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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Linear baroclinic instability in the presence of large scale topography

The effect of a planetary-scale, wavenumber 2 topography on baroclinically active disturbances is investigated for a channel domain in a two-layer, quasi-geostrophic context. When the lower-layer zonal velocity is nonzero, the topography influences the disturbances by forcing a stationary wave, and the topography and the forced wave influence the growth rates and the spatial structures of the time-dependent solutions. The case of zero zonal velocity in the lower layer was also investigated, for which no forced wave exists. Asymptotic forms of the equations, valid when the topographic effect (governed by the ratio of the nondimensional topographic height to the rotational Froude number) is small, are used to obtain both the stationary and time-dependent solutions. The latter are also obtained using a numerical approach, in which is determined the eigenvalues and eigenfunctions of a matrix representing the dynamical equations. Agreement is good between the two approaches. Recent laboratory experiments with a baroclinic annulus in which there is a false bottom with wavenumber 2 topography, are used to select governing parameters. The simultaneous presence of a stationary forced wave of wavenumber 2 and a time-dependent baroclinic wave of wavenumber 4, which has wavenumber 2 and 6 sidebands due to the topography, yields a flow field that exhibits some principal features of the laboratory experiments. The position of the forced wave and the location of an excursion in latitude of the storm track show qualitative resemblance to those features observed in the atmosphere.

Reynolds, Nathaniel Dunton↗
NASA NTRS1989

Nonaxisymmetric instabilities in thin self-gravitating rings and disks

The stability of geometrically thin self-gravitating rings and disks is studied by computing the eigenvalues and eigenfunctions of linearized normal mode oscillations in these systems. For the vertically averaged incompressible models and models of gaseous and stellar disks with softened gravity, analytic treatment is possible. The existence of oscillatory normal modes is established using a variational principle and infer instability using perturbation theory. Effects due to the Lindblad and corotation resonances are analyzed in detail. The distribution of the ratio of vorticity to surface density is important for determining the stability of the systems.

Papaloizou, John C. B.↗
NASA NTRS1990

Invariant criteria for bound states, degree of ionization, and plasma phase transition

Basis invariant characterizations of bound states and bound fraction of a partially ionized hydrogen plasma are given in terms of properties of the spectrum of eigenvalues and eigenfunctions of the equilibrium quantum statistical one-proton-one-electron reduced density matrix. It is suggested that these can be used to place theories of a proposed plasma-ionization phase transition on a firm foundation. This general approach may be relevant to cosmological questions such as the quark deconfinement-confinement transition.

Girardeau, M. D.↗
NASA NTRS1993

Quantized discrete space oscillators

A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.

Uzes, C. A.↗
NASA NTRS1988

Modal parameter identification in space structures

The objective of this project is to identify modal properties such as the eigenvalues and eigenfunctions of structures. The formal means for accomplishing this task, Structural Identification, is viewed as a two step procedure: (1) identify the eigensolution; and (2) using the identified eigensolution, identify the mass and stiffness. The eigensolution is identified as a correction on a postulated model based on erroneous parameters.

Baruh, H.↗
NASA NTRS1993

Efficient, massively parallel eigenvalue computation

In numerical simulations of disordered electronic systems, one of the most common approaches is to diagonalize random Hamiltonian matrices and to study the eigenvalues and eigenfunctions of a single electron in the presence of a random potential. An effort to implement a matrix diagonalization routine for real symmetric dense matrices on massively parallel SIMD computers, the Maspar MP-1 and MP-2 systems, is described. Results of numerical tests and timings are also presented.

Huo, Yan↗
NASA NTRS1995

Analysis of gas absorption to a thin liquid film in the presence of a zero-order chemical reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

Rajagopalan, S.↗
NASA NTRS1979

The wave structures of the Eady model of baroclinic instability

By solving the linear quasi-geostrophic set of equations pertinent to the Eady model, the complex eigenvalues and the eigenfunctions are obtained. The propagation speed and the growth rate are computed. Quantitative information is provided about the wave structures for several unstable models, a marginally stable mode, and a stable mode. The peculiarities concerning the amplitude and the phase variations of the waves are noted as the wavenumber varies from the unstable region to the stable region. Physical interpretations of the interrelationships among the dynamical variables are given, with a view toward revealing important aspects of the energy transfer from the basic state to the growing waves.

