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NASA NTRS1988

Real-time optical laboratory solution of parabolic differential equations

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Casasent, David↗

NASA NTRS1989

Dynamic loading of spur gears with linear or parabolic tooth profile modification

A computer simulation was conducted to investigate the effects of both linear and parabolic tooth profile modification on the dynamic response of low-contact-ratio spur gears. The effect of the total amount of modification and the length of the modification zone were studied at various loads and speeds to find the optimal profile modification for minimal dynamic loading. Design charts consisting of normalized maximum dynamic load curves were generated for gear systems operated at various loads and with different tooth profile modification. An optimum profile modification can be determined from these design charts to minimize the dynamic loads of spur gear systems.

Lin, Hsiang Hsi↗

NASA NTRS1988

Life science experiments during parabolic flight: The McGill experience

Over the past twelve years, members of the Aerospace Medical Research Unit of McGill University have carried out a wide variety of tests and experiments in the weightless condition created by parabolic flight. This paper discusses the pros and cons of that environment for the life scientist, and uses examples from the McGill program of the types of activities which can be carried out in a transport aircraft such as the NASA KC-135.

Watt, D. G. D.↗

NASA NTRS1989

Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques

A general approximation framework is discussed for computation of optimal feedback controls in linear quadratic regular problems for nonautonomous parabolic distributed parameter systems. This is done in the context of a theoretical framework using general evolution systems in infinite dimensional Hilbert spaces. Conditions are discussed for preservation under approximation of stabilizability and detectability hypotheses on the infinite dimensional system. The special case of periodic systems is also treated.

Banks, H. T.↗

NASA NTRS1988

Directional solidification of Cu-Pb and Bi-Ga monotectic alloys under normal gravity and during parabolic flight

Cu-Pb and Bi-Ga monotectic alloys of nominal hypermonotectic compositions were directionally solidified under various furnace translation rates, temperature gradients, and gravity levels. Gravity was varied by solidifying the alloys under ground conditions and in the furnace aboard NASA KC-135 aircraft, flying on parabolic trajectories. High translation rates, high gradients, high gravity levels, and higher density and lower thermal conductivity of the L2 phase favored the formation of fiber composite structure, while the opposite conditions resulted in structures consisting of L2 droplets in alpha matrix. A modified particle engulfment theory as originally enunciated by Ulhmann et al. (1964) is proposed to explain these observations.

Dhindaw, B. K.↗

NASA NTRS1988

Ocular torsion in upright and tilted positions during hypo- and hypergravity of parabolic flight

Four subjects considered resistant to motion sickness were tested in KC-135 parabolic flight to examine ocular torsion at hypo-gravity and hypergravity. Three of these subjects showed no significant torsion at zero G in either the upright position or when tilted 30 deg to right or left. At 1.8 G in the tilted positions, they showed greater ocular counterrolling than at 1 G. None of these three subjects became motion sick. The fourth subject showed eye torsion toward his left in all positions at zero G. This leftward bias could also be seen at 1.8 G when tilted left ear down, the side that induces rightward counterrolling. There he had less eye torsion than at 1 G. This subject became motion sick. These results support the hypothesis that asymmetry of the utricular system may be well compensated in the normal 1 G environment, but unmasked in unaccustomed gravitational situations, suggesting a possible predictive test for space adaptation syndrome.

Diamond, Shirley G.↗

NASA NTRS1989

Optical testing of off-axis parabolic segments without auxiliary optical elements

The traditional optical test for an off-axis segment of a parabolic mirror utilizes an autocollimation flat and requires considerable test-bay space. Several other test configurations that will minimize space requirements are described. One method involves a null corrector, and three others require no auxiliary test optics. Combinations of the methods described will be useful in providing full independent evaluation of the figure of the segment under test.

Meinel, Aden B.↗

NASA NTRS1989

Parabolized Navier-Stokes algorithm for chemically reacting flows

A second-order parabolized Navier-Stokes algorithm based on the MacCormack (1969) explicit scheme is used to study three-dimensional chemically reacting flows with finite-rate chemistry. The method can treat the chemical source term implicitly, and it accounts for the multicomponent diffusion and convection of the chemical species. The method is demonstrated with the nonreacting case of a Mach-3 flow over a double-wedge compression corner and the case of streamwise hydrogen injection at sonic velocity in a Mach-2.44 vitiated air stream.

Kamath, H.↗

NASA NTRS1989

A three-dimensional upwind parabolized Navier-Stokes code for real gas flows

A real gas, upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional hypersonic flow of equilibrium air around various body shapes. The new code is an extension of the upwind (perfect gas) PNS code of Lawrence et al. (1986). The upwind algorithm is based on Roe's (1981) flux-difference splitting scheme which has been modified to account for real gas effects using the nearly exact approach of Vinokur and Liu (1988). Simplified curve fits are employed to obtain the thermodynamic and transport properties of equilibrium air. The new code has been validated by computing the M-infinity = 25 laminar flow of air over cones at various angles of attack. The results of these computations are compared with the results from a conventional centrally-differenced, real gas PNS code and the previous axisymmetric, upwind, real gas code. The agreement is excellent in all cases.

