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NASA NTRS2018

Detonation to Deflagration-Mode Transitions in Pulsed Plasma Accelerators

PULSED plasma accelerators typically operate by storing energy in a capacitor bank and then discharging this energy through a gas. The current in such discharges will ionize the gas and produce a strong magnetic field, which interacts with the flowing current to accelerate the plasma through the Lorentz body force. For the present work, two plasma accelerator types employing this general scheme are of interest: the gas-fed pulsed plasma thruster (PPT) 1 and the quasi-steady magnetoplasmadynamic (MPD) accelerator. 2 The gas-fed pulsed plasma accelerator is generally understood as a completely transient device discharging in ∼1-10 μs. When the capacitor bank is discharged through the gas, a current sheet forms at the breech of the thruster and propagates forward under a j × B body force, entraining and accelerating propellant it encounters. This process is sometimes referred to in literature as 'snowplowing' the propellant or accelerating the gas in a detonation-mode because the current sheet representation approximates that of a strong detonation shockwave propagating through the gas. For these devices, acceleration of the initial current sheet ceases when either the current sheet reaches the end of the device and is ejected or when the current in the circuit reverses, striking a new 'crowbar' discharge at the breech and depriving the initial sheet of additional acceleration. In general, PPTs typically claim thrust efficiencies (ratio of jet kinetic energy to input electrical energy) registering in the teens or lower. 3 In the quasi-steady MPD accelerator, the pulse is lengthened to ∼1 ms or longer and maintained at an approximately constant level during discharge through the use of a pulse-forming network (PFN) of capacitors. After an initial transient discharge, which is typically short relative to the overall discharge period, the plasma assumes a relatively steady-state configuration, known as 'quasi-steady' MPD operation. 2 In this state, ionized gas flows through a stationary current channel in a manner that is sometimes referred to as deflagration-mode operation owing to the similarities to deflagration waves in gases. The plasma experiences electromagnetic acceleration as the plasma flows through the current channel towards the exit of the device. Quasi-steady MPD thrusters claim efficiencies up to 50% for certain propellants.4 There has been significant and sustained research over several decades on both gas-fed PPTs and quasi-steady MPD thrusters, however there have been pulsed thrusters that do not appear to exactly fit either classification, instead possessing a mixture of operational qualities characteristic of both thruster variants. The Coaxial High ENerGy (CHENG) thruster by Cheng, et al.5 operated on the short 10 μs timescales characteristic of PPTs, but claimed the high thrust densities, high efficiencies, and low electrode erosion rates that are more consistent with the MPD/deflagration mode of plasma acceleration. Gas-fed PPT research by Ziemer, et al. 3, 6 identified two separate regimes of performance in those thrusters. The regime at higher mass bits (termed Mode I in that work) possessed relatively constant thrust efficiency as a function of mass bit, while the second regime at very low mass bits (termed Mode II) exhibited an increase in efficiency with decreasing mass bit. Work by Poehlmann et al.7 and by Sitaraman and Raja8 sought to understand the performance of the CHENG thruster and the Mode I/Mode II performance in PPTs by modeling the acceleration using the Hugoniot Relation, with the detonation and deflagration modes of plasma acceleration representing two distinct sets of solutions to the relevant conservation laws. In these works, it was proposed that the values of the various controllable parameters determined whether the accelerator would operate in detonation or deflagration mode. Our hypothesized view of the acceleration process in the CHENG thruster and in PPTs experiencing a transition from Mode I to Mode II is inspired by observations of the transition from the PPT mode of operation to the quasi-steady MPD mode. Specifically, the quasi-steady MPD was discovered by driving a PPT to extended pulse lengths. Above a certain pulse length threshold the transient plasma current sheet transitions into a stable plasma acceleration mode that 'replicates in every observable detail steady flow self-field magnetoplasmadynamic acceleration.' 9 In the present work, instead of treating the accelerator as if it were only operating in a single mode during a pulse, we consider the initial stage of the discharge in all cases as a current sheet forming at the breach of the accelerator and moving towards the exit as a detonation wave. If the current sheet reaches the exit of the accelerator before the discharge is completed, the view of the acceleration mode transitions to the deflagration mode-type found in quasi-steady MPD thrusters. In previous work10 we presented a modeling framework that first captured the time-evolution of the current sheet (detonation) mode of the thruster and then transitioned into the quasi-steady MPD (deflagration) mode of plasma acceleration. In the present work, variations of the controllable parameters - specifically the pulsed circuit properties, the amount of mass injected into the thruster, and the relative timing between the initial gas injection and the initiation of the plasma current sheet - will be used to explore the thruster performance. A range of parameters are explored to demonstrate that standard gas-fed pulsed plasma accelerators, the CHENG thruster, and the quasi-steady MPD accelerator are variations of the same device, with the overall acceleration of the plasma depending upon the behavior of the plasma discharge during initial transient phase and the relative lengths of the detonation and deflagration modes of operation.

