Fujio Kuwahara

A Macroscopic Turbulence Model for Flow in a Porous Medium

A complete set of macroscopic two-equation turbulence model equations has been established for analyzing turbulent flow and heat transfer within porous media. The volume-averaged transport equations for the mass, momentum, energy, turbulence kinetic energy and its dissipation rate were derived by spatially averaging the Reynolds-averaged set of the governing equations. The additional terms representing production and dissipation of turbulence kinetic energy are modeled introducing two unknown model constants, which are determined from a numerical experiment using a spatially periodic array. In order to investigate the validity of the present macroscopic turbulence model, a macroscopically unidirectional turbulent flow through an infinite array of square rods is considered from both micro- and macroscopic-views

A Numerical Study of Thermal Dispersion in Porous Media

Thermal dispersion in convective flow in porous media has been numerically investigated using a two-dimensional periodic model of porous structure. A macroscopically uniform flow is assumed to pass through a collection of square rods placed regularly in an infinite space, where a macroscopically linear temperature gradient is imposed perpendicularly to the flow direction. Due to the periodicity of the model, only one structural unit is taken for a calculation domain to resolve an entire domain of porous medium. Continuity, Navier-Stokes and energy equations are solved numerically to describe the microscopic velocity and temperature fields at a pore scale. The numerical results thus obtained are integrated over a unit structure to evaluate the thermal dispersion and the molecular diffusion due to tortuosity. The resulting correlation for a high-Peclet-number range agrees well with available experimental data.

A two-energy equation model for conduction and convection in porous media

Abstract A two-energy equation model is proposed for analyzing conduction and convection within porous media in local thermal non-equilibrium. Hsus closure model for the tortuosity effect has been extended to treat not only conduction but also convection in porous media. The two energy equations for the individual phases are combined into a fourth-order ordinary differential equation, so as to treat one-dimensional steady-state problems. Then, the exact solutions are obtained for two fundamental cases, namely, one-dimensional steady conduction in a porous slab with internal heat generation within a solid, and also thermally developing unidirectional flow through a semi-infinite medium.

Heat and Fluid Flow Within an Anisotropic Porous Medium

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

An analysis on forced convection in a channel filled with a Brinkman-Darcy porous medium: Exact and approximate solutions

An analysis was made to investigate non-Darcian fully developed flow and heat transfer in a porous channel bounded by two parallel walls subjected to uniform heat flux. The Brinkmanextended Darcy model was employed to study the effect of the boundary viscous frictional drag on hydrodynamic and heat transfer characteristics. An exact expression has been derived for the Nusselt number under the uniform wall heat flux condition. Approximate results were also obtained by exploiting a momentum integral relation and an auxiliary relation implicit in the Brinkmanextended Darcy model. Excellent agreement was confirmed between the approximate and exact solutions even in details of velocity and temperature profiles.ZusammenfassungDiese Studie untersucht voll entwickelte „Non-Darcy“-Strömung und Wärmetransport in einem porösen Kanal, der durch zwei parallele Wände gebildet und einem einheitlichen Wärmestrom ausgesetzt wird. Das erweiterte „Brinkman-Darcy-Modell” wurde angewandt, um den Effekt des viskosen Reibungswiderstands der Wände auf die hydrodynamischen Charakteristiken und die Wärmeübertragung zu untersuchen. Ein exakter Ausdruck wurde für die Nusselt-Zahl unter einheitlichem Wandwärmestrom abgeleitet. Annähernde Ergebnisse wurden durch die Auswertung einer Impuls-Integral-Beziehung und einer im erweiterten „Brinkman-Darcy-Modell“ implizierten Hilfsfunktion erhalten. Ausgezeichnete Übereinstimmung zwischen den genäherten und den exakten Lösungen konnten sogar in den Geschwindigkeits- und Temperaturprofilen festgestellt werden.

A General Macroscopic Turbulence Model for Flows in Packed Beds, Channels, Pipes, and Rod Bundles

This study focuses on Nakayama and Kuwaharas two-equation turbulence model and its modifications, previously proposed for flows in porous media, on the basis of the volume averaging theory. Nakayama and Kuwaharas model is generalized so that it can be applied to most complex turbulent flows such as cross flows in banks of cylinders and packed beds, and longitudinal flows in channels, pipes, and rod bundles. For generalization, we shall reexamine the extra production terms due to the presence of the porous media, appearing in the transport equations of turbulence kinetic energy and its dissipation rate. In particular, we shall consider the mean flow kinetic energy balance within a pore, so as to seek general expressions for these additional production terms, which are valid for most kinds of porous media morphology. Thus, we establish the macroscopic turbulence model, which does not require any prior microscopic numerical experiments for the structure. Hence, for the given permeability and Forchheimer coefficient, the model can be used for analyzing most complex turbulent flow situations in homogeneous porous media without a detailed morphological information. Preliminary examination of the model made for the cases of packed bed flows and longitudinal flows through pipes and channels reveals its high versatility and performance.

