model, the peak molar fraction of ethyl acrylate should be 3.5 times higher, which

Figure 3 . 19 .

 319 Figure 3.19. Mole fraction profiles of oxygenated products in the stoichiometric flame of ethyl pentanoate at 50 Torr. Symbols: experimental data; black lines: Dayma mechanism; red lines: new mechanism

Figure 3 .

 3 Figure 3.20 shows an integral rate of production analysis (IROP) of the primary reaction pathways of ethyl acetate destruction in the near-stoichiometric flame (φ = 1.1). Three mechanisms were used to simulate EA flames. In this regard, this figure represents the generalized scheme of EA destruction in the flame. The values on the scheme indicate the percentage contributions of specific reactions to the complete consumption of particular component. Black values correspond to the mechanism of Dayma, blue values correspond to the Sun model, which is used in our new model of EPe combustion, and green values correspond to the model of Ahmed. Let's look an example of the scheme interpretation: from the presented analyses it follows that according to the model of Dayma 42.4% of ethyl acetate is consumed in the reaction of unimolecular decomposition with formation of ethylene and acetic acid. According to the Sun mechanism the contribution of this reaction to the consumption of EA is 30.74%, and in the model of Ahmed it is 28.94%. In addition to the unimolecular decomposition, the mechanisms include three more pathways for the primary destruction of EA through the H atom eliminations with free radicals. Three H-atom abstractions correspond to three carbon atoms where C-H bond could be ruptured. As a result of the hydrogen elimination fuel radicals are formed. These species are represented on the figure as the EA molecule with an asterisk in the position where an H atom was

Figure 3 .

 3 Figure 3.20. IROP analyses of the main oxidation pathways of EA in nearstoichiometric flame (φ = 1.1) at atmospheric pressure. Black values: percentage contribution to the total component consumption according to the mechanism of Dayma; blue values: according to the model of Sun; green values: according to the model of Ahmed.

Figure 3 .Figure 3 . 3 )

 333 Figure 3.21. IROP analyses of the main oxidation pathways of EA in rich flame (φ = 1.7) at atmospheric pressure. Black values: percentage contribution to the total component consumption according to the mechanism of Dayma; blue values: according to the model of Sun; green values: according to the model of Ahmed.

Figure 3 . 22 .

 322 As in the previous diagrams, the black values correspond to the model of Dayma. The blue values correspond to the mechanism proposed in this work. As discussed above, the rate constants of the primary H-abstraction reactions by various radicals were revised in the new mechanism. Therefore, the reaction contributions with each of the radicals H, OH, O and CH3 are shown in the figure separately for a more detailed analysis.

Figure 3 . 22 .

 322 Figure 3.22. According to the Dayma model the most probable pathways of EB destruction in the stoichiometric flame are unimolecular decomposition (20%) and H-abstraction with the formation of two fuel radicals: EBEJ (17.7%) and EB2J (21.3%). Further in the flame, most of the EB2J radicals is isomerized into EBEEJ radicals, which in turn decompose completely with acetaldehyde (CH3CHO) formation. As in the EA flames, this pathway is the main reaction pathway of acetaldehyde formation. The same path is realized in the new mechanism. It can be seen from Figure 3.11 that the Dayma model overestimates a few the mole fraction of acetaldehyde, while the new mechanism predicts the values that are closer to experiment. This is most likely due to the slower consumption of acetaldehyde by H-atom abstractions in the model of Dayma.

Figure 3 .

 3 Figure 3.22. IROP analyses of the main oxidation pathways of EB in stoichiometric flame at atmospheric pressure. Black values: percentage contribution to the total component consumption according to the mechanism of Dayma; blue values: according to the new model.

Figure 3 .

 3 Figure 3.23. IROP analyses of the main oxidation pathways of EB in rich (φ = 1.5) flame at atmospheric pressure. Black values: percentage contribution to the total component consumption according to the mechanism of Dayma; blue values: according to the new model.

Figure 3 .Figure 3 .

 33 Figure 3.23 shows that the radical reaction contributions in both mechanisms are 2-3 times less than those in the stoichiometric flame. However, the general trends remain. It is important to discuss the formation of ethane (C2H6) and propane (C3H8) in the rich flame, since the model predictions for these compounds have diverged from experiment by more than 2 times (see Figure 3.10). The main pathway of ethane formation is the recombination of two methyl radicals (CH3). If we go back to Figure 3.8, we can see that the new mechanism describes the maximum mole fraction of CH3 more accurately than the Dayma

Figure 3 .

