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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗
NASA NTRS1980

Numerical studies of new stellarator concepts

A three-dimensional computer code has been developed to study the magnetohydrodynamic equilibrium and stability of a diffuse or sharp boundary plasma in toroidal geometry. It is shown how equilibria with net toroidal current identically zero can be determined and how growth rates of instabilities can be calculated. Applications are made to an l = 2, 3 stellarator configuration that offers the possibility of achieving a critical value as high as 10% for the plasma parameter

Bauer, F.↗
NASA NTRS1990

Numerical simulation of particle-wave interaction in boundary layers

The effects of wall injection and particle motion on the spatial stability of two-dimensional plane channel flow are investigated. For this purpose, an accurate Navier-Stokes solver to simulate the space-time evolution of disturbances in three-dimensional flows has been developed. The code is operational on the NASA Langley CRAY2 and can be ported to any other supercomputer. The code has been tested extensively in tracking the spatial evolution of two-dimensional disturbances in plane channel flow and provided excellent agreement with the linear theory including at the inflow/outflow boundaries. Preliminary calculations have been performed to investigate the effects of stationary and moving sources of vortical disturbances simulating a particle traveling in the flow field. Results suggest that even at very low amplitudes, vortical disturbances act as amplifiers on the Tollmien-Schlichting waves promoting rapid instability. It is also found that slow moving particles are more dangerous than both stationary and fast moving particles for the same disturbance levels.

Biringen, S.↗
NASA NTRS1977

Effects of finite plasma beta on the lower-hybrid-drift instability

The local dispersion relation for the lower-hybrid-drift (LHD) instability is derived and analyzed, taking into account the finite-beta effects associated with transverse electromagnetic perturbations as well as with resonant and nonresonant electron-orbit modifications due to magnetic-field gradients. The influence of finite-beta effects on the LHD instability is calculated in a fully self-consistent manner for arbitrary values of electron-ion temperature ratio, local beta, cross-field ExB velocity/ion thermal speed ratio, and other plasma parameters. Stability properties are investigated analytically for the case of cold electrons, and the local dispersion relation is solved numerically in the parameter regime of most interest for high-density plasma pinches. The results show that for all parameter regimes studied, the net effect of finite plasma beta is to reduce the maximum growth rate of the LHD instability, although the details can vary, depending on the plasma parameters. Except in the limit where the electron/ion temperature ratio tends to zero, it is found that there is a critical value of plasma beta above which the LHD instability is completely stabilized.

Davidson, R. C.↗
NASA NTRS1996

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

Source record↗
NASA NTRS1974

Aeroelastic stability of coupled flap-lag motion of hingeless helicopter blades at arbitrary advance ratios

Equations for large amplitude coupled flap-lag motion of a hingeless elastic helicopter blade in forward flight are derived. Only a torsionally rigid blade excited by quasi-steady aerodynamic loads is considered. The effects of reversed flow together with some new terms due to radial flow are included. Using Galerkin's method the spatial dependence is eliminated and the equations are linearized about a suitable equilibrium position. The resulting system of homogeneous periodic equations is solved using multivariable Floquet-Liapunov theory, and the transition matrix at the end of the period is evaluated by two separate methods. Computational efficiency of the two numerical methods is compared. Results illustrating the effects of forward flight and various important blade parameters on the stability boundaries are presented.

Friedmann, P.↗
NASA NTRS1991

Controls for space structures

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control. A theory for disturbance accommodating controllers based on reduced order models of structures was developed, and stability results for these controllers in closed-loop with large-scale finite element models of structures were obtained.

Balas, Mark↗
NASA NTRS1963

INVESTIGATION OF PROBLEMS IN THERMAL CONVECTION

Numerical solution of thermal convection equations for velocity and temperature fluctuations as well as the stability analysis and heat transport for free boundary conditions

THERMAL CONVECTION↗
NASA NTRS1980

Dynamic analysis of noncontacting face seals

The dynamic behavior of a noncontacting coned face seal is analyzed taking into account various design parameters and operating conditions. The primary seal ring motion is expressed by a set of nonlinear equations for three degrees of freedom. These equations, which are solved numerically, allow identification of two dimensionless groups of parameters that affect the seal dynamic behavior. Stability maps for various seals are presented. These maps contain a stable-to-unstable transition region in which the ring wobbles at half the shaft frequency. The effect of various parameters on seal stability is discussed and an empirical expression for critical stability is offered.

