This thesis describes the implementation of the conditional moment closure (CMC) combustion model in a numerical scheme and its application to the modelling of enclosure fires. Prediction of carbon monoxide (CO) in the upper smoke layer of enclosure fires is of primary interest because it is a common cause of death. The CO concentration cannot be easily predicted by empirical means, so a method is needed which models the chemistry of a quenched, turbulent fire plume and subsequent mixing within an enclosed space. CMC is a turbulent combustion model which has been researched for over a decade. It has provided predictions of major and minor species in jet diffusion flames. The extension to enclosure fires is a new application for which the flow is complex and temperatures are well below adiabatic conditions. Advances are made in the numerical implementation of CMC. The governing combustion equations are cast in a conserved, finite volume formulation for which boundary conditions are uniquely defined. Computational efficiency is improved through two criteria which allow the reduction in the size of the computational domain without any loss of accuracy. Modelling results are compared to experimental data for natural gas fires burning under a hood. Comparison is made in the recirculating, post-flame region of the flow where temperatures are low and reactions are quenched. Due to the spatial flux terms contained in the governing equations, CMC is able to model the situation where chemical species are produced in the high temperature fire-plume and then transported to non-reacting regions. Predictions of CO and other species are in reasonable agreement with the experimental data over a range of lean and rich hood-fire conditions. Sensitivity of results to chemistry, temperature and modelling closures is inves- tigated. Species predictions are shown to be quite different for the two detailed chemical mechanisms used. Temperature conditions within the hood effect the for- mation of species in the plume prior to quenching and subsequently species predic- tions in the post-flame region are also effected. Clipped Gaussian and ß-function probability density functions (PDFs) are used for the stochastic mixture fraction. Species predictions in the plume are sensitive to the form of the PDF but in the post-flame region, where the ß-function approaches a Gaussian form, predictions are relatively insensitive. Two models are used for the conditional scalar dissipation: a uniform model, where the conditional quantity is set equal to the unconditional scalar dissipation across all mixture fraction space; and a model which is consistent with the PDF transport equation. In the plume, predictions of minor species are sensitive to the modelling used, but in the recirculating, post-flame region species are not significantly effected.

This thesis describes the implementation of the conditional moment closure (CMC) combustion model in a numerical scheme and its application to the modelling of enclosure fires. Prediction of carbon monoxide (CO) in the upper smoke layer of enclosure fires is of primary interest because it is a common cause of death. The CO concentration cannot be easily predicted by empirical means, so a method is needed which models the chemistry of a quenched, turbulent fire plume and subsequent mixing within an enclosed space. CMC is a turbulent combustion model which has been researched for over a decade. It has provided predictions of major and minor species in jet diffusion flames. The extension to enclosure fires is a new application for which the flow is complex and temperatures are well below adiabatic conditions. Advances are made in the numerical implementation of CMC. The governing combustion equations are cast in a conserved, finite volume formulation for which boundary conditions are uniquely defined. Computational efficiency is improved through two criteria which allow the reduction in the size of the computational domain without any loss of accuracy. Modelling results are compared to experimental data for natural gas fires burning under a hood. Comparison is made in the recirculating, post-flame region of the flow where temperatures are low and reactions are quenched. Due to the spatial flux terms contained in the governing equations, CMC is able to model the situation where chemical species are produced in the high temperature fire-plume and then transported to non-reacting regions. Predictions of CO and other species are in reasonable agreement with the experimental data over a range of lean and rich hood-fire conditions. Sensitivity of results to chemistry, temperature and modelling closures is inves- tigated. Species predictions are shown to be quite different for the two detailed chemical mechanisms used. Temperature conditions within the hood effect the for- mation of species in the plume prior to quenching and subsequently species predic- tions in the post-flame region are also effected. Clipped Gaussian and ß-function probability density functions (PDFs) are used for the stochastic mixture fraction. Species predictions in the plume are sensitive to the form of the PDF but in the post-flame region, where the ß-function approaches a Gaussian form, predictions are relatively insensitive. Two models are used for the conditional scalar dissipation: a uniform model, where the conditional quantity is set equal to the unconditional scalar dissipation across all mixture fraction space; and a model which is consistent with the PDF transport equation. In the plume, predictions of minor species are sensitive to the modelling used, but in the recirculating, post-flame region species are not significantly effected.

