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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Large-scale white noise and cosmology

The generation of white noise on large scales is a generic property of the dynamics of physical systems described by local nonlinear partial differential equations. Nonlinearities prevent the small-scale dynamics from being erased by smoothing. Unresolved small-scale dynamics act as an uncorrelated (white or Poissonian) noise (seemingly stochastic but actually deterministic) contribution to large-scale dynamics. This white noise exists even when the dynamics is very nearly linear. In cases where the power spectrum is sub-Poissonian on large scales, this noise will dominate on the largest scale power no matter the amplitude of the inhomogeneities. Such is the case in the standard model of cosmology, where the primordial density power spectrum is expected to have an almost Harrison-Zel’dovich, P [ k ] ∼ k , spectrum on a much broader range of scales than can be observed. Even though linear gravitational evolution dominates nonlinear corrections by a factor of ∼ 10 5 , the nonobservation of white noise on the Hubble scale precludes the extrapolation of this power law below the comoving 1 pc scale. More generally, observation or nonobservation of large-scale white noise provides a powerful probe of the Universe on very small scales in the early Universe. Gravitational radiation, phase transitions, vorticity, and running of the spectral index are all phenomena that can be probed with large-scale white noise. Large-scale white noise is a nonoptional feature of all cosmological models but one which has not heretofore been appreciated.

Barenboim, Gabriela [Valencia U., IFIC; Valencia U↗
DOE OSTI2017

Quantifying drivers of wild pig movement across multiple spatial and temporal scales

The movement behavior of an animal is determined by extrinsic and intrinsic factors that operate at multiple spatio-temporal scales, yet much of our knowledge of animal movement comes from studies that examine only one or two scales concurrently. Understanding the drivers of animal movement across multiple scales is crucial for understanding the fundamentals of movement ecology, predicting changes in distribution, describing disease dynamics, and identifying efficient methods of wildlife conservation and management. We obtained over 400,000 GPS locations of wild pigs from 13 different studies spanning six states in southern U.S.A., and quantified movement rates and home range size within a single analytical framework. We used a generalized additive mixed model framework to quantify the effects of five broad predictor categories on movement: individual-level attributes, geographic factors, landscape attributes, meteorological conditions, and temporal variables. We examined effects of predictors across three temporal scales: daily, monthly, and using all data during the study period. We considered both local environmental factors such as daily weather data and distance to various resources on the landscape, as well as factors acting at a broader spatial scale such as ecoregion and season. We found meteorological variables (temperature and pressure), landscape features (distance to water sources), a broad-scale geographic factor (ecoregion), and individual-level characteristics (sex-age class), drove wild pig movement across all scales, but both the magnitude and shape of covariate relationships to movement differed across temporal scales. The analytical framework we present can be used to assess movement patterns arising from multiple data sources for a range of species while accounting for spatio-temporal correlations. Our analyses show the magnitude by which reaction norms can change based on the temporal scale of response data, illustrating the importance of appropriately defining temporal scales of both the movement response and covariates depending on the intended implications of research (e.g., predicting effects of movement due to climate change versus planning local-scale management). We argue that consideration of multiple spatial scales within the same framework (rather than comparing across separate studies post-hoc) gives a more accurate quantification of cross-scale spatial effects by appropriately accounting for error correlation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Montana Community-Scale Solar Strategy Project (Final Technical Report)

