Deep knowledge of combustion phenomenon is of great scientific and technological interest due to its presence in a wide range of industrial processes and equipment. Being the most important worldwide energy support provided by combustion of fossil fuels, the goal of developing more efficient and cleaner systems or equipment is clearly justified. In the last decade, the importance of the reduction of pollutant emissions has increased considerably due to both environmental consciousness and to governmental policies, being one of the most important aspects to assure the competitiveness of combustion-related industries.Traditionally, a high number of experimental studies based on trial-and-error analysis were necessary on the optimisation of thermal equipment, where heat and mass transfer and fluid flow have a dominant role. In the last decades, in agreement with the development of computational capabilities, CFD simulations have become a worthful complement to experimental investigations, reducing in this sense production costs and time to market. However, the considerable complexity of combustion phenomena and the strong feedback between the flow and the chemistry, makes more difficult the task of develop accurate, computationally capable and robust numerical codes for combustion phenomena in industrial applications. This goal remains a promising challenge today and for the foreseeable future.The work developed in this thesis contributes to this objective. Rather than assuming less accurate mathematical approaches and consider their application to engineering problems, our main intention has been centred to the development of numerical tools that enable the feasible resolution of combustion problems with the highest level of detail.On the detailed numerical simulation of combustion problems, main difficulties arise from the stiffness of the governing equations, the presence of flame fronts, and the huge number of species and reactions involved in the reaction mechanisms. In order to overcome these numerical difficulties, a parallel multiblock algorithm able to work efficiently with loosely coupled computers, has been developed. The employment of numerical strategies to deal with the commented stiffness, and the use of multiblock techniques to optimise the discretisation and to parallelise the code, are the main attributes that can be pointed out. An excellent ratio between computational time and resources have been obtained.In the analysis of the numerical solutions, special attention is given to their verification. The accuracy of the results has been analysed providing uncertainty estimations. The numerical methodology employed in this thesis to simulate reactive flows is one of the most relevant contributions presented.The numerical infrastructure developed has been applied to the numerical analysis of laminar flames. Although combustion nearly always takes place within a turbulence flow field to increase the mixing process and thereby enhance combustion, laminar flames are considered as an illustrative example of combustion phenomenon and its experimental and detailed numerical analysis is a basic ingredient on the modelling of turbulent combustion processes as well as for pollutant formation. Special attention has been given to co-flow non-premixed and partially premixed methane-air laminar flames. The wide application of these flames in house-hold and industrial heating systems due to both their intense combustion process and the relatively clean nature of natural gas (composed mainly by methane), has motivated extensive research on the experimental and numerical modelling of such flames.Detailed numerical simulations have been performed to analyse fundamental aspects of these flames, and the adequacy of several mathematical approaches employed on their modelling. Available experimental data have been taken into account both on the analysis of the influence of partially premixing to main flame properties and on the mathematical approaches comparison. Special attention has also been given to pollutant formation, NOx and CO emission indexes.

Deep knowledge of combustion phenomena is of great scientific and technological interest. In fact, better design of combustion equipments (furnaces, boilers, engines, etc) can contribute both in the energy efficiency and in the reduction of pollutant formation. One of the limitations to design combustion equipments, or even predict simple flames, is the resolution of the mathematical formulation. Analytical solutions are not feasible, and recently numerical techniques have received enormous interest. Even though the ever-increasing computational capacity, the numerical resolution requires large computational resources due to the inherent complexity of the phenomenon (viz. multidimensional flames, finite rate kinetics, radiation in participating media, turbulence, etc). Thus, development of capable mathematical models reducing the complexity and the stiffness as well as efficient numerical techniques are of great interest.The main contribution of the thesis is the analysis and application of the laminar flamelet concept to the numerical simulation of both laminar and turbulent non-premixed flames. Assuming a one-dimensional behavior of combustion phenomena in the normal direction to the flame front, and considering an appropriate coordinates transformation, flamelet approaches reduce the complexity of the problem.The numerical methodology employed is based on the finite volume technique and a parallel multiblock algorithm is used obtaining an excellent parallel efficiency. A post-processing verification tool is applied to assess the quality of the numerical solutions.Before dealing with flamelet approaches, a co-flow partially premixed methane/air laminar flame is studied for different levels of partial premixing. A comprehensive study is performed considering different mathematical formulations based on the full resolution of the governing equations and their validation against experimental data from the literature. Special attention is paid to the prediction of pollutant formation.After the full resolution of the governing equations, the mathematical formulation of the flamelet equations and a deep study of the hypothesis assumed are presented. The non-premixed methane/air laminar flame is considered to apply the flamelet modelling approach, comparing the results with the simulations obtained with the full resolution of the governing equations. Steady flamelets show a proper performance to predict the main flame features when differential diffusion and radiation are neglected, while unsteady flamelets are more suitable to account for these effects as well as pollutant formation. Assumptions of the flamelet equations, the scalar dissipation rate modelling, and the evaluation of the Lagrangian flamelet time for unsteady flamelets are specially analysed. For the numerical simulation of turbulent flames, the mathematical formulation based on mass-weighted time-averaging techniques, using RANS EVM two-equation models is considered. The laminar flamelet concept with a presumed PDF is taken into account. An extended Eddy Dissipation Concept model is also applied for comparison purposes. A piloted non-premixed methane/air turbulent flame is studied comparing the numerical results with experimental data from the literature. A clear improvement in the prediction of slow processes is shown when the transient term in the flamelet equations is retained. Radiation is a key aspect to properly define the thermal field and, consequently, species such as nitrogen oxides. Finally, the consideration of the round-jet anomaly is of significant importance to estimate the flame front position.In conclusion, flamelet modelling simulations are revealed to be an accurate approach for the numerical simulation of laminar and turbulent non-premixed flames. Detailed chemistry can be taken into account and the stiffness of the chemistry term is solved in a pre-processing task. Pollutant formation can be predicted considering unsteady flamelets.