M.J.S. De Lemos

Modeling Turbulence in Porous Media

Abstract Four available methodologies for developing macroscopic turbulence models for incompressible single-phase flow in rigid, fully saturated porous media are reviewed. The first method, known as the Antohe–age (A–) method, starts with the closed volume-averaged equations, which are then averaged in time to produce the turbulence equations. The second, known as the Nakayama–uwahara (N–) method, makes use, first, of the closed time-averaged equations, and then proceeds with volume-averaging for deriving the turbulence equations. These two methodologies lead, in general, to distinct sets of turbulence equations because of the different averaging order, i.e., space–ime and time–pace, respectively. A third, and probably the most consistent method, based on double-decomposition, is the Pedras–e Lemos (P–L) method. In this method, the momentum equation is closed by using the Hazen–upuit–Darcy model for the total drag effect only after the space-time averaging (or time-space averaging) is performed. Although for the P–dL method the averaging order is immaterial when deriving the turbulence momentum equation, the difference between space-time and time-space averaging remains in the k–e equations. Unfortunately, detailed experimental model validation, which remains to be seen, is tremendously challenging because of the need to obtain time-averaged and volume-averaged quantities simultaneously in order to compare experimental and analytical (numerical) results directly. A fourth method, the Travkin–Catton (T–C) morphology method, is discussed only briefly because it follows the N–K method (time-space integrating order) and no closure to the final equations is yet available.

Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

The present work investigates the existence of optimal algorithm parameters for multigrid numerical solutions of a two-dimensional steady-state conductive-convective problem. The velocity field inside the rectangular domain and the temperature distribution at its four boundaries are known and kept constant. The numerical method includes finite volume discretization and Weighted Upstream Differencing Scheme (WUDS) interpolation on structured, orthogonal and regular meshes. Multigrid is implemented according to the correction storage (CS) formulation. Minimum computational effort is sought as a function of control-volume Peclet number, different numbers of grids, number of smoothing sweeps in each level and distinct combinations of iterative solution algorithm.

THE DOUBLE-DECOMPOSITION CONCEPT FOR TURBULENT TRANSPORT IN POROUS MEDIA

Abstract Environmental impact analyses as well as engineering equipment design can both benefit from reliable modeling of turbulent flow in porous media. A number of natural and engineering systems can be characterized by a permeable structure through which a working fluid permeates. Turbulence models proposed for such flows depend on the order of application of time- and volume-average operators. Two methodologies, following the two orders of integration, lead to different governing equations for the statistical quantities. This chapter reviews recently published methodologies to mathematically characterize turbulent transport in porous media. A new concept, called double-decomposition, is here discussed and models for turbulent transport in porous media are classified in terms of the order of application of the time- and volume-averaging operators, among other peculiarities. Within this chapter instantaneous local transport equations are reviewed for clear flow before time- and volume-averaging procedures are applied to them. The double-decomposition concept is presented and thoroughly discussed prior to the derivation of macroscopic governing equations. Equations for turbulent transport follow, showing detailed derivation for the mean and turbulent field quantities. The statistical k-ɛ model for clear domains, used to model macroscopic turbulence effects, serves also as the basis for heat transfer modeling. Mass transfer in porous matrices is further reviewed in the light of the double-decomposition concept.

Turbulent Heat and Mass Transfer in Porous Media

Modeling of macroscopic transport for incompressible flows in porous media has been based on the volume-average methodology for either heat, see Hsu and Cheng [10

Spatial Averaging over a Variable Volume and Its Application to Boundary-Layer Flows over Permeable Walls

AbstractDouble-averaging methodology is very convenient for investigating spatially heterogeneous flows such as boundary-layer flows over permeable walls. However, spatial averaging volumes suitable for boundary-layer flows over rough walls are very thin in the wall-normal direction whereas those for porous-media flows usually have similar length in all three directions. This scale mismatch can be addressed by allowing the averaging volume to vary in space so that its size can be adjusted to the physical characteristics of particular flow regions. This paper presents a new spatial averaging theorem derived for a spatially variable averaging volume that may contain a stationary solid phase and that may also extend beyond the boundary of the problem domain. The theorem provides the expression for the difference between the average of a spatial derivative and the derivative of the spatial average (of a general flow quantity), here named the commutation correction (CC) term. The CC term contains three parts a...

Filtration Gas Combustion in a Porous Ceramic Annular Burner for Thermoelectric Power Conversion

ABSTRACT A numerical study of the combustion of lean methane/air mixtures in a porous media burner is performed using novelty geometry, cylindrical annular space. The combustion process takes place in the porous space located between two pipes, which are filled with alumina beads of 5.6 mm diameter forming a porosity of 0.4. The outer tube diameter of 3.82 cm is isolated; meanwhile the inner tube of 2 cm in diameter is covered by a continuous set of thermoelectric elements (TE) for transforming heat energy into electricity. To achieve and maintain the proper temperature gradient on TE, convective heat losses are considered from the TE. Computer simulations focus on the two-dimensional (2D) temperature analysis and displacement dynamics of the combustion front inside the reactor, depending on the values of the filtration velocity (0.1 to 1.0 m/s), the heat loss coefficient from the internal cylinder (400–1500 W/m2/K), and the fuel equivalence ratio (0.06– 0.5). The conditions that maximized the overall performance of the process of energy conversion are: 0.7 m/s of the filtration velocity, 0.363 of the fuel equivalence ratio and 1500 W/(m2·K) of the heat transfer coefficient from the internal cylinder, to obtain 2.05 V electrical potential, 21 W of electrical power, and 5.64% of the overall process efficiency. The study shows that the cylindrical annular geometry can be used for converting the energy of combustion from lean gas mixtures into electricity, with a performance similar to the specified by manufacturers of thermoelectric elements (TE).