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At least 415 records · Page 23
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NASA NTRS1974

Decomposition-aggregation stability analysis of the spinning Skylab

Stability of an 11-th order linear model of the spinning Skylab is determined by the decomposition-aggregation method based upon the comparison principle and vector Liapunov functions. To reduce the inherent conservativeness of the method an optimization problem is formulated and resolved producing the optimum comparison system. The system provides the best estimate of the stability region of the important structural parameter - asymmetry in the boom settings.

Cuk, S. M.↗
NASA NTRS1991

A geometric approach to regulator and tracker design for an aerospace plane

The paper presents a nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control, that leads to regulators with automatic gain scheduling which exhibit similar dynamic behavior over the entire flight envelope of the aerospace plane. Additionally, design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. The unifying feature of the three nonlinear feedback control methodologies is that they all have a geometric interpretation. First, the translational dynamics are decomposed into reduced-order slow and fast dynamics by way of a formal singular perturbation analysis. After feedback linearization the fast dynamics are robustly stabilized via a variable structure control approach. The slow dynamics are stabilized using conventional proportional-integral compensation based on the nominal slow dynamics. A number of sample command and disturbance responses at opposite ends of the flight envelope are presented for a nonlinear aerospace plane model.

Van Buren, Mark A.↗
NASA NTRS1992

Secondary instability in three-dimensional magnetic reconnection

We consider the transition to turbulence in three-dimensional reconnection of a magnetic neutral sheet. We find that the transition can occur via a three-step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two-dimensional quasi-steady state. Third, this secondary equilibrium is itself unstable when it is perturbed by three-dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three-dimensional linear stability properties of the two-dimensional saturated tearing layer. The numerical simulations are performed with a semi-implicit, pseudospectral-Fourier collocation algorithm. We identify a three-dimensional secondary linear stability which grows on the ideal timescale. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three-dimensional field, with the two-dimensional field acting as a catalyst.

Dahlburg, R. B.↗
NASA NTRS1996

Migrational Instabilities in Particle Suspensions

This work deals with an instability arising from the shear-induced migration of particles in dense suspensions coupled with a dependence of viscosity on particle concentration. The analysis summarized here treats the inertialess (Re = O) linear stability of homogeneous simple shear flows for a Stokesian suspension model of the type proposed by Leighton and Acrivos (1987). Depending on the importance of shear-induced migration relative to concentration-driven diffusion, this model admits short-wave instability arising from wave-vector stretching by the base flow and evolving into particle-depleted shear bands. Moreover, this instability in the time-dependent problem corresponds to loss of ellipticity in the associated static problem (Re = O, Pe = O). While the isotropic version of the Leighton-Acrivos model is found to be stable with their experimentally determined parameters for simple shear, it is known that the stable model does not give a good quantitative description of particle clustering in the core of pipe flow (Nott and Brady 1994). This leads to the conjecture that an appropriate variant on the above model could explain such clustering as a two-phase bifurcation in the base flow.

Goddard, Joe D.↗
NASA NTRS1962

Use of an Inertia Sphere to Damp the Angular Motions of Spinning Space Vehicles

The general moment equations for a spin-stabilized vehicle with an inertia-reaction angular rate damper were considered, and it was noted that simplification would result if the damper had a spherical inertia distribution. A control system incorporating such a damper was postulated. The resulting equations were linearized, and conditions for stability were obtained from an analysis of the cubic characteristic equation. Two numerical examples were included.

