Results for “characteristic equations” — Page 67

NASA NTRS1984

Simulation Applications at NASA Ames Research Center

Aeronautical applications of simulation technology at Ames Research Center are described. The largest wind tunnel in the world is used to determine the flow field and aerodynamic characteristics of various aircraft, helicopter, and missile configurations. Large computers are used to obtain similar results through numerical solutions of the governing equations. Capabilities are illustrated by computer simulations of turbulence, aileron buzz, and an exhaust jet. Flight simulators are used to assess the handling qualities of advanced aircraft, particularly during takeoff and landing.

Inouye, M.↗

NASA NTRS1986

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

Consideration is given to the static force-free equilibrium of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conventiently described in terms of the scalar function psi, which is the stream function for the incompressible wrapping and interweaving of the lines of force. Local compression and expansion of the lines of force is described in terms of the scalar function Phi. Equilibrium in the field requires satisfaction of two independent equations which cannot be accomplished without the full freedom of both psi and Phi. It is shown that discontinuities in the torsional characteristics of the lines occur when psi is predetermined by an arbitrary pattern. Discontinuities in the winding pattern of the lines can lead to discontinuities in the associated current sheets.

Parker, E. N.↗

NASA NTRS1987

New dimension analyses with error analysis for quaking aspen and black spruce

Dimension analysis for black spruce in wetland stands and trembling aspen are reported, including new approaches in error analysis. Biomass estimates for sacrificed trees have standard errors of 1 to 3%; standard errors for leaf areas are 10 to 20%. Bole biomass estimation accounts for most of the error for biomass, while estimation of branch characteristics and area/weight ratios accounts for the leaf area error. Error analysis provides insight for cost effective design of future analyses. Predictive equations for biomass and leaf area, with empirically derived estimators of prediction error, are given. Systematic prediction errors for small aspen trees and for leaf area of spruce from different site-types suggest a need for different predictive models within species. Predictive equations are compared with published equations; significant differences may be due to species responses to regional or site differences. Proportional contributions of component biomass in aspen change in ways related to tree size and stand development. Spruce maintains comparatively constant proportions with size, but shows changes corresponding to site. This suggests greater morphological plasticity of aspen and significance for spruce of nutrient conditions.

Woods, K. D.↗

NASA NTRS1986

An integrated micromechanical and macromechanical approach to fracture behavior of fiber-reinforced composites

A novel integrated micromechanical and macromechanical fracture criterion (IMMFC) was developed for the purpose of characterizing fractures in fiber-reinforced composites. The Griffith energy balance equation was modified to include the energy absorption due to matrix yielding, matrix cracks, fiber breaks, and fiber-matrix interface debonds characteristic for these materials. Parameters which are a measure of the size and density of the microflaws are introduced into the development of the IMMFC, and the concept of the R-curve is used to bridge the micromechanics and macromechanics approaches.

Mahishi, Jayant M.↗

NASA NTRS1987

Dynamical response to pulse excitations in large space structures

Finite dimensional approximations of large space structures as distributed parameter systems may lead to a loss of contribution of high frequencies to the dynamic response in case of impulsive or concentrated loads. It is shown that the unmodeled part of this response can be represented by a system of thin pulses which propagate as characteristic waves. It is demonstrated that the dynamical response to such a system of pulses can be modeled by a system of equations with delay argument. Fundamental dynamical properties of this system such as Liapunov stability, structural stability, loss of periodicity and transition to ergodicity are analyzed in this study. The results are illustrated by examples.

Zak, Michail↗

NASA NTRS1989

Dynamics of planetary-scale baroclinic waves during Southern Hemisphere winter

The characteristics of linear and finite amplitude baroclinic waves during Southern Hemisphere winter were investigated using a three-dimensional global primitive-equation spectral mode, with emphasis on the dynamics of planetary scale modes which propagate into the stratosphere. Linear stability computations showed that the winter zonally averaged basic state is baroclinically unstable, with the most unstable modes being Charney-type modes; however, the results showed that Green-type modes also exist; these give much larger relative amplitude in the stratosphere although they have smaller growth rates. The results suggest that the existence of both Charney and Green modes might explain certain observed properties of the eastward traveling waves, such as the lack of coherence between troposphere and stratosphere at zonal wavenumbers 1 and 2.

