Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur

Numerical Investigation of Variable Transpiration Cooling Effectiveness in Laminar and Turbulent Flows for Hypersonic Cruise Vehicles

The thermal management of hypersonic air-breathing vehicles presents formidable challenges. Reusable thermal protection systems (TPS) are one of the key technologies that mustbe improved in order to use hypersonic vehicles as practical, long-range transportation systems. The active cooling systems, such as transpiration cooling,have to be considered foraffordable,long duration flights to achieveefficient temperature reduction and coolant mass saving.With this technique, it is important to understand the physics that characterize the boundary layer and its interaction with the vehicle-s surface. This paper investigatesthe effectiveness of a variable-velocitytranspiration strategy for fully laminar, transitional, and fully turbulent flowsover a 2-D blunt bodywith a cylindricalleading edge and a wedge region. Thetransitional flow cases areevaluated for a range of transitionlocations to see the influence of this parameter on the variable transpiration strategy introduced. For all flow typespresented in this paper, asaw-tooth wall velocity distribution(variable transpiration strategy) iscompared to a uniform-velocitytranspiration approach. An equalamountof coolantusage has been imposed in order to compare the cooling effectivenessbetween bothstrategiesfor variousflow types in different regions of the body. The results show that the uniform-velocitytranspiration allows areduction of 68% in the stagnation point heat flux and 77% for variable-velocity transpiration with respect to the no-transpiration casein both laminar and turbulent flow cases. The computational results show that the efficiency of the transpiration cooling is much higher in laminar flowcompared to turbulent flow in regions downstream of the stagnation point.In such regions, for turbulent flows, the amount of total coolant must be increased by 110% (factor of roughly 2) to match the cooling efficiency observed in laminar flows. In addition tothe analysis of cooling effectiveness, the thermal response of TPS material with the variable transpiration strategy isalsoinvestigated for both fully laminar and fully turbulent flow

The Effect of Void Structure on the Permeability of Fibrous Networks

A Kozeny–Carman-based model of permeability for fibrous networks is proposed: the original model is extended by incorporating information about the local structure of the void space. Furthermore, it is demonstrated how in practice this added structural information can be retrieved from a three-dimensional digital image of a fibrous material. The proposed model is then validated for both foam- and water-deposited laboratory sheets of bleached kraft pulp (Scots pine) and chemi-thermo-mechanical pulp (CTMP, Norway spruce). The validation is carried out by comparing the model predictions against computationally determined permeability values. The related fluid-flow simulations are executed using the lattice-Boltzmann method together with high-resolution X-ray microtomography images. For both pulp materials, the sample sets had nearly equal porosities, but deviated substantially in their permeabilities. The proposed model was shown to improve prediction of permeability for the fibrous materials considered: the deviation between the predicted and computationally determined values was no more than 8%