Hyun, J. M.↗
NASA NTRS1993

Numerical solution of wave equations for the stability of the inner cometo-sheath

Numerical solution of the MHD wave equations for stability of the cometary sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is obtained by using a two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. The magnetic field structure discovered in the ionosphere of Comets Halley and Giacobini-Zinner is found to be unstable. The effects of finite plasma pressure, dissociative recombination, and mass loading due to photoionization are found to be stabilizing but are unable to quench the instability completely. It is also found that the higher the neutral production rate the lesser is the growth rate for the instability.

Srivastava, Krishna M.↗
NASA NTRS1993

Stability of the Halley cometosheath with resistivity and plasma motion

The MHD stability of the cometary inner sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is investigated by numerically solving the wave equations which include resistivity, plasma motion and plasma pressure with the help of two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, that is, the diamagnetic cavity boundary. To gain insight into the problem, certain limiting cases of the wave equations are also discussed. The diamagnetic cavity boundary and the adjacent layer of about 100-km thickness of Comet Halley is found to be unstable. The effects of finite plasma pressure, dissociative recombination, mass loading due to photoionization, resistivity, and plasma motion are found to be stabilizing but are unable to quench the instability completely. Motion of the Halley ionopause has been confirmed by observations.

Srivastava, Krishna M.↗
NASA NTRS1994

Nonlinear stability of Halley comethosheath with transverse plasma motion

Weakly nonlinear Magneto Hydrodynamic (MHD) stability of the Halley cometosheath determined by the balance between the outward ion-neutral drag force and the inward Lorentz force is investigated including the transverse plasma motion as observed in the flanks with the help of the method of multiple scales. The eigenvalues and the eigenfunctions are obtained for the linear problem and the time evolution of the amplitude is obtained using the solvability condition for the solution of the second order problem. The diamagnetic cavity boundary and the adjacent layer of about 100 km thickness is found unstable for the travelling waves of certain wave numbers. Halley ionopause has been observed to have strong ripples with a wavelength of several hundred kilometers. It is found that nonlinear effects have stabilizing effect.

Srivastava, Krishna M.↗
NASA NTRS1996

The Effects of Acoustic Treatment on Pressure Disturbances From a Supersonic Jet in a Circular Duct

The pressure disturbances generated by an instability wave in the shear layer of a supersonic jet are studied for an axisymmetric jet inside a lined circular duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions at each axial location. These values are used to determine the growth rates and phase velocities of the instability waves and the near field pressure disturbance patterns. The study is confined to the dominant Kelvin-Helmholtz instability mode and to the region just downstream of the nozzle exit where the shear layer is growing but is still small in size compared to the radius of the duct. Numerical results are used to study the effects of changes in the outer flow, growth in the shear layer thickness, wall distance, and wall impedance, and the effects of these changes on non-axisymmetric modes. The primary results indicate that the effects of the duct wall on stability characteristics diminish as the outer flow increases and as the jet azimuthal mode number increases. Also, wall reflections are reduced when using a finite impedance boundary condition at the wall; but in addition, reflections are reduced and growth rates diminished by keeping the imaginary part of the impedance negative when using the negative exponential for the harmonic dependence.