 3 Figure 3.24 shows a diagram of the ethyl pentanoate conversion pathways in stoichiometric flame at a pressure of 50 Torr. Black values also correspond to the mechanism of Dayma, blue values correspond to the analysis of the new mechanism. The IROP analysis was carried out similarly to the EB analysis described above, i.e. the contributions of H-abstractions by different radicals are separately distinguished.As can be seen from the figure, in contrast to the lighter esters, the unimolecular decomposition contribution to the total EPe destruction is insignificant compared to the H-abstraction pathways. Only about 7-8% of the fuel is consumed through this path according to the models. Such a low contribution is due to the long alkyl chain. It was expected that the contribution of the six-centered unimolecular decomposition in the homologous series of FAEEs decreases, since the number of sites for radical attacks increases with the alkyl chain lengthening. Thus, most of EPe in the stoichiometric flame is consumed in the Habstraction reactions by the main flame radicals (H, OH, O and CH3). Therefore, the results of the latest studies[START_REF] Sun | Experimental and modeling efforts towards a better understanding of the high-temperature combustion kinetics of C3C5 ethyl esters[END_REF],[START_REF] Wang | Theoretical and kinetic study of the hydrogen atom abstraction reactions of ethyl esters with hydrogen radicals[END_REF],[START_REF] Mendes | Theoretical Study of the Rate Constants for the Hydrogen Atom Abstraction Reactions of Esters with •OH Radicals[END_REF] of the hydrogen abstraction reactions from the ester group in FAEEs (positions E and M, see Figure2.11) were taken into account during the new mechanism developing. The H-abstractions at these positions lead to the formation of the fuel radicals EPEEJ and EPEMJ.

Figure 3 .

 3 Figure 3.24. IROP analyses of the main oxidation pathways of EPe in stoichiometric flame at 50 Torr. Black values: percentage contribution to the total component consumption according to the mechanism of Dayma; blue values: according to the new model.

Figure 3 .

 3 Figure 3.25. IROP analyses of the main oxidation pathways of EPe in stoichiometric flame at atmospheric pressure. Black values: percentage contribution to the total component consumption according to the mechanism of Dayma; blue values: according to the new model.

Figure 3 .

 3 Figure 3.26 shows the results of the laminar flame velocity calculations based on the new kinetic mechanism (red lines) in comparison with experimental data (symbols) and calculations by the Dayma model (black lines). The experiments and corresponding calculations were carried out for pressures of 1,

Figure 3 . 26 .

 326 Figure 3.26. Laminar burning velocities of EPe/air mixtures at various equivalence ratios and pressures. Initial mixture temperature Ti = 423 K. Symbols: experimental data from [79]; black lines: mechanism of Dayma; red lines: new mechanism.

Figure 3 . 27 .

 327 Figure 3.27. The highest sensitivity coefficients of EPe laminar burning velocity to the reaction rate constants in the new mechanism (above) and the model of Dayma et al. (bottom). Sensitivity analysis performed for EPe/air mixtures in lean (φ = 0.7), stoichiometric (φ = 1.0) and fuel rich (φ = 1.4) ratios.

1 . 2 . 3 . 4 . 6 .

