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At least 271 records · Page 15

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NASA NTRS1977

Non-symmetric two-stream instability

A theoretical investigation is performed concerning the instability spectrum of quasi-electrostatic waves at shifted half-odd-integer values of the cyclotron frequency due to nonsymmetric counterstreaming electron beams. The beam velocities parallel and perpendicular to the static magnetic field are represented by double Dirac delta functions with no imposition of parameter limitations. Systematic consideration is given to the coupling between plasma modes and cyclotron modes as well as the coupling between cyclotron modes of the two beams that result in shifted half-odd-integer multiples of the cyclotron frequency. The general dispersion equation for quasi-electrostatic waves is analyzed, and plasma-cyclotron coupling in the nonsymmetric case is treated by deriving approximate analytical expressions for maximum growth rates and marginal stability. Exact numerical solutions in both frequency and wavenumber space are obtained and compared with the analytical expressions. Cyclotron-cyclotron coupling modes are treated in the same way, and the results for both types of coupling are compared. It is found that certain modes may be weakened or completely suppressed when the Bessel functions for specific plasma parameters vanish.

Cuperman, S.↗

NASA NTRS1978

On a new algorithm for time step integration of nonlinear systems

A new implicit algorithm for time step integration of finite element structural dynamic equations is presented. Convergence, stability and numerical damping properties are discussed. Due to the way nonlinear structural behavior is taken into account, the algorithm is expected to compare favorably with existing ones. Some simple numerical results are presented. A related explicit algorithm is also derived and shortly discussed.

Anderheggen, E.↗

NASA NTRS1981

Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives

A new explicit, time splitting algorithm has been developed for finite difference modelling of the full two and three-dimensional time-dependent, compressible, viscous Navier-Stokes equations of fluid mechanics. The scheme is optimal in the sense that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number. The algorithm allows a conservation-form formulation. Stability is proven analytically and verified numerically. In proving stability it was shown that all nine matrix coefficients of the Navier-Stokes equations are simultaneously symmetrizable by a similarity transformation. Two such transformations and their resulting symmetric matrix coefficients are presented explicitly.

Abarbanel, S.↗

NASA NTRS1982

Accurate numerical solution of compressible, linear stability equations

The present investigation is concerned with a fourth order accurate finite difference method and its application to the study of the temporal and spatial stability of the three-dimensional compressible boundary layer flow on a swept wing. This method belongs to the class of compact two-point difference schemes discussed by White (1974) and Keller (1974). The method was apparently first used for solving the two-dimensional boundary layer equations. Attention is given to the governing equations, the solution technique, and the search for eigenvalues. A general purpose subroutine is employed for solving a block tridiagonal system of equations. The computer time can be reduced significantly by exploiting the special structure of two matrices.

Malik, M. R.↗

NASA NTRS1982

Space environmental effects on materials

Research efforts at NASA-Langley to characterize the durability of composite materials which are candidates for use as components on various space hardware systems are reviewed. The material applications include large space structures, antennas, cables, thermal control coatings, solar reflectors, and satellite power systems. Simulation facilities have been built to study radiation effects on polymer matrix composites, and the dimensional stability of the matrix composites and tension stabilized cables. Numerical models are being developed for radiation effects on the mechanical, physical, and optical properties. Additionally, chemical and microstructural analyses are performed to identify damage mechanisms and the limits of effectiveness of accelerating life tests. It is noted that no residual strength reduction has been detected in polymer films after dosages of 5 billion rads of electron radiation.

Tenney, D. R.↗

NASA NTRS1984

Stability of a dual-spin spacecraft with spherical dampers

The present investigation is concerned with the stability characteristics of a specific dual-spin satellite configuration marked by a high degree of symmetry. The configuration includes a platform and a rotor. Both components contain arbitrarily located internal spherical dampers. The symmetry of the system configuration makes it possible to illustrate clearly the relationship between Routhian analysis, energy sink analysis, and digital simulation of the full nonlinear equations. Although the dual-spin spacecraft configuration contains energy dissipating devices on both platform and rotor, it is still possible to employ the rigorous, but relatively simple, Routh stability method. This method, unlike Floquet theory, has the potential of producing closed-form stability criteria. The energy sink method is capable of providing a closed-form stability criterion. Numerical simulation is a necessary requirement in the latter stages of design when the realistic perturbation environment must be considered.

Laskin, R. A.↗

NASA NTRS1985

New stability criteria for difference approximations of hyperbolic initial-boundary value problems

New convenient stability criteria are provided for a large class of finite difference approximations to initial-boundary value problems associated with the hyperbolic system u sub t = Au sub x + Bu + f in the quarter plane x greater than or equal to 0, t greater than or equal to 0. The criteria are used to easily establish stability for numerous combinations of well known basic schemes and boundary conditions, thus generalizing many special cases studied in the recent literature. A number of examples are examined, including the unitary unconditionally stable Crank-Nicholson scheme and an almost-dissipative unconditionally stable backward Euler scheme.

Goldberg, M.↗

NASA NTRS1987

A numerical study of the thermal stability of solar loops

An important property of all loops is their thermal stability. If low lying hot loops were thermally unstable, for example, a great majority of the low loops on the Sun might be expected to be cool. How small perturbations evolve in low lying, linearly unstable hot loops was determined and how high lying, linearly stable hot loops respond to large amplitude disturbances such as might be expected on the Sun were examined. Only general descriptions and results are given.

Klimchuk, J. A.↗

NASA NTRS1991

A General-Coordinate Formulation For Boundary-Layer Flow

Formulation for solution of equations of boundary-layer flow in general body-fitted curvilinear coordinates retains velocities in Cartesian coordinates. Increases stability of numerical simulations by avoiding coordinate source terms. In formulation, curvilinear coordinates do not have to be orthogonal, and much of software developed previously for use in numerical simulations of flow based on Navier-Stokes equations used.

