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At least 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The virtual element method for linear elastodynamics models: Design, analysis, and implementation

We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the L 2 norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally seen in the p-refinement setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On the Estimation of Circumbinary Orbital Properties

We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity—the random motion of a satellite relative to a dynamically cool orbit—from oscillatory modes driven by the central binary’s time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto–Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to promote mergers and growth. These results illustrate how dynamical cooling can set the stage for the formation of Tatooine-like planets around stellar binaries and the small moons around the Pluto–Charon binary planet.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1962

Analytical Study of the Tumbling Motions of Vehicles Entering Planetary Atmospheres

The tumbling motion of vehicles entering planetary atmospheres is analyzed. A differential equation governing the tumbling motion, its arrest, and the subsequent oscillatory motion is obtained and identified as the equation for the fifth Painleve transcendant. An approximate analytical solution for the transcendant is derived. Comparisons with results obtained from numerical integration of the exact equations of motion indicate that the solution for the angle-of-attack history is sufficiently accurate to be of practical use.

PLANETARY ENTRY↗
NASA NTRS1972

Study of low Reynolds number nozzle flows, including radial pressure gradients

An analysis is presented of the laminar, axisymmetric flow in a nozzle, including both axial and radial variations of the pressure. The system of equations derived is believed to contain all of the terms necessary for describing the flow through a relatively sharp throat (i.e., one for which the longitudinal radius of curvature of the throat is comparable to, or less than, the transverse radius). A finite difference approximation of these equations is described, together with a computer program for finding numerical solutions. An instability was found in the starting solution; a series of attempts to eliminate this instability is described.

Rae, W. J.↗
NASA NTRS1972

VLF/ELF input impedance of an arbitrarily oriented loop antenna in a cold collisionless multicomponent magnetoplasma.

A study is made of the input impedance Z of a small strip-loop antenna with arbitrary orientation in a cold collisionless uniform multicomponent magnetoplasma. Assuming a uniform current distribution, an integral expression for Z is derived which is valid for arbitrary values of driving frequency, plasma composition and density, loop orientation angle, and static magnetic field strength. The integral expression is evaluated numerically for the VLF/ELF range in a plasma modeled upon the inner magnetosphere. Approximate closed-form expressions for Z are also developed. It is found that the loop VLF/ELF input reactance is essentially identical to its free space self inductance. Also the loop radiation resistance is found to be a strong function of the loop orientation angle for frequencies near the lower-hybrid-resonance frequency or below the proton gyrofrequency.

Wang, T. N. C.↗
NASA NTRS1972

Laser-induced gas breakdown - Electron cascade.

Development of a theory of electron cascade which takes explicitly into account the electron energy distribution. For the particular case of a Boltzmann distribution, it is shown that the monoenergetic approximation is valid, except for low flux densities (less than 20 MW per sq cm) of the laser beam. It is emphasized that the equilibrium temperature can be calculated easily. When electron-ion inverse bremsstrahlung comes into play, this approximation becomes invalid; there is a pressure below which the cascade cannot develop. Numerical results are presented for model calculations of helium and argon.

De Montgolfier, P.↗
NASA NTRS1972

Numerical calculations of flow fields

The solutions to the equations of motion for inviscid fluid flow around a pointed elliptic cone at incidence are presented. The numerical method used, MacCormack's second order preferential predictor-corrector finite difference approximation, is applied to the fluid flow equations derived in conservation-law form. The entropy boundary condition, hitherto unused for elliptic cone problems, is investigated and compared to reflection boundary condition solutions. The stagnation streamline movement of the inclined elliptic cone is noted and surface pressure coefficients are plotted. Also presented are solutions for an elliptic cone and a circular cone at zero incidence and a circular cone at a small angle of attack. Comparisons are made between these present solutions and previously published theory.