Grid-tied solar photovoltaic (PV) development began gradually in Montana, initially taking root in the early 2000s, largely in the form of small residential systems, rarely larger than two kilowatts. Utility support for solar technology through public benefit funding triggered the installation of the state’s first solar PV installations on community-owned facilities including schools, libraries, fire stations and local government buildings in the mid-2000s. By 2016, solar PV installations totaled approximately 28 megawatts of installed capacity, generating less than 0.05% of electricity sold in Montana. Montana’s solar fleet in 2016 included 17 megawatts of utility-scale solar farms, and three shared solar projects developed by rural electric cooperatives that ranged from 25 to 50 kilowatts in size. However, with only 3,000 households utilizing solar PV, either through an on-site installation or participation in a shared solar project, the potential benefits and reach of solar technology was limited. The Montana Solar Community Project (MSCP) was developed by the Montana Energy Office (MEO) at the Department of Environmental Quality in order to implement a “community-scale” solar energy strategy for the state that would cost-effectively expand Montanans’ access to solar PV. This project defines three types of community-scale solar projects: shared solar, community-sited solar, and group purchasing programs. The MSCP project conducted research and stakeholder engagement that helped to inform and develop model community-scale initiatives and an overarching community-scale solar strategy for Montana. Specifically, the project included a solar market assessment, stakeholder meetings across Montana, development of a menu of community-scale solar options, a study of solar potential on schools, community solar market research, and community-scale project implementation support. MSCP activities were successful in implementing solar projects and supporting solar development in communities across Montana. Project activities realized 280 kW of newly installed solar from two solarize programs, a shared solar array at a rural electric cooperative, and a solar array atop a Bozeman high school. The community-scale project implementation support and Solar on Schools components of the project resulted directly in the analysis and design of nearly 2 MW of distributed solar systems across the state. The Solar on Schools analysis alone produced solar designs for 25 schools, representing 920.8 kW of solar potential. Many of the deliverables from this project provide guidance on future development of community-scale solar in Montana, and resulted in a number of important conclusions about community-scale solar in Montana. There is strong interest in community-scale solar in Montana, as noted during stakeholder meetings, in response to solar market research surveys, and as seen by applications for implementation support grants provided by MEO. Project activities also suggest that Montanans demonstrated a desire and need for more information about solar energy technology, solar financing options, and the state’s policy and regulatory framework. Additionally, the project found that schools will be key partners for future community-scale solar programs. In addition to being excellent hosts for solar arrays, schools have the opportunity to use the installation of a solar array to develop educational materials and curricula to educate Montana’s future leaders about these technologies, which can be shared and replicated across the state. Project activities laid a clear path forward for solar energy in Montana. Certain activities have concrete next steps. For example, numerous solar arrays were designed for schools and other public buildings around the state. Many of those designs will be used as soon as funding becomes available. Other activities have less developed next steps, though lay the foundation for future work. The solar market assessment, solar market research, and community stakeholder meetings are good examples. These documents can be used as stepping stones to increase renewable energy education, increase stakeholder outreach, and support communities as they seek to develop community-scale solar projects.

14 SOLAR ENERGY↗
NASA NTRS1996

Further evaluation of traditional icing scaling methods

This report provides additional evaluations of two methods to scale icing test conditions; it also describes a hybrid technique for use when scaled conditions are outside the operating envelope of the test facility. The first evaluation is of the Olsen method which can be used to scale the liquid-water content in icing tests, and the second is the AEDC (Ruff) method which is used when the test model is less than full size. Equations for both scaling methods are presented in the paper, and the methods were evaluated by performing icing tests in the NASA Lewis Icing Research Tunnel (IRT). The Olsen method was tested using 53 cm diameter NACA 0012 airfoils. Tests covered liquid-water-contents which varied by as much as a factor of 1.8. The Olsen method was generally effective in giving scale ice shapes which matched the reference shapes for these tests. The AEDC method was tested with NACA 0012 airfoils with chords from 18 cm to 53 cm. The 53 cm chord airfoils were used in reference tests, and 1/2 and 1/3 scale tests were made at conditions determined by applying the AEDC scaling method. The scale and reference airspeeds were matched in these tests. The AEDC method was found to provide fairly effective scaling for 1/2 size tests, but for 1/3 size models, scaling was generally less effective. In addition to these two scaling methods, a hybrid approach was also tested in which the Olsen method was used to adjust the LWC after size was scaled using the constant Weber number method. This approach was found to be an effective way to test when scaled conditions would otherwise be outside the capability of the test facility.

Anderson, David N.↗
NASA NTRS1997

Theories of Simplification and Scaling of Spatially Distributed Processes

The problem of scaling is at the heart of ecological theory, the essence of understanding and of the development of a predictive capability. The description of any system depends on the spatial, temporal, and organizational perspective chosen; hence it is essential to understand not only how patterns and dynamics vary with scale, but also how patterns at one scale are manifestations of processes operating at other scales. Evolution has shaped the characteristics of species in ways that result in scale displacement: Each species experiences the environment at its own unique set of spatial and temporal scales and interfaces the biota through unique assemblages of phenotypes. In this way, coexistence becomes possible, and biodiversity is enhanced. By averaging over space, time, and biological interactions, a genotype filters variation at fine scales and selects the arena in which it will face the vicissitudes of nature. Variation at finer scales is then noise, of minor importance to the survival and dynamics of the species, and consequently of minor importance in any attempt at description. In attempting to model ecological interactions in space, contributors throughout this book have struggled with a trade-off between simplification and "realistic" complexity and detail. Although the challenge of simplification is widely recognized in ecology, less appreciated is the intertwining of scaling questions and scaling laws with the process of simplification. In the context of this chapter simplification will in general mean the use of spatial or ensemble means and low-order moments to capture more detailed interactions by integrating over given areas. In this way, one can derive descriptions of the system at different spatial scales, which provides the essentials for the extraction of scaling laws by examination of how system properties vary with scale.

