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At least 415 records · Page 23

Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays

The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.

Chiu, H. H.↗

Jet Mixing Noise Scaling Laws SHJAR Data Vs. Predictions

High quality jet noise spectral data measured at the anechoic dome at the NASA Glenn Research Center is used to examine a number of jet noise scaling laws. Configurations considered in the present study consist of convergent as well as convergent-divergent axisymmetric nozzles. The spectral measurements are shown in narrow band and cover 8193 equally spaced points in a typical Strouhal number range of (0.01 10.0). Measurements are reported as lossless (i.e. atmospheric attenuation is added to as-measured data), and at 24 equally spaced angles (50deg to 165deg) on a 100-diameter arc. Following the work of Viswanathan [Ref. 1], velocity power laws are derived using a least square fit on spectral power density as a function of jet temperature and observer angle. The goodness of the fit is studied at each angle, and alternative relationships are proposed to improve the spectral collapse when certain conditions are met. On the application side, power laws are extremely useful in identifying components from various noise generation mechanisms. From this analysis, jet noise prediction tools can be developed with physics derived from the different spectral components.

Khavaran, Abbas↗

Trade Space Assessment for Human Exploration Mission Design

Many human space exploration mission architecture assessments have been performed over the years by diverse organizations and individuals. Direct comparison of metrics among these studies is extremely difficult due to widely varying assumptions involving projected technology readiness, mission goals, acceptable risk criteria, and socio-political environments. However, constant over the years have been the physical laws of celestial dynamics and rocket propulsion systems. A finite diverse yet finite architecture trade space should exist which captures methods of human exploration - particularly of the Moon and Mars - by delineating technical trades and cataloging the physically realizable options of each. A particular architectural approach should then have a traceable path through this "trade tree". It should be pointed out that not every permutation of paths will result in a physically realizable mission approach, but cataloging options that have been examined by past studies should help guide future analysis. This effort was undertaken in two phases by multi-center NASA working groups in the spring and summer of 2004 using more than thirty years of past studies to "flesh out" the Moon-Mars human exploration trade space. The results are presented, not as a "trade tree", which would be unwieldy, but as a "menu" of potential technical options as a function of mission phases. This is envisioned as a tool to aid future mission designers by offering guidance to relevant past analyses.

Joosten, B. Kent↗

A consistent and conservative model and its scheme for N -phase- M -component incompressible flows

Here, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Revision of Paschen's Law Relating to the ESD of Aerospace Vehicle Surfaces

The purpose of this work is to develop a form of Paschen's law that takes into account the flow of gas past electrode surfaces. This work was performed under a NASA Science Innovation Fund (SIF) project at the Kennedy Space Center in collaboration with the University of Central Florida. In 2010 the Electrostatics and Surface Physics Laboratory (ESPL) at the Kennedy Space Center performed an electrostatic safety analysis on the flight termination system (FTS) antenna for the Ares I rocket. Paschen's law, derived by Friedrich Paschen in 1889 to relate sparking voltage to gas pressure and electrode separation, does not take into account the effect of flowing gas between the electrodes. The safety of the FTS housing to triboelectric charging was shown only after extensive laboratory testing. Potential benefits are of a form of Paschen's law that considers gas velocity. This work is applicable to current and planned rockets and aerospace vehicles and could lead to possible relaxation of electrostatic launch criteria. Launch aborts can cost up to about a million US dollars depending on the vehicle. [ElectroStatic Discharge (ESD)]

Paschen↗

Space cannot stretch too fast

Here, in this paper, we argue that black holes microstates leave an imprint on the gravitational vacuum through their virtual fluctuations. This imprint yields a power law fall off — rather than an exponential fall off — for the entanglement of planck scale fluctuations at different points. These entanglements generate an extra energy when space stretches too fast, since causality prevents a relaxation of these entanglements to their vacuum values. We obtain semiclassical dynamics for slow processes like star formation, but a radical departure from semiclassicality when a black hole horizon forms even though curvatures remain low everywhere. This resolution of the information puzzle also implies an extra energy source at the scale of the cosmological horizon, which may explain the mysteries of dark energy and the Hubble tension.

