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NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗

NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

Hall, Kenneth C.↗

NASA NTRS1993

Termination shock - Solar cycle variations of location and speed

Plasma and magnetic field data from Voyagers 1 and 2 over an 11-year period (1978-1988) together with a one-fluid MHD model are used to study the motion of the termination shock. The observed large fluctuations in solar wind parameters cause variations in the speed, in the jump conditions, and in the location of the termination shock. If the interstellar stagnation pressure is equivalent to a magnetic field of 0.5 nT plus draping enhancements, the termination shock moves between 88 AU and 102 AU. The location of the termination shock is anticorrelated with the sunspot number. The termination shock is very strong with pressure ratios of a few thousands, the fast Mach number is about 12, and the plasma beta ratio jumps from about 0.1 to about 14. During the declining phase of the solar cycle, the shock speed is often greater than or comparable to the spacecraft speed. If the crossing of the termination shock by a spacecraft occurs during the declining phase, the spacecraft will cross the termination shock 3 or more times over a period of about 4 years.

Whang, Y. C.↗

NASA NTRS1983

Quasi-steady solar wind dynamics

Progress in understanding the large scale dynamics of quasisteady, corotating solar wind structure was reviewed. The nature of the solar wind at large heliocentric distances preliminary calculations from a 2-D MHD model are used to demonstrate theoretical expectations of corotating structure out to 30 AU. It is found that the forward and reverse shocks from adjacent CIR's begin to interact at about 10 AU, producing new shock pairs flanking secondary CIR's. These sawtooth secondary CIR's interact again at about 20 AU and survive as visible entities to 30 AU. The model predicts the velocity jumps at the leading edge of the secondary CIR's at 30 AU should be very small but there should still be sizable variations in the thermodynamic and magnetic parameters. The driving dynamic mechanism in the distant solar wind is the relaxation of pressure gradients. The second topic is the influence of weak, nonimpulsive time dependence in quasisteady dynamics. It is suggested that modest large scale variations in the coronal flow speed on periods of several hours to a day may be responsible for many of the remaining discrepancies between theory and observation. Effects offer a ready explanation for the apparent rounding of stream fronts between 0.3 and 1.0 AU discovered by Helios.

Pizzo, V. J.↗

NASA NTRS1983

Closed-form solutions for feedback control with terminal constraints

The problem of closed-loop control of maneuvers between two states for linear dynamical systems, subject to an arbitrarily specified terminal state, is considered. The feedback controller design is based on finite-time quadratic regulator theory. Closed-form expressions for the optimal control law are developed. Solutions are presented for both conventional and smoothed control profiles with fixed and/or free end condition problems. In the maneuvers using control-rate penalties, smooth profiles are generated throughout the maneuvers, in the sense that the initial condition jump discontinuities have been eliminated. Several examples involving large-angle maneuvers of a spacecraft are demonstrated. Results include control maneuvers from one state to another such as rest to rest and spin to rest, which effectively justify the solutions developed in this paper.

Juang, J.-N.↗

NASA NTRS2004

The Severe Weather Outbreak of 10 November 2002: Lightning and Radar Analysis of Storms in the Deep South

On the afternoon and evening of 10 November 2002, the Midwest and Deep South were struck by a major outbreak of severe storms that produced some 80 tornadoes. In terms of number of tornadoes, this was the largest outbreak in the United States since November 1992. Some 32 of the tornadoes occurred in Tennessee, Mississippi, Alabama and Georgia, including several long-track killers. We use the North Alabama Lightning Mapping Array (LMA) and other data sources to perform a comprehensive analysis of the structure and evolution of the outbreak. Most of the Southern tornadoes occurred in isolated, fast-moving supercell storms that formed in warm, moist air ahead of a major cold front. Storms tended to form in lines parallel to storm cell motion, resulting in many communities being hit multiple times by severe storms that evening. Supercells in Tennessee produced numerous strong tornadoes with short to medium-length track paths, while the supercells further south produced several very long-track tornadoes. Radar data indicate that the Tennessee storms tended to split frequently, apparently limiting their ability to sustain long-lived tornadoes, while storms further south split at most one time. The differences between these storms appear to be related to the presence of stronger jetstream winds in Tennessee relative to those present in Mississippi, Alabama and Georgia. LMA-derived flash rates associated with most of the supercell storm cores were about 1-2 flashes per second. Rapid increases in lightning rates (or "jumps") occurred prior to tornado touchdown in many instances. Lightning "holes" (lightning-free regions associated with the echo-free vault) occurred in two of the Tennessee supercells. The complexity of the relationship between lightning and storm severity is revealed by the behavior of one Alabama supercell, which produced a peak flash rate of nearly 14 flashes per second, well after the end of its long-track tornado, while interacting and ultimately merging with a daughter supercell on its southwest flank. Close examination of this powerful storm indicates that its prodigious flash rate was the result of strong flash activity over an unusually large area, rather than a concentrated core of extremely high flash rate activity.

