Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Heterogeneity”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗
DOE OSTI2025

Experimental Investigation of Buoyant Flow in Realistic Bedforms With Heterogeneous Wettability

Submeter-scale geologic heterogeneity greatly affects CO 2 plume migration and retention. In this work, we present meter-scale laboratory experiments that can capture the impact of realistic submeter-scale geologic heterogeneity on multiphase flow and trapping. We produce realistic sedimentary formations consisting of ripple deposits with varying grain size contrast and wettability in a meter-scale slab chamber. Then, we conduct multiphase flow experiments with analog fluids through these structures and measure the saturation patterns, capillary heterogeneity trapping (CHT), and overall trapping performance. When we alter the ripple bedform architecture, variations in trapped saturation and CHT (10–20%) increment are exhibited. Similar growth in trapping performance is also observed when grain size contrast increases. Finally, wettability changes (water- to oil-wet) can increase nonwetting saturation and CHT up to 5% and 10–20%, respectively. These results emphasize the importance of correctly characterizing the impact of small-scale heterogeneities and wettability changes. We believe this is the first time that multiphase flow experiments were conducted in meter-scale domains with realistic ripple bedforms and heterogeneous wettability to investigate plume migration and trapping.

58 GEOSCIENCES↗
DOE OSTI2022

OpenMP Target Task: Tasking and Target Offloading on Heterogeneous Systems

This work evaluated the use of OpenMP tasking with target GPU offloading as a potential solution for programming productivity and performance on heterogeneous systems. Also, it is proposed a new OpenMP specification to make the implementation of heterogeneous codes simpler by using OpenMP target task, which integrates both OpenMP tasking and target GPU offloading in a single OpenMP pragma. As a test case, the authors used one of the most popular and widely used Basic Linear Algebra Subprogram Level-3 routines: triangular solver (TRSM). To benefit from the heterogeneity of the current high-performance computing systems, the authors propose a different parallelization of the algorithm by using a nonuniform decomposition of the problem. This work used target GPU offloading inside OpenMP tasks to address the heterogeneity found in the hardware. This new approach can outperform the state-of-the-art algorithms, which use a uniform decomposition of the data, on both the CPU-only and hybrid CPU-GPU systems, reaching speedups of up to one order of magnitude. The performance that this approach achieves is faster than the IBM ESSL math library on CPU and competitive relative to a highly optimized heterogeneous CUDA version. One node of Oak Ridge National Laboratory’s supercomputer, Summit, was used for performance analysis.

Valero Lara, Pedro↗
DOE OSTI2024

MatRIS: Addressing the Challenges for Portability and Heterogeneity Using Tasking for Matrix Decomposition (Cholesky)

The ubiquitous in-node heterogeneity of HPC and cloud computing platforms makes software portability and performance optimization extremely challenging. Described here, the MatRIS multilevel math library abstraction framework employs tasking to alleviate these difficulties. MatRIS includes the IRIS task-based runtime on the bottom level and exposes different layers of abstraction to render algorithms architecturally agnostic. MatRIS ensures the decomposition and creation of tasks that represent the necessary encapsulation of the optimized kernels from both vendor and open-source math libraries. Once built, MatRIS can select different combinations of accelerators at runtime, making it portable even on diverse heterogeneous architectures. By leveraging the IRIS runtime’s features for managing heterogeneity, MatRIS deploys algorithms that remove the need to specify orchestration and data transfer. This study describes how the serial task abstraction of a tiled Cholesky factorization is made portable and scalable in the case of multi-device and multi-vendor heterogeneity on a node with NVIDIA and AMD GPUs by using MatRIS. First, we demonstrate that Cholesky in MatRIS provides multi-GPU scalability that offers competitive performance versus cuSolverMG. Then, we present the challenges and opportunities for heterogeneous execution.