 12346 [START_REF] Lange | Valeric Biofuels: A Platform of Cellulosic Transportation Fuels[END_REF], stoichiometric (φ=1.0) and rich (φ=1.4) flame at atmospheric pressure and Ti=423 K. The coefficients obtained are presented in Figure3.27 in comparison with the sensitivity analysis from the work of Dayma. The figure shows elementary chemical reactions, to the which rate constants the highest (in absolute value) sensitivity was found.It is obvious that the burning velocity depends most strongly on the rate of the branching reaction H+O2  OH+O, that was demonstrated by the analysis of the mechanisms. However, the sensitivity to the rate constant of this reaction in the new mechanism is about 20-30% higher than in the Dayma mechanism.Moreover, the values of the constant itself are also different. Another most important reaction is the reaction CO+OH ↔ CO2+H which was also expected. This reaction has the same rate constant in both mechanisms and the sensitivity to this reaction, as can be seen, seems to be the same. Apart from these two reactions, the most important reactions in the mechanisms are the radical recombination reactions: H+O2+M  HO2+M H+OH+M  H2O+M HCO+H  CO+H2 Thus, as in the case of shorter esters[START_REF] Wang | Oxidation of small alkyl esters in flames[END_REF], EPe laminar burning velocity is controlled by the basic H2/O2 kinetics and the kinetics of light C0-C2 hydrocarbons. Unfortunately, despite significant efforts focused on the studies of oxidation kinetics of light compounds, the scientific community still does not have an unified understanding of the processes taking place. As a result, there is currently not a generally accepted set of reaction rate constants for the basic chemistry of hydrogen and light hydrocarbons[START_REF] Curran | Developing detailed chemical kinetic mechanisms for fuel combustion[END_REF].In the Dayma mechanism and the AramcoMech 1.3, which underlies the new mechanism, the sets of kinetic parameters of the basic chemistry differ markedly, especially in terms of pressure dependence. This is expressed in the accuracy of describing the mole fraction profiles of C2-C4 hydrocarbons. The sensitivity analysis has shown that the kinetics of the conversion of acetylene to vinyl radical plays a more important role in the new mechanism than in the Dayma model, especially under fuel-rich flame conditions. The rate constant of the reaction C2H2+H (+M) ↔ C2H3 (+M) has an explicit dependence on pressure.Considering it the differences in the chemistry of acetylene formation and consumption might be responsible for discrepancies in the predictions of the combustion velocities by the models at elevated pressures. It should be noted that in all the flames studied, the new mechanism described most accurately the mole fraction profiles of acetylene. Hence, it can be assumed that, thanks to AramcoMech 1.3, kinetics of the C2H4 → C2H3 → C2H2 transformation chain in the new mechanism is described better. In general, the new mechanism has shown a good predictive ability at different pressures and in a wide range of φ. Despite the differences in the kinetic parameters incorporated into the Dayma mechanism and the new mechanism, it is impossible to draw an unambiguous conclusion about the higher accuracy of one or the other mechanism from the available data. For this reason, additional experimental studies of the EPе laminar burning velocities at elevated pressures are of great practical and academic interest. It should also be noted that the study of the burning speeds of EPе mixtures with model components of gasoline and diesel is of particular interest. Molecular-beam mass-spectrometry was used to measure the mole fraction profiles of reactants, main products and key intermediate species in the atmospheric flames of the model components of biofuels based on fatty acid ethyl esters: ethyl acetate, ethyl butanoate and ethyl pentanoate. The chemical flame structure of ethyl pentanoate at a pressure of 50 Torr was measured by gas chromatography. Using the chemical kinetics mechanisms of high-temperature oxidation of light ethyl esters presented in the literature, a numerical simulation of the chemical flame structures was carried out. Comparison of the simulation results with experimental data has shown the unsatisfactory predictions of the mole fraction profiles of individual flame components, in particular, light hydrocarbons. An updated detailed combustion mechanism of ethyl pentanoate was proposed on the basis of modern literature data on the kinetics of hightemperature oxidation of small ethyl esters. The mechanism developed includes oxidation stages of lighter ethyl esters and could be used for their simulations. A special attention has been paid to the reaction rate constants of H atom abstractions from a fuel molecule. The new mechanism was verified against experimental data obtained and in comparison with the combustion mechanism of ethyl pentanoate presented in the literature. A more accurate mole fraction predictions of light hydrocarbons by the new model compared to the literature known model ware observed. A slightly lower accuracy of the new mechanism in describing the concentrations of individual oxygenated species was also noted. 5. A numerical simulation of laminar burning velocities of ethyl pentanoate/air mixtures by the new mechanism has been carried out. The simulation results were compared with the experimental data presented in the literature. It was shown that the new mechanism describes experimental data very well in a wide range of equivalence ratios and pressures. The main advantages and key disadvantages of the proposed combustion mechanism were analysed by the sensitivity analyses and the integral rate of production analysis. It was determined that the use of more recent rate constants for the H-abstraction reactions from the fuel molecule significantly effected the redistribution of the primary oxidation pathways of ethyl butanoate and ethyl pentanoate. At the same time, the use of AramcoMech 1.3 mechanism has helped to describe the mole fraction profiles of several light compounds. It is shown that it is necessary to revise the isomerization reactions of fuel radicals and the formation of acetic acid from them in the new mechanism for a more accurate description of the chemical structure of ethyl acetate flames. It is necessary to conduct additional experiments in a wide range of conditions, especially at elevated pressures to improve accuracy of the model predictions. Also, quantum-chemical calculations of the H-abstraction rate constants from ethyl pentanoate and ethyl butanoate are needed, as well as refinement of the rate constants of the six-centered unimolecular decomposition of ethyl esters.

