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NASA NTRS1984

MHD stability of compressible coronal loops with radiative energy loss

The effect of radiative energy loss on the stability of compressible plasma in coronal loops is studied. By taking the limit as poloidal wavenumber m approaches infinity, stability conditions for local modes are derived. It was found that the radiation effect can trigger MHD instabilities of coronal loops which are in ideally marginally stable states. Compressibility is a stabilizing effect for ideal MHD local modes because the compression of magnetic field lines exerts a restoring force by increasing magnetic pressure. Compression of plasma induces two modes in a radiatively unstable plasma, magnetosonic and condensation modes. Compressibility affects the stability of ideally stable (or unstable) coronal plasmas through magnetosonic modes, which are a stabilizing (destabilizing) effect for ideally stable (unstable) plasmas. For coronal plasmas in ideally marginally stable states, condensation as well as magnetosonic modes can trigger MHD instability. Because of these two modes, the effect of radiation on compressible coronal plasmas is more destabilizing than it is on incompressible plasmas when the plasmas are in ideal MHD unstable or marginally stable states.

An, C.-H.↗

NASA NTRS1984

Transonic calculation of airfoil stability and response with active controls

Transonic aeroelastic stability and response analyses are performed for the MBB A-3 supercritical airfoil. Three degrees of freedom are considered: plunge, pitch, and aileron pitch. The objective of this study is to gain insight into the control of airfoil stability and response in transonic flow. Stability analyses are performed using a Padeaeroelastic model based on the use of the LTRAN2-NLR transonic small-disturbance finite-difference computer code. Response analyses are performed by coupling the structural equations of motion to the unsteady aerodynamic forces of LTRAN2-NLR. The focus of the present effort is on transonic time-marching transient response solutions using modal identification to determine stability. Frequency and damping of these modes are directly compared in the complex s-plane with Pademodel eigenvalues. Transonic stability and response characteristics of two-dimensional airfoils are discussed and comparisons are made. Application of the Padeaeroelastic model and time-marching analyses to flutter suppression using active controls is demonstrated.

Batina, J. T.↗

NASA NTRS1985

A new theory for multistep discretizations of stiff ordinary differential equations: Stability with large step sizes

A large set of variable coefficient linear systems of ordinary differential equations which possess two different time scales, a slow one and a fast one is considered. A small parameter epsilon characterizes the stiffness of these systems. A system of o.d.e.s. in this set is approximated by a general class of multistep discretizations which includes both one-leg and linear multistep methods. Sufficient conditions are determined under which each solution of a multistep method is uniformly bounded, with a bound which is independent of the stiffness of the system of o.d.e.s., when the step size resolves the slow time scale, but not the fast one. This property is called stability with large step sizes. The theory presented lets one compare properties of one-leg methods and linear multistep methods when they approximate variable coefficient systems of stiff o.d.e.s. In particular, it is shown that one-leg methods have better stability properties with large step sizes than their linear multistep counter parts. The theory also allows one to relate the concept of D-stability to the usual notions of stability and stability domains and to the propagation of errors for multistep methods which use large step sizes.

Majda, G.↗

NASA NTRS1985

Whirl and whip: Rotor/bearing stability problems

A mathematical model of a symmetric rotor supported by one rigid and one fluid lubricated bearing is proposed. The rotor model is represented by generalized (modal) parameters of its first bending mode. The rotational character of the bearing fluid force is taken into account. The model yields synchronous vibrations due to rotor unbalance as a particular solution of the equations of motion, rotor/bearing system natural frequencies and corresponding self-excited vibrations known as oil whirl and oil whip. The stability analysis yields rotative speed threshold of stability. The model also gives the evaluation of stability of the rotor synchronous vibrations. In the first balance resonance speed region two more thresholds of stability are yielded. The width of this stability region is directly related to the amount of rotor unbalance. The results of the analysis based on this model stand with very good agreement with field observations of rotor dynamic behavior and the experimental results.

