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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Stability Analysis of Roughness Array Wake in a High-Speed Boundary Layer

Computations are performed to examine the effects of both an isolated and spanwise periodic array of trip elements on a high-speed laminar boundary layer, so as to identify the potential physical mechanisms underlying an earlier transition to turbulence as a result of the trip(s). In the context of a 0.333 scale model of the Hyper-X forebody configuration, the time accurate solution for an array of ramp shaped trips asymptotes to a stationary field at large times, indicating the likely absence of a strong absolute instability in the mildly separated flow due to the trips. A prominent feature of the wake flow behind the trip array corresponds to streamwise streaks that are further amplified in passing through the compression corner. Stability analysis of the streaks using a spatial, 2D eigenvalue approach reveals the potential for a strong convective instability that might explain the earlier onset of turbulence within the array wake. The dominant modes of streak instability are primarily sustained by the spanwise gradients associated with the streaks and lead to integrated logarithmic amplification factors (N factors) approaching 7 over the first ramp of the scaled Hyper-X forebody, and substantially higher over the second ramp. Additional computations are presented to shed further light on the effects of both trip geometry and the presence of a compression corner on the evolution of the streaks.

Choudhari, Meelan↗
NASA NTRS1960

Application of Variational Methods to the Thermal Entrance Region of Ducts

A variational method is presented for solving eigenvalue problems which arise in connection with the analysis of convective heat transfer in the thermal entrance region of ducts. Consideration is given, to both situations where the temperature profile depends upon one cross-sectional coordinate (e.g. circular tube) or upon two cross-sectional coordinates (e.g. rectangular duct). The variational method is illustrated and verified by application to laminar heat transfer in a circular tube and a parallel-plate channel, and good agreement with existing numerical solutions is attained. Then, application is made to laminar heat transfer in a square duct as a check, an alternate computation for the square duct is made using a method indicated by Misaps and Pohihausen. The variational method can, in principle, also be applied to problems in turbulent heat transfer.

Sparrow, E. M.↗
NASA NTRS2004

Entangled Biphoton Virtual-State Spectroscopy of the A(exp 2)Sigma(sup +)-X(exp 2)Pi System of OH

This Letter describes the first application of entanglement-induced virtual-state spectroscopy to a molecular system. Non-classical, non-monotonic behavior in a two-photon absorption cross section of the OH A-X system, induced by an entangled biphoton state is theoretically demonstrated. A Fourier transform analysis of the biphoton cross section permits access to the energy eigenvalues of intermediate rovibronic states with a fixed excitation photon energy. The dependence of the Fourier spectrum on the tuning range of the entanglement time (T(sub e)) and the relative path delay (tau(sub e)) is discussed. Our analysis reveals that the implementation of molecular virtual-state spectroscopy for the OH A-X system requires the tuning of tau(sub e) over a pico-second range with femto-second resolution.

Kojima, Jun↗
NASA NTRS2004

Entangled Biphoton Virtual-State Spectroscopy of the A(exp 2)Sigma(+) - X(exp 2)Pi System of OH

This Letter describes the first application of entanglement-induced virtual-state spectroscopy to a molecular system. Non-classical, non-monotonic behavior in a two-photon absorption cross section of the OH A-X system, induced by an entangled biphoton state is theoretically demonstrated. A Fourier transform analysis of the biphoton cross section permits access to the energy eigenvalues of intermediate rovibronic states with a fixed excitation photon energy. The dependence of the Fourier spectrum on the tuning range of the entanglement time T(sub e), and the relative path delay tau(sub e) is discussed. Our analysis reveals that the implementation of molecular virtual-state spectroscopy for the OH A-X system requires the tuning of tau(sub e) over a pico-second range with femto-second resolution.

Kojima, Jun↗
NASA NTRS1973

The inference of atmospheric ozone using satellite nadir measurements in the 1042/cm band

A description and detailed analysis of a technique for inferring atmospheric ozone information from satellite nadir measurements in the 1042 cm band are presented. A method is formulated for computing the emission from the lower boundary under the satellite which circumvents the difficult analytical problems caused by the presence of atmospheric clouds and the watervapor continuum absorption. The inversion equations are expanded in terms of the eigenvectors and eigenvalues of a least-squares-solution matrix, and an analysis is performed to determine the information content of the radiance measurements. Under favorable conditions there are only two pieces of independent information available from the measurements: (1) the total ozone and (2) the altitude of the primary maximum in the ozone profile.

Russell, J. M., III↗
NASA NTRS1990

The unpolarized component in polarimetric radar observations of forested areas

A polarimetric radar measures the complete scattering matrix of a target. For the forest and other natural targets, the average return is, in general, partially polarized. Conditions on the second-order statistics of the scattering matrix under which the return is fully polarized are derived, and it is shown that these conditions are connected with the eigenvalues of the covariance matrix. The result of this analysis is a set of three quantities which indicate the ability of a scatterer to generate an unpolarized component. These quantities for forested areas are shown.

Durden, Stephen L.↗
NASA NTRS2012

Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates

Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.

Nemeth, Michael P.↗
NASA NTRSDate not supplied

A Look at the Truths and Misconceptions of the Variational Quantum Eigensolver and the Implications of Overparameterization

In this work, we investigate loss landscapes of the variational quantum eigensolver (VQE) by quantifying the number of local minima through empirical analyses. We focus on minimal models in chemistry and physics so that we can do a complete analysis using more computationally expensive tools. We employ Hessian eigenvalue calculations and the nudged elastic band algorithm to characterize these landscapes. Our results expand upon the existing literature by highlighting the optimization challenges faced by VQE. We find that, as the number of parameters in our ansatz increases, the number of basins increases while the corresponding loss function values converge toward the global minimum value. This observation implies that overparameterization may lead to an ``effective convexity'' in VQE loss landscapes, a phenomenon supported by theoretical and numerical work in classical machine learning.

quantum computing↗
NASA NTRS1973

Free vibration analysis of spinning structural systems.

