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Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
A thermal distortion analysis of the ATS-6 Satellite parabolic reflector was performed using NASTRAN level 15.1. The same NASTRAN finite element method was used to conduct a one g static load analysis and a dynamic analysis of the reflector. In addition, a parametric study was made to determine which parameters had the greatest effect on the thermal distortions. The method used to model the construction of the reflector is described and the results of the analyses are presented.
Tests in which persons were subjected to a negative acceleration in an automobile are reported. The acceleration was obtained by stopping a moving car on the runway of an airport. The acceleration was found to produce a rotational movement of the subject's eyeball proportional to the degree of acceleration. Other investigations were conducted with a jet aircraft and a sports aircraft. G forces of up to 3 G were obtained during pull up of the aircraft, while values in the range from 0 to 1 G could be produced with the aid of a parabolic flight path. The effects of the flight conditions on the subject's direction of sight are discussed.
The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.
Extensive antenna-noise temperature measurements at 1.6 GHz (L-band) were made using a 1.2 m (4 ft. diameter) parabolic dish antenna mounted on the flying bridge of a modern 15,690-ton, commercial-container ship. Both in-harbor and at-sea radiometer measurements were made that indicated a steady background, antenna-noise temperature value slightly less than 70 degrees Kelvin (K) at elevation angles of 5 percent, and greater, at 1.6 GHz. A comparison of theoretical and measured values indicate excellent agreement within about 5K for at-sea data. These measurements are helpful to RF equipment designers of maritime, L-band shipboard terminals for operation with the two, geostationary, maritime satellites, Marisat-A and -B.
NASTRAN solution techniques are shown for a numerical analysis of a class of coupled vector flow processes described by simultaneous parabolic differential equations. To define one physical problem type where equations of this form arise, the differential equations describing the coupled transfers of heat and mass in mechanical equilibrium with negligible mass average velocity are presented and discussed. Also shown are the equations describing seepage when both electrokinetic and hydrodynamic forces occur. Based on a variational statement of the general problem type, the concepts of scalar transfer elements and parallel element systems are introduced. It is shown that adoptation of these concepts allows the direct use of NASTRAN's existing Laplace type elements for uncoupled flow (the heat transfer elements) for treating multicomponent coupled transfer. Sample problems are included which demonstrate the application of these techniques for both steady-state and transient problems.
A computer algorithm has been developed to determine the blunt-body flowfields supporting symmetric parabolic and paraboloidal shock waves at infinite free-stream Mach number. Solutions are expressed in an analytic form as high-order power series, in the coordinate normal to the shock, whose coefficients can be determined exactly. Analytic continuation is provided by the use of Pade approximations. Test cases provide solutions of very high accuracy. In the axisymmetric case for gamma equals 715 the solution has been found far downstream, where it agrees with the modified blast-wave results. For plane flow, on the other hand, a limit line appears within the shock layer, a short distance past the sonic line, suggesting the presence of an imbedded shock. Local solutions in the downstream limit are discussed.
A numerical method is presented which is valid for integration of the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to the three-dimensional supersonic flow of a jet issuing into a supersonic free stream. Difficulties associated with the imposition of free-stream boundary conditions are noted, and a coordinate transformation, which maps the point at infinity onto a finite value, is introduced to alleviate these difficulties. Results are presented for calculations of a square jet and varying-aspect-ratio rectangular jets. The solution behavior varies from axisymmetry for the square jet to nearly two-dimensional for the high-aspect-ratio rectangle, although the computation always calculates the flow as though it were truly three-dimensional.
The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations.
A prototype apparatus for exposing persons to rotation about their Z-axis in parabolic flight is described. Although it resembles earth-horizontal axis devices, added features are its strength and portability, and the fiber glass 'couch' with adjustable elements providing support and restraint. Even under ground-based conditions, this device provides unique opportunities for investigations involving not only canalicular and macular mechanoreceptors, but also touch, pressure, and kinesthetic receptor systems.
