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Magnetic fields coupled through apertures in an aircraft structure were calculated. These fields were shown to be important since some apertures are quite large and since the waveshape of interior fields is not retarded but tends to be the same for small apertures as for that of the external magnetic field. Aperture geometry and reflecting surfaces were considered for computations of field strength and direction.
Accurate and efficient numerical simulation of flows through turbomachinery blade rows depends on the topology of the computational grids. These grids must reflect the periodic nature of turbomachinery blade row geometries and conform to the blade shapes. Three types of grids can be generated that meet these minimal requirements: through-flow grids, O-type grids, and C-type grids. A procedure which can be used to generate all three types of grids is presented. The resulting grids are orthogonal and can be stretched to capture the essential physics of the flow. A discussion is also presented detailing the extension of the generation procedure to three dimensional geometries.
The theory of X-ray diffraction by periodic structures is applied to the layered synthetic microstructures (LSMs) made possible by recent developments in thin film technology, and approximate formulas for estimating their performance are presented. A more complete computation scheme based on optical multilayer theory is also described, and it is shown that the diffracting properties may be tailored to specific applications by adjusting the refractive indices and thicknesses of the component layers. The theory may be modified to take account of imperfections in the LMS structure, and the properties of nonperiodic structures thereby computed. Structures with high integrated reflectivity constructed according to the methods defined have potential application in many areas of X-ray or EUV research and instrumentation.
The relative importance of aerosol optical thickness and absorption is illustrated through computing radiances for radiative transfer models. The radiance of sunlight reflected from models of the earth-atmosphere system is computed as a function of the aerosol optical thickness and its albedo of single scattering; it is noted that the albedo varies from 0.6 in urban environment to nearly 1 in areas with low graphitic carbon content. The calculations are applied to the example of satellite measurements of biomass. It is found that when surface classifications are made by means of clustering techniques the presence of gradients in the aerosol optical properties results in the dispersion of points in the plot correlating radiances viewed in two different directions. Finally, though such a remote sensing parameter as contrast is weakly affected by aerosol absorption, it is highly dependent on its optical thickness.
Mean-square errors of antenna surface reduced. Compensating function helps point deformable antenna without inducing excessive pointing oscillations or deformations of reflecting surface. When implemented on computer in real time, function enables calculation of control signals in response to several sensor inputs: Function devised so signals control torque actuator of antenna-pointing mechanism in way to reduce or minimize squares of errors of antenna surface over long time.
A numerical method is presented for calculating the three-dimensional unsteady, transonic flow past a helicopter rotor blade of arbitrary geometry. The method solves the full-potential equations in a blade-fixed frame of reference by a time-marching implicit scheme. At the far-field, a set of first-order radiation conditions is imposed, thus minimizing the reflection of outgoing wavelets from computational boundaries. Computed results are presented to highlight radial flow effects in three dimensions, to compare surface pressure distributions to quasi-steady predictions, and to predict the flow field on a swept-tip blade. The results agree well with experimental data for both straight- and swept-tip blade geometries.
An explanation based upon reaction kinetics is presented to account for the deviation of measured ionization levels obtained from reflection experiments from the values computed assuming chemical equilibrium. The heat transfer to the unburned fuel is also considered.
An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.
From the viewpoint of a project manager responsible for the V&V (verification and validation) of a software system, mathematical verification techniques provide a possibly useful orthogonal dimension to otherwise standard empirical testing. However, the value they add to an empirical testing regime both in terms of coverage and in fault detection has been difficult to quantify. Furthermore, potential cost savings from replacing testing with mathematical verification techniques cannot be realized until the tradeoffs and synergies can be formulated. Integration of formal verification with empirical testing is also difficult because the idealized view of mathematical verification providing a correctness proof with total coverage is unrealistic and does not reflect the limitations imposed by computational complexity of mathematical techniques. This paper first describes a framework based on software reliability and formalized fault models for a theory of software design fault detection - and hence the utility of various tools for debugging. It then describes a utility model for integrating mathematical and empirical techniques with respect to fault detection and coverage analysis. It then considers the optimal combination of black-box testing, white-box (structural) testing, and formal methods in V&V of a software system. Using case studies from NASA software systems, it then demonstrates how this utility model can be used in practice.
