TURBULENT TRANSPORT OF MOMENTUM, HEAT AND MASS IN A TWO-LEVEL HIGHLY POROUS MEDIA
Special models are developed to describe turbulent flow, diffusion of admixtures, and energy processes in a highly porous media. The models account for the medium morphology characteristics. Using second order turbulent models, equation sets are obtained for turbulent filtration and two-temperature or two-concentration diffusion in non-isotropic porous media and interphase exchange and micro-roughness. The equations differ from those found in the literature. This theoretical approach was used to develop turbulent flow and heat transport models at the previous level of the hierarchy - at the pore level. The work has shown that the flow resistance and heat transfer in a rough channel or pipe can be properly predicted using the technique of averaging the transport equations over the near surface representative elementary volume (REV). Prescribing the statistical structure of the capillary or globular porous medium morphology gives the basis for transforming the integro-differential transport equations into differential equations with probability density functions governing their stochastic coefficients and source terms. Several different closure models for these terms for some uniform, non-uniform, non-isotropic and specifically random non-isotropic highly porous layers were developed. A model of turbulent flow and two-temperature heat transfer in a highly porous medium was evaluated numerically for a layer of regular packed particles. Quite different situations arise when described processes occur in unregular or random morphology. These problems of transport modeling were evaluated for a few 2-dimensional capillary lattice patterns as well as spherical structures. An irregular prescribed four-coordinate lattice with different orientations of the bonds and random lattice patterns based on the same spatial structure were used. The theoretical model was explored to obtain the covariance functions for the morpho-convective and morpho-diffusive terms.
In this way the theories of space averaging modeling and stochastic Markov diffusion processes were combined in this development.