Monil, M. A. H.↗
DOE OSTI2025

Microstructural heterogeneities in additively manufactured refractory alloy C103 and their implications for room and elevated temperature mechanical behavior

Considering the vast component design space enabled by fusion-based additive manufacturing (F-BAM) processes, e.g., directed energy deposition (DED), the scale-up manufacturing of Nb-alloys with F-BAM is advantageous for structural applications. However, varying thermokinetic parameters-induced microstructural heterogeneities are prevalent within the F-BAM processed alloys. Such microstructural heterogeneities can have significant implications for the room and elevated temperature mechanical behavior. While a few studies investigating F-BAM processed alloy C103 are available, none of these studies investigate the microstructural heterogeneities – including those associated with solidification growth modes and second phase particles – and the effect thereof on the mechanical behavior. To this end, we investigate the microstructurally heterogeneous regions with varying solidification growth morphologies, segregation behavior, and second phase particle attributes within the laser-DED processed alloy C103. The implications of such heterogeneous regions for room- and elevated-temperature tensile behavior and damage mechanisms are revealed. Particularly, the interface between the cellular and planar region is identified as susceptible to deformation localization. The implications of hot isostatic pressing (HIP) for the consolidation behavior, microstructural evolution, and resulting mechanical behavior are also discussed. Although the recrystallization and grain growth led to a reduced yield strength in the HIPed condition, the homogenization of microstructure alleviated the deformation localization sites, such as the planar/cellular interface within the melt pool. The homogenized microstructure alongside the enhanced consolidation upon HIP led to an enhanced elongation to failure. Findings establish microstructural design considerations in F-BAM processed Nb alloys and also facilitate design of post-processing heat treatments for achieving improved mechanical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Assessing the Atmospheric Response to Subgrid Surface Heterogeneity in the Single-Column Community Earth System Model, Version 2 (CESM2)

Land-atmosphere interactions are central to the evolution of the atmospheric boundary layer and the subsequent formation of clouds and precipitation. Existing global climate models represent these connections with bulk approximations on coarse spatial scales, but observations suggest that small-scale variations in surface characteristics and co-located turbulent and momentum fluxes can significantly impact the atmosphere. Recent model development efforts have attempted to capture this phenomenon by coupling existing representations of subgrid-scale (SGS) heterogeneity between land and atmosphere models. Such approaches are in their infancy and it is not yet clear if they can produce a realistic atmospheric response to surface heterogeneity. Here, we implement a parameterization to capture the effects of SGS heterogeneity in the Community Earth System Model (CESM2), and compare single-column simulations against high-resolution Weather Research and Forecasting (WRF) large-eddy simulations (LESs), which we use as a proxy for observations. The CESM2 experiments increase the temperature and humidity variances in the lowest atmospheric levels, but the response is weaker than in WRF-LES. In part, this is attributed to an underestimate of surface heterogeneity in the land model due to a lack of SGS meteorology, a separation between deep and shallow convection schemes in the atmosphere, and a lack of explicitly represented mesoscale secondary circulations. These results highlight the complex processes involved in capturing the effects of SGS heterogeneity and suggest the need for parameterizations that communicate their influence not only at the surface but also vertically.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Heterogeneity in Permeability and Particulate Organic Carbon Content Controls the Redox Condition of Riverbed Sediments at Different Timescales

Abstract The hydrological and biogeochemical properties of the hyporheic zone in stream and riverine ecosystems have been extensively studied over the past two decades. Although it is widely acknowledged that sediment heterogeneity can influence biogeochemical reactions, little effort has been made to understand the role of heterogeneity on the spatiotemporal variability of riverbed redox conditions under changing flow dynamics at different timescales. Here we integrate a mechanistic model and field data to demonstrate that heterogeneity in permeability plays a vital role in modulating sediment redox conditions at both seasonal (annual) and event (daily‐to‐weekly) timescales, whereas heterogeneity in particulate organic carbon (POC) content only has a comparable influence on redox conditions at the seasonal timescale. These findings underscore the importance of accurately characterizing sediment heterogeneity, in terms of permeability and POC content, in quantifying biogeochemical dynamics in the riverbed and hyporheic zones of riverine ecosystems.