Spin-stabilization maneuvers are typically performed by spacecraft entering low-earth orbit to maintain attitude stability. These maneuvers induce periodic fluid movement inside the spacecraft's propellant tank known as fuel slosh, which is responsible for creating forces and moments on the sidewalls of the propellant tank. These forces and moments adversely affect spin-stabilization and risk jeopardizing the mission of the spacecraft. Therefore, propellant tanks are designed with propellant management devices (PMD's) such as barnes or diaphragms which work to counteract the forces and moments associated with fuel slosh. However, despite the presence of PMD's, the threat of spin-stabilization interference still exists should the propellant tank be excited at its natural frequency. When the fluid is excited at its natural frequency, the forces and moments acting on the propellant tank are amplified and may result in destabilizing the spacecraft. Thus, a computational analysis is conducted concerning diaphragm-implemented propellant tanks excited at their natural frequencies. Using multi-disciplinary computational fluid dynamics (CFD) software, computational models are developed to reflect potential scenarios that spacecraft propellant tanks could experience. By simulating the propellant tank under a wide array of parameters and variables including fill-level, gravity and diaphragm material and shape, a better understanding is gained as to how these parameters individually and collectively affect liquid propellant tanks and ultimately, spacecraft attitude dynamics.
An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.
In this paper, we report a version of the Space-Time Conservation Element and Solution Element (CE/SE) Method in which the 2D and 3D unsteady Euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes, respectively. In the present method, mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for. At each mesh point, the value of a flow variable is obtained by imposing a flux conservation condition. On the other hand, the spatial derivatives are evaluated using a finite-difference/weighted-average procedure. Note that the present extension retains many key advantages of the original CE/SE method which uses triangular and tetrahedral meshes, respectively, for its 2D and 3D applications. These advantages include efficient parallel computing ease of implementing non-reflecting boundary conditions, high-fidelity resolution of shocks and waves, and a genuinely multidimensional formulation without using a dimensional-splitting approach. In particular, because Riemann solvers, the cornerstones of the Godunov-type upwind schemes, are not needed to capture shocks, the computational logic of the present method is considerably simpler. To demonstrate the capability of the present method, numerical results are presented for several benchmark problems including oblique shock reflection, supersonic flow over a wedge, and a 3D detonation flow.
Category 1, Problems 1 and 2, Category 2, Problem 2, and Category 3, Problem 2 are solved computationally using the Dispersion-Relation-Preserving (DRP) scheme. All these problems are governed by the linearized Euler equations. The resolution requirements of the DRP scheme for maintaining low numerical dispersion and dissipation as well as accurate wave speeds in solving the linearized Euler equations are now well understood. As long as 8 or more mesh points per wavelength is employed in the numerical computation, high quality results are assured. For the first three categories of benchmark problems, therefore, the real challenge is to develop high quality numerical boundary conditions. For Category 1, Problems 1 and 2, it is the curved wall boundary conditions. For Category 2, Problem 2, it is the internal radiation boundary conditions inside the duct. For Category 3, Problem 2, they are the inflow and outflow boundary conditions upstream and downstream of the blade row. These are the foci of the present investigation. Special nonhomogeneous radiation boundary conditions that generate the incoming disturbances and at the same time allow the outgoing reflected or scattered acoustic disturbances to leave the computation domain without significant reflection are developed. Numerical results based on these boundary conditions are provided.
An absorbing non-reflecting boundary condition (NRBC) for practical computations in fluid dynamics and aeroacoustics is presented with theoretical proof. This paper is a continuation and improvement of a previous paper by the author. The absorbing NRBC technique is based on a first principle of non reflecting, which contains the essential physics that a plane wave solution of the Euler equations remains intact across the boundary. The technique is theoretically shown to work for a large class of finite volume approaches. When combined with the hyperbolic conservation laws, the NRBC is simple, robust and truly multi-dimensional; no additional implementation is needed except the prescribed physical boundary conditions. Several numerical examples in multi-dimensional spaces using two different finite volume schemes are illustrated to demonstrate its robustness in practical computations. Limitations and remedies of the technique are also discussed.
An optical transfer function was computed for the retroreflector array carried by the Starlette satellite (1975 10A). The range correction is given for extrapolating laser range measurements to the center of mass of the satellite. The gain function and active reflecting area of the array are computed for estimating laser-echo signal strengths.
