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Results for “asymptotic analysis”

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 505 records · Page 28

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NASA NTRS1982

Three-dimensional inviscid analysis of the scramjet inlet flow field

A computer code has been developed to analyze the inviscid flow field in a supersonic combustion ramjet (scramjet) inlet. The code uses the three-dimensional Euler equations in full conservation form to describe the inlet flow. An algebraic numerical coordinate transformation is used to generate a set of boundary-fitted curvilinear coordinates. The governing equations are solved by a time-asymptotic, unsplit, two-step, finite-difference method. This method is highly efficient on the vector processing computers for which the current code is written. Detailed results are presented for two scramjet inlet configurations over a range of Mach numbers. The calculated results are compared with the available experimental and theoretical results.

Kumar, A.↗

NASA NTRS1988

The search for solar gravity modes

A solar oscillations observing program of more than 13 yr is reviewed. The observations are most sensitive to low degree solar modes and were used for the study of long period p-mode and g-mode oscillations. At the start of the 1987 observing season (summer) long-standing problems with the instrument were corrected which (along with good weather) allowed the cleanest set of data to date. The search for evidence of g-modes in this data is described. Analysis of this data shows good evidence for g-modes. Various methods were used for mode identification with a statistical search for a simple pattern of even spacing in period selected as the most robust. Using this method, a possible g-mode identification was made with an asymptotic period separation T0 = 37.1 min. This identification is consistent with a rotation splitting of 1.6 MicroHz. Tests with randomly generated spectral peaks find as significant a possible set of modes in only 2 out of 100 cases.

Henning, Harald M.↗

NASA NTRS1994

Large Eddy Simulation of Homogeneous Rotating Turbulence

Study of turbulent flows in rotating reference frames has proven to be one of the more challenging areas of turbulence research. The large number of theoretical, experimental, and computational studies performed over the years have demonstrated that the effect of solid-body rotation on turbulent flows is subtle and remains exceedingly difficult to predict. Because of the complexities associated with non-homogeneous turbulence, it is worthwhile to examine the effect of steady system rotation on the evolution of an initially isotropic turbulent flow. The assumption of statistical homogeneity considerably simplifies analysis and computation; calculation of homogeneous turbulence is further motivated since it possesses the essential physics found in more complex rotating flows. The principal objectives of the present study have therefore been to increase our fundamental understanding of turbulent flows in rotating reference frames through an examination of the asymptotic state of homogeneous rotating turbulence; particularly as to the existence of an asymptotic state which is self similar. Knowledge of an asymptotic similarity state permits prediction of the ultimate statistical evolution of the flow without requiring detailed knowledge of the complex, and not well understood, non-linear transfer processes. Aside from examination of possible similarity states in rotating turbulence, of further interest in this study has been an examination of the degree to which solid-body rotation induces a two-dimensional state in an initially isotropic flow.

Squires, Kyle D.↗

NASA NTRS1974

On the accuracy of Whitham's method

The steady flow of an ideal gas past a conical body is studied by the method of matched asymptotic expansions and by Whitham's method in order to assess the accuracy of the latter. It is found that while Whitham's method does not yield a correct asymptotic representation of the perturbation field to second order in regions where the flow ahead of the Mach cone of the apex is disturbed, it does correctly predict the changes of the second-order perturbation quantities across a shock (the first-order shock strength). The results of the analysis are illustrated by a special case of a flat, rectangular plate at incidence.

Zahalak, G. I.↗

NASA NTRS1976

The use of dispersion to eliminate multipath in planetary radio occultations

Occultation geometry is analyzed with a view toward eliminating all multipath resulting from layer effects. It is assumed that the spacecraft moves behind the planet with a constant velocity perpendicular to the direction from the spacecraft to the earth, and that for radio frequencies of 1 to 2 GHz the angle of refraction of a radio ray passing through the ionosphere is so small as to be imperceptible if drawn to scale. It is shown that if a particular amount of dispersion is inserted into the process at any stage prior to signal detection, the frequency vs time curve will be converted to a frequency vs ray asymptote height curve. Because there can be only one mode from any one ray asymptote height in a layered medium, frequency must be a single-valued function of this parameter. The introduction of an appropriate dispersion will therefore eliminate all multipath insofar as it is caused by spherically symmetric planetary layers. The degree of accuracy to be provided in flight and during postflight analysis is discussed.

