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At least 1,171 records · Page 65

Prominence formation in a coronal loop

A model is presented which depends on the preferential deposition of heating in the legs of a coronal loop and which produces a stable prominence-scale condensation at the loop top. Dynamic stability is attained by the subsequent adjustment of local parallel gravity by a magnetic inversion at the loop (or arcade) apex. A nonlinear numerical simulation of this process, which includes a deep chromosphere, a heating rate with a fixed dissipation length, and full solar gravity is described.

Mok, Y.↗

A fully Galerkin method for the recovery of stiffness and damping parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness and damping parameters in Euler-Bernoulli beam models is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which converges exponentially and is valid on the infinite time interval. Hence the method avoids the time-stepping which is characteristic of many of the forward schemes which are used in parameter recovery algorithms. Tikhonov regularization is used to stabilize the resulting inverse problem, and the L-curve method for determining an appropriate value of the regularization parameter is briefly discussed. Numerical examples are given which demonstrate the applicability of the method for both individual and simultaneous recovery of the material parameters.

Smith, R. C.↗

Stochastic robustness synthesis for a benchmark problem

Stochastic robustness analysis guides the synthesis of robust linear quadratic Gaussian (LQG) regulators for a benchmark control problem. Probabilities of exceeding allowable design limits, including stability, setting time, and control usage, are estimated by Monte Carlo evaluation. Robust, low-gain compensators that fulfill objectives are designed by numerically minimizing quadratic functions of these probabilities. The method is straightforward and makes use of uncomplicated design principles.

Stengel, Robert F.↗

Advanced Transportation Systems, Alternate Propulsion Subsystem Concepts

An understanding of the basic flow of of the subject hybrid model has been gained through this series of testing. Changing injectors (axial vs. radial) and inhibiting the flow between the upstream plenum and the CP section changes the basic flow structure, as evidenced by streamline and velocity contour plots. Numerous shear layer structures were identified in the test configurations; these structures include both standing and traveling vortices which may affect combustion ion stability. Standing vortices may play a role in the heat addition process as the oxidizer enters the motor, while traveling vortices may be instability mechanisms in themselves. Finally, the flow visualization and LVD measurements give insight into determining the effects of flow induced shear layers.

Source record↗

Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave break-down. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the 2-D test problem. This discrepancy is attributed to far-field boundary- condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.

Joslin, R. D.↗

Chapter 12 - Flight Envelope

The term "flight envelope" is used to refer to the boundaries of aircraft loading and flight conditions within which operation of the aircraft is satisfactory, and beyond which some aspect becomes unacceptable. This flight envelope represents, in fact, the limiting conditions arising from a matrix of inter-related flight envelopes covering the appropriate variables. Thus, for each loading (i.e., external stores configuration and its associated range of weight and center of gravity (c.g.) position) and aircraft configuration (i.e., position of undercarriage (u/c), flaps, slats, etc.), the envelopes of airspeed versus altitude, airspeed versus load factor, angle of attack versus angle of sideslip, etc., must be investigated to establish the limits within which all aspects such as handling qualities, engine behavior, structural loads, etc., remain acceptable. Flight testing of new or derivative aircraft models is carried out with the initial purpose of defining a flight envelope which is, first and foremost, safe and secondarily, which enables the effective use of the vehicle for its intended purpose. Flight testing occurs only after numerous reviews of the design and review of results from ground tests and predictions of flight characteristics in such areas as structures, aerodynamics, stability and control, flight controls (particularly fly-by-wire control systems, propulsion, etc.). Accordingly, opening and expanding the envelope is a task that must be approached cautiously, systematically, and with coordination and cooperation of the many disciplines involved in the design and test of an airplane. (Sections 8 and 10 cover test planning and safety of flight considerations, respectively). The fundamental tenet in establishing a flight envelope via flight test is risk reduction. This is reflected in the typical sequence of events leading to initial flight test - design reviews (both hardware and software), then ground test involving singular disciplines (windtunnel tests for aerodynamics, structurally loading the wing/fuselage/nacelle on a ground test article with loads anticipated to occur in flight, flight control system control law checkout, propulsion test cell runs and/or flying test bed tests, etc.), and then ground tests involving multi-disciplines (See Section 9). Only after these have been accomplished will an initial, limited, low-risk, flight envelope be established. The limited envelope will typically be in the middle of the projected final flight envelope. Subsequent flight tests will then be devoted to expanding the initial envelope by operating the airplane at increasing ranges - representing increasing risk - of engine operation, airspeeds both fast and slow, altitude, load factor both above and below 1g, centers of gravity (fore and aft), and with system/subsystem failures. Whether flight tests are to define a flight envelope on a new model airplane with the attendant new airframe, new engine(s), and new subsystems (hydraulics, pressurization, etc.), or on an airplane involving only a few of these areas such as new engines in an old airframe, the fundamental approach to establishing an envelope is the same.

