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NASA NTRS1975

Prediction of airframe noise

Methods of predicting airframe noise generated by aircraft in flight under nonpowered conditions are discussed. Approaches to predictions relying on flyover data and component theoretical analyses are developed. A nondimensional airframe noise spectrum of various aircraft is presented. The spectrum was obtained by smoothing all the measured spectra to remove any peculiarities due to airframe protrusions, normalizing each spectra by its overall sound pressure level and a characteristics frequency, and averaging the spectra together. A chart of airframe noise sources is included.

Hardin, J. C.↗

NASA NTRS1979

Laminar and turbulent flows over spherically blunted cone and hyperboloid with massive surface blowing

Numerical solutions are presented for the flow over a spherically blunted cone and hyperboloid with massive surface blowing. Time-dependent viscous shock-layer equations are used to describe the flow field. The boundary conditions on the body surface include a prescribed blowing-rate distribution. The governing equations are solved by a time-asymptotic finite-difference method. Results presented here are only for a perfect gas-type flow at zero angle of attack. Both laminar and turbulent flow solutions are obtained. It is found that the effect of the surface blowing on the laminar flow field is to smooth out the curvature discontinuity at the sphere-cone juncture point, which results in a positive pressure gradient over the body. The shock slope increases on the downstream portion of the body as the surface blowing rate is increased. The turbulent flow with surface blowing is found to redevelop a boundary-layer-like region near the surface. The effects of this boundary-layer region on the flow field and heating rates are discussed.

Kumar, A.↗

NASA NTRS1979

Laser-zone Growth in a Ribbon-to-ribbon (RTR) Process Silicon Sheet Growth Development for the Large Area Silicon Sheet Task of the Low Cost Solar Array Project

A technique for growing limited-length ribbons continually was demonstrated. This Rigid Edge technique can be used to recrystallize about 95% of the polyribbon feedstock. A major advantage of this method is that only a single, constant length silicon ribbon is handled throughout the entire process sequence; this may be accomplished using cassettes similar to those presently in use for processing Czochralski waters. Thus a transition from Cz to ribbon technology can be smoothly affected. The maximum size being considered, 3 inches x 24 inches, is half a square foot, and will generate 6 watts for 12% efficiency at 1 sun. Silicon dioxide has been demonstrated as an effective, practical diffusion barrier for use during the polyribbon formation.

Baghdadi, A.↗

NASA NTRS1989

Algorithm For Solution Of Navier-Stokes Equations

Advantages of two previous algorithms combined. Steady-state Navier-Stokes equations put in implicit finite-difference form solved by approximate Newton iteration. LU-SSOR scheme is new relaxation method combining advantages of LU factorization with Gauss-Seidel relaxation. Vectorizable LU-SSOR scheme, based on central differences, requires scalar diagonal inversions. Application of scheme to approximate Newton iteration of Navier-Stokes equations yields set of equations requiring no implicit smoothing on left side. Only adaptive, total-variation-diminishing, flux-limited dissipation terms added to right side. Algorithm used to predict laminar, turbulent, and hypersonic flows.

Yoon, Seokkwan↗

NASA NTRS1992

The void spectrum in two-dimensional numerical simulations of gravitational clustering

An algorithm for deriving a spectrum of void sizes from two-dimensional high-resolution numerical simulations of gravitational clustering is tested, and it is verified that it produces the correct results where those results can be anticipated. The method is used to study the growth of voids as clustering proceeds. It is found that the most stable indicator of the characteristic void 'size' in the simulations is the mean fractional area covered by voids of diameter d, in a density field smoothed at its correlation length. Very accurate scaling behavior is found in power-law numerical models as they evolve. Eventually, this scaling breaks down as the nonlinearity reaches larger scales. It is shown that this breakdown is a manifestation of the undesirable effect of boundary conditions on simulations, even with the very large dynamic range possible here. A simple criterion is suggested for deciding when simulations with modest large-scale power may systematically underestimate the frequency of larger voids.

Kauffmann, Guinevere↗

NASA NTRS1993

A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems

The finite-volume approach is presently used to obtain a 2D, high-order accurate and basically nonoscillatory shock-capture method whose high-order spatial accuracy is obtained by means of a piecewise polynomial approximation of the solution from cell averages. Attention is given to a high-order spatial operator that is able to both retain high-order accuracy in smooth regions and avoid the oscillations that are associated with interpolations across steep gradients. The operator is extended to hyperbolic systems of equations and curvilinear meshes.

