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 NTRSDate not supplied

Impact of Future Low-Emissions Combustor Technology on Acoustic Scaling Laws

The work is a summary and further analysis of unlimited-rights acoustic data acquired under NRA Contract NNC16CA39C (September 2016 - November2019) with United Technologies (now Raytheon Technologies) Research Center, East Hartford, Connecticut. NASA/CR-20205011099/VOL1, https://ntrs.nasa.gov/citations/20205011099. The overall goal of the Contract was to develop a first-of-its- kind database of detailed unsteady measurements characterizing noise sources of far-term advanced low-emissions aero-combustors. The program addressed the need for fundamental combustion-noise experiments which, in the near term, enable improvements to reduced-order models for use in system level noise assessments at the preliminary design stage for advanced air transport vehicles. In addition, optical measurement techniques were refined and validated for usage at the higher pressures and temperatures relevant to future combustor designs. In the long term, results from this program can be utilized to validate high-fidelity prediction methods suited for detailed multi-disciplinary acoustics/emissions combustor design. This presentation concentrates on one aspect of the overall project, namely an examination of the legacy scaling laws for broadband combustor noise.

aeroacoustics, turbomachinery noise, combustor noi↗
NASA NTRS2022

Universal Scaling Laws for Solar and Stellar Atmospheric Heating: Catalog of Power-law Index between Solar Activity Proxies and Various Spectral Irradiances

The formation of extremely hot outer atmospheres is one of the most prominent manifestations of magnetic activity common to late-type dwarf stars, including the Sun. It is widely believed that these atmospheric layers, the corona, transition region, and chromosphere, are heated by the dissipation of energy transported upwards from the stellar surface by the magnetic field. This is signified by the spectral line fluxes at various wavelengths, scaled with power-law relationships against the surface magnetic flux over a wide range of formation temperatures, which are universal to the Sun and Sunlike stars of different ages and activity levels. This study describes a catalog of power-law indices between solar activity proxies and various spectral line fluxes. Compared to previous studies, we expanded the number of proxies, which now includes the total magnetic flux, total sunspot number, total sunspot area, and the F10.7 cm radio flux, and further enhanced the number of spectral lines by a factor of 2. This provides the data to study in detail the flux–flux scaling laws from the regions specified by the temperatures of the corona (log(T/K) = 6–7) to those of the chromosphere (log(T/K) ∼ 4), as well as the reconstruction of various spectral line fluxes of the Sun in the past, F-, G-, and K-type dwarfs, and the modeled stars.

Stellar coronae↗
NASA NTRS1988

Scaling laws for homogeneous turbulent shear flows in a rotating frame

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.

Speziale, Charles G.↗
NASA NTRS1989

Scaling laws for homogeneous turbulent shear flows in a rotating frame

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri = -2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.

Speziale, Charles G.↗
NASA NTRS2002

Scaling Laws Applied to a Modal Formulation of the Aeroservoelastic Equations

A method of scaling is described that easily converts the aeroelastic equations of motion of a full-sized aircraft into ones of a wind-tunnel model. To implement the method, a set of rules is provided for the conversion process involving matrix operations with scale factors. In addition, a technique for analytically incorporating a spring mounting system into the aeroelastic equations is also presented. As an example problem, a finite element model of a full-sized aircraft is introduced from the High Speed Research (HSR) program to exercise the scaling method. With a set of scale factor values, a brief outline is given of a procedure to generate the first-order aeroservoelastic analytical model representing the wind-tunnel model. To verify the scaling process as applied to the example problem, the root-locus patterns from the full-sized vehicle and the wind-tunnel model are compared to see if the root magnitudes scale with the frequency scale factor value. Selected time-history results are given from a numerical simulation of an active-controlled wind-tunnel model to demonstrate the utility of the scaling process.

Pototzky, Anthony S.↗
NASA NTRS1999

Scaling Laws of Microactuators and Potential Applications of Electroactive Polymers in MEMS

Besides the scale factor that distinguishes the various spices fundamentally biological muscles changes little between species indicating a highly optimized system. Electroactive polymer actuators offer the closest resemblance to biological muscles however beside the large actuation displacement these materials are falling short with regards to the actuation force.

MEMS↗
NASA NTRS1995

Coronal heating by the resonant absorption of Alfven waves: Wavenumber scaling laws.

