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NASA NTRS1984

Analytical characterization of AOTV perigee aerothermodynamic regime

In preliminary design studies of AOTV (Aeroassisted Orbital Transfer Vehicle) configurations, it is desirable to have a simple analytical method for characterizing the aerothermodynamic regime at skip trajectory perigee as a function of vehicle L/D and m/CDA (ballistic coefficient). The present study derives an approximate perigee solution from the generalized equations of motion. For a prescribed entry velocity vector, the solution determines a Zeta function (proportional to density divided by m/CDA) at perigee as a parametric function of the exit velocity vector and (constant) L/D. The perigee Zeta function then determines perigee density (or altitude) as a parametric function of m/CDA. The solution allows the following classic aerothermodynamic parameters to be determined at perigee as parametric functions of m/CDA, L/D, and the exit velocity vector: Reynolds Number (viscous effects), Mach Number (compressibility effects), Knudsen Number (rarefaction effects), sphere and disk bow shock standoff distance, Damkohler Number (relaxation effects), viscous correlation parameter (viscid-inviscid interactions), and Stanton Number (convective heat transfer). Results of the analysis are given for low L/D and mid L/D AOTV configurations on return from geosynchronous and L5 orbits. It is concluded the method successfully provides preliminary estimates of the aerothermodynamic parameters through the use of simple algebraic equations and plots.

Desautel, D.↗

NASA NTRS1984

Analytical redundancy and the design of robust failure detection systems

The Failure Detection and Identification (FDI) process is viewed as consisting of two stages: residual generation and decision making. It is argued that a robust FDI system can be achieved by designing a robust residual generation process. Analytical redundancy, the basis for residual generation, is characterized in terms of a parity space. Using the concept of parity relations, residuals can be generated in a number of ways and the design of a robust residual generation process can be formulated as a minimax optimization problem. An example is included to illustrate this design methodology. Previously announcedd in STAR as N83-20653

Chow, E. Y.↗

NASA NTRS1984

Active control - A look at analytical methods and associated tools

A review of analytical methods and associated tools for active controls analysis and design problems is presented. Approaches employed to develop mathematical models suitable for control system analysis and/or design are discussed. Significant efforts have been expended to develop tools to generate the models from the standpoint of control system designers' needs and to develop the tools necessary to analyze and design active control systems. Representative examples of these tools are discussed. Examples where results from the methods and tools have been compared with experimental data are also presented. Finally, a perspective on future trends in analysis and design methods is presented.

Newsom, J. R.↗

NASA NTRS1984

Analytical estimates of turbulent MHD transport coefficients

Turbulent transfer rates from small-scale MHD excitations to large-scale Fourier modes are calculated algebraically, using the method of Biskamp and Welter. Three cases are considered: two-dimensional Navier-Stokes flows, two-dimensional incompressible MHD, and the weakly three-dimensional Strauss equations. In all cases, an initially large spectral gap between the small-scale and large-scale excitations is assumed, and attention focusses on the initial values of the back-transfer rates. The sign of the transfer is determined by the sign of an analytically calculable eddy viscosity and/or anomalous resistivity. We are able to confirm the results of Biskamp and Welter for the case of two-dimensional MHD, but find some differences for the case of the Strauss equations. It is argued that the Strauss equations may not exhibit an inverse cascade phenomenon for the spatially periodic case unless their initial spectra are such that the behavior is essentially that of two-dimensional MHD.

Montgomery, D.↗

NASA NTRS1985

Analytical and physical modeling program for the NASA Lewis Research Center's Altitude Wind Tunnel (AWT)

An effort is currently underway at the NASA Lewis Research Center to rehabilitate and extend the capabilities of the Altitude Wind Tunnel (AWT). This extended capability will include a maximum test section Mach number of about 0.9 at an altitude of 55,000 ft and a -20 F stagnation temperature (octagonal test section, 20 ft across the flats). In addition, the AWT will include an icing and acoustic research capability. In order to insure a technically sound design, an AWT modeling program (both analytical and physical) was initiated to provide essential input to the AWT final design process. This paper describes the modeling program, including the rationale and criteria used in program definition, and presents some early program results.

