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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
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.↗
NASA NTRS1982

Evaluation and reduction of errors induced by the Guyan transformation

The Guyan reduction refers to a method used to reduce the number of degrees of freedom in a structural model for dynamic analysis. Experience shows that, if the method is properly employed, then this reduction method does in fact provide a "reasonably" accurate approximation of the dynamic characteristics of the unreduced model. A method that provides an accurate estimate of the error in each mode of the reduced eigenvalue problem and, in addition, gives first order correction terms that greatly improve the accuracy of the eigenvectors and eigenvalues is presented. The method is demonstrated by standard COSMIC NASTRAN DAMP alters to rigid format 3, real normal mode analysis. Comparative computer time of modal extraction versus error analysis is discussed for the VAX-11/780 version of COSMIC NASTRAN.

Fox, G. L.↗
NASA NTRS1993

Acceleration of convergence and spectrum transformation of implicit finite difference operators associated with Navier-Stokes equations

Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.

Saleem, M.↗
NASA NTRS1974

On the flame spreading over a polymer surface

The characteristics of flame propagation along the interface between a solid fuel and a gaseous oxidizer are considered. It is found that difficulties in a study of this problem are related to the eigenvalue character of the relative velocity of the flame with respect to the oxidizer flow. In the proposed model of flame spreading the difficulties are overcome by retaining the ellipticity of the governing equations and by taking the surface pyrolysis into account. The solution procedure makes use of a sink-source approach and the Fourier-transform method. Flame propagation velocity data computed on the basis of the described approach are compared with experimental results.

Ohki, Y.↗
NASA NTRS1992

The relationship between pressure-based and density-based algorithms

The PISO, pressure-based algorithm, is compared with implicit time-marching systems to ascertain their similarities and differences. Both methods are expressed in vector form for comparison purposes. The vector form of the PISO method is triangular, allowing an uncoupled solution procedure, while the Euler implicit method requires the simultaneous solution of all equations. Upwind differencing is performed according to the direction of the eigenvalues in both systems, but this is the particle velocity in the PISO method and the acoustic velocity in the Euler method. Vector stability calculations show that the PISO method is conditionally stable depending on the time step, but that it provides adequate damping at small time steps to enable good convergence. Unconditional stability can be provided by retaining the energy coupling terms in the time derivative. Transforming the Euler implicit equations to the PISO variables along with a modification of the time derivatives gives the density-based method the same amplification factors at low speeds as the pressure-based method without affecting their behavior at high speeds.

Merkle, Charles L.↗
NASA NTRSDate not supplied

Composition-property correlations in NiTi-based shape memory alloys from the first principles

Development of shape memory alloys (SMA) has been traditionally accomplished by means of extensive empirical efforts, with a very limited support from phenomenological models and related tools. We present a theoretical framework based on the Hamiltonian formalism, which connects important thermodynamic properties directly to the relative energies (the eigenvalues of the Hamiltonian), computed from the first principles using density functional theory. The estimates based on this formalism allow to establish correlations between composition and physical properties, such as relative energies, phase transition temperatures, hysteresis, thermal expansion, and other thermodynamic information. Importantly, estimates and correlations not only provide a fast answer, but also elucidate underpinning of thermodynamic features in terms of the electronic structure. Using this framework, we consider phase transformations and correlations between the selected properties and composition in the NiTi-based ternary and multicomponent shape memory alloys. Our theoretical guidance facilitates design and development of future alloys.

shape memory alloys↗
NASA NTRS1986

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗
NASA NTRS1994

Coherent pulses in the diffusive transport of charged particles`

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

Kota, J.↗
NASA NTRS1978

Airplane stability calculations with a card programmable pocket calculator

Programs are presented for calculating airplane stability characteristics with a card programmable pocket calculator. These calculations include eigenvalues of the characteristic equations of lateral and longitudinal motion as well as stability parameters such as the time to damp to one-half amplitude or the damping ratio. The effects of wind shear are included. Background information and the equations programmed are given. The programs are written for the International System of Units, the dimensional form of the stability derivatives, and stability axes. In addition to programs for stability calculations, an unusual and short program is included for the Euler transformation of coordinates used in airplane motions. The programs have been written for a Hewlett Packard HP-67 calculator. However, the use of this calculator does not constitute an endorsement of the product by the National Aeronautics and Space Administration.

Sherman, W. L.↗
NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
NASA NTRSDate not supplied

Investigating the Feasibility and Stability for Modeling Broadband Acoustic Wave Scattering using a Time-Domain Boundary Integral Equation

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. Acoustic liners are an effective tool for reducing aircraft noise and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model is discussed in which the liner impedance is specified along a wide range of frequencies. An impedance boundary condition is derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate. It is assumed the flat plate has surfaces treated with acoustic liners. The stability of the numerical algorithm is assessed using eigenvalue analysis.

mathmatics↗
NASA NTRS1984

MMIC devices for active phased array antennas

The study of printed circuit discontinuities is necessary in order to design, for example, transitions between rectangular waveguides and printed circuits. New developments with respect to the analytical approaches to this problem are discussed. A summary of the progress in the experimental approach is presented. The accurate solution for the modes in various millimeter-wave waveguides is essential in the analysis of many integrated circuit components, such as filters and impedance transformers. Problems associated with the numerical computation of these modes in two frequently used waveguide forms, namely, the finline and microstrip, are presented. The spectral domain method of formulation, with a moment method solution, is considered. This approach can be readily extended to analyze an arbitrary configuration of dielectric and metallized regions in a shielded enclosure. Galerkin's method is used, where the testing and basic functions are the same. It is shown that the mode functions, or eigenfunctions, are more sensitive to errors than the phase constants, or eigenvalues. The approximate mode functions do not satisfy the orthogonality relationship well, resulting in difficulties when these modal solutions are used to form an approximate Green's function or are used in a mode matching analysis.

