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NASA NTRS1986

Analysis of the harmonic gyrotron traveling wave amplifier

A single nonlinear differential equation is derived for describing the spatial evolution of the wave field in a gyrotron amplifier on the cylindrical guide geometry. The equation is then used to determine the efficiencies and the optimized interaction lengths for gyrotron operated with TE sub N1 modes at the N-th cyclotron harmonic. The equation offers a significant advantage in simplifying numerical work in comparison with the brute force particle simulation approach. The efficiencies of the harmonic operations by using a hollow beam decrease quickly with increasing harmonic number, but are enhanced by using an axis-encircling beam instead.

Kuo, S. P.↗

NASA NTRS1992

Radiated noise of ducted fans

The differences in the radiated acoustic fields of ducted and unducted propellers of the same thrust operating under similar conditions are investigated. An FEM model is created for the generation, propagation, and radiation of steady, rotor alone noise and exit guide vane interaction noise of a ducted fan. For a specified number of blades, angular mode harmonic, and rotor angular velocity, the acoustic field is described in a cylindrical coordinate system reduced to only the axial and radial directions. It is found that, contrary to the usual understanding of the Tyler and Sofrin (1962) result, supersonic tip speed rotor noise can be cut off if the tip Mach number is only slightly in excess of unity and if the number of blades is relatively small. If there are many blades, the fundamental angular mode number is large, and the Tyler and Sofrin result for thin annuli becomes more relevant. Shrouding of subsonic tip speed propellers is a very effective means of controlling rotor alone noise.

Eversman, Walter↗

NASA NTRS1977

Ion sheath effects on RF plasma probes - Experimental results in laboratory plasmas

Laboratory work dealing with the frequency characteristic of the plasma impedance of spherical and cylindrical electrode systems is reported. The influence of the ion sheath on various features of the impedance characteristic is emphasized. Those features are the series and parallel resonance as well as additional resonances due to the excitation of electroacoustic and cyclotron harmonic waves. The dependence of the series and parallel resonances on dc biasing leads to a method of determining the ion sheath capacity for a cylindrical electrode system. The obtained values agree fairly well with those obtained from a theoretical model for the density and potential distribution in the sheath of a cylindrical sensor aligned with a supersonic plasma flow. The amplitude of resonances due to excitation of longitudinal plasma waves (electroacoustic and cyclotron harmonic) is reduced or even vanishes for sufficiently negative dc bias. Positive bias first leads to an increased amplitude up to a certain dc bias value above which, however, the amplitude decreases again due to electron absorption at the sensor surface.

Kist, R.↗

NASA NTRS1973

Theory for radiatively driven harmonic acoustic waves in a confined gas.

A detailed theoretical study is made of radiatively driven acoustic waves inside a closed cylindrical tube. The formulation accounts for all the essential phenomena for a gas in vibrational equilibrium - namely, gas motion, longitudinal and radial viscous dissipation, longitudinal and radial heat conduction, and radiative transfer with spectral detail included. An approximate expression is derived for the pressure response. This solution is applicable to arbitrary spectral distribution of the radiative absorption coefficient, under conditions attainable in the laboratory. The solution includes both tuned and untuned acoustic conditions as well as the spectrophone limit - that is, the condition where the length of the tube is much smaller than the length of the acoustic wave. The influence of spectral detail on the pressure response is illustrated.

Chapman, G. T.↗

NASA NTRS1981

Influence of exit impedance on finite difference solutions of transient acoustic mode propagation in ducts

The time-dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard-wall duct without flow and with spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the steady solutions of the acoustic field. The transient method did not converge to the steady-state solution for cutoff acoustic duct modes. This has implications as to its use in a variable-area duct, where modes may become cutoff in the smal-area portion of the duct. For single cutoff mode propagation the steady-state impedance boundary condition produced acoustic reflections during the initial transient that caused finite instabilities in the numerical calculations. The stability problem is resolved by reformulating the exit boundary condition. Example calculations show good agreement with exact analytical and numerical results for forcing frequencies above, below, and nearly at the cutoff frequency.

