Results for “Numerical stability” — Page 99

NASA NTRS1993

Thermomechanical buckling of multilayered composite panels with cutouts

A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.

Noor, Ahmed K.↗

NASA NTRS1994

A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka

Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the pertubations due to other planets.

Mikkola, Seppo↗

NASA NTRS1994

Thermomechanical buckling of multilayered composite panels with cutouts

A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.

THERMOMECHANICAL BUCKLING↗

NASA NTRS1994

Thermomechanical buckling of multilayered composite panels with cutouts

A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.

Noor, Ahmed K.↗

NASA NTRS1997

On Approximate Factorization Schemes for Solving the Full Potential Equation

An approximate factorization scheme based on the AF2 algorithm is presented for solving the three-dimensional full potential equation for the transonic flow about isolated wings. Two spatial discretization variations are presented, one using a hybrid first-order/second-order-accurate scheme and the second using a fully second-order-accurate scheme. The present algorithm utilizes a C-H grid topology to map the flow field about the wing. One version of the AF2 iteration scheme is used on the upper wing surface and another slightly modified version is used on the lower surface. These two algorithm variations are then connected at the wing leading edge using a local iteration technique. The resulting scheme has improved linear stability characteristics and improved time-like damping characteristics relative to previous implementations of the AF2 algorithm. The presentation is highlighted with a grid refinement study and a number of numerical results.

Holst, Terry L.↗

NASA NTRS2001

Model of Wave Driven Flow Oscillation for Solar Cycle

At low latitudes in the Earth's atmosphere, the observed zonal flow velocities are dominated by the semi-annual and quasi-biennial oscillations with periods of 6 months and 20 to 32 months respectively. These terrestrial oscillations, the SAO and QBO respectively, are driven by wave-mean flow interactions due to upward propagating planetary-scale waves (periods of days) and small-scale gravity waves (periods of hours). We are proposing (see also Mayr et al., GRL, 2001) that such a mechanism may drive long period oscillations (reversing flows) in stellar and planetary interiors, and we apply it to the Sun. The reversing flows would occur below the convective envelope where waves can propagate. We apply a simplified, one dimensional, analytical flow model that incorporates a gravity wave parameterization due to Hines (1997). Based on this analysis, our estimates show that relatively small wave amplitudes less than 10 m/s can produce zonal flow amplitudes of 20 m/s, which should be sufficient to generate the observed variations in the magnetic field. To produce the 22-year period of oscillation, a low buoyancy frequency must be chosen, and this places the proposed flow in a region that is close to (and below) the base of the convective envelope. Enhanced turbulence associated with this low stability should help to generate the dynamo currents. With larger stability at deeper levels in the solar interior, the model can readily produce also oscillations with much longer periods. To provide an understanding of the fluid dynamics involved, we present numerical results from a 2D model for the terrestrial atmosphere that exemplify the non-linear nature of the wave interaction for which a mechanical analog is the escapement mechanism of the clock.

Mayr, Hans G.↗

NASA NTRS2004

Lunar and Planetary Science XXXV: Meteorites to and from the Moon and Mars: My Planet or Yours?

The titles in this section include: 1) Meteorites from Mars - Constraints from Numerical Modeling; 2) Iron Oxidation Products in Martian Ordinary Chondrite Finds as Possible Indicators of Liquid Water Exposure at Mars Exploration Rover Landings Sites; 3) Meteorites on Mars; 4) Sulfide Stability of Planetary Basalts; 5) Exposure and Terrestrial Histories of New Lunar and Martian Meteorites.

Source record↗

NASA NTRS2006

Convergence Acceleration for Multistage Time-Stepping Schemes

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Swanson, R. C.↗

NASA NTRS1994

(abstract) Short Time Period Variations in Jupiter's Synchrotron Radiation

The long term time variability of Jupiter's synchrotron radiation on yearly time scales has been established for some time. For many years, theorists have speculated about the effects variations in the solar wind, solar flux, Io, the Io torus, and Jupiter's magnetic field have on the ultra-relativistic electron population responsible for the emission. Early observational results suggested the additional possibility of a short term time variability, on timescales of days to weeks. In 1989 a program designed to investigate the existence of short term time variability using the 85 foot Hat Creek radio telescope operating at 1400 MHz was initiated. The availability of a dedicated telescope provided the opportunity, for the first time, to obtain numerous observations over the full Jupiter rotation period. These and future observations will enable two important studies, characterization and confirmation of possible short term variations, and the investigation of the stability of Jupiter's synchrotron emission beaming curve. Analysis of Hat Creek observations and early results from the Maryland Point Naval research Laboratory will be presented.