Buechler, D. E.↗

NASA NTRS2009

The Origins of ITCZs, Monsoons, and Monsoon Onset

Intertropical convergence zones (ITCZs), monsoons and monsoon onset are among the most prominent of atmospheric phenomena. Understanding their origins is fundamental to a full understanding of the atmospheric general circulation and has challenged meteorologists for a very long time. There has been important progress in understanding these phenomena in recent years, and in this seminar, recent developments, to which the speaker has contributed, are reviewed. First, contrary to conventional belief, land-sea thermal contrast is not necessary for monsoons to form. Second, monsoon onset occurs when there is a sudden poleward jump of an ITCZ during its annual cycle of latitudinal movement. A monsoon, then, is an ITCZ after its poleward jump. Third, the SST latitudinal maximum is not the most significant, or even a necessary, factor in the formation of an ITCZ; there are other important, if not more important, factors. These factors are the interaction between convection and surface fluxes, the interaction between convection and radiation, and the earth's rotation. Finally, the recent understanding of how ITCZs form has led to a conceptual explanation for the origin of the double ITCZ bias in GCM simulations.

Chao, Winston C.↗

NASA NTRS1984

Relaxation and approximate factorization methods for the unsteady full potential equation

The unsteady form of the full potential equation is solved in conservation form, using implicit methods based on approximate factorization and relaxation schemes. A local time linearization for density is introduced to enable solution to the equation in terms of phi, the velocity potential. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity, to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi obtained from requirements of density continuity. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. Results are presented for flows over airfoils, cylinders, and spheres. Comparisons are made with available Euler and full potential results.

Shankar, V.↗

NASA NTRS1985

Modulational development of nonlinear gravity-wave groups

Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.

Chereskin, T. K.↗

NASA NTRS2015

NASA's Functional Task Test: Providing Information for an Integrated Countermeasure System

Exposure to the microgravity conditions of spaceflight causes astronauts to experience alterations in multiple physiological systems. These physiological changes include sensorimotor disturbances, cardiovascular deconditioning, and loss of muscle mass and strength. Some or all of these changes might affect the ability of crewmembers to perform critical mission tasks immediately after landing on a planetary surface. The goals of the Functional Task Test (FTT) study were to determine the effects of spaceflight on functional tests that are representative of critical exploration mission tasks and to identify the key physiological factors that contribute to decrements in performance. The FTT was comprised of seven functional tests and a corresponding set of interdisciplinary physiological measures targeting the sensorimotor, cardiovascular and muscular changes associated with exposure to spaceflight. Both Shuttle and ISS crewmembers participated in this study. Additionally, we conducted a supporting study using the FTT protocol on subjects before and after 70 days of 6 head-down bed rest. The bed rest analog allowed us to investigate the impact of body unloading in isolation on both functional tasks and on the underlying physiological factors that lead to decrements in performance, and then to compare them with the results obtained in our spaceflight study. Spaceflight data were collected on three sessions before flight, on landing day (Shuttle only) and 1, 6 and 30 days after landing. Bed rest subjects were tested three times before bed rest and immediately after getting up from bed rest as well as 1, 6, and 12 days after reambulation. We have shown that for Shuttle, ISS and bed rest subjects, functional tasks requiring a greater demand for dynamic control of postural equilibrium (i.e. fall recovery, seat egress/obstacle avoidance during walking, object translation, jump down) showed the greatest decrement in performance. Functional tests with reduced requirements for postural stability (i.e. hatch opening, ladder climb, manual manipulation of objects and tool use) showed little reduction in performance. These changes in functional performance were paralleled by similar decrements in sensorimotor tests designed to specifically assess postural equilibrium and dynamic gait control. Bed rest subjects experienced similar deficits both in functional tests with balance challenges and in sensorimotor tests designed to evaluate postural and gait control as spaceflight subjects indicating that body support unloading experienced during spaceflight plays a central role in post-flight alteration of functional task performance. To determine how differences in body-support loading experienced during in-flight treadmill exercise affect postflight functional performance, the loading history for each subject during in-flight treadmill (T2) exercise was correlated with postflight measures of performance. ISS crewmembers who walked on the treadmill with higher pull-down loads had enhanced post-flight performance on tests requiring mobility. Taken together the spaceflight and bed rest data point to the importance of supplementing inflight exercise countermeasures with balance and sensorimotor adaptability training. These data also support the notion that inflight treadmill exercise performed with higher body loading provides sensorimotor benefits leading to improved performance on functional tasks that require dynamic postural stability and mobility.

