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NASA NTRS2015

M-MRAC for SPHERES

This paper presents application of the modified reference model MRAC (M-MRAC) method to control the relative position and orientation of a cluster of satellites known collectively as the Synchronized Position Hold, Engage, Reorient Experimental Satellites (SPHERES). The approach uses fast estimation algorithms to achieve guaranteed tracking of reference commands for both input and output signals in the presence of uncertainties in mass and inertia data and external disturbances. The tracking errors can be systematically decreased by the proper selection of the design parameters in the identification model. The generated control signals have acceptable magnitudes and exhibit no oscillations. The benefits of the method are demonstrated in numerical simulations.

Relative motion↗

NASA NTRS2019

Searching for Hypermassive Neutron Stars with Short Gamma-Ray Bursts

Neutron star mergers can form a hypermassive neutron star (HMNS) remnant, which may be the engine of a short gamma-ray burst (SGRB) before it collapses to a black hole, possibly several hundred milliseconds after the merger.During the lifetime of an HMNS, numerical relativity simulations indicate that it will undergo strong oscillations and emit gravitational waves with frequencies of a few kilohertz, which are unfortunately too high for detection to be probable with the Advanced Laser Interferometer Gravitational-Wave Observatory. Here we discuss the current and future prospects for detecting these frequencies as modulation of the SGRB. The understanding of the physical mechanism responsible for the HMNS oscillations will provide information on the equation of state of the hot HMNS, and the observation of these frequencies in the SGRB data would give us insight into the emission mechanism of the SGRB.

Cecilia Chirenti↗

NASA NTRS1991

Calculation of far-field scattering from nonspherical particles using a geometrical optics approach

A numerical method was developed using geometrical optics to predict far-field optical scattering from particles that are symmetric about the optic axis. The diffractive component of scattering is calculated and combined with the reflective and refractive components to give the total scattering pattern. The phase terms of the scattered light are calculated as well. Verification of the method was achieved by assuming a spherical particle and comparing the results to Mie scattering theory. Agreement with the Mie theory was excellent in the forward-scattering direction. However, small-amplitude oscillations near the rainbow regions were not observed using the numerical method. Numerical data from spheroidal particles and hemispherical particles are also presented. The use of hemispherical particles as a calibration standard for intensity-type optical particle-sizing instruments is discussed.

Hovenac, Edward A.↗

NASA NTRS1993

Quantized discrete space oscillators

A quasi-canonical sequence of finite dimensional quantizations was found which has canonical quantization as its limit. In order to demonstrate its practical utility and its numerical convergence, this formalism is applied to the eigenvalue and 'eigenfunction' problem of several harmonic and anharmonic oscillators.

Uzes, C. A.↗

NASA NTRS2000

Candle Flames in Non-Buoyant Atmospheres

This paper addresses the behavior of a candle flame in a long-duration, quiescent microgravity environment both on the space Shuttle and the Mir Orbiting Station. On the Shuttle, the flames became dim blue after an initial transient where there was significant yellow (presumably soot) in the flame. The flame lifetimes were typically less than 60 seconds. The safety-mandated candlebox that contained the candle flame inhibited oxygen transport to the flame and thus limited the flame lifetime. The flames on the Mir were similar, except that the yellow luminosity persisted longer into the flame lifetime because of a higher initial oxygen concentration, The Mir flames burned for as long as 45 minutes. The difference in the flame lifetime between the Shuttle and Mir flames was primarily the redesigned candlebox that did not inhibit oxygen transport to the flame. In both environments, the flame intensity and the height-to-width ratio gradually decreased as the ambient oxygen content in the sealed chamber slowly decreased. Both sets of experiments showed spontaneous, axisymmetric flame oscillations just prior to extinction. The paper also presents a numerical model of a candle flame. The formulation is two-dimensional and time-dependent in the gas phase with constant specific heats, thermal conductivity and Lewis number (although different species can have different Lewis numbers), one-step finite-rate kinetics, and gas-phase radiative losses from CO2 and H2O. The treatment of the liquid/wick phase assumes that the, fuel evaporates from a constant diameter sphere connected to an inert cone. The model predicts a steady flame with a shape and size quantitatively similar to the Shuttle and Mir flames. The computation predicts that the flame size will increase slightly with increasing ambient oxygen mole fraction. The model also predicts pre-extinction flame oscillations if the rate of decrease in ambient oxygen is small enough, such as that which would occur for a flame burning in a sealed ambient.

