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Results for “Stability boundary”

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At least 1,153 records · Page 64

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NASA NTRS1975

Application of the comparison principle to analysis of nonlinear systems

A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.

Gunderson, R. W.↗

NASA NTRS1978

The relation between temporal and spatial stability in three-dimensional flows

An analysis is presented of the nonparallel spatial or temporal stability of three-dimensional incompressible, isothermal boundary-layer flows taking into account the transverse velocity component as well as the axial and crossflow variations of the mean flow. The method of multiple scales is used to derive partial differential equations that describe the axial and crossflow variations of the disturbance amplitude, phase and wavenumbers. This equation is used to derive the expressions that relate the temporal and spatial instabilities. These relations are functions of the complex group velocities. Moreover, this equation is used to derive the expression that relates the spatial amplification in any direction to a calculated amplification in any other direction. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.

Nayfeh, A. H.↗

NASA NTRS1982

Effects of heat loss, preferential diffusion, and flame stretch on flame-front instability and extinction of propane/air mixtures

Flame configurations, flame-front cellular instability, and extinction of propane/air mixtures in the stagnation-point flow are experimentally studied for their dependence on downstream heat loss, preferential diffusion, and flame stretch. Boundaries for lean- and rich-limit extinction, stabilization of corrugated flames, and local extinction caused by sharp curvatures are mapped for varying propane concentrations and freestream velocities. Flame location and temperature at extinction are determined as functions of stagnation surface temperature, extent of preheating, propane concentration, and freestream velocity. Results substantiate the theoretical predictions of the different extinction modes for lean and rich flames in the absence of downstream heat loss, and yield useful insight on the extinction characteristics when finite downstream heat loss does exist. It is further shown that flame-front instability occurs only for rich mixtures in accordance with preferential diffusion considerations, and that flame stretch has a stabilizing effect such that flame-front instability is completely inhibited before the onset of extinction.

Ishizuka, S.↗

NASA NTRS1982

Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma

A general stability analysis is given of the Kevin-Helmholtz instability, for the case of sheared MHD flow of finite thickness in a compressible plasma which allows for the arbitrary orientation of the magnetic field, velocity flow, and wave vector in the plane perpendicular to the velocity gradient. The stability problem is reduced to the solution of a single second-order differential equation including a gravitational term to represent the coupling between the Kelvin-Helmholtz mode and the interchange mode. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects, with destabilization of only the fast magnetosonic mode in the transverse case, and the presence of both Alfven and slow magnetosonic components in the parallel case. Analysis results are used in a discussion of the stability of sheared plasma flow at the magnetopause boundary and in the solar wind.

Miura, A.↗

NASA NTRS1982

The development of a two-dimensional wavepacket in a growing boundary layer

The evolution of a two-dimensional wavepacket in a growing boundary layer is discussed in terms of linear stability theory. The wavepacket is represented by an integral of periodic wavetrains, each of which is defined as a series in terms of the inverse of the local displacement thickness Reynolds number to the one half power. Comparisons are made between the waveforms computed directly from the integral, a steepest-descent expansion of the integral, and a global expansion about the peak of the wavepacket.

Gaster, M.↗

NASA NTRS1984

Evaluation of 2 1-D cloud models for the analysis of VAS soundings

Evaluation of the satellite Visual Infrared Spin Scan Radiometer Atmospheric Sounder (VISSR) has begun to document several of its critical shortcomings as far as numerical cloud models are concerned: excessive smoothing of thermal inversions; imprecise measurement of boundary layer moisture; and tendency to exaggerate atmospheric stability. The sensitivity of 1-D cloud models to their required inputs is stressed with special attention to those parameters obtained from atmospheric soundings taken by the VAS or rawinsonde. In addition to performing model experiments using temperature and moisture profiles having the general characteristics of VAS soundings, standard input sensitivity tests were made and 1-D model performance was compared with observations and the results of a 2-D model experiment using AVE/VAS data (Atmospheric Variability Experiment). Although very encouraging, the results are not sufficient to make any specific conclusions. In general, the VAS soundings are likely to be inadequate to provide the cloud base (and subcloud layer) information needed for inputs to current cumulus models. Above cloud base, the tendency to exaggerate the stability of the atmosphere requires solution before meaningful model experiments are run.

Emmitt, G. D.↗

NASA NTRS1984

A spectral collocation method for the Navier-Stokes equations

A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

Malik, M. R.↗

NASA NTRS1985

Parameterization in Grid Generation

The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature.

Mastin, C. W.↗

NASA NTRS1985

Inviscid analysis of advanced turboprop propeller flow fields

A three-dimensional Euler code, previously developed for high speed propellers, was rewritten and vectorized for the Cray computer. Calculations were compared with previous results and measurements. The new code requires less memory and is more than two times faster than its predecessor. The new boundary conditions produced more accurate results and improved stability. The accuracy and stability characteristics also resulted in reduced manual intervention required to obtain solutions. The code is a useful tool for examining the fluid dynamics and performance of propellers.

Barton, J. M.↗

NASA NTRS1985

A spectral collocation method for the Navier-Stokes equations

Malik, M. R.↗

NASA NTRS1986

Phase transitions and convection in icy satellites

The effects of solid-solid phase changes on subsolidus convection in the large icy moons of the outer solar system are considered. Phase transitions affect convection via processes that distort the phase change boundary and/or influence buoyancy through thermal expansion. Linear stability analyses are carried out for ice layers with a phase change at the midplane. Two exothermic phase transitions (ice I - ice II, ice VI - ice VIII) and two endothermic transitions (ice I - ice III, ice II - ice V) are considered. For the exothermic cases, the phase change can either impede or enhance whole-layer convection. For the endothermic cases, the phse change always inhibits whole-layer convective overturn and tends to enforce two-layer convection. These results play some constraints on possible models of icy satellite evolution and structure.