Introduction

  La demande toujours croissante de ressources énergétiques et la lutte pour le respect de l'environnement obligent les chercheurs du monde entier à développer des carburants alternatifs aux combustibles fossiles. Une attention particulière est accordée aux carburants alternatifs pour les transports terrestres, car ces carburants doivent répondre à de nombreuses contraintes physiques, chimiques et économiques. L'une des solutions les plus efficaces est l'utilisation de biodiesel à base d'esters d'acides gras. De tels carburants ont une densité d'énergie suffisamment élevée, ne forment pratiquement pas de suie et de composés polyaromatiques lors de la combustion, et présentent des caractéristiques physiques proches du diesel classique, ce qui leur permet d'être utilisés sans modification significative des moteurs. Le biodiesel est produit à partir d'huiles végétales dans une réaction de transestérification avec du méthanol ou de l'éthanol pour produire des esters méthyliques d'acide gras (EMAG) ou des esters éthyliques d'acide gras (EEAG). Le méthanol est moins cher, car la majeure partie est produite à partir de gaz naturel, donc la plus grande partie du biodiesel est produite en ce moment à base d'EMAG. Cependant, l'éthanol est moins toxique et volatil que le méthanol et l'éthanol est moins corrosif, ce qui rend la production d'éthanol plus sûre. De plus, cet alcool rend le carburant à base d'EEAG complètement renouvelable, puisque l'éthanol peut être obtenu à partir de la biomasse. De nouvelles approches de la production de bioéthanol à partir de la biomasse, par exemple des déchets agricoles, rendent le biodiesel à base d'EEAG économiquement viable. En raison de sa prévalence dans les carburants actuellement utilisés, la combustion du biodiesel à base d'EMAG a été étudiée beaucoup plus intensivement que les carburants à base d'EEAG. Cependant, d'un point de vue pratique et académique, la pyrolyse et la combustion d'EEAG sont également très intéressantes. Contrairement à des EMAG, la chimie des esters éthyliques est caractérisée par une réaction de la décomposition monomoléculaire en formant un état de transition cyclique à six centres avec la production finale d'éthylène et de l'acide carboxylique correspondant (Fig.1).

L

  'étude des flammes à la pression atmosphérique a été réalisée à l'aide d'une installation de spectrométrie de masse à faisceau moléculaire à l'Institut de cinétique chimique et de combustion, Novossibirsk, Russie. La flamme a été stabilisée sur un brûleur Botha-Spalding (diamètre 16 mm) qui été maintenu à une température constante de 368 K grâce à une chemise d'eau de refroidissement. La consommation d'oxygène et d'argon a été contrôlée par les régulateurs de débit massique étalonnés. L'ester liquide a été introduit par une seringue à un évaporateur en utilisant un moteur pas à pas. Le système de prélèvement par faisceau moléculaire a fourni un échantillonnage direct du gaz de la flamme. Le faisceau moléculaire était formé par une sonde conique en quartz avec un orifice de 80 µm ; l'angle du cône intérieur était de 40°. Le faisceau a été focalisé par un écorceur ou skimmer puis modulé avec un modulateur à disque pour faire la distinction entre les signaux utiles et de fond. La détection des composants de la flamme à partir d'un échantillon de gaz a été réalisée par un spectromètre de masse quadripolaire EZAN MS-7302 avec un système d'ionisation par impact d'électrons doux , c'est-à-dire de basse énergie (la dispersion des énergies électroniques était d'environ ±0,25 eV). L'énergie d'ionisation des électrons a été sélectionnée individuellement pour chaque composant afin d'obtenir le meilleur rapport signal sur bruit et de minimiser les problèmes de fragmentation.