Anderson, D. M.↗
NASA NTRS1974

Development of a global pollution model for CO, CH4, and CH2O

The current status of a global pollution model for carbon monoxide, methane, and formaldehyde is described. The physico-chemical action is considered of these three pollutants in the troposphere. This geographic restriction is convenient since the tropopause provides a natural boundary across which little transport occurs. The data on sources and sinks for these pollutants is based on available information and assumptions relative to the major man-made and natural contributions. The distributions and concentrations of methane, formaldehyde, and carbon monoxide in the atmosphere are interrelated by the chemical reactions in which they participate. A chemical kinetic model based on the pseudo-steady state approximation for the intermediate species was developed to account for these reactions. The numerical procedure used to mathematically describe the pollution transport is a mass conservative scheme employing an integral flux approach.

Peters, L. K.↗
NASA NTRS1974

Lee surface flow phenomena over space shuttle at large angles of attack at M sub infinity equal 6

Surface pressure and heat transfer, flow separation, flow field, and oil flow patterns on the leeward side of a space shuttle orbiter model are investigated at a free stream Mach number of 6. The free stream Reynolds numbers are between 1.64 times 10 to the 7th power and 1.31 times 10 to the 8th power per meter, and the angle of attack is varied between 0 deg and 40 deg for the present experiments. The stagnation temperatures for the tests are approximately 500 K and the wall temperature is maintained at 290 K. Existing numerical methods of three-dimensional inviscid supersonic flow theory and compressible boundary layer theory are used to predict the present experimental measurements. Results of the present tests indicate two distinct types of flow separation and surface peak heating depending on the angle of attack.

Zakkay, V.↗
NASA NTRS1975

A wave model of near wakes

A new model for the near-wake studies is presented. It pertains to a tenuous plasma medium with negligible magnetic field effects. The wake-generating body moves at a mesothermal speed, i.e., intermediate between the thermal speeds of ions and electrons of the ambient plasma which is bithermal (Ti less than Te) and has a Debye length much smaller than the body size. The model is constructed by using the concept that the cavity left by a rapidly moving body acts as a generator of finite-amplitude ion acoustic waves which are excited by an initial discontinuity of plasma density at the leading edge of the cavity. This ionic wave motion, represented by fluid equations, is represented approximately by the time dependent one-dimensional Korteweg-de Vries equation. Numerical and analytic solutions are both given.

Liu, V. C.↗
NASA NTRS1976

On sound transmission into a stiffened cylindrical shell under flight conditions

In the context of airborne-noise transmission through an aircraft fuselage, a mathematical model is presented for sound transmission into a stiffened cylindrical shell. The stiffening effect of the ring frames and stringers is approximated by a 'smeared'-stiffener theory which includes the eccentricity of the stiffeners. Numerical results are presented for a typical narrow-bodied jet in cruising flight. A comparison is made between noise transmission into a monococque shell and into a stiffened shell. The stiffeners are shown to greatly increase TL for small incidence angles, so that the effective 'window' for noise transmission is restricted to the neighborhood of normal incidence. Flow is shown to increase TL for sound waves propagating 'upstream' against the flow. Stiffeners are also shown to raise the ring frequency at which a dip in cylinder TL occurs. Limitations of the 'smeared'-stiffener theory are also discussed.

Koval, L. R.↗
NASA NTRS1976

Effects of stream-associated fluctuations upon the radial variation of average solar-wind parameters

The effects of nonlinear fluctuations due to solar wind streams upon radial gradients of average solar wind parameters are computed, using a numerical MHD model for both spherically symmetric time dependent and corotating equatorial flow approximations. Significant effects of correlations are found between fluctuations upon the gradients of azimuthal magnetic fields, radial velocity, density and azimuthal velocity. Between 400 to 900 solar radii stream interactions have transferred the major portion of the angular momentum flux to the magnetic field; at even greater distances the plasma again carries the bulk of the angular momentum flux. The average azimuthal component of the magnetic field may decrease as much as 10% faster than the Archimedean spiral out to 6 AU due to stream interactions, but this result is dependent upon inner boundary conditions.