Bloomberg, J. J.↗

NASA NTRS2008

Shock-Strength Determination With Seeded and Seedless Laser Methods

Two nonintrusive laser diagnostics were independently used to demonstrate the measurement of time-averaged and spatially-resolved pressure change across a twodimensional (2-D) shock wave. The first method is Doppler global velocimetry (DGV) which uses water seeding and generates 2-D maps of 3-orthogonal components of velocity. A DGV-measured change in flow direction behind an oblique shock provides an indirect determination of pressure jump across the shock, when used with the known incoming Mach number and ideal shock relations (or Prandtl-Meyer flow equations for an expansion fan). This approach was demonstrated at Mach 2 on 2-D shocks and expansions generated from a flat plate at angles-of-attack approx. equals -2.4deg and +0.6deg, respectively. This technique also works for temperature jump (as well as pressure) and for normal shocks (as well as oblique). The second method, laser-induced thermal acoustics (LITA), is a seedless approach that was used to generate 1-D spatial profiles of streamwise Mach number, sound speed, pressure, and temperature across the same shock waves. Excellent agreement was obtained between the DGV and LITA methods, suggesting that either technique is viable for noninvasive shock-strength measurements.

Herring, G. C.↗

NASA NTRS2011

Short Wavelength Electromagnetic Perturbations Excited Near the Solar Probe Plus Spacecraft in the Inner Heliosphere: 2.5D Hybrid Modeling

A 2.5D numerical plasma model of the interaction of the solar wind (SW) with the Solar Probe Plus spacecraft (SPPSC) is presented. These results should be interpreted as a basic plasma model derived from the SW-interaction with the spacecraft (SC), which could have consequences for both plasma wave and electron plasma measurements on board the SC in the inner heliosphere. Compression waves and electric field jumps with amplitudes of about 1.5 V/m and (12-18) V/m were also observed. A strong polarization electric field was also observed in the wing of the plasma wake. However, 2.5D hybrid modeling did not show excitation of whistler/Alfven waves in the upstream connected with the bidirectional current closure that was observed in short-time 3D modeling SPPSC and near a tether in the ionosphere. The observed strong electromagnetic perturbations may be a crucial point in the electromagnetic measurements planned for the future Solar Probe Plus (SPP) mission. The results of modeling electromagnetic field perturbations in the SW due to shot noise in absence of SPPSC are also discussed.

Lipatov, Alexander S.↗

NASA NTRS1982

The origin of the Kirkwood gaps - A mapping for asteroidal motion near the 3/1 commensurability

A mapping of the phase space onto itself with the same low-order resonance structure as the 3/1 commensurability in the planar-elliptic restricted three-body problem is obtained. This mapping is about 1,000 times faster than the usual method of numerically integrating the averaged equations of motion. It exhibits some surprising behavior that might provide a key to the origin of the Kirkwood gaps. It is noted that a test asteroid placed in the gap may evolve for a million years with low eccentricity (less than 0.05) and then suddenly jump to large eccentricity (greater than 0.3), becoming a Mars crosser. The removal of the asteroid by a close encounter with Mars would then be possible. As a first test of this hypothesis, a distribution of 300 test asteroids in the area of the 3/1 commensurability was evolved for two million years. When the Mars crossers are removed, the distribution of initial conditions reveals a gap at the location of the 3/1 Kirkwood gap.

