Lean premixed combustion is at present one of the most promising methods to reduce emissions and to maintain high efficiency in combustion systems. As the emission legislation becomes more stringent, modelling of turbulent premixed combustion has become an important tool for designing efficient and environmentally friendlier combustion systems. However, in order to predict these emissions reliable predictive models are required. One of the methods used for predicting pollutants is the conditional moment closure (CMC), which is suitable to predict pollutants with slow time scales. Despite the fact that CMC has been successfully applied to various non-premixed combustion systems, its application to premixed flames is not fully tested and validated. The main difficulty is associated with the modelling of the conditional scalar dissipation rate (CSDR) of the conditioning scalar, the progress variable. In premixed CMC, this term is an important quantity and represents the rate of mixing at small scales of relevance for combustion. The numerical accuracy of the CMC method depends on the accuracy of the CSDR model. In this study, two different models for CSDR, an algebraic model and an inverse problem model, are validated using two different DNS data sets. The algebraic model along with standard k-ε turbulence modelling is used in the computations of stoichiometric and very lean pilot stabilized Bunsen flames using the RANS-CMC method. A first order closure is used for the conditional mean reaction rate. The computed nonreacting and reacting scalars are in reasonable agreement with the experiments and are consistent with earlier computations using flamlets and transported PDF methods for the stoichiometric flames, and transported PDF methods for the very lean flames. Sensitivity to chemical kinetics mechanism is also assessed.

L'allumage d'ergols injectés dans une chambre de combustion, la propagation du noyau de flamme puis sa stabilisation sont autant de paramètres déterminants pour la conception d'un moteur fusée. Pour ce type d'application, il est nécessaire - du point de vue de la modélisation - de tenir compte du couplage existant entre les effets de compressibilité, les processus de mélange turbulent ainsi que de cinétique chimique, dans un environnement diphasique puisque les ergols sont injectés à l'état liquide. Un modèle Lagrangien a été implanté dans le code de calcul compressible N3S-Natur afin de disposer d'un outil numérique capable de simuler le transitoire d'allumage d'un moteur fusée. La physique représentative de chacun des processus physiques impliqués pendant la phase d'allumage a été incorporée puis validée sur des configurations académiques. Ce travail a permis de mettre en évidence l'importance de la description du mélange à petites échelles pour capturer correctement le développement de la flamme. Il a aussi mis en exergue la nécessité de prendre en compte le transitoire thermique des gouttes d'oxygène liquide afin de reproduire fidèlement sa stabilisation. Enfin, il a nécessité l'extension de la notion de fraction de mélange à des cas pratiques présentant plus de deux entrées afin d'être en mesure de simuler la propagation de l'allumage sur la plaque d'injection. Cette approche basée sur l'introduction d'un injecteur fictif est non seulement utile pour la simulation de l'allumage des moteurs-fusées mais peut aussi être employée dans tout autre système impliquant le mélange entre des courants de réactifs issus de deux entrées ou plus. / In the field of liquid rocket propulsion, ignition, propagation and stabilization of the flame are of first importance for the design of the engine. Computational fluid dynamics (CFD) solvers may provide a great deal of help to proceed with the primary design choice but need to be fed with suited physical models. Important modelling efforts are therefore required to provide reliable computational representations able to take into account compressibility effects, turbulent mixing and chemical kinetics in two-phase flows since ergols are injected at the liquid state. A Lagrangian model has been implemented in the compressible solver N3S-Natur so as to obtain a computational tool able to compute the transient ignition of rocket engines. The physical processes involved at each step of this ignition sequence have been integrated and validated on academically configurations. Three significant contributions rose from this work. First of all, it is highlighted that the description of the micro-mixing is of first importance to correctly capture the flame development. This study also emphasized the need to consider the transient heating of liquid oxygen droplets in order to accurately compute the flame stabilization. Finally, the notion of mixture fraction must be extended to practical devices implying more than two inlets. The proposed approach which is based on the introduction of a fictive injector is not only well suited to rocket engine ignition application but also to deal with other practical devices implying two inlets and more.

The influence of stratification on the structure of turbulent methane/air combustion is investigated using experimental data from laboratory scale burners: a weakly turbulent slot burner, and a higher turbulence co-annular swirl burner. The degree of stratification can be controlled independently of the overall fuel/air flow rate. The resulting measurements of scalar and velocity fields provide detailed test cases for existing and emerging turbulent flame models, covering a range of u'/sL from 1 to 10, turbulence intensities from 5% to 60%, and stratification ratios from 1 to 3. Simultaneous Rayleigh/Raman/CO-LIF measurements of temperature and major species concentrations - CH4, CO2, CO, H2, H2O and O2 - along a line are used to investigate the structure of a series of flames in both the slot and swirl burners. Concurrent cross-planar OH-PLIF allows thermal gradients to be angle corrected to their three-dimensional values. Finally, non-reacting and reacting velocity fields complete the flame database. The behavior of major species concentrations in the slot and swirl burner with respect to temperature is found to agree well on the mean with unstrained premixed laminar flame calculations. Scalar means conditioned on stoichiometry also show good agreement, aside from hydrogen which is enhanced under stratified conditions. Surface density function and scalar dissipation are lower than calculated values in all cases, suggesting that turbulence-induced thickening dominates the effect of increased strain. Metrics commonly used to derive flame surface density (FSD) were investigated. FSD may be determined using a statistical method based on measurements of temperature and its gradient, or a geometric method based on 2D temperature or LIF imaging. A third metric, an extension of the geometric method, is proposed. Good agreement is observed between the three metrics. The current database provides the first detailed high resolution scalar measurements for premixed and stratified flames. The data analysis provides insight into the physics of stratification: for the flames considered, the effects of stratification appear to be surprisingly small compared to those of turbulence, even at significant stratification ratios. The datasets provide a means of validating current and future computational turbulent combustion models.

