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DOE OSTI2022

The Effect of Surface Heating Heterogeneity on Boundary Layer Height and Its Dependence on Background Wind Speed

The planetary boundary layer height (PBLH) is a fundamental variable of the planetary boundary layer (PBL). The effect of surface heterogeneity is challenging in the PBL parameterization for numerical weather and climate models. Here we use large eddy simulation data to investigate the impact of surface heating heterogeneity on the PBLH spatial variations and mean values over a domain of typical mesoscale model grid size. It is found that this impact depends on background wind condition. Variance decomposition and Fourier spectra both reveal that for the fully developed sheared convective PBL, surface heterogeneity contributes little to the spatial variation of PBLH, except for the case with heterogeneity scale of 14.4 km. This suggests that surface heterogeneity with length scales less than ~10 km, which is typical for mesoscale modeling, does not induce significant subgrid spatial variation of PBLH. The domain-averaged PBLH is found to generally increase as surface heterogeneity scale decreases, until reaching the scale on the order of PBLH. The findings can be used to inform the parameterization development of PBL processes over heterogeneous surface.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2017

Enhanced Groundwater Recharge Rates and Altered Recharge Sensitivity to Climate Variability Through Subsurface Heterogeneity

Our environment is heterogeneous. In hydrological sciences, the heterogeneity of subsurface properties, such as hydraulic conductivities or porosities, exerts an important control on water balance. This notably includes groundwater recharge, which is an important variable for efficient and sustainable groundwater resources management. Current large-scale hydrological models do not adequately consider this subsurface heterogeneity. Here we show that regions with strong subsurface heterogeneity have enhanced present and future recharge rates due to a different sensitivity of recharge to climate variability compared with regions with homogeneous subsurface properties. Our study domain comprises the carbonate rock regions of Europe, Northern Africa, and the Middle East, which cover 25 of the total land area. We compare the simulations of two large-scale hydrological models, one of them accounting for subsurface heterogeneity. Carbonate rock regions strongly exhibit karstification, which is known to produce particularly strong subsurface heterogeneity. Aquifers from these regions contribute up to half of the drinking water supply for some European countries. Our results suggest that water management for these regions cannot rely on most of the presently available projections of groundwater recharge because spatially variable storages and spatial concentration of recharge result in actual recharge rates that are up to four times larger for present conditions and changes up to five times larger for potential future conditions than previously estimated. These differences in recharge rates for strongly heterogeneous regions suggest a need for groundwater management strategies that are adapted to the fast transit of water from the surface to the aquifers.

water resources↗

DOE OSTI2016

Numerical Study of Critical Role of Rock Heterogeneity in Hydraulic Fracture Propagation

Log and seismic data indicate that most shale formations have strong heterogeneity. Conventional analytical and semi-analytical fracture models are not enough to simulate the complex fracture propagation in these highly heterogeneous formation. Without considering the intrinsic heterogeneity, predicted morphology of hydraulic fracture may be biased and misleading in optimizing the completion strategy. In this paper, a fully coupling fluid flow and geomechanics hydraulic fracture simulator based on dual-lattice Discrete Element Method (DEM) is used to predict the hydraulic fracture propagation in heterogeneous reservoir. The heterogeneity of rock is simulated by assigning different material force constant and critical strain to different particles and is adjusted by conditioning to the measured data and observed geological features. Based on proposed model, the effects of heterogeneity at different scale on micromechanical behavior and induced macroscopic fractures are examined. From the numerical results, the microcrack will be more inclined to form at the grain weaker interface. The conventional simulator with homogeneous assumption is not applicable for highly heterogeneous shale formation.

