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Two-mirror projection systems for simulating telescopes

Optical instruments designed for use with large telescopes need to be tested before being installed at their work site. This is especially true for space-based instruments. To perform these tests, an auxiliary optical system is required which simulates the telescope exit pupil. Two-mirror projection systems can be used for this purpose. In this paper the first-order geometric properties and third-order aberrations of the general two-mirror system used at finite conjugates are examined. Relations are given in terms of five design parameters: object distance, image distance, exit pupil size, and the two mirror magnifications. A particular application of these relations is presented for a system designed to simulate the HST, for ground testing of the next generation of scientific instruments to be installed in the observatory. We show that a sufficient number of degrees of freedom are available to meet requirements when both mirrors are conics.

Hannan, Paul G.

Lithospheric dynamics near plate boundaries

The progress report on research conducted between 15 Mar. - 14 Sep. 1992 is presented. The focus of the research during the first grant year has been on several problems broadly related to the nature and dynamics of time-dependent deformation and stress along major seismic zones, with an emphasis on western North America but with additional work on seismic zones in oceanic lithosphere as well. The principal findings of our research to date are described in the accompanying papers and abstract. Topics covered include: (1) Global Positioning System measurements of deformations associated with the 1987 Superstition Hills earthquake: evidence for conjugate faulting; (2) Global Positioning System measurements of strain accumulation across the Imperial Valley, California: 1986-1989; (3) present-day crustal deformation in the Salton Trough, southern California; (4) oceanic transform earthquakes with unusual mechanisms or locations: relation to fault geometry and state of stress in the lithosphere; and (5) crustal strain and the 1992 Mojave Desert earthquakes.

Solomon, Sean C.

A combined finite element-boundary element formulation for solution of two-dimensional problems via CGFFT

A method for the computation of electromagnetic scattering from arbitrary two-dimensional bodies is presented. The method combines the finite element and boundary element methods leading to a system for solution via the conjugate gradient Fast Fourier Transform (FFT) algorithm. Two forms of boundaries aimed at reducing the storage requirement of the boundary integral are investigated. It is shown that the boundary integral becomes convolutional when a circular enclosure is chosen, resulting in reduced storage requirement when the system is solved via the conjugate gradient FFT method. The same holds for the ogival enclosure, except that some of the boundary integrals are not convolutional and must be carefully treated to maintain O(N) memory requirement. Results for several circular and ogival structures are presented and shown to be in excellent agreement with those obtained by traditional methods.

Collins, Jeffery D.

C/NOFS Remote Sensing of Ionospheric Reflectance

Alfvn waves play critical roles in the electrodynamic coupling of plasmas at magnetically conjugate regions in near-Earth space. Associated electric (E*) and magnetic (dec B*) field perturbations sampled by sensors on satellites in low-Earth orbits are generally super positions of incident and reflected waves. However, lack of knowledge about ionospheric reflection coefficients (alpha) hinders understanding of generator outputs and load absorption of Alfvn wave energies. Here we demonstrate a new method for estimating using satellite measurements of ambient E* and dec B* then apply it to a case in which the Communication Navigation Outage Forecasting System (CNOFS) satellite flew conjugate to the field of view of a 630.0 nm all-sky imager at El Leoncito, Argentina, while medium-scale traveling ionosphere disturbances were detected in its field of view. In regions of relatively large amplitudes of E* and B*,calculated values ranged between 0.67 and 0.88. This implies that due to impedance mismatches, the generator ionosphere puts out significantly more electromagnetic energy than the load can absorb. Our analysis also uncovered caveats concerning the methods range of applicability in regions of low E* and B*. The method can be validated in future satellite-based auroral studies where energetic particle precipitation fluxes can be used to make independent estimates of alpha.

Burke, W. J.

The High Spectral Resolution Lidar

The High Spectral Resolution Lidar (HSRL) system was developed for the remote measurement of atmospheric optical properties. Measurements are obtained by the separation of the backscattered signal into aerosol and molecular channels using a high spectral resolution Fabry-Perot optical interferometer to separate the aerosol contributions to backscatter near the laser wavelength from the Doppler-shifted molecular component of the backscatter. The transmitter consists of an optically pumped pulsed dye laser of the oscillator-amplifier design which emits at 467.88 nm, with a bandwidth of less than 0.3 pm. The transmitter and receiver share a common Schmidt-Cassegrain telescope, although they do not share the same field stop, but rather two conjugate stops. The HSRL system uses a computer-controlled dual-channel photon-counting data acquisition system providing for stable measurements at very low power levels and an excellent dynamic range. The system has been used to obtain airborne measurements of height profiles of aerosol and molecular backscatter cross sections.

Eloranta, E. W.