Wisdom, J.↗

NASA NTRS2017

Feature Detection and Curve Fitting Using Fast Walsh Transforms for Shock Tracking: Applications

Walsh functions form an orthonormal basis set consisting of square waves. Square waves make the system well suited for detecting and representing functions with discontinuities. Given a uniform distribution of 2p cells on a one-dimensional element, it has been proven that the inner product of the Walsh Root function for group p with every polynomial of degree < or = (p - 1) across the element is identically zero. It has also been proven that the magnitude and location of a discontinuous jump, as represented by a Heaviside function, are explicitly identified by its Fast Walsh Transform (FWT) coefficients. These two proofs enable an algorithm that quickly provides a Weighted Least Squares fit to distributions across the element that include a discontinuity. The detection of a discontinuity enables analytic relations to locally describe its evolution and provide increased accuracy. Time accurate examples are provided for advection, Burgers equation, and Riemann problems (diaphragm burst) in closed tubes and de Laval nozzles. New algorithms to detect up to two C0 and/or C1 discontinuities within a single element are developed for application to the Riemann problem, in which a contact discontinuity and shock wave form after the diaphragm bursts.

Gnoffo, Peter A.↗

NASA NTRS2025

Functional Task Tests in Partial Gravity During Parabolic Flight

BACKGROUND Understanding how critical mission tasks are performed in partial gravity such as on the moon or Mars is necessary to define effective and comprehensive countermeasure strategies for preserving crew performance during exploration missions. We studied the performance of tasks such as standing, balancing, walking, and jumping during the partial gravity phases of parabolic flight. We hypothesized that the acute effects of partial gravity on vestibular, proprioceptive, and sensorimotor functions would negatively impact performance. METHODS Twelve subjects (6F, 6M; 40.2 ± 8.5 years) were tested over three flights of 30 parabolas each, including 10 parabolas at 0.25g, 10 parabolas at 0.5g, and 10 parabolas at 0.75g. Subjects also performed tests in 1g between parabolas. During the seat egress and walk task, subjects rose from a seated position and walked as quickly as possible straight ahead towards a cone (4 m distance), stepped over a 30 cm high obstacle, walked around the cone making a 180° left turn, returned to the chair, and sat down in the chair. Other tasks included a tandem stance on rails, jump down from a 30cm platform, recovery from fall (prone to stand), and limits of stability tasks. Data were collected using inertial measurement units (Opal V2, APDM, Portland, OR) worn on the head and trunk, heart rate monitors (Polar, Finland), and a force plate (Bertec, Columbus, OH). During the jump down and limits of stability tasks, falls were recorded if subjects took extra steps, lifted their heels/toes, or used their arms to recover balance. RESULTS Gravity level had a significant effect on performance, with the greatest changes from 1g tending to be at the 0.25g level (Table 1). Lower gravity levels were associated with increased times to complete the seat egress and walk task and the recovery from fall task, increased head-trunk coordination, decreased tandem stance rail balance times, decreased change in heart rate during the recovery from fall task, and increased cone of stability distance in the anterior-posterior direction. In addition, there were significantly more falls recorded at the lower gravity levels: 31 falls at 0.25g, 14 falls at 0.5g, 6 falls at 0.75g, and 6 falls at 1g. DISCUSSION These data suggest that there is a dose-response relationship between gravity level and functional task performance. The largest changes in performance were expected at the lowest gravity level (0.25g) because subjects would no longer be able to use the gravitational reference for the perception of upright. Understanding the extent of performance deficits informs the risks and design of countermeasures for exploration spaceflight missions.

