The Forchheimer equation: A theoretical development

In this paper we illustrate how the method of volume averaging can be used to derive Darcy's law with the Forchheimer correction for homogeneous porous media. Beginning with the Navier-Stokes equations, we find the volume averaged momentum equation to be given by $$\langle v_\beta \rangle = - \frac{K}{{\mu _\beta }} \cdot (\nabla \langle p_\beta \rangle ^\beta - \rho _\beta g) - F\cdot \langle v_\beta \rangle .$$ The Darcy's law permeability tensor, K, and the Forchheimer correction tensor, F, are determined by closure problems that must be solved using a spatially periodic model of a porous medium. When the Reynolds number is small compared to one, the closure problem can be used to prove that F is a linear function of the velocity, and order of magnitude analysis suggests that this linear dependence may persist for a wide range of Reynolds numbers.     

The Evolution of High-Throughput Macromolecular Crystallography at Synchrotrons

On May 11 and 12, 2000, the Stanford Synchrotron Radiation Laboratory, as it was then known, hosted a “Workshop on Techniques for Automated Mounting, Viewing and Centering Pre-Cooled Protein Crystals” [1 http://www-ssrl.slac.stanford.edu/conferences/workshops/px-robotics/. [Google Scholar], 2 E. Abola, Nature Structural Biology 7, 973–977 (2000).[Crossref], [PubMed] , [Google Scholar]]. The 12 presentations during the meeting all focused on the impact that automation could have on the performance of synchrotron beamlines and thus on research in structural biology. Two principal themes ran through the workshop: (1) robotics to mount crystals on a diffractometer; and (2) methods to place a crystal in the X-ray beam. Five conceptual and prototype robotic systems for automated mounting were described—the original ACTOR from Abbott Laboratories, later modified and marketed by Rigaku/MSC, and the systems which in final form become the ALS [3 G. Snell, Structure 12, 537–545 (2004).[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], EMBL/ESRF SC3 [4 F. Cipriani, Acta Cryst. D62(10), 1251–1259 (2006). [Google Scholar]], APS/SBC [5 D. Shu, AIP Conference Proceedings 705(1), 1201–1204 (2004).[Crossref] , [Google Scholar]], and SSRL SAM robots [6 A. E. Cohen, J. Appl. Cryst. 5(6), 720–726 (2002).[Crossref], [Web of Science ®] , [Google Scholar]]. By December of that year, the ACTOR had been installed for testing at Sector 32 of the Advanced Photon Source (Figure 1). Within three years, by the end of 2003, several of these robots, plus the commercial MARcsc from MAR Research, had been deployed to handle frozen protein crystals at beamlines for macromolecular crystallography (MX). Currently, at least 13 distinct robot types, not including variants of the ALS automounter, are employed at synchrotron beamlines to transfer crystals from storage to beam position.     

Impact of M1A1 main battle tank disturbance on soil quality, invertebrates, and vegetation characteristics

Military training commonly results in land degradation, but protocols for assessing and predicting long-term environmental impact are lacking. An ability to assess the impact of repeated disturbance and subsequent recovery is needed to balance training requirements against environmental quality. To develop methodology for assessing soil quality, a study evaluating disturbance resulting from tank maneuvers was initiated on Fort Riley Military Installation, Kansas. The objectives were to identify and quantify soil-quality indicators on two soil types exposed to controlled tank traffic. We examined physical, chemical, and biotic indicators after treatments were applied during wet and dry soil conditions. A randomized complete-block design, with three blocks per soil type and three treatments per block, was used. Treatments consisted of disturbance created by a 63-ton M1A1 tank making five passes in a figure-8 pattern during either dry or wet soil conditions. The M1A1 was operated at a speed of approximately 8 km/h. Control plots received no tank traffic. Soil-quality indicators evaluated were soil compaction, soil penetration resistance, rut depth, soil bulk density, soil texture, soil chemical composition, plant biomass, soil microbial diversity, and nematode and earthworm taxa. Soil-quality indicators were sampled within one week after tank disturbance. Preliminary data indicate soil-texture-dependent treatment effects (p  0.05) for bulk density and porosity. Bulk density increased and porosity decreased on trafficked areas, in the silt loam soil, but showed no change in the silty clay loam soil. Disturbance during wet soil conditions raised penetrometer resistance and gravimetric water content more than disturbance during dry soil conditions (p  0.05). A significant difference in disturbance was measured between the outside and inside portion of the same track (p  0.01 and 0.001, respectively). The outside track caused the greatest amount of disturbance, as measured by the height of the disturbed soil ridge above the track bed. Tank disturbance significantly reduced total vegetative biomass (p  0.05) compared with that of un-trafficked areas. Disturbance under wet soil conditions significantly reduced grass biomass (p = 0.040), whereas disturbance under dry soil conditions significantly reduced forb biomass (p = 0.0247) compared to un-trafficked areas. Total earthworm abundance (p = 0.011) was reduced by 82% when disturbance occurred during wet soil conditions regardless of soil type.     

