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At least 451 records · Page 25

Effect of the Reconnection Electric Field on Electron Distribution Functions in the Diffusion Region of Magnetotail Reconnection

Electron distribution functions in the electron diffusion region during symmetric magnetic reconnection are investigated by means of theory and fully kinetic simulations. Crescent‐like striations are formed in distribution functions in the velocity plane perpendicular to the magnetic field. Using an analytical current sheet, we solve the equation of motion for electrons, and derive the shape of a crescent distribution, as a function of the distance from the neutral line, field gradients, and the reconnection electric field. Each crescent is tilted in the velocity plane because of the acceleration by the reconnection electric field, and multiple stripes appear due to multiple meandering bounces. Applying the theory to distribution functions observed in Earth's magnetotail, we deduce the amplitude of the reconnection electric field.

Bessho, N.↗

Fast and Reliable Approximations for Interplanetary Low-Thrust Transfers

A three-step process bridges the gap between lower-fidelity solutions that ignore optimal dynamics and fully optimized solutions that are computationally expensive to generate. First, analytic solutions for transfers with free time and angle characterize the evolution of the shape and orientation of the orbit. Next, optimal control theory supplies the thrust vector with variable specific impulse while satisfying flight time and transfer angle constraints. Transfers with the additional constraint of constant specific impulse then provide a more realistic thruster model for preliminary trade studies. These approximations deliver a hundredfold improvement in run time at the expense of a few percent error in mass.

Landau, Damon↗

The Dynamics of Ultrasonically Levitated Drops in an Electric Field

Ultrasonic and electrostatic leviation techniques have allowed the experimental investigation of the nonlinear oscillatory dynamics of free droplets with diameter between 0.1 and 0.4 cm. The measurement of the resonance frequencies of the first three normal modes of large amplitude shape oscillations in an electric field of varying magnitude has been carried out with and without surface charges for weakly conducting liquids in air. These oscillations of nonspherical levitated drops have been driven by either modulating the ultrasonic field or by using a time-varying electric field, and the free decay from the oscillatory state has been recorded. A decrease in the resonance frequency of the driven fundamental quadrupole mode has been measured for increasing oblate deformation in the absence of an electric field. Similarly, a decrease in this frequency has also been found for increasing DC electric field magnitude. A soft nonlinearity exists in the amplitude dependence of the resonant mode frequencies for freely decaying as well as ultrasonically and electrically driven uncharged drops. This decrease in resonance frequency is accentuated by the presence of free surface charge on the drop. Subharmonic resonance excitation has been observed for drops in a time-varying electric field, and hysteresis exists for resonant modes driven to large amplitude. Mode coupling from lower-order resonances to higher-order modes has been found to be very weak, even for fairly large amplitude shape oscillations. Most of these results are in general agreement with predictions from recent analytical and numerical investigations.

Ultrasonically↗

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗

Flow analysis and design optimization methods for nozzle afterbody of a hypersonic vehicle

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the three dimensional Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Argon. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. In the second phase of this project, the Aerodynamic Design Optimization with Sensitivity analysis (ADOS) was developed. Pre and post optimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Baysal, Oktay↗

Simple Analytical Expressions for Electron Pitch Angle Diffusion Coefficients

In the present paper, we have calculated electron pitch angle diffusion coefficients due to resonant interactions with whistler mode lower band chorus (LBC), upper band chorus (UBC), and electrostatic electron cyclotron harmonic (ECH) waves. Calculations have been performed at two values of the ratio of electron plasma frequency to gyro-frequency and thirteen representative values of electron energies for the plasma sheet electrons. The numerical data of diffusion coefficients have been fitted to simple analytical expressions for each wave mode. These analytical expressions allow for simple evaluation of pitch angle diffusion coefficients for the arbitrary pitch angle, energy, the ambient magnetic field, the wave amplitude, and the ratio of plasma frequency to gyro-frequency. In the case of LBC waves, the analytical coefficients are generally within a factor of two to the numerical coefficients, except at higher pitch angles where the numerical coefficients drop to show negligible values. Likewise, also for UBC waves, the analytical coefficients are generally within a factor of two to the numerical coefficients. The analytical coefficients for ECH waves are generally in agreement with numerical coefficients. However, the analytical expressions developed for ECH waves do not reproduce sharp fluctuations, dips, and gaps, the so-called banded structure observed in the data of numerical coefficients. The effect of the shape variation on the profile of the wave spectral intensity and the effect of cold temperature on the numerical coefficients are also investigated. Applications of the analytical expressions of diffusion coefficients are discussed.

coefficients↗

Experimental measurements of the rotating frequencies and mode shapes of a full scale helicopter rotor in a vacuum and correlations with calculated results

