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At least 991 records · Page 55

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NASA NTRS1981

Influence of boundary approximations and conditions on finite difference solutions

Numerical representations of boundary approximations and conditions for three problems are investigated to determine the resulting global accuracy of the steady state solution. Numerical accuracy with various boundary approximations is determined for quasi-one-dimensional inviscid flow in a duct with the interior grid points evaluated using the MacCormack scheme. When an extrapolation approximation with first order local truncation error is used, the global second order accuracy of the difference scheme can be destroyed. For one dimensional flow in a porous medium, an implicit midpoint difference scheme which is consistent with the boundary conditions is developed without the need of boundary approximations. A dissipative model problem is solved with the boundary conditions discretized with first and second order accuracy. The overall second order accuracy of the difference scheme is destroyed if first order numerical representation of one of the boundary conditions is used. With a boundary approximation, the second order global accuracy of the model problem is retained if either second order extrapolation or first order representation of the governing equation is used.

Blottner, F. G.↗

NASA NTRS1981

Stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations

Implicit, noniterative, finite difference schemes were recently developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations. When applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable (A-stable). As applied in practice the algorithms often face a severe time step restriction. A major source of the difficulty is the treatment of the numerical boundary conditions. One conjecture was that unconditional stability requires implicit numerical boundary conditions. An apparent counter example was the space time extrapolation considered by Gustafsson, Kreiss, and Sunstrom. Spatial (implicit) and space time (explicit) extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals are examined. The results indicate that for unconditional stability with a finite number of spatial mesh intervals, the numerical boundary conditions must be implicit.

Beam, R. M.↗

NASA NTRS1981

Implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows

A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.

Barnett, M.↗

NASA NTRS1981

Collapses of stellar protogalaxies from aspheric initial conditions

Numerical experimens are presented which were intended to verify the independence of bar formation in rotating galaxy models from special initial conditions. Three-dimensional n-body programs were run starting from aspherical initial conditions characterized by particle rotational and peculiar velocities and offsets from sphericity for a set of 100,000 particles. All the initial configurations examined are observed to collapse to a thin form, overshoot, collapse again and again overshoot, with diameters and central densities similar to those observed under spheric initial conditions. Every aspheric collapse is also found to result in bar formation within two rotation periods, which is even sooner than in initially spherical conditions. In the intermediate stages of collapse, transient sheet patterns are found to be destroyed at asymmetries of 2-3%, while transient rings survived asymmetries of 6-7% but not 15-18%. It is noted that the results may be applicable to galaxy formation in the early universe, and possible mechanisms for the arresting of protogalactic collapse are indicated.

Miller, R. H.↗

NASA NTRS1981

Boundary conditions for subsonic compressible Navier-Stokes calculations

A systematic study of inflow and outflow boundary conditions for the numerical solution of the compressible Navier-Stokes equations is presented. Combinations of several representative inflow and outflow boundary conditions are applied in the solution of subsonic flow over a flat plate in a finite computational domain. These boundary conditions are evaluated in terms of their effect on the accuracy of the solution and the rate of convergence to a steady state. It is shown that errors in the data specified at the inflow boundary can produce significant errors in the computed flow field. It is also shown that a non-reflecting outflow boundary condition can significantly reduce the total computational time required.

Rudy, D. H.↗

NASA NTRS1958

A Flight Evaluation and Analysis of the Effect of Icing Conditions on the ZPG-2 Airship

A series of test flights was conducted by the U. S. Navy over a 3- year period to evaluate the effects of icing on the operation of the ZPG-2 airship. In supercooled. clouds, ice formed only on the forward edges of small protuberances and wires and presented no serious hazard to operation. Ice accretions of the glaze type which occurred in conditions described as freezing drizzle adversely affected various components to a somewhat greater extent. The results indicated, a need for protection of certain components such as antennas, propellers, and certain parts of the control system. The tests showed that icing of the large surface of the envelope occurred only in freezing rain or drizzle. Because of the infrequent occurrence of these conditions, the potential maximum severity could not be estimated from the test results. The increases in heaviness caused by icing in freezing rain and drizzle were substantial, but well within the operational capabilities of the airship. In order to estimate the potential operational significance of icing in freezing rain, theoretical calculations were used to estimate: (1) the rate of icing as a function of temperature and rainfall intensity, (2) the climatological probability of occurrence of various combinations of these variables, and (3) the significance of the warming influence of the ocean in alleviating freezing-rain conditions. The results of these calculations suggest that, although very heavy icing rates are possible in combinations of low temperature and high rainfall rate, the occurrence of such conditions is very infrequent in coastal areas and virtually impossible 200 or 300 miles offshore.

