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NASA NTRS2010

Active Damping Using Distributed Anisotropic Actuators

A helicopter structure experiences substantial high-frequency mechanical excitation from powertrain components such as gearboxes and drive shafts. The resulting structure-borne vibration excites the windows which then radiate sound into the passenger cabin. In many cases the radiated sound power can be reduced by adding damping. This can be accomplished using passive or active approaches. Passive treatments such as constrained layer damping tend to reduce window transparency. Therefore this paper focuses on an active approach utilizing compact decentralized control units distributed around the perimeter of the window. Each control unit consists of a triangularly shaped piezoelectric actuator, a miniature accelerometer, and analog electronics. Earlier work has shown that this type of system can increase damping up to approximately 1 kHz. However at higher frequencies the mismatch between the distributed actuator and the point sensor caused control spillover. This paper describes new anisotropic actuators that can be used to improve the bandwidth of the control system. The anisotropic actuators are composed of piezoelectric material sandwiched between interdigitated electrodes, which enables the application of the electric field in a preferred in-plane direction. When shaped correctly the anisotropic actuators outperform traditional isotropic actuators by reducing the mismatch between the distributed actuator and point sensor at high frequencies. Testing performed on a Plexiglas panel, representative of a helicopter window, shows that the control units can increase damping at low frequencies. However high frequency performance was still limited due to the flexible boundary conditions present on the test structure.

Schiller, Noah H.↗

NASA NTRS1991

IRAS low-resolution spectral observations of the 10 and 18 micron silicate emission feature

The IRAS LRS Atlas contains 8-23 micron spectra of 1816 stars with silicate emission features. In order to study the shapes of the silicate dust features, the 117 stars whose emission features appear to be optically thin and which have the best signal-to-noise ratio at the longest wavelengths were analyzed. Simple spherical dust shell models were calculated in both the optically thin and the slightly optical thick approximations. From the comparison of the predicted spectra of the dust and stellar continuum, the emissivity function Kappa(lambda) was derived. In the different stars, the shape of the 10-micron feature is either narrow or broad and it is peaked either at about 9.7 microns or at 10 microns. Either particle size effects (particles above 0.75 microns in radius) or optical depth effects (central optical depth about 1) could broaden the 10-micron feature. Chemical composition differences no doubt are also important, particularly as regards the position of the peak of the 10-micron feature. The stars with the peak at 10 microns are more closely confined to the Galactic plane than the stars with the peak at 9.7 microns. The shape of the 18-micron feature is essentially the same in all stars, and can be used to extend the interstellar extinction curve past 13 to 22 microns.

Simpson, Janet P.↗

NASA NTRS1992

Effect of crash pulse shape on seat stroke requirements for limiting loads on occupants of aircraft

An analytical study was made to provide comparative information on various crash pulse shapes that potentially could be used to test seats under conditions included in Federal Regulations Part 23 Paragraph 23.562(b)(1) for dynamic testing of general aviation seats, show the effects that crash pulse shape can have on the seat stroke requirements necessary to maintain a specified limit loading on the seat/occupant during crash pulse loadings, compare results from certain analytical model pulses with approximations of actual crash pulses, and compare analytical seat results with experimental airplace crash data. Structural and seat/occupant displacement equations in terms of the maximum deceleration, velocity change, limit seat pan load, and pulse time for five potentially useful pulse shapes were derived; from these, analytical seat stroke data were obtained for conditions as specified in Federal Regulations Part 23 Paragraph 23.562(b)(1) for dynamic testing of general aviation seats.

Carden, Huey D.↗

NASA NTRS1986

Modeling, estimation and identification methods for static shape determination of flexible structures

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Rodriguez, G.↗

NASA NTRS1974

An approximate inviscid radiating flow-field analysis for sphere-cone Venusian entry vehicles

A computational method based on the earlier work of one of the authors has been improved and modified to provide an accurate and rapid prediction of the radiating flow about blunt conical probes entering the atmosphere of Venus. Special features include a more general approximate equation of state, a more rapidly converging iteration scheme, a 38-step absorption coefficient model for a Venus atmosphere gas mixture model, and a shock-shape formula which yields a computed body shape in excellent agreement with the desired body. The method was used to calculate distributions of radiative heating for a large spherically blunted conical probe vehicle (1.219 m base diameter) and for three small spherically blunted conical probe vehicles (0.724 m base diameter). Solutions obtained with the presently developed approximate method required short computing times of the order of 1 to 3 minutes for each complete solution and gave agreements of 10% to 15% with the more exact predictions.