Suddath, Jerrold H.↗
NASA NTRS2000

The Generation of Smooth High Speed Solar Wind From Plume-Interplume Mixing

Ulysses has shown that fast solar wind is extremely smooth, with a variance of less than 5%, in contrast to slow wind with a variance of approximately 30%. Now UVCS has produced the surprising result that the flow speed within coronal holes, the source of fast wind, is not at all smooth. Specifically, Giordano et al. (ApJ, v531, L79-L82, 2000) report that at 1.7 R(sub SUN) the interplume flow speed is typically more than twice the plume flow speed. Other less direct evidence supports this same result, with speeds from less than 300 to over 1000 km/s reported at approximately 5 R(sub SUN). This presents the paradox of how strongly differing plume and interplume flow speeds can exist near the Sun and be absent far from the Sun. The only answer is that plume and interplume material or momentum must be strongly mixed and that the mixing must occur mainly inside 0.3 AU to be consistent with Helios observations of smooth fast wind. Pressure balance structures (PBSs) and He abundance anomalies (Reisenfeld, et al., GRL, v26(13), 1805-1808, 1999) have been identified as interplanetary remnants of plumes, implying momentum mixing is the dominant coronal process. One possible source for plume/interplume momentum mixing is MHD Kelvin-Helmholtz (KH) shear instabilities occurring on the velocity shear interfaces. The velocity shear is a source of free energy and KH fluctuations could, through nonlinear cascade, provide the forcing required for the plasma oscillations (Cranmer, ApJ, v532, 1197-1208, 2000) reported to exist in coronal holes. The physical properties in coronal holes are now sufficiently well known that we can show plume/interplume shear interfaces become unstable to the KH instability at 5 - 10 R(sub SUN). The KH dispersion relation can be used to analyze marginal stability, the most unstable wavelengths, and linear growth rates. Numerical simulations can be used to verify results from the linear analysis and study the nonlinear development of KH modes. Here we will describe the marginal stability criterion for the KH instability, how and where this condition is met in the corona, and the possible character of the resultant fluctuations.

Suess, Steve↗
NASA NTRS1985

Perturbations of the Richardson number field by gravity waves

An analytic solution is presented for a stratified fluid of arbitrary constant Richardson number. By computer aided analysis the perturbation fields, including that of the Richardson number can be calculated. The results of the linear analytic model were compared with nonlinear simulations, leading to the following conclusions: (1) the perturbations in the Richardson number field, when small, are produced primarily by the perturbations of the shear; (2) perturbations of in the Richardson number field, even when small, are not symmetric, the increase being significantly larger than the decrease (the linear analytic solution and the nonlinear simulations both confirm this result); (3) as the perturbations grow, this asymmetry increases, but more so in the nonlinear simulations than in the linear analysis; (4) for large perturbations of the shear flow, the static stability, as represented by N2, is the dominating mechanism, becoming zero or negative, and producing convective overturning; and (5) the convectional measure of linearity in lee wave theory, NH/U, is no longer the critical parameter (it is suggested that (H/u sub 0) (du sub 0/dz) takes on this role in a shearing flow).

Wurtele, M. G.↗
NASA NTRS1992

Failure analysis of thick composite cylinders under external pressure

Failure of thick section composites due to local compression strength and overall structural instability is treated. Effects of material nonlinearity, imperfect fiber architecture, and structural imperfections upon anticipated failure stresses are determined. Comparisons with experimental data for a series of test cylinders are described. Predicting the failure strength of composite structures requires consideration of stability and material strength modes of failure using linear and nonlinear analysis techniques. Material strength prediction requires the accurate definition of the local multiaxial stress state in the material. An elasticity solution for the linear static analysis of thick anisotropic cylinders and rings is used herein to predict the axisymmetric stress state in the cylinders. Asymmetric nonlinear behavior due to initial cylinder out of roundness and the effects of end closure structure are treated using finite element methods. It is assumed that local fiber or ply waviness is an important factor in the initiation of material failure. An analytical model for the prediction of compression failure of fiber composites, which includes the effects of fiber misalignments, matrix inelasticity, and multiaxial applied stresses is used for material strength calculations. Analytical results are compared to experimental data for a series of glass and carbon fiber reinforced epoxy cylinders subjected to external pressure. Recommendations for pretest characterization and other experimental issues are presented. Implications for material and structural design are discussed.

Caiazzo, A.↗
NASA NTRS1991

Guaranteed properties of gain scheduled control for linear parameter-varying plants

Gain scheduling has proven to be a successful design methodology in many engineering applications. However, in the absence of a sound theoretical analysis, these designs come with no guarantees on the robustness, performance, or even nominal stability of the overall gain scheduled design. This paper presents such an analysis for one type of gain scheduled system, namely, a linear parameter-varying plant scheduling on its exogenous parameters. Conditions are given which guarantee that the stability, robustness, and performance properties of the fixed operating point designs carry over to the global gain scheduled design. These conditions confirm and formalize popular notions regarding gain scheduled design, such as the scheduling variable should 'vary slowly'.

