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NASA NTRS1983

On numerical simulation of viscous flows

Numerical simulation methods for viscous incompressible laminar flows are reviewed, with a focus on finite-difference schemes. The approaches to high/moderate-Reynolds-number flows (strong-viscous-interaction model or single sets of equations) and the factors affecting the versatility, reliability, and accuracy of the analysis algorithms are considered; approximate-factorization implicit solution techniques for low-Reynolds-number flows are discussed; and the procedures used in a number of specific problems are indicated.

Ghia, K. N.↗

NASA NTRS1987

Computational fluid dynamics applications at McDonnel Douglas

Representative examples are presented of applications and development of advanced Computational Fluid Dynamics (CFD) codes for aerodynamic design at the McDonnell Douglas Corporation (MDC). Transonic potential and Euler codes, interactively coupled with boundary layer computation, and solutions of slender-layer Navier-Stokes approximation are applied to aircraft wing/body calculations. An optimization procedure using evolution theory is described in the context of transonic wing design. Euler methods are presented for analysis of hypersonic configurations, and helicopter rotors in hover and forward flight. Several of these projects were accepted for access to the Numerical Aerodynamic Simulation (NAS) facility at the NASA-Ames Research Center.

Hakkinen, R. J.↗

NASA NTRS1990

Analysis of spectral projectors in one-dimensional domains

A class of projection operators with values in a subspace of polynomials is analyzed. These projection operators are related to the Hilbert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthoronality relation satisfied by the Chebyshev polynomials. These results are used to study the approximation of a model fourth-order problem.

Maday, Y.↗

NASA NTRS1992

Structural dynamics and vibrations of damped, aircraft-type structures

Engineering preliminary design methods for approximating and predicting the effects of viscous or equivalent viscous-type damping treatments on the free and forced vibration of lightly damped aircraft-type structures are developed. Similar developments are presented for dynamic hysteresis viscoelastic-type damping treatments. It is shown by both engineering analysis and numerical illustrations that the intermodal coupling of the undamped modes arising from the introduction of damping may be neglected in applying these preliminary design methods, except when dissimilar modes of these lightly damped, complex aircraft-type structures have identical or nearly identical natural frequencies. In such cases, it is shown that a relatively simple, additional interaction calculation between pairs of modes exhibiting this 'modal response' phenomenon suffices in the prediction of interacting modal damping fractions. The accuracy of the methods is shown to be very good to excellent, depending on the normal natural frequency separation of the system modes, thereby permitting a relatively simple preliminary design approach. This approach is shown to be a natural precursor to elaborate finite element, digital computer design computations in evaluating the type, quantity, and location of damping treatment.

Young, Maurice I.↗

NASA NTRS1993

A three-dimensional pressure flux-split RNS application to sub/supersonic flow in inlets and ducts

The reduced Navier-Stokes (RNS) formulation is combined with a pressure based flux split procedure for the computational analysis of three dimensional flow. Only lowest order diffusion, that is required to satisfy the no-slip boundary condition is retained in this approximation. The governing equations are appropriately differenced such that the physical boundary conditions are closely coupled and combined to form a closed discrete system. No numerical or characteristic type boundary conditions are required. A global pressure relaxation procedure, i.e. multi-sweep PNS, is considered. A sparse matrix direct solver is applied to the crossplane solution. At the outflow boundary only the pressure or pressure gradient is prescribed. The resulting formulation has been applied to the solution of three-dimensional subsonic/supersonic internal flows in inlets and ducts.

Khosla, P. K.↗

NASA NTRS1984

Nonlinear potential analysis techniques for supersonic-hypersonic aerodynamic design

Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance and full potential theory was utilized to meet this objective. Numerical codes were developed for relatively general three dimensional geometries to evaluate the capability of the approximate equations of motion considered. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes.

Shankar, V.↗

NASA NTRS1974

A finite element method for potential aerodynamics around complex configurations

A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flow around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of the flow field around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with a hyperboloidal surface. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, intrinsically general and flexible, is also fast, accurate and in excellent agreement with existing results.

Chen, L.-T.↗

NASA NTRS1984

Two dimensional nonlinear analysis of sound transmission through a near-sonic throat flow

A two-dimensional nonlinear theory of sound transmission through a nonuniform duct carrying a near-sonic throat flow is described. The mean flow in the duct is treated according to a generalized quasi-one dimensional model, and the analysis of the unsteady perturbations is carried out using the Method of Matched Asymptotic Expansions. The linearized acoustic field in the subsonic regions of the duct is approximated by a Wave Envelope model which is matched asymptotically with a nonlinear inner solution valid in the near-sonic throat region. Numerical results are presented to illustrate the predictions of the theory. It is found that, in general, shock waves develop in the acoustic field during transmission through the near-sonic flow. Unlike previous one-dimensional theories, the current study shows that dispersion can play a major role in the propagation process.