Polzin, Kurt A.↗

NASA NTRS2012

Regional Warming from Aerosol Removal over the United States: Results from a Transient 2010-2050 Climate Simulation

We use a general circulation model (NASA Goddard Institute for Space Studies GCM 3) to investigate the regional climate response to removal of aerosols over the United States. We perform a pair of transient 2010e2050 climate simulations following a scenario of increasing greenhouse gas concentrations, with and without aerosols over the United States and with present-day aerosols elsewhere. We find that removing U.S. aerosol significantly enhances the warming from greenhouse gases in a spatial pattern that strongly correlates with that of the aerosol. Warming is nearly negligible outside the United States, but annual mean surface temperatures increase by 0.4e0.6 K in the eastern United States. Temperatures during summer heat waves in the Northeast rise by as much as 1e2 K due to aerosol removal, driven in part by positive feedbacks involving soil moisture and low cloud cover. Reducing U.S. aerosol sources to achieve air quality objectives could thus have significant unintended regional warming consequences.

Mickley, L. J.↗

NASA NTRSDate not supplied

Development of an analytical transient evacuation model for the fairing jettison process

A general, lumped-parameter, control volume equation is developed to describe the rapid loss of pressure associated with a launch vehicle fairing jettison event in its initial phase. Beginning with a general mass conservation statement, a sonic constraint is applied to the expanding gap between receding fairing halves to produce a statement for transient density. This is related to fairing pressure by assuming the expansion may be described by a polytropic process. A generic, single-step, lateral fairing half separation case is created and explored for illustrative purposes.

Fairing depressurization↗

NASA NTRSDate not supplied

Development of an analytical transient evacuation model for the fairing jettison process

fairing depressurization↗

NASA NTRSDate not supplied

Development of an Analytical Transient Evacuation Model for the Fairing Jettison Process

fairing depressurization, jettison, venting↗

NASA NTRS1976

Investigation of Critical Burning of Fuel Droplets

An earlier analysis for the combustion response of a liquid monopropellant strand (hydrazine) was extended to consider individual droplets and sprays. While small drops gave low or negative response, large droplets provided response near unity at low frequencies, with the response declining at frequencies greater than the characteristic liquid phase frequency. Temperature gradients in the liquid phase resulted in response peaks greater than unity. A second response peak was found for large drops which corresponded to gas phase transient effects. Spray response was generally reduced from the response of the largest injected droplet, however, even a small percentage of large droplets can yield appreciable response. An apparatus was designed and fabricated to allow observation of bipropellant fuel spray combustion at elevated pressures. A locally homogeneous model was developed to describe this combustion process which allows for high pressure phenomena associated with the thermodynamic critical point.