Goldstein, B. E.↗
NASA NTRS1977

Unsteady aerodynamic modeling for arbitrary motions

A study is presented on the unsteady aerodynamic loads due to arbitrary motions of a thin wing and their adaptation for the calculation of response and true stability of aeroelastic modes. In an Appendix, the use of Laplace transform techniques and the generalized Theodorsen function for two-dimensional incompressible flow is reviewed. New applications of the same approach are shown also to yield airloads valid for quite general small motions. Numerical results are given for the two-dimensional supersonic case. Previously proposed approximate methods, starting from simple harmonic unsteady theory, are evaluated by comparison with exact results obtained by the present approach. The Laplace inversion integral is employed to separate the loads into 'rational' and 'nonrational' parts, of which only the former are involved in aeroelastic stability of the wing. Among other suggestions for further work, it is explained how existing aerodynamic computer programs may be adapted in a fairly straightforward fashion to deal with arbitrary transients.

Edwards, J. W.↗
NASA NTRS1977

Kinetic theory analysis of rarefied gas flow through finite length slots

A kinetic-theory analysis is made of the flow of a rarefied monatomic gas through a two-dimensional slot connecting two reservoirs. Numerical solutions are obtained by the moment and discrete-ordinate methods. The former method portrays the transition-regime characteristics well but has limitations in the free-molecule regime. The latter method gives accurate results in the free-molecule and slip regimes and bolsters confidence in the accuracy of the transition-regime results. The numerical solution for the mass flux through the slot agrees well with an approximate analytical solution of the moment equations for length-to-width ratios from 6 to 0.5, pressure ratios from 0.8 to 0.1, and Knudsen numbers from 5 to 0.5.

Raghuraman, P.↗
NASA NTRS1977

Finite element analysis of aeroacoustic jet-flap flows

A computational analysis was performed on the steady, turbulent aerodynamic flowfields associated with a jet-blown flap. For regions devoid of flow separation, a parabolic approximation to the governing time-averaged Navier-Stokes equations was applied. Numerical results are presented for the symmetry plane flow of a slot-nozzle planar jet flap geometry, including prediction of flowfield evolution within the secondary mixing region immediately downstream of the trailing edge. Using a two equation turbulence kinetic energy closure model, rapid generation and decay of large spatial gradients in mean and correlated fluctuating velocity components within the immediate wake region were predicted. Modifications to the turbulent flow structure, as induced by porous surface treatment of the flap, were evaluated. The recirculating flow within a representative discrete slot in the surface was evaluated, using the two dimensional, time-averaged Navier-Stokes equations.

Baker, A. J.↗
NASA NTRS1980

Response of a panel to a supersonic turbulent boundary layer - Studies on a theoretical model

A study of the response of a clamped panel to a supersonic turbulent boundary layer, based on a recently developed theoretical model, is presented. It is demonstrated that the model incorporates the effect of coupling between the panel motion and the flow of the surrounding fluid. Further, a Ritz-Galerkin method is used to obtain approximate solutions for the statistics of the panel response to the turbulence. The numerical results are compared with previous experimental data and the theoretical model is assessed.

Yen, D. H. Y.↗
NASA NTRS1981

Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

Yee, H. C.↗
NASA NTRS1982

Numerical analysis of confined turbulent flow

The considered investigation is concerned with the development of an efficient computational method for obtaining a physical understanding of an internal turbulent field. The employed approach makes use of a 'two equation' type model for the turbulence to obtain the numerical solution of a two-dimensional confined turbulent flow. The mean flow governing equations are considered along with the governing equation of the mean temperature and concentrations, and the boundary conditions. The numerical procedure for solving the turbulent flow is discussed, taking into account an approximation to the nonlinear terms, and the inner and outer coupling. Attention is given to a stability convergence analysis, the stability characteristics, and computational examples.

Lin, A.↗