Levin, Simon A.↗
NASA NTRS2021

Comparing Theoretically Scaled Biomechanical Models

BACKGROUND An investigation into incorporating space suit aspects required a 50th-percentile male model which was not part of the existing dataset of models. Previously, theoretical models for 5th-percentile female and 95th-percentile male were created utilizing a scaled test subject as close as possible to the target height and weight. Scaling factors were created by taking the height ratio and applying it uniformly to the model body segments, then fine tuning to ensure the theoretical model’s height is as expected. This study was initiated to examine the existing method of isometrically scaling in OpenSim [1,2] and to create alternative methods which do not rely on an existing subject being close in height and weight to the theoretical model of interest. Generating a theoretical biomechanical model provides additional abilities without the reliance on available OpenSim models or real subjects. Gained abilities include creating different percentile models and attaining representative anthropometry for any target height/weight, such as targeting specific crew populations or gaps within the current dataset. METHODS AND RESULTS This study includes 3 methods for generating the theoretical model; utilizing the modified unscaled OpenSim Full Body Rajagopal Model (FBRM) [3,4], a dataset of scaled OpenSim models, and existing scaling factors from Dumas et al. [5]. All methods use the Anthropometric Survey of US Army Personnel (ANSUR II) [6] as an input of necessary anthropometric measurements. The following measurements are retrieved from the ANSUR II collection: mass, stature, cervicale height, acromial height, axilla height, waist height, trochanterion height, lateral femoral epicondyle height, lateral malleolus height, acromion-radiale length, radiale-stylion length, palm length, ball of foot length, bicristal breadth, bimalleolar breadth. Some of the measurements are direct segment lengths and others are utilized to derive segment lengths. Height, weight, and age ranges are the required inputs to parse the collection for a mean value of the measurements. A simple iterative process may be necessary for the output of mean mass and stature consistent with the theoretical model of interest. In some cases, one may specify exact values instead of a range but that is dependent upon whether those exact values pertain to a single subject from the ANSUR II collection. Equations from Dumas et al. were used to calculate scaling factors for the two methods that utilize OpenSim scaled and unscaled models. In the third method, Dumas’ scaling factors were used directly instead of generating our own. After scaling factors are achieved, they are applied along with the mass and segment lengths retrieved from ANSUR II in order to calculate the segment mass, Center of Mass (CoM), mass Moment of Inertia (MoI), and the joint location in the parent frame. The theoretical models from the different methods were compared to the previous existing method of isometrically scaling in OpenSim, as well as the standards found in NASA STD-3000 [7] and the NASA Human Integration Design Handbook [8]. The whole-body center of mass is the main comparison performed between the models and the standards. The body segment mass properties were also compared when possible. In some cases, the standards do not provide complete data, or the center of mass location is not provided with respect to the appropriate joint coordinate system. For a 50th-percentile male subject, results from isometric scaling in OpenSim and the method utilizing the unscaled FBRM were compared to the standards in NASA STD-3000. According to the standard, the whole-body vertical CoM location was taken from the head vertex to the CoM. The standards provide 80.2 cm for the CoM vertical component whereas isometric scaling in OpenSim and utilizing the unscaled FBRM provide 82.2 and 82.3 cm, respectively. Through definition, the whole-body CoM in the medial/lateral direction agreed across the models. Investigation is on-going to clearly identify the reference point pertaining to dorsal/ventral whole-body CoM position in standards and relate that to the theoretical models. REFERENCES [1] Delp, S.L., et al., “OpenSim: Open-source Software to Create and Analyze Dynamic Simulations of Movement”, IEEE Transactions on Biomedical Engineering, (2007). [2] Seth, A., Hicks J.L., Uchida, T.K., Habib, A., Dembia, C.L., Dunne, J.J., Ong, C.F., DeMers, M.S., Rajagopal, A., Millard, M., Hamner, S.R., Arnold, E.M., Yong, J.R., Lakshmikanth, S.K., Sherman,n M.A., Delp, S.L. OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. Plos Computational Biology, 14(7). (2018) [3] R. K. Huffman, W. K. Thompson, C. A. Gallo, L. J. Quiocho, “Improvement of Scaling and Inverse Kinematic Results with Additional Upper Body Joints Added to Opensim Rajagopal Model”, NASA Human Research Program Investigator’s Workshop, (2019). [4] Huffman R.K., Thompson W., Gallo C., “Modified OpenSim Rajagopal Full Body Model”, New Technology Report, MSC-26872-1. (August 2020). [5] Dumas R., Cheze L. and Verriest J., 2007. “Adjustments to McConville et al. and Young et al. body segment inertial parameters”. Journal of Biomechanics 40, pp. 543-553 [6] Gordon C.C., 2012 “Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics”, US Army Natick Soldier RD&E Center. [7] NASA STD-3000/REV-B, 1995. “The Man-System Integration Standards” [8] NASA/SP-2010-3407/REV-1, 2014. “The Human Integration Design Handbook (HIDH)”