A numerical method is presented for solving the parabolic-elliptic Navier-Stokes equations. The solution procedure is applied to three-dimensional supersonic laminar jet flow issuing parallel with a supersonic free stream. A coordinate transformation is introduced which maps the boundaries at infinity into a finite computational domain in order to eliminate difficulties associated with the imposition of free-stream boundary conditions. Results are presented for an approximate circular jet, a square jet, varying aspect ratio rectangular jets, and interacting square jets. The solution behavior varies from axisymmetric to nearly two-dimensional in character. For cases where comparisons of the present results with those obtained from shear layer calculations could be made, agreement was good.
A segmented design and fabrication and assembly techniques were developed for a 1.8 m (6 ft) diameter parabolic concentrator for space application. This design and these techniques were adaptable to a low cost, mass-produced concentrator. Minimal machining was required. Concentrator segments of formed magnesium were used. The concentrator weighed only 1.6 kg sq m (0.32 lbm/sq ft).
A tutorial overview of point-focusing parabolic collectors is presented. Optical and thermal characteristics are discussed. Data representing typical achievable collector efficiencies are presented and the importance of balancing collector cost with concentrator quality is argued through the development of a figure of merit. Various types of two-axis tracking collectors are described. The Department of Energy program to develop these devices is briefly discussed, as are present and projected costs for these collectors.
Alternating direction implicit (ADI) schemes for two-dimensional parabolic equations with a mixed derivative are constructed by using the class of all A sub 0-stable linear two-step methods in conjunction with the method of approximation factorization. The mixed derivative is treated with an explicit two-step method which is compatible with an implicit A sub 0-stable method. The parameter space for which the resulting ADI schemes are second order accurate and unconditionally stable is determined. Some numerical examples are given.
A class of explicit numerical formulas which involve next nearest neighbor as well as nearest neighbor points are explored in this paper. These formulas are formal approximations to the linear parabolic partial-differential equation of first order in time and second order in distance. It was found that some of these formulas can employ time steps as much as four times that for the conventional explicit technique without becoming unstable. Others showed improved accuracy for a given time step and spatial grid spacing. One formula achieved a steady-state solution of specified accuracy for an example problem in less than 4 percent of the total computational time required by the conventional explicit technique.
Activities of two projects at JPL in support of DOE's Small Power Systems Program are reported. These two projects are the Point-Focusing Distributed Receiver (PFDR) Technology Project and the Point-Focusing Thermal and Electric Applications (PFTEA) Project. The PFDR Technology Project's major activity is developing the technology of solar concentrators, receivers and power conversion subsystems suitable for parabolic dish or point-focusing distributed receiver power systems. Other PFDR activities include system integration and cost estimation under mass production, as well as the testing of the hardware. The PFTEA Project's first major activity is applications analysis, that is seeking ways to introduce PFDR systems into appropriate user sectors. The second activity is systems engineering and development wherein power plant systems are analyzed for specific applications. The third activity is the installation of a series of engineering experiments in various user environments to obtain actual operating experience
Point focus distributed receiver solar thermal technology for the production of electric power and of industrial process heat is addressed. The thermal power systems project which emphasizes the development of cost effective systems which will accelerate the commercialization and industrialization of plants up to 10 MWe, using parabolic dish collectors is described. The projected size of the isolated load market in the 1990-2000 time period is 300 to 1000 MW/year. Although this market is small in comparison to the grid connected utility market, it is indicated that by assuming only a 20 percent market penetration, up to 10,000 power modules per year would be required to meet this need. At a production rate of 25,000 units/year and assuming no energy storage, levelized bus bar energy costs of 75 mills/kWeh are projected. These numbers are based on what is believed to be a conservative estimate regarding engine-generator conversion efficiency (40 percent) for the 1990 time period. With a more optimistic estimate of efficiency (i.e., 45 percent), the bus bar cost decreases to about 67 mills/kWeh. At very large production rates (400,000 modules/years), the costs decrease to 58 mills/kWeh. Finally, the present status of the technology development effort is discussed.
A parabolic dish test site (PDTS) was established in the California Mojave Desert to carry out work in testing solar point focusing concentrator systems and related hardware. The site was chosen because of its high solar insolation level and year around clear sky conditions. The various facilities and equipment at the PDTS, and the concentrator experiments being performed are described.