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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2

A Wind-driven Origin for the Firework Morphology of the Supernova Remnant Pa 30

Pa 30—the likely remnant of the Galactic Type Iax supernova of 1181 AD—displays an unusual, firework-like morphology, consisting of radial filaments extending from a common center, where a white dwarf (WD) currently drives a very fast wind (speed ≳10 4 km s −1 ). We propose the filaments arose from the Rayleigh–Taylor-unstable nature of the interface between the circumstellar medium (CSM) and the shocked wind launched by the natal WD; the filaments then elongated intact due to the Kelvin–Helmholtz-stable nature of the large initial density contrast between the wind and CSM, supplemented by the slowly declining wind density profile (relative to homologously expanding ejecta). To support this interpretation, we present two-dimensional hydrodynamical simulations and derive the filament properties, including their speed, density, and temperature, all of which are consistent with observations. We suggest the filaments elongate until the wind and CSM densities become comparable at the contact discontinuity, which occurs within 1–10 yr, and then truncate because the Rayleigh–Taylor instability (RTI) halts. The subsequent Kelvin–Helmholtz instability growth timescale across the current width of the filaments is longer than the age of Pa 30, so they remain intact. The filament-less central region in Pa 30 is therefore more likely a consequence of the finite timescale over which the RTI operates, rather than a wind termination shock. In general, firework-like filaments may form in other systems, provided there is a sufficiently large density contrast between the ejecta and its surroundings.

79 ASTRONOMY AND ASTROPHYSICS↗

Diffraction of shock wave by moving thin wing.

Flow field pressure distribution due to plane shock wave impinging by thin wing moving in opposite direction, discussing mathematical formulation, analytic solution and applications

Gunzburger, M.↗

Skylab experience with Apollo docking/latching loads.

Description of the four-year development of Skylab analytical programs, mathematical model complexity, and vibration and load analyses associated with the docking/latching maneuver. Examples are shown where coarse models produced loads in excess of structural capability. However, subsequent model refinement lowered the loads to the point where redesign was not required. A summary of experience gained over a four-year period is presented in the conclusions.

Heath, R. A.↗

Space processing convection evaluation - G-jitter convection of confined fluids in low gravity

G-jitter convection, caused by time-varying accelerations imparted on a heated container of fluid in low gravity, is investigated analytically. The mathematical model used is constructed from the Navier-Stokes equations which are solved with a finite-difference method on a digital computer. Results are presented for typical space processing configurations and anticipated g-jitter levels, with emphasis on sounding rocket applications. The calculations indicate that g-jitter can cause significant temperature oscillations, increase or decrease local heat transfer and produce oscillatory convective flow patterns. These factors can have significant effects on important processes such as crystal growth (banding, for example) and separation techniques.

Spradley, L. W.↗

Fundamental studies of structure borne noise for advanced turboprop applications

The transmission of sound generated by wing-mounted, advanced turboprop engines into the cabin interior via structural paths is considered. The structural model employed is a beam representation of the wing box carried into the fuselage via a representative frame type of carry through structure. The structure for the cabin cavity is a stiffened shell of rectangular or cylindrical geometry. The structure is modelled using a finite element formulation and the acoustic cavity is modelled using an analytical representation appropriate for the geometry. The structural and acoustic models are coupled by the use of hard wall cavity modes for the interior and vacuum structural modes for the shell. The coupling is accomplished using a combination of analytical and finite element models. The advantage is the substantial reduction in dimensionality achieved by modelling the interior analytically. The mathematical model for the interior noise problem is demonstrated with a simple plate/cavity system which has all of the features of the fuselage interior noise problem.

Eversman, W.↗

Disentangling the Entangled Linkages of Magnetic Helicity

Magnetic helicity, H, measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in V bounded by ∂V. For magnetically closed systems, V ∈ R -3 = V + V∗, no magnetic flux threads the boundary, n̂ · B|∂V = 0. Berger & Field (1984) and Finn & Antonsen (1985) extended the definition of helicity to relative helicity, H, for magnetically open systems where magnetic flux may thread the boundary. Berger (1999, 2003) expressed this relative helicity as two gauge invariant terms that describe the self helicity of magnetic field that closes inside V and the mutual helicity between the magnetic field that threads the boundary ∂V and the magnetic field that closes inside V. The total magnetic field that permeates V entangles magnetic fields that are produced by current sources J in V with magnetic fields that are produced by current sources J∗ in V∗. Building on this fact, we extend Berger’s expressions for relative magnetic helicity to eight gauge invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents J in V and/or J∗ in V∗, thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy is discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.