Etsion, I.↗
NASA NTRS1982

Application of the Finite Element Method to Rotary Wing Aeroelasticity

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Straub, F. K.↗
NASA NTRS1985

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

Yee, H. C.↗
NASA NTRS1985

Morphological Stability and Fluid Dynamics of Vapor Crystal Growth

A fundamental understanding of the conditions under which crystals can retain morphological stability, i.e., shape stability of the advancing interface, during growth from vapors was studied. Morphological stability (MS) is a necessary condition for the growth of homogeneous single crystals required for numerous device applications. For crystallization from melts, the MS concepts are well developed and are essentially based on heat and mass transfer conditions about the advancing interface. For crystallization from vapors, the MS requirements are more complex and not well understood. The added complexity arises from the fact that anisotropies in interfacial kinetics are typically stronger in crystallization from vapors than from melts. These pronounced anisotropies root in the distinctly lower atomic roughness of most vapor-solid interfaces.

Rosenberger, F.↗
NASA NTRS1987

Roll-up of vorticity in adverse-pressure-gradient boundary layers

It is shown how the unsteady, nonlinear critical-layer equation determines the evolution of instability waves in a weak adverse-pressure-gradient boundary layer. Numerical solutions show that the nonlinearity halts the growth of these inviscidly unstable waves. The stabilizing effect of nonlinearity, in the present case, can be described as a consequence of either the increase (toward zero) of the phase jump across the critical layer or the roll-up of the critical-layer disturbance vorticity.

Goldstein, M. E.↗
NASA NTRS1988

Active control of helicopter air resonance in hover and forward flight

A coupled rotor/fuselage helicopter analysis is presented. The accuracy of the model is illustrated by comparing it with experimental data. The sensitivity of the open loop damping of the unstable resonance mode to such modeling effects as blade torsional flexibility, unsteady aerodynamics, forward flight, periodic terms, and trim solution is illustrated by numerous examples. Subsequently, the model is used in conjunction with linear optimal control theory to stabilize the air resonance mode. The influence of the modeling effects mentioned before on active resonance control is then investigated.

Takahashi, M. D.↗
NASA NTRS1989

Mechanics of unsymmetric laminates

Theoretical models describing the mechanical behavior of fiber-reinforced composite laminates are developed analytically and demonstrated. The curing of composite structures and the out-of-plane shapes of unsymmetric laminates are discussed and illustrated with photographs; the derivation of the governing equations is outlined; numerical results for typical laminates are presented in graphs; and particular attention is given to stability considerations and the effects of material properties, laminate thickness, aspect ratio, and stacking sequence.

Hyer, M. W.↗
NASA NTRS1990

An aerodynamic tradeoff study of the scissor wing configuration

A scissor wing configuration, consisting of two independently sweeping wings was numerically studied. This configuration was also compared with an equivalent fixed wing baseline. Aerodynamic and stability and control characteristics of these geometries were investigated over a wide range of flight Mach numbers. It is demonstrated that in the purely subsonic flight regime, the scissor wing can achieve higher aerodynamic efficiency as the result of slightly higher aspect ratio. In the transonic regime, the lift to drag ratio of the scissor wing is shown to be higher than that of the baseline, for higer values of the lift coefficient. This tends to make the scissor wing more efficient during transonic cruise at high altitudes as well as during air combat at all altitudes. In supersonic flight, where the wings are maintained at maximum sweep angle, the scissor wing is shown to have a decided advantage in terms of reduced wave drag. From the view point of stability and control, the scissor wing is shown to have distinct advantages. It is shown that this geometry can maintain a constant static margin in supersonic as well as subsonic flight, by proper sweep scheduling. Furthermore, it is demonstrated that addition of wing mounted elevons can greatly enhance control authority in pitch and roll.

Selberg, Bruce P.↗
NASA NTRS1988

A model for active control of helicopter air resonance in hover and forward flight

A coupled rotor/fuselage helicopter analysis is presented. The accuracy of the model is verified by comparing it with the experimental data. The sensitivity of the open loop damping of the unstable air resonance mode to such modeling effects as blade torsional flexibility, unsteady aerodynamics, forward flight, periodic terms, and trim solution is illustrated by numerous examples. Subsequently, the model is used in conjunction with linear optimal control theory to stabilize the air resonance mode. The influence of the modeling effects mentioned before on active air resonance control is then investigated.

Takahashi, M. D.↗