Chanin, S. P.↗

NASA NTRS1981

Engine dynamic analysis with general nonlinear finite-element codes. I Overall approach and development of bearing damper element

NASA-sponsored research on engine dynamic simulation using general finite element nonlinear time transient computer codes available on the open market is reviewed. The approach taken was to develop software packages to model engine components which are not typically found on dynamical structures and are therefore not already computer codes. The software package developed for squeeze-film bearing dampers is outlined, and the results of a parametric study of damper pressure for a variety of specified circular orbits are presented for both long-bearing and short-bearing solutions. The data from a four-degree-of-freedom rotor-damper-stator model under conditions of small rotor unbalance through large rotor unbalance are also given.

Adams, M. L.↗

NASA NTRS1982

Terrestrial cooling and solar variability

Observational evidence from surface temperature records is presented and discussed which suggests a significant cooling trend over the Northern Hemisphere from 1940 to the present. This cooling trend is associated with an increase of the latitudinal gradient of temperature and the lapse rate, as predicted by climate models with decreased solar input and feedback mechanisms. Evidence suggests that four of these 80- to 100-year cycles of global surface temperature fluctuation may have occurred, and in succession, from 1600 to the present. Interpretation of sunspot activity were used to infer a direct thermal response of terrestrial temperature to solar variability on the time scale of the Gleissberg cycle (90 years, an amplitude of the 11-year cycles). A physical link between the sunspot activity and the solar parameter is hypothesized. Observations of sensible heat flux by stationary planetary waves and transient eddies, as well as general circulation modeling results of these processes, were examined from the viewpoint of the hypothesis of cooling due to reduced insolation.

Agee, E. M.↗

NASA NTRS1986

Wave propagation in anisotropic medium due to an oscillatory point source with application to unidirectional composites

The far-field displacements in an infinite transversely isotropic elastic medium subjected to an oscillatory concentrated force are derived. The concepts of velocity surface, slowness surface and wave surface are used to describe the geometry of the wave propagation process. It is shown that the decay of the wave amplitudes depends not only on the distance from the source (as in isotropic media) but also depends on the direction of the point of interest from the source. As an example, the displacement field is computed for a laboratory fabricated unidirectional fiberglass epoxy composite. The solution for the displacements is expressed as an amplitude distribution and is presented in polar diagrams. This analysis has potential usefulness in the acoustic emission (AE) and ultrasonic nondestructive evaluation of composite materials. For example, the transient localized disturbances which are generally associated with AE sources can be modeled via this analysis. In which case, knowledge of the displacement field which arrives at a receiving transducer allows inferences regarding the strength and orientation of the source, and consequently perhaps the degree of damage within the composite.

Williams, J. H., Jr.↗

NASA NTRS1987

Thermal-Analysis Program

Temperature changes with time modeled with traditional electrical analog. General Thermal Analyzer program solves transient and steadystate thermal problems using desk-top computers. Program written in BASIC.

Levine, D. I.↗

NASA NTRS1990

Microgravity acoustic mixing for particle cloud combustors

Experimental and theoretical investigations of acoustic mixing procedures designed to uniformly distribute fuel particles in a combustion tube for application in the proposed Particle Cloud Combustion Experiment (PCCE) are described. Two acoustic mixing methods are investigated: mixing in a cylindrical tube using high frequency spinning modes generated by suitably phased, or quadrature speakers, and acoustic premixing in a sphere. Quadrature mixing leads to rapid circumferential circulation of the powder around the tube. Good mixing is observed in the circulating regions. However, because axial inhomogeneities are necessarily present in the acoustic field, this circulation does not extend throughout the tube. Simultaneous operation of the quadrature-speaker set and the axial-speaker was observed to produce considerably enhanced mixing compared to operation of the quadrature-speaker set alone. Mixing experiments using both types of speakers were free of the longitudinal powder drift observed using axial-speakers alone. Vigorous powder mixing was obtained in the sphere for many normal modes: however, in no case was the powder observed to fill the sphere entirely. Theoretical analysis indicated that mixing under steady conditions cannot fill more than a hemisphere except under very unusual conditions. Premixing in a hemisphere may be satisfactory; otherwise, complete mixing in microgravity might be possible by operating the speaker in short bursts. A general conclusion is that acoustic transients are more likely to produce good mixing than steady state conditions. The reason is that in steady conditions, flow structures like nodal planes are possible and often even unavoidable. These tend to separate the mixing region into cells across which powder cannot be transferred. In contrast, transients not only are free of such structures, they also have the characteristics, desirable for mixing, of randomness and disorder. This conclusion is corroborated by mixing experiments using axial waves.

