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NASA NTRS1989

Three-dimensional multigrid Navier-Stokes computations for turbomachinery applications

The fully three-dimensional, time-dependent compressible Navier-Stokes equations in cylindrical coordinates are presently used, in conjunction with the multistage Runge-Kutta numerical integration scheme for solution of the governing flow equations, to simulate complex flowfields within turbomechanical components whose pertinent effects encompass those of viscosity, compressibility, blade rotation, and tip clearance. Computed results are presented for selected cascades, emphasizing the code's capabilities in the accurate prediction of such features as airfoil loadings, exit flow angles, shocks, and secondary flows. Computations for several test cases have been performed on a Cray-YMP, using nearly 90,000 grid points.

Subramanian, S. V.↗

NASA NTRS1987

Numerical experiments on transition control in wall-bounded shear flows

Results are presented from a numerical simulation of transition control in plane channel and boundary layer flows. The analysis is based on a pseudo-spectral/finite difference semi-implicit solution procedure employed to numerically integrate the time-dependent, three-dimensional, incompressible Navier-Stokes equations in a doubly periodic domain. In the channel flow, it was found that the active periodic suction/blowing method was effective in controlling strongly three-dimensional disturbances. In the boundary layer, the preliminary analysis indicated that in the early stages, passive control by suction is as effective as active control to suppress instabilities. The current work is focused on a detailed comparison of active and passive control by suction/blowing in the boundary layer.

Biringen, S.↗

NASA NTRS1989

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Lan, C. Edward↗

NASA NTRS1989

Electron positron pair winds and the Eddington limit

The dynamics of pair winds in the environment of the central engine of Active Galactic Nuclei (AGN) are investigated assuming super Eddington accretion onto black holes. If the accretion is assumed to be spherically symmetric with the accreting matter occurring in discrete cool blobs, and pairs are produced by a nonthermal mechanism, these pairs are blown out by radiation pressure if the coupling between the pairs and accreting blobs is not complete. The coupling also determines the escaping luminosity. If the maximal coupling constraint is relaxed, then a qualitative argument shows that the classical Eddington limit may be exceeded. When the pairs are considered to be noninteracting particles, the outflow is optically thin. Frame dependent effects are considered. Equations are derived considering pair production in the rest frame of the wind and also in the rest frame of the accreting cool blobs. The hydrodynamic equations are integrated numerically.

Leighly, K. M.↗

NASA NTRS1990

Natural melting within a spherical shell

Fundamental heat transfer experiments were performed on the melting of a phase change medium in a spherical shell. Free expansion of the medium into a void space within the sphere was permitted. A step function temperature jump on the outer shell wall was imposed and the timewise evolution of the melting process and the position of the solid-liquid interface was photographically recorded. Numerical integration of the interface position data yielded information about the melted mass and the energy of melting. It was found that the rate of melting and the heat transfer were significantly affected by the movement of the solid medium to the base of the sphere due to gravity. The energy transfer associated with melting was substantially higher than that predicted by the conduction model. Furthermore, the radio of the measured values of sensible energy in the liquid melt to the energy of melting were nearly proportional to the Stefan number. The experimental results are in agreement with a theory set forth in an earlier paper.

Bahrami, Parviz A.↗

NASA NTRS1989

A shallow water model of the winter stratosphere

The shallow water equations are used to investigate the interaction of planetary wave-breaking with a 'diabatic' forcing. The numerical integrations demonstrate the formation of a sharp gradient in potential vorticity at the edge of the polar vortex, despite 'diabatic relaxation' toward a smooth gradient. Successive cycles of Rossby wave-breaking accentuate the distinction between the vortex and the surf-zone. Persistent easterly acceleration in the tropics eventually produces a flow regime of little relevance to the atmosphere. For the period when the flow has some qualitative resemblance to the middle stratosphere diffusion coefficients are calculated from the meridional fluxes of potential vorticity and of passive tracers. It is found that the unique dynamical nature of potential vorticity among tracers is not reflected in its diffusion coefficient.

Juckes, Martin↗

NASA NTRS1989

Dynamics of Pluto

The present study of the Pluto orbit yielded by the LONGSTOP 1B, 100-Myr numerical integration of the outer planets has given attention to the 3:2 resonance in mean motion with Neptune up to degree 2 in eccentricities and inclinations. Confirmations are obtained for both the 19,900-year period longitudinal libration and the 3.78-Myr period libration of the Pluto pericenter argument. Because chaos originates with small divisors, possible resonances have been searched for among the frequencies associated with the critical arguments. The macroscopic stability of the orbit of Pluto is explainable in terms of the association of high-order resonances with small chaotic regions.