Geology↗
DOE OSTI2024

Deconvolution of dynamic heterogeneity in protein structure

Heterogeneity is intrinsic to the dynamic process of a chemical reaction. As reactants are converted to products via intermediates, the nature and extent of heterogeneity vary temporally throughout the duration of the reaction and spatially across the molecular ensemble. The goal of many biophysical techniques, including crystallography and spectroscopy, is to establish a reaction trajectory that follows an experimentally provoked dynamic process. It is essential to properly analyze and resolve heterogeneity inevitably embedded in experimental datasets. We have developed a deconvolution technique based on singular value decomposition (SVD), which we have rigorously practiced in diverse research projects. In this review, we recapitulate the motivation and challenges in addressing the heterogeneity problem and lay out the mathematical foundation of our methodology that enables isolation of chemically sensible structural signals. We also present a few case studies to demonstrate the concept and outcome of the SVD-based deconvolution. Finally, we highlight a few recent studies with mechanistic insights made possible by heterogeneity deconvolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The role of pre-existing heterogeneities in materials under shock and spall

There has been a challenge for many decades to understand how heterogeneities influence the behavior of materials under shock loading, eventually leading to spall formation and failure. Experimental, analytical, and computational techniques have matured to the point where systematic studies of materials with complex microstructures under shock loading and the associated failure mechanisms are feasible. This is enabled by more accurate diagnostics as well as characterization methods. As interest in complex materials grows, understanding and predicting the role of heterogeneities in determining the dynamic behavior becomes crucial. Early computational studies, hydrocodes, in particular, historically preclude any irregularities in the form of defects and impurities in the material microstructure for the sake of simplification and to retain the hydrodynamic conservation equations. Contemporary computational methods, notably molecular dynamics simulations, can overcome this limitation by incorporating inhomogeneities albeit at a much lower length and time scale. This review discusses literature that has focused on investigating the role of various imperfections in the shock and spall behavior, emphasizing mainly heterogeneities such as second-phase particles, inclusions, and voids under both shock compression and release. Pre-existing defects are found in most engineering materials, ranging from thermodynamically necessary vacancies, to interstitial and dislocation, to microstructural features such as inclusions, second phase particles, voids, grain boundaries, and triple junctions. This literature review explores the interaction of these heterogeneities under shock loading during compression and release. Systematic characterization of material heterogeneities before and after shock loading, along with direct measurements of Hugoniot elastic limit and spall strength, allows for more generalized theories to be formulated. Further, continuous improvement toward time-resolved, in situ experimental data strengthens the ability to elucidate upon results gathered from simulations and analytical models, thus improving the overall ability to understand and predict how materials behave under dynamic loading.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Diffusion Synthetic Acceleration for Heterogeneous Domains, Compatible with Voids

A standard approach to solving the S N transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using O(1) AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Vegetation heterogeneity reflects soil thermal state and surface soil displacement in a thawing permafrost landscape

Thawing permafrost has the potential to dramatically alter the physical and ecological structure of northern landscapes. Warming of the Arctic and subsequent degradation of permafrost have created a need to assess the stability and movement of soils on hillslopes and the potential impacts on ecosystem structure. In this work, we explore the relationships among vegetation heterogeneity, soil temperature, and soil surface displacements observed from 2019 to 2022 in a watershed in the discontinuous permafrost region on the Seward Peninsula of Alaska. Vegetation heterogeneity was measured as the standard deviation (SD) of the normalized difference vegetation index (NDVI) from 3 m PlanetScope satellite imagery around each soil temperature and active layer thickness observation. Locations of observations were clustered into three soil thermal groups, warm, intermediate, and cold, based on soil temperature and active layer thickness. Average annual horizontal surface displacements were significantly lower for soils within the warm thermal group (median = 0.033 m yr −1 ) compared to soils within the cold thermal group (median = 0.090 m yr −1 ; p < 0.001). Conversely, vegetation heterogeneity was significantly higher in the warm (median = 0.014 SD NDVI; p = 0.002) and intermediate (median = 0.015 SD NDVI; p = 0.002) groups compared with the cold thermal group (median = 0.012 SD NDVI), suggesting a warming-induced shift in vegetation community complexity. Because of the observed associations of ground surface displacement rates and vegetation heterogeneity with soil thermal state, we hypothesize that warming soil conditions induce changes in the rates and patterns of hillslope erosion due to an increase in surface movement as near-surface permafrost thaws, followed by a decrease as the permafrost table deepens and excess ice content diminishes. The transition to warm soils promotes surface ecosystem transformation, shifting the dominant vegetation at the site, given the warming climatic conditions of the region. We integrated our observations of soil temperature, vegetation heterogeneity, and soil surface displacements into a conceptual model that describes the co-evolution of hillslopes and vegetation in warming permafrost environments, which is currently unrepresented in earth system models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Chemical Heterogeneity in PAN/LLZTO Composite Electrolytes by Synchrotron Imaging

