Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “characteristic equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Internal Radiation Effects in Zirconia Thermal Barrier Coatings

Using thermal barrier coatings on combustor liners, turbine vanes, and rotating blades is important for reducing metal temperatures in current and advanced aircraft engines. Zirconia is a common coating material, and it is partially transparent to thermal radiation. Radiation becomes more significant as temperatures are raised for higher efficiency in advanced engines. Calculations are often made with radiation effects neglected inside the coating. The effect of radiation is illustrated here, where an analytical procedure is provided by using the two-flux method for the radiative contribution. A detailed study was made of ceramic thermal barrier coatings for diesel engines, and a two-flux analysis was developed for radiation in semitransparent multilayer composites. These efforts provide the basis for the present analysis where illustrative solutions are obtained for typical conditions in an aircraft engine. The formulation and solution of the exact spectral radiative transfer equations including large scattering, as is characteristic of zirconia, are rather complicated. The two-flux method is used here to provide a simplified method.

Siegel, Robert↗
NASA NTRS1997

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

Baysal, Oktay↗
NASA NTRS1999

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗
NASA NTRS1965

Introduction to SST-ATC Study Program

The purpose of this brief introduction is to define the objectives of the program and to describe the manner in which it is being pursued. The study is directed toward problems anticipated with the introduction of the supersonic transport into the air-traffic-control system. The primary objectives are: (1) The determination of the effects of the SST (supersonic transport) on requirements of the ATC (air traffic control) system. (2) The determination of the effects of the ATC system on requirements for the SST design and for its equipment. Basically, the program is a simulation effort involving equipment both at Langley and at the NAFEC facility. A block diagram illustrating the manner in which the equipment of the two agencies has been integrated to carry out the program. The Langley equipment includes a cockpit, or flight compartment that is generally representative of transport equipment, and an analog computer for solving the six-degree-of-freedom motion equations for an aircraft having the characteristics of the SST design under study.

Toll, Thomas A.↗
NASA NTRS1998

Characterization of Thin Film Microstrip Lines on Polyimide

This paper presents an in depth characterization of thin film microstrip (TFMS) lines fabricated on Dupont PI-2611 polyimide. Measured attenuation and effective dielectric constant is presented for TFMS lines with thicknesses from 2.45-7.4 microns and line widths from 5-34.4 microns over the frequency range of 1-110 GHz. The attenuation is separated into conductor and dielectric losses to determine the loss tangent of Dupont PI-2611 polyimide over the microwave frequency range. In addition, the measured characteristics are compared to closed form equations for a and eff from the literature. Based on the comparisons, recommendations for the best dosed form design equations for TFMS are made.

Ponchak, George E.↗
NASA NTRS2004

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗
NASA NTRS2006

The Design of a High-Q, MACH-5 Nozzle for the Langley 8-Foot HTT

A new nozzle has ben designed for the NASA Langley Research Center 8-Foot High Temperature Tunnel. The new nozzle was designed with a Mach-5 exit flow at a Mach-5 flight-enthalpy test condition and has a smaller throat area than the existing Mach-5 nozzle which significantly increases the range of dynamic pressures that can be achieved in the facility. The nozzle was designed using the NASA Langley IMOCND computer program which solves the potential equation using the classical method of characteristics. Several axisymmetric nozzle contours were generated and evaluated using viscous computational fluid dynamics. A number of items were considered in the evaluation, including flow uniformity, thermal and structural design, manufacturing schedule and cost. Once the final contour was selected, studies were done to determine the effects of manufacturing irregularities (steps and cavities at joints). These studies were done to develop manufacturing specifications and assembly tolerances.

Gaffey, Richard L., Jr.↗
NASA NTRS2008

Design of a Mach-3 Nozzle for TBCC Testing in the NASA LaRC 8-ft High Temperature Tunnel

A new nozzle is being constructed for the NASA Langley Research Center 8-Foot High Temperature Tunnel. The axisymmetric nozzle was designed with a Mach-3 exit flow for testing Turbine-Based Combined-Cycle engines at a Mach number in the vicinity of the transition from turbojet to ramjet operation. The nozzle contour was designed using the NASA Langley IMOCND computer program which solves the potential equation using the classical method of characteristics. To include viscous effects, the design procedure iterated the MOC contour generation with CFD Navier-Stokes calculations, adjusting MOC input parameters until target nozzle-exit conditions were achieved in the Navier-Stokes calculations. The design process was complicated by a requirement to use the final 29.5 inches of an existing 54.5-inch exit-diameter Mach-5 nozzle contour. This was accomplished by generating a Mach-3 contour that matched the radius of the Mach-5 contour at the match point and using a 3rd order polynomial to create a smooth transition between the two contours. During the final evaluation of the design it was realized that the throat diameter is more than half that of the upstream mixing chamber. This led to the concern that large vortical structures generated in the mixer would persist downstream, affecting nozzle-exit flow. This concern was addressed by analyzing the results of three-dimensional, viscous, numerical simulations of the entire flowfield, from the exit of the facility combustor to the nozzle exit. An analysis of the solution indicated that large scale structures do not pass through the throat and that both the total temperature and species (CO2) are well mixed in the mixer, providing uniform flow to the nozzle and subsequently the test cabin.