Young, Richard E.↗

NASA NTRS1951

Theoretical Investigation of Submerged Inlets at Low Speeds

The general characteristics of the flow field in a submerged air inlet are investigated by theoretical, wind-tunnel, and visual-flow studies. Equations are developed for calculating the laminar and turbulent boundary-layer growth along the ramp floor for parallel, divergent, and convergent ramp walls, and a general equation is derived relating the boundary-layer pressure losses to the boundary-layer thickness. It is demonstrated that the growth of the boundary layer on the floor of the divergent-ramp inlet is retarded and that a vortex pair is generated in such an inlet. Functional relationships are established between the pressure losses in the vortices and the geometry of the inlet. A general discussion of the boundary layer and vortex formations is included, in which variations of the various losses and of the incremental external drag with mass-flow ratio are considered. Effects of compressibility are also discussed.

Sacks, Alvin H.↗

NASA NTRS1991

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

Khavaran, Abbas↗

NASA NTRS1992

Computation of supersonic jet mixing noise for an axisymmetric CD nozzle using k-epsilon turbulence model

The turbulent mixing noise of a supersonic jet is calculated for a round convergent-divergent nozzle at the design pressure ratio. Aerodynamic computations are performed using the PARC code with a k-epsilon turbulence model. Lighthill's acoustic analogy combined with Ribner's assumption is adopted. The acoustics solution is based upon the methodology followed by GE in the MGB code. The source correlation function is expressed as a linear combination of second-order tensors. Assuming separable second-order correlations and incorporating Batchelor's isotropic turbulence model, the source term was calculated from the kinetic energy of turbulence. A Gaussian distribution for the time-delay of correlation was introduced. The computational fluid dynamics (CFD) solution was used to obtain the source strength as well as the characteristic time-delay of correlation. The effect of sound/flow interaction was incorporated using the high frequency asymptotic solution to Lilley's equation for axisymmetric geometries. Acoustic results include sound pressure level directivity and spectra at different polar angles. The aerodynamic and acoustic results demonstrate favorable agreement with experimental data.

Khavaran, A.↗

NASA NTRS1992

Progress on single barrier varactors for submillimeter wave power generation

Theoretical work on Single Barrier Varactor (SBV) diodes, indicate that the efficiency for a multiplier has a maximum for a considerably smaller capacitance variation than previously thought. The theoretical calculations are performed, both with a simple theoretical model and a complete computer simulation using the method of harmonic balance. Modeling of the SBV is carried out in two steps. First, the semiconductor transport equations are solved simultaneously using a finite difference scheme in one dimension. Secondly, the calculated I-V, and C-V characteristics are input to a multiplier simulator which calculates the optimum impedances, and output powers at the frequencies of interest. Multiple barrier varactors can also be modeled in this way. Several examples on how to design the semiconductor layers to obtain certain characteristics are given. The calculated conversion efficiencies of the modeled structures, in a multiplier circuit, are also presented. Computer simulations for a case study of a 750 GHz multiplier show that InAs diodes perform favorably compared to GaAs diodes. InAs and InGaAs SBV diodes have been fabricated and their current vs. voltage characteristics are presented. In the InAs diode, was the large bandgap semiconductor AlSb used as barrier. The InGaAs diode was grown lattice matched to an InP substrate with InAlAs as a barrier material. The current density is greatly reduced for these two material combinations, compared to that of GaAs/AlGaAs SBV diodes. GaAs based diodes can be biased to higher voltages than InAs diodes.

Nilsen, Svein M.↗

NASA NTRS1992

Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

Earl, James A.↗

NASA NTRS1956

Effect of interaction on landing-gear behavior and dynamic loads in a flexible airplane structure

The effects of interaction between a landing gear and a flexible airplane structure on the behavior of the landing gear and the loads in the structure have been studied by treating the equations of motion of the airplane and the landing gear as a coupled system. The landing gear is considered to have nonlinear characteristics typical of conventional gears, namely, velocity-squared damping, polytropic air-compression springing, and exponential tire force-deflection characteristics. For the case where only two modes of the structure are considered, an equivalent three-mass system is derived for representing the airplane and landing-gear combination, which may be used to simulate the effects of structural flexibility in jig drop tests of landing gears. As examples to illustrate the effects of interaction, numerical calculations, based on the structural properties of two large airplanes having considerably different mass and flexibility characteristics, are presented.

