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Results for “asymptotic stability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions, are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Shaw, Stephen J.↗
NASA NTRS1992

The inviscid stability of supersonic flow past heated or cooled axisymmetric bodies

The inviscid, linear, nonaxisymmetric, temporal stability of the boundary layer associated with the supersonic flow past axisymmetric bodies (with particular emphasis on long thin, straight circular cylinders), subject to heated or cooled wall conditions is investigated. The eigenvalue problem is computed in some detail for a particular Mach number or 3.8, revealing that the effect of curvature and the choice of wall conditions both have a significant effect on the stability of the flow. Both the asymptotic, large azimuthal wavenumber solution and the asymptotic, far downstream solution are obtained for the stability analysis and compared with numerical results. Additionally, asymptotic analyses valid for large radii of curvature with cooled/heated wall conditions are presented. In general, important differences were found to exist between the wall temperature conditions imposed and the adiabatic wall conditions considered previously.

Shaw, Stephen J.↗
NASA NTRS1971

Stability of uncertain systems

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Blankenship, G. L.↗
NASA NTRS1994

The stability of two-phase flow over a swept-wing

We use numerical and asymptotic techniques to study the stability of a two-phase air/water flow above a flat porous plate. This flow is a model of the boundary layer which forms on a yawed cylinder and can be used as a useful approximation to the air flow over swept wings during heavy rainfall. We show that the interface between the water and air layers can significantly destabilize the flow, leading to traveling wave disturbances which move along the attachment line. This instability occurs for lower Reynolds numbers than in the case of the absence of a water layer. We also investigate the instability of inviscid stationary modes. We calculate the effective wavenumber and orientation of the stationary disturbance when the fluids have identical physical properties. Using perturbation methods we obtain corrections due to a small stratification in viscosity, thus quantifying the interfacial effects. Our analytical results are in agreement with the numerical solution which we obtain for arbitrary fluid properties.

Coward, Adrian↗
NASA NTRS2010

Asymptotic Linearity of Optimal Control Modification Adaptive Law with Analytical Stability Margins

Optimal control modification has been developed to improve robustness to model-reference adaptive control. For systems with linear matched uncertainty, optimal control modification adaptive law can be shown by a singular perturbation argument to possess an outer solution that exhibits a linear asymptotic property. Analytical expressions of phase and time delay margins for the outer solution can be obtained. Using the gradient projection operator, a free design parameter of the adaptive law can be selected to satisfy stability margins.

Nguyen, Nhan T.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗
NASA NTRS1970

Stability of the Schwarzschild metric

Schwarzschild exterior metric stability against perturbations from asymptotic behavior of Einstein field equations solution in Kruskal coordinates

Vishveshwara, C. V.↗
NASA NTRS1990

Instability and transition; Proceedings of the Workshop, Hampton, VA, May 15-June 9, 1989. Vols. 1 & 2

The proceedings of the workshop on instability and transition, sponsored by the Institute for Computer Applications in Science and Engineering and the Langley Research Center, during May-June 1989 are presented. The proceedings contain panel discussions and the research papers resulting from the collaborative projects started during the workshop and completed shortly thereafter. Six panels are represented: theory, low-speed experiment, high-speed experiment, computation, receptivity, and roughness panels. Focus is concentrated on receptivity, advanced asymptotics, boundary-layer stability, free shear flows, compressible stability and transition, transition simulation, and transition modeling. The panel summaries and the position papers by the panelists as well as research papers of the experiment group and the receptivity group are discussed.

Hussaini, M. Y.↗
NASA NTRS1994

Control of mechanical systems with rolling constraints: Application to dynamic control of mobile robots

There are many examples of mechanical systems that require rolling contacts between two or more rigid bodies. Rolling contacts engender nonholonomic constraints in an otherwise holonomic system. In this article, we develop a unified approach to the control of mechanical systems subject to both holonomic and nonholonomic constraints. We first present a state space realization of a constrained system. We then discuss the input-output linearization and zero dynamics of the system. This approach is applied to the dynamic control of mobile robots. Two types of control algorithms for mobile robots are investigated: trajectory tracking and path following. In each case, a smooth nonlinear feedback is obtained to achieve asymptotic input-output stability and Lagrange stability of the overall system. Simulation results are presented to demonstrate the effectiveness of the control algorithms and to compare the performane of trajectory-tracking and path-following algorithms.