Casper, Jay↗

NASA NTRS1994

The expanding photosphere method applied to SN 1992am AT cz = 14 600 km/s

We present photometry and spectroscopy of Supernova (SN) 1992am for five months following its discovery by the Calan Cerro-Tololo Inter-American Observatory (CTIO) SN search. These data show SN 1992am to be type II-P, displaying hydrogen in its spectrum and the typical shoulder in its light curve. The photometric data and the distance from our own analysis are used to construct the supernova's bolometric light curve. Using the bolometric light curve, we estimate SN 1992am ejected approximately 0.30 solar mass of Ni-56, an amount four times larger than that of other well studied SNe II. SN 1992am's; host galaxy lies at a redshift of cz = 14 600 km s(exp -1), making it one of the most distant SNe II discovered, and an important application of the Expanding Photsphere Method. Since z = 0.05 is large enough for redshift-dependent effects to matter, we develop the technique to derive luminosity distances with the Expanding Photosphere Method at any redshift, and apply this method to SN 1992am. The derived distance, D = 180(sub -25) (sup +30) Mpc, is independent of all other rungs in the extragalactic distance ladder. The redshift of SN 1992am's host galaxy is sufficiently large that uncertainties due to perturbations in the smooth Hubble flow should be smaller than 10%. The Hubble ratio derived from the distance and redshift of this single object is H(sub 0) = 81(sub -15) (sup +17) km s(exp -1) Mpc(exp -1). In the future, with more of these distant objects, we hope to establish an independent and statistically robust estimate of H(sub 0) based solely on type II supernovae.

Schmidt, Brian P.↗

NASA NTRSDate not supplied

Using the Dimensionality Reduction (DR) Approach to Treat Singular and Near-Singular Source and Test Integrals on Triangles for Moment Methods

Recently, the authors presented preliminary results of an initial study of a dimensional reduction scheme for treating (near-)singular integrals (D. R. Wilton et al., “Dimensionality Reduction Approach for Treating Singular and Near-Singular Multidimensional Integrals of Electromagnetics,” 2022 URSI USNC National Radio Science Meeting, Boulder, CO, Jan. 2022). The approach reported there refined and extended several ideas appearing in a recent paper (R. R. Chang, Z. Wang, and Q. Xie, "Fast Convergent Quadrature Method for Evaluating the RWG- and SWG-Related Convolutional Integrals," IEEE Trans. Antennas Propagat., 69, Dec. 2021). That paper reported a curated collection of important, previously published results all leading to very efficient and accurate line integral methods for handling the most common (near-)singular integrals associated with triangles and tetrahedrons with RWG and SWG bases, respectively. Our contributions provided a simpler exposition as well as a more unified, systematic, and robust overall framework for deriving and applying the approach. This presentation further elucidates our extensions to the approach and broadens our initial study to examine the convergence behaviors of the various potential forms over a wider range of triangular source element shape and observation point parameters for various smoothing transformations; we also examine convergence, not just at the subtriangle level, but also overcomplete triangles. In addition, we investigate the application of the recently reported “vertex function” concept to develop faster converging test integrals (Rivero et al., “Acceleration of the Surface Test Integral Using Vertex Functions,” 2021 IEEE Int’l Symp. Ant. Propagat. and USNC-URSI Rad. Sci. Meeting,” Singapore, 4-10 Dec. 2021). Combining these separate schemes has the potential for yielding a near-optimal approach for accurately evaluating singular and near-singular integrals for moment methods.

Singular Integrals↗

NASA NTRS2007

Enhanced Elliptic Grid Generation

An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Kaul, Upender K.↗

NASA NTRS2011

Multiangle Implementation of Atmospheric Correction (MAIAC):: Radiative Transfer Basis and Look-up Tables - 1

This paper describes a radiative transfer basis of the algorithm MAIAC which performs simultaneous retrievals of atmospheric aerosol and bidirectional surface reflectance from the Moderate Resolution Imaging Spectroradiometer (MODIS). The retrievals are based on an accurate semianalytical solution for the top-of-atmosphere reflectance expressed as an explicit function of three parameters of the Ross-Thick Li-Sparse model of surface bidirectional reflectance. This solution depends on certain functions of atmospheric properties and geometry which are precomputed in the look-up table (LUT). This paper further considers correction of the LUT functions for variations of surface pressure/height and of atmospheric water vapor, which is a common task in the operational remote sensing. It introduces a new analytical method for the water vapor correction of the multiple ]scattering path radiance. It also summarizes the few basic principles that provide a high efficiency and accuracy of the LUT ]based radiative transfer for the aerosol/surface retrievals and optimize the size of LUT. For example, the single-scattering path radiance is calculated analytically for a given surface pressure and atmospheric water vapor. The same is true for the direct surface-reflected radiance, which along with the single-scattering path radiance largely defines the angular dependence of measurements. For these calculations, the aerosol phase functions and kernels of the surface bidirectional reflectance model are precalculated at a high angular resolution. The other radiative transfer functions depend rather smoothly on angles because of multiple scattering and can be calculated at coarser angular resolution to reduce the LUT size. At the same time, this resolution should be high enough to use the nearest neighbor geometry angles to avoid costly three ]dimensional interpolation. The pressure correction is implemented via linear interpolation between two LUTs computed for the standard and reduced pressure levels. A linear mixture and a modified linear mixture methods are used to represent different aerosol types in the aerosol/surface retrievals from several base models of the fine and coarse aerosol fractions. In summary, the developed LUT algorithm allows fast high-accuracy simulations of the outgoing radiance with full variability of the atmospheric and surface bidirectional reflectance properties for the aerosol/surface remote sensing.