The North Atlantic circulation in the early 1980s - An estimate from inversion of a finite-difference model

A finite-difference model of the North Atlantic is constructed for the purpose of making an estimate of the circulation through an inverse calculation. The data base is eclectic, and includes hydrography, oxygen, nutrients, current meter and float records, atmospheric momentum, heat and water vapor transfers, as well as estimates of certain integral fluxes. Owing to the available hydrographic database, the model resolution is restricted to 1 deg at best, and is much coarser in many aspects. This limited resolution is a major obstacle to accurate estimates of climatological fluxes. In its final form, there are about 9000 constraints in 29,000 formal unknowns plus 9000 noise unknowns. The system is solved as a tapered least-squares system by a sparse conjugate gradient algorithm. With the exception of a few float velocities, all constraints are found to be consistent within error estimates. The model produces estimates of large-scale fluxes and flux divergences for all conventional properties including heat and nutrients as well as carbon dioxide and alkalinity. Meridional fluxes of carbon are found to be indistinguishable from zero, whereas the North Atlantic tends to export nutrients to the south, but carry heat to the north. Traditional oceanographic depictions of the circulation through combination of nonsynoptic data into steady models may have reached their useful limit in the present calculation, as the conflicts between the data and physical requirements become quantitatively apparent.

Martel, Francoise

The effect of gravity modulation on thermosolutal convection in an infinite layer of fluid

The effect of time-periodic vertical gravity modulation on the onset of thermosolutal convection in an infinite horizontal layer with stress-free boundaries is investigated using Floquet theory for the linear stability analysis. Situations for which the fluid layer is stably stratified in either the fingering or diffusive regimes of double-diffusive convection are considered. Results are presented both with and without steady background acceleration. Modulation may stabilize an unstable base solution or destabilize a stable base solution. In addition to synchronous and subharmonic response to the modulation frequency, instability in the double diffusive system can occur via a complex conjugate mode. In the diffusive regime, where oscillatory onset occurs in the unmodulated system, regions of resonant instability occur and exhibit strong coupling with the unmodulated oscillatory frequency. The response to modulation of the fundamental instability of the unmodulated system is described both analytically and numerically; in the double-diffusive system this mode persists under subcritical conditions as a high-frequency lobe.

Saunders, B. V.

Use of Generalized Fluid System Simulation Program (GFSSP) for Teaching and Performing Senior Design Projects at the Educational Institutions

This paper describes the experience of the authors in using the Generalized Fluid System Simulation Program (GFSSP) in teaching Design of Thermal Systems class at University of Alabama in Huntsville. GFSSP is a finite volume based thermo-fluid system network analysis code, developed at NASA/Marshall Space Flight Center, and is extensively used in NASA, Department of Defense, and aerospace industries for propulsion system design, analysis, and performance evaluation. The educational version of GFSSP is freely available to all US higher education institutions. The main purpose of the paper is to illustrate the utilization of this user-friendly code for the thermal systems design and fluid engineering courses and to encourage the instructors to utilize the code for the class assignments as well as senior design projects. The need for a generalized computer program for thermofluid analysis in a flow network has been felt for a long time in aerospace industries. Designers of thermofluid systems often need to know pressures, temperatures, flow rates, concentrations, and heat transfer rates at different parts of a flow circuit for steady state or transient conditions. Such applications occur in propulsion systems for tank pressurization, internal flow analysis of rocket engine turbopumps, chilldown of cryogenic tanks and transfer lines, and many other applications of gas-liquid systems involving fluid transients and conjugate heat and mass transfer. Computer resource requirements to perform time-dependent, three-dimensional Navier-Stokes computational fluid dynamic (CFD) analysis of such systems are prohibitive and therefore are not practical. Available commercial codes are generally suitable for steady state, single-phase incompressible flow. Because of the proprietary nature of such codes, it is not possible to extend their capability to satisfy the above-mentioned needs. Therefore, the Generalized Fluid System Simulation Program (GFSSP1) has been developed at NASA Marshall Space Flight Center (MSFC) as a general fluid flow system solver capable of handling phase changes, compressibility, mixture thermodynamics and transient operations. It also includes the capability to model external body forces such as gravity and centrifugal effects in a complex flow network. The objectives of GFSSP development are: a) to develop a robust and efficient numerical algorithm to solve a system of equations describing a flow network containing phase changes, mixing, and rotation; and b) to implement the algorithm in a structured, easy-to-use computer program. The analysis of thermofluid dynamics in a complex network requires resolution of the system into fluid nodes and branches, and solid nodes and conductors as shown in Figure 1. Figure 1 shows a schematic and GFSSP flow circuit of a counter-flow heat exchanger. Hot nitrogen gas is flowing through a pipe, colder nitrogen is flowing counter to the hot stream in the annulus pipe and heat transfer occurs through metal tubes. The problem considered is to calculate flowrates and temperature distributions in both streams. GFSSP has a unique data structure, as shown in Figure 2, that allows constructing all possible arrangements of a flow network with no limit on the number of elements. The elements of a flow network are boundary nodes where pressure and temperature are specified, internal nodes where pressure and temperature are calculated, and branches where flowrates are calculated. For conjugate heat transfer problems, there are three additional elements: solid node, ambient node, and conductor. The solid and fluid nodes are connected with solid-fluid conductors. GFSSP solves the conservation equations of mass and energy, and equation of state in internal nodes to calculate pressure, temperature and resident mass. The momentum conservation equation is solved in branches to calculate flowrate. It also solves for energy conservation equations to calculate temperatures of solid nodes. The equations are coupled and nonlinear; therefore, they are solved by an iterative numerical scheme. GFSSP employs a unique numerical scheme known as simultaneous adjustment with successive substitution (SASS), which is a combination of Newton-Raphson and successive substitution methods. The mass and momentum conservation equations and the equation of state are solved by the Newton-Raphson method while the conservation of energy and species are solved by the successive substitution method. GFSSP is linked with two thermodynamic property programs, GASP2 and WASP3 and GASPAK4, that provide thermodynamic and thermophysical properties of selected fluids. Both programs cover a range of pressure and temperature that allows fluid properties to be evaluated for liquid, liquid-vapor (saturation), and vapor region. GASP and WASP provide properties of 12 fluids. GASPAK includes a library of 36 fluids. GFSSP has three major parts. The first part is the graphical user interface (GUI), visual thermofluid analyzer of systems and components (VTASC). VTASC allows users to create a flow circuit by a 'point and click' paradigm. It creates the GFSSP input file after the completion of the model building process. GFSSP's GUI provides the users a platform to build and run their models. It also allows post-processing of results. The network flow circuit is first built using three basic elements: boundary node, internal node, and branch.

