Search NASA⌕ Search

SEARCH · Search NASA

Results for “Scaling laws”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Swept shock/boundary-layer interactions: Scaling laws, flowfield structure, and experimental methods

A general review is given of several decades of research on the scaling laws and flowfield structures of swept shock wave/turbulent boundary layer interactions. Attention is further restricted to the experimental study and physical understanding of the steady-state aspects of these flows. The interaction produced by a sharp, upright fin mounted on a flat plate is taken as an archetype. An overall framework of quasiconical symmetry describing such interactions is first developed. Boundary-layer separation, the interaction footprint, Mach number scaling, and Reynolds number scaling are then considered, followed by a discussion of the quasiconical similarity of interactions produced by geometrically-dissimilar shock generators. The detailed structure of these interaction flowfields is next reviewed, and is illustrated by both qualitative visualizations and quantitative flow images in the quasiconical framework. Finally, the experimental techniques used to investigate such flows are reviewed, with emphasis on modern non-intrusive optical flow diagnostics.

Settles, Gary S.↗
DOE OSTI2020

Stability of heterogeneous single-atom catalysts: a scaling law mapping thermodynamics to kinetics

Heterogeneous single-atom catalysts (SACs) hold the promise of combining high catalytic performance with maximum utilization of often precious metals. We extend the current thermodynamic view of SAC stability in terms of the binding energy (E bind ) of single-metal atoms on a support to a kinetic (transport) one by considering the activation barrier for metal atom diffusion. A rapid computational screening approach allows predicting diffusion barriers for metal–support pairs based on E bind of a metal atom to the support and the cohesive energy of the bulk metal (E c ). Metal–support combinations relevant to contemporary catalysis are explored by density functional theory. Assisted by machine-learning methods, we find that the diffusion activation barrier correlates with (E bind ) 2 /E c in the physical descriptor space. This diffusion scaling-law provides a simple model for screening thermodynamics to kinetics of metal adatom on a support.

36 MATERIALS SCIENCE↗
NASA NTRS1971

Improved scaling laws for stage inert mass space Propulsion systems. Volume 3: Propulsion synthesis program users and programmers manual

The analytical models developed for the Space Propulsion Automated Synthesis Modeling (SPASM) program are presented. Weight scaling laws developed during this study are incorporated into the program's scaling data bank. A detail listing, logic diagram and input/output formats are supplied for the SPASM program. Two test examples for one to four-stage vehicles performing different types of missions are shown to demonstrate the program's capability and versatility.

Source record↗
NASA NTRS1990

Scaling laws for light weight optics, studies of light weight mirrors mounting and dynamic mirror stress, and light weight mirror and mount designs

Scaling laws for light-weight optical systems are examined. A cubic relationship between mirror diameter and weight has been suggested and used by many designers of optical systems as the best description for all light-weight mirrors. A survey of existing light-weight systems in the open literature was made to clarify this issue. Fifty existing optical systems were surveyed with all varieties of light-weight mirrors including glass and beryllium structured mirrors, contoured mirrors, and very thin solid mirrors. These mirrors were then categorized and weight to diameter ratio was plotted to find a best curve for each case. A best fitting curve program tests nineteen different equations and ranks a goodness-to-fit for each of these equations. The resulting relationship found for each light-weight mirror category helps to quantify light-weight optical systems and methods of fabrication and provides comparisons between mirror types.

Vukobratovich, Daniel↗
NASA NTRS2008

Jet Mixing Noise Scaling Laws SHJAR Data Vs. Predictions

High quality jet noise spectral data measured at the anechoic dome at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent as well as convergent-divergent axisymmetric nozzles. The spectral measurements are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of (0.01 10.0). Measurements are reported as lossless (i.e. atmospheric attenuation is added to as-measured data), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter arc. Following the work of Viswanathan [Ref. 1], velocity power laws are derived using a least square fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit is studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. On the application side, power laws are extremely useful in identifying components from various noise generation mechanisms. From this analysis, jet noise prediction tools can be developed with physics derived from the different spectral components.