T R Macaulay↗

NASA NTRS1975

Effect of attitude constraints on solar-electric geocentric transfers

The present work assesses the increase in flight time and fuel consumption due to introducing attitude constraints on both the thrust vector and the plane of the solar cell arrays on geocentrically orbiting spacecraft. A modified version of the SECKSPOT computer program calculates nearly time-optimal trajectories for the constrained case of zero pitch and roll. Unconstrained cases are generated with the SECKSPOT code. It is concluded that with a pitch constraint but without a roll constraint, power would not be a function of thrust direction, and so the time-optimal thruster direction would be along the projection of the primer vector in the plane normal to the radius vector. The roll constraint would cause power to become a function of thrust angle and sun angle. For certain sun angles the locus of the ratio of power to maximum power is concave and thus there may be jumps in the control angle. Comparisons are made for a SERT-C type mission between constrained and unconstrained cases in an inverse square gravity field.

Sackett, L. L.↗

NASA NTRS1985

Hypersonic merged-layer flow on a sphere

With the objective to achieve the desired reduction in velocity by aerodynamic forces, an aeroassisted orbital transfer vehicle (AOTV) is expected to fly in the higher region of the atmosphere for a sustained period of time. This aeroassist maneuver will occur in the transitional regime, if the vehicle is designed for a low ballistic coefficient. In this case, a merged-layer (ML) is formed around the space vehicle. The flow characteristics of the vehicle can be studied by making use of the full Navier-Stokes (NS) equations, taking into account slip and temperature jump conditions. The present investigation has the objective to obtain a two-term series solution of the full Navier-Stokes equations with surface slip and temperature jump conditions for the ML flow on a sphere. Attention is given to the mathematical formulation of the problem, the numerical method of integration, and the results.

Jain, A. C.↗

NASA NTRS2013

Observations from Hinode and SDO of a Twisting and Writhing Start to a Solar-filament-eruption Cascade

Active region eruption of 1 June 2011. Ejective eruption. GOES class C4.1 flare. SDO/AIA, various filters (94, 131, 171, 193, 211, 304, 335 Ang.) High time cadence (24 s) and high spatial resolution (0 .6 pixels). SDO/HMI line-of-sight magnetograms. Hinode observed the onset, and the later decay phase. There are two filament eruptions (filament 1 and filament 2). Filament 1 has slow rise with steps, as in several previous cases. GOES "episodes" play role of "microflares" in other events; that is, filament jumps <=> intensity peaks. Episode 1 brightening: Accompanied by filament 1 s initial motions. (Rest of talk.) Filament 1 becomes unstable, and.. Episode 2 brightening: Flare ribbons following filament 1 s fast liftoff. This destabilizes neighboring filament 2, and... Episode 3 brightening: Flare ribbons of whole system following filament 2 s eruption.Something leads to reconnection; not totally clear what. Reconnection -> twisted flux rope in approx.20 min; episode 1 microflare (flare ribbons; TC) and filament jump. Twist -> writhe, via kink instability; filament-trajectory plateau, approx. 20 min. Writhe -> jump and eruption of filament 1, via instability; episode 2 microflare (flare ribbons; TC). (E.g., Williams et al.) First eruption -> second filament eruption (episode 3 flare ribbons; TC). (E.g., Sterling, Moore; Liu et al.; Torok et al.; Schrijver & Title.). Estimate amount of free energy in newly-twisted field (cf. Moore 1988): where we have taken L and r = 50, 3 arcsec. Energy of the total system is likely 1030 ergs or more. So "no" is answer to question. Additional energy comes from remainder of sheared large loop, shear (free energy) of second filament, etc. (Normally assumed situation.) Some history of twist-induced instability in filament eruptions: e.g., Sakurai, Torok & Kliem, Fan & Gibson, Gilbert et al., van Driel-Gesztelyi et al. Criterion : Kink instability for line-tied tube (Hood & Priest): 2.5pi; for Titov & Demoulin loop (Torok et al): approx.3.5pi We observe here: approx.1.5 turns (3.0pi) over ~50. => consistent with kink instability acting. (Cf. Srivastava et al. (2010): Small flare seen in TRACE and Hinode: approx.6.0pi)

Sterling, Alphonse C.↗