Dietrich, D. L.↗

NASA NTRS1978

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown that these problems can be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate filtering can reduce the intensity of these oscillations and possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and nonconservation differencing. The entire spectrum of filtered equations retains a three point character as well as second order spatial accuracy. Burgers equation was considered as a model.

Khosla, P. K.↗

NASA NTRS1979

Filtering of non-linear instabilities

For Courant numbers larger than one and cell Reynolds numbers larger than two, oscillations and in some cases instabilities are typically found with implicit numerical solutions of the fluid dynamics equations. This behavior has sometimes been associated with the loss of diagonal dominance of the coefficient matrix. It is shown here that these problems can in fact be related to the choice of the spatial differences, with the resulting instability related to aliasing or nonlinear interaction. Appropriate 'filtering' can reduce the intensity of these oscillations and in some cases possibly eliminate the instability. These filtering procedures are equivalent to a weighted average of conservation and non-conservation differencing. The entire spectrum of filtered equations retains a three-point character as well as second-order spatial accuracy. Burgers equation has been considered as a model. Several filters are examined in detail, and smooth solutions have been obtained for extremely large cell Reynolds numbers.

Khosla, P. K.↗

NASA NTRS1989

An Entropy-Based Approach to Nonlinear Stability

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Merriam, Marshal L.↗

NASA NTRS1987

High resolution absorption cross-sections and band oscillator strengths of the Schumann-Runge bands of oxygen at 79 K

Cross sections of O2 at 79 K have been obtained from photoabsorption measurements at various pressures throughout the wavelength region 179.3-198.0 nm with a 6.65-m photoelectric scanning spectrometer equipped with a 2400-lines/mm grating and having an instrumental width (FWHM) of 0.0013 nm. The measured absorption cross sections of the Schumann-Runge bands (12,0) through (2,0) are independent of the instrumental width. The measured cross-sections are presented graphically here and are available at wavenumber intervals of about 0.1/cm as numerical compilations stored on magnetic tape from the National Space Science Data Center, NASA/Goddard. Band oscillator strengths of these bands have been determined by direct numerical integration of the measured cross sections.

Yoshino, K.↗

NASA NTRS1981

Umbral oscillations as resonant modes of magneto-atmospheric waves

Umbral oscillations in sunspots are identified as a resonant response of the umbral atmosphere to forcing by oscillatory convection in the subphotosphere. The full, linearized equations for magnetoatmospheric waves are solved numerically for a detailed model of the umbral atmosphere, for both forced and free oscillations. Resonant 'fast' modes are found, the lowest mode having a period of 153 s, typical of umbral oscillations. A comparison is made with a similar analysis by Uchida and Sakurai (1975), who calculated resonant modes using an approximate ('quasi-Alfven') form of the wave equations. Whereas both analyses give an appropriate value for the period of oscillation, several new features of the motion follow from the full equations. The resonant modes are due to upward reflection in the subphotosphere (due to increasing sound speed) and downward reflection in the photosphere and low chromosphere (due to increasing Alfven speed); downward reflection at the chromosphere-corona transition is unimportant for these modes.

Scheuer, M. A.↗

NASA NTRS1987

Downstream boundary effects on the frequency of self-excited oscillations in transonic diffuser flows

An investigation of downstream boundary effects on the frequency of self-excited oscillations in two-dimensional, separated transonic diffuser flows has been conducted numerically by solving the compressible, Reynolds-averaged, thin-layer Navier-Stokes equation with a two-equation turbulence model. It was found that the unsteady diffuser flowfields are very sensitive to the location of the downstream boundary. Extension of the diffuser downstream boundary significantly reduces the frequency and amplitude of oscillations for pressure, velocity and shock. Computational results suggest that the mechanism causing the self-excited oscillation changes from viscous convective wave dominated oscillations to inviscid acoustic wave dominated oscillations when the location of downstream boundary varies from 8.66 to 134.7 throat height. The existence of a suction slot in the experimental setup obscures the physical downstream boundary and, therefore, presents a difficulty for quantitative comparisons between computation and experiment.

