AbstracG-The hydrodynamic boundary condition at the interface between a porous and a plain medium is examined by direct simulation of the two-dimensional flow field near the interface of a porous medium made of cylinders. The existing slip boundary condition, which contains a slip coefficient a, and the noslip boundary condition, which contains an effective viscosity p', are examined. The dependence of a on the direction of the flow (with respect to the interfacial plane), the porosity, the Reynolds number (based on the unit cell length and the Darcean velocity), the selection of the interfacial location, and the arrangement of the cylinders (structure) is examined in detail. The numerical results show that a is not only a function of the structure but also depends on the flow direction, the Reynolds number, the extent of the plain medium, and the nonuniformities in the arrangement of the surface particles. It is also shown that for an accurate prediction of the local velocity near the interface (inside the porous medium), p' must vary within the porous medium. This shows that the Brinkman extension based on a uniform $, and the associated screening distance, do not satisfactorily model the flow field in the porous medium.

For the case of flame thickness being of the order of the pore linear dimension, the flame structure and speed in adiabatic, premixed methane-air combustion in porous media are examined. The local, volume-averaged conservation equations that assume a local thermal equilibrium between the solid and the gas phases (i.e. the single-medium treatment) or allow for a thermal nonequilibrium (i.e. the twomedium treatment) are used along with the direct application of the pointwise conservation equations to a two-dimensional porous medium model (ordered arrangement of discrete or connected square cylinders). The,effective properties of the porous medium in the volume-averaged treatments, including the interfacial Nusselt number, are found by applying the local volume-averaging principles. The results show that, although significant variations of the temperature and species concentrations occur over a pore, the flame structure, thickness, speed, and excess temperature (i.e. local gas temperature in excess of the adiabatic temperature) are fairly well predicted by the two-medium model (the single-medium treatment is unable to predict the local excess temperature). However, the volume-averaged treatments are unable to predict the pore-level, local high temperature region in the gas phase (which can be up to 40% above the adiabatic temperature), and the pore-level variation in the flame speed with respect to the flame location in the pore (which can vary by up to 20%). Other shortcomings of the volume-averaged treatments are also revealed through a parametric examination involving the pore-geometry variables, solid to gas conductivity ratio, equivalence ratio, porosity, and flame location within the pore.

Near the interface of porous plain media, convective heat transfer may be noticeably affected by the nonuniformity of the phase distributions. The boundary effects are modeled by using interfacial slip or no-slip temperature boundary conditions. The latter uses a variable transverse total diffusivity giving a continuous variation of the temperature near and across the interface. The former uses a constant transverse total diffusivity which requires a temperature slip cross the interface (in order to obtain accurate heat flux calculations).In this study these boundary conditions are examined by the direct simulation of the momentum and energy equations for a model porous medium made of two-dimensional periodic arrangements of cylinders. The slip coefficient is found to depend on the bulk Peclet number Pe,. the ratio of solid to fluid conductivity k,/k,, and the gap size /I. For the no-slip boundary condition, the magnitude and the distribution of D, (~>)/a, also depend on Pe,, k,/k,, and h. For a solid bounding surface, and when k,/kr > I. the effective transverse conductivity k,,/k, dominates over the hydrodynamic dispersion, and therefore, the accurate description of the variation of k,, (r)/ki becomes critical. For a fluid bounding medium, the results show that D, (J) is nonuniform on both sides of the interface. The nonuniformity of DL(y) in the fluid medium is due to the local two dimensionality of the flow. The total diffusivity tensor D in the bulk of a two-dimensional periodic structure is also examined. The effects of the Reynolds number, Prandtl number, particle shape, particle arrangement. and flow direction, on the bulk value of D are examined. It is found that for oblique flows, the ensemble-averaged longitudinal total diffusivity D, /ccr, over the tilt angle, approaches a Pe, relation instead of a Pe: relation expected for periodic structures.

The phase distribution nonuniformities near bounding surfaces result in anisotropy and nonuniformity of the effective thermal conductivity tensor. For a two-dimensional porous medium made of cylindrical particles, we evaluate the properties of this tensor for cases where the medium is bounded by the fluid saturating it or by a solid surface. The use of a uniform effective conductivity, such as the bulk (far from the surface) value, along with the near surface temperature distribution results in an error in the calculated heat flux. We examine this error and the errors resulting from the use of other approximations of the effective conductivity near the surface. We also point out a slip in the surface temperature occurring when the bulk effective conductivity and the temperature distribution away from the surface are used to extrapolate the temperature at the interface. A slip coefficient is used to account for this slip in temperature.

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