The recent advances in numerical methods and the vast development of computers had directed the designers to better development and modifications to air flow pattern and heat transfer in combustion chambers. Extensive efforts are exerted to adequately predict the air velocity and turbulence intensity distributions in the combustor zones and to reduce the emitted pollution and noise abatement to ultimately produce quite and energy efficient combustor systems. The Present work presents a review of mathematical modeling techniques to primarily predict what happens in three dimensional combustion chambers simulating boiler furnaces, aero engines in terms of flow regimes and interactions. The present work also demonstrates the effect of chamber design, swirl number and operational parameters on performance, flame behavior under various operating parameters. The governing equations of mass, momentum and energy are commonly expressed in a preset form with source terms to represent pressure gradients, turbulence and viscous action. The physical and chemical characteristics of the air and fuel are obtained from tabulated data in the literature. The flow regimes and heat transfer plays an important role in the efficiency and utilization of energy. The behavior was found to be strongly dependent on turbulent shear, mixing, blockages, wall conditions and location of fuel and air inlets. It is therefore very important to detect any recirculation flow a zone in the horizontal x-y plane, normally characterized by the existence of eddies of various sizes and strength. Eddies can be strong enough to have higher velocities typically near reactants supply openings. Excessive transverse flow velocities cause extra macro mixing; the air flow regimes are complex and of three-dimensional nature; with the advance of computational techniques it is possible to accurately simulate three dimensional flows. The results are obtained in this work with the aid of the numerous three-dimensional programs of commercial and teaching origins such as Fluent and 3DCOMB; applied to axisymmetrical and three-dimensional complex geometry with and without swirl. The present numerical grid comprises, typically, 600000-grid node covering the combustion chamber volume in the X, R or Y and Z coordinates directions. The numerical residual in the governing equations typically less than 0.001 %. The strength of the recirculation zones; however is characterized by, negative velocities as well as the introduction of the vorticity as a measure of flow rotation, and consequent turbulent shear and mixing. The obtained results include velocity vectors, turbulence intensities and local shear stresses distributions in combustors. Examples of large industrial furnaces are shown and are in good agreement with available measurements in the open literature .One may conclude that flow patterns, turbulence and heat transfer in combustors are strongly affected by the inlet swirl, inlet momentum ratios, combustor geometry ; both micro and macro mixing levels are influential [1-3] . Higher tangential velocities and turbulence characteristics are demonstrated in situations with higher swirl intensities. The present modeling capabilities can adequately predict the local flow pattern and turbulence kinetic energy levels in Complex combustors
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