This paper presents results of an experimental program conducted to obtain data which can be used for correlations of rotor blade dynamic analyses. Measurements were made of the rotating frequencies and mode shapes of a representative full-scale, two-bladed helicopter rotor in a vacuum. The blades were cantilevered to the hub. Mode shape data were obtained optically using a system of cameras developed specifically for this purpose. Excitation of the rotor was provided by vertical oscillatory motion of the hub. To compare experimental and analytical results, correlations of some experimental measurements with calculations from an existing blade modes computer program based on a Holzer-Myklestad procedure are presented, and the differences between the results are discussed. The experimental and analytical natural frequencies were generally in good agreement as were the principal components of the modal deflections for the flap and lag modes. The torsion mode shape indicated disagreement between the measured and calculated results in regard to the amount of flap and lag motions present in this mode, while the spanwise variations of the measured and calculated torsional components were in agreement.

Lee, B. L.↗

Analysis of Seismic Signals Generated by Vehicle Traffic with Application to Derivation of Subsurface Q-Values

Correct identification and modeling of anthropogenic sources of ground motion are of considerable importance for many studies, including detection of small earthquakes and imaging seismic properties below the surface. Here, to understand signals generated by common vehicle traffic, we use seismic data recorded by closely spaced geophones normal to roads at two sites on San Jacinto fault zone. To quantify the spatiotemporal and frequency variations of the recorded ground motions, we develop a simple analytical solution accounting for propagation and attenuation of surface waves. The model reproduces well-observed bell-shaped spectrograms of car signals recorded by geophones close to roads, and it can be used to estimate frequency-dependent Q-values of the subsurface materials. The data analysis indicates Q-values of 3–40, for frequencies up to 150 Hz for road-receiver paths at the two examined sites. The derived Q-values are consistent with attenuation factors of surface waves previously obtained with other methods. The analytical results and analysis procedure provide a highly efficient method for deriving Q-values of shallow subsurface materials.

58 GEOSCIENCES↗

Acoustic Rectification in Dispersive Media

It is shown that the shapes of acoustic radiation-induced static strain and displacement pulses (rectified acoustic pulses) are defined locally by the energy density of the generating waveform. Dispersive properties are introduced analytically by assuming that the rectified pulses are functionally dependent on a phase factor that includes both dispersive and nonlinear terms. The dispersion causes an evolutionary change in the shape of the energy density profile that leads to the generation of solitons experimentally observed in fused silica.

Cantrell, John H.↗

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Analytical approximation of a distorted reflector surface defined by a discrete set of points

Reflector antennas on Earth orbiting spacecrafts generally cannot be described analytically. The reflector surface is subjected to a large temperature fluctuation and gradients, and is thus warped from its true geometrical shape. Aside from distortion by thermal stresses, reflector surfaces are often purposely shaped to minimize phase aberrations and scanning losses. To analyze distorted reflector antennas defined by discrete surface points, a numerical technique must be applied to compute an interpolatory surface passing through a grid of discrete points. In this paper, the distorted reflector surface points are approximated by two analytical components: an undistorted surface component and a surface error component. The undistorted surface component is a best fit paraboloid polynomial for the given set of points and the surface error component is a Fourier series expansion of the deviation of the actual surface points, from the best fit paraboloid. By applying the numerical technique to approximate the surface normals of the distorted reflector surface, the induced surface current can be obtained using physical optics technique. These surface currents are integrated to find the far field radiation pattern.

Acosta, Roberto J.↗

Analytic Study of Induced Pressure on Long Bodies of Revolution with Varying Nose Bluntness at Hypersonic Speeds

Pressure distributions and shock shapes for a series of cylindrical afterbodies having nose fineness ratios from 0.4 to 4 have been calculated by using the method of characteristics for a perfect gas. The fluid mediums investigated were air and helium and the Mach number range was from 5 to 40. Flow parameters obtained from blast-wave analogy gave good correlations of blunt-nose induced pressures and shock shapes. Experimental results are found to be in good agreement with the characteristic calculations. The concept of hypersonic similitude enables good correlation of the results with respect to body shape, Mach number, and ratio of specific heats.

VanHise, Vernon↗

Separable shape tensors for aerodynamic design

Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of two-dimensional (2D) and three-dimensional (3D) aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, and translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers: (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.

