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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Energy Stability of Thermocapillary Convection in Models of the Float Zone Process

The energy-stability of thermocapillary convection in models of the float-zone, crystal-growing process was studied. Stability limits, as functions of pertinent parameters, that will identify conditions which will not allow the existence of an undesirable oscillatory flow instability were determined. Such instabilities may occur in the space processing of semiconductor materials. The determination of the stability limits will involve two sets of numerical computations: (1) solution of the nonlinear governing equations together with the appropriate boundary conditions to determine the basic state (in general, velocity, pressure and temperature fields and the displacement of free surfaces and interfaces); and (2) solution of a nonlinear Euler-Lagrange systems for the energy-stability limit. Both computations, while difficult, should be within the scope of available computer capability and available concepts in numerical analysis. Finite-element methods are attractive candidates for the numerical work.

Neitzel, G. P.↗
NASA NTRS1993

Bifurcation analysis of a simple analytic model of self-propagating star formation

We investigate the structure and stability of rotationally symmetric nonhomogeneous time-independent solutions derived from a simple analytic model of self-propagating star formation. For this purpose we employ two methodologies: We use bifurcation theoretical methods to prove the existence of nonhomogeneous axisymmetric stationary solutions of an appropriate nonlinear evolution equation for the stellar density. We show that the nonhomogeneous solution branch bifurcates from the homogeneous one at a critical parameter value of the star formation rate. Further, the analytical theory allows us to show that the new solution set is stable in the weakly nonlinear regime near the bifurcation point. To follow the solution branch further, we use numerical methods. The numerical calculation shows the structure and stability of these solutions. We conclude that no periodic time-dependent solutions of this special model exist, and no further bifurcations can be found. The same results have been found in simulations of stochastic self-propagating star formation based on similar models. Therefore, our findings provide a natural explanation, why long-lived large-scale structure have not been found in those simulations.

Neukirch, Thomas↗
NASA NTRS1986

The effect of beam-driven return current instability on solar hard X-ray bursts

The problem of electrostatic wave generation by a return current driven by a small area electron beam during solar hard X-ray bursts is discussed. The marginal stability method is used to solve numerically the electron and ion heating equations for a prescribed beam current evolution. When ion-acoustic waves are considered, the method appears satisfactory and, following an initial phase of Coulomb resistivity in which T sub e/T sub i rise, predicts a rapid heating of substantial plasma volumes by anomalous ohmic dissipation. This hot plasma emits so much thermal bremsstrahlung that, contrary to previous expectations, the unstable beam-plasma system actually emits more hard X-rays than does the beam in the purely collisional thick target regime relevant to larger injection areas. Inclusion of ion-cyclotron waves results in ion-acoustic wave onset at lower T sub e/T sub i and a marginal stability treatment yields unphysical results.

Cromwell, D.↗
NASA NTRS1989

The inviscid axisymmetric stability of the supersonic flow along a circular cylinder

The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary layer flow (i.e., the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results. The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so called doubly generalized inflexion condition is derived, which is a condition for the existence of so called subsonic neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two freestream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to rapidly disappear as curvature is introduced, while the second (and generally the most important) mode suffers a substantially reduced amplification rate.

Duck, Peter W.↗
DOE OSTI2022

Diagnostics for multiple frequency heating and investigation of underlying processes

The development of new facilities routinely challenges ion source designers to build and operate sources that can achieve ever higher beam intensities and energies. As shown in this work, electron cyclotron resonance ion sources have proven to be extremely capable in meeting these challenges through the production of intense beams of medium and high-charge state ions. As performance boundaries are pushed, source stability becomes an issue as does the technology required to meet the challenge. Multiple frequency heating, the simultaneous use of two or more plasma heating frequencies, is a powerful tool in meeting the simultaneous need of intensity and stability. Relatively straightforward to utilize, the technique has been employed at numerous facilities to increase beam current and achievable charge state while also stabilizing the plasma. Its application has expanded the operational boundaries of existing and next generation sources, demonstrating that these devices have not yet achieved their full operational potential. To better understand the underlying physics, the diagnostics used to probe the source operational boundaries and the plasma properties have become increasingly sophisticated. In concert with detailed modeling, they are beginning to provide insight into the heating mechanism and, with that, the prospect of future advances.