telescope magnetic field↗

NASA NTRS2006

AIRS: Improving Weather Forecasting and Providing New Data on Greenhouse Gases

This paper discusses the performance of AIRS and examines how it is meeting its operational and research objectives based on the experience of more than 2 yr with AIRS data. We describe the science background and the performance of AIRS in terms of the accuracy and stability of its observed spectral radiances. We examine the validation of the retrieved temperature and water vapor profiles against collocated operational radiosondes, and then we assess the impact thereof on numerical weather forecasting of the assimilation of the AIRS spectra and the retrieved temperature. We close the paper with a discussion on the retrieval of several minor tropospheric constituents from AIRS spectra.

remote sensing↗

NASA NTRS1991

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Korte, John J.↗

DOE OSTI2023

Full Technical Report: High-Rate Carbide Growth by Evaporation

Boron carbide (B 4 C) is an attractive inertial confined fusion (ICF) ablator and a unique ultra-hard material with numerous current and potential applications. What makes B 4 C attractive as an ablator is its relatively high density and the ability to form a stable glassy phase combined with excellent chemical and mechanical stability. Despite these advantages, the fabrication of B 4 C ablators has remained a challenge. Magnetron sputtering, our current frontrunner approach for B 4 C deposition, exhibits low deposition rates (< 2 μm/h) and undesirable nodular defects within the film structure that are believed to generate from the dusty plasma around the sputtering source. The goals of this project were to (1) establish alternative plasma-free, electron beam evaporation (EBE) capabilities for the deposition of thin films that are needed in mission-critical programs and; (2) demonstrate the feasibility to deposit B 4 C films at high rates by EBE in a bottom-up geometry and characterize their stoichiometry. In this feasibility study, we initially developed the capability to convert a general-use vacuum chamber into an electron beam evaporator as needed, or on demand. Then, we successfully used this setup to deposit films made of boron carbide and various other materials. By adjusting the deposition parameters and the evaporation source material, we were able to demonstrate the feasibility of reaching deposition rates as high as 8 μm/h, which is about 4 times the maximum rates obtained through sputtering methods. We predict that these values can still be further improved by implementing enhanced thermal control measures for the target source and optimizing electron beam parameters (ie. current, sweeping and frequency) since ceramic materials with similar densities to B 4 C can exhibit deposition rates of about twice this value. We anticipate that the skills and capabilities developed throughout this project will prove relevant not only to the HED and ICF campaigns but also to numerous existing and prospective applications focused on the development of ultra-hard carbide coatings. The fresh set of tools here developed will also facilitate the preparation and research on future new target materials of interest beyond B 4 C.

36 MATERIALS SCIENCE↗

NASA NTRS2018

Exploration of Double Clad Fibers for Increased Stability of Bidirectional Free Space Optical Links

Bidirectional, high data rate, low size, weight, and power (SWaP), and low cost free space optical links are needed for space communication applications to send and receive large volumes of data. We are exploring design strategies for optical transceivers to reduce SWaP and cost through increased misalignment tolerance (pointing requirement reduction) and sharing the optical transmit and receive paths (imposing optical symmetry). In applications where the detector is fiber coupled, the fiber numerical aperture is the main driver of the pointing accuracy requirement. Unfortunately, reducing the pointing requirement by increasing the fiber numerical aperture symmetrically causes instability in received power over small environmental changes. This paper explores double clad fibers as a solution to both reduce the power instability and increase the pointing accuracy tolerance. Double clad fibers can transmit a Gaussian beam from a single mode fiber and receive in a multi-mode aperture. Results show that double clad fiber have an improved misalignment tolerance and a higher stability for small changes in temperature when compared to single mode fibers and multimode fibers. Also, double clad fibers are shown to match the performance of an asymmetrical link design with a single mode transmit fiber and a multimode receive fiber.

Double Clad fibers↗

NASA NTRS2018

Exploration of Double Clad Fibers for Increased Stability of Bidirectional Free Space Optical Links

Bidirectional, high data rate, low size, weight, and power (SWaP), and low cost free space optical links are needed for space communication applications to send and receive large volumes of data. We are exploring design strategies for optical transceivers to reduce SWaP and cost through increased misalignment tolerance (pointing requirement reduction) and sharing the optical transmit and receive paths (imposing optical symmetry). In applications where the detector is fiber coupled, the fiber numerical aperture is the main driver of the pointing accuracy requirement. Unfortunately, reducing the pointing requirement by increasing the fiber numerical aperture symmetrically causes instability in received power over small environmental changes. This paper explores double clad fibers as a solution to both reduce the power instability and increase the pointing accuracy tolerance. Double clad fibers can transmit a Gaussian beam from a single mode fiber and receive in a multi-mode aperture. Results show that double clad fiber have an improved misalignment tolerance and a higher stability for small changes in temperature when compared to single mode fibers and multimode fibers. Also, double clad fibers are shown to match the performance of an asymmetrical link design with a single mode transmit fiber and a multimode receive fiber.