Majumdar, A. K.

On the application of Chimera/unstructured hybrid grids for conjugate heat transfer

A hybrid grid system that combines the Chimera overset grid scheme and an unstructured grid method is developed to study fluid flow and heat transfer problems. With the proposed method, the solid structural region, in which only the heat conduction is considered, can be easily represented using an unstructured grid method. As for the fluid flow region external to the solid material, the Chimera overset grid scheme has been shown to be very flexible and efficient in resolving complex configurations. The numerical analyses require the flow field solution and material thermal response to be obtained simultaneously. A continuous transfer of temperature and heat flux is specified at the interface, which connects the solid structure and the fluid flow as an integral system. Numerical results are compared with analytical and experimental data for a flat plate and a C3X cooled turbine cascade. A simplified drum-disk system is also simulated to show the effectiveness of this hybrid grid system.

Kao, Kai-Hsiung

Comparing direct and iterative equation solvers in a large structural analysis software system

Two direct Choleski equation solvers and two iterative preconditioned conjugate gradient (PCG) equation solvers used in a large structural analysis software system are described. The two direct solvers are implementations of the Choleski method for variable-band matrix storage and sparse matrix storage. The two iterative PCG solvers include the Jacobi conjugate gradient method and an incomplete Choleski conjugate gradient method. The performance of the direct and iterative solvers is compared by solving several representative structural analysis problems. Some key factors affecting the performance of the iterative solvers relative to the direct solvers are identified.

Poole, E. L.

Novel High Efficient Organic Photovoltaic Materials: Final Summary of Research

The objectives and goals of this project were to investigate and develop high efficient, lightweight, and cost effective materials for potential photovoltaic applications, such as solar energy conversion or photo detector devices. Specifically, as described in the original project proposal, the target material to be developed was a block copolymer system containing an electron donating (or p-type) conjugated polymer block coupled to an electron withdrawing (or n-type) conjugated polymer block through a non-conjugated bridge unit. Due to several special requirements of the targeted block copolymer systems, such as electron donating and withdrawing substituents, conjugated block structures, processing requirement, stability requirement, size controllability, phase separation and self ordering requirement, etc., many traditional or commonly used block copolymer synthetic schemes are not suitable for this system. Therefore, the investigation and development of applicable and effective synthetic protocols became the most critical and challenging part of this project. During the entire project period, and despite the lack of a proposed synthetic polymer postdoctoral research associate due to severe shortage of qualified personnel in the field, several important accomplishments were achieved in this project and are briefly listed and elaborated. A more detailed research and experimental data is listed in the Appendix.

Sun, Sam

Phase control system concepts and simulations

A phase control system concept for a solar power satellite is proposed which partitions the system into three major levels. The first level of phase control consists of a reference phase distribution system implemented in the form of phase distribution tree structure. The major purpose of the tree structure is to electronically compensate for the phase shift due to the transition path lengths from the center of the spacetenna to each phase control center located in each subarray. In the reference system, this is accomplished using the master slave returnable timing system technique. The second level of phase control consists of the beam steering and microwave power generating system which houses the power transponders. This transponder consists of a set of phase conjugation multipliers driven by the reference phase distribution system output and the output of a pilot spread spectrum receiver which accepts the received pilot via a diplexer connected to a separate receive horn or the subarray itself. The output of the phase conjugation circuits serve as inputs to the third level of the phase control system. The third level of phase control is associated with maintaining an equal and constant phase shift through the microwave power amplifier devices while minimizing the associated phase noise effects on the generated power beam. This is accomplished by providing a phase locked loop around each high power amplifier.

