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NASA NTRS1976

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained.

Klimas, A. J.↗

NASA NTRS1976

Vibroacoustic test plan evaluation: Parameter variation study

Statistical decision models are shown to provide a viable method of evaluating the cost effectiveness of alternate vibroacoustic test plans and the associated test levels. The methodology developed provides a major step toward the development of a realistic tool to quantitatively tailor test programs to specific payloads. Testing is considered at the no test, component, subassembly, or system level of assembly. Component redundancy and partial loss of flight data are considered. Most and probabilistic costs are considered, and incipient failures resulting from ground tests are treated. Optimums defining both component and assembly test levels are indicated for the modified test plans considered. modeling simplifications must be considered in interpreting the results relative to a particular payload. New parameters introduced were a no test option, flight by flight failure probabilities, and a cost to design components for higher vibration requirements. Parameters varied were the shuttle payload bay internal acoustic environment, the STS launch cost, the component retest/repair cost, and the amount of redundancy in the housekeeping section of the payload reliability model.

Stahle, C. V.↗

NASA NTRS1976

Consideration of design and calibration of terrestrial reference solar cells

A discussion is presented on the problems encountered in the design of a reference cell that meets basic criteria, starting with basic design considerations, and proceeding with the precautions taken to ensure a global monitoring capability. The effects of the variations in atmospheric conditions on the calibration and use of reference cells are presented along with a discussion of the simplifications brought about by the use of spectrally matched test and reference cells. Finally, a method of matching test modules and arrays to reference cells by a red/blue response ratio technique is described.

Weizer, V. G.↗

NASA NTRS1977

Pure field theories and MACSYMA algorithms

A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.

Ament, W. S.↗

NASA NTRS1977

The variety of variables in mathematical expressions

Various distinctions are discussed which can be made regarding evaluation of mathematical expressions: regular evaluation vs. infinite evaluation vs. finite evaluation, regular variables vs. mathematical variables vs. shadow variables vs. labels, simplification vs. evaluation vs. solution of equations. The unsatisfactory state of evaluation strategies in symbolic systems is due to insufficient use of such distinctions in the past.

Moses, J.↗

NASA NTRS1977

Symbolic manipulation techniques for vibration analysis of laminated elliptic plates

A computational scheme is presented for the free vibration analysis of laminated composite elliptic plates. The scheme is based on Hamilton's principle, the Rayleigh-Ritz technique and symmetry considerations and is implemented with the aid of the MACSYMA symbolic manipulation system. The MACYSMA system, through differentiation, integration, and simplification of analytic expressions, produces highly-efficient FORTRAN code for the evaluation of the stiffness and mass coefficients. Multiple use is made of this code to obtain not only the frequencies and mode shapes of the plate, but also the derivatives of the frequencies with respect to various material and geometric parameters.

Andersen, C. M.↗

NASA NTRS1977

Skylab environmental and crew microbiology studies

The objectives of the Skylab microbiology studies were to detect the presence of potentially pathogenic micro-organisms on the crewmembers and their spacecraft and to obtain data which would contribute to an understanding of the response of the crew's microbial flora to the space flight environment. These data were interpreted in light of the theories of microbial simplification, intercrew transfer of medically important microorganisms, in-flight auto infections, and postflight microbial shock, which have been proposed by various authors.

Gerald R Taylor↗

NASA NTRS1976

A mathematical analysis of the theory of interplanetary scintillation in the weak scattering approximation

A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.

Mitchell, D. G.↗

NASA NTRS1976

K/S two-point-boundary-value problems

A method for developing the missing general K/S (Kustaanheimo/Stiefel) boundary conditions is presented, with use of the formalism of optimal control theory. As an illustrative example, the method is applied to the K/S Lambert problem to derive the missing terminal condition. The necessary equations are developed for a solution to this problem with the generalized eccentric anomaly, E, as the independent variable. This formulation, requiring the solution of only one nonlinear, well-behaved equation in one unknown, E, results in considerable simplification of the problem.

Jezewski, D. J.↗

NASA NTRS1977

Variable thickness shear layer aerodynamics revisited

The constant boundary-layer thickness (BLT) figuring in the Ventres (1975) Kernel function can be replaced by a slowly varying BLT, in the case of shear layers of slowly varying thickness. A simplification of the extension by Chi (1976) of Ventres' solution is put forward. The Kernel function in this instance relates pressure on the lifting surface to downwash over the surface. The results should also apply, formally, to three-dimensional compressible unsteady flows, but the accuracy in assuming slowly varying shear BLT remains to be determined. All variants of the shear layer model fail when the shear layer thickness varies rapidly.

Dowell, E. H.↗

NASA NTRS1977

Effect of 30 months in a locked environment on the microbial flora of dogs

It has been proposed that the microbial flora of mammals would simplify to a few microbial species if the host animal was confined to a 'locked' environment and provided with sterile food, water, and air. This paper updates information on the microbial profile (feces, nose and throat) of purebred beagles housed in the above-mentioned conditions through a 30-month study period and demonstrates that no drastic decrease or simplification of the microbial profile occurred in isolated or control dogs.

