A numerical experiment at a pore scale using a full set of Navier-Stokes and energy equations has been conducted to simulate laminar fluid flow and heat transfer through an anisotropic porous medium. A collection of square rods placed in an infinite two-dimensional space has been proposed as a numerical model of microscopic porous structure. The degree of anisotropy was varied by changing the transverse center-to-center distance with the longitudinal center-to-center distance being fixed. Extensive calculations were carried out for various sets of the macroscopic flow angle, Reynolds number and degree of anisotropy. The numerical results thus obtained were integrated over a space to determine the permeability tensor, Forchheimer tensor and directional interfacial heat transfer coefficient. It has been found that the principal axes of the permeability tensor (which controls the viscous drag in the low Reynolds number range) differ significantly from those of the Forchheimer tensor (which controls the form drag in the high Reynolds number range), The study also reveals that the variation of the directional interfacial heat transfer coefficient with respect to the macroscopic flow angle is analogous to that of the directional permeability. Simple subscale model equations for the permeability tensor, Forchheimer tensor and directional Nusselt number have been proposed for possible applications of VAT to investigate flow and heat transfer within complex heat and fluid flow equipment consisting of small scale elements.
A numerical model for a three-dimensional heat and fluid flow through a bank of infinitely long cylinders in yaw has been proposed to investigate complex flow and heat transfer characteristics associated with manmade structures such as extended fins and plate fins in heat transfer equipment. By exploiting the periodicity of the structure, only one structural unit has been taken as a calculation domain. An economical quasi-three-dimensional calculation procedure has been proposed to replace exhaustive full three-dimensional numerical manipulations. It has been shown that, under macroscopically uniform flow, the three-dimensional governing equations reduce to quasi-three-dimensional forms, in which all derivatives associated with the axis of the cylinder can be either eliminated or replaced by other determinable expressions. Thus, only two-dimensional storage is required for the dependent variables in question. Extensive numerical calculations were carried out for various sets of the porosity, degree of anisotropy, Reynolds number and macroscopic flow direction in a three-dimensional space. The numerical results thus obtained for periodically fully developed flow and temperature fields were integrated over a structural unit to determine the permeability tensor, Forchheimer tensor and directional interfacial heat transfer coefficient, to elucidate the effects of yaw angle on these macroscopic flow and heat transfer characteristics. Upon examining these numerical data, a useful set of explicit expressions has been established for the permeability tensor, Forchheimer tensor and directional interfacial heat transfer coefficient to characterize flow and heat transfer through a bank of cylinders in yaw.
A finite-volume calculation of the three-dimensional reacting flow in a porous burner is presented. The Navier-Stokes, energy and species transport equations are solved, and radiative heat transfer under local thermal non-equilibrium between the solid and gas phases is considered. Strong dissipation of the jets from the perforated plate is observed, contributing to the flame stabilization inside the ceramic foam. Simulation results for several operating conditions point to the potential for damage of the perforated plate, owing to the high radiative and conductive fluxes, and to the necessity of using smaller pore diameters to avoid flashback.
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