  Les profils de température des flammes ont été déterminés comme le changement de température de la flamme en fonction de la hauteur au-dessus du brûleur. Dans les expériences à basse pression, le profil de température a été mesuré à l'aide d'un thermocouple PtRh (6%) -PtRh (30%) (diamètre de fil 100 μm). Le fil a été recouvert d'un revêtement céramique BeO-Y2O3 pour éviter les réactions catalytiques sur la surface du thermocouple. Pour prendre en compte les pertes de chaleur par rayonnement, la méthode de compensation électrique a été utilisée. L'erreur de mesure de température était d'environ ± 100 K. Des mesures de température à pression atmosphérique ont également été réalisées par la méthode du thermocouple. Un thermocouple Pt -PtRh (10%) avec une épaisseur de fil de 50 µm a été utilisé. Pour éviter les réactions catalytiques, un revêtement de SiO2 a été appliqué sur la surface.Pour prendre en compte les pertes au rayonnement, la correction de température a été calculée par la méthode analytique. Les structures chimiques des flammes étudiées ont été simulées numériquement en utilisant le code PREMIX du package CHEMKIN-PRO. Les profils de température mesurés ont été utilisés comme paramètres d'entrée pour prendre en compte les perturbations par la sonde et les pertes de chaleur vers le brûleur. Pour les simulations des structures des flammes d'esters éthyliques, le mécanisme de Dayma et al. 2012 été utilisé. Ce mécanisme est le premier mécanisme cinétique détaillé de l'oxydation de pentanoate d'éthyle (EPe) proposé dans la littérature. Puisque seules les flammes sont étudiées dans la thèse, la chimie à basse température a été supprimée du mécanisme. La version réduite qui a été utilisée dans le travail comprend 232 espèces et 1845 réactions.

Figure. 2 .

 2 Figure. 2. Structure pentanoate d'éthyle avec marquages d'atomes de carbone.

  In the work[START_REF] Hakka | Oxidation of methyl and ethyl butanoates[END_REF] a comparative study of two heavier esters, methyl butanoate (MB) and ethyl butanoate (EB), was carried out. Experiments were carried out in a shock tube and in a jet-stirred reactor. The experiments have demonstrated again that ethyl ester is slightly more reactive than the methyl one. A new kinetic model was proposed taking into account the experimental results obtained. Basing on the analysis of production pathways and sensitivity analysis the authors suggested that the difference in the reactivity between MB and EB corresponds to easier unimolecular initiation of ethyl ester with the formation of H atoms. The authors also emphasize the different decomposition pathways of methyl and ethyl ester. Unfortunately, the experimental results with the jet-stirred reactor

They have noted a satisfactory agreement of the model with the data observed in the experiments with EF and EA and a poor agreement between the predictions of the model and experimental data on EF.

were reproduced unsatisfactorily by the mechanism proposed in the work. In conclusion the authors have pointed out the need for additional studies of esters in reactors of various types. In the work of Bennadji et al.

[START_REF] Bennadji | Experimental and kinetic modeling study of ethyl butanoate oxidation in a laminar tubular plug flow reactor[END_REF]

new experimental data were obtained on the oxidation of EB in a tubular plug-flow reactor.

Table 2 .

 2 List of kinetic studies of oxidation and combustion of small ethyl

	esters.

Table 3 .

 3 Physical properties of the esters investigated in the work.

	These compounds are the most

Table 4

 4

	/s Qm,g/(s•cm 2 )	φ

. Composition and mass-flow rates of combustible mixtures of ethyl esters studied at atmospheric pressure.

Table 5

 5

	Fuel	X (ester)	X (O2)	X (Ar)	Qv . cm 3 /s	Qm. g/(s•cm 2 )	φ
	EA	0.042	0.208	0.75	91.7	0.00584	1.0
	EPe	0.024	0.226	0.75	100.1	0.00577	1.0

shows compositions and flow rates of the combustible mixtures in experiments at low pressure. Here X is the mole fraction of the substance in the combustible mixture, Qv is the total volumetric flow rate of the fuel mixture under the standard conditions (25 °C, 1 atm), Qm is the total mass flow rate of the mixture, φ is the equivalence ratio.