Cook, Francis E↗

NASA NTRS1995

Simulated dynamic response of a multi-stage compressor with variable molecular weight flow medium

A mathematical model of a multi-stage compressor with variable molecular weight flow medium is derived. The modeled system consists of a five stage, six cylinder, double acting, piston type compressor. Each stage is followed by a water cooled heat exchanger which serves to transfer the heat of compression from the gas. A high molecular weight gas (CFC-12) mixed with air in varying proportions is introduced to the suction of the compressor. Condensation of the heavy gas may occur in the upper stage heat exchangers. The state equations for the system are integrated using the Advanced Continuous Simulation Language (ACSL) for determining the system's dynamic and steady state characteristics under varying operating conditions.

Babcock, Dale A.↗

NASA NTRS1999

A One Dimensional, Time Dependent Inlet/Engine Numerical Simulation for Aircraft Propulsion Systems

The NASA Lewis Research Center (LeRC) and the Arnold Engineering Development Center (AEDC) have developed a closely coupled computer simulation system that provides a one dimensional, high frequency inlet/engine numerical simulation for aircraft propulsion systems. The simulation system, operating under the LeRC-developed Application Portable Parallel Library (APPL), closely coupled a supersonic inlet with a gas turbine engine. The supersonic inlet was modeled using the Large Perturbation Inlet (LAPIN) computer code, and the gas turbine engine was modeled using the Aerodynamic Turbine Engine Code (ATEC). Both LAPIN and ATEC provide a one dimensional, compressible, time dependent flow solution by solving the one dimensional Euler equations for the conservation of mass, momentum, and energy. Source terms are used to model features such as bleed flows, turbomachinery component characteristics, and inlet subsonic spillage while unstarted. High frequency events, such as compressor surge and inlet unstart, can be simulated with a high degree of fidelity. The simulation system was exercised using a supersonic inlet with sixty percent of the supersonic area contraction occurring internally, and a GE J85-13 turbojet engine.

Doug Garrard↗

NASA NTRS2000

Impact of Energy Gain and Subsystem Characteristics on Fusion Propulsion Performance Balances

Rapid transportation of large payloads and human crews to destinations throughout the solar system will require propulsion systems having not only very high exhaust velocities (I (sub sp) greater than or equal to 10 (exp 4) to 10 (exp 5) sec) but also extremely low mass-power ratios (alpha less than or equal to 10 (exp -1) kg/kW). Such low a are difficult to achieve with power-limited propulsion systems. but may be attainable with fusion and other high I (sub SP) nuclear concepts that produce energy within the propellant. The magnitude of this energy gain is of fundamental importance. It must be large enough to sustain the nuclear process while still providing a high jet power relative to the massive power-intensive subsystems associated with these types of concepts. This paper evaluates the energy gain and mass-power characteristics required for a consistent with 1-year roundtrip planetary missions ranging up to 100 AU. Central to this analysis is an equation for overall system a, which is derived from the power balance of a generalized "gain-limited" propulsion system. Results show that the gain required to achieve alpha approximately 10 (exp -1) kg/kW with foreseeable subsystem technology can vary from 50 to as high as 10,000, which is 2 to 5 orders of magnitude greater than current state-of-the art. However, order of magnitude improvements in propulsion subsystem mass and efficiency could reduce gain requirements to 10 to 1,000 - still a very challenging goal.

Chakrabarti, Suman↗

NASA NTRS2001

Development of an Innovative Algorithm for Aerodynamics-Structure Interaction Using Lattice Boltzmann Method

The lattice Boltzmann equation (LBE) is a kinetic formulation which offers an alternative computational method capable of solving fluid dynamics for various systems. Major advantages of the method are owing to the fact that the solution for the particle distribution functions is explicit, easy to implement, and the algorithm is natural to parallelize. In this final report, we summarize the works accomplished in the past three years. Since most works have been published, the technical details can be found in the literature. Brief summary will be provided in this report. In this project, a second-order accurate treatment of boundary condition in the LBE method is developed for a curved boundary and tested successfully in various 2-D and 3-D configurations. To evaluate the aerodynamic force on a body in the context of LBE method, several force evaluation schemes have been investigated. A simple momentum exchange method is shown to give reliable and accurate values for the force on a body in both 2-D and 3-D cases. Various 3-D LBE models have been assessed in terms of efficiency, accuracy, and robustness. In general, accurate 3-D results can be obtained using LBE methods. The 3-D 19-bit model is found to be the best one among the 15-bit, 19-bit, and 27-bit LBE models. To achieve desired grid resolution and to accommodate the far field boundary conditions in aerodynamics computations, a multi-block LBE method is developed by dividing the flow field into various blocks each having constant lattice spacing. Substantial contribution to the LBE method is also made through the development of a new, generalized lattice Boltzmann equation constructed in the moment space in order to improve the computational stability, detailed theoretical analysis on the stability, dispersion, and dissipation characteristics of the LBE method, and computational studies of high Reynolds number flows with singular gradients. Finally, a finite difference-based lattice Boltzmann method is developed for inviscid compressible flows.