Sarkar, Nilanjan↗
NASA NTRS1982

The dependence of the shape and stability of captive rotating drops on multiple parameters

Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.

Ungar, L. H.↗
NASA NTRS1983

Higher modes of the Orr-Sommerfeld problem for boundary layer flows

The discrete spectrum of the Orr-Sommerfeld problem of hydrodynamic stability for boundary layer flows in semi-infinite regions is examined. Related questions concerning the continuous spectrum are also addressed. Emphasis is placed on the stability problem for the Blasius boundary layer profile. A general theoretical result is given which proves that the discrete spectrum of the Orr-Sommerfeld problem for boundary layer profiles (U(y), 0,0) has only a finite number of discrete modes when U(y) has derivatives of all orders. Details are given of a highly accurate numerical technique based on collocation with splines for the calculation of stability characteristics. The technique includes replacement of 'outer' boundary conditions by asymptotic forms based on the proper large parameter in the stability problem. Implementation of the asymptotic boundary conditions is such that there is no need to make apriori distinctions between subcases of the discrete spectrum or between the discrete and continuous spectrums. Typical calculations for the usual Blasius problem are presented.

Lakin, W. D.↗
NASA NTRS1989

Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.

Gaffey, J. D., Jr.↗
NASA NTRS1991

Post-asymptotic giant branch nonradial instability strips

Stability analyses are performed for nonradial g(+)-mode pulsations of postasymptotic AGB stellar models to determine the location of their pulsational instability strips in the Hertzsprung-Russell diagram. Stellar models are analyzed that are assumed to have undergone a major mass loss event either near the tip of the AGB or shortly thereafter and, therefore, consist of a 50-percent carbon 50-percent oxygen core. Their mass is 0.6 solar mass, which is in good agreement with the peak of the observed distribution of white dwarf masses. The results are compared both to the observed planetary nebula nuclei variables and the hot pulsating DO variables. An analysis is also presented of the stability of DB white dwarfs, which have much deeper and stronger convection zones, and an instability strip is found between about 18,000 and 26,000 K approximately as observed for the known variable stars.

Stanghellini, Letizia↗
NASA NTRS1974

Stability analysis of nonlinear systems by multiple time scaling

The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.

Morino, L.↗
NASA NTRS2002

Stochastic Modeling of Laminar-Turbulent Transition

Stochastic versions of stability equations are developed in order to develop integrated models of transition and turbulence and to understand the effects of uncertain initial conditions on disturbance growth. Stochastic forms of the resonant triad equations, a high Reynolds number asymptotic theory, and the parabolized stability equations are developed.

Rubinstein, Robert↗
NASA NTRS1991

On the linear stability of compressible plane Couette flow

The linear stability of compressible plane Couette flow is investigated. The correct and proper basic velocity and temperature distributions are perturbed by a small amplitude normal mode disturbance. The full small amplitude disturbance equations are solved numerically at finite Reynolds numbers, and the inviscid limit of these equations is then investigated in some detail. It is found that instability can occur, although the stability characteristics of the flow are quite different from unbounded flows. The effects of viscosity are also calculated, asymptotically, and shown to have a stabilizing role in all the cases investigated. Exceptional regimes to the problem occur when the wavespeed of the disturbances approaches the velocity of either of the walls, and these regimes are also analyzed in some detail. Finally, the effect of imposing radiation-type boundary conditions on the upper (moving) wall (in place of impermeability) is investigated, and shown to yield results common to both bounded and unbounded flows.

Duck, Peter W.↗
NASA NTRS1991

Heteronuclear transition metal diatomics - The bonding and electronic structure of ScNi, YNi, ScPd, and YPd

High quality ab initio calculations show that ScNi, YNi, ScPd, and YPd all have 2Sigma(+) ground states in agreement with electron spin resonance experiments. For ScNi and YNi, this is expected based on the lowest atomic asymptote. For ScPd and YPd, the lowest atomic asymptote would give the order of stability 2Delta greater than 2Pi equal to about 2Sigma(+), but the calculations show that mixing in of the excited asymptotes preferentially lowers the 2Sigma(+) state. The calculations show that the quartet states are about 20-30 kcal/mol above the ground state, and therefore probably do not contribute significantly to the unexpected g(vertical) values found in experiment. Calculations of excited states for YPd reveal some strong transitions that should be amenable to spectroscopic studies.

Faegri, Knut, Jr.↗