Khavaran, Abbas↗
NASA NTRS1974

Laboratory study of sonic booms and their scaling laws

This program undertook to seek a basic understanding of non-linear effects associated with caustics, through laboratory simulation experiments of sonic booms in a ballistic range and a coordinated theoretical study of scaling laws. Two cases of superbooms or enhanced sonic booms at caustics have been studied. The first case, referred to as acceleration superbooms, is related to the enhanced sonic booms generated during the acceleration maneuvers of supersonic aircrafts. The second case, referred to as refraction superbooms, involves the superbooms that are generated as a result of atmospheric refraction. Important theoretical and experimental results are briefly reported.

Toong, T. Y.↗
NASA NTRS1987

Centrifuge impact cratering experiments: Scaling laws for non-porous targets

A geotechnical centrifuge was used to investigate large body impacts onto planetary surfaces. At elevated gravity, it is possible to match various dimensionless similarity parameters which were shown to govern large scale impacts. Observations of crater growth and target flow fields have provided detailed and critical tests of a complete and unified scaling theory for impact cratering. Scaling estimates were determined for nonporous targets. Scaling estimates for large scale cratering in rock proposed previously by others have assumed that the crater radius is proportional to powers of the impactor energy and gravity, with no additional dependence on impact velocity. The size scaling laws determined from ongoing centrifuge experiments differ from earlier ones in three respects. First, a distinct dependence of impact velocity is recognized, even for constant impactor energy. Second, the present energy exponent for low porosity targets, like competent rock, is lower than earlier estimates. Third, the gravity exponent is recognized here as being related to both the energy and the velocity exponents.

Schmidt, Robert M.↗
NASA NTRS1961

Heat-Transfer Tests of 20-Millimeter Projectiles at a Mach Number of 5 with an Analysis by Unsteady Scaling Laws to Predict Component Temperature Rises after Firing for Various Free-Flight Conditions

The temperature time history of various components of a 20-millimeter projectile was obtained by transient heating tests in a Mach number 5 blowdown tunnel. An unsteady scaling law is derived and used to predict the temperature time histories after firing in flight at various Mach numbers and altitudes.

Trimpi, Robert L.↗
DOE OSTI2024

Numerical validation of scaling laws for stratified turbulence

Recent theoretical progress using multiscale asymptotic analysis has revealed various possible regimes of stratified turbulence. Notably, buoyancy transport can either be dominated by advection or diffusion, depending on the effective Péclet number of the flow. Two types of asymptotic models have been proposed, which yield measurably different predictions for the characteristic vertical velocity and length scale of the turbulent eddies in both diffusive and non-diffusive regimes. The first, termed a ‘single-scale model’, is designed to describe flow structures having large horizontal and small vertical scales, while the second, termed a ‘multiscale model’, additionally incorporates flow features with small horizontal scales, and reduces to the single-scale model in their absence. By comparing predicted vertical velocity scaling laws with direct numerical simulation data, we show that the multiscale model correctly captures the properties of strongly stratified turbulence within regions dominated by small-scale isotropic motions, whose volume fraction decreases as the stratification increases. Meanwhile its single-scale reduction accurately describes the more orderly, layer-like, quiescent flow outside those regions.

Mechanics↗
NASA NTRS2003

Goldilocks and the Three Complex Crater Scaling Laws

Formed in the gravity regime, complex craters are larger than their simple crater equivalents, due to a combination of slumping and uplift. Just how much larger is a matter of great interest for, for example, age dating studies. We examine three empirical scaling laws for complex crater size, examining their strengths and weaknesses, as well as asking how well they accord with previously published and new data from lunar, terrestrial, and venusian craters.

McKinnon, William B.↗
NASA NTRS2003

Goldilocks and the Three Complex Crater Scaling Laws

Formed in the gravity regime, complex craters are larger than their simple crater equivalents, due to a combination of slumping and uplift. Just how much larger is a matter of great interest for, for example, age dating studies. We examine three empirical scaling laws for complex crater size, examining their strengths and weaknesses, as well as asking how well they accord with previously published and new data from lunar, terrestrial, and Venusian craters.