F N Matari↗
NASA NTRSDate not supplied

Control and Scaling Approach for the Emulation of Dynamic Subscale Torque Loads

Research and development of electrified aircraft propulsion powertrains is moving toward the use electro-mechanical systems to emulate the loads a system imparts on another. Replacing a prime mover with a model driving an electro-mechanical system capable of emulating loads that regulate the system to produce a desired response is a lower risk, lower cost alternative to using the traditional prime mover for control system verification. This paper outlines a control and scaling approach for emulating scaled dynamic torque loads using electric machine (EM) hardware for electrified aircraft propulsion research and development purposes. The approach, known as the Sliding Mode Impedance Controller with Scaling (SMICS), drives a mechanically coupled two-EM system that provides a scaled hardware representation of an electrified turbomachinery shaft. One EM reflects inertial dynamics and load of the shaft under steady-state and transient operation while the second EM represents a motor/generator connected to the shaft. This closed loop system applies impedance and sliding mode control schemes to match desired dynamics in real-time along with parameter scaling to effectively scale full scale torque inputs, a full-scale desired inertia, and sub-scale speed feedback. The result is a sub-scale hardware implementation of a coupled EM system that is command-able by a model and control system designed for a full-scale electrified aircraft propulsion powertrain. The paper elaborates on the need for closed loop control and scaling as well as impedance and sliding mode control theory, shows a derivation of the controller and scaling, its implementation, and presents a comparison of theoretical and actual simulation results acquired during hardware-in-the-loop testing of a partial turboelectric propulsion concept at the NASA Electric Aircraft Testbed (NEAT).

Santino J Bianco↗
DOE OSTI2015

Multi-scale Material Parameter Identification Using LS-DYNA® and LS-OPT®

Ever-tightening regulations on fuel economy, and the likely future regulation of carbon emissions, demand persistent innovation in vehicle design to reduce vehicle mass. Classical methods for computational mass reduction include sizing, shape and topology optimization. One of the few remaining options for weight reduction can be found in materials engineering and material design optimization. Apart from considering different types of materials, by adding material diversity and composite materials, an appealing option in automotive design is to engineer steel alloys for the purpose of reducing plate thickness while retaining sufficient strength and ductility required for durability and safety. A project to develop computational material models for advanced high strength steel is currently being executed under the auspices of the United States Automotive Materials Partnership (USAMP) funded by the US Department of Energy. Under this program, new Third Generation Advanced High Strength Steel (i.e., 3GAHSS) are being designed, tested and integrated with the remaining design variables of a benchmark vehicle Finite Element model. The objectives of the project are to integrate atomistic, microstructural, forming and performance models to create an integrated computational materials engineering (ICME) toolkit for 3GAHSS. The mechanical properties of Advanced High Strength Steels (AHSS) are controlled by many factors, including phase composition and distribution in the overall microstructure, volume fraction, size and morphology of phase constituents as well as stability of the metastable retained austenite phase. The complex phase transformation and deformation mechanisms in these steels make the well-established traditional techniques obsolete, and a multi-scale microstructure-based modeling approach following the ICME [0]strategy was therefore chosen in this project. Multi-scale modeling as a major area of research and development is an outgrowth of the Comprehensive Test Ban Treaty of 1996 which banned surface testing of nuclear devices [1]. This had the effect that experimental work was reduced from large scale tests to multiscale experiments to provide material models with validation at different length scales. In the subsequent years industry realized that multi-scale modeling and simulation-based design were transferable to the design optimization of any structural system. Horstemeyer [1] lists a number of advantages of the use of multiscale modeling. Among these are: the reduction of product development time by alleviating costly trial-and-error iterations as well as the reduction of product costs through innovations in material, product and process designs. Multi-scale modeling can reduce the number of costly large scale experiments and can increase product quality by providing more accurate predictions. Research tends to be focussed on each particular length scale, which enhances accuracy in the long term. This paper serves as an introduction to the LS-OPT and LS-DYNA methodology for multi-scale modeling. It mainly focuses on an approach to integrate material identification using material models of different length scales. As an example, a multi-scale material identification strategy, consisting of a Crystal Plasticity (CP) material model and a homogenized State Variable (SV) model, is discussed and the parameter identification of the individual material models of different length scales is demonstrated. The paper concludes with thoughts on integrating the multi-scale methodology into the overall vehicle design.