47 OTHER INSTRUMENTATION↗
NASA NTRS2019

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference boundary closure of Ols- son & Oliger (1994), Gerritsen & Olsson (1996), and Yee et al. (2000) is revisited. The entropy splitting is a form of skew-symmetric splitting of the nonlinear Euler flux derivatives. Central differencing applied to the entropy splitting form of the Euler flux derivatives together with SBP difference operators will, hereafter, be referred to as entropy split schemes. This study is prompted by the recent growing interest in numerical methods for which a discrete entropy conservation law holds, a discrete global entropy conservation can be proved and/or the numerical method possesses a stable entropy in the framework of SBP difference operators and L2-energy norm estimate. The objective of this paper is to recast the entropy split scheme as the re- cent definition of an entropy stable method for central differencing with SBP operators for both periodic and non-periodic boundary conditions for non- linear Euler equations. Standard high order spatial central differencing as well as high order central spatial DRP (dispersion relation preserving) spatial differencing is part of the entropy stable methodology framework. Long time integration of 2D and 3D test cases is included to show the comparison of this efficient entropy stable method with the Tadmor-type of entropy conservative methods. Studies also include the comparison among the three skew-symmetric splittings on their nonlinear stability and accuracy performance without added numerical dissipations for smooth flows. These are, namely, entropy splitting, Ducros et al. splitting and the Kennedy & Grub- ber splitting.

Sjogreen, Bjorn↗
NASA NTRS1990

The inviscid axisymmetric stability of the supersonic flow along a circular cylinder

The supersonic flow past a thin straight circular cylinder is investigated. The associated boundary-layer flow (i.e. the velocity and temperature field) is computed; the asymptotic, far downstream solution is obtained, and compared with the full numerical results. The inviscid, linear, axisymmetric (temporal) stability of this boundary layer is also studied. A so-called 'doubly generalized' inflexion condition is derived, which is a condition for the existence of so-called 'subsonic' neutral modes. The eigenvalue problem (for the complex wavespeed) is computed for two free-stream Mach numbers (2.8 and 3.8), and this reveals that curvature has a profound effect on the stability of the flow. The first unstable inviscid mode is seen to disappear rapidly as curvature is introduced, while the second (and generally the most important) mode suffers a substantially reduced amplification rate.

Duck, Peter W.↗
NASA NTRS2021

Transition Analysis for Isolated Trips on BOLT-II Wind-Tunnel and Flight Configuration

The BOLT-II configuration designed for an upcoming flight experiment exemplifies the complexities of hypersonic boundary layer transition in the presence of multiple and potentially interacting instability mechanisms. The present paper is related to the NASA-led roughness experiment on the secondary side of the BOLT-II configuration. First, computations are performed to aid mean-flow based correlations for the transition measurements acquired during an experimental campaign in the Ludwieg Tube facility at the United States Air Force Academy. To that end, both laminar and turbulent flow computations are performed for selected conditions of the experiment with a 1:3 scale model of the slightly shorter BOLT configuration. The variation in well-known correlation parameters for transition due to isolated roughness elements with respect to element position, height, and flow Reynolds number is delineated. Furthermore, the wake instability theory is used to examine the amplification of unstable disturbances behind the centerline trip at the design conditions of the BOLT-II flight experiment and for its dynamically scaled version on the 1:3 scale model of the wind tunnel experiment. To our knowledge, this study represents the first analysis of the wake instabilities in the presence of a prominent entropy layer outside the boundary layer. At the nominal flight design condition of Re ∞ ) = 5.44 and Re ∞ = 2.5 x 10 6 /m, a diamond planform (“pizza-box”) trip with k/δ = 0.70 and planform-halfwidth-to-height ratio of b/k = 3.0 at X/L = 0.254 induces a strong distortion of the boundary-layer flow in the vicinity of the symmetry plane, such that the wake structure includes a centerline streak produced by the flow retardation behind the trip along with multiple additional, prominent vorticity structures representing the necklace vortex system. Stability results reveal that each of these streaks can support a strong amplification of wake instabilities within a frequency band of 95 kHz–255 kHz, with a peak N-factor of greater than 15 beyond X/L ≈ 0.42. The dynamically scaled wind tunnel configuration with Re ∞ = 20.25 x 10 6 /m is also found to support N > 15 at similar axial stations.