Abbott, J. M.↗

NASA NTRS1985

Experimental and analytical study of ceramic-coated turbine-tip shroud seals for small turbine engines

The results of an experimental and analytical evaluation of ceramic turbine tip shrouds within a small turbine engine operating environment are presented. The ceramic shrouds were subjected to 1001 cycles between idle and high power and steady-state conditions for a total of 57.8 engine hr. Posttest engine inspection revealed mud-flat surface cracking, which was attributed to microcracking under tension with crack penetration to the ceramic and bond coat interface. Sections and micrographs tend to corroborate the thesis. The engine test data provided input to a thermomechanical analysis to predict temperature and stress profiles throughout the ceramic gas-path seal. The analysis predicts cyclic thermal stresses large enough to cause the seal to fail. These stresses are, however, mitigated by inelastic behavior of the shroud materials and by the microfracturing that tensile stresses produce. Microfracturing enhances shroud longevity during early life but provides the failure mechanism during life but provides the failure mechanism during extended life when coupled with the time dependent inelastic materials effects.

Biesiadny, T. J.↗

NASA NTRS1985

Analytical Fuel Property Effects - Small Combustors. Phase II

A test program was conducted to study the effects of non-standard aviation fuels on a typical small gas turbine combustor, and to evaluate the effectiveness of design changes intended to counter the effects of these fuels. This study was a follow on to an earlier analytical study to predict the fuel effects and generate the design modifications evaluated in this program. The T700/CT7 engine family was chosen for both studies as being representative of the class of aircraft power plants desired for this study. Fuel properties, as specified by NASA, are characterized by low hydrogen content and high aromatics levels. No. 2 diesel fuel was also evaluated in this program. The tests demonstrated the anticipated higher than normal smoke output and flame radiation intensity with resulting increased metal temperatures on the baseline T700 combustor. Three new designs were evaluated using the non standard fuels. The three designs incorporated enhanced cooling features and smoke reduction features. All three designs, when burning the broad specification fuels, exhibited metal temperatures at or below the baseline combustor temperatures on JP-5. Smoke levels were acceptable but higher than predicted. This was partly due to the increase in baseline combustor smoke levels with the broad spec fuels being higher than anticipated. One combustor of the three clearly demonstrated the best smoke and metal temperature characteristics. It was also easiest to manufacture and incorporate into a production design. GE with NASA's concurrence selected and subjected this combustor to a final component test program.

Monty, J.↗

NASA NTRS1985

Analytical simulation of weld effects in creep range

The inelastic analysis procedure used to investigate the effect of welding on the creep rupture strength of a typical Liquid Metal Fast Breeder Reactor (LMFBR) nozzle is discussed. The current study is part of an overall experimental and analytical investigation to verify the inelastic analysis procedure now being used to design LMFBR structural components operating at elevated temperatures. Two important weld effects included in the numerical analysis are: (1) the residual stress introduced in the fabrication process; and (2) the time-independent and the time-dependent material property variations. Finite element inelastic analysis was performed on a CRAY-1S computer using the ABAQUS program with the constitutive equations developed for the design of LMFBR structural components. The predicted peak weld residual stresses relax by as much as 40% during elevated temperature operation, and their effect on creep-rupture cracking of the nozzle is considered of secondary importance.

Dhalla, A. K.↗

NASA NTRS1985

Analytical-numerical methods of calculations of energy and three-dimensional particle distributions in electromagnetic cascades

Analytical and numerical methods of calculation of the energy and three dimensional EPS characteristics are reported. The angular and lateral functions of electrons in EPS have been obtained by the Landau and small angle approximations A and B and compared with earlier data. A numerical method of solution of cascade equations for the EPS distribution function moments has been constructed. Considering the equilibrium rms angle as an example, errors appearing when approximating the elementary process cross sections by their asymptotic expressions are analyzed.

Ivanenko, I. P.↗

NASA NTRS1984

Effects of gravity on interdendritic flow - An analytic approach

The present investigation attempts to provide an aid to the understanding of the essence of the gravitational influence on interdendritic flow. An analytic solution of the equations governing interdendritic fluid flow is presented for a simple case, involving a semiinfinite mushy zone whose isotherms are flat, parallel, and inclined at an angle to the force of gravity. It is found that gravity in ingots with narrow mushy zones mainly produces interdendritic flow parallel to the liquidus confined to the vicinity of the liquidus. This flow can be large in comparison to the usual shrinkage-induced flows. Its existence is caused by the rapid increase of permeability with fraction liquid near the liquidus. For this reason, it cannot appear in numerical calculations which ignore the rapid variation of permeability.

Simpson, M.↗

NASA NTRS1984

Sensor failure detection for jet engines using analytical redundancy

Analytical redundant sensor failure detection, isolation and accommodation techniques for gas turbine engines are surveyed. Both the theoretical technonlogy base and demonstrated concepts are discussed. Also included is a discussion of current technology needs and angoing Government sponsored programs to meet those needs.