Lindsay, V. C.

Three-dimensional aerodynamic shape optimization using discrete sensitivity analysis

An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: (1) the demand for significant efficiency improvements over current design methods; (2) a general and flexible three-dimensional surface representation; and (3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: (1) employing fully implicit (Newton) methods for the CFD analyses; (2) adopting a Bezier-Bernstein polynomial parameterization of two- and three-dimensional surfaces; and (3) using preconditioned conjugate gradient-like linear system solvers. Whereas each of these extensions independently yields an improvement in computational efficiency, the combined effect of implementing all the extensions simultaneously results in a significant factor of 50 decrease in computational time and a factor of eight reduction in memory over the most efficient design strategies in current use. The new aerodynamic shape optimization procedure is demonstrated in the design of both two- and three-dimensional inviscid aerodynamic problems including a two-dimensional supersonic internal/external nozzle, two-dimensional transonic airfoils (resulting in supercritical shapes), three-dimensional transport wings, and three-dimensional supersonic delta wings. Each design application results in realistic and useful optimized shapes.

Burgreen, Gregory W.

Programming substructure computations for elliptic problems on the CHiP system

A number of studies have been conducted with the aim to apply parallel computation to problems associated with solving finite element equations arising in structural mechanics and fluid dynamics. These studies have provided many important results. The present investigation is concerned with a set of experiments designed to test two ideas, including configurability and substructuring. The considered algorithms and tests are intended for implementation on the Configurable, Highly Parallel (CHiP) family of architecture described by Snyder (1982). The ChiP computer is composed of homogeneous processing elements (PEs) placed at regular intervals in a lattice of programmable switches. Two examples of the role of configurability and substructuring for simple iterative algorithms are considered, giving attention to conjugate gradient iterations, and tridiagonal systems of equations.

Gannon, D.

White-Light Phase-Conjugate Mirrors as Distortion Correctors

White-light phase-conjugate mirrors would be incorporated into some optical systems, according to a proposal, as means of correcting for wavefront distortions caused by imperfections in large optical components. The proposal was given impetus by a recent demonstration that white, incoherent light can be made to undergo phase conjugation, whereas previously, only coherent light was known to undergo phase conjugation. This proposal, which is potentially applicable to almost any optical system, was motivated by a need to correct optical aberrations of the primary mirror of the Hubble Space telescope. It is difficult to fabricate large optical components like the Hubble primary mirror and to ensure the high precision typically required of such components. In most cases, despite best efforts, the components as fabricated have small imperfections that introduce optical aberrations that adversely affect imaging quality. Correcting for such aberrations is difficult and costly. The proposed use of white-light phase conjugate mirrors offers a relatively simple and inexpensive solution of the aberration-correction problem. Indeed, it should be possible to simplify the entire approach to making large optical components because there would be no need to fabricate those components with extremely high precision in the first place: A white-light phase-conjugate mirror could correct for all the distortions and aberrations in an optical system. The use of white-light phase-conjugate mirrors would be essential for ensuring high performance in optical systems containing lightweight membrane mirrors, which are highly deformable. As used here, "phase-conjugate mirror" signifies, more specifically, an optical component in which incident light undergoes time-reversal phase conjugation. In practice, a phase-conjugate mirror would typically be implemented by use of a suitably positioned and oriented photorefractive crystal. In the case of a telescope comprising a primary and secondary mirror (see figure) white light from a distant source would not be brought to initial focus on one or more imaging scientific instrument(s) as in customary practice. Instead, the light would be brought to initial focus on a phase-conjugate mirror. The phase-conjugate mirror would send a phase-conjugate image back, along the path of the incoming light, to the primary mirror. A transparent, highly efficient diffractive thin film deposited on the primary mirror would direct the phase-conjugate image to the imaging instrument(s).

Frazier, Donald

Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.

Wong, Yau Shu

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.

Algorithmic aspects of transient heat transfer problems in structures

It is noted that the application of finite element or finite difference techniques to the solution of transient heat transfer problems in structures often results in a stiff system of ordinary differential equations. Such systems are usually handled most efficiently by implicit integration techniques which require the solution of large and sparse systems of algebraic equations. The assembly and solution of these systems using the incomplete Cholesky conjugate gradient algorithm is examined. Several examples are used to demonstrate the advantage of the algorithm over other techniques.

Haftka, R. T.