H Walgemoed↗

Ice Melt, Sea Level Rise and Superstorms: Evidence from Paleoclimate Data, Climate Modeling, and Modern Observations that 2C Global Warming Could Be Dangerous

We use numerical climate simulations, paleoclimate data, and modern observations to study the effect of growing ice melt from Antarctica and Greenland. Meltwater tends to stabilize the ocean column, inducing amplifying feedbacks that increase subsurface ocean warming and ice shelf melting. Cold meltwater and induced dynamical effects cause ocean surface cooling in the Southern Ocean and North Atlantic, thus increasing Earth's energy imbalance and heat flux into most of the global ocean's surface. Southern Ocean surface cooling, while lower latitudes are warming, increases precipitation on the Southern Ocean, increasing ocean stratification, slowing deepwater formation, and increasing ice sheet mass loss. These feedbacks make ice sheets in contact with the ocean vulnerable to accelerating disintegration. We hypothesize that ice mass loss from the most vulnerable ice, sufficient to raise sea level several meters, is better approximated as exponential than by a more linear response. Doubling times of 10, 20 or 40 years yield multi-meter sea level rise in about 50, 100 or 200 years. Recent ice melt doubling times are near the lower end of the 10-40-year range, but the record is too short to confirm the nature of the response. The feedbacks, including subsurface ocean warming, help explain paleoclimate data and point to a dominant Southern Ocean role in controlling atmospheric CO2, which in turn exercised tight control on global temperature and sea level. The millennial (500-2000-year) timescale of deep-ocean ventilation affects the timescale for natural CO2 change and thus the timescale for paleo-global climate, ice sheet, and sea level changes, but this paleo-millennial timescale should not be misinterpreted as the timescale for ice sheet response to a rapid, large, human-made climate forcing. These climate feedbacks aid interpretation of events late in the prior interglacial, when sea level rose to C6-9m with evidence of extreme storms while Earth was less than 1 C warmer than today. Ice melt cooling of the North Atlantic and Southern oceans increases atmospheric temperature gradients, eddy kinetic energy and baroclinicity, thus driving more powerful storms. The modeling, paleoclimate evidence, and ongoing observations together imply that 2 C global warming above the preindustrial level could be dangerous. Continued high fossil fuel emissions this century are predicted to yield (1) cooling of the Southern Ocean, especially in the Western Hemisphere; (2) slowing of the Southern Ocean overturning circulation, warming of the ice shelves, and growing ice sheet mass loss; (3) slowdown and eventual shutdown of the Atlantic overturning circulation with cooling of the North Atlantic region; (4) increasingly powerful storms; and (5) nonlinearly growing sea level rise, reaching several meters over a timescale of 50-150 years. These predictions, especially the cooling in the Southern Ocean and North Atlantic with markedly reduced warming or even cooling in Europe, differ fundamentally from existing climate change assessments. We discuss observations and modeling studies needed to refute or clarify these assertions.

Computer simulation↗

Numerical simulations of plasma double layers

The results of analytical studies of quasi-static electric fields along geomagnetic field lines are discussed. The calculations were targeted at the structure, generation mechanisms and stability parameters. The field consists of two oppositely charged layers, either weakly or strongly charged, with an electric field between. Existence conditions are defined for the double layer field and balancing requirements are explored. Details of the simulation techniques, i.e., particle in cell and Vlasov simulations, for studying the double layer are outlined, noting that both periodic and quasi-periodic simulations are used. Solutions to Poisson's equation for fixed and floating point boundary conditions are generated. Finally, attention is also given to oblique and two-dimensional magnetic double layers.

Goertz, C. K.↗

On the stability of Galerkin methods for initial-boundary value problems for hyperbolic systems

The stability of approximating the solution of mixed initial-boundary value problems for hyperbolic systems by semidiscrete Galerkin methods is studied. It is shown that a particular straightforward Galerkin method yields an unstable approximation, and that this numerical instability is caused by an improper treatment of the boundary. Stable schemes are then presented, one of which differs from the unstable scheme only insofar as the treatment of the boundary is concerned. These stable schemes make use of a particular matrix which symmetrizes the differential system. It is therefore shown that the use of this matrix is crucial to the stability of the computations as well as for obtaining a priori bounds on the energy of the continuous system. This symmetrizing matrix is also related to the diagonalizing matrix for the system of hyperbolic equations and to the Liapunov matrix for the system of ordinary differential equations resulting from the application of Galerkin's method.

