Flow structure and wall layer control in a lower half heated upper half cooled enclosure with superimposed temperature deviations

This paper presents an investigation on the effects of superimposed temperature deviations as a control technique for the flows and mixing in lower half heated upper half cooled enclosures. Results show that the strength of the wall layer depends on the difference between the wall surface temperature and the fluid core temperature. The location of the head-on collision between a pair of upward/downward wall layers, which controls the mixing and fluid exchange between the two halves, is determined by the wall layer flow momentum strengths. Elevating/reducing the wall temperature by a superimposed temperature deviation is an effective control for the flow and mixing in such enclosures. Heat transfer analysis shows that the superimposed temperature deviations have minor effects on the total heat flow rate from the lower walls. Thus, this technique can be applied onto reactor vessels without modifying the reactor vessel configuration.     

Flow structure and transport mechanism in lower half heated upper half cooled enclosures in laminar flow regime

This paper presents an investigation on the transport mechanism in autoclave/thermosyphon type enclosures. Without a baffle to separate the lower- from the upper-half, the flow structure and the transport mechanisms are the same in rectangular and cylindrical enclosures. Thus, the efficiency of the fluid exchange and heat transfer between the enclosure’s two halves due to wall-layers feeding structure ensures that the center cores have almost uniform temperature. However, when a baffle separates the two halves, the wall layers’ interactions are eliminated and two temperature zones are established.     

Conjugate free convection of non-Newtonian fluids about a vertical cylindrical fin in porous media

Conjugate free convection along a vertical cylindrical fin in a non-Newtonian fluid-saturated porous medium has been investigated theoretically. The boundary layer equations based on the power lay model appropriate for the Darcy flows are solved numerically exploiting a very efficient finite difference method. Effects of the power-law index, conjugate convection-conduction parameter and the surface curvature parameter on the fin temperature distribution, local heat transfer-coefficient and local heat flux are studied and presented in graphical and tabular form.     

Flows of variable-viscosity fluids in ducts with heated walls

An asymptotically valid analytical solution is presented of the equations governing high Graetz number, high Pearson number, low Nahme number flows of power-law fluids in ducts with heated walls. Thus the flows are developing and the imposed difference between the wall temperature and the entry temperature of the fluid is sufficiently large to cause significant viscosity variations, but temperature differences due to heat generation by viscous dissipation are not. Three different duct geometries are considered: channels, pipes and discs. Estimates are made of the pressure drop, maximum temperature and flow-average temperature rise for flows in each of the geometries.     

Exchange model of displacement in porous media

A displacement model constructed on the assumption of the exchange of components between the volumes of the pore space moving and not moving in the direction of displacement is considered. The theoretical solution is shown to be in good agreement with the actual results of the displacement of oil by water. Criterial equations for predicting the interphase exchange coefficient and the relation between the nonmoving and moving volumes of the pore space are constructed on the basis of a series of experiments in uncemented porous media.Translated from Izvestiya Akademii Nauk SSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–97. January–February, 1991.     

Conditional model for sorption in porous media with fractal properties

In this study, the conditional moment closure approach, which is proven to be very useful for modelling of reactions in turbulent flows, is extended to characterise adsorbing, desorbing or reacting flows in porous media. A complete specification of the porous distance conditioned moment closure model, which is formulated in terms of single-conditioned expectations, is presented. The closure of the model equations is obtained assuming the diffusion approximation for fluxes of the reactive species. The model simulates complex multi-cascade processes of convective and diffusive transport of species between pores in a continuous and consistent manner and is a generalisation of dual (or triple) porosity concept. The model addresses the major difficulty of describing transport, entrapment and sorption processes in porous media with fractal properties, where distant transport occurs in the largest pores or fractures, while the adsorbing or desorbing surface is mainly allocated in small pores. The model is able to simulate various regimes of methane replacement by CO₂ in a coal sample, which makes it useful for optimising the design and parameters of enhanced coal bed methane recovery operations. It is demonstrated that the power-low decrease in downstream methane concentration, which has been observed experimentally, can be accurately reproduced by the model.     

