Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “spherical harmonics”

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 865 records · Page 48

Prediction of BVI Noise for an Active Twist Rotor Using a Loosely Coupled CFD/CSD Method and Comparison to Experimental Data

Numerical predictions of the acoustic characteristics of an Active Twist Rotor (ATR), using two methods to compute the rotor blade aerodynamics and elastic blade motion are compared to experimental data from a wind tunnel test in the NASA Langley Transonic Dynamics Tunnel (TDT) in 2000. The first method, a loosely coupled iterative method, utilizes the Computational Fluid Dynamics (CFD) code OVERFLOW 2 and the Computational Structural Dynamics (CSD) code CAMRAD II. The second method utilizes the CAMRAD II free-wake model only. The harmonic active-twist control to the main rotor blade system is identified with three parameters - harmonic actuation frequency, actuation amplitude, and control phase angle. The resulting aerodynamics and blade motion data from the two methods are then used in the acoustics code PSU-WOPWOP to predict acoustic pressure on a spherical array of equally spaced observers surrounding the rotor. This spherical distribution of pressure is used to compute the sound power level representing baseline and actuated conditions. Sound power levels for three categories of noise are defined as - blade-vortex interaction sound power level (BVIPWL), low frequency sound power level (LFPWL), and overall sound power level, OAPWL. Comparisons with measured data indicate the CFD/CSD analysis successfully captures the trends in sound power levels and the effects of active-twist control at advance ratios of 0.14 and 0.17. The free-wake model predictions show inconsistent sound power levels relative to the trends in the experimental and CFD data. This paper presents the first ever comparison between CFD/CSD acoustic predictions for an active-twist rotor and experimental measurements.

Fogarty, David E.↗

Incompressible fluid ellipsoids in halos. I - The second-harmonic oscillations of the Maclaurin spheroids

The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.

Durisen, R. H.↗

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗

Dynamic compensation of Venus's geoid: A comparison with Earth

Unlike Earth, on Venus long wavelength geoid anomalies correlate well with topography. Venus's admittance curve between harmonic degrees 3 and 18 is inconsistent with Airy isostasy but is consistent with dynamic support from convection being the dominant mechanism of compensation on Venus. We model dynamic compensation on Venus using simple flow models which assume a spherically symmetric Newtonian mantle viscosity profile. Preliminary models parameterize the viscosity variation with depth as a 2 layer model with a boundary at 720 km depth. A model in which viscosity in the lower mantle is a factor of 10 lower than in the upper mantle can explain Venus's observed admittance curve for degrees 3 through 18. Dynamic models which include a chemical boundary between the upper and lower mantle do not successfully explain the observed admittance curve, indicating that Venus does not have a chemically layered mantle.

Kiefer, W. S.↗

Drag-Free Control and Drag Force Recovery of Small Satellites

Drag-free satellites provide autonomous precision orbit determination, accurately map the static and time varying components of Earth's mass distribution, aid in our understanding of the fundamental force of gravity, and will ultimately open up a new window to our universe through the detection and observation of gravitational waves. At the heart of this technology is a gravitational reference sensor, which (a) contains and shields a free-floating proof mass from all non-gravitational forces, and (b) precisely measures the position of the test mass inside the sensor. Thus, both test mass and spacecraft follow a pure geodesic in spacetime. By tracking the position of a low Earth orbiting drag-free satellite we can directly determine the detailed shape of geodesics and through analysis, the higher order harmonics of the Earths geopotential. This paper explores two different drag-free control systems on small satellites. The first drag-free control system is a continuously compensated single thruster 3-unit CubeSat with a suspension-free spherical proof-mass. A feedback control system commands the thruster and Attitude and Determination Control System to fly the tender spacecraft with respect to the test mass. The spheres position is sensed with a LED-based differential optical shadow sensor, its electric charge controlled by photoemission using UV LEDs, and the spacecraft position is maintained with respect to the sphere using an ion electrospray propulsion system. This configuration is the most fuel-efficient drag-free system possible today. The second drag-free control system is an electro-statically suspended cubical proof-mass that is operated with a low duty cycle, limiting suspension force noise over brief, known time intervals on a small GRACE-II -like satellite. The readout is performed using a laser interferometer, which is immune to the dynamic range limitations of voltage references. This system eliminates the need for a thruster, enabling drag-free control systems for passive satellites. In both cases, the test mass position, GPS tracking data, and commanded actuation, either thrust or suspension system, can be analyzed to estimate the 3-axis drag forces acting on the satellite. The data produces the most precise maps of upper atmospheric drag forces and with additional information, detailed models that describe the dynamics of the upper atmosphere and its impact on all satellites that orbit the Earth. This paper highlights the history, applications, design, laboratory technology development and highly detailed simulation results of each control system.