Mittra, R.↗
NASA NTRS2020

TPSAS-NF1676L-36025-DND

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A broadband impedance model will be discussed in which the liner impedance is specified along a wide range of frequencies. The liner impedance boundary condition will be derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate consisting of both un-lined and lined surfaces. The scattering solution will be obtained iteratively using both spatial and temporal basis functions and the stability will be demonstrated through eigenvalue analysis.

Michelle E Rodio↗
NASA NTRSDate not supplied

Investigating the Numerical Stability of Using an Impedance Boundary Condition to Model Broadband Noise Scattering With Acoustic Liners

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model will be discussed in which the liner impedance is specified along a wide range of frequencies. The liner impedance boundary condition will be derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate consisting of both un-lined and lined surfaces. The scattering solution will be obtained iteratively using both spatial and temporal basis functions and the stability will be demonstrated through eigenvalue analysis. Stability will be assessed for its dependence on time step, spatial discretization, as well as temporal basis function order. Both second- and third-order Lagrange temporal basis functions are considered.

acoustics↗
NASA NTRSDate not supplied

Investigating the Numerical Stability of Using an Impedance Boundary Condition to Model Broadband Noise Scattering With Acoustic Liners

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for achieving aircraft noise reduction and are characterized by a frequency-dependent impedance value. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering by geometric bodies treated with acoustic liners. A Broadband Impedance Model will be discussed in which the liner impedance is specified along a wide range of frequencies. The liner impedance boundary condition will be derived and coupled with a time-domain boundary integral equation to model acoustic scattering by a flat plate consisting of both un-lined and lined surfaces. The scattering solution will be obtained iteratively using both spatial and temporal basis functions and the stability will be demonstrated through eigenvalue analysis. Stability will be assessed for its dependence on time step, spatial discretization, as well as temporal basis function order. Both second- and third-order Lagrange temporal basis functions are considered.

acoustics↗
NASA NTRS2018

Simulation of Sound Absorption by Scattering Bodies Treated with Acoustic Liners Using a Time-Domain Boundary Element Method

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance, Z(w). Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering of geometric bodies treated with acoustic liners. This work uses an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Y(w) = 1/Z(w). An admittance boundary condition will be derived and coupled with a time domain boundary integral equation. The solution will be obtained iteratively using spatial and temporal basis functions and will allow for acoustic scattering problems to be modeled with geometries consisting of both unlined and soft surfaces. Stability will be demonstrated through eigenvalue analysis.

Pizzo, Michelle E.↗
NASA NTRS1989

A fast, preconditioned conjugate gradient Toeplitz solver

A simple factorization is given of an arbitrary hermitian, positive definite matrix in which the factors are well-conditioned, hermitian, and positive definite. In fact, given knowledge of the extreme eigenvalues of the original matrix A, an optimal improvement can be achieved, making the condition numbers of each of the two factors equal to the square root of the condition number of A. This technique is to applied to the solution of hermitian, positive definite Toeplitz systems. Large linear systems with hermitian, positive definite Toeplitz matrices arise in some signal processing applications. A stable fast algorithm is given for solving these systems that is based on the preconditioned conjugate gradient method. The algorithm exploits Toeplitz structure to reduce the cost of an iteration to O(n log n) by applying the fast Fourier Transform to compute matrix-vector products. Matrix factorization is used as a preconditioner.

Pan, Victor↗
NASA NTRS1990

Dynamic substructuring by the boundary flexibility vector method of component mode synthesis

Component mode synthesis (CMS) is a method of dynamic analysis, for structures having a large number of degrees of freedom (DOF). These structures often required lengthy computer CPU time and large computer memory resources, if solved directly by the finite-element method (FEM). In CMS, the structure is divided into independent components in which the DOF are defined by a set of generalized coordinates defined by displacement shapes. The number of the generalized coordinates are much less than the original number of physical DOF, in the component. The displacement shapes are used to transform the component property matrices and any applied external loads, to a reduced system of coordinates. Reduced system property matrices are assembled, and any type of dynamic analysis is carried out in the reduced coordinate system. Any obtained results are back transformed to the original component coordinate systems. In all conventional methods of CMS, the mode shapes used for components are dynamic mode shapes, supplemented by static deflected shapes. Historically, all the dynamic mode shapes used in conventional CMS are the natural modes (eigenvectors) of components. A new method of CMS, namely the boundary flexibility vector method of CMS, is presented. The method provides for the incorporation of a set of static Ritz vectors, referred to as boundary flexibility vectors, as a replacement and/or supplement to conventional eigenvectors, as displacement shapes for components. The generation of these vectors does not require the solution of a costly eigenvalue problem, as in the case of natural modes in conventional CMS, and hence a substantial saving in CPU time can be achieved. The boundary flexibility vectors are generated from flexibility (or stiffness) properties of components. The formulation presented is for both free and fixed-interface components, and for both the free and forced vibration problems. Free and forced vibration numerical examples are presented to verify the accuracy of the method and the saving in CPU time. Compared to conventional methods of CMS, the results indicate that by using the new method, more accurate results can be obtained with a substantial saving in CPU time.

Abdallah, Ayman Ahmed↗