An elastoplasticity model in porous media theories

In this article, porous media theories are referred to as mixture theories extended by the well-known concept of volume fractions. This approach implies the diverse field functions of both the porous solid matrix and the pore fluid to be represented by average functions of the macroscale.The present investigations are based on a binary model of incompressible constituents, solid skeleton, and pore liquid, where, in the constitutive range, use is made of the second-grade character of general heterogeneous media. Within the framework of geometrically finite theories, the paper offers a set of constitutive equations for the solid matrix, the viscous pore liquid and the different interactions between the constituents. The constitutive model applies to saturated as well as to empty solid materials, taking into account the physical nonlinearities based on elasto-plastic solid deformations. In particular, the constitutive model concentrates on granular materials like soil or concrete, where the elastic deformations are usually small and the plastic range is governed by kinematically hardening properties.     

Thermal-hydraulic core analysis of the VVER-1000 reactor using a porous media approach

In this study, a thermal-hydraulic analysis of the VVER-1000 reactor core is performed using a porous media approach. Based on this approach, each fuel assembly was modeled and was divided into a network of lumped regions, each of which was characterized by a volume average parameter. The conservation equations of mass, linear momentum and energy are derived and discretized using the finite volume method in a hexagonal coordinate system. The pressure, velocity and temperature fields are achieved using a numerical analysis of the above mentioned coupled equations. To validate the applied approach, the numerical analysis and COBRA EN code results were compared and showed good agreement.     

Non-darcy double-diffusive mixed convection from heated vertical and horizontal plates in saturated porous media

The non-darcy mixed convection flows from heated vertical and horizontal plates in saturated porous media have been considered using boundary layer approximations. The flows are considered to be driven by multiple buoyancy forces. The similarity solutions for both vertical and horizontal plates have been obtained. The governing equations have been solved numerically using a shooting method. The heat transfer, mass transfer and skin friction are reduced due to inertial forces. Also, they increase with the buoyancy parameter for aiding flow and decrease for the opposing flow. For aiding flow, the heat and mass transfer coefficients are found to approach asymptotically the forced or free convection values as the buoyancy parameter approaches zero or infinity.     

Convective motions in a porous medium heated from below

Convective motions in a porous medium filling a horizontal cylinder with a cross section of arbitrary shape and heated from below are studied. The small-parameter method is used to obtain infinitely many stationary motions forming a one-parameter family. For small values of the parameter, all of these motions are stable with respect to small perturbations. The article also discusses the case of heating which is not strictly vertical. It is found that in this case only one stationary motion is stable.     

Jots - a mathematical model of microscopic fluid flow in porous media

The model described in this paper is an approach to simulating flow through porous media on a microscopic scale. It is based on a variation of diffusion limited aggregation. The model is shown to match coreflood average saturation profiles and production histories as predicted by Darcy's equations while generating saturation distributions resembling viscous fingering. The model also is shown to simulate the limiting cases of infinite mobility ratio and zero flow rates as previously modeled by diffusion limited aggregation and percolation theory. With some simplifying assumptions, differential equations very similar to Darcy's equations are derived from the microscopic interpretation of fluid behavior in porous media used in this model.     

A LGA model for dispersion in heterogeneous porous media

The lattice gas automaton (LGA) model proposed in the previous paper is applied to the problem of simulating dispersion and mixing in heterogeneous porous media. We demonstrate here that tracer breakthrough profiles and longitudinal dispersion coefficients can be computed for heterogeneous porous media.     