Lewis, Willilam↗

NASA NTRS1953

Maximum Evaporation Rates of Water Droplets Approaching Obstacles in the Atmosphere Under Icing Conditions

When a closed body or a duct envelope moves through the atmosphere, air pressure and temperature rises occur ahead of the body or, under ram conditions, within the duct. If cloud water droplets are encountered, droplet evaporation will result because of the air-temperature rise and the relative velocity between the droplet and stagnating air. It is shown that the solution of the steady-state psychrometric equation provides evaporation rates which are the maximum possible when droplets are entrained in air moving along stagnation lines under such conditions. Calculations are made for a wide variety of water droplet diameters, ambient conditions, and flight Mach numbers. Droplet diameter, body size, and Mach number effects are found to predominate, whereas wide variation in ambient conditions are of relatively small significance in the determination of evaporation rates. The results are essentially exact for the case of movement of droplets having diameters smaller than about 30 microns along relatively long ducts (length at least several feet) or toward large obstacles (wings), since disequilibrium effects are then of little significance. Mass losses in the case of movement within ducts will often be significant fractions (one-fifth to one-half) of original droplet masses, while very small droplets within ducts will often disappear even though the entraining air is not fully stagnated. Wing-approach evaporation losses will usually be of the order of several percent of original droplet masses. Two numerical examples are given of the determination of local evaporation rates and total mass losses in cases involving cloud droplets approaching circular cylinders along stagnation lines. The cylinders chosen were of 3.95-inch (10.0+ cm) diameter and 39.5-inch 100+ cm) diameter. The smaller is representative of icing-rate measurement cylinders, while with the larger will be associated an air-flow field similar to that ahead of an airfoil having a leading-edge radius comparable with that of the cylinder. It is found that the losses are less than 5 percent. It is concluded that such losses are, in general, very small (less than 1 percent) in the case of smaller obstacles (of icing-rate measurement- cylinder size); the motional dynamics are such, however, that exceptions will occur by reason of failure of very small droplets (moving along stagnation lines) to impinge upon obstacle surfaces. In such cases, the droplets will evaporate completely.

Lowell, H. H.↗

NASA NTRS1981

Terrestrial photovoltaic performance reference conditions

The rationale behind the selection of key photovoltaic performance reference (reporting) conditions, including the standard Air Mass 1.5 solar spectrum and reference irradiance and cell temperature levels, is investigated. Besides providing a repeatable reference for performance comparisons, it is shown that the choice of reference conditions directly controls the accuracy of array energy output prediction calculations. Conclusions are drawn on the accuracy associated with present reference conditions, and recommendations are made concerning alternative reference conditions with improved accuracy.

Ross, R. G., Jr.↗

NASA NTRS1982

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

Source record↗

NASA NTRS1983

Tip clearance flow in a compressor rotor passage at design and off-design conditions

The flow field in the tip clearance region of a compressor rotor at an off-design condition is reported in this paper. The earlier data at the design condition has also been re-interpreted and correlated with the blade and the flow parameters. The measurements inside the rotor tip region are acquired using a miniature hot wire sensor of 'V' configuration. The instantaneous velocity data is analyzed by the ensemble averaging technique to derive the blade-to-blade velocity field at various axial and radial locations between the rotor tip and the casing. The flow and the blade pressure data at the design condition are compared with the data at the off-design condition (lower blade loading). In addition to a reduction in the leakage velocities, its chordwise variation is also altered substantially at the lower blade loading.

Lakshminarayana, B.↗

NASA NTRS1985

Thermal stability of static coronal loops: Part 1: Effects of boundary conditions

The linear stability of static coronal-loop models undergoing thermal perturbations was investigated. The effect of conditions at the loop base on the stability properties of the models was considered in detail. The question of appropriate boundary conditions at the loop base was considered and it was concluded that the most physical assumptions are that the temperature and density (or pressure) perturbations vanish there. However, if the base is taken to be sufficiently deep in the chromosphere, either several chromospheric scale heights or several coronal loop lengths in depth, then the effect of the boundary conditions on loop stability becomes negligible so that all physically acceptable conditions are equally appropriate. For example, one could as well assume that the velocity vanishes at the base. The growth rates and eigenmodes of static models in which gravity is neglected and in which the coronal heating is a relatively simple function, either constant per-unit mass or per-unit volume were calculated. It was found that all such models are unstable with a growth rate of the order of the coronal cooling time. The physical implications of these results for the solar corona and transition region are discussed.

