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Optimum thrust nozzle contours for chemically reacting gas flows, obtaining set of partial differential equations for gas dynamic properties
Optimum thrust nozzle contours for chemically reacting gas flows, obtaining set of partial differential equations for gas dynamic properties
Dual-shaped reflectors have been used for many years. Thus, these reflectors have been used as high gain antennas on Voyagers 1 and 2. The objectives of the geometrical optics (GO) dual shaped synthesis are considered. Concerning the synthesis of dual shaped reflectors, it has been shown for circular symmetric reflectors that an exact GO solution can be found to the problem of transforming, by two reflections, any feed pattern into any aperture distribution. This problem involves solving two simultaneous nonlinear ordinary differential equations. The same approach for offset geometry leads to two simultaneous nonlinear partial differential equations. It is shown that these equations could also be integrated numerically, except that in general these equations are not total and therefore, in general, they do not have a 'smooth' solution. It is further shown that the offset partial differentials often very nearly form a total differential in many cases of practical importance.
Absolute differential, integral, and momentum-transfer cross sections for electrons elastically scattered from helium are reported for the impact energy range of 5 to 200 eV. Angular distributions for elastically scattered electrons are measured in a crossed-beam geometry using a collimated, differentially pumped atomic-beam source which requires no effective-path-length correction. Below the first inelastic threshold the angular distributions were placed on an absolute scale by use of a phase-shift analysis. Above this threshold, the angular distributions from 10 to 140 deg were fitted using the phase-shift technique, and the resulting integral cross sections were normalized to a semiempirically derived integral elastic cross section. Depending on the impact energy, the data are estimated to be accurate to within 5 to 9%.
Analyses and numerical procedures are presented for infrared radiative energy transfer in gases when other modes of energy transfer occur simultaneously. Two types of geometries are considered, a parallel plate duct and a circular duct. Fully developed laminar incompressible flows of absorbing-emitting species in black surfaced ducts are considered under the conditions of uniform wall heat flux. The participating species considered are OH, CO, CO2, and H2O. Nongray as well as gray formulations are developed for both geometries. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. Tien and Lowder's wide band model correlation was used in nongray formulation. Numerical procedures are presented to solve the integro-differential equations for both geometries. The range of physical variables considered are 300 to 2000 K for temperature, 0.1 to 100.0 atm for pressure, and 0.1 to 100 cm spacings between plates/radius of the tube. An extensive parametric study based on nongray formulation is presented. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows.
We have previously given well-set exterior differential systems for Ricci-flat 4-geometries as.
Transferred electron bulk negative differential conductivity devices, analyzing combined doping and geometry effects on space charge and domain dynamics
The process of 'differential memory' in the earth's magnetotail is studied in the framework of the modified Harris magnetotail geometry. It is verified that differential memory can generate non-Maxwellian features in the modified Harris field model. The time scales and the potentially observable distribution functions associated with the process of differential memory are investigated, and it is shown that non-Maxwelllian distributions can evolve as a test particle response to distribution function boundary conditions in a Harris field magnetotail model. The non-Maxwellian features which arise from distribution function mapping have definite time scales associated with them, which are generally shorter than the earthward convection time scale but longer than the typical Alfven crossing time.
The fast computation of geometry control in adaptive truss structures involves two distinct parts: the efficient integration of the inverse kinematic differential equations that govern the geometry control and the fast computation of the Jacobian, which appears on the right-hand-side of the inverse kinematic equations. This paper present an efficient parallel implementation of the Jacobian computation on an MIMD machine. Large speedup from the parallel implementation is obtained, which reduces the Jacobian computation to an O(M-squared/n) procedure on an n-processor machine, where M is the number of members in the adaptive truss. The parallel algorithm given here is a good candidate for on-line geometry control of adaptive structures using attached processors.
Functional differential equation applications using geometric approach
Utilizing a crossed electron-beam-molecular-beam scattering geometry, relative values of differential electron scattering cross sections for cesium chloride at 5 and 20 eV electron impact energies and at scattering angles between 10 and 120 deg have been measured. These relative cross sections have been normalized to the cross section at 15 deg scattering angle calculated by the hybrid S-matrix technique. In the angular range between 0 and 10 deg and between 120 and 180 deg extrapolations have been made to obtain integral and momentum transfer cross sections. An energy-loss spectrum is also presented which gives various spectral features lying between the 4 and 10 eV regions in CsCl.
The numerical solution of partial differential equations about irregular geometries and with varying characteristic scales has created the need for coordinate systems and associated transformations which reflect both geometric and physical requirements. The process of finding coordinate transformations in discrete representations is called 'grid generation'. The present investigation is concerned with three algebraic grid generation methods. The methods include transfinite interpolation, the multisurface method, and the two-boundary technique. Interpolation formulas, in terms of homotopic mappings and constraints in terms of point positions and/or derivatives are the essential elements of the techniques. The methods are relatively simple to understand, they are explicit and do not require extensive computational effort, and they have a high degree of generality.