Stander, Nielen↗
DOE OSTI2022

Exceptional Mineral Scaling Resistance from the Surface Gas Layer: Impacts of Surface Wetting Properties and the Gas Layer Charging Mechanism

Mineral scaling is a phenomenon that occurs on submerged surfaces in contact with saline solutions. In membrane desalination, heat exchangers, and marine structures, mineral scaling reduces process efficiency and eventually leads to process failure. Therefore, achieving long-term scaling resistance is beneficial to enhancing process performance and reducing operating and maintenance costs. While evidence shows that superhydrophobic surfaces may reduce mineral scaling kinetics, prolonged scaling resistance is limited due to the finite stability of the entrained gas layer present in a Cassie–Baxter wetting state. Additionally, superhydrophobic surfaces are not always feasible for all applications, but strategies for long-term scaling resistance with smooth or even hydrophilic surfaces are often overlooked. In this study, we elucidate the role of interfacial nanobubbles on the scaling kinetics of submerged surfaces of varied wetting properties, including those that do not entrain a gas layer. We show that both solution conditions and surface wetting properties that promote interfacial bubble formation enhances scaling resistance. In the absence of interfacial bubbles, scaling kinetics decrease as surface energy decreases, while the presence of bulk nanobubbles enhances the scaling resistance of the surface with any wetting property. The findings in this study allude to scaling mitigation strategies that are enabled by solution and surface properties that promote the formation and stability of interfacial gas layers and provide insights to surface and process design for greater scaling resistance.

calcite↗
DOE OSTI2020

On the regeneration of fish scales: structure and mechanical behavior

Fish scales serve as a dermal armor that provides protection from physical injury. Owing to a number of outstanding properties, fish scales are inspiring new concepts for layered engineered materials and next-generation flexible armors. Although past efforts have primarily focused on the structure and mechanical behavior of ontogenetic scales, the structure–property relationships of regenerated scales have received limited attention. In the present study, common carp ( Cyprinus carpio ) acquired from the wild were held live in an aquatic laboratory at 10°C and 20°C. Ontogenetic scales were extracted from the fish for analysis, as well as regenerated scales after approximately 1 year of development and growth. Their microstructure was characterized using microscopy and Raman spectroscopy, and the mechanical properties were evaluated in uniaxial tension to failure under hydrated conditions. We note the strength, strain to fracture and toughness of the regenerated scales were significantly lower than those of ontogenetic scales from the same fish, regardless of the water temperature. Scales that regenerated at 20°C exhibited significantly higher strength, strain to fracture and toughness than those regenerated at 10°C. The regenerated scales exhibited a highly mineralized outer layer, but no distinct limiting layer or external elasmodine; they also possessed a significantly lower number of plies in the basal layer than the ontogenetic scales. The results suggest that a mineralized layer develops preferentially during scale regeneration with the topology needed for protection, prior to the development of other qualities.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRSDate not supplied

Adaptive Control and Scaling Approach for the Emulation of Dynamic Subscale Torque Loads