Analytical model of steam zone propagation in porous media

Steam injected into oil-bearing porous media forms a steam zone which propagates in three-dimensional space. The injected steam forms the condensation front bounding the seam zone. Simultaneous mass and the energy transfers take place through this moving boundary, between the rocks and fluids inside and outside the steam zone. The energy transfer is by conduction and convection. A new mathematical model describes the propagation growth of the steam zone subject to initial and boundary conditions, and is applicable in a general case of heterogeneous steam zone of arbitrary geometry. The model is based on the simultaneous analytical solution of the coupled overall mass and energy balance equations for a multi-phase steam zone, and is presented here for the first time. The resulting nonlinear integral equation does not have an analytical solution for a general case. The exact solution is found for a cylindrical homogeneous steam zone. For a special case of a one-dimensional, two phase steam zone, this solution shows excellent agreement with available experimental data.     

Stability of a nonuniformly heated fluid in a porous horizontal layer

We investigate the stability of a nonuniformly heated fluid in the gravitational field in a plane horizontal porous layer through which vertical forced motion is effected. A similar system was studied in [1, 2]. In the present paper, the nonuniformity of the permeability of the porous layer with respect to the depth and the dependence of the viscosity of the saturating fluid on the temperature are taken into account in addition. As a result of the application of the linear stability theory, an eigenvalue problem arises, which is solved numerically. A family of curves representing the dependence of the critical modified Rayleigh number Ra _k ^⋆ on the injection parameter (the Péclet number Pe) for different degrees of inhomogeneity of the permeability and the viscosity is obtained. It is found that although Pe=0 corresponds to Ra _k ^⋆ for uniform permeability and viscosity and the stability increases monotonically as Pe increases, the presence of nonuniformity of the permeability or the viscosity leads to the appearance of a stability minimum in the region Pe≈1, while under the simultaneous influence of these two factors, the minimum is shifted into the region Pe≈2. The results of the paper can be used, for example, in the investigation of heat transfer in the case of forced fluid motion in the fissures of a permeable rock mass, when, in the case of pumping through a horizontal fissure, the fluid penetrates vertically across its permeable walls into the stratum. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–7, November–December, 1986.     

Combustion in a horizontal channel partially filled with a porous media

Experiments were carried out to investigate the combustion propagation phenomenon in a horizontal channel partially filled with ceramic-oxide spherical beads. A 1.22 m long, 43 mm nominally thick layer of spherical beads is located at the ignition end of a 2.44 m long, 76 mm square channel. Tests were performed with 6.4 and 12.7 mm diameter beads. A flame is ignited at the bead end wall by an automotive spark ignition system. Flame propagation and pressure measurements are obtained via ionization probes and piezoelectric pressure transducers mounted on the top and bottom surfaces of the channel. High-speed schlieren video was used to visualize the structure of the explosion front. Experiments were performed with a 31% nitrogen diluted stoichiometric methane–oxygen mixture at room temperature and at an initial pressure in the range of 15–50 kPa. For initial pressures of 15 and 20 kPa the flame accelerates to a velocity close to the speed of sound in the combustion products. For initial pressure of 30 kPa and higher DDT occurs in the gap above the bead layer. An explosion front propagating at a velocity just under the CJ detonation velocity is detected in the bead layer even though the bead layer pore size is much smaller than the detonation cell size. It is demonstrated that flame propagation within the bead layer is the driving force behind the very rapid flame acceleration observed, however the DDT event occurring in the gap above the bead layer is not affected by the bead layer porosity. Schlieren video indicates that the structure of the explosion front varies across the channel height and with propagation distance down the channel.     

Heat transfer in a vertically-layered porous medium heated from below

Some studies already made have investigated the criterion for onset of convection and heat and mass flow distributions in a porous slab composed of horizontal layers of different materials. This paper reports a study of such criteria for the case where the slab is composed of vertically-aligned strata with different permeabilities and thermal conductivities. This has particular relevance to where blocks of different materials abut in a vertical plane, as well as the case of very narrow highly permeable vertical layers which represent vertical faults in a geological structure. Results indicate that permeability and/or thermal conductivity contrasts between layers can significantly affect the flow pattern and the spatial distribution of the surface heat flux. The concentration of flow in highly permeable faults produces marked irregularities in the heat flow through the surface above them.