Pla, Frederic↗

NASA NTRS1996

Waveform Perturbations os Spherical Transiet Waves Propagating in a Random Medium

Of those aspects of sonic-boom propagation that are not yet fully understood, one of the more important is that which relates to the perturbations of the waveform. This phenomenon, which arises also in connection with the propagation of other types of transient waves in real media, generally take the form, in the case of sonic-boom N-waves, of a random high-frequency structure (sometimes called fine structure) that is most prominent in the regions immediately behind each of the shocks. The perturbations in those regions can be large, occasionally attaining magnitudes comparable to that of th incident wave itself. Such magnitudes, in combination with the high-frequency character of the perturbations, can lead to a considerable increase in the perceived noisiness of the sonic boom. Waveform perturbations are consequently an important factor as regards the question of sonic-boom acceptability. On the basis of observations, and some early theoretical studies, it is now generally accepted that perturbations of sonic-boom waveforms are a manifestation of the effect on the propagating wave of relatively small-scale variations in the acoustic properties of the atmosphere- variations that are usually associated with turbulence. Although the mechanism underlying perturbations of sonic-boom waveforms seems thus to be well understood, no fully-satisfactory theory of such perturbations has emerged. Indeed, even for the relatively simple case of an incident step-function pulse, no theory of waveform perturbations, formulated in a realistic three-dimensional context, has been advanced that is valid in the region of strongest perturbations; viz., the region immediately behind, and including, the wave front. The work reported herein represents an attempt to develop such a theory.

Wenzel, Alan R.↗

NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗

NASA NTRS2018

Acceleration Modes and Transitions in Pulsed Plasma Accelerators

Pulsed plasma accelerators typically operate by storing energy in a capacitor bank and then discharging this energy through a gas, ionizing and accelerating it through the Lorentz body force. Two plasma accelerator types employing this general scheme have typically been studied: the gas-fed pulsed plasma thruster and the quasi-steady magnetoplasmadynamic (MPD) accelerator. The gas-fed pulsed plasma accelerator is generally represented as a completely transient device discharging in approximately 1-10 microseconds. When the capacitor bank is discharged through the gas, a current sheet forms at the breech of the thruster and propagates forward under a j (current density) by B (magnetic field) body force, entraining propellant it encounters. This process is sometimes referred to as detonation-mode acceleration because the current sheet representation approximates that of a strong shock propagating through the gas. Acceleration of the initial current sheet ceases when either the current sheet reaches the end of the device and is ejected or when the current in the circuit reverses, striking a new current sheet at the breech and depriving the initial sheet of additional acceleration. In the quasi-steady MPD accelerator, the pulse is lengthened to approximately 1 millisecond or longer and maintained at an approximately constant level during discharge. The time over which the transient phenomena experienced during startup typically occur is short relative to the overall discharge time, which is now long enough for the plasma to assume a relatively steady-state configuration. The ionized gas flows through a stationary current channel in a manner that is sometimes referred to as the deflagration-mode of operation. The plasma experiences electromagnetic acceleration as it flows through the current channel towards the exit of the device. A device that had a short pulse length but appeared to operate in a plasma acceleration regime different from the gas-fed pulsed plasma accelerators was developed by Cheng, et al. The Coaxial High ENerGy (CHENG) thruster operated on the 10-microseconds timescales of pulsed plasma thrusters, but claimed high thrust density, high efficiency and low electrode erosion rates, which are more consistent with the deflagration mode of acceleration. Separate work on gas-fed pulsed plasma thrusters (PPTs) by Ziemer, et al. identified two separate regimes of performance. The regime at higher mass bits (termed Mode I in that work) possessed relatively constant thrust efficiency (ratio of jet kinetic energy to input electrical energy) as a function of mass bit. In the second regime at very low mass bits (termed Mode II), the efficiency increased with decreasing mass bit. Work by Poehlmann et al. and by Sitaraman and Raja sought to understand the performance of the CHENG thruster and the Mode I / Mode II performance in PPTs by modeling the acceleration using the Hugoniot Relation, with the detonation and deflagration modes representing two distinct sets of solutions to the relevant conservation laws. These works studied the proposal that, depending upon the values of the various controllable parameters, the accelerator would operate in either the detonation or deflagration mode. In the present work, we propose a variation on the explanation for the differences in performance between the various pulsed plasma accelerators. Instead of treating the accelerator as if it were only operating in one mode or the other during a pulse, we model the initial stage of the discharge in all cases as an accelerating current sheet (detonation mode). If the current sheet reaches the exit of the accelerator before the discharge is completed, the acceleration mode transitions to the deflagration mode type found in the quasi-steady MPD thrusters. This modeling method is used to demonstrate that standard gas-fed pulsed plasma accelerators, the CHENG thruster, and the quasi-steady MPD accelerator are variations of the same device, with the overall acceleration of the plasma depending upon the behavior of the plasma discharge during initial transient phase and the relative lengths of the detonation and deflagration modes of operation.