Milani, A.↗

NASA NTRS1989

Numerical studies of incompressible flow around delta and double-delta wings

The subject has been jointly investigated at NASA Langley Research Center and the Aerodynamisches Institut of the RWTH Aachen over a substantial period. The aim of this investigation has been to develop numerical integration procedures for the Navier-Stokes equations - particularly for incompressible three-dimensional viscous flows about simple and double delta wings - and to study the low speed flow behavior, with its complex vortex structures on the leeward side of the wing. The low speed flight regime poses unusual problems because high incidence flight conditions may, for example, encounter symmetric and asymmetric vortex breakdown. Because of the many difficulties to be expected in solving the problem, it was divided into two - analysis of the flow without vortex breakdown and analysis of the breakdown of isolated vortices. The major results obtained so far on the two topics are briefly described.

Krause, E.↗

NASA NTRS1989

Quasiperiodic behavior in beam-driven strong Langmuir turbulence

The evolution of unmagnetized beam-driven strong Langmuir turbulence is studied in two dimensions by numerically integrating the Zakharov equations for systems pumped by monochromatic and broadband negative-damping drivers with nonzero central wavenumber. Long-time statistically steady states are reached for which the dependence of the evolution on the driver wavenumber, growth rate, and bandwidth is examined in detail. For monochromatic drivers, a quasiperiodic cycle is found to develop if the driver wavenumber is sufficiently large. The characteristic frequency of the quasiperiodic cycle and the average system energy are both approximately proportional to the growth rate. Broadening of the driver in wavenumber tends to degrade the system-wide coherence of the cycle, but its main features appear to survive on the scale of the coherence length of the driver.

Robinson, P. A.↗

NASA NTRS1989

Automated generation of influence functions for planar crack problems

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

Sire, Robert A.↗

NASA NTRS1990

Precision orbit determination at the NASA Goddard Space Flight Center

This paper describes the GEODYN computer program developed by the Geodynamics Branch at the NASA Goddard Space Flight Center and outlines the procedure for accurate satellite orbit and tracking-data analyses. The capabilities of the program allow the development of gravity fields as large as 90 by 90, and a complete modeling of tidal parameters. It is also feasible to numerically integrate a continuous orbit of a satellite such as Lageos for up to 12 years. The evolution of the orbit can be studied, and, by comparison with locally determined orbits, force model improvements can be made. The GEODYN flow diagrams are presented.

Putney, B.↗

NASA NTRS1990

A test of the galactic origin of gamma-ray bursts

Models in which gamma-ray bursters are young neutron stars may be difficult to reconcile with the apparently isotropic distribution of observed bursts. To justify this statement, the distribution of old neutron stars in the Galaxy was calculated by integrating numerically some 90,000 orbits in the Galactic gravitational potential for up to 10 to the 10th yr. Other calculations included the dipole moment in the angular distribution of neutron stars as a convenient measure of their concentration toward the Galactic center, the quadrupole moment in their angular distribution as a convenient measure of their concentration toward the Galactic plane, and the average value of V/Vmax as a convenient measure of the radial distribution of neutron stars. Models that require accretion from a cold circumstellar disk or from a close companion are only marginally consistent with the isotropic distribution of the observed bursts. Models that require accretion of interstellar matter are ruled out due to a very strong dipole anisotropy. Models that suggest the Galactic halo origin of gamma-ray bursts are briefly discussed. The GRANAT and GRO missions should provide evidence for or against the association of gamma-ray bursts with the Galactic disk neutron stars.

Paczynski, Bohdan↗

NASA NTRS1990

Radiative configuration factors from cylinders to coaxial axisymmetric bodies

Exact solutions are obtained for the radiative configuration factor between differential elements of arbitrary orientation and cylinders. A general method is then proposed for calculating the view factor from a cylinder to a coaxial axisymmetric body using only a single numerical integration. The method is illustrated for axisymmetric bodies with function generators described by a power law equation. The method may be useful in calculating radiative heat transfer between cylindrical bodies and high-density exhaust gases and between annular radiative fins and their bases.