The importance of global modes in coronal loop heating is well established. In the present work the scaling of the global-mode resonant heating rate with the perturbation wavenumbers is studied with the numerical solution of the linearized time-dependent MHD equations for a full compressible, low-beta, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomogeneties in the background Alfven speed occurs in narrow resonant layer with the highest heating rate at the global-mode frequency. The global-mode heating rate H (sub r) was found to scale as H (Sub r) approximately k (sub y) (exp 1.03) when k (sub z) = 0.1, and as H (sub r) approximately k (sub y) (exp -1.93) when k (sub z) = 0.75, where k (sub y) and k (sub z) are the wavenumbers in the perpendicular and parallel to the magnetic field directions, respectively, while the dependence of H (sub r) on k (sub z) is more complex. The quality factor Q of the MHD resonance cavity scales as Q approximately k (sub y) (exp -1.8) for k (sub z) = 0.75 and as Q approximately k (sub y) (exp -1.46) for k (sub z) = 0.1. The numerically determined heating rate scaling, the global-mode fequency, and the quality factor are in good agreement with the analytical linear theory. The magnitude of the perturbed velocities was found to decrease with k (sub y). Assuming typical coronal loop parameters (B (sub 0) = 100-200 G, upsilon (sub A) = 2000-4000 km/s), the Alfven waves can supply the required heating to a low-Q loops.

Ofman, L.↗
NASA NTRS1998

Effect of Finite Computational Domain on Turbulence Scaling Law in Both Physical and Spectral Spaces

The well-known translation between the power law of energy spectrum and that of the correlation function or the second order structure function has been widely used in analyzing random data. Here, we show that the translation is valid only in proper scaling regimes. The regimes of valid translation are different for the correlation function and the structure function. Indeed, they do not overlap. Furthermore, in practice, the power laws exist only for a finite range of scales. We show that this finite range makes the translation inexact even in the proper scaling regime. The error depends on the scaling exponent. The current findings are applicable to data analysis in fluid turbulence and other stochastic systems.

Hou, Thomas Y.↗
NASA NTRS1987

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

This research is a continuation of an ongoing program whose objective is to perform experiments and to develop scaling relationships for large body impacts onto planetary surfaces. The development of the centrifuge technique has been pioneered by the present investigator and is used to provide experimental data for actual target materials of interest. With both powder and gas guns mounted on a rotor arm, it is possible to match various dimensionless similarity parameters, which have been shown to govern the behavior of large scale impacts. Current work is directed toward the determination of scaling estimates for nonporous targets. The results are presented in summary form.

Schmidt, Robert M.↗
NASA NTRS1992

Structural similitude and scaling laws for laminated beam-plates

The establishment of similarity conditions between two structural systems is discussed. Similarity conditions provide the relationship between a scale model and its prototype and can be used to predict the behavior of the prototype by extrapolating the experimental data of the corresponding small-scale model. Since satisfying all the similarity conditions simultaneously is difficult or even impossible, distorted models with partial similarity (with at least one similarity condition relaxed) are more practical. Establishing similarity conditions based on both dimensional analysis and direct use of governing equations is discussed, and the possibility of designing distorted models is investigated. The method is demonstrated through analysis of the cylindrical bending of orthotropic laminated beam-plates subjected to transverse line loads.

Simitses, George J.↗
NASA NTRS1992

Structural similitude and scaling laws for laminated beam-plates

The establishment of similarity conditions between two structural systems is discussed. Similarity conditions provide the relationship between a scale model and its prototype and can be used to predict the behavior of the prototype by extrapolating the experimental data of the corresponding small-scale model. Since satisfying all the similarity conditions simultaneously is difficult or even impossible, distorted models with partial similarity (with at least one similarity condition relaxed) are more practical. Establishing similarity conditions based on both dimensional analysis and direct use of governing equations is discussed, and the possibility of designing distorted models is investigated. The method is demonstrated through analysis of the cylindrical bending of orthotropic laminated beam-plates subjected to transverse line loads.

Simitses, G. J.↗
NASA NTRS1992

Scaling laws for buckling instability in monolayer networks

In this comment a power law is argued to govern the thickening of cell widths relative to their lengths in buckling monolayer networks. A scaling relation is derived for general instabilities in cellular networks, and a reply is given that questions the use of the amplitude of the buckling undulation in an already buckled wall in the Euler relation. Both treatments provided shed light on the stability/instability of wavelengths for buckling monolayer networks.