Double Clad fibers↗

NASA NTRS1996

The Effects of Acoustic Treatment on Pressure Disturbances From a Supersonic Jet in a Circular Duct

The pressure disturbances generated by an instability wave in the shear layer of a supersonic jet are studied for an axisymmetric jet inside a lined circular duct. For the supersonic jet, locally linear stability analysis with duct wall boundary conditions is used to calculate the eigenvalues and the eigenfunctions at each axial location. These values are used to determine the growth rates and phase velocities of the instability waves and the near field pressure disturbance patterns. The study is confined to the dominant Kelvin-Helmholtz instability mode and to the region just downstream of the nozzle exit where the shear layer is growing but is still small in size compared to the radius of the duct. Numerical results are used to study the effects of changes in the outer flow, growth in the shear layer thickness, wall distance, and wall impedance, and the effects of these changes on non-axisymmetric modes. The primary results indicate that the effects of the duct wall on stability characteristics diminish as the outer flow increases and as the jet azimuthal mode number increases. Also, wall reflections are reduced when using a finite impedance boundary condition at the wall; but in addition, reflections are reduced and growth rates diminished by keeping the imaginary part of the impedance negative when using the negative exponential for the harmonic dependence.

Dahl, Milo D.↗

NASA NTRS1993

On the spectral stability of time integration algorithms for a class of constrained dynamics problems

Incomplete field formulations have recently been the subject of intense research because of their potential in coupled analysis of independently modeled substructures, adaptive refinement, domain decomposition, and parallel processing. This paper discusses the design and analysis of time-integration algorithms for these formulations and emphasizes the treatment of their inter-subdomain constraint equations. These constraints are shown to introduce a destabilizing effect in the dynamic system that can be analyzed by investigating the behavior of the time-integration algorithm at infinite and zero frequencies. Three different approaches for constructing penalty-free unconditionally stable second-order accurate solution procedures for this class of hybrid formulations are presented, discussed and illustrated with numerical examples. The theoretical results presented in this paper also apply to a large family of nonlinear multibody dynamics formulations. Some of the algorithms outlined herein are important alternatives to the popular technique consisting of transforming differential/algebraic equations into ordinary differential equations via the introduction of a stabilization term that depends on arbitrary constants and that influences the computed so1ution.

Farhat, Charbel↗

NASA NTRS1958

Estimation of Directional Stability Derivatives at Small Angles and Subsonic and Supersonic Speeds

Methods are presented for estimating the directional stability derivative increments contributed by the stabilizing surfaces of subsonic and supersonic aircraft. These methods are strictly applicable at zero angle of attack and small angles of sideslip. The procedure of totaling the incremental coefficients to obtain an estimation of the total empennage side-force and yawing-moment coefficient derivatives is also shown, together with numerical examples. A correlation is presented between estimated and experimental incremental coefficients which indicates that the methods of this report generally estimate the increment of side force gained by the addition of a panel to within +/-10 percent of the experimental value while the yawing-moment increment is generally estimated to within +/-20 percent. This is true for both subsonic and supersonic Mach numbers. An example application of the methods to one of the problems in directional stability, that of minimizing the effect of Mach number on the side-force coefficient derivative of the empennage, is discussed.

Goodwin, Frederick K.↗

DOE OSTI2021

De Sitter decays to infinity

Bubbles of nothing are a class of vacuum decay processes present in some theories with compactified extra dimensions. We investigate the existence and properties of bubbles of nothing in models where the scalar pseudomoduli controlling the size of the extra dimensions are stabilized at positive vacuum energy, which is a necessary feature of any realistic model. We map the construction of bubbles of nothing to a four-dimensional Coleman-De Luccia problem and establish necessary conditions on the asymptotic behavior of the scalar potential for the existence of suitable solutions. We perform detailed analyses in the context of five-dimensional theories with metastable dS 4 x S 1 vacua, using analytic approximations and numerical methods to calculate the decay rate. We find that bubbles of nothing sometimes exist in potentials with no ordinary Coleman-De Luccia decay process, and that in the examples we study, when both processes exist, the bubble of nothing decay rate is typically faster. Our methods can be generalized to other stabilizing potentials and internal manifolds.

classical theories of gravity↗