Hsieh, T.↗

NASA NTRS1984

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

Connor, J. N. L.↗

NASA NTRS1971

Aperiodic behaviour of a non-linear oscillator.

The aperiodic behavior of the solution of the equation of motion derived previously (1966) when considering a model thermomechanical oscillator is examined. Periodic solutions of this equation are studied numerically and analytically. Conditions for the instability of the solutions are determined. This instability seems to be the cause of the observed aperiodicity.

Baker, N. H.↗

NASA NTRS1974

A finite difference method for the solution of the transonic flow around harmonically oscillating wings

A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.

Ehlers, E. F.↗

NASA NTRS1982

Nonlinear dynamo oscillations

The stability of steady equilibrium amplitudes of magnetic fields generated by convection flows is investigated. Two cases are considered in detail, for which steady solutions are available from the previous work of Busse (1973) and Busse (1977). In the first case instability occurs primarily because of magnetic flux expulsion at high magnetic Reynolds numbers. In the second case the change in the velocity field caused by the Lorentz force enhances dynamo action. This subcritical finite amplitude dynamo is potentially unstable. In typical cases the nonlinear dynamo oscillations that replace the steady equilibrium solutions are investigated by numerical integration.

Busse, F. H.↗

NASA NTRS2001

Large Lewis No. Edge-Flame Instabilities

Edge-flames play an important role in a number of microgravity investigations, and in the general study of flames. Examples include the candle-flame experiments carried out on board both the Space Shuttle and the Mir Space Station; the flame-spread-over-liquid work carried out by H. Ross and W. Sirignano amongst others and lifted turbulent diffusion flames. In all of these configurations a local two-dimensional flame structure can be identified which looks like a flame-sheet with an edge, and these structures exhibit dynamical behavior which characterizes them and distinguishes them from ad hoc 2D flame structures. Edge-flames can exist in both a non-premixed context (edges of diffusion flames) and in a premixed context (edges of deflagrations), but the work reported here deals with the edges of diffusion flames. It is particularly relevant, we believe, to oscillations that have been seen in both the candle-flame context, and the flame-spread-over-liquid context. These oscillations are periodic edge-oscillations (in an appropriate reference frame), sans oscillation of the trailing diffusion flame. It is shown that if the Lewis number of the fuel is sufficiently large (the Lewis number of the oxidizer is taken to be 1), and the Damkohler number is sufficiently small, oscillating-edge solutions can be found. Oscillations are encouraged by an on-edge convective flow and the insertion of a cold probe, discouraged by an off-edge convective flow. In the present work, the nature of these oscillations is examined in more depth, using a variety of numerical strategies.

Buckmaster, J.↗

NASA NTRS2009

Numerical Studies of a Fluidic Diverter for Flow Control

The internal flow structure in a specific fluidic diverter is studied over a range from low subsonic to sonic inlet conditions by a time-dependent numerical analysis. The understanding will aid in the development of fluidic diverters with minimum pressure losses and advanced designs of flow control actuators. The velocity, temperature and pressure fields are calculated for subsonic conditions and the self-induced oscillatory behavior of the flow is successfully predicted. The results of our numerical studies have excellent agreement with our experimental measurements of oscillation frequencies. The acoustic speed in the gaseous medium is determined to be a key factor for up to sonic conditions in governing the mechanism of initiating the oscillations as well as determining its frequency. The feasibility of employing plasma actuation with a minimal perturbation level is demonstrated in steady-state calculations to also produce oscillation frequencies of our own choosing instead of being dependent on the fixed-geometry fluidic device.

Gokoglu, Suleyman A.↗

NASA NTRS2013

High-Order Space-Time Methods for Conservation Laws

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

Huynh, H. T.↗