Noever, David A.↗
NASA NTRS1988

Planetary scaling laws and predictions for Neptune

This paper offers a prediction concerning Neptune's low-frequency radio emission based on the radiometric Bode's law in combination with a recent prediction for Neptune's global magnetic field strength. The latter is based on a dynamo scaling relation derived from the magnetospheric balance condition within planetary cores. The radio emission frequency range is predicted to extend from approximately 100 to 1000 kHz, with a spectral peak between 350 and 500 kHz. A crude estimate of the emission spectral shape, based on Saturn and earth-like models, is shown. If radiation is beamed approximately in the sunward direction, Neptune should be detectable by the Planetary Radio Astronomy experiment onboard the Voyager spacecraft sometime between 45 and 60 days before closest approach.

Desch, Michael D.↗
NASA NTRS1986

Scaling laws for the catastrophic collisions of asteroids

Collisions of asteroids have traditionally been studied through laboratory experiments involving targets with masses some 15 to 20 orders of magnitude less than the bodies they are intended to simulate. Here the problem of extrapolation of experimental results up to the size regimes of interest is considered. Scaling relations are developed for the shattering threshold and the size and velocity distributions of collisional fragments. A methodology which has often been used assumes that collisional outcomes (e.g., the size of the largest remaining fragment) are completely characterized by Q, the kinetic energy of the impactor normalized by the mass of the target body. This scaling is shown to be an unlikely special case of a more general scaling theory which indicates that collisional outcomes should depend on target size and encounter velocity, even when Q is held constant. In particular, as target size increases, the critical value of Q required to shatter a body, and the characteristic fragment velocities should initially decrease (in qualitative agreement with the recent model of Farinella et al., 1982) up to an asteroid size of perhaps 40 to 50 km; then, as the gravitational forces start to dominate, the value of Q will again increase (in qualitative agreement with the recent model of Davis et al., 1983 and 1985).

Holsapple, K. A.↗
NASA NTRS1985

Impact Crater Scaling Laws

The effects of the impactor size and velocity, of the material properties of the impactor and impacted body, and of the gravitational field strength were examined. The dependence of the coupling parameter on the Gruniesen parameter and the us/up slope values that characterize a Tillotson material model were tested. Whether a code calculation can recover the scaling exponents that can be derived theoretically for an idealized perfectly-porous material that crushes at zero strength and subsequently is incompressible was investigated. A model that was close to the idealized case was generated in a form suitable for code calculations and utilized for a series of one dimensional calculations. The code calculation demonstrated the theoretical coupling parameter. Calculations of impacts using a physically real porous material model seem to indicate a coupling parameter of the same form applicable to a nonporous material, distinctly different from that expected from other theoretical and experimental results for porous materials. The one dimensional calculations are being extended to two dimensional impacts.

Holsapple, K. A.↗
NASA NTRS1987

A scaling law for accretion zone sizes

Current theories of runaway planetary accretion require small random velocities of the accreted particles. Two body gravitational accretion cross sections which ignore tidal perturbations of the Sun are not valid for the slow encounters which occur at low relative velocities. Wetherill and Cox have studied accretion cross sections for rocky protoplanets orbiting at 1 AU. Using analytic methods based on Hill's lunar theory, one can scale these results for protoplanets that occupy the same fraction of their Hill sphere as does a rocky body at 1 AU. Generalization to bodies of different sizes is achieved here by numerical integrations of the three-body problem. Starting at initial positions far from the accreting body, test particles are allowed to encounter the body once, and the cross section is computed. A power law is found relating the cross section to the radius of the accreting body (of fixed mass).

Greenzweig, Yuval↗
NASA NTRS2007

Coronal Heating, Weak MHD Turbulence, and Scaling Laws

Long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry are carried out, within the framework of reduced magnetohydrodynamics (RMHD), to understand coronal heating driven by the motion of field lines anchored in the photosphere. We unambiguously identify MHD anisotropic turbulence as the physical mechanism responsible for the transport of energy from the large scales, where energy is injected by photospheric motions, to the small scales, where it is dissipated. As the loop parameters vary, different regimes of turbulence develop: strong turbulence is found for weak axial magnetic fields and long loops, leading to Kolmogorov-like spectra in the perpendicular direction, while weaker and weaker regimes (steeper spectral slopes of total energy) are found for strong axial magnetic fields and short loops. As a consequence we predict that the scaling of the heating rate with axial magnetic field intensity B, which depends on the spectral index of total energy for given loop parameters, must vary from B3/2 for weak fields to B2 for strong fields at a given aspect ratio. The predicted heating rate is within the lower range of observed active region and quiet-Sun coronal energy losses.

corona↗