Saltiel, C.↗

NASA NTRS1990

Theory of Influence of a Low-Volatility, Soluble Impurity on Spherically-Symmetric Combustion of Fuel Droplets

Analyses are given for the evolution of liquid-phase mass fraction profiles and temperature during combustion of fuel droplets composed of binary miscible mixtures of low-volatility and high-volatility constituents, with small initial mass fractions of the low-volatility material, or slow introduction of low-volatility material into the liquid phase by absorption from the gas phase. The gas phase is assumed to remain quasi-steady and the liquid temperature spatially uniform. The ratio of the liquid-phase diffusion coefficient to the initial burning-rate constant is treated as a small parameter. Asymptotic analyses in this parameter are developed, and the conservation equations are integrated numerically in obtaining descriptions of the combustion history. It is shown that at the surface of the droplet a boundary layer arises in which the mass fraction of the low-volatility component increases with time. The results are used to explain qualitatively some observed conditions of flame contraction and liquid disruption in droplet combustion.

Shaw, B. D.↗

NASA NTRS1989

The nonlinear breakup of the sun's toroidal field

There are good reasons for believing that the sun has a strong toroidal magnetic field in the stably stratified region of convective overshoot sandwiched between the radiative zone and convective zone proper. The magnetic field in this region is modeled by studying the behavior of a layer of uniform field embedded in a subadiabatic atmosphere. Since the field can support extra mass, such a configuration is top-heavy, and instabilities of the Rayleigh-Taylor type can occur. Numerical integration of the two-dimensional compressible MHD equations makes it possible to follow the evolution of this instability into the nonlinear regime. The initial buoyancy-driven instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The somewhat surprising subsequent motions are determined primarily by the strong interactions between vortices.

Hughes, D. W.↗

NASA NTRS1990

Recurrence in truncated Boussinesq models for nonlinear waves in shallow water

The rapid spatial recurrence of weakly nonlinear and weakly dispersive progressive shallow-water waves is examined using a numerical integration technique on the discretized and truncated form of the Boussinesq equations. This study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that the rapid spatial recurrence is not an inherent property of the considered Boussinesq systems for evolution distances of 10-50 wavelengths. The main result of the study is that highly truncated Boussinesq models of resonant shallow-water ocean surface gravity waves predict rapid multiple recurrence cycles, but that this is an artifact dependent on the number of allowed modes. For initial conditions consisting of essentially all energy concentrated in a single mode, damping of the recurrence cycles increases as the number of low-power background modes increases. When more than 32 modes are allowed, the recurrence behavior is relatively insensitive to the number of allowed modes.

Elgar, Steve↗

NASA NTRS1990

Computation of convective flow with gravity modulation in rectangular cavities

In this work, a computational study is presented for the investigation of gravity modulation (g-jitter) effects in thermally driven cavity flows at terrestrial and microgravity environments. The two-dimensional, time-dependent Navier-Stokes equations are numerically integrated by a time-split method using direct matrix solvers. Computations at terrestrial gravity are utilized to assess the effects of adiabatic side-wall boundary conditions as well as the full nonlinearity of the governing equations on the sinusoidally forced Benard problem studied by Gresho and Sani. The low-g calculations focus on the establishment of critical frequency ranges and consider the effects of modulation direction and randomness. The applicability of linear analysis in the excitable frequency range at low g is also discussed.

Biringen, S.↗

NASA NTRS1990

A statistical study of the differential very long baseline interferometry delay rate error budget

The delta differential one-way Doppler (delta-DOD) error budget is assessed by analyzing 12 years of dual-frequency Deep Space Network very long baseline interferometry data. A typical delta-DOD observation is outlined, and the Magellan error budget along with tropospheric effects are considered. Formation of quasar-quasar observables, RMS delta-DOD residual, angular source separation and time separation between observations are discussed, along with elevation angle and atmospheric pathlength dependence, solar-plasma and ionospheric effects. It is concluded that the weak dependence of the delta-DOD error on angular source separation can mean that quasars with larger angular separation from a spacecraft may be used as navigation reference with little increase in the delta-DOD error. It is also indicated that the delta-DOD errors are dominated by wet troposphere fluctuations, and the results of numerical integrations for the single-station RMS delay rate at different elevation angles are presented.

Edwards, Charles D.↗