Merrill, W. C.↗

NASA NTRS1984

Heat and mass transfer in combustion - Fundamental concepts and analytical techniques

Fundamental combustion phenomena and the associated flame structures in laminar gaseous flows are discussed on physical bases within the framework of the three nondimensional parameters of interest to heat and mass transfer in chemically-reacting flows, namely the Damkoehler number, the Lewis number, and the Arrhenius number which is the ratio of the reaction activation energy to the characteristic thermal energy. The model problems selected for illustration are droplet combustion, boundary layer combustion, and the propagation, flammability, and stability of premixed flames. Fundamental concepts discussed include the flame structures for large activation energy reactions, S-curve interpretation of the ignition and extinctin states, reaction-induced local-similarity and non-similarity in boundary layer flows, the origin and removal of the cold boundary difficulty in modeling flame propagation, and effects of flame stretch and preferential diffusion on flame extinction and stability. Analytical techniques introduced include the Shvab-Zeldovich formulation, the local Shvab-Zeldovich formulation, flame-sheet approximation and the associated jump formulation, and large activation energy matched asymptotic analysis. Potentially promising research areas are suggested.

Law, C. K.↗

NASA NTRS1985

Analytical and physical modeling program for the NASA Lewis Research Center's Altitude Wind Tunnel (AWT)

Abbott, J. M.↗

NASA NTRS1985

Analytical model for large-scale turbulence

The paper presents an analytical model for large-scale turbulence, based on a new closure which depends on the growth rate of the instability-generating turbulence. For convection in stars the results of the mixing-length theory are recovered, and for laboratory convection the N = R to the 1/3 power law is recovered. The present model can readily be extended to include magnetic fields and rotation.

Canuto, V. M.↗

NASA NTRS1985

Analytic structure of cosmic radio jets - A preliminary investigation

The structure of the steady radio jet is discussed by analyzing the relativistic Euler equation in the case where surfaces of constant angular momentum coincide with surfaces of constant angular velocities. A closed analytic expression for the potential and other physical quantities is derived in a general stationary background geometry. The effect of the angular momentum component and the radial momentum component on the structure of the jet is studied in detail for Schwarzschild geometry. The jets are found to be pressure-confined and angular momentum-supported. The possibility of obtaining arbitrarily well-collimated jets very near to a black hole is discussed.

Chakrabarti, S. K.↗

NASA NTRS1985

Galactic chemical evolution and nucleocosmochronology - Analytic quadratic models

Quadratic models of the chemical evolution of the Galaxy for a star formation rate proportional to the square of the gas mass are studied. The search for analytic solutions to the gas mass and star mass for time-dependent rates of gaseous infall onto the disk is examined. The quadratic models are compared to models having linear star formation rates. The mass, metallicity, number of stars, and U-235/U-238 isotopic ratio for the models which are subjected to the same infall rate, the same initial disk mass, and the same final gas fraction are compared. The results of the comparison indicate that: (1) the average dwarf age is greater in the quadratic model, (2) the metallicity grows initially faster in the quadratic model, (3) the quadratic model has a smaller percentage of low-Z dwarfs, and (4) the U-235/U-238 isotopic ratio indicates a younger quadratic model.

Clayton, D. D.↗

NASA NTRS1984

A surface-analytical examination of stringer particles in aluminum-lithium-copper alloys

A surface analytical examination of powder metallurgy processed Al-Li-Cu alloys was conducted. The oxide stringer particles often found in these alloys are characterized. Particle characterization is important to more fully understand their impact on the stress corrosion and fracture properties of the alloy. The techniques used where SIMS (Secondary Ion Mass Spectroscopy) and SAM (Scanning Auger Microscopy). The results indicate that the oxide stringer particles contain both Al and LI with relatively high Li content and the Li compounds may be associated with the stringer particles, thereby locally depleting the adjacent matrix of Li solute.

Larson, L. A.↗

NASA NTRS1985

Experimental and analytical derivation of arc-heater scaling laws for simulating high-enthalpy environments for Aeroassisted Orbital Transfer Vehicle application

The computer code ARCFLO II was used as a guide to increase the performance of the Interaction Heating Facility at Ames Research Center. A closed-form scaling law relation was derived that provides an understanding of the factors that affect enthalpy in the constricted-arc heater. From a study of this scaling law, it is concluded that at constant pressure, enthalpy is proportional to current density raised to the 0.60 power for current densities from 80 to 150 A/sq cm. At constant current density, enthalpy is inversely proportional to pressure to the nth power, where n varies from 0.14 to 0.43, depending on the current density. Radiative heat losses are responsible for the falloff in performance at combinations of high current density and high pressure. An analytical, closed form scaling law based on a constant-temperature arc-core model agrees qualitatively with the scaling law deduced from ARCFLO II.

Winovich, W.↗