Balish, E.↗

NASA NTRS1977

Study of igniter design and applications to low smoke solid rockets

A simple analysis of igniter design is described which is sufficiently general to be applicable to any 'basket'-type housing containing one or more charges. The gas equation of state is used in conjunction with the experimentally determined propellant burning-rate law to predict the pressure-time histories in the igniter housing and the rocket motor. Typical numerical results are presented for three cases which represent three experimental conditions tested in a project on low-smoke motors where the requirements on the exhaust were sufficiently stringent to preclude condensible matter from the igniter. Pressure was measured continuously in time at two locations in the igniter housing and at the head end of the motor case. The agreement between theoretical and experimental results is felt to be encouraging considering the complexity of the problem and the many simplifications in the analysis.

Ramohalli, K.↗

NASA NTRS1976

Laser induced fluorescence applied to turbulent reacting flows

The saturated fluorescence method makes use of the great simplifications which occur when under conditions of intense radiation the excitation process becomes saturated. A description is presented of the saturated fluorescence method, taking into account rate equations and saturation, radiative transfer, the two-level system, a multilevel system, and measurements under saturation conditions. The detectability limits of the method are investigated. Fluorescence trapping is found to place an upper limit on the number density of the fluorescing species that can be measured without signal loss. Turbulence places time and spatial constraints on the measurements, but otherwise poses no difficulties. Saturated laser induced fluorescence spectroscopy appears to be a most promising method for measuring species concentrations in flames.

Daily, J. W.↗

NASA NTRS1977

Advanced development of Pb-salt semiconductor lasers for the 8.0 to 15.0 micrometer spectral region

The technology was studied for producing Pb-salt diode lasers for the 8-51 micron spectral region suitable for use as local oscillators in a passive Laser Heterodyne Spectrometer (LHS). Consideration was given to long range NASA plans for the utilization of the passive LHS in a space shuttle environment. The general approach was to further develop the method of compositional interdiffusion (CID) recently reported, and used successfully at shorter wavelength. This technology was shown to provide an effective and reproducible method of producing a single-heterostructure (SH) diode of either the heterojunction or single-sided configuration. Performance specifications were exceeded in several devices, with single-ended CW power outputs as high as 0.88 milliwatts in a mode being achieved. The majority of the CID lasers fabricated had CW operating temperatures of over 60K; 30% of them operated CW above the boiling temperature of liquid nitrogen. CW operation above liquid nitrogen temperature was possible for wavelengths as long as 10.3 microns. Operation at 77K is significant with respect to space shuttle operations since its allows considerable simplification of cooling method.

Linden, K. J.↗

NASA NTRS1977

Evaluation of algorithms for geological thermal-inertia mapping

The errors incurred in producing a thermal inertia map are of three general types: measurement, analysis, and model simplification. To emphasize the geophysical relevance of these errors, they were expressed in terms of uncertainty in thermal inertia and compared with the thermal inertia values of geologic materials. Thus the applications and practical limitations of the technique were illustrated. All errors were calculated using the parameter values appropriate to a site at the Raft River, Id. Although these error values serve to illustrate the magnitudes that can be expected from the three general types of errors, extrapolation to other sites should be done using parameter values particular to the area. Three surface temperature algorithms were evaluated: linear Fourier series, finite difference, and Laplace transform. In terms of resulting errors in thermal inertia, the Laplace transform method is the most accurate (260 TIU), the forward finite difference method is intermediate (300 TIU), and the linear Fourier series method the least accurate (460 TIU).

Miller, S. H.↗

NASA NTRS1977

Current status of droplet and liquid combustion

The present understanding of spray combustion in rocket engine, gas turbine, Diesel engine and industrial furnace applications is reviewed. In some cases, spray combustion can be modeled by ignoring the details of spray evaporation and treating the system in the same manner as a gaseous diffusion flame; however, in many circumstances, this type of simplification is not adequate and the turbulent two-phase flow must be considered. The behavior of individual droplets is a necessary component of two-phase models and recent work on transient droplet evaporation, ignition and combustion is considered, along with a discussion of important simplifying assumptions involved with modeling these processes. Methods of modeling spray evaporation and combustion processes are also discussed including: one-dimensional models for rocket engine and prevaporized combustion systems, lumped zone models (utilizing well-stirred reactor and plug flow regions) for gas turbine and furnace systems, locally homogeneous turbulent models, and two-phase models. The review highlights the need for improved injector characterization methods, more information of droplet transport characteristics in turbulent flow and continued development of more complete two-phase turbulent models.

Faeth, G. M.↗

NASA NTRS1977

Temporal evolution of the equatorial K-corona

Variation of the equatorial K-corona radiance at 2.5 solar radii from the sun center was studied on a daily basis during the Skylab mission (May 1973 to February 1974). The radiance data may be divided into three periods, the first characterized by a smooth variation in time, the second by a signal that is neither persistent in the short term nor recurrent from one limb passage to the next, and the third (and longest period) by a signal exhibiting an orderly, periodically increasing intensity. The data may be interpreted as indicating a general simplification of the coronal magnetic field; harmonic analysis of the surface field provides additional information on the evolution of the equatorial K-corona structures.

Macqueen, R. M.↗

NASA NTRS1978

The thermoelastic patch contact problem for large Peclet number

An equation in the form of a Fourier series was derived in an earlier study to give displacements of the originally straight edge of a plate as the result of a small heat input patch moving at speed c along that edge. That unwieldly formulation is reduced to a simple integral equation, which is shown to be manageable in an example calculation. The integral equation is shown to be closely related to that of Ling and Mow, although it is much simpler to use. Comparison of the results of the simplification to results of the original series formulation suggest that the equation proposed for 'high Peclet number' may be a valid approximation for Peclet number as low as 2.5.

Kilaparti, S. R.↗