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Capillary heterogeneity has been identified over the last decade as a key control on subsurface CO 2 flow behavior during geological CO 2 sequestration. These heterogeneities can be formed in all sedimentary rocks, ranging from slight variations in the sand grain sizes to extensive sequences of interbedded sands, shales, and limestones. Capillary heterogeneity has been largely, although not entirely, overlooked in subsurface flow modeling because it is assumed to only directly influence fluid redistribution over scales of centimeters to meters. However, even small-scale fluid movements can result in dramatic impacts on the mobility and trapping of the CO 2 over kilometers. Therefore, neglecting capillary heterogeneity at multiple scales could potentially lead to errors in modeling and predicting field-scale plume migration. In this review paper, we aim to provide a consistent overview to (1) establish that capillary heterogeneity can have a major impact on CO 2 plume migration, (2) establish the respective length scales at which capillary heterogeneity matters, and (3) provide guidance for numerical modeling. This review covers pertinent literature and extracts key observations from the core to the field scales. Experimental studies have shown that millimeter-decimeter scale capillary heterogeneity can cause the so-called capillary heterogeneity trapping in addition to pore-scale residual trapping. Even at such a small scale, capillary heterogeneity can already lead to complex upscaled constitutive relationships, such as flow-rate dependent and anisotropic relative permeability, which affects field-scale CO 2 migration even when field-scale heterogeneities are present. Under gravity-dominated flow regimes, centimeter-meter scale capillary heterogeneity can entrap a significant amount of CO 2 at field scale, not just after imbibition but also during drainage. In certain cases, the presence of capillary heterogeneity can even completely stop the vertical movement of the CO 2 plume, hence greatly reducing leakage risks. At meter-kilometer scale, the influence of capillary heterogeneity is more pronounced and can hinder or redirect CO 2 migration in both lateral and vertical directions. The impact of capillary heterogeneity across multiple spatial scales poses a great challenge in modeling CO 2 migration at field scale, because it is practically impossible to build a field-scale earth model with grid blocks at millimeter scale. We recommend a hierarchical modeling approach to address this challenge. At field scale, earth models are built to capture geological features and heterogeneities in high but still practical grid resolutions. For each facies or rock type of the field-scale model, high- resolution meter-scale “conceptual” models are built with millimeter-scale grid blocks to capture representative fine-scale bedding geometries and heterogeneities in various environments of deposition, bridging the gap from subcore scale to the size of a field-scale simulation grid block. Upscaling is then used to preserve the smaller-scale flow dynamics of various rock types in field-scale simulations. Here, future work is needed to (1) refine, improve, and validate the hierarchical modeling approach; (2) build libraries of fine-scale bedding models for facies in various environments of deposition; (3) quantify multiscale capillary heterogeneity effects under subsurface uncertainties; (4) gain learning from different storage formations; and (5) establish best practices that balance accuracy and computational speed.
Equivalent plate analysis is often used to replace the computationally expensive finite element analysis in initial design stages or in conceptual design of aircraft wing structures. The equivalent plate model can also be used to design a wind tunnel model to match the stiffness characteristics of the wing box of a full-scale aircraft wing model while satisfying strength-based requirements An equivalent plate analysis technique is presented to predict the static and dynamic response of an aircraft wing with or without damage. First, a geometric scale factor and a dynamic pressure scale factor are defined to relate the stiffness, load and deformation of the equivalent plate to the aircraft wing. A procedure using an optimization technique is presented to create scaled equivalent plate models from the full scale aircraft wing using geometric and dynamic pressure scale factors. The scaled models are constructed by matching the stiffness of the scaled equivalent plate with the scaled aircraft wing stiffness. It is demonstrated that the scaled equivalent plate model can be used to predict the deformation of the aircraft wing accurately. Once the full equivalent plate geometry is obtained, any other scaled equivalent plate geometry can be obtained using the geometric scale factor. Next, an average frequency scale factor is defined as the average ratio of the frequencies of the aircraft wing to the frequencies of the full-scaled equivalent plate. The average frequency scale factor combined with the geometric scale factor is used to predict the frequency response of the aircraft wing from the scaled equivalent plate analysis. A procedure is outlined to estimate the frequency response and the flutter speed of an aircraft wing from the equivalent plate analysis using the frequency scale factor and geometric scale factor. The equivalent plate analysis is demonstrated using an aircraft wing without damage and another with damage. Both of the problems show that the scaled equivalent plate analysis can be successfully used to predict the frequencies and flutter speed of a typical aircraft wing.