Previous research by the authors proposed a control and scaling approach for emulating dynamic sub-scale torque loads. This approach produced an emulation controller that successfully regulated the dynamic behavior of a sub-scale electro-mechanical system intended to be a dynamical representation of the sub-scale turboelectric powertrain of a single-aisle commercial aircraft. The sub-scale system provides an environment without turbomachinery or rotors for the initial testing of electrified aircraft propulsion (EAP) control algorithms as they would be applied to a full-scale EAP system. The sub-scale turbomachinery/rotor torque loads were produced by electric machines (EMs) driven by the control and scaling approach, a full-scale turboelectric powertrain model, and an advanced EAP control algorithm. Although successfully tested, this approach produces an emulation controller that does not guarantee asymptotic stability. Modifying the original control law and integrating adaptive control techniques into the emulation controller allows the designer to guarantee asymptotic stability. This paper introduces the idea behind the emulation controller modifications, derives the controller, proves asymptotic stability, describes the implementation of the controller on a sub-scale electro-mechanical system intended to represent a parallel hybrid-electric turbofan engine, and describes the testing of a full-scale advanced EAP control algorithm. The turbofan engine and emulation controller performance are compared to results obtained using the previous, non-adaptive control and scaling approach.

adaptive↗
DOE OSTI2016

Fragmentation Prediction for a Brittle Ceramic: a Two-Scale Model Approach

Glass and oxide-ceramic radioactive material forms (e.g., PuO{sub 2}) are susceptible to brittle fracture during handling and transportation. Fracture of these materials may result in the generation of fragments small enough to become airborne, and thus easily dispersed and inhaled. Entrainment and dispersal of particles with dimensions less than 10 μm is generally anticipated under normal aerodynamic conditions. The assessment of the risk to the public and the environment from these materials due to events resulting in their fracture is based on the determination of the source term for environmental release. This source term is typically quantified by an airborne release fraction (ARF) and a respirable fraction (RF) of material generated by a given event. While the recommended empirical bounding values prove satisfactory to comply with the regulatory process for handling and transportation of these materials, they are based on test data for only a few materials subjected to a limited range of loading conditions. Because the final state of fragmentation (in terms of the size and distribution of fragments) is strongly dependent not only on the properties of the material and the energetic loading conditions that lead to breakup, but also on the many intrinsic length scales associated with fragmentation, it is difficult to precisely predict fragmentation characteristics for other brittle solid wastes forms subjected to a wider range of loading conditions based on the test data alone. The purpose of this manuscript is to present a two-scale modeling approach that may be used to simulate the dynamic fragmentation of brittle solid radioactive material forms subjected to general loading and boundary conditions. The method provides the resulting fragment characteristics (average size and size distribution) across the entire fragment range of interest. At the macro-scale, the approach uses a gradient damage elastic continuum mechanics material model within a finite element framework to simulate dynamic fracture under general loading and boundary conditions. Results from the macroscopic calculations are passed to a one-dimensional (1-D) lower length scale model that incorporates the relevant fine scale effects to determine the micro-scale fragmentation. This 1-D micro-scale fragmentation model simulates the internal crack nucleation and opening processes to predict the average fragment size and the fragment size distribution as a function of the material properties, loading conditions, and microscopic characteristic length scale of the material. Results from the lower length scale model are then combined with the macro-scale model fragmentation information to determine the resulting fragment size distribution spanning both length scales. This two-scale model has been exercised on a representative problem drawn from experimental studies, consisting of an impact of a falling weight onto a brittle ceramic. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2021

Scale interactions and anisotropy in Rayleigh–Taylor turbulence

We study energy scale transfer in Rayleigh–Taylor (RT) flows by coarse graining in physical space without Fourier transforms, allowing scale analysis along the vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work Λ, due to large-scale pressure gradients acting on small scales of density and velocity; and deformation work Π, due to multiscale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to the RT mixing layer. We find that Λ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where Π takes over. In three dimensions, Π continues a persistent cascade to smaller scales, whereas in two dimensions Π rechannels the energy back to larger scales despite the lack of vorticity conservation in two-dimensional (2-D) variable density flows. This gives rise to a positive feedback loop in 2-D RT (absent in three dimensions) in which mixing layer growth and the associated potential energy release are enhanced relative to 3-D RT, explaining the oft-observed larger α values in 2-D simulations. Despite higher bulk kinetic energy levels in two dimensions, small inertial scales are weaker than in three dimensions. Moreover, the net upscale cascade in two dimensions tends to isotropize the large-scale flow, in stark contrast to three dimensions. Furthermore, our findings indicate the absence of net upscale energy transfer in three-dimensional RT as is often claimed; growth of large-scale bubbles and spikes is not due to ‘mergers’ but solely due to baropycnal work Λ.