A differential equation governing the geometry of a two-dimensional ballute in hypersonic flow and its constraining boundary conditions are derived under idealized assumptions. By solving these equations, the shape of the ballute is determined over a range of conditions. Lift, drag, pitching moment, and the allowed limit of center-of-gravity location for stability (meta-center) are then calculated using Newtonian hypersonic approximation. It is shown that the meta-center occurs near the forward end because of compliance of the ballute membrane to the shock layer pressures, especially at low free-stream densities. In order for the vehicle employing the ballute to be stable at all densities, the center of gravity must be within approximately the forward 20 percent of overall length of the vehicle. However, typical flight trajectories of an aeroassisted orbital transfer vehicle employing the ballute for aerobraking show that the vehicle may be able to complete its atmospheric flight without tumbling provided that the center of gravity is located within the forward 43 percent of the vehicle length because of the relatively short duration of flight through the destabilizing low-density regime.
The influence is investigated of a curvilinear fiber format on load carrying capacity of a layered fiber reinforced plate with a centrally located hole. A curvilinear fiber format is descriptive of layers in a laminate having fibers which are aligned with the principal stress directions in those layers. Laminates of five curvilinear fiber format designs and four straightline fiber format designs are considered. A quasi-isotropic laminate having a straightline fiber format is used to define a baseline design for comparison with the other laminate designs. Four different plate geometries are considered and differentiated by two values of hole diameter/plate width equal to 1/6 and 1/3, and two values of plate length/plate width equal to 2 and 1. With the plates under uniaxial tensile loading on two opposing edges, alignment of fibers in the curvilinear layers with the principal stress directions is determined analytically by an iteration procedure. In-plane tensile load capacity is computed for all of the laminate designs using a finite element analysis method. A maximum strain failure criterion and the Tsai-Wu failure criterion are applied to determine failure loads and failure modes. Resistance to buckling of the laminate designs to uniaxial compressive loading is analyzed using the commercial code Engineering Analysis Language. Results indicate that the curvilinear fiber format laminates have higher in-plane tensile load capacity and comparable buckling resistance relative to the straightline fiber format laminates.
NASA's Descent System Studies (DSS) Program is studying various concept vehicles to enable landing of heavy payloads on the surface of Mars. While it is desirable to run high-fidelity CFD simulations to accurately assess the aerodynamic and aerothermal effects of various design changes during EDL, it is usually difficult to quickly generate high-quality grids suitable for such analyses. One approach to address this bottleneck in mesh generation is through the use oversetting grids. Although the overset approach is efficient and powerful in solving partial differential equations on complex geometries, new users often find it challenging to apply overset concepts for their simulations. For example, generating hyperbolic grids with sufficient overlap; priority in hole-cutting on multiple overlapping grids; and fixes to assemble overlapping viscous grids at the body surface. The objective of this presentation is to introduce a simple process that combines the advantages of near-body, point-matched, structured grids with oversetting background grids suitable for grid alignment. This approach allows for grids that can be sequenced, reclustering of mesh spacing at the wall, and grid alignment with the bow shock. The current methodology is tested on a Mid-L/D configuration using the overset DPLR code.
An interesting new high-energy pulsar sub-population is emerging following early discoveries of gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope (LAT). We present results from 3D emission modeling, including the Special Relativistic effects of aberration and time-of-flight delays and also rotational sweepback of 13-field lines, in the geometric context of polar cap (PC), slot gap (SG), outer gap (OG), and two-pole caustic (TPC) pulsar models. In contrast to the general belief that these very old, rapidly-rotating neutron stars (NSs) should have largely pair-starved magnetospheres due to the absence of significant pair production, we find that most of the light curves are best fit by SG and OG models, which indicates the presence of narrow accelerating gaps limited by robust pair production -- even in these pulsars with very low spin-down luminosities. The gamma-ray pulse shapes and relative phase lags with respect to the radio pulses point to high-altitude emission being dominant for all geometries. We also find exclusive differentiation of the current gamma-ray MSP population into two MSP sub-classes: light curve shapes and lags across wavebands impose either pair-starved PC (PSPC) or SG / OG-type geometries. In the first case, the radio pulse has a small lag with respect to the single gamma-ray pulse, while the (first) gamma-ray peak usually trails the radio by a large phase offset in the latter case. Finally, we find that the flux correction factor as a function of magnetic inclination and observer angles is typically of order unity for all models. Our calculation of light curves and flux correction factor f(_, _, P) for the case of MSPs is therefore complementary to the "ATLAS paper" of Watters et al. for younger pulsars.
Navigation strategies for determining highly elliptical orbits with VLBI are described. The predicted performance of wideband VLBI and Delta VLBI measurements obtained by orthogonal baseline pairs are compared for a 16-hr equatorial orbit. It is observed that the one-sigma apogee position accuracy improves two orders of magnitude to the meter level when Delta VLBI measurements are added to coherent Doppler and range, and the simpler VLBI strategy provides nearly the same orbit accuracy. The effects of differential measurement noise and acquisition geometry on orbit accuracy are investigated. The data reveal that quasar position uncertainty limits the accuracy of wideband Delta VLBI measurements, and that polar motion and baseline uncertainties and offsets between station clocks affect the wideband VLBI data. It is noted that differential one-way range (DOR) has performance nearly equal to that of the more complex Delta DOR and is recommended for use on spacecraft in high elliptical orbits.
The ADIFOR2.0 automatic differentiator is applied to the FPX rotor code along with the grid generator GRGN3. The FPX is an eXtended Full-Potential CFD code for rotor calculations. The automatic differentiation version of the code is obtained, which provides both non-geometry and geometry sensitivity derivatives. The sensitivity derivatives via automatic differentiation are presented and compared with divided difference generated derivatives. The study shows that automatic differentiation method gives accurate derivative values in an efficient manner.