A method to estimate the full-scale noise suppression from a scale model distributed exhaust nozzle (DEN) is presented. For a conventional scale model exhaust nozzle, Strouhal number scaling using a scale factor related to the nozzle exit area is typically applied that shifts model scale frequency in proportion to the geometric scale factor. However, model scale DEN designs have two inherent length scales. One is associated with the mini-nozzles, whose size do not change in going from model scale to full scale. The other is associated with the overall nozzle exit area which is much smaller than full size. Consequently, lower frequency energy that is generated by the coalesced jet plume should scale to lower frequency, but higher frequency energy generated by individual mini-jets does not shift frequency. In addition, jet-jet acoustic shielding by the array of mini-nozzles is a significant noise reduction effect that may change with DEN model size. A technique has been developed to scale laboratory model spectral data based on the premise that high and low frequency content must be treated differently during the scaling process. The model-scale distributed exhaust spectra are divided into low and high frequency regions that are then adjusted to full scale separately based on different physics-based scaling laws. The regions are then recombined to create an estimate of the full-scale acoustic spectra. These spectra can then be converted to perceived noise levels (PNL). The paper presents the details of this methodology and provides an example of the estimated noise suppression by a distributed exhaust nozzle compared to a round conic nozzle.
Models of photosynthetic production at ecosystem and global scales require multiple input parameters specifying physical and physiological surface features. While certain physical parameters (e.g., absorbed photosynthetically active radiation) can be derived from current satellite sensors, other physiologically relevant measures (e.g., vegetation type, water status, carboxylation capacity, or photosynthetic light-use efficiency), are not generally directly available from current satellite sensors at the appropriate geographic scale. Consequently, many model parameters must be assumed or derived from independent sources, often at an inappropriate scale. An abundance of ecophysiological studies at the leaf and canopy scales suggests strong physiological control of vegetation-atmosphere CO2 and water vapor fluxes, particularly in evergreen vegetation subjected to diurnal or seasonal stresses. For example hot, dry conditions can lead to stomatal closure, and associated "downregulation" of photosynthetic biochemical processes, a phenomenon often manifested as a "midday photosynthetic depression". A recent study with the revised simple biosphere (SiB2) model demonstrated that photosynthetic downregulation can significantly impact global climate. However, at the global scale, the exact significance of downregulation remains unclear, largely because appropriate physiological measures are generally unavailable at this scale. Clearly, there is a need to develop reliable ways of extracting physiologically relevant information from remote sensing. Narrow-band spectrometers offer many opportunities for deriving physiological parameters needed for ecosystem and global scale photosynthetic models. Experimental studies on the ground at the leaf- to stand-scale have indicated that several narrow-band features can be used to detect plant physiological status. One physiological signal is caused by xanthophyll cycle pigment activity, and is often expressed as the Photochemical Reflectance Index (PRI). Because the xanthophyll cycle pigments are photoregulatory pigments closely linked to photosynthetic function, this index can be used to derive relative photosynthetic rates. An additional signal with physiological significance is the 970 nm water absorption band, which provides a measure of liquid water content. This feature has been quantified both using a simple 2-band ratio (900/970 nm, here referred to as the "Water Band Index" or WBI;), and using the "continuum removal" method. Current atmospheric correction methods for AVIRIS imagery also obtain quantitative expressions of surface liquid water absorption based on the 970 nm water band and may be comparable to ground-based estimates of water content using this feature. However, physiological interpretations of both the PRI and the WBI are best understood at the leaf and canopy scales, where complications of atmospheric interference and complex stand and landscape features can be minimized, and where experimental manipulations can be readily applied. Currently it is not known whether these physiological indices can be used to derive meaningful physiological information from AVIRIS imagery. In addition to the problem of atmospheric interference, another challenge is that any simple physiological index can be confounded by multiple factors unrelated to physiology, and this problem can become more severe at progressively larger spatial scales. For example, previous work has suggested that both the PRI and the WBI, are strongly correlated with other optical measures of canopy structure (e.g., the Normalized Difference Vegetation Index or green vegetation fraction), indicating a confounding effect of structure on physiological signals at the larger, landscape scale. Furthermore, the normal operating mode of most imaging spectrometers does not allow simultaneous, ground truthing at a level of detail needed for physiological sampling. Additionally, manipulative experiments of physiology are difficult to apply at a geographic scale suitable for comparison with remote imagery, which often works at spatial scales that are several orders of magnitude larger than those typically used for physiological studies. These limitations require the consideration of alternative approaches to validating physiological information derived from AVIRIS data. In this report, we present a multi-scale sampling approach to detecting physiologically significant signals in narrow-band spectra. This approach explores the multi-dimensional data space provided by narrow-band spectrometry, and combines AVIRIS imagery at a large scale, with ground spectral sampling at an intermediate scale, and detailed ecophysiological measurements at a fine scale, to examine seasonally and spatially changing relationships between multiple structural and physiological variables. Examples of this approach are provided by simultaneous sampling of the Normalized Difference Vegetation Index (NDVI), an index of fractional PAR interception and green vegetation cover, the Water Band Index (WBI, an index of liquid water absorption, and the Photochemical Reflectance Index (PRI, an index of xanthophyll cycle pigment activity and photosynthetic light-use efficiency. By directly linking changing optical properties sampled on the ground with measurable physiological states, we hope to develop a basis for interpreting similar signals in AVIRIS imagery.
Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, in this work, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography 𝐶 and yield stress 𝑌 follow power laws as a function of scale 𝜆, such that 𝐶∼𝜆 −𝑚 and 𝑌∼𝜆 −𝑛 , respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as 1−𝑛. We also show that the plasticity is expected to erode the contacts if 𝑚 is lower than 𝑛−3, which corresponds to a Hurst exponent lower than 1−𝑛/2. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.
The excellent mechanical properties of laminated composite structures make them prime candidates for wide variety of applications in aerospace, mechanical and other branches of engineering. The enormous design flexibility of advanced composites is obtained at the cost of large number of design parameters. Due to complexity of the systems and lack of complete design based informations, designers tend to be conservative in their design. Furthermore, any new design is extensively evaluated experimentally until it achieves the necessary reliability, performance and safety. However, the experimental evaluation of composite structures are costly and time consuming. Consequently, it is extremely useful if a full-scale structure can be replaced by a similar scaled-down model which is much easier to work with. Furthermore, a dramatic reduction in cost and time can be achieved, if available experimental data of a specific structure can be used to predict the behavior of a group of similar systems. This study investigates problems associated with the design of scaled models. Such study is important since it provides the necessary scaling laws, and the factors which affect the accuracy of the scale models. Similitude theory is employed to develop the necessary similarity conditions (scaling laws). Scaling laws provide relationship between a full-scale structure and its scale model, and can be used to extrapolate the experimental data of a small, inexpensive, and testable model into design information for a large prototype. Due to large number of design parameters, the identification of the principal scaling laws by conventional method (dimensional analysis) is tedious. Similitude theory based on governing equations of the structural system is more direct and simpler in execution. The difficulty of making completely similar scale models often leads to accept certain type of distortion from exact duplication of the prototype (partial similarity). Both complete and partial similarity are discussed. The procedure consists of systematically observing the effect of each parameter and corresponding scaling laws. Then acceptable intervals and limitations for these parameters and scaling laws are discussed. In each case, a set of valid scaling factors and corresponding response scaling laws that accurately predict the response of prototypes from experimental models is introduced. The examples used include rectangular laminated plates under destabilizing loads, applied individually, vibrational characteristics of same plates, as well as cylindrical bending of beam-plates.
Scale model technology represents one method of investigating the behavior of advanced, weight-efficient composite structures under a variety of loading conditions. It is necessary, however, to understand the limitations involved in testing scale model structures before the technique can be fully utilized. These limitations, or scaling effects, are characterized. in the large deflection response and failure of composite beams. Scale model beams were loaded with an eccentric axial compressive load designed to produce large bending deflections and global failure. A dimensional analysis was performed on the composite beam-column loading configuration to determine a model law governing the system response. An experimental program was developed to validate the model law under both static and dynamic loading conditions. Laminate stacking sequences including unidirectional, angle ply, cross ply, and quasi-isotropic were tested to examine a diversity of composite response and failure modes. The model beams were loaded under scaled test conditions until catastrophic failure. A large deflection beam solution was developed to compare with the static experimental results and to analyze beam failure. Also, the finite element code DYCAST (DYnamic Crash Analysis of STructure) was used to model both the static and impulsive beam response. Static test results indicate that the unidirectional and cross ply beam responses scale as predicted by the model law, even under severe deformations. In general, failure modes were consistent between scale models within a laminate family; however, a significant scale effect was observed in strength. The scale effect in strength which was evident in the static tests was also observed in the dynamic tests. Scaling of load and strain time histories between the scale model beams and the prototypes was excellent for the unidirectional beams, but inconsistent results were obtained for the angle ply, cross ply, and quasi-isotropic beams. Results show that valuable information can be obtained from testing on scale model composite structures, especially in the linear elastic response region. However, due to scaling effects in the strength behavior of composite laminates, caution must be used in extrapolating data taken from a scale model test when that test involves failure of the structure.