42 ENGINEERING↗
DOE OSTI2021

Filtering, averaging, and scale dependency in homogeneous variable density turbulence

We investigate relationships between statistics obtained from filtering and from ensemble or Reynolds-averaging turbulence flow fields as a function of length scale. Generalized central moments in the filtering approach are expressed as inner products of generalized fluctuating quantities, q ' ( ξ , x ) = q ( ξ ) - q ¯ ( x ) , representing fluctuations of a field q ( ξ ) , at any point ξ, with respect to its filtered value at x. For positive-definite filter kernels, these expressions provide a scale-resolving framework, with statistics and realizability conditions at any length scale. In the small-scale limit, scale-resolving statistics become zero. In the large-scale limit, scale-resolving statistics and realizability conditions are the same as in the Reynolds-averaged description. Using direct numerical simulations (DNS) of homogeneous variable density turbulence, we diagnose Reynolds stresses, T i j , resolved kinetic energy, kr, turbulent mass-flux velocity, a i , and density-specific volume covariance, b, defined in the scale-resolving framework. These variables, and terms in their governing equations, vary smoothly between zero and their Reynolds-averaged definitions at the small and large scale limits, respectively. At intermediate scales, the governing equations exhibit interactions between terms that are not active in the Reynolds-averaged limit. For example, in the Reynolds-averaged limit, b follows a decaying process driven by a destruction term; at intermediate length scales, it is a balance between production, redistribution, destruction, and transport, where b grows as the density spectrum develops and then decays when mixing becomes strong enough. This work supports the notion of a generalized, length-scale adaptive model that converges to DNS at high resolutions and to Reynolds-averaged statistics at coarse resolutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Scaling patch analysis of planar turbulent wakes

In this work, a scaling patch approach is used to investigate the proper scales in planar turbulent wakes. A proper scale for the mean axial flow is the well-known maximum velocity deficit U ref = U ∞ –U ctr , where U ∞ is the free stream velocity and U ctr is the mean axial velocity at the wake centerline. From an admissible scaling of the mean continuity equation, a proper scale for the mean transverse flow is found as V ref = (dδ/dx)U ref , where dδ/dx is the growth rate of the wake width. From an admissible scaling of the mean momentum equation, a proper scale for the kinematic Reynolds shear stress is found as R uv,ref = U ∞ V ref , which is a mixed scale of the free stream velocity and the mean transverse flow scale. Expressions are derived for the scaled mean transverse velocity and Reynolds shear stress in the far field of planar turbulent wakes. Using a Gaussian function for the mean axial velocity deficit, approximate functions for the scaled mean transverse velocity and Reynolds shear stress are developed and found to agree well with experimental and simulation data. This work reveals that the mean transverse flow, despite its small magnitude, plays an important role in the scaling and understanding of the planar turbulent wake.

42 ENGINEERING↗
DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2003

Comparisons of the Impact Responses of a 1/5-Scale Model and a Full-Scale Crashworthy Composite Fuselage Section

A 25-fps vertical drop test of a 1/5-scale model composite fuselage section was conducted to replicate a previous test of a full-scale fuselage section. The purpose of the test was to obtain experimental data characterizing the impact response of the 1/5-scale model fuselage section for comparison with the corresponding full-scale data. This comparison is performed to assess the scaling procedures and to determine if scaling effects are present. For the drop test, the 1/5-scale model fuselage section was configured in a similar manner as the full-scale section, with lead masses attached to the floor through simulated seat rails. Scaled acceleration and velocity responses are compared and a general assessment of structural damage is made. To further quantify the data correlation, comparisons of the average acceleration data are made as a function of floor location and longitudinal position. Also, the percentage differences in the velocity change (area under the acceleration curve) and the velocity change squared (proportional to kinetic energy) are compared as a function of floor location. Finally, correlation coefficients are calculated for corresponding 1/5- and full-scale data channels and these values are plotted versus floor location. From a scaling perspective, the differences between the 1/5- and full-scale tests are relatively small, indicating that appropriate scaling procedures were used in fabricating the test specimens and in conducting the experiments. The small differences in the scaled test data are attributed to minor scaling anomalies in mass, potential energy, and impact attitude.