Dual Lattice Discrete Element Method↗

DOE OSTI2024

Investigation of Ring-heterogeneous Geometry Approximation for Efficient and Practical SFR Analysis

A novel geometry approximation scheme named ring-heterogeneous approximation for intermediate resolution multiphysics analysis of SFRs is presented. This approach particularly targets neutronics coupled with thermo-mechanics feedback, which dominate the passive safety of SFR designs. The ring-heterogeneous approximation casts an array of pins into volume-preserving bands of materials that constitute the pins. It allows to efficiently simulate SFRs with an unstructured mesh and also to explicitly consider the deformation of each material by retaining their heterogeneity. Verification results with single assembly and core problems of the ABTR benchmark demonstrated that the ring-heterogeneous approximation is a reasonable approximation for SFRs. For a 2D full core problem, the ring-heterogeneous approximation significantly reduced the number of elements by at least a factor of 70 from a fully-heterogeneous mesh while almost exactly preserving the reference fully-heterogeneous solutions with the RMS error of only 0.02% in the ring-wise fission reaction rate.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Dispersion and Mixing in Three-Dimensional Discrete Fracture Networks: Nonlinear Interplay Between Structural and Hydraulic Heterogeneity: DISPERSION AND MIXING-REGULAR VERSUS DISORDERED NETWORKS

We investigate the relative impact of topological, geometric, and hydraulic heterogeneity on transport processes in three-dimensional fracture networks. Focusing on the two largest scales of heterogeneity in these systems, individual fracture and network structure, we compare transport through analogous structured and disordered three-dimensional fracture networks with varying degrees of hydraulic heterogeneity. For the moderate levels of hydraulic heterogeneity we consider, network structure is the dominant control of transport through the networks. Less dispersion, both longitudinal and transverse, is observed in structured networks than in disordered networks, due in part to the higher connectivity in the former, independent of the level of hydraulic heterogeneity. However, increases in dispersion with higher hydraulic heterogeneity are larger in the disordered networks than in the structured networks, thereby indicating that the interplay between structural and hydraulic heterogeneity is nonlinear. Here, we propose a measure of disorder in fracture networks by computing the Shannon entropy of the spectrum of the Laplacian of a weighted graph representation of the networks, where the weights are given by a combination of topological, geometric, and hydraulic properties. Finally, this metric, as a relative indicator by comparison between two networks, is a first approach to the dispersion potential and “mixing capacity” of a fracture network.

58 GEOSCIENCES↗

DOE OSTI2022

Near‐Surface Hydrology and Soil Properties Drive Heterogeneity in Permafrost Distribution, Vegetation Dynamics, and Carbon Cycling in a Sub‐Arctic Watershed

Abstract Discontinuous permafrost environments exhibit strong spatial heterogeneity at scales too small to be driven by weather forcing or captured by Earth System Models. Here we analyze effects of observed spatial heterogeneity in soil and vegetation properties, hydrology, and thermal dynamics on ecosystem carbon dynamics in a watershed on the Seward Peninsula in Alaska. We apply a Morris global sensitivity analysis to a process‐rich, successfully tested terrestrial ecosystem model (TEM), ecosys , varying soil properties, boundary conditions, and weather forcing. We show that landscape heterogeneity strongly impacts soil temperatures and vegetation composition. Snow depth, O‐horizon thickness, and near‐surface water content, which vary at scales of O(m), control the soil thermal regime more than an air temperature gradient corresponding to a 140 km north–south distance. High shrub productivity is simulated only in talik (perennially unfrozen) soils with high nitrogen availability. Through these effects on plant and permafrost dynamics, landscape heterogeneity impacts ecosystem productivity. Simulations with near‐surface taliks have higher microbial respiration (by 78.0 gC m −2 yr −1 ) and higher net primary productivity (by 104.9 gC m −2 yr −1 ) compared to runs with near‐surface permafrost, and simulations with high shrub productivity have outlying values of net carbon uptake. We explored the prediction uncertainty associated with ignoring observed landscape heterogeneity, and found that watershed net carbon uptake is 60% larger when heterogeneity is accounted for. Our results highlight the complexity inherent in discontinuous permafrost environments and demonstrate that missing representation of subgrid heterogeneity in TEMs could bias predictions of high‐latitude carbon budget.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Spatial correlation of elastic heterogeneity tunes the deformation behavior of metallic glasses