Analytical mathematics↗

Hyper Illumination of Exoplanets: Analytical and Numerical Approaches

This work describes the illumination of exoplanets whose orbits are close enough to their host star that the finite angular size of their host star causes hyper illumination, in which more than 50% of the planet receives light. Such exoplanets include the hot Jupiters KELT-9 b (64.5% illuminated) and Kepler-91 b (69.6% illuminated). We describe the geometry of three primary illumination zones: the fully illuminated zone, penumbral zone, and unilluminated zone. The integrals required to determine the incident radiation as a function of position from the substellar point on the exoplanet are explained and derived, and the analytical solution is presented within the fully illuminated zone. We find that the illumination predicted by our model is greater at the substellar point than the typical plane-parallel ray model used would suggest. In addition, it is greater within the region of the penumbral zone extending into the antistellar side of the exoplanet. Finally, we compare our model to that used in starry, an open-source software package used to create albedo maps. It appears that starry may be overestimating the illumination of closely orbiting exoplanets because the foreshortening of the area element of the host star is not included in its calculation.

Exoplanets↗

Immersive Digital Twins and Decision Making

This work focuses on developing and implementing immersive digital twins to support decision-making processes in construction automation and energy simulation analysis. The use of digital twins enables users to explore and interact with virtual replicas of physical systems, providing a unique and valuable perspective for problem-solving. In the context of construction automation, we present two case studies that integrate immersive visualization and worker-machine interaction. In the context of energy simulation analysis using digital twins, we describe our digital twin framework that combines interactive visualization with machine learning techniques to approximate computationally expensive simulations, allowing for faster and more efficient analysis of complex energy systems. Through these research endeavors, we demonstrate the potential of immersive digital twins in decision-making across various domains.

digital twins↗

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

Relative motion of orbiting particles under the influence of perturbing forces. Volume 2: Analytical results

The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.

Eades, J. B., Jr.↗

Rotor systems research aircraft simulation mathematical model

An analytical model developed for evaluating and verifying advanced rotor concepts is discussed. The model was used during in both open loop and real time man-in-the-loop simulation during the rotor systems research aircraft design. Future applications include: pilot training, preflight of test programs, and the evaluation of promising concepts before their implementation on the flight vehicle.

Houck, J. A.↗

Computer-Based Mathematics Instructions for Engineering Students

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Khan, Mustaq A.↗

Influence of Design Variations on Systems Performance

High-risk aerospace components have to meet very stringent quality, performance, and safety requirements. Any source of variation is a concern, as it may result in scrap or rework. poor performance, and potentially unsafe flying conditions. The sources of variation during product development, including design, manufacturing, and assembly, and during operation are shown. Sources of static and dynamic variation during development need to be detected accurately in order to prevent failure when the components are placed in operation. The Systems' Health and Safety (SHAS) research at the NASA Ames Research Center addresses the problem of detecting and evaluating the statistical variation in helicopter transmissions. In this work, we focus on the variations caused by design, manufacturing, and assembly of these components, prior to being placed in operation (DMV). In particular, we aim to understand and represent the failure and variation information, and their correlation to performance and safety and feed this information back into the development cycle at an early stage. The feedback of such critical information will assure the development of more reliable components with less rework and scrap. Variations during design and manufacturing are a common source of concern in the development and production of such components. Accounting for these variations, especially those that have the potential to affect performance, is accomplished in a variety ways, including Taguchi methods, FMEA, quality control, statistical process control, and variation risk management. In this work, we start with the assumption that any of these variations can be represented mathematically, and accounted for by using analytical tools incorporating these mathematical representations. In this paper, we concentrate on variations that are introduced during design. Variations introduced during manufacturing are investigated in parallel work.

Tumer, Irem Y.↗

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

A complete mathematical model is formulated to analyze the effects of mean-flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field but coupled to it through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. The flow model and solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating-flat-plate and Sears transverse-gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.

Chiang, Hsiao-Wei D.↗

An analytic performance model of disk arrays and its application

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

Lee, Edward K.↗

Using emergent order to shape a space society

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Graps, Amara L.↗