Jackson, Karen E.↗
NASA NTRSDate not supplied

TOWARD A METHOD FOR SCALING HUMAN BODY MODELS IN AN IMU-BASED WORKFLOW

BACKGROUND Scaled biomechanical models can more accurately inform crew health decisions when tailored to the wide range of astronaut sizes. One component to improve scaling of existing models to better represent each unique astronaut’s size is the individual length scaling of limbs. Traditionally, these lengths are determined by motion capture or manual measurement. A new method is herein proposed for length scaling which can be done by measuring linear and angular accelerations at a desired point during isolated motion around a point of rotation, then calculating the distance between the desired point and point of rotation. When an Inertial Measurement Unit (IMU) device is placed at the distal point of a limb, the isolated motion is about that limb’s proximal joint. For example, to measure forearm length, an IMU is placed at the wrist, the point of rotation is at the elbow, and the isolated motion is forearm flexion and extension. These calculated lengths are then used to scale models to each unique astronaut’s size, thereby improving the applicability of the model. This method of scaling limb segments can be used for any limb that has an easily defined proximal joint for the limb to rotate around including hands, arms, legs, feet. Utilizing IMUs for data collection also provides the synergistic ability to record data without a dedicated space in a room with many cameras, therefore reducing the data collection footprint, or record data where optical motion capture is not possible, such as inside a spacesuit. METHODS AND RESULTS To test this method, upper body data collection was performed with 5 Xsens DOT IMUs on a single subject. IMUs consist of an accelerometer, a gyroscope, and a magnetometer which collect linear acceleration, angular velocity, and magnetic fluctuations, respectively. Before any ground-based laboratory collection, the magnetic fluctuations are used to correct the heading of the IMU in space relative to the Earth’s magnetic field. The direct measurement of angular velocity is integrated to calculate angular acceleration. Then the linear acceleration ( a ) and angular acceleration (α) are solved using r = at/α to calculate the radius, which in this case is the distance between the IMU and the point of rotation (i.e., segment length). The IMU must be placed at the most distal point of the limb being measured (i.e., ankle if measuring lower leg length) and the test plan must consist of an isolated motion about that limb’s proximal joint (i.e., knee flexion and extension if measuring lower leg length). The distances (radii) calculated at every time interval were filtered (bandpass filter keeping 5th-90th percentile data) to eliminate outliers and spurious data that occur when the isolated motion was stopped or nearly stopped. The remaining distances were averaged, resulting in the calculated limb length. Scaling factors were then computed by dividing the calculated limb length by the unscaled model’s length. These scale factors are plugged into the Scale Tool in OpenSim [1,2] to apply the scaling to the OpenSim Full Body Rajagopal Model [3,4]. Manual measurements of limb lengths were taken before data collection started and used for comparing against the calculated lengths. The Anthropometric Survey of US Army Personnel (ANSUR II) [5] was also used as a third source of reference for limb length measurements. The following measurements were retrieved from the subject before data collection: 34.5 cm from L1 to C7 (thorax), 25.7 cm from C7 Joint Center (JC) to head vertex (neck and head), 36.3 cm from shoulder JC to elbow JC (humerus), 29.5 cm from elbow JC to wrist JC (forearm), and 16.2 cm from clavicle to acromion (clavicle). Of those five, forearm and humerus lengths were calculated using this proposed method to obtain preliminary results. The forearm length after filtering and averaging was calculated to be 37.6 cm. This is a 28% overestimation from the measured forearm length (29.5 cm). The humerus length after filtering and averaging was calculated to be 47.8 cm. This is a 31% difference from the measured subject length (36.3 cm). Sources of error include imperfect isolated motion (method currently expects that motion should be perfectly circular in a 2D plane, include no rotation of the IMU, and be relatively smooth; a more secure IMU attachment method will help), unrefined filter techniques (removed highest and lowest values with 20% high and low pass filters and no smoothing filters), arbitrary removal of stopped or near stopped data (kept data for only a short range before and after the angular velocity peaking), and a more representative method for removing gravitational acceleration is needed (current method is to zero all accelerations against a baseline taken just before the isolated motion which does not account for the gravitational acceleration changed due to IMU rotation during movement). Addressing these error sources will improve the accuracy of the limb length calculation. Next steps include creating a method for whole-body scaling estimation using individual limb scale factors. Continued pursuit of these techniques is expected to enable acquiring anthropometric information using only IMUs in real-time.

E. K. Marecki↗