Myers, M. K.↗

NASA NTRS1988

Predicting Temperatures In Ball Bearings

Computer simulations speed design studies. Analyses performed in two or three dimensions. Sizes and shapes of components approximated by zones or nodes connected by gridlines. From geometric information about grids and boundary conditions, properties of bearing and lubricant materials, and information supplied by users, thermal-analysis programs generate mathematical models for thermal transport. Thermal analysis of high-speed rolling contact bearings matured so much that computerized numerical simulations replace expensive time consuming full scale experiments.

Wagner, William R.↗

NASA NTRS1988

Quantum-classical electron distributions in atoms and atomic ions

A quantum-classical approach is used to obtain the velocity distributions in atoms and positive and negative ions in both ground and excited states. In the analysis, Hartree-Fock electronic wavefunctions are used to determine the radial electron distributions, and the central-field approximation is used to study the the dynamic properties of the localized electrons. The distributions for the outer and inner shells are found to agree well with exact results obtained by numerical calculations.

Kunc, Joseph A.↗

NASA NTRS1989

Flow of rarefied gases over two-dimensional bodies

A kinetic-theory analysis is made of the flow of rarefied gases over two-dimensional bodies of arbitrary curvature. The Boltzmann equation simplified by a model collision integral is written in an arbitrary orthogonal curvilinear coordinate system, and solved by means of finite-difference approximation with the discrete ordinate method. A numerical code is developed which can be applied to any two-dimensional submerged body of arbitrary curvature for the flow regimes from free-molecular to slip at transonic Mach numbers. Predictions are made for the case of a right circular cylinder.

Jeng, Duen-Ren↗

NASA NTRS2012

The Near-Earth Encounter of Asteroid 308635 (2005 YU55): Thermal IR Observations

The near-Earth approach (0.00217 AU, or 0.845 lunar distances) of the C-type asteroid 308635 (2005 YU55) in November 2011 presented a rare opportunity for detailed observations of a low-albedo NEA in this size range. As part of a multi-telescope campaign to measure visible and infrared spectra and photometry, we obtained mid-infrared (approx. 8 to 22 micron) photometry and spectroscopy of 2005 YU55 using Michelle on the Gemini North telescope on UT November 9 and 10,2011. An extensive radar campaign together with optical light-curves established the rotation state of YU55. In addition, the radar imaging resulted in a shape model for the asteroid, detection of numerous boulders on its surface, and a preliminary estimate of its equatorial diameter at 380 +/- 20 m. In a preliminary analysis, applying the radar and lightcurve-derived parameters to a rough-surface thermophysical model fit to the Gemini/Michelle thermal emission photometry results in a thermal inertia range of approximately 500 to 1500 J/sq m/0.5s/K, with the low-thermal-inertia solution corresponding to the small end of the radar size range and vice versa. Updates to these results will be presented and modeling of the thermal contribution to the measured near-infrared spectra from Palomar/Triplespec and IRTF/SpeX will also be discussed.

Lim, Lucy F.↗

NASA NTRS1989

New computing systems and their impact on structural analysis and design

A review is given of the recent advances in computer technology that are likely to impact structural analysis and design. The computational needs for future structures technology are described. The characteristics of new and projected computing systems are summarized. Advances in programming environments, numerical algorithms, and computational strategies for new computing systems are reviewed, and a novel partitioning strategy is outlined for maximizing the degree of parallelism. The strategy is designed for computers with a shared memory and a small number of powerful processors (or a small number of clusters of medium-range processors). It is based on approximating the response of the structure by a combination of symmetric and antisymmetric response vectors, each obtained using a fraction of the degrees of freedom of the original finite element model. The strategy was implemented on the CRAY X-MP/4 and the Alliant FX/8 computers. For nonlinear dynamic problems on the CRAY X-MP with four CPUs, it resulted in an order of magnitude reduction in total analysis time, compared with the direct analysis on a single-CPU CRAY X-MP machine.

Noor, Ahmed K.↗

NASA NTRS1988

Fully-coupled analysis of jet mixing problems. Three-dimensional PNS model, SCIP3D

Numerical procedures formulated for the analysis of 3D jet mixing problems, as incorporated in the computer model, SCIP3D, are described. The overall methodology closely parallels that developed in the earlier 2D axisymmetric jet mixing model, SCIPVIS. SCIP3D integrates the 3D parabolized Navier-Stokes (PNS) jet mixing equations, cast in mapped cartesian or cylindrical coordinates, employing the explicit MacCormack Algorithm. A pressure split variant of this algorithm is employed in subsonic regions with a sublayer approximation utilized for treating the streamwise pressure component. SCIP3D contains both the ks and kW turbulence models, and employs a two component mixture approach to treat jet exhausts of arbitrary composition. Specialized grid procedures are used to adjust the grid growth in accordance with the growth of the jet, including a hybrid cartesian/cylindrical grid procedure for rectangular jets which moves the hybrid coordinate origin towards the flow origin as the jet transitions from a rectangular to circular shape. Numerous calculations are presented for rectangular mixing problems, as well as for a variety of basic unit problems exhibiting overall capabilities of SCIP3D.