Lyapustin, Alexei↗

NASA NTRS1975

Computer simulation of transonic flow past airfoils with boundary layer correction

A computer program has been developed to solve the compressible flow equation for the velocity potential. The exterior of the airfoil is mapped onto the unit circle and the flow is computed on a grid in the circle plane. A relaxation method using backward differencing in the flow direction at supersonic points permits solutions for large supersonic areas. The pressure distribution resulting from the flow becomes the input to the von Karman momentum equation which when integrated gives the displacement thickness. This displacement thickness is smoothed and added to the airfoil to account for the turbulent boundary layer. The boundary layer correction is computed iteratively with the flow. Results from this program and test data agree well.

Bauer, F.↗

NASA NTRS1980

Supersonic flow development in slotted wind tunnels

The development of test section slot shapes for achieving smooth supersonic Mach number distribution without overexpansion or waviness has, in the past, been largely an experimentally iterative or 'cutand try' procedure for each wind tunnel. To overcome the obvious disadvantages of time and expense involved in such an experimental approach, a simple analytical method has been developed to predict the supersonic flow development in a two-dimensional slotted tunnel given only the variation of open area ratio with downstream distance and the Mach number corresponding to the plenum static pressure. The well known method of characteristics is used with the constraint that it be compatible with the quadratic cross-flow pressure drop boundary condition at the slotted wall. The predicted results from this method agree remarkably well with the experimental calibration data available for some of the existing facilities. The flow mechanism responsible for causing overexpansion in the centerline Mach number distribution with some slot shapes has been brought to light.

Ramaswamy, M. A.↗

NASA NTRS1990

3D Euler analysis of ducted propfan flowfields

A numerical method is presented for predicting the steady inviscid flow through a ducted propfan based on a time-marching solution of the three-dimensional Euler equations. A four-stage multiple-block Runge-Kutta finite volume numerical technique, utilizing implicit residual smoothing and a blended second and fourth difference dissipation, is applied to predict the transonic flowfield about both single-rotation and counter-rotations ducted rotors. Counter-rotation predictions are based on an average-passage system of equations approach. Calculations are performed for both a single sheared H-type grid system and a multiple-block grid system incorporating a C-type grid about the cowl. Numerical results are compared with experimental data for two cases: a low speed ducted propeller and a 1.15 pressure ratio fan stage.

Hall, Edward J.↗

NASA NTRS1991

A millimeter wave technique for measuring ice thickness on the Space Shuttle's external tank

A solution is presented for detecting and measuring ice that can form on the spray-on foam insulation protecting Space Shuttle fueltanks. The method involves the measurement of the emission properties of the fueltank with a mm-wave radiometer. Emission from the insulated panel is measured for the case of insulation with the original rough surface and the case of insulation sanded down to have a smooth surface. The radiative transfer calculations are facilitated by using a smooth surface, and experimental evidence demonstrates the effective and accurate prediction of ice thickness on the smooth surface. The panel with a rough surface is measured, and the emmision levels are higher than those predicted by model calculations. Sensitivity to ice thickness is similar in both situations in spite of the bias introduced by the rough surface.

Kendra, John E.↗

NASA NTRS1996

Development of an Automatic Grid Generator for Multi-Element High-Lift Wings

The procedure to generate the grid around a complex wing configuration is presented in this report. The automatic grid generation utilizes the Modified Advancing Front Method as a predictor and an elliptic scheme as a corrector. The scheme will advance the surface grid one cell outward and the newly obtained grid is corrected using the Laplace equation. The predictor-corrector step ensures that the grid produced will be smooth for every configuration. The predictor-corrector scheme is extended for a complex wing configuration. A new technique is developed to deal with the grid generation in the wing-gaps and on the flaps. It will create the grids that fill the gap on the wing surface and the gap created by the flaps. The scheme recognizes these configurations automatically so that minimal user input is required. By utilizing an appropriate sequence in advancing the grid points on a wing surface, the automatic grid generation for complex wing configurations is achieved.

Eberhardt, Scott↗

NASA NTRS2004

Representation of Ice Geometry by Parametric Functions: Construction of Approximating NURBS Curves and Quantification of Ice Roughness--Year 1: Approximating NURBS Curves

Software was developed to construct approximating NURBS curves for iced airfoil geometries. Users specify a tolerance that determines the extent to which the approximating curve follows the rough ice. The user can therefore smooth the ice geometry in a controlled manner, thereby enabling the generation of grids suitable for numerical aerodynamic simulations. Ultimately, this ability to smooth the ice geometry will permit studies of the effects of smoothing upon the aerodynamics of iced airfoils. The software was applied to several different types of iced airfoil data collected in the Icing Research Tunnel at NASA Glenn Research Center, and in all cases was found to efficiently generate suitable approximating NURBS curves. This method is an improvement over the current "control point formulation" of Smaggice (v.1.2). In this report, we present the relevant theory of approximating NURBS curves and discuss typical results of the software.

Dill, Loren H.↗

NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.

Park, Michael A.↗

NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment.

Park, Michael A.↗