The accurate description of the turbulence chemistry interactions that can determine chemical conversion rates and flame stability in turbulent combustion modelling is a challenging research area. This thesis presents the development and implementation of a model for the treatment of fluctuations around the conditional mean (i.e., the auto-ignition and extinction phenomenon) of realistic turbulence-chemistry interactions in computational fluid dynamics (CFD) software. The wider objective is to apply the model to advanced combustion modelling and extend the present analysis to larger hydrocarbon fuels and particularly focus on the ability of the model to capture the effects of particulate formation such as soot. A comprehensive approach for modelling of turbulent combustion is developed in this work. A direct quadrature conditional moment closure (DQCMC) method for the treatment of realistic turbulence-chemistry interactions in computational fluid dynamics (CFD) software is described. The method which is based on the direct quadrature method of moments (DQMOM) coupled with the Conditional Moment Closure (CMC) equations is in simplified form and easily implementable in existing CMC formulation for CFD code. The observed fluctuations of scalar dissipation around the conditional mean values are captured by the treatment of a set of mixing environments, each with its pre-defined weight. In the DQCMC method the resulting equations are similar to that of the first-order CMC, and the “diffusion in the mixture fraction space” term is strictly positive and no correction factors are used. Results have been presented for two mixing environments, where the resulting matrices of the DQCMC can be inverted analytically. Initially the DQCMC is tested for a simple hydrogen flame using a multi species chemical scheme containing nine species. The effects of the fluctuations around the conditional means are captured qualitatively and the predicted results are in very good agreement with observed trends from direct numerical simulations (DNS). To extend the analysis further and validate the model for larger hydrocarbon fuel, the simulations have been performed for n-heptane flame using detailed multi species chemical scheme containing 67 species. The hydrocarbon fuel showed improved results in comparison to the simple hydrogen flame. It suggests that higher hydrocarbons are more sensitive to local scalar dissipation rate and the fluctuations around the conditional means than the hydrogen. Finally, the DQCMC is coupled with a semi-empirical soot model to study the effects of particulate formation such as soot. The modelling results show to predict qualitatively the trends from DNS and are in very good agreement with available experimental data from a shock tube concerning ignition delays time. Furthermore, the findings suggest that the DQCMC approach is a promising framework for soot modelling.

Autoignition of non-premixed methane-air mixtures is investigated using first-order Conditional Moment closure (CMC). In CMC, scalar quantities are conditionally averaged with respect to a conserved scalar, usually the mixture fraction. The conditional fluctuations are often of small order, allowing the chemical source term to be modeled as a function of the conditional species concentrations and the conditional enthalpy (temperature). The first-order CMC derivation leaves many terms unclosed such as the conditional scalar dissipation rate, velocity and turbulent fluxes, and the probability density function. Submodels for these quantities are discussed and validated against Direct Numerical Simulations (DNS). The CMC and the turbulent velocity and mixing fields calculations are decoupled based on the frozen mixing assumption, and the CMC equations are cross-stream averaged across the flow following the shear flow approximation. Finite differences are used to discretize the equations, and a two-step fractional method is implemented to treat separately the stiff chemical source term. The stiff ODE solver LSODE is used to solve the resulting system of equations. The recently developed detailed chemical kinetics mechanism UBC-Mech 1.0 is employed throughout this study, and preexisting mechanisms are visited. Several ignition criteria are also investigated. Homogeneous and inhomogeneous CMC calculations are performed in order to investigate the role of physical transport in autoignition. Furthermore, the results of the perfectly homogeneous reactor calculations are presented and the critical value of the scalar dissipation rate for ignition is determined. The results are compared to the shock tube experimental data of Sullivan et al. The current results show good agreement with the experiments in terms of both ignition delay and ignition kernel location, and the trends obtained in the experiments are successfully reproduced. The results were shown to be sensitive to the scalar dissipation model, the chemical kinetics, and the ignition criterion.

Autoignition of non-premixed methane-air mixtures is investigated using first-order Conditional Moment closure (CMC). In CMC, scalar quantities are conditionally averaged with respect to a conserved scalar, usually the mixture fraction. The conditional fluctuations are often of small order, allowing the chemical source term to be modeled as a function of the conditional species concentrations and the conditional enthalpy (temperature). The first-order CMC derivation leaves many terms unclosed such as the conditional scalar dissipation rate, velocity and turbulent fluxes, and the probability density function. Submodels for these quantities are discussed and validated against Direct Numerical Simulations (DNS). The CMC and the turbulent velocity and mixing fields calculations are decoupled based on the frozen mixing assumption, and the CMC equations are cross-stream averaged across the flow following the shear flow approximation. Finite differences are used to discretize the equations, and a two-step fractional method is implemented to treat separately the stiff chemical source term. The stiff ODE solver LSODE is used to solve the resulting system of equations. The recently developed detailed chemical kinetics mechanism UBC-Mech 1.0 is employed throughout this study, and preexisting mechanisms are visited. Several ignition criteria are also investigated. Homogeneous and inhomogeneous CMC calculations are performed in order to investigate the role of physical transport in autoignition. Furthermore, the results of the perfectly homogeneous reactor calculations are presented and the critical value of the scalar dissipation rate for ignition is determined. The results are compared to the shock tube experimental data of Sullivan et al. The current results show good agreement with the experiments in terms of both ignition delay and ignition kernel location, and the trends obtained in the experiments are successfully reproduced. The results were shown to be sensitive to the scalar dissipation model, the chemical kinetics, and the ignition criterion.

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.