Gaffney, Richard L., Jr.↗
NASA NTRS2012

Scattering and Absorption Properties of Polydisperse Wavelength-sized Particles Covered with Much Smaller Grains

Using the results of direct, numerically exact computer solutions of the Maxwell equations, we analyze scattering and absorption characteristics of polydisperse compound particles in the form of wavelength-sized spheres covered with a large number of much smaller spherical grains.The results pertain to the complex refractive indices1.55 + i0.0003,1.55 + i0.3, and 3 + i0.1. We show that the optical effects of dusting wavelength-sized hosts by microscopic grains can vary depending on the number and size of the grains as well as on the complex refractive index. Our computations also demonstrate the high efficiency of the new superposition T-matrix code developed for use on distributed memory computer clusters.

Dlugach, Jana M.↗
NASA NTRS1978

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

May, C. E.↗
NASA NTRS1978

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

May, C. E.↗
NASA NTRS1981

Time and frequency domain analysis of sampled data controllers via mixed operation equations

Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods.

Frisch, H. P.↗
NASA NTRS1987

A method of calculating the total flow from a given sea surface topography

Using a simple dynamical model of a wind-driven ocean circulation of the Stommel type, and an analytical basis developed to objectively analyze the sea surface height residuals from an altimeter and, in the process, to determine the total flow instead of just the near surface geostrophic component associated with the given sea surface topography. The method is based on first deriving the solution to the forced problem for a given wind stress required to develop a hypothetical true or perfect data field and to establishing the basis for the objective analysis. The stream function and the surface height field for the forced problem are developed in terms of certain characteristic functions with the same expansion coefficients for both fields. These characteristic functions are simply the solutions for a homogeneous elliptic equation for the stream function and the solutions of an inhomogeneous balance equation for the height field. For the objective analysis, using a sample of randomly selected height values from the true data field, the height field characteristic functions are used to fit the given topography in a least squares sense. The resulting expansion coefficients then permit the synthesis of the total flow field via the stream function characteristic modes and the solution is perfectly well behaved even along the equator. The method of solution is easily adaptable to realistic ocean basis by straight forward numerical methods. The analytical basis of the theory and the results for an ideal rectangular basin on a beta plane are described.

Rao, Desiraju B.↗
NASA NTRS1992

Design of optimally smoothing multistage schemes for the Euler equations

A recently derived local preconditioning of the Euler equations is shown to be useful in developing multistage schemes suited for multigrid use. The effect of the preconditioning matrix on the spatial Euler operator is to equalize the characteristic speeds. When applied to the discretized Euler equations, the preconditioning has the effect of strongly clustering the operator's eigenvalues in the complex plane. This makes possible the development of explicit marching schemes that effectively damp most high-frequency Fourier modes, as desired in multigrid applications. The technique is the same as developed earlier for scalar convection schemes: placement of the zeros of the amplification factor of the multistage scheme in locations where eigenvalues corresponding to high-frequency modes abound.

Van Leer, Bram↗
NASA NTRS1983

Application of a full potential method for predicting supersonic flow fields and aerodynamic characteristics

A nonlinear aerodynamic prediction technique which solves the conservative full potential equation has been applied to the analysis of three waverider configurations. This technique was selected based on its capability to analyze the off-design characteristics of the waveriders. Very good correlations were achieved with surface pressure data for both the Mach 4 elliptic cone waverider and the Mach 6 caret-wing derivative. Off-design Mach number and angle-of-attack pressure correlations were very good for the elliptic cone waverider. The range of correlation with data exceeded that expected based on the theory limitations. A surface pressure integration routine was demonstrated and agreement between predicted aerodynamic forces and experimental force data for the Mach 4 waverider was excellent. Analysis of a nonconical waverider configuration was initiated where a discrete input option is used to achieve the computational gridding. Preliminary analysis of this configuration indicates the correct shock location will be predicted.

Jones, K. M.↗
NASA NTRS1975

A Theoretical Investigation of the Input Characteristics of a Rectangular Cavity-Backed Slot Antenna

Equations which represent the magnetic and electric stored energies are derived for an infinite section of rectangular waveguide and a rectangular cavity. These representations which are referred to as being physically observable are obtained by considering the difference in the volume integrals appearing in the complex Poynting theorem. It is shown that the physically observable stored energies are determined by the field components that vanish in a reference plane outside the aperture. These physically observable representations are used to compute the input admittance of a rectangular cavity-backed slot antenna in which a single propagating wave is assumed to exist in the cavity. The slot is excited by a voltage source connected across its center; a sinusoidal distribution is assumed in the slot. Input-admittance calculations are compared with measured data. In addition, input-admittance curves as a function of electrical slot length are presented for several size cavities. For the rectangular cavity backed slot antenna, the quality factor and relative bandwidth were computed independently by using these energy relationships. It is shown that the asymptotic relationship which is usually assumed to exist between the quality bandwidth and the reciprocal of relative bandwidth is equally valid for the rectangular cavity backed slot antenna.

Cockrell, C. R.↗