Dahl, Milo D.↗
NASA NTRS1997

Effects of Acoustically Lined Cylindrical Ducts on Instability Waves in Confined Supersonic Jets

The pressure disturbances generated by an instability wave in the shear layer of a supersonic jet are studied for an axisymmetric jet inside a lined cylindrical duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions. These values are used to determine the growth rates and phase velocities of the instability waves and the radial pressure disturbance patterns. The study is confined to the dominant Kelvin-Helmholtz instability mode and to the region just downstream of the nozzle exit where the shear layer is growing but is still small in size compared to the radius of the duct. Numerical results are used to study the effects of changes in the outer flow, growth in the shear layer thickness, wall distance, wall impedance, and frequency. Results indicate that the effects of the duct wall on shear layer growth rates diminish as the outer flow increases. Also, wall reflections cause variations in growth rates depending on wall height and Strouhal number. These variations are due to the phase relationship between the outgoing and the reflected incoming pressure disturbances at the shear layer. The growth rate variations can be reduced and the maximum growth rate minimized by keeping the imaginary part of the impedance negative.

Dahl, Milo D.↗
DOE OSTI2022

Extension of the PINN diffusion model to k-eigenvalue problems

This paper extends our recent work on the Physics-Informed Neural Networks (PINN) approach for the fixed source diffusion models and applies it to the diffusion theory based k-eigenvalue problems. To make the PINN equitable for the eigenvalue problems, we introduce a novel integral regularization term to the loss function in the framework, and allow the direct inference of the principal eigenvalue and the associated eigenfunction. The regularization term enforces a pre-defined value on the integration of the model predictions, and this value can be directly related to a physical property of the system. We also introduce an additional learnable parameter to approximate the principal eigenvalue. As a proof of principle, we solve the one-group two-dimensional k-eigenvalue neutron diffusion equation in this work. We then provide two numerical examples to demonstrate the applicability of the PINN approach. In each example, we solve the k-eigenvalue diffusion equation in a multi-region configuration constrained with a set of Robin boundary conditions for generality. We use a FEM solution based on the power-iteration method to verify the results of the PINN solution. The results showed relative percentage error in the predicted eigenvalue of about 0.77% and about 1.2% for example 1 and example 2, respectively. The mean absolute error in the predicted flux for example 1 is ∼ 0.002 and for example 2 is ∼ 0.0024. These results indicate some preliminary successes of the PINN application to k-eigenvalue problems. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1981

Efficient computation of the stability of three-dimensional compressible boundary layers

Methods for the computer analysis of the stability of three-dimensional compressible boundary layers are discussed and the user-oriented Compressible Stability Analysis (COSAL) computer code is described. The COSAL code uses a matrix finite-difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, M. R.↗
NASA NTRS1982

Finite-difference solution of the compressible stability eigenvalue problem

A compressible stability analysis computer code is developed. The code uses a matrix finite difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black box stability code. Sample stability calculations are presented for the boundary layer profiles of a Laminar Flow Control (LFC) swept wing.

Malik, M. R.↗
NASA NTRS1987

Linear stability analysis of three-dimensional compressible boundary layers

A compressible stability analysis computer code is developed. The code uses a matrix finite-difference method for local eigenvale solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used inital-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed that may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, Mujeeb R.↗
DOE OSTI2023

Accurate Prediction of HSE06 Band Structures for a Diverse Set of Materials Using Δ-Learning

Here we used machine learning (ML) to accurately predict eigenvalues of the hybrid HSE06 functional using eigenvalues computed by the less computationally expensive PBE functional and associated electronic features based on the k-point resolved atomic band character. The ML model was trained by using eigenvalues from only one k-point for each of the 168 compounds in the training set. The HSE06 eigenvalues across all k-points were then predicted for a separate set of 169 compounds with a mean absolute error (MAE) of 0.13 eV, representing a significant improvement over the error of PBE-computed eigenvalues relative to that of HSE06 (MAE = 0.96 eV). These accurately predicted eigenvalues result in remarkably accurate predictions for the band structures, projected density of states, and band gaps, even though the model was not explicitly trained on these other properties. Finally, we demonstrate that our ML model has a similar accuracy for both ternary and quaternary compounds well outside the initial training set and on systems with 112 and 160 atoms, demonstrating its potential to rapidly predict HSE06-quality electronic structures of complex materials that are practically unfeasible for HSE06.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