Wolf, D. E.↗

NASA NTRS1971

An analysis and comparison of several trajectory optimization methods

The sensitivities of the convergence characteristics of the methods to initially assumed parameters and trial solution, convergence times, computer logic, and storage requirements are discussed. Numerical comparison of the convergence characteristics is made by considering a minimum time, low thrust, Earth-Mars transfer trajectory. A modified quasi-linearization method reduces convergence time by approximately 70% when compared with the generalized Newton-Raphson method and allows the terminal boundary to be specified by a general function of the problem variables. A uniquely specified and easily determined, time dependent weighting matrix for the gradient techniques accelerates the shaping of the optimal control program and improves the convergence characteristics during the terminal iterations. Convergence envelopes, indicating how sensitive the convergence characteristics are to initially assumed parameters, are plotted for the perturbation and quasi-linearization methods. Several iteration schemes are proposed which increase the size of the convergence envelopes and decrease the sensitivity of the method to initially assumed parameters.

Lewallen, J. M.↗

NASA NTRS1974

Quasi-three-dimensional flow solution by meridional plane analysis

A computer program has been developed to obtain subsonic or shock-free transonic, nonviscous flow analysis on the hub-shroud midchannel flow surface of a turbomachine. The analysis may be for any annular passage, with or without blades. The blades may be fixed or rotating and may be twisted and leaned. The flow may be axial, radial, or mixed. Blade surface velocities over the entire blade are approximated, based on the rate of change of angular momentum. This gives a three-dimensional flow picture based on a two-dimensional analysis. This paper discusses the method used for the program and shows examples of the type of passages and blade rows which can be analyzed. Also, some numerical examples are given to show how the program can be used for practical assistance in design of blading, annular passages, and annular diffusers.

Katsanis, T.↗

NASA NTRS1976

Calculations of molecular ionization energies using a self-consistent-charge Hartree-Fock-Slater method

A numerical-variational method for performing self-consistent molecular calculations in the Hartree-Fock-Slater (HFS) model is presented. Molecular wavefunctions are expanded in terms of basis sets constructed from numerical HFS solutions of selected one-center atomlike problems. Binding energies and wavefunctions for the molecules are generated using a discrete variational method for a given molecular potential. In the self-consistent-charge (SCC) approximation to the complete self-consistent-field (SCF) method, results of a Mulliken population analysis of the molecular eigenfunctions are used in each iteration to produce 'atomic' occupation numbers. The simplest SCC potential is then obtained from overlapping spherical atomlike charge distributions. Molecular ionization energies are calculated using the transition-state procedure; results are given for CO, H2O, H2S, AlCl, InCl, and the Ni5O surface complex. Agreement between experimental and theoretical ionization energies for the free-molecule valence levels is generally within 1 eV. The simple SCC procedure gives a reasonably good approximation to the molecular potential, as shown by comparison with experiment, and with complete SCF calculations for CO, H2O, and H2S.

Rosen, A.↗

NASA NTRS2004

Chemical Ionization Mass Spectrometry-Based Measurements of HO2 and RO2 During TRACE-P

The Transport and Chemical Evolution over the Pacific (TRACE-P) mission extends NASA's Global Tropospheric Experiment (GTE) series of campaigns. TRACE-P was an aircraft-based campaign that was part of a larger ground-based and aircraft-based program (APARE) under the auspices of the International Global Atmospheric Chemistry (IGAC) program. TRACE-P was designed to (1) determine the chemical composition of Asian outflow over the western Pacific, and to (2) determine the chemical evolution of the Asian outflow. These objectives were addressed through a variety of observations and numerical modeling exercises. In particular, the goals included sampling strategies that would improve understanding of the budgets of odd hydrogen species (OH and HO2), budgets of NOx (NO, NO2, and their reservoirs), and impacts of oxidants produced in the outflow on air quality in the United States. The NASA DC-8 and P-3B aircraft were deployed in the March and April, 2001 out of primary bases of operation in Hong Kong and Yokota Air Base in Japan. These two aircraft have complementary capabilities which allow high altitude and long range impacts, as well as low altitude, local impacts to be assessed. In order to quantify the composition and evolution of Asian outflow, it is important to quantify as many species as possible including photochemically active species (e.g. NO2, CH2O, O3, acetone, etc.), sources species (VOCs, CO, NOx, SO2, aerosols), reactive intermediates including free radicals (OH, HO2, RO2, and their reservoirs), and end products (nitric acid, sulfuric acid, secondary aerosols, etc.). The more complete the measurement suite, the more tightly constrained the numerical modeling can be (within the uncertainties of the measurements). The numerical models range in sophistication from simple steady state box models (as employed in this study) to multi-dimensional chemical transport models. Data were collected on approximately 20 flights of the DC-8 and 21 flights of the P-3B. Observations from both aircraft were used in the present analysis, but primarily focused on the P-3B flights since that was the platform on which the peroxy radical instrumentation was based.

Cantrell, Christopher A.↗