Croft, T. A.↗

DOE OSTI2023

Momentum in single-trace $T$$\overline{T}$ holography

We continue our exploration of the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and AdS 3 in the IR, and the corresponding boundary theories. In previous papers, [1], [2], we showed that states in the bulk theory that are described by non-trivial asymptotically linear dilaton geometries, such as black holes and deformed global AdS 3 , can be described in the boundary theory by a single-trace $T$$\overline{T}$ deformation of a symmetric product theory. In those papers, we restricted to states with vanishing (angular) momentum; in this paper, we extend the analysis to states with arbitrary momentum, and show that the picture presented in the earlier papers generalizes to this case.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Simulations and models for the Richtmyer–Meshkov instability with broadband perturbations

The Richtmyer–Meshkov instability (RMI) is shock driven and affects many phenomena from inertial fusion to supernova explosions. The behavior of single-modes in the RMI has been studied extensively but less is known with the broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with an initial power spectrum of the form P ∝ km, where k is the wavenumber. The hydrodynamic condition is the same as in the θ-Group Collaboration [Thornber et al., “Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)] with a Mach ∼1.86 shock and gamma-law = 5/3 fluids with Atwood number A = −0.5. The bubble amplitude hB is found to grow in two stages. Initially, hB undergoes a phase-inversion and grows linearly in time (t) at a rate consistent with a linear theory. Asymptotically, hB grows as a power law ∼tθ when k|hB| > O(1), where k is the average wavenumber for the initial spectrum. The RMI behavior in simulations and modeling agree over a wide range of exponent m, spectral width, initial amplitude, and time. The agreement is quantified objectively using statistical analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Breakdown of order fractionalization in the CPT model

Here, we present an analysis of the half-filled CPT model, an analytically tractable Kondo lattice model with Yao-Lee spin-spin interactions on a 3D hyperoctagon lattice, proposed by Coleman, Panigrahi, and Tsvelik. Previous studies have established that the CPT model exhibits odd-frequency triplet superconductivity and order fractionalization. Through asymptotic analyses in the small- and large- Kondo coupling limits, we identify a quantum critical point at , marking a transition from a superconductor to a Kondo insulator. By estimating the vison gap energy to account for thermal gauge fluctuations, we determine the energy scales governing the thermal breakdown of order fractionalization. Moreover, at large the Kondo insulator undergoes orbital decoupling, leading to the formation of a decoupled Kitaev orbital liquid. These findings and analogies with the -gauged model lead us to propose a tentative phase diagram for the CPT model at half-filling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1976

Optimal three-dimensional reusable tug trajectories for planetary missions including correction for nodal precession

Equations are derived by using the maximum principle to maximize the payload of a reusable tug for planetary missions. The analysis includes a correction for precession of the space shuttle orbit. The tug returns to this precessed orbit (within a specified time) and makes the required nodal correction. A sample case is analyzed that represents an inner planet mission as specified by a fixed declination and right ascension of the outgoing asymptote and the mission energy. The reusable stage performance corresponds to that of a typical cryogenic tug. Effects of space shuttle orbital inclination, several trajectory parameters, and tug thrust on payload are also investigated.

Borsody, J.↗

NASA NTRS1989

Modeling and control of flexible space stations (slew maneuvers)

Large orbiting space structures are expected to experience mechanical vibrations arising from several disturbing forces such as those induced by shuttle takeoff or docking and crew movements. The problem is considered of modeling and control of large space structures subject to these and other disturbing forces. The system consists of a (rigid) massive body, which may play the role of experimental modules located at the center of the space station and flexible configurations, consisting of several beams, forming the space structure. A complete dynamic model of the system was developed using Hamilton's principle. This model consists of radial equations describing the translational motion of the central body, rotational equations describing the attitude motions of the body and several beam equations governing the vibration of the flexible members (platform) including appropriate boundary conditions. In summary, the dynamics of the space structure is governed by a complex system of interconnected partial and ordinary differential equations. Using Lyapunov's approach the asymptotic stability of the space structure is investigated. For asymptotic stability of the rest state (nominal trajectory), feedback controls are suggested. In the investigation, stability of the slewing maneuvers is also considered. Several numerical results are presented for illustration of the impact of coupling and the effectiveness of the stabilizing controls. Some insight is provided into the complexity of modeling, analysis and stabilization of actual space structures.