Falanga, R. A.↗

NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗

NASA NTRS1999

Combustion Instabilities Modeled

NASA Lewis Research Center's Advanced Controls and Dynamics Technology Branch is investigating active control strategies to mitigate or eliminate the combustion instabilities prevalent in lean-burning, low-emission combustors. These instabilities result from coupling between the heat-release mechanisms of the burning process and the acoustic flow field of the combustor. Control design and implementation require a simulation capability that is both fast and accurate. It must capture the essential physics of the system, yet be as simple as possible. A quasi-one-dimensional, computational fluid dynamics (CFD) based simulation has been developed which may meet these requirements. The Euler equations of mass, momentum, and energy have been used, along with a single reactive species transport equation to simulate coupled thermoacoustic oscillations. A very simple numerical integration scheme was chosen to reduce computing time. Robust boundary condition procedures were incorporated to simulate various flow conditions (e.g., valves, open ends, and choked inflow) as well as to accommodate flow reversals that may arise during large flow-field oscillations. The accompanying figure shows a sample simulation result. A combustor with an open inlet, a choked outlet, and a large constriction approximately two thirds of the way down the length is shown. The middle plot shows normalized, time-averaged distributions of the relevant flow quantities, and the bottom plot illustrates the acoustic mode shape of the resulting thermoacoustic oscillation. For this simulation, the limit cycle peak-to-peak pressure fluctuations were 13 percent of the mean. The simulation used 100 numerical cells. The total normalized simulation time was 50 units (approximately 15 oscillations), which took 26 sec on a Sun Ultra2.

Paxson, Daniel E.↗

NASA NTRS1989

A unified model of accretion flows and X ray emission in low mass X ray binary systems

Recent work on a unified model of accretion flows and X-ray emission in low mass X-ray binaries is summarized. In this model, a weakly magnetic neutron star accretes gas simultaneously from a Keplerian disk and a corona above the inner part of the disk. Photons are produced and escape through an approximately radial inflow of gas captured from the inner disk corona. Changes in the optical depths of the central corona and the radial flow may explain the Z-shaped hardness-intensity and color-color tracks observed in the most luminous sources. Numerical simulations show that the radial flow oscillates when the luminosity rises to within a few percent of the Eddington critical luminosity L sub E, and that the oscillation frequency is approximately 5 to 10 Hz if the radial flow develops approximately 300 km from the neutron star. The 10 to 20 Hz oscillations observed in Sco X-1 when it is on the flaring branch are discussed.

Lamb, F. K.↗

DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1995

The luminosity function of quasars

We propose a new evolutionary model for the optical luminosity function of quasars. Our analytical model is derived from fits to the empirical luminosity function estimated by Hartwick and Schade and Warren, Hewett, and Osmer on the basis of more than 1200 quasars over the range of redshifts 0 approximately less than z approximately less than 4.5. We find that the evolution of quasars over this entire redshift range can be well fitted by a Gaussian distribution, while the shape of the luminosity function can be well fitted by either a double power law or an exponential L(exp 1/4) law. The predicted number counts of quasars, as a function of either apparent magnitude or redshift, are fully consistent with the observed ones. Our model indicates that the evolution of quasars reaches its maximum at z approximately = 2.8 and declines at higher redshifts. An extrapolation of the evolution to z approximately greater than 4.5 implies that quasars may have started their cosmic fireworks at z(sub f) approximately = 5.2-5.5. Forthcoming surveys of quasars at these redshifts will be critical to constrain the epoch of quasar formation. All the results we derived are based on observed quasars and are therefore subject to the bias of obscuration by dust in damped Ly alpha systems. Future surveys of these absorption systems at z approximately greater than 3 will also be important if the formation epoch of quasars is to be known unambiguously.

Pei, Yichuan C.↗

DOE OSTI2020

Au x Pd (300‐ x ) Alloy Nanoparticles for the Oxygen Reduction Reaction in Alkaline Media

Abstract Au x Pd (300‐ x ) nanoalloys were prepared using a dendrimer‐templating method and their electrocatalytic efficiencies towards the oxygen reduction reaction (ORR) were analyzed in alkaline media. The composition‐dependent PdO x reduction potentials of the Au x Pd (300‐ x ) nanoalloys were correlated to the oxygen‐binding (O‐binding) energy of the catalysts. Multiple PdO x reduction peaks were present for the Au 150 Pd 150 and Au 50 Pd 250 catalysts. These peaks were assigned to the alloyed and bulk‐like Pd active sites on the alloyed surface. The results described here are significant because modulation of the O‐binding energies improved the ORR activity on the nanoalloys. Specifically, a linear trend in O‐binding energies of Au x Pd (300‐ x ) dendrimers (DENs) as a function of Pd composition resulted in a volcano‐shaped trend in ORR activity. The optimal O‐binding energy of Au 50 Pd 250 resulted in an approximate 89 mV shift in PdO x reduction relative to Pd 300 and a shift of approximately 76 mV in ORR peak potential.