Table 5

 5

. Composition and flow rates of unburnt gas mixtures of ethyl esters studied at low pressure.

Table 5 .

 5 It includes 506 compounds and 2809 reactions, it was included to the work with the aim to check it against the new experimental data on the flame structure of EA at atmospheric pressure. List of reactions which rate constants were modified in the new model.

	Reaction	A (cm 3 /mol•s)	n	E (cal/mol)	Reference
	EB+H=EB4J+H2	6.07E+10	1.18	8600.00	[131]
	EB+H=EB3J+H2	1.43E+10	1.2	6050.00	[131]
	EB+H=EB2J+H2	9.12E+09	1.22	4470.00	[131]
	EB+H=EBMJ+H2	4.83E+10	1.22	9860.00	[131]
	EB+H=EBEJ+H2	1.44E+10	1.25	5970.00	[131]
	EB+OH=EB2J+H2O	4.87E+02	2.94	-2107.00	[132]
	EB+OH=EBMJ+H2O	4.19E+01	3.72	-19.00	as EP in [84]
	EB+OH=EBEJ+H2O	4.63E-02	4.32	-1640.00	as EP in [84]
	EB+O=EB2J+OH	4.77E+04	2.71	2106.00	as MP in [135]
	EB+O=EBMJ+OH	1.07E+03	3.6	6560.00	as EP in [84]
	EB+O=EBEJ+OH	2.91E+02	3.6	3890.00	as EP in [84]
	EB+CH3=EB2J+CH4	7.82E-05	4.92	3383.00	as MP in [135]
	EB+CH3=EBMJ+CH4	1.77E-16	8.57	2637.00	as EP in [84]
	EB+CH3=EBEJ+CH4	4.70E-25	11.28	-3624.00	as EP in [84]
	EPE+H=EPE2J+H2	1.69E+10	1.21	4870.00	as EP in [131]
	EPE+H=EPEMJ+H2	6.07E+11	0.93	10850.00	average from [131]
	EPE+H=EPEEJ+H2	1.18E+10	1.27	5940.00	average from [131]
	EPE+OH=EPE2J+H2O	9.15E+01	3.23	-1542.00	as MP in [132]
	EPE+OH=EPEMJ+H2O	4.19E+01	3.72	-19.00	as EP in [84]
	EPE+OH=EPEEJ+H2O	4.63E-02	4.32	-1640.00	as EP in [84]
	EPE+O=EPE2J+OH	4.77E+04	2.71	2106.00	as MP in [132]
	EPE+O=EPEMJ+OH	1.07E+03	3.6	6560.00	as EP in [84]
	EPE+O=EPEEJ+OH	2.91E+02	3.6	3890.00	as EP in [84]
	EPE+CH3=EPE2J+CH4	7.82E-05	4.92	3383.00	as MP in [132]
	EPE+CH3=EPEMJ+CH4	1.77E-16	8.57	2637.00	as EP in [84]
	EPE+CH3=EPEEJ+CH4	4.70E-25	11.28	-3624.00	as EP in [84]
	C2H5OH(+M)=C2H5+OH(+M)	1.25E+23	-1.54	96005.00	[133]

  Table of species detected in the low-pressure experiments. Retention times and corresponding calibration coefficients are provided.

	Formula	Name	Retention time, min	Calibration coefficient	Detector
	Agilent 7890 A
	CO2	carbon dioxide	4,35	7916	FID
	C2H4	ethylene	6,03		FID
	C2H2	acethylene	6,61		FID
	C2H6	ethane	7,24		FID
	H2O	water	11,88-12,24	282	TCD
	C3H6	propene	12,53		FID
	C3H8	propane	12,93		FID
	a-C3H4	allene	13,19		FID
	CH2O	formaldehyde	13,47	7807	FID
	p-C3H4	propyne	13,48		FID
	CH3CHO	acetaldehyde	15,30		FID
	iC4H10	iso-butane	16,31		FID
	1-C4H8	1-butene	16,68		FID
	1,3-C4H6	1,3-butadiene	16,84		FID
	nC4H10	n-butane	17,07		FID
	2-C4H8	2-butene	17,28		FID
	C2H5OH	ethanol	18,41		FID
	CH3COCH3	acetone	20,34		FID
	C4H8O2	ethyl acetate	30,79		FID
	CH3COOH	acetic acid	35,21		FID
	C7H14O2	ethyl pentanoate	76,33		FID
	C4H9COOH	pentanoic acid	107,60		FID
	Ar*	argon	120,57	684	TCD
	CH4*	methane	122,47	7807	FID
	CO*	carbon monooxide	124,35	7567	FID
	HP 5890 Series II
	H2	hydrogen	8,35	3451	TCD
	O2	oxygen	18,16	189	TCD
	*depends on the method time