Solid polymer/ceramic composite electrolytes are promising for batteries due to their attractive thermal stability and mechanical properties. Chemical heterogeneity in solid composite electrolytes, such as the inhomogeneity in the ceramic phase and salt distribution at the polymer/ceramic interface, is critical to the performance of solid composite electrolytes. However, such heterogeneity has not been well understood yet. In this work, we use Synchrotron-based X-ray fluorescence imaging (XRF) and Transmission X-ray Microscope (TXM) to image nanoscale chemical heterogeneity in polyacrylamide/Li 7+x La 3 Zr 2–x Ta x O 12 (LLZTO) composite electrolytes and investigate the effects of lithium salt, salt concentration, and plasticizer. We find that LLZTO particles show strong inter- and intra-particles chemical heterogeneities, and the off-stoichiometry of Zr in an LLZTO particle is unlikely to be only balanced by Ta substitution. Moreover, statistical analysis suggests that LiI tends to accumulate at the ceramic/polymer interface at a low concentration of 5 wt%, but no such tendency was observed in samples with 10 wt% LiI. However, composite electrolytes with LiTFSI show interfacial accumulation at both 5 wt% and 10 wt%. Furthermore, this report provides insight into element distributions in solid composite electrolytes, and we hope further researches can shed light on the connections between chemical heterogeneity and ionic transport pathway inside.

36 MATERIALS SCIENCE↗
NASA NTRS1988

Heterogeneous physicochemistry of the winter polar stratosphere

Present chemical theories of the Antarctic ozone hole assume that heterogeneous reactions involving polar stratospheric clouds (PSCs) are the precursor of springtime ozone depletions. However, none of the theories quantify the rates of proposed heterogeneous processed, and none utilize the extensive data base on PSC's. Thus, all of the theories must be considered incomplete until the heterogeneous mechanisms are properly defined. A unified treatment developed of the cloud related processes, both physical and chemical, and the importance of these processes using observation data is calibrated. The rates are compared competitive heterogeneous processes to place reasonable limits on critical mechanisms such as the denitrification and dechlorination of the polar winter stratosphere. Among the subjects addressed here are the physical/chemical properties of PSC's including their relevant microphysical, optical and compositional characteristics, mass transfer rates of gaseous constituents to cloud particles, adsorption, accommodation and sticking coefficients on cloud particles, time constants for condensation, absorption and other microphysical processes, effects of solubility and vapor pressure on cloud composition, the statistics of cloud processing of chemically active condensible species, rate limiting steps in heterogeneous chemical reactions, and the nonlinear dependence of ozone loss on physical and chemical parameters.

Turco, R. P.↗
NASA NTRS1992

The effect of material heterogeneity in curved composite beams for use in aircraft structures

A design tool is presented for predicting the effect of material heterogeneity on the performance of curved composite beams for use in aircraft fuselage structures. Material heterogeneity can be induced during processes such as sheet forming and stretch forming of thermoplastic composites. This heterogeneity can be introduced in the form of fiber realignment and spreading during the manufacturing process causing a gradient in material properties in both the radial and tangential directions. The analysis procedure uses a separate two-dimensional elasticity solution for the stresses in the flanges and web sections of the beam. The separate solutions are coupled by requiring the forces and displacements match at the section boundaries. Analysis is performed for curved beams loaded in pure bending and uniform pressure. The beams can be of any general cross-section such as a hat, T-, I-, or J-beam. Preliminary results show that geometry of the beam dictates the effect of heterogeneity on performance. Heterogeneity plays a much larger role in beams with a small average radius to depth ratio, R/t, where R is the average radius of the beam and t is the difference between the inside and outside radius. Results of the analysis are in the form of stresses and displacements, and they are compared to both mechanics of materials and numerical solutions obtained using finite element analysis.