black holes↗

Impact of shorter wavelengths on optical quality for laws

This study explores parametrically as a function of wavelength the degrading effects of several common optical aberrations (defocus, astigmatism, wavefronttilts, etc.), using the heterodyne mixing efficiency factor as the merit function. A 60 cm diameter aperture beam expander with an expansion ratio of 15:1 and a primary mirror focal ratio of f/2 was designed for the study. An HDOS copyrighted analysis program determined the value of merit function for various optical misalignments. With sensitivities provided by the analysis, preliminary error budget and tolerance allocations were made for potential optical wavefront errors and boresight errors during laser shot transit time. These were compared with the baseline 1.5 m CO2 laws and the optical fabrication state of the art (SOA) as characterized by the Hubble Space Telescope. Reducing wavelength and changing optical design resulted in optical quality tolerances within the SOA both at 2 and 1 micrometer. However, advanced sensing and control devices would be necessary to be tightened by a factory of 1.8 for a 2 micrometer system and by 3.6 for a 1 micrometer system relative to the baseline CO2 LAWS. Available SOA components could be used for operation at 2 micrometers but operation at 1 micrometer does not appear feasible.

Wissinger, Alan B.↗

Predictive control and estimation - State space approach

A modified output prediction procedure and a new controller design based on the predictive control law are presented. A new predictive estimator enhances system performance. The predictive controller was designed and applied to the tracking control of the NASA/JPL 70-m antenna. Simulation results show significant improvement in tracking performance over the linear quadratic controller and estimator presently in use.

Gawronski, W.↗

Role of the manned maneuvering unit for the Space Station

The performance specifications to be realized in the Manned Maneuvering Unit (MMU) for Space Station operations will be the culmination of design efforts which began during the Gemini project. The types of MMUs which have been built and tested over the past two decades are described, including handheld, jet shoe, and initial rigid backpack configurations. Efforts to enhance the control laws and human factors aspects of the Skylab MMU to meet long-duration, flexible use Space Station requirements are summarized, noting the successes and deficiencies with the Shuttle MMU. The design requirements which must be met to allow the Space Station MMU to be used to perform rescue, transportation, inspection, assembly, contingency, and programmatic missions are explored.

Whitsett, C. E.↗

Nonlinear singularly perturbed optimal control problems with singular arcs

A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.

Ardema, M. D.↗

A viable suboptimal controller for robotic manipulators

A simple algebraic solution is obtained to an optimal control problem in joint space for a general robotic manipulator. Open loop and closed loop control laws are obtained. The resulting control algorithm is similar in form to a commonly used heuristic controller using cubic polynomial trajectories.

Turner, T. L.↗

Sensor/Actuator Selection for the Constrained Variance Control Problem

The problem of designing a linear controller for systems subject to inequality variance constraints is considered. A quadratic penalty function approach is used to yield a linear controller. Both the weights in the quadratic penalty function and the locations of sensors and actuators are selected by successive approximations to obtain an optimal design which satisfies the input/output variance constraints. The method is applied to NASA's 64 meter Hoop-Column Space Antenna for satellite communications. In addition the solution for the control law, the main feature of these results is the systematic determination of actuator design requirements which allow the given input/output performance constraints to be satisfied.

Delorenzo, M. L.↗

Active stability augmentation of large space structures: A stochastic control problem

A problem in SCOLE is that of slewing an offset antenna on a long flexible beam-like truss attached to the space shuttle, with rather stringent pointing accuracy requirements. The relevant methodology aspects in robust feedback-control design for stability augmentation of the beam using on-board sensors is examined. It is framed as a stochastic control problem, boundary control of a distributed parameter system described by partial differential equations. While the framework is mathematical, the emphasis is still on an engineering solution. An abstract mathematical formulation is developed as a nonlinear wave equation in a Hilbert space. That the system is controllable is shown and a feedback control law that is robust in the sense that it does not require quantitative knowledge of system parameters is developed. The stochastic control problem that arises in instrumenting this law using appropriate sensors is treated. Using an engineering first approximation which is valid for small damping, formulas for optimal choice of the control gain are developed.