Small Satellites↗

Characterizing the initial state and dynamical evolution in XeXe and PbPb collisions using multiparticle cumulants

For the first time, correlations among mixed-order moments of two or three flow harmonics —( v n k , v m l ) and ( v n k , v m l , v p q ), with k, l, and q denoting the respective orders—are measured in xenon–xenon (XeXe) collisions and compared with lead–lead (PbPb) results, providing a novel probe of collective behavior in heavy ion collisions. These measurements compare a nearly spherical, doubly-magic 208 Pb nucleus to a triaxially deformed 129 Xe nucleus, emphasizing the sensitivity to initial-state geometry fluctuations arising from nuclear deformation. The dependence of these results (v n , n = 2 , 3 , 4 ) on the shape and size of the nuclear overlap region is studied. Comparisons between v 2 , v 3 , and v 4 demonstrate the importance of v 3 and v 4 in exploring the nonlinear hydrodynamic response of the quark-gluon plasma (QGP) to the initial spatial anisotropy. The results constrain initial-state model parameters that influence the evolution of the QGP. The CMS detector was used to collect XeXe and PbPb data at nucleon-nucleon center-of-mass energies of S N N = 5.44 and 5.36 TeV, respectively. Correlations are extracted using multiparticle mixed-harmonic cumulants (up to eight-particle cumulants) with charged particles in the pseudorapidity range |η| < 2.4 and transverse momentum range 0.5 < p T < 3 GeV/c.

CMS↗

Ion sheath effects on RF plasma probes - Experimental results in laboratory plasmas

Laboratory work dealing with the frequency characteristic of the plasma impedance of spherical and cylindrical electrode systems is reported. The influence of the ion sheath on various features of the impedance characteristic is emphasized. Those features are the series and parallel resonance as well as additional resonances due to the excitation of electroacoustic and cyclotron harmonic waves. The dependence of the series and parallel resonances on dc biasing leads to a method of determining the ion sheath capacity for a cylindrical electrode system. The obtained values agree fairly well with those obtained from a theoretical model for the density and potential distribution in the sheath of a cylindrical sensor aligned with a supersonic plasma flow. The amplitude of resonances due to excitation of longitudinal plasma waves (electroacoustic and cyclotron harmonic) is reduced or even vanishes for sufficiently negative dc bias. Positive bias first leads to an increased amplitude up to a certain dc bias value above which, however, the amplitude decreases again due to electron absorption at the sensor surface.

Kist, R.↗

Constrained sloshing of liquid mercury in a flexible spherical tank

The mercury propellant tank system developed for use with solar electric propulsion was studied to analytically determine the resonant frequencies of the tank system and compare them with the anticipated control natural frequency of the spacecraft. The system consisted of a stainless steel spherical shell and a hemispherical elastomeric diaphram which separates the mercury propellant and the gaseous nitrogen pressurant. The major analytical tool used was the NASTRAN program. Six mathematical models, which represent various amounts of mercury in the tank system were developed. Resonant frequencies for six harmonics were obtained for each of the six models considered. The results show that the lowest resonant frequency for the tank system is about an order of magnitude greater than the anticipated control frequency of the spacecraft.

Lestingi, J.↗

Symplectic effective field theory for nuclear structure studies

Here, a Symplectic Effective Field Theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for 20 Ne, 22 Ne and 22 Mg are presented that yield energy spectra, B(E2) values, and matter radii in good agreement with experimentally measured results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Pedestal stability analysis on MAST in preparation for MAST-U

In preparation for the upcoming MAST-U campaign, pedestal stability of spherical tokamaks is revisited by investigating standard H-mode discharges on MAST. As a step beyond previous studies, both ion and electron profiles are used for obtaining equilibria and a diverse set of pedestals is evaluated. Stability analysis with the ELITE and CGYRO codes shows that MAST pedestals are constrained by kinetic ballooning modes and medium toroidal mode number peeling-ballooning modes, with most unstable modes ranging from n = 25 to n = 45. In discharges with a steep q profile at the edge a larger number of poloidal harmonics is excited for each toroidal mode. In conclusion, a comparison with discharges on DIII-D with matched shape and similar non-dimensional parameters indicates that the increased shear at lower aspect ratio stabilizes low n peeling modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advanced Containerless Processing Technology

