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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Nonlinear spatial equilibration of an externally excited instability wave in a free shear layer

A two-dimensional disturbance evolving from a strictly linear, finite-growth-rate instability wave, with nonlinear effects first becoming important in the critical layer is considered. The analysis is carried out for a general weakly nonparallel mean flow using matched asymptotic expansions. The flow in the critical layer is governed by a nonlinear vorticity equation which includes a spatial-evolution term. As in Goldstein and Hultgren (1988), the critical layer ages into a quasi-equilibrium one and the initial exponential growth of the instability wave is converted into a weak algebraic growth during the roll-up process. This leads to a next stage of evolution where the instability-wave growth is simultaneously affected by mean-flow divergence and nonlinear critical-layer effects and is eventually converted to decay. Expansions for the various streamwise regions of the flow are combined into a single composite formula accounting for both shear-layer spreading and nonlinear critical-layer effects and good agreement with the experimental results of Thomas and Chu (1989) and Freymuth (1966) is demonstrated.

Hultgren, Lennart S.↗
NASA NTRS1992

Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.

Khabibrakhmanov, I. KH.↗
NASA NTRS1989

Two-dimensional magnetohydrodynamic model of emerging magnetic flux in the solar atmosphere

The nonlinear undular mode of the magnetic buoyancy instability in an isolated horizontal magnetic flux embedded in a two-temperature layered atmosphere (solar corona-chromosphere/photosphere) is investigated using a two-dimensional magnetohydrodynamic code. The results show that the flux sheet with beta of about 1 is initially located at the bottom of the photosphere, and that the gas slides down the expanding loop as the instability develops, with the evacuated loop rising as a result of enhanced magnetic buoyancy. The expansion of the magnetic loop in the nonlinear regime displays self-similar behavior. The rise velocity of the magnetic loop in the high chromosphere (10-15 km/s) and the velocity of downflow noted along the loop (30-50 km/s) are consistent with observed values for arch filament systems.

Shibata, K.↗
NASA NTRS1993

Nonlinear response of graphite-epoxy wide columns subject to eccentric load

It is shown that including the effects of bend-twist coupling and material nonlinearity on the large displacement flexural response of graphite-epoxy wide columns is necessary to adequately model their response. Results from static tests on 0(30)T and (30/0/-30 sub 5)s laminated specimens under eccentric axial compression are compared to a nonlinear analysis. The analysis is based on a Kantrovich expansion of the displacements in the width coordinate and a finite element representation in the axial coordinate. An incremental, updated Lagrangian formulation and element corotational coordinates are employed. Nonlinear elastic material behavior was measured in a separate set of material characterization tests, and these data are used to compute tangent stillnesses in the updated configuration.

Griffin, O. H., Jr.↗
NASA NTRS1977

Optimum acoustic design of free-running low speed propellers

A theoretical analysis is conducted concerning the effect of blade loading on the noise output of a free-running propeller in axial motion. The minimization of the mean square sound pressure at a point in space is considered, taking into account constraints on propeller thrust and torque. Attention is given to aerodynamic equations, acoustic equations, the expansion of the aerodynamic variables, and the nonlinear programming formulation.

Ormsbee, A. I.↗
NASA NTRS1980

Composite materials research and education program: The NASA-Virginia Tech composites program

Major areas of study include: (1) edge effects in finite width laminated composites subjected to mechanical, thermal and hygroscopic loading with temperature dependent material properties and the influence of edge effects on the initiation of failure; (2) shear and compression testing of composite materials at room and elevated temperatures; (3) optical techniques for precise measurement of coefficients of thermal expansion of composites; (4) models for the nonlinear behavior of composites including material nonlinearity and damage accumulation and verification of the models under biaxial loading; (5) compressive failure of graphite/epoxy plates with circular holes and the buckling of composite cylinders under combined compression and torsion; (6) nonlinear mechanical properties of borsic/aluminum, graphite/polyimide and boron/aluminum; (7) the strength characteristics of spliced sandwich panels; and (8) curved graphite/epoxy panels subjected to internal pressure.

Herakovich, C. T.↗
NASA NTRS2014

Space Launch System Ascent Flight Control Design

A robust and flexible autopilot architecture for NASA's Space Launch System (SLS) family of launch vehicles is presented. The SLS configurations represent a potentially significant increase in complexity and performance capability when compared with other manned launch vehicles. It was recognized early in the program that a new, generalized autopilot design should be formulated to fulfill the needs of this new space launch architecture. The present design concept is intended to leverage existing NASA and industry launch vehicle design experience and maintain the extensibility and modularity necessary to accommodate multiple vehicle configurations while relying on proven and flight-tested control design principles for large boost vehicles. The SLS flight control architecture combines a digital three-axis autopilot with traditional bending filters to support robust active or passive stabilization of the vehicle's bending and sloshing dynamics using optimally blended measurements from multiple rate gyros on the vehicle structure. The algorithm also relies on a pseudo-optimal control allocation scheme to maximize the performance capability of multiple vectored engines while accommodating throttling and engine failure contingencies in real time with negligible impact to stability characteristics. The architecture supports active in-flight disturbance compensation through the use of nonlinear observers driven by acceleration measurements. Envelope expansion and robustness enhancement is obtained through the use of a multiplicative forward gain modulation law based upon a simple model reference adaptive control scheme.