This thesis is concerned with investigations on two related issues of turbulent jet diffusion flame, namely (a) stabilization at liftoff and (b) autoignition in a turbulent jet diffusion flame. The approach of Conditional Moment Closure (CMC) has been taken. Fully elliptic first order CMC equations are solved with detailed chemistry to simulate lifted H2/N2 flame in vitiated coflow. The same approach is further used to simulate transient autoignition process in inhomogeneous mixing layers. In Chapter 1, difficulties involved in numerical simulation of turbulent combustion problems are explained. Different numerical tools used to simulate turbulent combustion are briefly discussed. Previous experimental, theoretical and numerical studies of lifted jet diffusion flames and autoignition are reviewed. Various research issues related to objectives of the thesis are discussed. In Chapter 2, the first order CMC transport equations for the reacting flows are presented. Various closure models that are required for solving the governing equations are given. Calculation of mean reaction rate term for detailed chemistry is given with special focus on the reaction rates for pressure dependent reactions. In Chapter 3, starting with the laminar flow code, further extension is carried to include kε turbulence model and PDF model. The code is validated at each stage of inclusion of different model. In this chapter, the code is first validated for the test problem of constant density, 2D, axisymmetric turbulent jet. Further, validation of PDF model is carried out by simulating the problem of nonreacting jet of cold air issuing into a vitiated coflow. The results are compared with the published data from experiments as well as numerical simulations. It is shown that the results compare well with the data. In Chapter 4, numerical results of lifted jet diffusion flame are presented. Detailed chemistry is modelled using Mueller mechanism for H2/O2 system with 9 species and 21 reversible reactions. Simulations are carried out for different jet velocities and coflow stream temperatures. The predicted liftoff generally agrees with experimental data, as well as joint PDF results. Profiles of mean scalar fluxes in the mixture fraction space, for different coflow temperatures reveal that (1) Inside the flamezone, the chemical term balances the molecular diffusion term, and hence the structure is of a diffusion flamelet for both cases. (2) In the preflame zone, the structure depends on the coflow temperature: for low coflow temperatures, the chemical term being small, the advective term balances the axial diffusion term. However, for the high coflow temperature case, the chemical term is large and balances the advective term, the axial diffusion term being small. It is concluded that, liftoff is controlled (a) by turbulent premixed flame propagation for low cofflow temperature while (b) by autoignition for high coflow temperature. In Chapter 5, the numerical results of autoignition in inhomogeneous mixing layer are presented. The configuration consists of a fuel jet issued into hot air for which transient simulations are performed. It is found that the constants assumed in various modelling terms can severely influence the results, particularly the flame temperature. Hence, modifications to these constants are suggested to obtain improved predictions. Preliminary work is carried out to predict autoignition lengths (which may be defined by Tign × Ujet incase of jet- and coflowvelocities being equal) by varying the coflow temperature. The autoignition lengths show a reasonable agreement with the experimental data and LES results. In Chapter 6, main conclusions of this thesis are summarized. Possible future studies on this problem are suggested.

This thesis aims at improving our knowledge on swirl combustors. The work presented here is based on Large Eddy Simulations (LES) coupled to an advanced combustion model: the Conditional Moment Closure (CMC). Numerical predictions have been systematically compared and validated with detailed experimental datasets. In order to analyze further the physics underlying the large numerical datasets, Proper Orthogonal Decomposition (POD) has also been used throughout the thesis. Various aspects of the aerodynamics of swirling flames are investigated, such as precession or vortex formation caused by flow oscillations, as well as various combustion aspects such as localized extinctions and flame lift-off. All the above affect flame stabilization in different ways and are explored through focused simulations. The first study investigates isothermal air flows behind an enclosed bluff body, with the incoming flow being pulsated. These flows have strong similarities to flows found in combustors experiencing self-excited oscillations and can therefore be considered as canonical problems. At high enough forcing frequencies, double ring vortices are shed from the air pipe exit. Various harmonics of the pulsating frequency are observed in the spectra and their relation with the vortex shedding is investigated through POD. The second study explores the structure of the Delft III piloted turbulent non-premixed flame. The simple configuration allows to analyze further key combustion aspects of combustors, with further insights provided on the dynamics of localized extinctions and re-ignition, as well as the pollutants emissions. The third study presents a comprehensive analysis of the aerodynamics of swirl flows based on the TECFLAM confined non-premixed S09c configuration. A periodic component inside the air inlet pipe and around the central bluff body is observed, for both the inert and reactive flows. POD shows that these flow oscillations are due to single and double helical vortices, similar to Precessing Vortex Cores (PVC), that develop inside the air inlet pipe and whose axes rotate around the burner. The combustion process is found to affect the swirl flow aerodynamics. Finally, the fourth study investigates the TECFLAM configuration again, but here attention is given to the flame lift-off evident in experiments and reproduced by the LES-CMC formulation. The stabilization process and the pollutants emission of the flame are investigated in detail.