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Implementation and validation of the discrete ordinates method for calculation of radiative heat transfer in the CFD software AVL FIRE™

It is known, that the radiative heat transfer has an impact on overall heat transfer and emissions in the engineering systems that operate at the high temperatures. The radiative heat transfer in the numerical simulations is often not considered due to its additional computational complexity and demanding of computational time. However, to precisely calculate the emissions concentrations, it is no longer enough to exclude the influence of radiative heat transfer on emission formation process. If the participation of medium in the radiative heat transfer is considered the radiative transfer equation must be solved. To solve such an integrodifferential equation, approximation with the numerical models has to be employed. In this work, the Discrete Ordinates Method (DOM) approximation featuring finite volume approach was implemented into the computational fluid dynamics software AVL FIRE™. The implemented DOM considers all radiation phenomena: absorbing, emitting, and scattering. The absorptivity and emissivity are modelled as a constant value and with the weighted-sum-of-grey-gases approach, while the scattering coefficient and scattering phase function were modelled for the homogeneous and isotropic medium. Additionally, the algorithm for spatial discretization with an arbitrary number of theta and phi angles was implemented, where to the each defined spatial angle is attributed one ordinate. After the spatial discretization is conducted, the transport equations for incident radiation in each ordinate is calculated, and its contribution is added as the radiative source term in the energy conservation equation. Furthermore, the symmetry and diffusive opaque boundary conditions are implemented for the description of incident radiation in all ordinates directions at the domain boundaries. Validation of the implemented model was conducted on simple geometry cases for which the analytical results exist, where the good agreement with analytical results is obtained. Finally, the aim of this work is to present capabilities for modelling of the radiative heat transfer in participating media with DOM and to investigate its capabilities in combination with AVL FIRE™ on a complex verification case.

Discrete Ordinates Method, Radiative Heat Transfer in Participating Media

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