Antiochos, S. K.↗

NASA NTRS1985

Study of photon emission by electron capture during solar nuclei acceleration. 2: Delimitation of conditions for charge transfert establishment

The conditions for establishment of charge transfer during acceleration of nuclei up to Fe, for typical conditions of solar flare regions T = 5 x 10 to the 3rd power to 2.5 x 10 to the 8th power degrees K were explored. Results show that such conditions are widely assorted, depending on the acceleration mechanism, the kind of projections and their velocity, the target elements, the source temperature and consequently on the degree of ionization of matter and the local charge state of the accelerated ions. Nevertheless, in spite of that assorted behavior, there are some general tendencies that can be summarized as follows. In atomic H electron capture is systematically established from thermal energies up to high energies, whatever the element and for both acceleration process. For a given element and fixed temperature (T), the probability and energy domain of electron capture and loss with Fermi are higher than with Betatron acceleration. For a given acceleration process the heavier the ion the higher the probability and the wider the energy range for electron capture and loss. For given acceleration mechanism and fixed element the importance and energy domain of capture and loss increase with T: for those reasons, the energy range of charge equilibrium (illustrated with solid lines on the next figs.) is wider with Fermi and increases with temperature and atomic number of projectiles. For the same reasons, electron loss is smaller while the lighter the element, the lower the temperature and the Betatron process, such that there are conditions for which electron loss is not allowed at low energies, but only electron capture is established.

Perez-Peraza, J.↗

NASA NTRS1984

A generalized sine condition and performance comparison of Wolter type II and Wolter-Schwarzschild extreme ultraviolet telescopes

An equation similar to the Abbe sine condition is derived for a Wolter type II telescope. This equation and the sine condition are then combined to produce a so called generalized sine condition. Using the law of reflection, Fermat's principle, the generalized sine condition, and simple geometry the surface equations for a Wolter type II telescope and an equivalent Wolter-Schwarzschild telescope are calculated. The performances of the telescopes are compared in terms of rms blur circle radius at the Gaussian focal plane and at best focus.

Saha, T. T.↗

NASA NTRS1985

Initial conditions for parabolic calculation of reacting flows

A parabolic combustion code called CHARNAL was run for a variety of measured and estimated inlet boundary conditions. A parametric study was carried out to determine what compromises in accuracy would occur if estimated, rather than experimentally measured, inlet conditions were used and what values of the dissipation length scale would give the best results. The conclusions were that a dissipation length scale of approximately 0.03 gave the best results regardless of the type of inlet conditions used. Both subsonic and supersonic flow were examined and the effect of finite-rate versus equilibrium-chemistry calculations was briefly considered. No significant compromises in accuracy were found when estimated inlet boundary conditions were used.

Brown, E. F.↗

NASA NTRS1985

Thermal stability of static coronal loops. I - Effects of boundary conditions

Antiochos, S. K.↗

NASA NTRS1986

Early warning and crop condition assessment research

The Early Warning Crop Condition Assessment Project of AgRISTARS was a multiagency and multidisciplinary effort. Its mission and objectives were centered around development and testing of remote-sensing techniques that enhance operational methodologies for global crop-condition assessments. The project developed crop stress indicators models that provide data filter and alert capabilities for monitoring global agricultural conditions. The project developed a technique for using NOAA-n satellite advanced very-high-resolution radiometer (AVHRR) data for operational crop-condition assessments. This technology was transferred to the Foreign Agricultural Service of the USDA. The project developed a U.S. Great Plains data base that contains various meteorological parameters and vegetative index numbers (VIN) derived from AVHRR satellite data. It developed cloud screening techniques and scan angle correction models for AVHRR data. It also developed technology for using remotely acquired thermal data for crop water stress indicator modeling. The project provided basic technology including spectral characteristics of soils, water, stressed and nonstressed crop and range vegetation, solar zenith angle, and atmospheric and canopy structure effects.

Boatwright, G. O.↗

NASA NTRS1985

Existence and stability, and discrete BB and rank conditions, for general mixed-hybrid finite elements in elasticity

In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.

Xue, W.-M.↗

NASA NTRS1986

Coupling conditions for integrating boundary layer and rotational inviscid flow

The matching of a boundary layer and a rotational inviscid flow is reexamined by extending the Johnson and Sockol (1979) coupling conditions to include the case where the boundary layer solution includes the second-order effects of the freestream vorticity and the total temperature gradient. It is pointed out that two of the three conditions are not independent. If the boundary layer solution satisfies the appropriate momentum and energy integral equations, it follows that the imposition of the normal mass flux condition insures that the conditions on a normal flux of streamwise momentum and total enthalpy will also be satisfied.

Sockol, P. M.↗