42 ENGINEERING↗

Simulations of biomass pyrolysis using glued-sphere CFD-DEM with 3-D intra-particle models

The shape of biomass particles influences intra-particle heat transfer, particle-particle collisions, interphase momentum, heat transfer, and pyrolysis yield. In this research, the effects of these multi-scale phenomena are captured using a glued-sphere computational fluid dynamic discrete element method (CFD-DEM) with 3-D intra-particle models. The glued-spheres resolved the shapes of particles and intra-particle temperature and species distributions. The implementation was validated using the pyrolysis data of a spherical particle and a cylindrical particle. Then, the influences of biomass shapes and sizes on pyrolysis were investigated. The results revealed the significant influence of surface areas and mass distributions on interphase heat transfer and chemical reactions. The intra-particle heat transfer is neglectable for a Biot number smaller than 0.41. Finally, the pyrolysis of irregularly shaped biomass particles in a fixed bed, fluidized bed, and spouted bed was simulated. Analysis of conversion distributions showed the largest deviations in the fixed bed and the slowest conversion rate in the spouted bed. A good balance between uniform and fast conversion is achieved in the fluidized bed. The multi-scale method proposed in this research provides a tool for the evaluation of large irregular-shaped biomass particle pyrolysis in different types of reactors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The effects of seeing on the reflected spectrum of Uranus and Neptune

The results of a redetermination of the rotational periods of Uranus and Neptune, based on spectrograms obtained with the coude spectrograph of the 5 m Hale telescope, are presented. The effects of image motion on the shape of the spectral lines reflected by a planet rotating as a solid body and coherently scattering solar light, has been studied analytically. A general relation between the seeing transformed velocities at any point on the disk and those at the equator is established. It is shown that, for the case of Gaussian seeing, the brightness continuum of the smeared disk contains all the information required to derive the shape of the reflected lines. The shift, change in r.m.s. width, and asymmetry of the seeing transformed lines at the equator have been numerically evaluated for the brightness distribution of Uranus determined from Stratoscope II.

Muench, G.↗

Interacting dust grains in complex plasmas: Ion wake formation and the electric potential

Dust grains have been used as minimally invasive probes to determine plasma parameters including the plasma density, temperature, and electric field in a plasma discharge. However, the dust grains in a plasma generate local potential disturbances due to the collection of charge and the subsequent electrostatic interactions between the dust and charged plasma particles. Dust grains in close proximity to one another exhibit interesting non-reciprocal interactions and self-organize into structures such as one-dimensional filamentary chains, two-dimensional “zigzags,” and three-dimensional helices, among others. The formation of these structures suggests that although the dust grains may be less invasive than traditional plasma probes, the disturbance to the local plasma environment introduced by dust grains is non-trivial. Commonly used analytic forms of the electric potential describing complex plasmas have failed to resolve the near-dust region, and as a result are insufficient to provide insight about the formation of complex dust structures. Here, we use an N-body simulation to compute the electric potential from ion densities near various dust grain configurations. We provide an alternative description to the standard analytic model for the electric potential of dust and ion wakes based on a Gaussian shaped cloud of ions. The electric potential obtained from simulations is used to identify minimum energy configurations for two and three dust grains. It is further demonstrated that the minimum potential region identified for N dust grains and their associated ion wakes does not predict the minimum-energy configuration of N + 1 dust grains.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stress-induced phase transitions in nanoscale CuInP 2 S 6

Using the Landau-Devonshire approach and available experimental results, we constructed multiwell thermodynamic potential of the layered ferroelectric CuInP 2 S 6 (CIPS). The analysis of temperature dependences of the dielectric permittivity and lattice constants for different applied pressures unexpectedly reveals the critically important role of a nonlinear electrostriction in this material. With the nonlinear electrostriction included we calculated the temperature and pressure phase diagrams and spontaneous polarization of a bulk CIPS, within the assumed range of applicable temperatures and applied pressures. Using the developed thermodynamic potential, we revealed the strain-induced phase transitions in thin epitaxial СIPS films, as well as the stress-induced phase transitions in СIPS nanoparticles, the shape of which varies from prolate needles to oblate disks. Furthermore, w also revealed the strong influence of a mismatch strain, elastic stress, and shape anisotropy on the phase diagrams and polar properties of a nanoscale CIPS, and derived analytical expressions allowing for elastic control of the nanoscale CIPS polar properties. Hence obtained results can be of particular interest for the strain engineering of nanoscale layered ferroelectrics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Input guide for computer programs to generate thermodynamic data for air and Freon CF4

FORTRAN computer programs were developed to calculate the thermodynamic properties of Freon 14 and air for isentropic expansion from given plenum conditions. Thermodynamic properties for air are calculated with equations derived from the Beattie-Bridgeman nonstandard equation of state and, for Freon 14, with equations derived from the Redlich-Quang nonstandard equation of state. These two gases are used in scale model testing of model rocket nozzle flow fields which requires simulation of the prototype plume shape with a cold flow test approach. Utility of the computer programs for use in analytical prediction of flow fields is enhanced by arranging card or tape output of the data in a format compatible with a method-of-characteristics computer program.

Tevepaugh, J. A.↗