BOLT↗
NASA NTRS1989

Modeling and control of flexible space stations (slew maneuvers)

Large orbiting space structures are expected to experience mechanical vibrations arising from several disturbing forces such as those induced by shuttle takeoff or docking and crew movements. The problem is considered of modeling and control of large space structures subject to these and other disturbing forces. The system consists of a (rigid) massive body, which may play the role of experimental modules located at the center of the space station and flexible configurations, consisting of several beams, forming the space structure. A complete dynamic model of the system was developed using Hamilton's principle. This model consists of radial equations describing the translational motion of the central body, rotational equations describing the attitude motions of the body and several beam equations governing the vibration of the flexible members (platform) including appropriate boundary conditions. In summary, the dynamics of the space structure is governed by a complex system of interconnected partial and ordinary differential equations. Using Lyapunov's approach the asymptotic stability of the space structure is investigated. For asymptotic stability of the rest state (nominal trajectory), feedback controls are suggested. In the investigation, stability of the slewing maneuvers is also considered. Several numerical results are presented for illustration of the impact of coupling and the effectiveness of the stabilizing controls. Some insight is provided into the complexity of modeling, analysis and stabilization of actual space structures.

Ahmed, N. U.↗
NASA NTRS2007

Effects of Nose Bluntness on Stability of Hypersonic Boundary Layers over Blunt Cone

Receptivity and stability of hypersonic boundary layers are numerically investigated for boundary layer flows over a 5-degree straight cone at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves, we solve the Navier-Stokes equations in axisymmetric coordinates. The governing equations are solved using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. Generation of instability waves from leading edge region and receptivity of boundary layer to slow acoustic waves are investigated. Computations are performed for a cone with nose radii of 0.001, 0.05 and 0.10 inches that give Reynolds numbers based on the nose radii ranging from 650 to 130,000. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of axisymmetric boundary layers. The transition Reynolds number for a cone with the nose Reynolds number of 65,000 is increased by a factor of 1.82 compared to that for a sharp cone. The receptivity coefficient for a sharp cone is about 4.23 and it is very small, approx.10(exp -3), for large bluntness.

Kara, K.↗
NASA NTRS1993

An efficient procedure for cascade aeroelastic stability determination using nonlinear, time-marching aerodynamic solvers

A numerical eigenvalue problem formulation and a practical calculation procedure for exact eigenvalues and corresponding eigenvectors are developed and applied to a nonlinear, two-dimensional, time-marching full potential solver for cascade aeroelastic stability analysis. This procedure is based on the Lanczos recursive method and it directly calculates stability information about a nonlinear steady state. It is compared to conventional approaches in the frequency and time domains developed earlier and is found to be 100-10.000 times more computationally efficient. Eigenvalue constellations and the flutter results for flow through a cascade SR5 propfan airfoil are presented.

Mahajan, Aparajit J.↗
NASA NTRS1987

Stability and transition in supersonic boundary layers

The full three-dimensional time-dependent compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation algorithm to study the stability of supersonic flows over a flat plate. Several non-linear numerical experiments suggest the existence of a secondary instability which might provide a possible route to transition. The interaction of the modes involved in this secondary instability is possibly amenable to a Floquet theory. Pertinent differences between this instability and the more common incompressible K-type instabilities are pointed out.

