Development and assessment of an unstructured discrete ordinates method for radiative heat transfer in non-gray media

Lima, Kwenda L. Merkel (2010) Development and assessment of an unstructured discrete ordinates method for radiative heat transfer in non-gray media. (PhD thesis), Kingston University,


The current thesis is the first step in the development of and unstructured Discrete Ordinates Method (DOM) scheme to be implemented in computational fluid dynamics (CFD) codes for fire and combustion applications. Unstructured DOM solvers have not yet been implemented into CFD tools employed for fires applications and the ultimate goal of the present work would be to bridge this gap. The specific goal of the present thesis is to develop an unstructured DOM solver and validate it for a wide range of non-gray scenarios typical of fires and combustion systems. In a second step (future PhD work) the unstructured DOM solver coded would be coupled to the CFD code, Fire-Foam, employed for fire simulations. FireFoam (fire component of the OPENFOAM solver) is an open source code under development through a collaboration between FM Global (USA) and the Centre for Fire and Explosions Studies (CFES) at Kingston University. The main contributions of the thesis are: (i) the development of a non-gray Unstructured DOM solver for cartesian and cylindrical axisymmetric geometries, (ii) the verification study for a wider range of applications scenarios typical of fire and combustion, never undertaken before. As such, the study aims to prove the suitability of the non-gray unstructured exponential DOM scheme for these fire applications (iii) the development of an unstructured mesh generator that offers more flexibility with DOM than commercial ones. Fire and combustion media are non-gray i.e. their interaction with radiant heat is strongly dependant on the wavelength of radiation contrary to gray media. The original DOM exponential scheme of Sakami et al. has been extended to non-gray media by the author, and validated for different scenarios. The-present thesis allows an assessment and a better understanding of the method for fire and combustion systems. It is important to emphasize that in the present thesis the author has developed 2-D and 3-D DOM codes for structured meshes, for a better understanding of the DOM technique and also as a preliminary study to the development of unstructured meshes DOM. The structured DOM code was also employed to support another PhD work within the group on the behavior of glazing in fires. The work presents the different solution methods for the Radiative Transfer Equation (RTE) and existing formulations of the DOM. Their limitations and advantages are also discussed and a DOM for a three dimensional structured DOM approach has been coded in FORTRAN and validated for simple radiation scenarios as a preliminary investigation into the DOM technique. Some results are presented and discussed. In the work presented, the extended unstructured non-gray exponential scheme is coupled with a statistical narrow-band/ correlated-k (SNB-CK) gas model and meshes generated using the authors' own mesh generator. Different non-gray scenarios involving spectral gas absorption by H[sub]20 and CO[sub]2 and soot particles, which are typical to what is encountered in real combustion and fire applications, are investigated. A comparative analysis is carried out between heat flux and radiative source terms, calculated by the model and some literature data based on ray-tracing and Monte Carlo methods. The unstructured mesh generator developed by the author, for more flexibility with the DOM, is also presented for geometries specified by implicit functions. The algo-rithm, used in the in-house mesh generator, generalizes to any dimension and typically produces meshes of good quality. The overall analysis for different validation scenarios studied demonstrates the suit-ability of the non-gray unstructured DOM exponential scheme for fire and combustion applications. Therefore the method could be employed in any general CFD code for fire and combustion studies. The thesis paves the way for the next implementation of the Non-gray unstructured exponential DOM method developed and coded, into the CFD code FireFoam.

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