Baumeister, K. J.↗

NASA NTRS1980

Time dependent difference theory for sound propagation in axisymmetric ducts with plug flow

The time dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard wall duct with a plug mean flow and spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solutions of the acoustic field. The time dependent finite difference analysis has two advantages over the steady state finite difference and finite element techniques: (1)the elimination of large matrix storage requirements, and (2)shorter solution times under most conditions.

Baumeister, K. J.↗

NASA NTRS1980

Time dependent difference theory for sound propagation in axisymmetric ducts with plug flow

The time dependent governing/acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard wall duct with a plug mean flow and spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solutions of the acoustic field. The time dependent finite difference analysis has two advantages over the steady state finite difference and finite element techniques: (1) the elimination of large matrix storage requirements, and (2) shorter solution times under most conditions.

Baumeister, K. J.↗

NASA NTRS1985

Long range downwind propagation of low-frequency sound

The propagation of low-frequency noise outdoors was studied using as the source a large (80-m diameter) 4-megawatt horizontal axis wind turbine. Acoustic measurements were made with low-frequency microphone systems placed on the ground at five downwind sites ranging from 300 m to 10,000 m (6.3 mile) away from the wind turbine. The wind turbine fundamental was 1 Hz and the wind speed was generally 12 - 15 m/s at the hub height (80 m). The harmonic levels, when plotted versus propagation distance, exhibit a 3 dB per doubling of distance divergence. Two plausible explanations identified for this cylindrical spreading behavior were propagation of the low frequency wind turbine noise via a surface wave and downwind refraction. Surface was amplitude predictions were found to be more than 20 dB smaller than the measured levels. Ray-tracing results were used to qualitatively explain measured trends. A normal mode approach was identified as a candidate method for low-frequency acoustic refraction prediction.

Willshire, W. L., Jr.↗

NASA NTRS1986

Active control of propeller induced noise fields inside a flexible cylinder

An active noise control model has been evaluated for reducing aircraft interior noise. The structural noise transmission properties of an aircraft fuselage were modelled as a flexible cylinder excited by external acoustic dipoles simulating the noise produced by twin propellers. The amplitudes of an internal distribution of monopole control sources were determined such that the area-weighted mean square acoustic pressure was minimized in the propeller plane. The noise control model was evaluated at low frequencies corresponding to the blade passage frequency and first few harmonics of a typical turbo-prop aircraft. Interior noise reductions of 20 25 dB were achieved, over a substantial region of the cylindrical cross-section, with just a few monopole control sources. The most favorable interior noise reductions were achieved when the active noise control model was used in combination with propeller source phasing.

Lester, H. C.↗

NASA NTRS1973

Experiments on radiatively driven harmonic acoustic waves in a confined gas.

Measurements are presented of the acoustic pressure resulting from the periodic absorption and emission of radiative energy by an infrared-active gas contained in a closed, cylindrical tube. The acoustic waves are generated by means of an external, sinusoidally time-modulated blackbody source. The pressure measurements are for both resonant and nonresonant conditions at acoustic frequencies from about 60 to 600 Hz. Comparison of the measurements with predictions shows that the response is due primarily to the modified-classical acoustic wave, but that a small contribution from the so-called radiation-induced wave can be measured in certain of the tests. Strong effects of vibrational nonequilibrium, similar to those observed previously in spectrophone studies, were found in some of the tests.

Compton, D. L.↗

NASA NTRS1980

Spontaneous emission of radiation from localized Langmuir perturbation

The radiation at the first and second harmonics of the electron plasma frequency from localized Langmuir oscillations is computed for a field-free plasma. The localized perturbations are assumed to have cylindrical symmetry about the direction of propagation of the localized perturbation. It is shown that when the wavelengths of the excited modes are much greater than the scale lengths of the Langmuir perturbation, a quadrupole radiation pattern is recovered for emission at twice the electron plasma frequency. An application to type III solar radio bursts is discussed briefly.

Freund, H. P.↗

NASA NTRS1986

Waveguide submillimeter mixers

A waveguide Schottky barrier diode mixer, which in preliminary tests has yielded a single sideband receiver noise temperature of 4300 K at 692 GHz, when cooled to 77 K is presented. Further refinements and operation at 20 K should produce a significant improvement in performance. From a system point of view, the very high efficiency of the radiation pattern produced by the conical feedhorn with cylindrical corrector mirror enhances the effective sensitivity by a factor of 1.5 to 2 compared to open-structure corner-reflector systems. A second-harmonic mixer for 557 GHz, also in the fundamental mode rectangular waveguide was developed. When combined with a frequency-tripled Gunn oscillator, this makes an extremely compact and lightweight submillimeter radiometer.