Bercovici, D.↗

NASA NTRS1986

Unsteady separation characteristics of airfoils operating under dynamic stall conditions

Unsteady viscous/inviscid interaction phenomena are investigated for airfoils operating under dynamic stall conditions, using coupling procedures between a time-dependent inviscid panel method and two-dimensional unsteady boundary layer codes. Two strategies are pursued: a coupling of the inviscid panel method with the boundary layer code, and a strong coupling of the inviscid panel method with the boundary layer code. Attention is given to the main features of the unsteady time-marching panel method and boundary layer codes, as well as to numerical stability and the phenomenon of unsteady separation.

Geissler, Wolfgang↗

NASA NTRS1989

Two-measured variable method for wall interference assessment/correction

An iterative method for wall interference assessment and/or correction is presented for transonic flow conditions in wind tunnels equipped with two component velocity measurements on a single interface. The iterative method does not require modeling of the test article and tunnel wall boundary conditions. Analytical proof for the convergence and stability of the iterative method is shown in the subsonic flow regime. The numerical solutions are given for both 2-D and axisymmetrical cases at transonic speeds with the application of global Mach number correction.

Lo, C. F.↗

NASA NTRS1989

Noise produced by turbulent flow into a rotor: Theory manual for atmospheric turbulence prediction and mean flow and turbulence contraction prediction

Prediction of helicopter main rotor noise due to ingestion of atmospheric turbulence was analyzed. The analysis combines several different models that describe the fluid mechanics of the turbulence and the ingestion process. Two models, atmospheric turbulence, and mean flow and turbulence contraction were covered. The third model, covered in a separate report, describes the rotor acoustic mode. The method incorporates the atmospheric turbulence model and a rapid distortion turbulence contraction description to determine the statistics of the anisotropic turbulence at the rotor plane. The analytical basis for a module was provided which was incorporated in NASA's ROTONET helicopter noise prediction program. The mean flow and turbulence statistics associated with the atmospheric boundary layer were modeled including effects of atmospheric stability length, wind speed, and altitude. The turbulence distortion process is modeled as a deformation of vortex filaments (which represent the turbulence field) by a mean flow field due to the rotor inflow.

Simonich, J. C.↗

NASA NTRS1989

Vortex breakdown simulation - A circumspect study of the steady, laminar, axisymmetric model

The incompressible axisymmetric steady Navier-Stokes equations are written using the streamfunction-vorticity formulation. The resulting equations are discretized using a second-order central-difference scheme. The discretized equations are linearized and then solved using an exact LU decomposition, Gaussian elimination, and Newton iteration. Solutions are presented for Reynolds numbers (based on vortex core radius) 100-1800 and swirl parameter 0.9-1.1. The effects of inflow boundary conditions, the location of farfield and outflow boundaries, and mesh refinement are examined. Finally, the stability of the steady solutions is investigated by solving the time-dependent equations.

Salas, M. D.↗

NASA NTRS1990

Ballooning instability of the earth's plasma sheet region in the presence of parallel flow

Stability of the plasma sheet and plasma sheet boundary layer against the ballooning mode instability is investigated. The equilibrium state of a two-dimensional plasma sheet configuration with parallel sheared flow is modeled. This equilibrium is shown to be ballooning unstable when delta-W is not positive definite, where delta-W is the potential energy. The eigenmode structure of the ballooning mode is found by imposing the boundary conditions that the waves are totally reflected from the ionosphere, and that no waves are coming in from infinity. The eigenmode structure of the unstable balloning modes is highly oscillatory, extending beyond about 100 R(E). The ballooning modes are thus a possible candidate for explaining the MHD waves and other dynamical events observed in the magnetotail by ISEE 3 and other spacecraft.

Lakhina, G. S.↗

NASA NTRS1991

Ammonia-water mixtures at high pressures - Melting curves of ammonia dihydrate and ammonia monohydrate and a revised high-pressure phase diagram for the water-rich region

The phase relations of some mixtures of ammonia and water are investigated to create a phase diagram in pressure-temperature-composition space relevant to the geophysical study of bodies in the outer solar system. The mixtures of NH3(x)H2O(1-x), where x is greater than 0.30 but less than 0.51, are examined at pressures and temperatures ranging from 0-6.5 GPa and 125-400 K, respectively. The ruby luminescence technique monitors the pressure and a diamond-anvil cell compresses the samples, and the phases are identified by means of normal- and polarized-light optical microscopy. The melting curve for NH3H2O(2) is described by the equation T = 176 + 60P - 8.5P squared for the ranges of 0.06-1.4 GPa and 179-243 K. The equation for NH3H2O is T = 194 + 37P - P squared, which represents a minor correction of a previous description by Johnson et al. (1985). Observed phase transitions are consistent with the high-pressure stability limit of NH3H2O(2), and the transition boundary is found to be linear.

Boone, S.↗

NASA NTRS1993

The effect of gravitational modulation on convection in vertical Bridgman growth

During vertical directional solidification of a binary alloy at constant velocity, buoyancy-driven solutal convection may occur due to the solute gradient associated with the solidification process. This problem is further complicated if time-periodic forcing is considered, which is relevant to materials processing in a microgravity environment or as a means of dynamic control of flow instabilities. The effect of time-periodic modulation is studied by introducing a gravitational acceleration which is a sinusoidal function of time. The onset of solutal convection is treated by a stability analysis of the linearized governing equations and boundary conditions. Solutions are obtained numerically employing two distinct computational implementations of Floquet theory. Results are presented for materials with large Schmidt number, and an analysis for large frequency and large Schmidt number yields a more complete description of the behavior in this relevant limit.

Murray, B. T.↗