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At least 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

On the global dynamics of adaptive systems - A study of an elementary example

The inherent nonlinear character of adaptive systems poses serious theoretical problems for the analysis of their dynamics. On the other hand, the importance of their dynamic behavior is directly related to the practical interest in predicting such undesirable phenomena as nonlinear oscillations, abrupt transients, intermittence or a high sensitivity with respect to initial conditions. A geometrical/qualitative description of the phase portrait of a discrete-time adaptive system with unmodeled disturbances is given. For this, the motions in the phase space are referred to normally hyperbolic (structurally stable) locally invariant sets. The study is complemented with a local stability analysis of the equilibrium point and periodic solutions. The critical character of adaptive systems under rather usual working conditions is discussed. Special emphasis is put on the causes leading to intermittence. A geometric interpretation of the effects of some commonly used palliatives to this problem is given. The 'dead-zone' approach is studied in more detail. The predicted dynamics are compared with simulation results.

Espana, Martin D.↗
NASA NTRS1926

Inertia Factors of Ellipsoids for Use in Airship Design

This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author)

Tuckerman, L. B.↗
NASA NTRS1942

Contribution to the ideal efficiency of screw propellers

The stipulation of best thrust distribution is applied to the annular elements of the screw propeller with infinitely many blades in frictionless, incompressible flow and an ideal jet propulsion system derived possessing hyperbolic angular velocity distribution along the blade radius and combining the advantage of uniform thrust distribution over the section with minimum slipstream and rotation losses. This system is then compared with a propeller possessing the same angular velocity at all blade elements and the best possible thrust distribution secured by means of an induced efficiency varying uniformly over the radius. Lastly, the case of the lightly loaded propeller also is discussed.

Hoff, Wilhelm↗
NASA NTRS1994

Unstable-Resonator Oscillator/Amplifier Diode Laser

Fabricated as single-chip integrated circuit. Device based partly on concept proved in commercial solid-state lasers: using unstable-resonator oscillator to define electromagnetic mode and, following oscillator, traveling-wave amplifier to generate high power. Mode-definition and power-amplification functions optimized separately. Hyperbolic-grating, unstable-resonator oscillator/amplifier diode laser produces single-longitudinal-mode, broad, laterally coherent, diffraction-limited, high-power beam.

Lang, Robert J.↗
NASA NTRS1990

Space vehicle deployment from Space Station

When launching a spacecraft from Earth parking orbit to deep space, it is highly desirable to have the hyperbolic excess velocity vector (v-infinity) contained in the parking orbit plane. Ground launches can force the parking orbit plane to contain the v-infinity vector by using launch azimuth and lift-off time as independent variables. When launching from the Space Station, a new set of variables comes into play. The Space Station orbit is of fixed inclination but precessing due to the Earth's oblateness. Its plane will seldom (and may never) contain the desired v-infinity vector. Consequently, the departure strategy will usually require multiple burns and include a plane change. Also, the concept of 'launch window' will be somewhat different from Earth surface launches. An analysis of the deployment of interplanetary spacecraft from the Space Station is described, with emphasis on the effect of the trajectory characteristics on station operations. Several planetary mission types are analyzed, including manned Mars missions and unmanned high declination departures. The constraint of Space Station orbit nodal position is quantified and the operational implications for Space Station reboost strategy are examined.

Henry, Paul K.↗
NASA NTRS1993

Canonical forms of multidimensional steady inviscid flows

Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants.

Taasan, Shlomo↗
NASA NTRS1993

The Chebyshev-Legendre method: Implementing Legendre methods on Chebyshev points

We present a new collocation method for the numerical solution of partial differential equations. This method uses the Chebyshev collocation points, but because of the way the boundary conditions are implemented, it has all the advantages of the Legendre methods. In particular, L2 estimates can be obtained easily for hyperbolic and parabolic problems.

Don, Wai Sun↗
NASA NTRS1993

Selected computations of transonic cavity flows

An efficient diagonal scheme implemented in an overset mesh framework has permitted the analysis of geometrically complex cavity flows via the Reynolds averaged Navier-Stokes equations. Use of rapid hyperbolic and algebraic grid methods has allowed simple specification of critical turbulent regions with an algebraic turbulence model. Comparisons between numerical and experimental results are made in two dimensions for the following problems: a backward-facing step; a resonating cavity; and two quieted cavity configurations. In three-dimensions the flow about three early concepts of the stratospheric Observatory For Infrared Astronomy (SOFIA) are compared to wind-tunnel data. Shedding frequencies of resolved shear layer structures are compared against experiment for the quieted cavities. The results demonstrate the progress of computational assessment of configuration safety and performance.