McKinnon, William B.↗
DOE OSTI2026

Constraining the Dynamo Layers in Jupiter and Saturn with Observations and Scaling Laws

The dipole-dominated magnetic fields of Jupiter and Saturn provide evidence for active dynamos operating within their deep interiors, yet the depth of the convecting dynamo layers remains poorly constrained. While magnetic field observations, gravity data, and interior models each provide partial insight, they have not been combined into a single, self-consistent picture of the internal structure. Here, we develop a framework that links observed magnetic field strength with intrinsic heat flux and gravity-constrained interior structure using energy-based dynamo scaling laws. By relating the axial magnetic field strength to the convective power, we infer the radial thickness of the dynamo-generating region for both Jupiter and Saturn. The constants of proportionality in the scaling relations are derived using independent constraints from Earth observations, Jupiter observations, and numerical dynamo simulations. Applied to Jupiter, this framework shows how the inferred dynamo layer thickness is coupled to the outer boundary of the dynamo region. Thinner dynamo layers are predicted when the outer boundary shifts to shallower depths, and no solutions are possible when the outer boundary is less than 73% of Jupiter’s radius. These results constrain plausible geometries for future numerical dynamo simulations. Extending the analysis to Saturn, we find a thick, deep-seated dynamo layer with an outer radius at 42% of the radius to be most plausible. An alternative solution with an inner radius of the dynamo region at 60% of the planetary radius, as suggested by ring seismology models, requires a very thin dynamo layer, occupying only 2%–3% of the total radius.

Geosciences↗
NASA NTRS1971

Improved scaling laws for stage inert mass of space propulsion systems. Volume 2: System modeling and weight data

Technical models and analytical approaches used to develop the weight data for vehicle system concepts using advanced technology are reported. Weight data are supplied for the following major system elements: engine, pressurization, propellant containers, structural shells and secondary structure, and environmental protection shields for the meteoroid and thermal design requirements. Scaling laws, improved and a simplified set, are developed from the system weight data. The laws consider the implications of the major design parameters and mission requirements on the stage inert mass.

Source record↗
DOE OSTI2024

Cosmic quenching and scaling laws for the evolution of supermassive black holes and host galaxies

ABSTRACT Observations suggest a co-evolution of supermassive black holes (SMBHs) and host galaxies. In this paper, we consider the mass and energy flow in a near-equilibrium bulge suffused by gases of varying temperatures. By assuming the rate of energy flow independent of the distance r from the bulge center and the local virial equilibrium for permeated gases on scale r, a key parameter $\varepsilon _b$ was identified that quantifies the mass and energy flow in gases and the efficiency of gas cooling (or the "specific" cooling rate per unit mass), and thus regulates the co-evolution of both SMBHs and hosts. With the help of Illustris simulations and observations, we determined the redshift variation $\varepsilon _b\propto (1+z)^{5/2}$. A higher $\varepsilon _b$ in the early Universe means a higher specific cooling rate that allows rapid evolution of SMBHs and hosts. This simple theory, characterized by a single parameter $\varepsilon _b$, provides the dominant mean cosmic evolution of SMBHs and hosts. All other transient phenomena may only contribute to the dispersion around this mean evolution. Based on this theory and relevant assumptions, scaling laws involving $\varepsilon _b$ were identified for the evolution of SMBHs and hosts. For host galaxies, the mass–size relation $M_b\propto \varepsilon _b^{2/3}r_b^{5/3}G^{-1}$, the dispersion–size relation $\sigma _b^2\propto (\varepsilon _b r_b)^{2/3}\propto (1+z)$, or the mass–dispersion relation $M_b\propto \varepsilon _b^{-1}G^{-1}\sigma _b^5$ were identified, where $r_b\propto (1+z)^{-1}$ is the bulge size. For SMBHs, three evolution phases were found involving an initial rapid growth stage with a rising luminosity $L_B\propto (\varepsilon _b M_{\rm BH})^{4/5}$, a transition stage with a declining $L_B\propto \varepsilon _b^2 M_{\rm BH} \propto (1+z)^5$, and a dormant stage with $L_B\propto (\varepsilon _b M_{\rm BH})^{4/3}$. Our results suggest a rapid initial super-Eddington growth in a short period with a new redshift-dependent luminosity limit $L_X\propto\varepsilon _b^{4/5}M_{\rm BH}^{4/5}G^{-1/5}c$, in contrast to the Eddington limit. Analytical solutions were formulated for the BH mass function $\Phi _{\rm BH}$, active galactic nucleus (AGN) mass function $\Phi _{\rm AGN}$, and duty cycle U that predict $\Phi _L\propto L^{-1/5}$ for the faint-end luminosity function, $\Phi _{\rm AGN}\propto M^{-1/5}$ for small-mass-end AGN mass function $\Phi _L$, and $U\propto M^{-1/5}$ at high redshift.