Metallic glasses (MGs) possess remarkably high strength but often display only minimal tensile ductility due to the formation of catastrophic shear bands. Purposely enhancing the inherent heterogeneity to promote distributed flow offers new possibilities in improving the ductility of monolithic MGs. Here, we report the effect of the spatial heterogeneity of elasticity, resulting from the inherently inhomogeneous amorphous structures, on the deformation behavior of MGs, specifically focusing on the ductility using multiscale modeling methods. A highly heterogeneous, Gaussian-type shear modulus distribution at the nanoscale is revealed by atomistic simulations in Cu 64 Zr 36 MGs, in which the soft population of the distribution exhibits a marked propensity to undergo the inelastic shear transformation. By employing a mesoscale shear transformation zone dynamics model, we find that the organization of such nanometer-scale shear transformation events into shear-band patterns is dependent on the spatial heterogeneity of the local shear moduli. A critical spatial correlation length of elastic heterogeneity is identified for the simulated MGs to achieve the best tensile ductility, which is associated with a transition of shear-band formation mechanisms, from stress-dictated nucleation and growth to structure-dictated strain percolation, as well as a saturation of elastically soft sites participating in the plastic flow. This discovery is important for the fundamental understanding of the role of spatial heterogeneity in influencing the deformation behavior of MGs. We believe that this can facilitate the design and development of new ductile monolithic MGs by a process of tuning the inherent heterogeneity to achieve enhanced ductility in these high-strength metallic alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2025

IRIS-MEMFLOW: Data Flow-Enabled Portable Memory Orchestration in IRIS Runtime for Diverse Heterogeneity

Task-based programming models and execution paradigms provide a means to decompose a computation by expressing it as a graph in which each node represents a specific computation operating on memory objects and the edges define the dependencies in the execution flow. In this execution model, independent nodes in the graph can be executed concurrently in different computing devices, making it suitable for heterogeneous systems in which computing devices with different architectures coexist. However, careful memory orchestration across heterogeneous devices is needed because copies of the same memory object may reside in multiple devices during execution. Manually ensuring such an orchestration is quite challenging. Not only must an application developer guard against race conditions, but they must also optimize data movement between the host and devices because unnecessary data movement significantly impacts performance. To mitigate these challenges, we enhance the IRIS heterogeneous runtime and introduce IRIS-MEMFLOW–a data flow–enabled portable memory abstraction for seamlessly orchestrating memory in diverse heterogeneous computing environments. By using data-flow analysis, IRIS-MEMFLOW guards against race conditions while multiple heterogeneous devices access memory objects. IRIS-MEMFLOW also optimizes data movement between the host and devices without manual intervention. As a result, IRIS provides improved programming productivity, performance, and portability for multidevice heterogeneous executions in high-performance computing and cloud systems that run diverse architectures from different vendors. The efficacy of IRIS-MEMFLOW is evaluated through experiments that show its capability in terms of programming productivity, multidevice heterogeneity, portability, and low overhead versus the state of the art.

Monil, M. A. H. [ORNL] (ORCID:0000000334194037)↗

DOE OSTI2013

Evaluation of material heterogeneity dosimetric effects using radiochromic film for COMS eye plaques loaded with {sup 125}I seeds (model I25.S16)