Breadboards for high temperature containerless processing systems are to be developed, the principles of operation are to be studied, the performance is to be characterized, the limitations identified, and the influence of the acoustic field on the samples established. The subjects to be addressed are experimental and theoretical studies of: (1) acoustic positioning and manipulation capabilities in a high temperature gradient environment (from 26 C to 990 C); (2) acoustic waveforms, harmonic contents, power transfer, sample transport and stability associated with high temperature gradient system; (3) high temperature ground based levitation systems which will allow melting, processing, and solidifying samples without crucibles in the laboratory, (4) KC-135 and laboratory tests of various acoustic geometries which may have spherical applications in the Materials Processing in Space Program; and (5) provide technical information to Acoustics Containerless Experimental System (ACES) engineering team and establish the operation conditions for ACES.

Wang, T. G.↗

Efficient ECCD non-inductive plasma current start-up, ramp-up, and sustainment for an ST fusion reactor

The elimination of the need for an Ohmic heating solenoid may be the most impactful design driver for the realization of economical compact fusion tokamak reactor systems. However, this would require fully non-inductive start-up and current ramp-up from zero plasma current and low electron temperature of sub-keV to the full plasma current of ~10–15 MA at 20–30 keV electron temperature. To address this challenge, an efficient solenoid-free start-up and ramp-up scenario utilizing a low-field-side-launched extraordinary mode at the fundamental electron cyclotron harmonic frequency (X–I) is proposed, which has more than two orders of magnitude higher electron cyclotron current drive (ECCD) efficiency than the conventional ECCD for the sub-keV start-up regime. A time dependent model was developed to simulate the start-up scenarios. For the Spherical Tokamak Advanced Reactor (STAR) (Menard et al 2023 Next-Step Low-Aspect-Ratio Tokamak Design Studies (IAEA)), it was found that to fully non-inductively ramp-up to 15 MA, it would take about 25 MW of EC power at 170 GHz. Because of the relatively large plasma volume of STAR, radiation losses must be considered. It is important to make sure that high Z impurities are kept sufficiently low during the early current start-up phase where the temperature is sub-keV range. Since the initial current ramp up takes place at a factor of ten lower density compared to the sustained regimes, it is important to transition into a higher bootstrap fraction discharge at lower density to minimize the ECCD power requirement during the densification. For the sustainment phase an array of eight gyrotron launchers with a total of about 60 MW of fundamental O-mode was found to be sufficient to provide the required axis-peaked external current drive. High efficiencies between 19–57 kA MW –1 were found with optimal aiming, and these were resilient to small changes in aiming angles and density and temperature profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dirac oscillator: An alternative basis for nuclear structure calculations

The isotropic harmonic oscillator supplemented by a strong spin-orbit interaction has been the cornerstone of nuclear structure since its inception more than seven decades ago. In this paper we introduce—or rather re-introduce—the “Dirac oscillator,” a fully relativistic basis that has all the desired attributes of the ordinary harmonic oscillator while naturally incorporating a strong spin-orbit coupling. To assess the power and flexibility of the Dirac oscillator basis in the solution of nuclear structure problems within the framework of covariant density-functional theory. Here, self-consistent calculations of binding energies and ground-state densities for a selected set of doubly magic nuclei are performed using the Dirac oscillator basis and are then compared against results obtained with the often-used Runge-Kutta method. Results obtained using the Dirac oscillator basis reproduce with high accuracy those derived using the Runge-Kutta method and suggest a clear path for a generalization to systems with axial symmetry. Although the harmonic oscillator with spin-orbit corrections has been the staple of the nuclear shell model since the beginning, the Dirac oscillator is practically unknown among the nuclear physics community. In this paper we illustrate the power and flexibility of the Dirac oscillator and suggest extensions to the study of systems without spherical symmetry, as required in constrained calculations of nuclear excitations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Method for predicting impulsive noise generated by wind turbine rotors