Polzin, Kurt A.↗

NASA NTRS1991

Finite difference time domain calculation of transients in antennas with nonlinear loads

In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Luebbers, Raymond J.↗

NASA NTRS1991

Finite difference time domain calculation of transients in antennas with nonlinear loads

Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Luebbers, Raymond J.↗

NASA NTRS1977

Variability and transport of ozone at the tropopause from the first year of GASP data

The relationships of ozone near the tropopause with potential vorticity temperature, and distance from the tropopause are examined. Data are also used to estimate the vertical and horizontal fluxes of ozone near the tropopause. The present estimates of the total flux of ozone into the troposphere verify the model results. Although the distribution of flux between mean motions and diffusion is different and thus suggests that models with coarse horizontal resolution must continue to parameterize much vertical transport by diffusion coefficients. Monthly estimates of the horizontal transient eddy flux of ozone are generally smaller than seasonal or yearly results based on ozonesonde data. This is perhaps because the present estimates are made over monthly periods to reduce the influence of correlation between the annual variations in ozone and meridional wind. The available data support the hypothesis that transient eddy fluxes of ozone have large longitudinal variations.

Nastrom, G. D.↗

NASA NTRS1977

Vertical and horizontal fluxes of ozone at the tropopause from the first year of GASP data

Ozone measurements taken from commercial airlines (GASP data) are used to estimate the vertical and horizontal fluxes of ozone near the tropopause. The annual average flux of O3 into the troposphere at 30 to 50 deg N is nearly the same as indirect estimates based on surface O3 data, thus supporting the hypothesis that the amount of ozone in the troposphere is essentially controlled by injection from the stratosphere. The present GASP estimates of the total flux of O3 into the troposphere verify the model results of Cunnold et al. (1975), although the distribution of flux between mean motions and diffusion is different and suggests that models with coarse horizontal resolution must continue to parameterize much vertical transport by diffusion coefficients. A significant variation in the east-west spatial autocorrelation function of O3 near the tropopause is found to be about 1900 km. Monthly estimates of the horizontal transient eddy flux of ozone are generally smaller than seasonal or yearly results based on ozonesonde data. This is perhaps because the present estimates are made over monthly periods to reduce the influence of correlation between the annual variations in ozone and meridional wind. The available data support the hypothesis that transient eddy fluxes of O3 have large longitudinal variations.

Nastrom, G. D.↗