Erlebacher, Gordon↗
NASA NTRS1994

The stabilizing effect of compressibility in turbulent shear flow

Direct numerical simulation of turbulent homogeneous shear flow is performed in order to clarify compressibility effects on the turbulence growth in the flow. The two Mach numbers relevant to homogeneous shear flow are the turbulent Mach number M(t) and the gradient Mach number M(g). Two series of simulations are performed where the initial values of M(g) and M(t) are increased separately. The growth rate of turbulent kinetic energy is observed to decrease in both series of simulations. This 'stabilizing' effect of compressibility on the turbulent energy growth rate is observed to be substantially larger in the DNS series where the initial value of M(g) is changed. A systematic companion of the different DNS cues shows that the compressibility effect of reduced turbulent energy growth rate is primarily due to the reduced level of turbulence production and not due to explicit dilatational effects. The reduced turbulence production is not a mean density effect since the mean density remains constant in compressible homogeneous shear flow. The stabilizing effect of compressibility on the turbulence growth is observed to increase with the gradient Mach number M(g) in the homogeneous shear flow DNS. Estimates of M(g) for the mixing and the boundary layer are obtained. These estimates show that the parameter M(g) becomes much larger in the high-speed mixing layer relative to the high-speed boundary layer even though the mean flow Mach numbers are the same in the two flows. Therefore, the inhibition of turbulent energy production and consequent 'stabilizing' effect of compressibility on the turbulence (over and above that due to the mean density variation) is expected to be larger in the mixing layer relative to the boundary layer in agreement with experimental observations.

Sarkar, S.↗
NASA NTRS1994

Coupled Marangoni-Benard/Rayleigh-Benard Instability with Temperature Dependent Viscosity

The onset of convection induced by coupled surface tension gradient and buoyancy forces is investigated with temperature dependent viscosity. Both surface tension and viscosity are assumed to vary linearly with temperature. The limiting case, Ma=0, is the buoyancy driven convection problem typically referred to as the Rayleigh-Benard stability problem. The other limiting case, Ra=0, is the surface tension (gradient) driven flow problem referred to as the Marangoni-Benard problem. The equations and boundary conditions obtained from the linear analysis are solved numerically as a generalized eigenvalue problem. Neutral stability curves for different viscosity slopes have been generated for the Marangoni-Benard and Rayleigh-Benard problems. It is shown that the curves can be collapsed to a single curve by appropriately scaling the results for each of the limiting cases. The critical Marangoni number is determined as a function of the slope of the viscosity temperature variation, epsilon, for different values of the Rayleigh number. When the viscosity decreases linearly with temperature, the coupled buoyancy-surface tension problem, including the limiting cases of Ra=0 and Ma=0, is found to be more stable than the constant viscosity case.

Skarda, J. Raymond Lee↗
NASA NTRS1971

Nutational stability of a dual-spin satellite under the influence of applied reaction torques

It is assumed that since the solar paddle attachments to the hub of the spacecraft are not rigidly locked, the effect of the solar panels can be replaced by a constant reaction torque acting on the hub of the spacecraft. This could result in the satellite having an equilibrium motion about an axis displaced from the nominal axis of symmetry. The variational equations of motion are developed about such an equilibrium position using the SAS-A spacecraft as a model. Energy dissipation on the rotor as well as the main body is included. This nonautonomous set of differential equations are linearized and transformed to an autonomous set using the Liapunov reducibility theorem. The stability of the kinematically similar system is examined numerically using representative SAS-A parameters for the case when either pair of solar panels is assumed to be loosely attached. Stability is verified for small system nutation angles (0.1 degree).

Bainum, P. M.↗
NASA NTRS1972

Nutational stability of a dual-spin satellite under the influence of applied reaction torques.

The nutational stability of a dual-spin satellite under the influence of an applied reaction torque is analyzed. It is assumed that since the solar paddle attachments to the hub of the spacecraft are not rigidly locked, the effect of the solar panels can be replaced by a constant reaction torque acting on the hub of the spacecraft. This could result in the satellite having an equilibrium motion about an axis displaced from the nominal axis of symmetry. The variational equations of motion are developed about such an equilibrium position using the SAS-A spacecraft as a model. Energy dissipation on the rotor as well as the main body is included. This nonautonomous set of differential equations are linearized and transformed to an autonomous set using the Lyapunov Reducibility Theorem. The stability of the kinematically similar system is examined numerically using representative SAS-A parameters for the case when either pair of solar panels is assumed to be loosely attached. Stability is verified for small system nutation angles (0.1 degree) although the time constant associated with the least damped mode is approximately one order of magnitude larger than that for the SAS-A system without the influence of the reaction torques.

Bainum, P. M.↗
NASA NTRS1994

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Nash, Stephen G.↗