Tannehill, John C.↗

NASA NTRS1989

Upwind algorithm for the parabolized Navier-Stokes equations

A new upwind algorithm based on Roe's scheme has been developed to solve the two-dimensional parabolized Navier-Stokes equations. This method does not require the addition of user-specified smoothing terms for the capture of discontinuities such as shock waves. Thus, the method is easy to use and can be applied without modification to a wide variety of supersonic flowfields. The advantages and disadvantages of this adaptation are discussed in relation to those of the conventional Beam-Warming (1978) scheme in terms of accuracy, stability, computer time and storage requirements, and programming effort. The new algorithm has been validated by applying it to three laminar test cases, including flat-plate boundary-layer flow, hypersonic flow past a 15-deg compression corner, and hypersonic flow into a converging inlet. The computed results compare well with experiment and show a dramatic improvement in the resolution of flowfield details when compared with results obtained using the conventional Beam-Warming algorithm.

Lawrence, Scott L.↗

NASA NTRS1989

Optimal feedback control of infinite-dimensional parabolic evolution systems - Approximation techniques

Banks, H. T.↗

NASA NTRS1988

A review of test results on parabolic dish solar thermal power modules with dish-mounted Rankine engines and for production of process steam

This paper presents results of development testing of various solar thermal parabolic dish modules and assemblies. Most of the tests were at modules and assemblies that used a dish-mounted, organic Rankine cycle turbine for production of electric power. Some tests were also run on equipment for production of process steam or for production of electricity using dish-mounted reciprocating steam engines. These tests indicate that early modules achieve efficiencies of about 18 percent in converting sunlight to electricity (excluding the inverter but including parasitics). A number of malfunctions occurred. The performance measurements, as well as the malfunctions and other operating experience, provided information that should be of value in developing systems with improved performance and reduced maintenance.

Jaffe, Leonard D.↗

NASA NTRS1990

Upwind Algorithm For Parabolized Navier-Stokes Equations

Supersonic flow about cone calculated accurately. Report presents theoretical basis of computer code solving parabolized Navier-Stokes equations of supersonic and hypersonic flow. For increased accuracy in resolution of details of strong aerodynamic shocks, code incorporates implicit, finite-volume, upwind numerical-integration scheme. Performs well in numerical simulations of flows around simple bodies.

Lawrence, Scott L.↗

NASA NTRS1989

On the parallel solution of parabolic equations

Parallel algorithms for the solution of linear parabolic problems are proposed. The first of these methods is based on using polynomial approximation to the exponential. It does not require solving any linear systems and is highly parallelizable. The two other methods proposed are based on Pade and Chebyshev approximations to the matrix exponential. The parallelization of these methods is achieved by using partial fraction decomposition techniques to solve the resulting systems and thus offers the potential for increased time parallelism in time dependent problems. Experimental results from the Alliant FX/8 and the Cray Y-MP/832 vector multiprocessors are also presented.

Gallopoulos, E.↗

NASA NTRS1990

A three-dimensional upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional flow of chemically reacting air around hypersonic vehicles. The code is a modification of the perfect gas, three-dimensional UPS code of Lawrence et al. (1986) which has been extended in the present study to permit the calculation of hypersonic, viscous flows in chemical nonequilibrium. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for real gas effects. The present code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. Results are presented for the hypersonic laminar flow over a cone at 0- and 10-deg angles of attack and for a generic hypersonic vehicle. Calculations are performed assuming either perfect gas, equilibrium air, or finite-rate chemistry.

Buelow, Philip E.↗

NASA NTRS1989

Dynamic loading of spur gears with linear or parabolic tooth profile modifications

Lin, H. H.↗

NASA NTRS1989

Test results on parabolic dish concentrators for solar thermal power systems

This paper presents results of development testing of various solar thermal parabolic dish concentrators. The concentrators were mostly designed for the production of electric power using dish-mounted Rankine, Brayton or Stirling cycle engines, intended to be produced at low cost. Measured performance for various dishes included optical efficiencies ranging from 0.32 to 0.86 at a geometric concentration ratio of 500, and from about 0.09 to 0.85 at a geometric concentration ratio of 3000. Some malfunctions were observed. The tests should provide operating information of value in developing concentrators with improved performance and reduced maintenance.

Jaffe, Leonard D.↗

NASA NTRS1989

Conceptual design of a self-deployable, high performance parabolic concentrator for advanced solar-dynamic power systems

A summary is presented of the concentrator conceptual design work performed under a NASA-funded project. The design study centers around two basic efforts: conceptual design of a self-deploying, high-performance parabolic concentrator; and materials selection for a lightweight, shape-stable concentrator. The primary structural material selected for the concentrator is PEEK/carbon fiber composite. The deployment concept utilizes rigid gore-shaped reflective panels. The assembled concentrator takes a circular shape with a void in the center. The deployable solar concentrator concept is applicable to a range of solar dynamic power systems of 25 kWe to more than 75 kWe.

Dehne, Hans Joachim↗