(galaxies:) quasars: supermassive black holes↗
DOE OSTI2025

Scaling Laws of Graph Neural Networks for Atomistic Materials Modeling

Atomistic materials modeling is a critical task with wide-ranging applications, from drug discovery to materials science, where accurate predictions of the target material property can lead to significant advancements in scientific discovery. Graph Neural Networks (GNNs) represent the state-of-the-art approach for modeling atomistic material data thanks to their capacity to capture complex relational structures. While machine learning performance has historically improved with larger models and datasets, GNNs for atomistic materials modeling remain relatively small compared to large language models (LLMs), which leverage billions of parameters and terabyte-scale datasets to achieve remarkable performance in their respective domains. To address this gap, we explore the scaling limits of GNNs for atomistic materials modeling by developing a foundational model with billions of parameters, trained on extensive datasets in terabytescale. Our approach incorporates techniques from LLM libraries to efficiently manage large-scale data and models, enabling both effective training and deployment of these large-scale GNN models. This work addresses three fundamental questions in scaling GNNs: the potential for scaling GNN model architectures, the effect of dataset size on model accuracy, and the applicability of LLM-inspired techniques to GNN architectures. Specifically, the outcomes of this study include (1) insights into the scaling laws for GNNs, highlighting the relationship between model size, dataset volume, and accuracy, (2) a foundational GNN model optimized for atomistic materials modeling, and (3) a GNN codebase enhanced with advanced LLM-based training techniques. Our findings lay the groundwork for large-scale GNNs with billions of parameters and terabyte-scale datasets, establishing a scalable pathway for future advancements in atomistic materials modeling.

Li, Chaojian [ORNL] (ORCID:0000000340309777)↗
NASA NTRSDate not supplied

Scaling Laws of Ejecta Streaks in Lunar Landings

From the crewed Apollo missions of the 1960s to the recent Chang’e uncrewed lunar missions, the interaction between the supersonic exhaust and the lunar surface generates a striking ray system of ejecta particles that travel radially outward at high speeds. While this intriguing pattern has been observed in experiments and simulations, the underlying mechanism remains unclear. These radial ejecta streaks were also observed during an experimental campaign using a Mach 5.3 jet impinging on a granular bed within a large-scale vacuum chamber. Our findings reveal that the radial ejecta streaks are caused by the Gortler instability, which, due to the curvature of the extremely underexpanded jet, induces counter-rotating streamwise vortices within the jet shear layer. These vortices impact the ground and entrain particles in their upwash regions. Experimental measurements from both ground tests and the literature show that the number of streaks strongly depends on the jet diameter at impact and the shear layer thickness, further revealing a power-law scaling with the jet pressure ratio. These insights highlight the pivotal role of fluid dynamics in extraterrestrial landings and provide a foundation for mitigating risks in future planetary missions.

Lunar Landing↗
NASA NTRS1989

Experiments and scaling laws for catastrophic collisions

The existing data on shattering impacts are reviewed using natural silicate, ice, and cement-mortar targets. A comprehensive data base containing the most important parameters describing these experiments was prepared. The collisional energy needed to shatter consolidated homogeneous targets and the ensuing fragment size distributions have been well studied experimentally. However, major gaps exist in the data on fragment velocity and rotational distributions, as well as collisional energy partitioning for these targets. Current scaling laws lead to predicted outcomes of asteroid collisions that are inconsistent with interpretations of astronomical data.

Fujiwara, A.↗