Ahmed, N. U.↗

NASA NTRS1994

The effects of viscosity on the stability of a trailing-line vortex in compressible flow

We consider the effects of viscosity on the inviscid stability of the Batchelor vortex in a compressible flow. The problem is tackled asymptotically, in the limit of large (streamwise and azimuthal) wavenumbers, together with large Mach numbers. Previous studies, with viscous effects neglected, found that the nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumber. This structure persists when viscous effects are included in the analysis. In the present study the mode present in the incompressible case ceases to be unstable at high Mach numbers and a center mode forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find generally that viscosity has a stabilizing influence on the flow, while in the case of center modes, viscous effects become important at much larger Reynolds numbers than for the first class of disturbance.

Stott, Jillian A. K.↗

NASA NTRS1972

Launch window analysis in a new perspective with examples of departures from Earth to Mars

Earth-departure windows are investigated for two round trip stopover missions to Mars. These are the 1981 inbound Venus swingby mission and the 1986 direct minimum-energy mission. The secular effects of planetary oblateness are used to predict the motion of the parking orbit. A procedure is developed for matching the motion of the parking orbit and the escape asymptote. Earth-departure velocity penalties, caused by orbital plane misalinement, are reduced by synchronizing the motion of the parking orbit and the escape trajectory.

Thibodeau, J. R., III↗

NASA NTRS1990

The analysis and simulation of compressible turbulence

Compressible turbulent flows at low turbulent Mach numbers are considered. Contrary to the general belief that such flows are almost incompressible (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a nondimensional time scale which is the inverse of the fluctuating Mach number. An asymptotic theory which enables one to obtain a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

Erlebacher, Gordon↗

DOE OSTI2021

ASCEND: Asymptotically compatible strong form foundations for nonlocal discretization

Nonlocal models naturally handle a range of physics of interest to SNL, but discretization of their underlying integral operators poses mathematical challenges to realize the accuracy and robustness commonplace in discretization of local counterparts. This project focuses on the concept of asymptotic compatibility, namely preservation of the limit of the discrete nonlocal model to a corresponding well-understood local solution. We address challenges that have traditionally troubled nonlocal mechanics models primarily related to consistency guarantees and boundary conditions. For simple problems such as diffusion and linear elasticity we have developed complete error analysis theory providing consistency guarantees. We then take these foundational tools to develop new state-of-the-art capabilities for: lithiation-induced failure in batteries, ductile failure of problems driven by contact, blast-on-structure induced failure, brittle/ductile failure of thin structures. We also summarize ongoing efforts using these frameworks in data-driven modeling contexts. This report provides a high-level summary of all publications which followed from these efforts.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1986

On the uniqueness of the constrained space orbital variation (CSOV) technique

Several CSOV analyses are performed for the 1Sigma(+) state of NiCO, and it is shown that the importance of the CO sigma donation, Ni pi back donation, and interunit polarizations are virtually independent of the order of the CSOV steps, provided that the open-shell 3d sigma and 4s Ni orbitals are orthogonalized to the CO. This order of orthogonalization is consistent with the polarization of the Ni observed in the unconstrained SCF wavefunction. If instead the CO is orthogonalized to the open-shell Ni orbitals, the frozen orbital repulsion and entire CSOV analysis becomes unphysical. A comparison of the SCF and CAS SCF descriptions for the NiCO 1Sigma(+) state shows the importance of the s to d promotion and sd hybridization in reducing the repulsion and increasing the Ni to CO pi bonding. For LiF, CSOV analyses starting from both the neutral and ionic asymptotes show the bonding to be predominantly Li(+) - F(-). These examples show the uniqueness of the CSOV decomposition.

Bauschlicher, C. W., Jr.↗

NASA NTRS1994

Hubble Space Telescope observations of planetary nebulae in the magellanic clouds. 2: SMP 85, a young planetary