Purpose: (1) To measure absolute dose distributions in eye phantom for COMS eye plaques with {sup 125}I seeds (model I25.S16) using radiochromic EBT film dosimetry. (2) To determine the dose correction function for calculations involving the TG-43 formalism to account for the presence of the COMS eye plaque using Monte Carlo (MC) method specific to this seed model. (3) To test the heterogeneous dose calculation accuracy of the new version of Plaque Simulator (v5.3.9) against the EBT film data for this seed model. Methods: Using EBT film, absolute doses were measured for {sup 125}I seeds (model I25.S16) in COMS eye plaques (1) along the plaque's central axis for (a) uniformly loaded plaques (14-20 mm in diameter) and (b) a 20 mm plaque with single seed, and (2) in off-axis direction at depths of 5 and 12 mm for all four plaque sizes. The EBT film calibration was performed at {sup 125}I photon energy. MC calculations using MCNP5 code for a single seed at the center of a 20 mm plaque in homogeneous water and polystyrene medium were performed. The heterogeneity dose correction function was determined from the MC calculations. These function values at various depths were entered into PS software (v5.3.9) to calculate the heterogeneous dose distributions for the uniformly loaded plaques (of all four sizes). The dose distributions with homogeneous water assumptions were also calculated using PS for comparison. The EBT film measured absolute dose rate values (film) were compared with those calculated using PS with homogeneous assumption (PS Homo) and heterogeneity correction (PS Hetero). The values of dose ratio (film/PS Homo) and (film/PS Hetero) were obtained. Results: The central axis depth dose rate values for a single seed in 20 mm plaque measured using EBT film and calculated with MCNP5 code (both in ploystyrene phantom) were compared, and agreement within 9% was found. The dose ratio (film/PS Homo) values were substantially lower than unity (mostly between 0.8 and 0.9) for all four plaque sizes, indicating dose reduction by COMS plaque compared with homogeneous assumption. The dose ratio (film/PS Hetero) values were close to unity, indicating the PS Hetero calculations agree with those from the film study. Conclusions: Substantial heterogeneity effect on the {sup 125}I dose distributions in an eye phantom for COMS plaques was verified using radiochromic EBT film dosimetry. The calculated doses for uniformly loaded plaques using PS with heterogeneity correction option enabled were corroborated by the EBT film measurement data. Radiochromic EBT film dosimetry is feasible in measuring absolute dose distributions in eye phantom for COMS eye plaques loaded with single or multiple {sup 125}I seeds. Plaque Simulator is a viable tool for the calculation of dose distributions if one understands its limitations and uses the proper heterogeneity correction feature.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2013

A generalized 2D pencil beam scaling algorithm for proton dose calculation in heterogeneous slab geometries

Purpose: Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke ['Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media,' Phys. Med. Biol. 47, 3313-3330 (2002)] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth. Methods: Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Moliere scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam. Results: Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as much as 1.4 mm (21%) at the depth of the Bragg peak for a 220 MeV proton beam in homogeneous water. This translates into a 32% dose discrepancy for a 5 mm Gaussian proton beam. Similar trends were observed for calculations made in heterogeneous slab phantoms where it was also noted that errors tend to increase with greater beam penetration. The generalized 2D scaling model performs well in all situations, with a maximum dose error of 0.3% at the Bragg peak in a heterogeneous phantom containing 3 cm of hard bone. Conclusions: The authors have derived a generalized form of 2D pencil beam scaling which is independent of the proton scattering power model and robust to the functional form of the radial kernel width in water used for the calculations. Sample calculations made with this model show excellent agreement with expected values in both homogeneous water and heterogeneous phantoms.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2023

Tiling Framework for Heterogeneous Computing of Matrix based Tiled Algorithms

Tiling matrix operations can improve the load balancing and performance of applications on heterogeneous computing resources. Writing a tile-based algorithm for each operation with a traditional, hand-tuned tiling approach that uses for loops in C/C++ is cumbersome and error prone. Moreover, it must enable and support the heterogeneous memory management of data objects and also explore architecture-supported, native, tiled-data transfer APIs instead of copying the tiled data to continuous memory before the data transfer. The tiling framework provides a tiled data structure for heterogeneous memory mapping and parameterization to a heterogeneous task specification API. We have integrated our tiled framework into MatRIS (Math kernels library using IRIS). IRIS is a heterogeneous run-time framework with a heterogeneous programming model, memory model, and task execution model. Experiments reveal that the tiled framework for BLAS operations has improved the programmability of tiled BLAS and improved performance by ~20% when compared against the traditional method that copies the data to continuous memory locations for heterogeneous computing.