Trindell, Jamie A.↗

DOE OSTI2025

Convergence of Cloud Droplet Spectral Relative Dispersion During Entrainment‐Mixing Based on Particle‐Resolved Direct Numerical Simulations

Entrainment-mixing processes critically impact cloud microphysical properties, but their effects on the relative dispersion (d) of cloud droplet size distributions (CDSDs) remain elusive. A direct numerical simulation model is initialized with different CDSDs to fill the gap. These results show that d decreases for broad CDSDs and increases for narrow ones, ultimately converging to approximately 0.5 regardless of initial CDSDs during the evaporation-dominated mixing stage. The supersaturation fluctuation and the shape of CDSDs jointly influence the convergence behavior of d. Further sensitivity tests show that the initial microphysical/dynamical/thermodynamical conditions exert negligible effects on the final converged value of d but affect the convergence rate (k). The k generally increases with increasing droplet number concentration and dissipation rate, and increases with decreasing liquid water content, relative humidity of entrained air, and mixing fraction of cloudy air. A conceptual model with two timescales is proposed; k and the timescales are negatively correlated, meaning that slow mixing and/or evaporation process results in slow convergence of d. In conclusion, this finding provides an important reference for improving understanding and parameterization of d during the entrainment-mixing processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Experimental observation of open structures in elemental magnesium at terapascal pressures

Investigating how solid matter behaves at enormous pressures, such as those found in the deep interiors of giant planets, is a great experimental challenge. Over the past decade, computational predictions have revealed that compression to terapascal pressures may bring about counter-intuitive changes in the structure and bonding of solids as quantum mechanical forces grow in influence. Although this behavior has been observed at modest pressures in the highly compressible light alkali metals, it has not been established whether it is commonplace among high-pressure solids more broadly. We used shaped laser pulses at the National Ignition Facility to compress elemental Mg up to 1.3 TPa, which is approximately four times the pressure at the Earth’s core. By directly probing the crystal structure using nanosecond-duration X-ray diffraction, we found that Mg changes its crystal structure several times with non-close-packed phases emerging at the highest pressures. Our results demonstrate that phase transformations of extremely condensed matter, previously only accessible through theoretical calculations, can now be experimentally explored.

36 MATERIALS SCIENCE↗

NASA NTRS1971

Dynamics of plane stellar systems.

The evolution of initially balanced rotating disks of stars is investigated with a computer model for isolated disks of stars. An isolated, initially cold balanced disk is found to be violently unstable. Adding a sufficient amount of velocity dispersion will stabilize all small-scale disturbances. However, the disks are still unstable against slowly growing long wave-length modes and after about two rotations most disks tend to assume a bar-shaped structure. It is found that the final mass distribution over most of the disk can be closely approximated by an exponential variation, irrespective of the initial mass distribution. The gravitational two-stream instability is investigated by means of a modified computer model for infinite doubly periodic stellar systems.

Hohl, F.↗

NASA NTRS1972

Dynamics of plane stellar systems.

Hohl, F.↗

NASA NTRS1975

Effect of shape and size of lung and chest wall on stresses in the lung

To understand better the effect of shape and size of lung and chest wall on the distribution of stresses, strains, and surface pressures, we analyzed a theoretical model using the technique of finite elements. First we investigated the effects of changing the chest wall shape during expansion, and second we studied lungs of a variety of inherent shapes and sizes. We found that, in general, the distributions of alveolar size, mechanical stresses, and surface pressures in the lungs were dominated by the weight of the lung and that changing the shape of the lung or chest wall had relatively little effect. Only at high states of expansion where the lung was very stiff did changing the shape of the chest wall cause substantial changes. Altering the inherent shape of the lung generally had little effect but the topographical differences in stresses and surface pressures were approximately proportional to lung height. The results are generally consistent with those found in the dog by Hoppin et al (1969).

Vawter, D. L.↗

NASA NTRS1982

A porous flow model for the geometrical form of volcanoes - Critical comments

A critical evaluation is presented of the assumptions on which the mathematical model for the geometrical form of a volcano arising from the flow of magma in a porous medium of Lacey et al. (1981) is based. The lack of evidence for an equipotential surface or its equivalent in volcanoes prior to eruption is pointed out, and the preference of volcanic eruptions for low ground is attributed to the local stress field produced by topographic loading rather than a rising magma table. Other difficulties with the model involve the neglect of the surface flow of lava under gravity away from the vent, and the use of the Dupuit approximation for unconfined flow and the assumption of essentially horizontal magma flow. Comparisons of model predictions with the shapes of actual volcanoes reveal the model not to fit lava shield volcanoes, for which the cone represents the solidification of small lava flows, and to provide a poor fit to composite central volcanoes.

Wadge, G.↗

NASA NTRS1982

On the energy dependence of the radial diffusion coefficient and spectra of inner radiation belt particles - Analytic solutions and comparison with numerical results

A theoretical method by which the energy dependence of the radial diffusion coefficient may be deduced from spectral observations of the particle population at the inner edge of the earth's radiation belts is presented. This region has previously been analyzed with numerical techniques; in this report an analytical treatment that illustrates characteristic limiting cases in the L shell range where the time scale of Coulomb losses is substantially shorter than that of radial diffusion (L approximately 1-2) is given. It is demonstrated both analytically and numerically that the particle spectra there are shaped by the energy dependence of the radial diffusion coefficient regardless of the spectral shapes of the particle populations diffusing inward from the outer radiation zone, so that from observed spectra the energy dependence of the diffusion coefficient can be determined. To insure realistic simulations, inner zone data obtained from experiments on the DIAL, AZUR, and ESRO 2 spacecraft have been used as boundary conditions. Excellent agreement between analytic and numerical results is reported.

Westphalen, H.↗