We have obtained Hubble Space Telescope Planetary Camera images in the (O III) lambda 5007 A emission line, and Faint Object Spectrograph (FOS) UV spectrophotometry of the low-excitation planetary nebula SMP 85 in the Large Magellanic Cloud. By combining these results with existing optical spectrophotometry, absolute flux measurements, and dynamical and density information, we have been able to construct a fully self-consistent nebular model. This proves that SMP 85 is a dense, young, carbon-rich object which started to be ionized about 500-1000 years ago, and which contains a substantial inner reservoir of atomic or molecular gas, probably in the form of many small cloudlets. These cloudlets have been ejected at a velocity not exceeding 6 km/s, a result which, together with the morphology is an important clue to mass loss during late asymptotic giant branch (AGB) evolution. We have directly detected the central star through its UV continuum emission, and from both Zanstra techniques and nebular modeling derive a stellar temperature of 46000 +/- 2000 K, a stellar luminosity of 7300 +/- 700 solar luminosity, and a core mass of 0.63-0.67 solar mass. The nebular analysis also demonstrates that there is severe depletion of the nebular gases onto dust grains, most likely of the calcium magnesium silicate variety; a surprising result in view of the carbon-rich nature of the ionized nebula.

Dopita, Michael A.↗

NASA NTRS1999

Human Mars Mission: Launch Window from Earth Orbit

The determination of orbital window characteristics is of major importance in the analysis of human interplanetary missions and systems. The orbital launch window characteristics are directly involved in the selection of mission trajectories, the development of orbit operational concepts, and the design of orbital launch systems. The orbital launch window problem arises because of the dynamic nature of the relative geometry between outgoing (departure) asymptote of the hyperbolic escape trajectory and the earth parking orbit. The orientation of the escape hyperbola asymptotic relative to earth is a function of time. The required hyperbola energy level also varies with time. In addition, the inertial orientation of the parking orbit is a function of time because of the perturbations caused by the Earth's oblateness. Thus, a coplanar injection onto the escape hyperbola can be made only at a point in time when the outgoing escape asymptote is contained by the plane of parking orbit. Even though this condition may be planned as a nominal situation, it will not generally represent the more probable injection geometry. The general case of an escape injection maneuver performed at a time other than the coplanar time will involve both a path angle and plane change and, therefore, a DELTA V penalty. Usually, because of the DELTA V penalty the actual departure injection window is smaller in duration than that determined by energy requirement alone. This report contains the formulation, characteristics, and test cases for five different launch window modes for Earth orbit. These modes are: (1) One impulsive maneuver from a Highly Elliptical Orbit (HEO) (2) Two impulsive maneuvers from a Highly Elliptical Orbit (HEO) (3) One impulsive maneuver from a Low Earth Orbit (LEO) (4) Two impulsive maneuvers from LEO (5) Three impulsive maneuvers from LEO.

Young, Archie↗

DOE OSTI2020

Modal analysis of the behavior of inertial particles in turbulence subjected to Stokes drag

The clustering of small heavy inertial particles subjected to Stokes drag in turbulence, which is the concern of present study, is known to be minimal at small and large Stokes number and substantial at St = $\textit{O}$(1). This nonmonotonic trend, which has been shown computationally and experimentally, is yet to be explained analytically. In this study, we obtain an analytical expression for the Lyapunov exponents that quantitatively predicts this trend. The sum of the exponents, which is the normalized rate of change of the signed volume of a small cloud of particles, is correctly predicted to be negative and positive at small and large Stokes numbers, respectively, asymptoting to $\textit{τQ}$ as $\textit{τ}$ → 0 and $τ^{–1/2}|Q|^{1/4}$ as $\textit{τ} → ∞$, where $\textit{τ}$ is the particle relaxation time and $\textit{Q(τ)}$ is the difference between the norm of the rotation- and strain-rate tensors computed along the particle trajectory, which remains negative at all $\textit{τ}$ in turbulent flows. Additionally, the trajectory crossing is predicted only in hyperbolic flows where Q < 0 for sufficiently inertial particles with a $\textit{τ}$ that scales with $|Q|^{–1/2}$. Following the onset of crossovers, a transition from clustering to dispersion is predicted correctly. We show these behaviors are not unique to three-dimensional isotropic turbulence and can be reproduced closely by a one-dimensional mono-harmonic flow, which appears as a fundamental canonical problem in the study of particle clustering. Analysis of this one-dimensional canonical flow shows that the rate of clustering, quantified as the product of the Lyapunov exponent and particle relaxation time, is bounded by –1/2, behaving with extreme nonlinearity in the hyperbolic flows and always remaining positive in the elliptic flows. Finally, this model problem also confirms that dispersion in a hyperbolic flow will occur only if particles' trajectory cross. These findings, which stem from our analysis, are corroborated by the direct numerical simulations.

42 ENGINEERING↗