Balakrishnan, A. V.↗

Status report and preliminary results of the spacecraft control laboratory experiment

The Spacecraft Control Laboratory Experiment (SCOLE) was conceived to provide a physical test bed for investigation of control techniques for large flexible spacecraft. The SCOLE problem is defined as two design challenges. The first challenge is to design control laws for a mathematical model of a large antenna attached to the space shuttle by a long flexible mast. The second challenge is to design and implement a control scheme on a laboratory representation of the structure modelled in the first part. Control sensors and actuators are typical of those which the control designer would have to deal with on an actual spacecraft. The primary control processing computer is representative of the capacity and speed which may be expected in actual flight computers. A brief description is given of the laboratory apparatus along with some preliminary results of structural dynamics tests and actuator effectiveness tests.

Williams, Jeffrey P.↗

Modes of interconnected lattice trusses using continuum models, part 1

This represents a continuing systematic attempt to explore the use of continuum models--in contrast to the Finite Element Models currently universally in use--to develop feedback control laws for stability enhancement of structures, particularly large structures, for deployment in space. We shall show that for the control objective, continuum models do offer unique advantages. It must be admitted of course that developing continuum models for arbitrary structures is no easy task. In this paper we take advantage of the special nature of current Large Space Structures--typified by the NASA-LaRC Evolutionary Model which will be our main concern--which consists of interconnected orthogonal lattice trusses each with identical bays. Using an equivalent one-dimensional Timoshenko beam model, we develop an almost complete continuum model for the evolutionary structure. We do this in stages, beginning only with the main bus as flexible and then going on to make all the appendages also flexible-except for the antenna structure. Based on these models we proceed to develop formulas for mode frequencies and shapes. These are shown to be the roots of the determinant of a matrix of small dimension compared with mode calculations using Finite Element Models, even though the matrix involves transcendental functions. The formulas allow us to study asymptotic properties of the modes and how they evolve as we increase the number of bodies which are treated as flexible. The asymptotics, in fact, become simpler.

Balakrishnan, A. V.↗

Estimation of Non-Seasonal Oceanic Mass Redistribution and its Geodynamic Effects from the Topex/Poseidon Observation

Mass redistribution in terms of angular momentum will change the Earth's rotation under the conservation of angular momentum. It also changes the external gravitational field according to Newton's gravitational law. These small geodynamic variations can be measured very accurately by modem space geodetic techniques. We report on new estimates of the oceanic tidal angular momentum and hence the tidal variations in the Earth's rotation rate and polar motion. These are deduced from the new tidal solutions GOT99 and TPXO.3, plus M2 and Mf estimates (with error bars) from TPXO.4a. Comparisons with observed diurnal/semidiurnal tidal variations are generally similar to previous model estimates. Comparisons of models and observations of Mf polar motion are confused, with neither models nor observations agreeing among themselves or with each other. Part of this is caused by differences in Mf currents; model TPXO.4 shows current-intensive Rossby modes along western boundaries of major basins, which are indeed expected on theoretical grounds. Unfortunately, there are no reliable in situ observations of Mf currents useful for comparing models. On non-tidal oceanic mass redistribution we compute the principal components of the multi-year T/P sea surface height (SSH) field using EOF (empirical orthogonal functions) taking into consideration of the latitude-dependent area weighting. Emphasis is placed upon non-seasonal and interannual oscillations on regional scales, including ENSO and the North Atlantic Oscillation. Steric corrections to the observed SSH due to sea surface temperature changes (which has no geodynamic effects) is now under study using POCM ocean model output.

Chao, Benjamin F.↗

Dynamical Signatures of Living Systems

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Zak, M.↗