In radiative heat transfer simulations, the geometrical view (configuration, form) factor plays a crucial role. Several different methods (deterministic and non-deterministic) such as integration, the Monte Carlo method, and the Hemi-Cube method have been introduced to calculate view factors in recent years. In this article, the Monte Carlo method combined with the finite-element (FE) technique is investigated. Results describing the relationships among different discretization schemes, number of rays used for the view factor calculation, CPU time, accuracy, and two origins of emanating rays are presented. The interesting case where reduced accuracy is obtained with increased refinement of FE mesh is discussed.
SUMMARYThe geometrical view (conÿguration) factor plays a crucial role in radiative heat transfer simulations and several methods, such as integration, the Monte Carlo and the hemi-cube method have been introduced to calculate view factors in recent years. In this paper the Monte Carlo method combined with the ÿnite element (FE) technique is investigated. Results describing the relationships between di erent discretization schemes, number of rays used for the view factor calculation, CPU time and accuracy are presented. The interesting case where reduced accuracy is obtained with increased reÿnement of FE mesh is discussed.
PurposeTo provide an analysis of turbulent flow in plane diffusers for graduate and postgraduate students (researchers) which can help them to understand turbulent flows and turbulence modelling.Design/methodology/approachSteady, incompressible, turbulent flow in two‐dimensional plane diffusers, where Reynolds averaged Navier‐Stokes (RANS) equations were simplified using the theory of turbulent boundary layers in integral form adjusted for the internal flow. To close the RANS equations, the mixing length model proposed by Michel et al., which was previously used for the calculation of turbulent flow in a straight channel with a uniform cross section, is applied for the calculation of the turbulent flow in plane diffusers. Also, in this paper, the velocity profile is approximated in every cross‐section of the diffuser by a six‐order polynomial, whose coefficients depend upon the three form parameters. Using this transformation, the system of governing equations was reduced to the three ordinary differential equations which were solved numerically.FindingsA comparison between results obtained (velocity profiles) and experimental data obtained using HWA and LDA shows very good agreement. The method of integral equations of boundary layer is a relatively old method and tends to be forgotten since more advanced methods have been introduced. However, the results obtained using this method for the calculation of turbulent flow in a plane diffuser show a very good agreement with experimental data. Therefore, in engineering applications when simplicity and low‐cpu times are required, the integral method can still be applied successfully.Originality/valueThis paper offers practical help to an individual starting his/her research in the computational fluid dynamics (turbulence modelling).
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