Exact Solutions for a Thermal Nonequilibrium Model of Fluid Saturated Porous Media Based on an Effective Porosity

An effective porosity concept has been introduced to account for the effects of tortuosity and thermal dispersion on the individual effective thermal conductivities of the solid and fluid phases in a fluid-saturated porous medium. Using this effective porosity concept, a thermal nonequilibrium model has been proposed to attack locally thermal nonequilibrium problems associated with convection within a fluid-saturated porous medium. Exact solutions are obtained, assuming a plug flow, for the two cases of thermally fully developed convective flows through a channel, namely, the case of isothermal hot and cold walls and the case of constant heat flux walls. These exact solutions for the cases of metal foam and air combination reveal that the local thermal equilibrium assumption may hold for the case of isothermal hot and cold walls, but may fail for the case of constant heat flux walls. [DOI: 10.1115/1.4004354]

A Lumped Parameter Heat Transfer Analysis for Composting Processes With Aeration

Composting is the biological decomposition and stabilization of rganic substrates. Heat is generated biologically to produce a nal product that is stable, free of pathogens and weed seeds, hich can be beneficially applied to land. As pointed out by Haug 1 and Li and Jenkins 2 , composting is an ancient art, yet enineering that is still often conducted using a “handbook aproach.” However, such an approach lacks the knowledge to conrol various factors involved to achieve the desired end product nd economics. A typical composting system with aeration is hown in Fig. 1, where the air is ventilated from the bottom to ccelerate the biological processes. The air carries sensible and atent heat away as passing through the matrix, while it is essential o maintain organic decomposition leading to biological heat genration. Thus, the control of aeration requires heat transfer analyis if we are to maintain the optimum temperature for the comosting system which, according to Nakasaki et al. 3 , coincides ith the optimum reaction temperature of around 60°C . Mathmatical modeling of composting processes in such a composting ystem is still in its infancy, although several attempts 3–8 have een made to simulate the composting reactions. The authors 9 have recently introduced the volume-averaging heory previously established for the study of porous media with eat generation e.g., Nakayama et al. 10 . We extended it to stablish a complete set of the volume-averaged governing equaions appropriate for the analysis of composting processes. As a rst step towards our strategic efforts to establish a complete nuerical prediction tool for composting operations, we propose a imple lumped parameter model, which can be obtained by interating the foregoing governing equations.

Similarity Solution for Non-Darcy Free Convection From a Nonisothermal Curved Surface in a Fluid-Saturated Porous Medium

Considerable attention has been directed to heat and fluid flow within fluid-saturated porous media because of its importance in geophysical and engineering applications such as geothermal energy conversion, thermal insulation of buildings, and packed-bed reactors. In this study, the authors shall investigate non-Darcy free convective flows using the Ergun model. It will be shown that there exists a certain family of body shape geometries and corresponding wall temperature distributions, which permit similarity solutions. The effects of inertia and geometric shape on the velocity and temperature fields are investigated and the corresponding heat transfer characteristics are discussed in detail.

A Porous Media Approach for Bifurcating Flow and Mass Transfer in a Human Lung

A porous media approach was proposed to investigate the characteristics of the bifurcating airflow and mass transfer within a lung. The theory of porous media was introduced in order to deal with a large number of bifurcations and a vast scale difference resulting from bifurcations. Upon introducing a two-medium treatment for the air convection and the diffusion in its surrounding wall tissue, the oxygen mass transfer between the inhaling air and the tissue was considered along with the effects of the blood perfusion on the mass transfer within the tissue. The overall mass transfer resistance between the inlet of the trachea and the blood in the capillaries was obtained on the basis of the porous media approach. The analysis reveals that there exists the optimal number of the bifurcation levels, namely, 23, that yields the minimum overall mass transfer resistance for the mass transport from the external air to the red blood cells. The finding is consistent with Bejans constructal law, namely, that for a flow system to persist in time, it must evolve in such a way that it provides easier access to its currents.