Large-eddy simulation (LES) and unsteady Reynolds-averaged Navier-Stokes (URANS) calculations have been performed to investigate the effects of different mathematical models for scalar variance and its dissipation rate as applied to both a non-reacting bluff-body turbulent flow and an extension to a reacting case. In the conserved scalar formalism, the mean value of a thermo-chemical variable is obtained through the PDF-weighted integration of the local description over the conserved scalar, the mixture fraction. The scalar variance, one of the key parameters for the determination of a presumed β-function PDF, is obtained by solving its own transport equation with the unclosed scalar dissipation rate modelled using either an algebraic expression or a transport equation. The proposed approach is first applied to URANS and then extended to LES. Velocity, length and time scales associated with the URANS modelling are determined using the standard two-equation k-ε transport model. In contrast, all three scales required by the LES modelling are based on the Smagorinsky subgrid scale (SGS) algebraic model. The present study proposes a new algebraic and a new transport LES model for the scalar dissipation rate required by the transport equation for scalar variance, with a time scale consistent with the Smagorinsky SGS model.

This thesis describes the application of the first-order Conditional Moment Closure (CMC) to the autoignition of high-pressure fuel jets, and to piloted and lifted turbulent jet flames using classical and advanced CMC submodels. A Doubly-Conditional Moment Closure (DCMC) formulation is further proposed. In the first study, CMC is applied to investigate the impact of C₂H₆, H₂ and N₂ additives on the autoignition of high-pressure CH₄ jets injected into lower pressure heated air. A wide range of pre-combustion air temperatures is considered and detailed chemical kinetics are employed. It is demonstrated that the addition of C₂H₆ and H₂ does not change the main CH₄ oxidisation pathways. The decomposition of these additives provides additional ignition-promoting radicals, and therefore leads to shorter ignition delays. N₂ additives do not alter the CH₄ oxidisation pathways, however, they reduce the amount of CH₄ available for reaction, causing delayed ignition. It is further shown that ignition always occurs in lean mixtures and at low scalar dissipation rates. The second study is concerned with the modelling of a piloted CH₄/air turbulent jet flame. A detailed assessment of several Probability Density Function (PDF), Conditional Scalar Dissipation Rate (CSDR) and Conditional Velocity (CV) submodels is first performed. The results of two β-PDF-based implementations are then presented. The two realisations differ by the modelling of the CSDR. Homogeneous (inconsistent) and inhomogeneous (consistent) closures are considered. It is shown that the levels of all reactive scalars, including minor intermediates and radicals, are better predicted when the effects of inhomogeneity are included in the modelling of the CSDR. The two following studies are focused on the consistent modelling of a lifted H₂/N₂ turbulent jet flame issuing into a vitiated coflow. Two approaches are followed to model the PDF. In the first, a presumed β-distribution is assumed, whereas in the second, the Presumed Mapping Function (PMF) approach is employed. Fully consistent CV and CSDR closures based on the β-PDF and the PMF-PDF are employed. The homogeneous versions of the CSDR closures are also considered in order to assess the effect of the spurious sources which stem from the inconsistent modelling of mixing. The flame response is analysed over a narrow range of coflow temperatures (Tc). The stabilisation mechanism is determined from the analysis of the transport budgets in mixture fraction and physical spaces, and the history of radical build-up ahead of the stabilisation height. The β-PDF realisations indicate that the flame is stabilised by autoignition irrespective of the value of Tc. On the other hand, the PMF realisations reveal that the stabilisation mechanism is susceptible to Tc. Autoignition remains the controlling stabilisation mechanism for sufficiently high Tc. However, as Tc is decreased, stabilisation is achieved by means of premixed flame propagation. The analysis of the spurious sources reveals that their effect is small but non-negligible, most notably within the flame zone. Further, the assessment of several H₂ oxidation mechanisms show that the flame is very sensitive to chemical kinetics. In the last study, a DCMC method is proposed for the treatment of fluctuations in non-premixed and partially premixed turbulent combustion. The classical CMC theory is extended by introducing a normalised Progress Variable (PV) as a second conditioning variable beside the mixture fraction. The unburnt and burnt states involved in the normalisation of the PV are specified such that they are mixture fraction-dependent. A transport equation for the normalised PV is first obtained. The doubly-conditional species, enthalpy and temperature transport equations are then derived using the decomposition approach and the primary closure hypothesis is applied. Submodels for the doubly-conditioned unclosed terms which arise from the derivation of DCMC are proposed. As a preliminary analysis, the governing equations are simplified for homogeneous turbulence and a parametric assessment is performed by varying the strain rate levels in mixture fraction and PV spaces.