Miniskar, Narasinga Rao↗

DOE OSTI2025

IRIS-MASH: Efficient Multi-device Asynchronous Multi-Stream Heterogeneous Computing

In the rapidly evolving field of high-performance computing (HPC), effectively leveraging heterogeneous devices through asynchronous task programming is paramount. This paper presents a robust asynchronous task programming model tailored for a multi-device, multi-stream execution environment that incorporates a diverse array of heterogeneous computing units, including GPUs from various vendors and other accelerators. Current state-of-the-art task programming models provide methodologies to support asynchronous task executions, but they typically handle homogeneous devices using native programming languages, while support for heterogeneous devices is limited to frameworks like OpenCL. This gap presents significant challenges in abstracting heterogeneous devices to harness their true asynchronous capabilities effectively using their native programming languages. By implementing asynchronous task execution, our model significantly boosts the performance of tiled algorithm task graphs through overlapping data transfers with computation and enabling the simultaneous execution of multiple kernels. We integrate this approach into a heterogeneous Intelligent Runtime System (IRIS) and assess its performance using a suite of tiled algorithm benchmarks from the heterogeneous math kernels library (MatRIS) based on IRIS. Experimental results demonstrate a performance improvement ranging from 1.6 × to 2 × over IRIS without asynchronous support, and a notable 22% performance enhancement compared to established runtime systems such as StarPU and PaRSEC. This approach significantly improves computation efficiency of HPC workflows and provides a solid base for future exploration and development in the area of asynchronous task programming in heterogeneous systems.

Miniskar, Narasinga Rao [ORNL] (ORCID:000000018259↗

DOE OSTI2012

Long-term Differences in Tillage and Land Use Affect Intra-aggregate Pore Heterogeneity

Recent advances in computed tomography provide measurement tools to study internal structures of soil aggregates at micrometer resolutions and to improve our understanding of specific mechanisms of various soil processes. Fractal analysis is one of the data analysis tools that can be helpful in evaluating heterogeneity of the intra-aggregate internal structures. The goal of this study was to examine how long-term tillage and land use differences affect intra-aggregate pore heterogeneity. The specific objectives were: (i) to develop an approach to enhance utility of box-counting fractal dimension in characterizing intra-aggregate pore heterogeneity; (ii) to examine intra-aggregate pores in macro-aggregates (4-6 mm in size) using the computed tomography scanning and fractal analysis, and (iii) to compare heterogeneity of intra-aggregate pore space in aggregates from loamy Alfisol soil subjected to 20 yr of contrasting management practices, namely, conventional tillage (chisel plow) (CT), no-till (NT), and native succession vegetation (NS). Three-dimensional images of the intact aggregates were obtained with a resolution of 14.6 {micro}m at the Advanced Photon Source, Argonne National Laboratory, Argonne, IL. Proposed box-counting fractal dimension normalization was successfully implemented to estimate heterogeneity of pore voxel distributions without bias associated with different porosities in soil aggregates. The aggregates from all three studied treatments had higher porosity associated with large (>100 {micro}m) pores present in their centers than in their exteriors. Pores 15 to 60 {micro}m were equally abundant throughout entire aggregates but their distributions were more heterogeneous in aggregate interiors. The CT aggregates had greater numbers of pores 15 to 60 {micro}m than NT and NS. Distribution of pore voxels belonging to large pores was most heterogeneous in the aggregates from NS, followed by NT and by CT. This result was consistent with presence of very large pores associated with former root channels in NT and NS aggregates. Our findings indicate that mechanisms of macro-aggregate formation might differ in their importance in different land use and management practices.