Orr, Jeb S.↗
NASA NTRS1980

Computer-aided analysis of nonlinear problems in transport phenomena

The paper describes algorithms for equilibrium and steady-state problems with coefficients in the expansions derived by the Galerkin weighted residual method and calculated from the resulting sets of nonlinear algebraic equations by the Newton-Raphson method. Initial approximations are obtained from nearby solutions by continuation techniques as parameters are varied. The Newton-Raphson technique is preferred because the Jacobian of the solution is useful for continuation, for analyzing the stability of solutions, for detecting bifurcation of solution families, and for computing asymptotic estimates of the effects on any solution of small changes in parameters, boundary conditions, and boundary shape.

Brown, R. A.↗
NASA NTRS1988

Optimal feedback control of a bioreactor with a remote sensor

Sensors used to monitor bioreactor conditions directly often perform poorly in the face of adverse nonphysiological conditions. One way to circumvent this is to use a remote sensor block. However, such a configuration usually causes a significant time lag between measurements and the actual state values. Here, the problem of implementing feedback control strategies for such systems, described by nonlinear equations, is addressed. The problem is posed as an optimal control problem with a linear quadratic performance index. The linear control law so obtained is used to implement feedback. A global linearization technique as well as an expansion using Taylor series is used to linearize the nonlinear system, and the feedback is subsequently implemented.

Niranjan, S. C.↗
NASA NTRS1981

Effects of static tensile load on the thermal expansion of Gr/PI composite material

The effect of static tensile load on the thermal expansion of Gr/PI composite material was measured for seven different laminate configurations. A computer program was developed which implements laminate theory in a piecewise linear fashion to predict the coupled nonlinear thermomechanical behavior. Static tensile load significantly affected the thermal expansion characteristics of the laminates tested. This effect is attributed to a fiber instability micromechanical behavior of the constituent materials. Analytical results correlated reasonably well with free thermal expansion tests (no load applied to the specimen). However, correlation was poor for tests with an applied load.

Farley, G. L.↗
NASA NTRS1991

Plasma expansion characteristics of ionized clouds in the ionosphere - Macroscopic formulation

A macroscopic plasma expansion model, based on a numerical solution of the type-dependent nonlinear coupled continuity and momentum equations for background O(+) ions and several released ion species, was used to examine plasma expansion characteristics of ionized clouds in the ionosphere. Information is obtained on Ba(+), Li(+), and Ba(+) - Li(+) clouds; different cloud sizes (Gaussian half widths of 0.1, 0.5, and 1 km); cloud/background ion density ratios covering two orders of magnitude; electron/ion temperature ratios of 1, 5, and 10; and several cloud-background relative velocities along B (0, 1, 2, 4, 6, and 8 km/sec). The macroscopic expansion features obtained were found to be in general agreement with those obtained from the small-scale numerical simulations.

Schunk, R. W.↗
NASA NTRS1987

Meridional transport of magnetic flux in the solar wind between 1 and 10 AU - A theoretical analysis

Observations suggesting that the mean solar wind azimuthal field strength B(theta) near the ecliptic plane falls off more rapidly with heliocentric distance than would be expected in a classic Parker expansion is reexamined from a theoretical perspective using a three-dimensional MHD nonlinear numerical model for steady, corotating flow. For realistic solar wind parameters, it is found that a purely axisymmetric expansion can produce sizable magnetic flux deficits only when there are substantial meridional gradients in mean flow conditions localized about the ecliptic plane near the sun. Calculations on three-dimensional cororating flows are presented which demonstrate that latitudinal transport of magnetic flux by stream interactions may be an important consideration in generating the deficits in mean B(theta).

Pizzo, V. J.↗
NASA NTRS2015

A Versatile Nonlinear Method for Predictive Modeling

As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.

nonlinear modeling↗
NASA NTRS1975

Gravitational collapse of a turbulent vortex with application to star formation

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitation and rotation terms in the equations are of first order in the space variables, the pressure gradient terms are of second order, and the turbulent viscosity term is of third order. The presence of a turbulent viscosity insures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial inflow plays an important role and allows collapse to occur even when the rotation is large. An approximate solution of the governing partial differential equations is also given; the equations are used to study the spacial distributions of the density and velocity.

Deissler, R. G.↗
NASA NTRS1975

Gravitational collapse of a turbulent vortex with application to star formation

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitation and rotation terms in the equations are of first order in the space variables, the pressure gradient terms are of second order, and the turbulent viscosity term is of third order. The presence of a turbulent viscosity insures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the intial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial inflow plays an important role and allows collapse to occur even when the rotation is large. An approximate solution of the governing partial differential equations is also given, in order to study the spacial distributions of the density and velocity.

Deissler, R. G.↗
NASA NTRS1976

Gravitational collapse of a turbulent vortex with application to star formation

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitational and rotational terms in the equations are of first order in the space variables, the pressure-gradient terms are of second order, and the turbulent-viscosity term is of third order. The presence of turbulent viscosity ensures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial flow is always inward and allows collapse to occur (axially) even when the rotation is large. An approximate solution of the governing partial differential equations is also given in order to study the spatial distributions of the density and velocity.

Deissler, R. G.↗
NASA NTRS1974

The application of MINIQUASI to thermal program boundary and initial value problems

The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

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