This thesis describes the application of the first-order Conditional Moment Closure (CMC) to the autoignition of high-pressure fuel jets, and to piloted and lifted turbulent jet flames using classical and advanced CMC submodels. A Doubly-Conditional Moment Closure (DCMC) formulation is further proposed. In the first study, CMC is applied to investigate the impact of C₂H₆, H₂ and N₂ additives on the autoignition of high-pressure CH₄ jets injected into lower pressure heated air. A wide range of pre-combustion air temperatures is considered and detailed chemical kinetics are employed. It is demonstrated that the addition of C₂H₆ and H₂ does not change the main CH₄ oxidisation pathways. The decomposition of these additives provides additional ignition-promoting radicals, and therefore leads to shorter ignition delays. N₂ additives do not alter the CH₄ oxidisation pathways, however, they reduce the amount of CH₄ available for reaction, causing delayed ignition. It is further shown that ignition always occurs in lean mixtures and at low scalar dissipation rates. The second study is concerned with the modelling of a piloted CH₄/air turbulent jet flame. A detailed assessment of several Probability Density Function (PDF), Conditional Scalar Dissipation Rate (CSDR) and Conditional Velocity (CV) submodels is first performed. The results of two β-PDF-based implementations are then presented. The two realisations differ by the modelling of the CSDR. Homogeneous (inconsistent) and inhomogeneous (consistent) closures are considered. It is shown that the levels of all reactive scalars, including minor intermediates and radicals, are better predicted when the effects of inhomogeneity are included in the modelling of the CSDR. The two following studies are focused on the consistent modelling of a lifted H₂/N₂ turbulent jet flame issuing into a vitiated coflow. Two approaches are followed to model the PDF. In the first, a presumed β-distribution is assumed, whereas in the second, the Presumed Mapping Function (PMF) approach is employed. Fully consistent CV and CSDR closures based on the β-PDF and the PMF-PDF are employed. The homogeneous versions of the CSDR closures are also considered in order to assess the effect of the spurious sources which stem from the inconsistent modelling of mixing. The flame response is analysed over a narrow range of coflow temperatures (Tc). The stabilisation mechanism is determined from the analysis of the transport budgets in mixture fraction and physical spaces, and the history of radical build-up ahead of the stabilisation height. The β-PDF realisations indicate that the flame is stabilised by autoignition irrespective of the value of Tc. On the other hand, the PMF realisations reveal that the stabilisation mechanism is susceptible to Tc. Autoignition remains the controlling stabilisation mechanism for sufficiently high Tc. However, as Tc is decreased, stabilisation is achieved by means of premixed flame propagation. The analysis of the spurious sources reveals that their effect is small but non-negligible, most notably within the flame zone. Further, the assessment of several H₂ oxidation mechanisms show that the flame is very sensitive to chemical kinetics. In the last study, a DCMC method is proposed for the treatment of fluctuations in non-premixed and partially premixed turbulent combustion. The classical CMC theory is extended by introducing a normalised Progress Variable (PV) as a second conditioning variable beside the mixture fraction. The unburnt and burnt states involved in the normalisation of the PV are specified such that they are mixture fraction-dependent. A transport equation for the normalised PV is first obtained. The doubly-conditional species, enthalpy and temperature transport equations are then derived using the decomposition approach and the primary closure hypothesis is applied. Submodels for the doubly-conditioned unclosed terms which arise from the derivation of DCMC are proposed. As a preliminary analysis, the governing equations are simplified for homogeneous turbulence and a parametric assessment is performed by varying the strain rate levels in mixture fraction and PV spaces.

Large-eddy simulation (LES) and unsteady Reynolds-averaged Navier-Stokes (URANS) calculations have been performed to investigate the effects of different mathematical models for scalar variance and its dissipation rate as applied to both a non-reacting bluff-body turbulent flow and an extension to a reacting case. In the conserved scalar formalism, the mean value of a thermo-chemical variable is obtained through the PDF-weighted integration of the local description over the conserved scalar, the mixture fraction. The scalar variance, one of the key parameters for the determination of a presumed β-function PDF, is obtained by solving its own transport equation with the unclosed scalar dissipation rate modelled using either an algebraic expression or a transport equation. The proposed approach is first applied to URANS and then extended to LES. Velocity, length and time scales associated with the URANS modelling are determined using the standard two-equation k-ε transport model. In contrast, all three scales required by the LES modelling are based on the Smagorinsky subgrid scale (SGS) algebraic model. The present study proposes a new algebraic and a new transport LES model for the scalar dissipation rate required by the transport equation for scalar variance, with a time scale consistent with the Smagorinsky SGS model.