43 PARTICLE ACCELERATORS↗

DOE OSTI2015

Scaling Effects of Cr(VI) Reduction Kinetics. The Role of Geochemical Heterogeneity

The natural subsurface is highly heterogeneous with minerals distributed in different spatial patterns. Fundamental understanding of how mineral spatial distribution patterns regulate sorption process is important for predicting the transport and fate of chemicals. Existing studies about the sorption was carried out in well-mixed batch reactors or uniformly packed columns, with few data available on the effects of spatial heterogeneities. As a result, there is a lack of data and understanding on how spatial heterogeneities control sorption processes. In this project, we aim to understand and develop modeling capabilities to predict the sorption of Cr(VI), an omnipresent contaminant in natural systems due to its natural occurrence and industrial utilization. We systematically examine the role of spatial patterns of illite, a common clay, in determining the extent of transport limitation and scaling effects associated with Cr(VI) sorption capacity and kinetics using column experiments and reactive transport modeling. Our results showed that the sorbed mass and rates can differ by an order of magnitude due to of the illite spatial heterogeneities and transport limitation. With constraints from data, we also developed the capabilities of modeling Cr(VI) in heterogeneous media. The developed model is then utilized to understand the general principles that govern the relationship between sorption and connectivity, a key measure of the spatial pattern characteristics. This correlation can be used to estimate Cr(VI) sorption characteristics in heterogeneous porous media. Insights gained here bridge gaps between laboratory and field application in hydrogeology and geochemical field, and advance predictive understanding of reactive transport processes in the natural heterogeneous subsurface. We believe that these findings will be of interest to a large number of environmental geochemists and engineers, hydrogeologists, and those interested in contaminant fate and transport, water quality and water composition, and natural attenuation processes in natural systems.

58 GEOSCIENCES↗

DOE OSTI2025

Shear-Wave Radiation Patterns from Explosive and Earthquake Sources in Scattering, Heterogeneous Media

Distinguishing whether a seismic event is an earthquake or an explosion is a core problem in explosion monitoring. For simplistic models, earthquakes produce a predictable S-wavefield based on their radiation pattern, while an explosion produces no S-wavefield. However, observations from nuclear tests show that explosions can produce significant S-wave energy on both horizontal components. We perform numerical experiments using SPECFEM to constrain when an S-wavefield generated from an explosion might differ from one produced by an earthquake. We generate the S-wavefield for our explosions by placing the source location within a small region consisting of large velocity heterogeneities. For the 2D cases investigated here, a crucial condition is that the size of the region of heterogeneities must be much smaller (approximately 1/12th) than the minimum wavelength of the wavefield for our simulation setups. We investigate both isotropic heterogeneities and anisotropic heterogeneities. Initial results demonstrate that the heterogeneous region lowers the P/S amplitude ratios of an explosion. The presence of strong anisotropic heterogeneities near the source can also produce an S-wavefield with similar amplitudes to the P-wavefield. Lastly, we show that S-wave polarization angles vary as a function of azimuth and distance for explosive sources in the presence of small-scale heterogeneities.

58 GEOSCIENCES↗

DOE OSTI2022

Representing surface heterogeneity in land–atmosphere coupling in E3SMv1 single-column model over ARM SGP during summertime

Abstract. The Earth's land surface features spatial and temporal heterogeneity over a wide range of scales below those resolved by current Earth system models (ESMs). State-of-the-art land and atmosphere models employ parameterizations to represent their subgrid heterogeneity, but the land–atmosphere coupling in ESMs typically operates on the grid scale. Communicating the information on the land surface heterogeneity with the overlying atmospheric boundary layer (ABL) remains a challenge in modeling land–atmosphere interactions. In order to account for the subgrid-scale heterogeneity in land–atmosphere coupling, we implement a new coupling scheme in the Energy Exascale Earth system model version 1 (E3SMv1) that uses adjusted surface variances and covariance of potential temperature and specific water content as the lower boundary condition for the atmosphere model. The new lower boundary condition accounts for both the variability of individual subgrid land surface patches and the inter-patch variability. The E3SMv1 single-column model (SCM) simulations over the Atmospheric Radiation Measurement (ARM) Southern Great Plain (SGP) site were performed to assess the impacts. We find that the new coupling parameterization increases the magnitude and diurnal cycle of the temperature variance and humidity variance in the lower ABL on non-precipitating days. The impacts are primarily attributed to subgrid inter-patch variability rather than the variability of individual patches. These effects extend vertically from the surface to several levels in the lower ABL on clear days. We also find that accounting for surface heterogeneity increases low cloud cover and liquid water path (LWP). These cloud changes are associated with the change in cloud regime indicated by the skewness of the probability density function (PDF) of the subgrid vertical velocity. In precipitating days, the inter-patch variability reduces significantly so that the impact of accounting for surface heterogeneity vanishes. These results highlight the importance of accounting for subgrid heterogeneity in land–atmosphere coupling in next-generation ESMs.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1998