The temperature of spacecraft is influenced by the solar absorptance and thermal emittance of the external spacecraft materials. Optical and thermal properties can degrade over time in the harsh low Earth orbital (LEO) space environment where spacecraft external materials are exposed to various forms of radiation, thermal cycling, and atomic oxygen. Therefore, it is important to test the durability of spacecraft materials in the space environment. One objective of the Polymers and Zenith Polymers Experiments was to determine the effect of LEO space exposure on the optical properties of various spacecraft polymers. These experiments were flown as part of the Materials International Space Station Experiment 7 (MISSE 7) mission on the exterior of the International Space Station (ISS) for 1.5 years. Samples were flown in ram, wake or zenith directions, receiving varying amounts of atomic oxygen and solar radiation exposure. Total and diffuse reflectance and transmittance of flight and corresponding control samples were obtained post-flight using a Cary 5000 UV-Vis-NIR Spectrophotometer. Integrated air mass zero solar absorptance (s) of the flight and control samples were computed from the total transmittance and reflectance, and compared. The optical data are compared with similar polymers exposed to space for four years as part of MISSE 2, and with atomic oxygen erosion data, to help understand the degradation of these polymers in the space environment. Results show that prolonged space exposure increases the solar absorptance of some materials. Knowing which polymers remain stable will benefit future spacecraft design.
Rectangular-waveguide inserts that are made of non-ferromagnetic metals and are sized and shaped to function as notch filters have been conceived as reference standards for use in the rectangular- waveguide method of characterizing materials with respect to such constitutive electromagnetic properties as permittivity and permeability. Such standards are needed for determining the accuracy of measurements used in the method, as described below. In this method, a specimen of a material to be characterized is cut to a prescribed size and shape and inserted in a rectangular- waveguide test fixture, wherein the specimen is irradiated with a known source signal and detectors are used to measure the signals reflected by, and transmitted through, the specimen. Scattering parameters [also known as "S" parameters (S11, S12, S21, and S22)] are computed from ratios between the transmitted and reflected signals and the source signal. Then the permeability and permittivity of the specimen material are derived from the scattering parameters. Theoretically, the technique for calculating the permeability and permittivity from the scattering parameters is exact, but the accuracy of the results depends on the accuracy of the measurements from which the scattering parameters are obtained. To determine whether the measurements are accurate, it is necessary to perform comparable measurements on reference standards, which are essentially specimens that have known scattering parameters. To be most useful, reference standards should provide the full range of scattering-parameter values that can be obtained from material specimens. Specifically, measurements of the backscattering parameter (S11) from no reflection to total reflection and of the forward-transmission parameter (S21) from no transmission to total transmission are needed. A reference standard that functions as a notch (band-stop) filter can satisfy this need because as the signal frequency is varied across the frequency range for which the filter is designed, the scattering parameters vary over the ranges of values between the extremes of total reflection and total transmission. A notch-filter reference standard in the form of a rectangular-waveguide insert that has a size and shape similar to that of a material specimen is advantageous because the measurement configuration used for the reference standard can be the same as that for a material specimen. Typically a specimen is a block of material that fills a waveguide cross-section but occupies only a small fraction of the length of the waveguide. A reference standard of the present type (see figure) is a metal block that fills part of a waveguide cross section and contains a slot, the long dimension of which can be chosen to tailor the notch frequency to a desired value. The scattering parameters and notch frequency can be estimated with high accuracy by use of commercially available electromagnetic-field-simulating software. The block can be fabricated to the requisite precision by wire electrical-discharge machining. In use, the accuracy of measurements is determined by comparison of (1) the scattering parameters calculated from the measurements with (2) the scattering parameters calculated by the aforementioned software.
The author has identified the following significant results. Bands 4, 5, and 7 and 5, 6, and 7 were best for distinguishing among crop and soil categories in ERTS-1 SCENES 1182-16322 (1-21-73) and 1308-16323 (5-21-73) respectively. Chlorotic sorghum areas 2.8 acres or larger in size were identified on a computer printout of band 5 data. Reflectance of crop residues was more often different from bare soil in band 4 than in bands 5, 6, and 7. Simultaneously acquired aircraft and spacecraft MSS data indicated that spacecraft surveys are as reliable as aircraft surveys. ERTS-1 data were successfully used to estimate acreage of citrus, cotton, and sorghum as well as idle crop land.