Soviet and Japanese oversnow vehicles

The Soviet Union has an overwhelming need for oversnow and adverse terrain transport since by their own definition over 60% of their country is considered as Arctic. They have developed a wide range of configurations and types of vehicles to fit their production capabilities and needs. Their vehicles in general are not sophisticated but rather emphasize ease of maintenance and simplicity. Their research however is based on investigating even exotic vehicle configurations.

Japan on the other hand has limited its work to a small number of vehicles to fit their limited needs in the Northern Islands. Their research has been based mainly on the development and improvement of a snow/road track which can be used to meet their specialized military requirements.     

Two-phase flow in heterogeneous porous media III: Laboratory experiments for flow parallel to a stratified system

Two-phase flow in stratified porous media is a problem of central importance in the study of oil recovery processes. In general, these flows are parallel to the stratifications, and it is this type of flow that we have investigated experimentally and theoretically in this study. The experiments were performed with a two-layer model of a stratified porous medium. The individual strata were composed of Aerolith-10, an artificial: sintered porous medium, and Berea sandstone, a natural porous medium reputed to be relatively homogeneous. Waterflooding experiments were performed in which the saturation field was measured by gamma-ray absorption. Data were obtained at 150 points distributed evenly over a flow domain of 0.1 × 0.6 m. The slabs of Aerolith-10 and Berea sandstone were of equal thickness, i.e. 5 centimeters thick. An intensive experimental study was carried out in order to accurately characterize the individual strata; however, this effort was hampered by both local heterogeneities and large-scale heterogeneities.The theoretical analysis of the waterflooding experiments was based on the method of large-scale averaging and the large-scale closure problem. The latter provides a precise method of discussing the crossflow phenomena, and it illustrates exactly how the crossflow influences the theoretical prediction of the large-scale permeability tensor. The theoretical analysis was restricted to the quasi-static theory of Quintard and Whitaker (1988), however, the dynamic effects described in Part I (Quintard and Whitaker 1990a) are discussed in terms of their influence on the crossflow.Roman Letters A interfacial area between the -region and the -region contained within V, m² - a vector that maps onto , m - b vector that maps onto , m - b vector that maps onto , m - B second order tensor that maps onto , m² - C second order tensor that maps onto , m² - E energy of the gamma emitter, keV - f fractional flow of the -phase - g gravitational vector, m/s² - h characteristic length of the large-scale averaging volume, m - H height of the stratified porous medium , m - i unit base vector in the x-direction - K local volume-averaged single-phase permeability, m² - K - {K}, large-scale spatial deviation permeability - { K} large-scale volume-averaged single-phase permeability, m² - K ^* large-scale single-phase permeability, m² - K ^** equivalent large-scale single-phase permeability, m² - K local volume-averaged -phase permeability in the -region, m² - K local volume-averaged -phase permeability in the -region, m² - K - {K } , large-scale spatial deviation for the -phase permeability, m² - K ^* large-scale permeability for the -phase, m² - l thickness of the porous medium, m - l characteristic length for the -region, m - l characteristic length for the -region, m - L length of the experimental porous medium, m - characteristic length for large-scale averaged quantities, m - n outward unit normal vector for the -region - n outward unit normal vector for the -region - n unit normal vector pointing from the -region toward the -region (n = - n ) - N number of photons - p pressure in the -phase, N/m² - p ₀ reference pressure in the -phase, N/m² - local volume-averaged intrinsic phase average pressure in the -phase, N/m² - large-scale volume-averaged pressure of the -phase, N/m² - large-scale intrinsic phase average pressure in the capillary region of the -phase, N/m² - - , large-scale spatial deviation for the -phase pressure, N/m² - p_c , capillary pressure, N/m² - p _c capillary pressure in the -region, N/m² - p capillary pressure in the -region, N/m² - {p _c } ^c large-scale capillary pressure, N/m² - q -phase velocity at the entrance of the porous medium, m/s - q -phase velocity at the entrance of the porous medium, m/s - S_wi irreducible water saturation - S /, local volume-averaged saturation for the -phase - S _i initial saturation for the -phase - S _r residual saturation for the -phase - S ^* { }^*/}^*, large-scale average saturation for the -phase - S saturation for the -phase in the -region - S saturation for the -phase in the -region - t time, s - v -phase velocity vector, m/s - v local volume-averaged phase average velocity for the -phase, m/s - {v } large-scale averaged velocity for the -phase, m/s - v local volume-averaged phase average velocity for the -phase in the -region, m/s - v local volume-averaged phase average velocity for the -phase in the -region, m/s - v -{v } , large-scale spatial deviation for the -phase velocity, m/s - v -{v } , large-scale spatial deviation for the -phase velocity in the -region, m/s - v -{v } , large-scale spatial deviation for the -phase velocity in the -region, m/s - V large-scale averaging volume, m³ - y position vector relative to the centroid of the large-scale averaging volume, m - {y}^c large-scale average of y over the capillary region, m Greek Letters local porosity - local porosity in the -region - local porosity in the -region - local volume fraction for the -phase - local volume fraction for the -phase in the -region - local volume fraction for the -phase in the -region - {}^* { }^*+{ }^*, large-scale spatial average volume fraction - { }^* large-scale spatial average volume fraction for the -phase - mass density of the -phase, kg/m³ - mass density of the -phase, kg/m³ - viscosity of the -phase, N s/m² - viscosity of the -phase, Ns/m² - V /V , volume fraction of the -region ( + =1) - V /V , volume fraction of the -region ( + =1) - attenuation coefficient to gamma-rays, m^-1 - -      

On using non-Gaussian distributions to perform statistical linearization

In statistical linearization non-linear elements are approximated by equivalent linear elements according to recipes proposed by the pioneers of the procedure. The recipes require the evaluation of certain statistics which, ideally, should be evaluated using the exact probability distribution of the non-linear response. Because the exact non-linear response distribution is unknown it has become traditional to use a Gaussian distribution as an approximation to the exact distribution. With the modern computing tools now available it is easy to use non-Gaussian distributions which can provide better approximations in cases where Gaussian distributions are not appropriate. Examples are displayed for power-law oscillators with stiffening and softening springs, and for the Duffing oscillator, and for a double-well oscillator. Two families of probability distributions with varying shape are studied.     

Full-field speckle pattern image correlation with B-Spline deformation function

A full-field speckle pattern image correlation method is presented that will determine directly the complete, two-dimensional deformation field during the image correlation process on digital images obtained using computer vision systems. In this work, a B-Spline function is used to represent the object deformation field throughout the entire image area. This is an improvement over subset-based image correlation methods by implicitly maintaining position and derivative continuity constraints among subsets up to a specified order. The control point variables within the B-Spline deformation function are optimized iteratively with the Levenberg-Marquardt method to achieve minimum disparity between the predicted and actual deformed images. Results have shown that the proposed method is computationally efficient, accurate and robust. The general framework of this method can be applied ton-dimensional image correlation systems that solve for multi-dimension vector fields.     

Fifteenth International Symposium on Biological and Environmental Reference Materials (BERM-15)

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