  • HP 5890 Série II avec colonne Carbosphère et détecteur de conductivité thermique utilisé pour déterminer les fractions molaires de H2 et O2. L'argon a été utilisé comme gaz vecteur.

	Ester	X (ester)	X (O2)	X (Ar)	Qv , cm 3 /s	Qm, g/(s•cm 2 )	φ
	EA	0,042	0,208	0,75	91,7	0,00584	1,0
	EPe	0,024	0,226	0,75	100,1	0,00577	1,0
		Tableau 1. Composition et débits de mélanges gazeux d'esters éthyliques étudiés
				à basse pression.

l'éthylène (C2H4) un peu plus précisément dans la flamme stoechiométrique. La même tendance dans la flamme d'EA a également été observée. En regardant la comparaison des profils de fractions molaires expérimentaux et calculés des composés oxygénés, en général, on peut noter la précision satisfaisante des modèles utilisées. Le plus grand écart entre l'expérience et la modélisation est observé dans le cas du formaldéhyde (CH2O). Les fractions molaires mesurées expérimentalement d'acide butanoïque (C3H7COOH) ont été décrites avec une précision acceptable par les deux modèles. Mais une meilleure concordance du modèle de Dayma avec l'expérience dans des conditions stoechiométriques peut être observée. Dans le même temps, dans la flamme riche, les deux modèles ont surestimé la fraction molaire maximale d'acide. Dans le cas de la flamme atmosphérique du pentanoate d'éthyle, les deux modèles ont montré une description généralement satisfaisante des données expérimentales. Pour cette flamme, le nouveau modèle semble être plus précis dans la description des profils de fraction molaire d'acétylène, d'éthane et de propane, et il est un peu moins précis avec la fraction molaire d'acide valérique. Au contraire, le modèle de Dayma prédit un peu plus précisément la fraction molaire d'acide maximale, mais l'a également sous-estimé de plus d'une fois et demie. La même sous-estimation de la fraction molaire acide a été observée dans le cas de la flamme d'EB qui a un poids moléculaire proche de l'EPe. Dans le cas de la flamme d'EPe à basse pression le nouveau mécanisme a très bien décrit les profils de fraction molaire de l'acétylène, de l'allène et du propyne, lors que le mécanisme de Dayma a sous-estimé les fractions molaires maximales de ces composés de 3 à 5 fois. Les fractions molaires maximales de méthane et d'éthane, au contraire, ont été calculées un peu mieux par le modèle Dayma, alors que dans le nouveau mécanisme, les fractions molaires maximales de ces espèces ont été sous-estimées de 1,5 à 2 fois. Pour les autres espèces intermédiaires détectées, les positions et les formes des profils des fractions molaires maximales ont été bien reproduites dans les simulations, mais il existe des écarts notables dans les valeurs absolues entre les prédictions du modèle et l'expérience. Pour la flamme d'EPe, le calcul et la comparaison avec les données expérimentales de la vitesse de flamme laminaire ont été effectués. Les simulations ont montré d'excellentes prédictions du nouveau modèle avec des expériences dans

of the oxygenated compounds, we can assume a satisfactory agreement between the model calculations and experiment. From the above comparisons of the experimental and calculated mole fraction profiles of intermediate compounds it can be concluded that the new model describes the chemical structure of ethyl butanoate flames under stoichiometric and fuel-rich conditions noticeably better than the mechanism of

MAIN RESULTS AND CONCLUSIONS APPENDIX 2

Operating conditions of methods during GC-analyses.

GC analizer

Agilent 7890 A

Sample loop V=2 ml Tvalve=200°C

Injector Split 1 :1 T=250°C

Switch valve event

0 min : Off (carrier gas passes through two columns)

L'approche méthodique