Muszynska, A.↗

NASA NTRS1985

Regions of stability with unequal saturation limits and non-zero set point

Constraints on the magnitudes of control variables limit the region where open-loop unstable systems can be stabilized using feedback control. Variations in regions of stability with unequal control saturation limits and non-zero set points are illustrated for single-input unstable linear systems which have one or two unstable eigenvalues. The regions of stability for saddle-point- and unstable-node-type singularities increase with the increase in one of the saturation limits, but they become invariant when the larger control limit exceeds a certain value; the stability regions vanish for non-zero set-points that saturate the controls. The unstable-focus-type singularity exhibits strikingly different characteristics. These results suggest guidelines for obtaining desired stability regions for different types of singularities.

Stengel, R. F.↗

NASA NTRS1987

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II

The results of Goldberg and Tadmor (1985) are extended to achieve improved stability criteria for a large class of approximations to the initial boundary value problem associated with a particular hyperbolic system in a quarter plane. In a stability analysis, it is shown that the entire approximation is stable if and only if the scalar outflow components of its principal part are stable. Thus, the global stability question is reduced to that of a scalar, homogeneous outflow problem. The stability criteria for the reduced problem, which depend both on the basic scheme and the boundary conditions, but very little on the interaction between the two, are stated and used to establish previous examples and new ones, including a host of dissipative and nondissipative examples. There is no difficulty in extending the stability criteria to two-boundary problems and initial-boundary value problems with variable coefficients.

Goldberg, Moshe↗

NASA NTRS1987

Stability of axisymmetric boundary layers on sharp cones at hypersonic Mach numbers

The stability of sharp-cone boundary layers at zero angle of attack is investigated. Standard linear stability theory is used to perform a numerical study at an edge Mach number M(e) of 6.8 of normal-mode stability characteristics on an adiabatic-wall cone with special reference to the conditions of the stability experiment of Stetson et al. (1983). Comparisons of the calculations with experimental measurements bring out major areas of disagreement which remain to be resolved even in this simple case. Finally, a series of calculations of both cone and flat-plate N factors at M(e) of 4.5, 5.8, and 6.8 is used to study the relation between transition on a cone and flat plate based on stability theory.

Mack, Leslie M.↗

NASA NTRS1988

Rotorcraft aeroelastic stability

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low-frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability in hover and forward flight, and analysis of tilt-rotor dynamic stability are considered. Results of parametric investigations of system behavior are presented, and correlation between theoretical results and experimental data from small and large scale wind tunnel and flight testing are discussed.

Ormiston, Robert A.↗

NASA NTRS1988

Aeromechanical stability analysis of COPTER

A plan was formed for developing a comprehensive, second-generation system with analytical capabilities for predicting performance, loads and vibration, handling qualities, aeromechanical stability, and acoustics. This second-generation system named COPTER (COmprehensive Program for Theoretical Evaluation of Rotorcraft) is designed for operational efficiency, user friendliness, coding readability, maintainability, transportability, modularity, and expandability for future growth. The system is divided into an executive, a data deck validator, and a technology complex. At present a simple executive, the data deck validator, and the aeromechanical stability module of the technology complex were implemented. The system is described briefly, the implementation of the technology module is discussed, and correlation data presented. The correlation includes hingeless-rotor isolated stability, hingeless-rotor ground-resonance stability, and air-resonance stability of an advanced bearingless-rotor in forward flight.

Yin, Sheng K.↗

NASA NTRS1988

Nonlinear stability of the dayside cometary ionopause

The MHD stability of the cometary ionopause is investigated by nonlinear analysis, describing that stability in terms of the finite perturbation amplitude of both Kelvin-Helmholtz and Rayleigh-Taylor modes. The evolution of the unstable modes is examined, determining the conditions under which finite amplitude effects are expected to stabilize a growing wave disturbance. The analysis is applied to the ionopause at Comet Halley and Comet Giacobini-Zinner, showing that the theoretical prediction concerning the stability of this interface based on an earlier linear analysis remains valid in both cases despite the nonlinear stabilization effects.