Large wind turbines can generate both broad band and impulsive noises. These noises can be controlled by proper choice of rotor design parameters such as rotor location with respect to the supporting tower, tower geometry and tip speed. A method was developed to calculate the impulsive noise generated when the wind turbine blade experiences air forces that are periodic functions of the rotational frequency. This phenomenon can occur when the blades operate in the wake of the support tower and the nonuniform velocity field near the ground due to wind shear. Results from this method were compared with measured sound spectra taken at locations of one to two rotor diameters from the DOE/NASA Mod-1 wind turbine. The calculated spectra generally agreed with the measured data in both the amplitude of the predominant harmonics and the roll of rate with frequency. Measured sound pressure levels far from the Mod-1 (15 rotor diameters), however, were higher than predicted. Simultaneous measurements in the near and far field indicated that the propagation effects could enhance the sound levels by more than 10 dB above that expected by spherical dispersion. These propagation effects are believed to be due to terrain and atmospheric characteristics of the Mod-1 site.

Viterna, L. A.↗

The effects of a hot outer atmosphere on acoustic-gravity waves

We examine the effects of a hot chromosphere and corona on acoustic-gravity waves in the Sun. We use a simple solar model consisting of a neutrally stable polytrope smoothly matched to an isothermal chromosphere or corona. The temperature of the isothermal region is higher than the minimum temperature of the model. We ignore sphericity, magnetic fields, changes in the gravitational potential, and nonadiabatic effects. We find a family of atmospheric g-modes whose cavity is formed by the extremum in the buoyancy frequency at the transition region. The f-mode is the zero-order member of this family. For large values of the harmonic degree l, f-mode frequencies are below the classic f-mode frequency, mu=(gk)(exp 1/2), whereas at small values of l, the f-mode is identical to the classical f-mode solution. We also find a family of g-modes residing in the low chromosphere. Frequency shifts of p-modes can be positive or negative. When the frequency is less than the acoustic cutoff frequency of the upper isothermal atmsophere, the frequency of the upper isothermal atmosphere, the frequency shift is negative, but when the frequency is above this cutoff, the shifts can be positive. High-frequency acoustic waves which are not reflected by the photospheric cutoff are reflected at the corona by the high sound speed for moderate values of l and v. This result is independent of the solar model as long as the corona is very hot. The data are inconsistent with this result, and reasons for this discrepancy are discussed.

Hindman, Bradley W.↗

Geodesic synchrotron radiation

This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits, a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions.

Breuer, R. A.↗

Dephasingless two-color terahertz generation

A laser pulse composed of a fundamental and an appropriately phased second harmonic can drive a time-dependent current of photoionized electrons that generates broadband THz radiation. Over the propagation distances relevant to many experiments, dispersion causes the relative phase between the harmonics to evolve. This “dephasing” slows the accumulation of THz energy and results in a multi-cycle THz pulse with significant angular dispersion. Here, we introduce a novel optical configuration that compensates the relative phase evolution, allowing for the formation of a half-cycle THz pulse with almost no angular dispersion. The configuration uses the spherical aberration of an axilens to map a prescribed radial phase variation in the near field to a desired longitudinal phase variation in the far field. Simulations that combine this configuration with an ultrashort flying focus demonstrate the formation of a half-cycle THz pulse with a controlled emission angle and 1/4 the angular divergence of the multi-cycle pulse created by a conventional optical configuration.

47 OTHER INSTRUMENTATION↗

MHD-induced SOL filaments and divertor heat flux striations in NSTX

Magnetohydrodynamic (MHD) activity in NSTX has been found to induce striated heat flux patterns at the divertor. These striated heat fluxes were previously interpreted as strike-point splitting caused by stochastic magnetic lobes near the X-point. Recent analysis indicates that MHD can directly generate filaments in the scrape-off layer (SOL), and the MHD-related filaments are consistent with the rotation and the frequency of the MHD. Magnetic field line tracing from the mid-plane of the MHD-related filaments to the divertor is consistent with the location of striated heat fluxes on the divertor. Additionally, gas puff imaging (GPI) diagnostic data shows the generation of regular blobs following each edge harmonic oscillation (EHO) toroidal mode number n = 1 perturbation, which indicates that the MHD perturbation directly drives the blobs. These blobs are responsible for the divertor heat flux striations. Here, this finding provides a new framework for understanding MHD-induced edge transport and has important implications for heat-load control in NSTX-U and future spherical tokamaks.

MHD↗