Mei, Ren-Wei↗

NASA NTRS2002

Small Particle Response to Fluid Motion using Tethered Particles to Simulate Microgravity

This paper reports on ground based work conducted to support the Spaceflight Definition project SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus). SHIVA will advance our understanding of the movement of a particle in a fluid. Gravity usually dominates the equations of motion, but in microgravity as well as on earth other terms can become important. Before two members of our team found an analytical solution of the equations, numerical methods and/or neglecting terms were required. The general solution predicts that the usually neglected history term becomes important when the characteristic viscous time is in the same order as the vibration period and peaks when the two times are equal. In this case three force terms, the Stokes drag, the added mass, and the history drag must all be included in predicting particle movement. We also developed diagnostic recording methods using holography to save all of the particle field data, allowing the experiment to essentially be transferred from space back to earth in what we call the "virtual apparatus". Using state-of-the-art methods in holography we will quantify the three-dimensional motion of sets of particles, allowing us to test and apply the new analytical solutions. The motion of particles up to 4 mm in diameter in a fluid that oscillates at frequencies up to 100 Hz with amplitudes up to 200 microns is being examined. Ground studies to support the flight development program have employed various schemes to simulate microgravity. One of the most reliable and meaningful methods uses spheres tethered to a fine hair suspended in the fluid. We have also investigated particles with nearly neutral buoyancy. Recordings are made at the peak amplitudes of vibration of the cell providing a measure of the ratio of fluid to particle amplitude. The experiment requires precise location of the particle at the time of recording. The hologram of the particle provides microscopic images of the particle that are used for finding the position with an accuracy of a few microns. To make the experiment more versatile, the spaceflight system will record holograms both on film and electronically. The electronic holograms can be downlinked providing real time data. Results of the ground experiments, the flight experiment design, and data analysis procedures are reported.

Trolinger, J. D.↗

NASA NTRS2002

Small Particle Response to Fluid Motion using Tethered Particles to Simulate Microgravity

This paper reports on ground based work conducted to support the Spaceflight Definition project SHIVA (Spaceflight Holography Investigation in a Virtual Apparatus). SHIVA will advance our understanding of the movement of a particle in a fluid. Gravity usually dominates the equations of motion, but in microgravity as well as on earth other terms can become important. Before two members of our team found an analytical solution of the equations, numerical methods and/or neglecting terms were required. The general solution predicts that the usually neglected history term becomes important when the characteristic viscous time is in the same order as the vibration period and peaks when the two times are equal. In this case three force terms, the Stokes drag, the added mass, and the history drag must all be included in predicting particle movement. We also developed diagnostic recording methods using holography to save all of the particle field data, allowing the experiment to essentially be transferred from space back to earth in what we call the "virtual apparatus". Using state-of-the-art methods in holography we will quantify the three-dimensional motion of sets of particles, allowing us to test and apply the new analytical solutions. The motion of particles up to 4 mm in diameter in a fluid that oscillates at frequencies up to 100 Hz with amplitudes up to 200 microns is being examined. Ground studies to support the flight development program have employed various schemes to simulate microgravity. One of the most reliable and meaningful methods uses spheres tethered to a fine hair suspended in the fluid. We have also investigated particles with nearly neutral buoyancy. Recordings are made at the peak amplitudes of vibration of the cell providing a measure of the ratio of fluid to particle amplitude. The experiment requires precise location of the particle at the time of recording. The hologram of the particle provides microscopic images of the particle that are used for finding the position with an accuracy of a few microns. To make the experiment more versatile, the spaceflight system will record holograms both on film and electronically. The electronic holograms can be downlinked providing real time data. Results of the ground experiments, the flight experiment design, and data analysis procedures are reported.

Trolinger, J. D.↗