Goldsmith, Paul F.↗

NASA NTRS1968

Large-amplitude inviscid fluid motion in an accelerating container

Study of dynamic behavior of the liquid-vapor interface of an inviscid fluid in an accelerating cylindrical container includes an analytical-numerical method for determining large amplitude motion. The method is based on the expansion of the velocity potential in a series of harmonic functions with time dependent coefficients.

Perko, L. M.↗

NASA NTRS1988

Mining volume measurement system

In a shaft with a curved or straight primary segment and smaller off-shooting segments, at least one standing wave is generated in the primary segment. The shaft has either an open end or a closed end and approximates a cylindrical waveguide. A frequency of a standing wave that represents the fundamental mode characteristic of the primary segment can be measured. Alternatively, a frequency differential between two successive harmonic modes that are characteristic of the primary segment can be measured. In either event, the measured frequency or frequency differential is characteristic of the length and thus the volume of the shaft based on length times the bore area.

Heyman, Joseph Saul↗

NASA NTRS1983

Radiation of sound from unflanged cylindrical ducts

Calculations of sound radiated from unflanged cylindrical ducts are presented. The numerical simulation models the problem of an aero-engine inlet. The time dependent linearized Euler equations are solved from a state of rest until a harmonic solution is attained. A fourth order accurate finite difference scheme is used and solutions are obtained from a fully vectorized Cyber-203 computer program. Cases of both plane waves and spin modes are treated. Spin modes model the sound generated by a turbofan engine. Boundary conditions for both plane waves and spin modes are treated. Solutions obtained are compared with experiments conducted at NASA Langley Research Center.

Hartharan, S. L.↗

NASA NTRS1975

Pulse width fluctuations in mode-locked Nd:YAG lasers

The experiment consisted of a flashlamp-pumped Nd:YAG laser rod in the Brewster-Brewster configuration, passively modelocked by a thick flowing dye in contact with the high reflectivity rear mirror. A single pulse was selected by a cylindrical-ring electrode Pockel's cell, and amplified by two Nd:YAG amplifiers. Calibrated photodiodes measured the total pulse energy at the fundamental frequency and the total pulse energy at the second harmonic frequency. The signals were monitored by a digital data acquisition system and displayed on a teletype printer.

Bechtel, J. H.↗

NASA NTRS1980

Analytical prediction of the interior noise for cylindrical models of aircraft fuselages for prescribed exterior noise fields. Phase 1: Development and validation of preliminary analytical models

The basic theoretical work required to understand sound transmission into an enclosed space (that is, one closed by the transmitting structure) is developed for random pressure fields and for harmonic (tonal) excitation. The analysis is used to predict the noise reducton of unpressurized unstiffened cylinder, and also the interior response of the cylinder given a tonal (plane wave) excitation. Predictions and measurements are compared and the transmission is analyzed. In addition, results for tonal (harmonic) mechanical excitation are considered.

Pope, L. D.↗

NASA NTRS1982

Effects of differential rotation on the gravitational figures of Jupiter and Saturn

It is assumed that observed zonal currents in the atmospheres of Jupiter and Saturn correspond to a state of permanent rotation, and that the angular velocity is constant on cylindrical surfaces parallel to the rotation axis. The equation of hydrostatic equilibrium for a rotating planet is solved under these restrictive assumptions, and the effect of the hypothesized rotation state on the planet's gravity harmonics and external shape is investigated. Spacecraft data on zonal currents are used to derive nearly model-independent corrections to the first four zonal gravity harmonic coefficients, which can be used to correct observed gravity harmonics to values appropriate for solid-body rotation. If the assumed rotation state is applicable, then zonal currents lead to measurable topography of isopycnic surfaces with respect to the reference figure defined by the magnetospheric rotation period and the gravity harmonics. The amplitude of the topography is on the order of 5 km for Jupiter and 60 km for Saturn.

Hubbard, W. B.↗