Ershkovich, A. I.↗

NASA NTRS1988

A spectral collocation solution to the compressible stability eigenvalue problem

A newly developed spectral compressible linear stability code (SPECLS) (staggered pressure mesh) is presented for analysis of shear flow stability, and applied to high speed boundary layers and free shear flows. The formulation utilizes the first application of a staggered mesh for a compressible flow analysis by a spectral technique. An order of magnitude less number of points is needed for equivalent accuracy of growth rates compared to those calculated by a finite difference formulation. Supersonic disturbances which are found to have oscillatory structures were resolved by a spectral multi-domain discretization, which requires a factor of three fewer points than the single domain spectral stability code. It is indicated, as expected, that stability of mixing layers is enhanced by viscosity and increasing Mach number. The mean flow involves a jet being injected into a quiescent gas. Higher temperatures of the injected gas is also found to enhance stability characteristics of the free shear layer.

Macaraeg, Michele G.↗

NASA NTRS1989

Stability of compressible boundary layers

The stability of compressible 2-D and 3-D boundary layers is reviewed. The stability of 2-D compressible flows differs from that of incompressible flows in two important features: There is more than one mode of instability contributing to the growth of disturbances in supersonic laminar boundary layers and the most unstable first mode wave is 3-D. Whereas viscosity has a destabilizing effect on incompressible flows, it is stabilizing for high supersonic Mach numbers. Whereas cooling stabilizes first mode waves, it destabilizes second mode waves. However, second order waves can be stabilized by suction and favorable pressure gradients. The influence of the nonparallelism on the spatial growth rate of disturbances is evaluated. The growth rate depends on the flow variable as well as the distance from the body. Floquet theory is used to investigate the subharmonic secondary instability.

Nayfeh, Ali H.↗

NASA NTRS1989

On wave stability in relativistic cosmic-ray hydrodynamics

Wave stability of a two-fluid hydrodynamical model describing the acceleration of cosmic rays by the first-order Fermi mechanism in relativistic, cosmic-ray-modified shocks is investigated. For a uniform background state, the short- and long-wavelength wave speeds are shown to interlace, thus assuring wave stability in this case. A JWKB analysis is performed to investigate the stability of short-wavelength thermal gas sound waves in the smooth, decelerating supersonic flow upstream of a relativistic, cosmic-ray-modified shock. The stability of the waves is assessed both in terms of the fluid velocity and density perturbations, as well as in terms of the wave action. The stability and interaction of the short-wavelength cosmic-ray coherent mode with the background flow is also studied.

Webb, G. M.↗

NASA NTRS1989

Longitudinal stability and control characteristics of the Quiet Short-Haul Research Aircraft (QSRA)

Flight experiments were conducted to evaluate various aerodynamic characteristics of the Quiet Short-Haul Research Aircraft (QSRA), an experimental aircraft that makes use of the upper-surface blown (USB) powered-lift concept. Time-history records from maneuvers performed with the aircraft in landing-approach and take-off configurations (with its stability augmentation system disengaged) were analyzed to obtain longitudinal stability and control derivatives and performance characteristics. The experiments included measuring the aircraft responses to variations in the deflection of direct-lift control spoilers and to thrust variations as well as to elevator inputs. The majority of the results are given for the aircraft in a landing configuration with the USB flaps at 50 degrees. For this configuration, if the static longitudinal stability is defined as the variation of the pitching-moment coefficient with the lift coefficient at a constant thrust coefficient, this stability decreases significantly with increasing angle of attack above 9 degrees. For this configuration, at small and negative angles of attack and high levels of thrust, the elevators and the horizontal stabilizer lost effectiveness owing to incipent stalling, but this occurred only during unsteady maneuvers and for brief time intervals.