Shamma, Jeff S.↗
NASA NTRS1987

Remarks on the stability analysis of reactive flows

A simple model of compressible reacting flow is studied. First, a dispersion relation is derived for the linearized problem making a distinction between frozen and equilibrium sound speed. Second, the stability of the Von Neumann-Richtmyer scheme applied to this model is studied. A natural generalization of the C.F.L. condition is found.

Scheurer, B.↗
NASA NTRS2004

LASTRAC.3d: Transition Prediction in 3D Boundary Layers

Langley Stability and Transition Analysis Code (LASTRAC) is a general-purpose, physics-based transition prediction code released by NASA for laminar flow control studies and transition research. This paper describes the LASTRAC extension to general three-dimensional (3D) boundary layers such as finite swept wings, cones, or bodies at an angle of attack. The stability problem is formulated by using a body-fitted nonorthogonal curvilinear coordinate system constructed on the body surface. The nonorthogonal coordinate system offers a variety of marching paths and spanwise waveforms. In the extreme case of an infinite swept wing boundary layer, marching with a nonorthogonal coordinate produces identical solutions to those obtained with an orthogonal coordinate system using the earlier release of LASTRAC. Several methods to formulate the 3D parabolized stability equations (PSE) are discussed. A surface-marching procedure akin to that for 3D boundary layer equations may be used to solve the 3D parabolized disturbance equations. On the other hand, the local line-marching PSE method, formulated as an easy extension from its 2D counterpart and capable of handling the spanwise mean flow and disturbance variation, offers an alternative. A linear stability theory or parabolized stability equations based N-factor analysis carried out along the streamline direction with a fixed wavelength and downstream-varying spanwise direction constitutes an efficient engineering approach to study instability wave evolution in a 3D boundary layer. The surface-marching PSE method enables a consistent treatment of the disturbance evolution along both streamwise and spanwise directions but requires more stringent initial conditions. Both PSE methods and the traditional LST approach are implemented in the LASTRAC.3d code. Several test cases for tapered or finite swept wings and cones at an angle of attack are discussed.

Chang, Chau-Lyan↗
NASA NTRS2010

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Li, Fei↗
NASA NTRS1977

Analysis of the passive stabilization of the long duration exposure facility

The nominal Long Duration Exposure Facility (LDEF) configurations and the anticipated orbit parameters are presented. A linear steady state analysis was performed using these parameters. The effects of orbit eccentricity, solar pressure, aerodynamic pressure, magnetic dipole, and the magnetically anchored rate damper were evaluated to determine the configuration sensitivity to variations in these parameters. The worst case conditions for steady state errors were identified, and the performance capability calculated. Garber instability bounds were evaluated for the range of configuration and damping coefficients under consideration. The transient damping capabilities of the damper were examined, and the time constant as a function of damping coefficient and spacecraft moment of inertia determined. The capture capabilities of the damper were calculated, and the results combined with steady state, transient, and Garber instability analyses to select damper design parameters.

Siegel, S. H.↗
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

Periodic-disturbance accommodating control of the Space Station for asymptotic momentum management

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Warren, Wayne↗
NASA NTRS1987

Boundary-layer stability analysis of Langley Research Center 8-foot LFC experimental data

An analytical study of linear-amplifying instabilities of a laminar boundary layer as found in the experimental data of the LaRC/8-foot laminar-flow control (LFC) experiment was completed and the results are presented. The LFC airfoil used for this experiment was a swept, supercritical design which removed suction air through spanwise slots. The amplification of small disturbances by linear processes on a swept surface such as this can be due to either Tollmien-Schlichting (TS) and/or crossflow (CF) mechanisms. This study consists of the examination of these two instabilities by both the commonly used incompressible (SALLY and MARIA) analysis and the more involved compressible (COSAL) analysis. A wide range of experimental test conditions with variations in Mach number, Reynolds number, and suction distributions were available for this study. Experimentally determined transition locations were found from thin-film techniques and were used to correlate the n-factors at transition for the range of test cases.

Berry, Scott↗
NASA NTRS1989

Periodic-disturbance accommodating control of the space station for asymptotic momentum management

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Warren, Wayne↗