Steger, Joseph L.↗

NASA NTRS1991

Use of satellite data and modeling to assess the influence of stratospheric processes on the troposphere

Over the past forty years, numerous linear stability studies have been performed in order to explain the origin and structure of observed waves in the atmosphere. Of these studies, only a small fraction have considered the stability of time-dependent, zonally varying flow or the influence of radiative-photochemical feedbacks on the stability of zonally uniform flow. The stability of such flows is described, and these flows may yield important information concerning the origin, structure, and transient time scales of free waves in the atmosphere. During the period 1990 to 1991, a beta-plane model that couples radiative transfer, ozone advection, and ozone photochemistry with the quasigeostrophic dynamical circulation was developed in order to study the diabatic effects of Newtonian cooling and ozone-dynamics interaction on the linear stability of free planetary waves in the atmosphere. The stability of a basic state consisting of a westward-moving wave and a zonal mean jet was examined using a linearized, nondivergent barotropic model on sphere. The sensitivity of the stability of the flow to the strength and structure of the zonal jet was emphasized. The current research is focused on the following problems: (1) examination of the finite amplitude interactions among radiation, ozone, and dynamics; and (2) examination of the role of seasonal forcing in short-term climate variability. The plans for next year are presented.

Nathan, Terrence↗

NASA NTRS1994

Direct Replacement of Arbitrary Grid-Overlapping by Non-Structured Grid

A new approach that uses nonstructured mesh to replace the arbitrarily overlapped structured regions of embedded grids is presented. The present methodology uses the Chimera composite overlapping mesh system so that the physical domain of the flowfield is subdivided into regions which can accommodate easily-generated grid for complex configuration. In addition, a Delaunay triangulation technique generates nonstructured triangular mesh which wraps over the interconnecting region of embedded grids. It is designed that the present approach, termed DRAGON grid, has three important advantages: eliminating some difficulties of the Chimera scheme, such as the orphan points and/or bad quality of interpolation stencils; making grid communication in a fully conservative way; and implementation into three dimensions is straightforward. A computer code based on a time accurate, finite volume, high resolution scheme for solving the compressible Navier-Stokes equations has been further developed to include both the Chimera overset grid and the nonstructured mesh schemes. For steady state problems, the local time stepping accelerates convergence based on a Courant - Friedrichs - Leury (CFL) number near the local stability limit. Numerical tests on representative steady and unsteady supersonic inviscid flows with strong shock waves are demonstrated.

Kao, Kai-Hsiung↗

NASA NTRS1994

Maneuvering and control of flexible space robots

This paper is concerned with a flexible space robot capable of maneuvering payloads. The robot is assumed to consist of two hinge-connected flexible arms and a rigid end-effector holding a payload; the robot is mounted on a rigid platform floating in space. The equations of motion are nonlinear and of high order. Based on the assumption that the maneuvering motions are one order of magnitude larger than the elastic vibrations, a perturbation approach permits design of controls for the two types of motion separately. The rigid-body maneuvering is carried out open loop, but the elastic motions are controlled closed loop, by means of discrete-time linear quadratic regulator theory with prescribed degree of stability. A numerical example demonstrates the approach. In the example, the controls derived by the perturbation approach are applied to the original nonlinear system and errors are found to be relatively small.

Meirovitch, Leonard↗

NASA NTRS1997

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Swanson, R. C.↗

NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗

NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗

NASA NTRS1987

Boundary layer stability calculations

In this paper numerical calculation of the spatial stability of disturbances in the parallel and nonparallel Blasius boundary layers is considered. Chebyshev polynomials are used for discretization. The problem with the boundary condition at infinity is overcome, and the resulting nonlinear matrix eigenvalue problem is attacked directly. The secondary eigenvalue problem for three-dimensional disturbances is shown to be uniformly stable, and particular solutions of this problem generated by the Orr-Sommerfeld equation are shown. A numerical solution of the nonparallel problem is considered using Chebyshev polynomials. The matrix equations are analyzed directly and the problem of uniqueness of the nonparallel correction is settled by careful application of the Fredholm alternative. Nonparallel corrections to the streamwise eigenfunction are shown.

Bridges, Thomas J.↗

NASA NTRS1993

Symmetry breaking in vortical flows over cones - Theory and numerical experiments

A stability analysis suggests that inviscid incompressible flow, independent from angle of attack and regardless whether attached or separated, over slender cones is only marginally stable in regions of decelerating circumferential flow. Reducing slenderness or surface curvature lowers the energy level of harmonic perturbations, and, thus, reduces their impact on the overall stability of flows over slender cones. Associating the notion of instabilities in such flows with the onset of vortex asymmetries provides a model for explaining a variety of flow phenomena in Navier-Stokes simulations of laminar incompressible flows over three right circular cones at moderate to high angles of attack.

Hartwich, Peter M.↗

NASA NTRS1994

Symmetry breaking in vortical flows over cones -- theory and numerical experiments

A stability analysis suggests that inviscid incompressible flow, independent from angle of attack and regardless whether attached or separated, over slender cones is only marginally stable in regions of decelerating circumferential flow. Reducing slenderness or surface curvature lowers the frequency spectrum of the harmonic perturbations and, thus, reduces their impact on the overall stability of flows over slender cones. Associating the notion of instabilities in such flows with the onset of vortex asymmetries provides a model for explaining a variety of flow phenomena in Navier-Stokes simulations of laminar incompressible flows over three right circular cones at moderate to high angles of attack.

Hartwich, Peter M.↗