This article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer functions associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin-stabilized and dual-spin-stabilized satellites. The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive-definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices.

Gupta, K. K.↗
NASA NTRS1994

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

Ibraheem, S. O.↗
NASA NTRS1971

Statistical analysis of the modal properties of large structural systems.

A theory is developed to predict eigenvalue and eigenvector uncertainty in large dynamic models. The uncertainty is based on physical property uncertainty and should not be confused with numerical roundoff, although the method can be extended to include the latter. The theory, when implemented on a computer, is used to analyze the uncertainties in frequencies and mode shapes based on uncertainties in mass, stiffness, modulus of elasticity, etc. The method incorporates a linear statistical model which is quite adequate for handling property uncertainties of 10% or more. The model is not limited to small systems but uses certain statistical assumptions as well as selective matrix manipulations to keep the size of all matrix operations to within the number of degrees of freedom of the system. Examples are given for two longitudinal vibration problems, and the results are supported by a Monte Carlo analysis.

Collins, J. D.↗
DOE OSTI2025

Bounds on spectral gaps of Hyperbolic spin surfaces

We describe a method for constraining Laplacian and Dirac spectra of two dimensional compact orientable hyperbolic spin manifolds and orbifolds. The key ingredient is an infinite family of identities satisfied by the spectra. These spectral identities follow from the consistency between 1) the spectral decomposition of functions on the spin bundle into irreducible representations of SL(2,R) and 2) associativity of pointwise multiplication of functions. Applying semidefinite programming methods to our identities produces rigorous upper bounds on the Laplacian spectral gap as well as on the Dirac spectral gap conditioned on the former. In several examples, our bounds are nearly sharp; a numerical algorithm based on the Selberg trace formula shows that the [0;3,3,5] orbifold, a particular surface with signature [1;3], and the Bolza surface nearly saturate the bounds at genus 0, 1 and 2 respectively. Under additional assumptions on the number of harmonic spinors carried by the spin-surface, we obtain more restrictive bounds on the Laplacian spectral gap. In particular, these bounds apply to hyperelliptic surfaces. We also determine the set of Laplacian spectral gaps attained by all compact orientable two-dimensional hyperbolic spin orbifolds. We show that this set is upper bounded by 12.13798; this bound is nearly saturated by the [0;3,3,5] orbifold, whose first non-zero Laplacian eigenvalue is λ^(0)_1 ≈ 12.13623.

Spectral theory↗
NASA NTRS1980

Stability of the stratifield cylindrical annulus flow

The linear stability analysis for the stratified flow between two rotating circular cylinders is formulated. Two approaches for the stability analysis are presented. The first approach results in an algebraic eigenvalue problem, while the second results in an initial value problem for the perturbation function. The advantages and disadvantages of both approaches are discussed and a preferable numerical solution technique is outlined.

Antar, B. N.↗
NASA NTRS1996

ASTROP2 Users Manual: A Program for Aeroelastic Stability Analysis of Propfans

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelastic STability and Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is divided into two modules: 2DSTRIP, which calculates the structural dynamic information; and 2DASTROP, which calculates the unsteady aerodynamic force coefficients from which the aeroelastic stability can be determined. In the original version of ASTROP2, these two aspects were performed in a single program. The improvements to version 2.0 include an option to account for counter rotation, improved numerical integration, accommodation for non-uniform inflow distribution, and an iterative scheme to flutter frequency convergence. ASTROP2 can be used for flutter analysis of multi-bladed structures such as those found in compressors, turbines, counter rotating propellers or propfans. The analysis combines a two-dimensional, unsteady cascade aerodynamics model and a three dimensional, normal mode structural model using strip theory. The flutter analysis is formulated in the frequency domain resulting in an eigenvalue determinant. The flutter frequency and damping can be inferred from the eigenvalues.

Reddy, T. S. R.↗
NASA NTRS1995

Sensitivity Analysis of Wing Aeroelastic Responses

Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency, and torsional frequency is calculated analytically. A strip theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model and solved as an eigenvalue problem to determine the critical speed of the wing. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming.

Issac, Jason Cherian↗
NASA NTRS1987

Aeroelastic effects in multirotor vehicles. Part 2: Methods of solution and results illustrating coupled rotor/body aeromechanical stability

This report is a sequel to the earlier report titled, Aeroelastic Effects in Multi-Rotor Vehicles with Application to Hybrid Heavy Lift System, Part 1: Formulation of Equations of Motion (NASA CR-3822). The trim and stability equations are presented for a twin rotor system with a buoyant envelope and an underslung load attached to a flexible supporting structure. These equations are specialized for the case of hovering flight. A stability analysis, for such a vehicle with 31 degrees of freedom, yields a total of 62 eigenvalues. A careful parametric study is performed to identify the various blade and vehicle modes, as well as the coupling between various modes. Finally, it is shown that the coupled rotor/vehicle stability analysis provides information on both the aeroelastic stability as well as complete vehicle dynamic stability. Also presented are the results of an analytical study aimed at predicting the aeromechanical stability of a single rotor helicopter in ground resonance. The theoretical results are found to be in good agreement with the experimental results, thereby validating the analytical model for the dynamics of the coupled rotor/support system.

Venkatesan, C.↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