Flammability of Heterogeneously Combusting Metals

Most engineering materials, including some metals, most notably aluminum, burn in homogeneous combustion. 'Homogeneous' refers to both the fuel and the oxidizer being in the same phase, which is usually gaseous. The fuel and oxidizer are well mixed in the combustion reaction zone, and heat is released according to some relation like q(sub c) = delta H(sub c)c[((rho/rho(sub 0))]exp a)(exp -E(sub c)/RT), Eq. (1) where the pressure exponent a is usually close to unity. As long as there is enough heat released, combustion is sustained. It is useful to conceive of a threshold pressure beyond which there is sufficient heat to keep the temperature high enough to sustain combustion, and beneath which the heat is so low that temperature drains away and the combustion is extinguished. Some materials burn in heterogeneous combustion, in which the fuel and oxidizer are in different phases. These include iron and nickel based alloys, which burn in the liquid phase with gaseous oxygen. Heterogeneous combustion takes place on the surface of the material (fuel). Products of combustion may appear as a solid slag (oxide) which progressively covers the fuel. Propagation of the combustion melts and exposes fresh fuel. Heterogeneous combustion heat release also follows the general form of Eq.(1), except that the pressure exponent a tends to be much less than 1. Therefore, the increase in heat release with increasing pressure is not as dramatic as it is in homogeneous combustion. Although the concept of a threshold pressure still holds in heterogeneous combustion, the threshold is more difficult to identify experimentally, and pressure itself becomes less important relative to the heat transfer paths extant in any specific application. However, the constants C, a, and E(sub c) may still be identified by suitable data reduction from heterogeneous combustion experiments, and may be applied in a heat transfer model to judge the flammability of a material in any particular actual-use situation. In order to support the above assertions, two investigations are undertaken: 1) PCT data are examined in detail to discover the pressure dependence of heterogeneous combustion experiment results; and 2) heterogeneous combustion in a PCT situation is described by a heat transfer model, which is solved first in simplified form for a simple actual-use situation, and then extended to apply to PCT data reduction (combustion constant identification).

Jones, Peter D.↗

DOE OSTI2012

Homogenization for Periodic Heterogeneous Materials with Arbitrary Position-Dependent Material Properties

We present a rigorous homogenization approach for efficient computation of a class of physical problems in a one-dimensional periodic heterogeneous material. This material is represented by a spatially periodic array of unit cells with a length of e. More specifically, the method is applied to the diffusion, heat conduction, and wave propagation problems. Heterogeneous materials can have arbitrary position-dependent continuous or discontinuous materials properties (for example heat conductivity) within the unit cell. The final effective model includes both effective properties at the leading order and high-order contributions due to the microscopic heterogeneity. A dimensionless heterogeneity parameter ß is defined to represent high-order contributions, shown to be in the range of [-1/12, 0], and has a universal expression for all three problems. Both effective properties and heterogeneity parameter ß are independent of e, the microscopic scale of heterogeneity. The homogenized solution describing macroscopic variations can be obtained from the effective model. Solution with sub-unit-cell accuracy can be constructed based on the homogenized solution and its spatial derivatives. The paper represents a general approach to obtain the effective model for arbitrary periodic heterogeneous materials with position-dependent properties.

conduction↗