Stephenson, Jack D.↗

NASA NTRS1990

Analysis of stability of a planar solid-liquid interface in a dilute binary alloy

This paper reconsiders the question of stability of a planar solid-liquid interface in an undercooled alloy melt without making the restrictive assumption of no heat flow in the solid (i.e., Gs = 0). The results of this analysis indicate that, provided the thermal gradient on the solid side of the interface, Gs, is positive, stability can be achieved in an undercooled alloy melt for growth rates R greater than Ra (where Ra is the absolute stability limit of Mullins and Sekerka, 1964). Thus, the absolute stability criterion for steady-state planar growth in an undercooled alloy melt is the same as derived earlier by Mullins and Sekerka for directional solidification. Relaxing the restrictive assumption of Gs = 0 also reveals that there is a regime of stability for low growth rates and low supercoolings.

Laxmanan, V.↗

NASA NTRS1989

Stability characteristics of a conical aerospace plane concept

Data on stability characteristics of a conical aerospace plane concept were collected for a number of model geometry variations and test conditions, using several NASA-Langley wind tunnels spanning Mach range 0.1-6. The baseline configuration of this plane concept incorporated a 5-deg cone forebody, a 75.96-deg delta wing, a 16-deg leading-edge sweep deployable canard, and a centerline vertical tail. The key results pertinent to stability considerations about all three axes of the model are presented together with data on the effect of the canard on pitch stability, the effect of vertical tail on lateral-directional stability, and the effect of forebody geometry on yaw asymmetries. The experimental stability data are compared with the results from an engineering predictive code.

Hahne, David E.↗

NASA NTRS1989

A Study of Strong Stability of Distributed Systems

The strong stability of distributed systems is studied and the problem of characterizing strongly stable semigroups of operators associated with distributed systems is addressed. Main emphasis is on contractive systems. Three different approaches to characterization of strongly stable contractive semigroups are developed. The first one is an operator theoretical approach. Using the theory of dilations, it is shown that every strongly stable contractive semigroup is related to the left shift semigroup on an L(exp 2) space. Then, a decomposition for the state space which identifies strongly stable and unstable states is introduced. Based on this decomposition, conditions for a contractive semigroup to be strongly stable are obtained. Finally, extensions of Lyapunov's equation for distributed parameter systems are investigated. Sufficient conditions for weak and strong stabilities of uniformly bounded semigroups are obtained by relaxing the equivalent norm condition on the right hand side of the Lyanupov equation. These characterizations are then applied to the problem of feedback stabilization. First, it is shown via the state space decomposition that under certain conditions a contractive system (A,B) can be strongly stabilized by the feedback -B(*). Then, application of the extensions of the Lyapunov equation results in sufficient conditions for weak, strong, and exponential stabilizations of contractive systems by the feedback -B(*). Finally, it is shown that for a contractive system, the first derivative of x with respect to time = Ax + Bu (where B is any linear bounded operator), there is a related linear quadratic regulator problem and a corresponding steady state Riccati equation which always has a bounded nonnegative solution.

Cataltepe, Tayfun↗

NASA NTRS1991

The stability to two-dimensional wakes and shear layers at high Mach numbers

This study is concerned with the stability properties of laminar free-shear-layer flows, and in particular symmetric two-dimensional wakes, for the supersonic through the hypersonic regimes. Emphasis is given to the use of proper wake profiles that satisfy the equations of motion at high Reynolds numbers. In particular the inviscid stability of a developing two-dimensional wake is studied as it accelerates at the trailing edge of a splitter plate. The nonparallelism of the flow is a leading-order effect in the calculation of the basic state, which is obtained numerically. Neutral stability characteristics are computed and the hypersonic stability is obtained by increasing the Mach number. It is found that the stability characteristics are altered significantly as the wake develops. Multiple modes (secondary modes) are found in the near wake that are closely related to the corresponding Blasius ones, but as the wake develops mode multiplicity is delayed to higher and higher Mach numbers. At a distance of about one plate length from the trailing edge, there is only one mode in a Mach number range of 0-20. The dominant mode emerging at all wake stations, and for high enough Mach numbers, is the so-called vorticity mode that is centered around the generalized inflection point layer. The structure of the dominant mode is also obtained analytically for all streamwise wake locations and it is shown how the far-wake limit is approached. Asymptotic results for the hypersonic mixing layer given by a tanh and a Lock distribution are also given.

Papageorgiou, Demetrios T.↗