Otoole, Brendan J.↗
NASA NTRS2002

Graph Partitioning for Parallel Applications in Heterogeneous Grid Environments

The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.

Bisws, Rupak↗
NASA NTRS2003

Mesoscale Computational Investigation of Shocked Heterogeneous Materials with Application to Large Impact Craters

The propagation of shock waves through target materials is strongly influenced by the presence of small-scale structure, fractures, physical and chemical heterogeneities. Pre-existing fractures often create craters that appear square in outline (e.g. Meteor Crater). Reverberations behind the shock from the presence of physical heterogeneity have been proposed as a mechanism for transient weakening of target materials. Pre-existing fractures can also affect melt generation. In this study, we are attempting to bridge the gap in numerical modeling between the micro-scale and the continuum, the so-called meso-scale. To accomplish this, we are developing a methodology to be used in the shock physics hydrocode (CTH) using Monte-Carlo-type methods to investigate the shock properties of heterogeneous materials. By comparing the results of numerical experiments at the micro-scale with experimental results and by using statistical techniques to evaluate the performance of simple constitutive models, we hope to embed the effect of physical heterogeneity into the field variables (pressure, stress, density, velocity) allowing us to directly imprint the effects of micro-scale heterogeneity at the continuum level without incurring high computational cost.

Crawford, D. A.↗
NASA NTRS2017

Assessment of the Impact of Spatial Heterogeneity on Microwave Satellite Soil Moisture Periodic Error

An accurate temporal and spatial characterization of errors is required for the efficient processing, evaluation, and assimilation of remotely-sensed surface soil moisture retrievals. However, empirical evidence exists that passive microwave soil moisture retrievals are prone to periodic artifacts which may complicate their application in data assimilation systems (which commonly treat observational errors as being temporally white). In this paper, the link between such temporally-periodic errors and spatial land surface heterogeneity is examined. Both the synthetic experiment and site-specified cases reveal that, when combined with strong spatial heterogeneity, temporal periodicity in satellite sampling patterns (associated with exact repeat intervals of the polar-orbiting satellites) can lead to spurious high frequency spectral peaks in soil moisture retrievals. In addition, the global distribution of the most prominent and consistent 8-day spectral peak in the Advanced Microwave Scanning Radiometer - Earth Observing System soil moisture retrievals is revealed via a peak detection method. Three spatial heterogeneity indicators - based on microwave brightness temperature, land cover types, and long-term averaged vegetation index - are proposed to characterize the degree to which the variability of land surface is capable of inducing periodic error into satellite-based soil moisture retrievals. Regions demonstrating 8-day periodic errors are generally consistent with those exhibiting relatively higher heterogeneity indicators. This implies a causal relationship between spatial land surface heterogeneity and temporal periodic error in remotely-sensed surface soil moisture retrievals.

Fangni Lei↗
DOE OSTI2023

Assessing pore network heterogeneity across multiple scales to inform CO2 injection models

Geologic heterogeneity is a key feature that must be considered when translations of scaled data are performed. This paper presents the assessment of geologic heterogeneity using a multiscale workflow that includes image analysis-based methods coupled with well log analysis to provide data in which fractals and machine learning methods estimate the carbon dioxide (CO 2 ) storage resource potential of a reservoir. The heterogeneity of rock properties of the complex Bell Creek reservoir in Montana, USA, was explored at the pore scale (~nm to mm), core scale (~mm to m), and well scale (~cm to m). The data used in this study included advanced image analysis of micro-CT (computed tomography) images (pore scale), thin sections (pore scale), plugs and core images (core scale) and well logs (well scale). The micro-CT images were segmented using a U-net segmentation approach into objects of pores and grains. Further, the segmented images were reconstructed into subvolumes of different sizes. Physical properties (porosity and permeability) and fractal dimensions were calculated for the various subvolumes, and Lorenz coefficient (Lc) values, a single parameter to describe the degree of heterogeneity within a pay zone section, were calculated from thin-section images and well logs. Porosity and fractal dimension values were used to estimate the 188-µm threshold of representative elementary volume (REV) in this study. Both the Lc and fractal dimension values were found to be negatively correlated. When these two parameters are combined, it is possible to discern differences in the complex porous networks of the samples analyzed in this study.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