Atwood, Christopher A.↗
NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗
NASA NTRS1993

The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A careful study of the boundary error

The conventional method of imposing time dependent boundary conditions for Runge-Kutta (RK) time advancement reduces the formal accuracy of the space-time method to first order locally, and second order globally, independently of the spatial operator. This counter intuitive result is analyzed in this paper. Two methods of eliminating this problem are proposed for the linear constant coefficient case: (1) impose the exact boundary condition only at the end of the complete RK cycle, (2) impose consistent intermediate boundary conditions derived from the physical boundary condition and its derivatives. The first method, while retaining the RK accuracy in all cases, results in a scheme with much reduced CFL condition, rendering the RK scheme less attractive. The second method retains the same allowable time step as the periodic problem. However it is a general remedy only for the linear case. For non-linear hyperbolic equations the second method is effective only for for RK schemes of third order accuracy or less. Numerical studies are presented to verify the efficacy of each approach.

Carpenter, Mark H.↗
NASA NTRS1994

Interaction of the sonic boom with atmospheric turbulence

Theoretical research was carried out to study the effect of free-stream turbulence on sonic boom pressure fields. A new transonic small-disturbance model to analyze the interactions of random disturbances with a weak shock was developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustics equation that describes the propagation of sound beams with narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed type elliptic-hyperbolic flows around the shock wave was also developed. Numerical calculations of shock wave interactions with various deterministic and random fluctuations will be presented in a future report.

Rusak, Zvi↗
NASA NTRS1994

Fourth-order 2N-storage Runge-Kutta schemes

A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations. A particular scheme is identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This scheme is competitive with the classical fourth-order method (high-storage) and is considerably more efficient and accurate than existing third-order low-storage schemes.

Carpenter, Mark H.↗
NASA NTRS1994

TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide

A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.

Miller, David P.↗
NASA NTRS1994

High-order centered difference methods with sharp shock resolution

In this paper we consider high-order centered finite difference approximations of hyperbolic conservation laws. We propose different ways of adding artificial viscosity to obtain sharp shock resolution. For the Riemann problem we give simple explicit formulas for obtaining stationary one and two-point shocks. This can be done for any order of accuracy. It is shown that the addition of artificial viscosity is equivalent to ensuring the Lax k-shock condition. We also show numerical experiments that verify the theoretical results.

Gustafsson, Bertil↗
NASA NTRS1994

Magnetobraking: Use of tether electrodynamic drag for Earth return from Mars

It has often been proposed that a vehicle returning from Mars will use aerobraking in the Earth's atmosphere to dissipate hyperbolic excess velocity to capture into Earth orbit. Here a different system for dissipating excess velocity without expenditure of reaction mass, magnetobraking, is proposed. Magnetobraking uses the force on an electrodynamic tether in the Earth's magnetic field to produce thrust. An electrodynamic tether is deployed from the spacecraft as it approaches the Earth. The Earth's magnetic field produces a force on electrical current in the tether. If the tether is oriented perpendicularly to the Earth's magnetic field and to the direction of motion of the spacecraft, force produced by the Earth's magnetic field can be used to either brake or accelerate the spacecraft without expenditure of reaction mass. The peak acceleration on the Mars return is 0.007 m/sq sec, and the amount of braking possible is dependent on the density and current-carrying capacity of the tether, but is independent of length. A superconducting tether is required. The required critical current is shown to be within the range of superconducting technology now available in the laboratory.

Landis, Geoffrey A.↗
NASA NTRS1994

Stability and error estimation for Component Adaptive Grid methods

Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.

Oliger, Joseph↗
NASA NTRS1994

Sonic boom interaction with turbulence

A recently developed transonic small-disturbance model is used to analyze the interactions of random disturbances with a weak shock. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. It shows that diffraction effects, nonlinear steepening effects, focusing and caustic effects and random induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite-difference algorithm to solve the mixed-type elliptic hyperbolic flows around the shock wave is presented. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicate shock wave structures and describe peaked as well as rounded pressure signatures behind the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.

Zvi Rusak↗
NASA NTRS1994

Effect of density gradients in confined supersonic shear layers, part 1

The effect of density gradients on the supersonic wall modes (acoustic modes) of a 2-D confined compressible shear layer were investigated using linear analysis. Due to the inadequacies of the hyperbolic tangent profile, the boundary layer basic profiles were used. First a test case was taken with the same parameters as in Tam and Hu's analysis with convective Mach number M(sub c) = 1.836 and density ratio of 1.398. Three generalized inflection points were found giving rise to three modes. The first two show similar properties to the Class A and B modes, and the third is an 'inner mode' which will be called a Class C mode. As the density ratio is increased, the smallest of the three neutral phase speeds tends towards the speed of the lower velocity stream, and the other two eventually coalesce and then disappear. These two effects lead to a linear resonance between the Class B modes which increases the cutoff frequency and growth rate of the lowest mode. In fact, growth rates of 2-4 times the test case were found as the density ratio was increased to 7. A similar trend is observed for the Class A modes when the density ratio is decreased from the test case, but the growth rate is not changed by much from the test case.

Peroomian, Oshin↗