Gunzburger, M. D.↗

Algorithm for Stabilizing a POD-Based Dynamical System

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Kalb, Virginia L.↗

Effect of Under-Resolved Grids on High Order Methods

There has been much discussion on verification and validation processes for establishing the credibility of CFD simulations. Since the early 1990s, many of the aeronautical and mechanical engineering related reference journals mandated that any accepted articles in numerical simulations (without known solutions to compared with) need to perform a minimum of one level of grid refinement and time step reduction. Due to the difficulty in analysis, the effect of under-resolved grids and the nonlinear behavior of available spatial discretizations, are scarcely discussed in the literature. Here, an under-resolved numerical simulation is one where the grid spacing being used is too coarse to resolve the smallest physically relevant scales of the chosen continuum governing equations that are of interest to the numerical modeler. With the advent of new developments in fourth-order or higher spatial schemes, it has become common to regard high order schemes as more accurate, reliable and require less grid points. The danger comes when one tries to perform computations with the coarsest grid possible while still hoping to maintain numerical results sufficiently accurate for complex flows, and especially, data-limited problems. On one hand, high order methods when applies to highly coupled multidimensional complex nonlinear problems might have different stability, convergence and reliability behavior than their well studied low order counterparts, especially for nonlinear schemes such as TVD, MUSCL with limiters, ENO, WENO and discrete Galerkin. On the other hand, high order methods involve more operation counts and systematic grid convergence study can be time consuming and prohibitively expansive. At the same time it is difficult to fully understand or categorize the different nonlinear behavior of finite discretizations, especially at the limits of under-resolution when different types of bifurcation phenomena might occur, depending on the combination of grid spacings, time steps, initial conditions and numerical treatments of boundary conditions.

Yee, H. C.↗

Increased ephemeris accuracy using attitude-dependent aerodynamic force coefficients for inertially stabilized spacecraft

The FREEMAC program used to generate the aerodynamic coefficients, as well as associated routines that allow the results to be used in other software is described. These capabilities are applied in two numerical examples to the short-term orbit prediction of the Gamma Ray Observatory (GRO) and Hubble Space Telescope (HST) spacecraft. Predictions using attitude-dependent aerodynamic coefficients were made on a modified version of the PC-based Ephemeris Generation Program (EPHGEN) and were compared to definitive orbit solutions obtained from actual tracking data. The numerical results show improvement in the predicted semi-major axis and along-track positions that would seem to be worth the added computational effort. Finally, other orbit and attitude analysis applications are noted that could profit from using FREEMAC-calculated aerodynamic coefficients, including orbital lifetime studies, orbit determination methods, attitude dynamics simulators, and spacecraft control system component sizing.

Folta, David C.↗

Martian thermal boundary layers: Subhourly variations induced by radiative-conductive heat transfer within the dust-laden atmosphere-ground system

Radiative-conductive heat transfer has been investigated for the ground-atmosphere system of the planet Mars. The basic goal was the quantitative determination of time dependent vertical distributions of temperature and static stability for Southern-Hemispheric summer season and middle and polar latitudes, for both dust-free and dust-laden atmospheric conditions. The numerical algorithm which models at high spatial and temporal resolution the thermal energy transports in the dual ground-atmosphere system, is based on solution of the applicable heating rate equation, including radiative and molecular-conductive heat transport terms. The two subsystems are coupled by an internal thermal boundary condition applied at the ground-atmosphere interface level. Initial data and input parameters are based on Mariner 4, 6, 7, and 9 measurements and the JPL Mars Scientific Model. Numerical experiments were run for dust-free and dust-laden conditions in the midlatitudes, as well as ice-free and ice-covered polar regions. Representative results and their interpretation are presented. Finally, the theoretical framework of the generalized problem with nonconservative Mie scattering and explicit thermal-convective heat transfer is formulated, and applicable solution algorithms are outlined.

Pallmann, A. J.↗

Nonlinear Equations of Motion for Cantilever Rotor Blades in Hover with Pitch Link Flexibility, Twist, Precone, Droop, Sweep, Torque Offset, and Blade Root Offset

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Hodges, D. H.↗

Stress waves in an isotropic elastic plate excited by a circular transducer

Steady state harmonic stress waves in an isotropic elastic plate excited on one face by a circular transducer are analyzed theoretically. The transmitting transducer transforms an electrical voltage into a uniform normal stress at the top of the plate. To solve the boundary value problem, the radiation into a half-space is considered. The receiving transducer produces an electrical voltage proportional to the average spatially integrated normal stress over its face due to an incident wave. A numerical procedure is given to evaluate the frequency response at a receiving point due to a multiply reflected wave in the near field. Its stability and convergence are discussed. Parameterization plots which determine the particular wave whose frequency response has maximum magnitude compared with other multiple reflected waves are given for a range of values of dimensionless parameters. The effects of changes in the values of the parameters are discussed.

Karagulle, H.↗

Analog simulation of stochastic satellite response

A numerical study was performed on the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The Euler equations for the motions of satellites yielded the stochastic principal moments and a Fokker-Planck analog simulation was employed to model the response vector of a rigid satellite. White noise inputs were obtained from a random number generator. Attention was given to both fast and slow spin satellites. Responses grew with time in all cases. The growth was initially exponential and eventually reached stable values. In comparison with other theoretical techniques, the Fokker-Planck model detailed the most responses and showed that spin-stabilization is preferable for satellites with low inertial noise levels.

Huang, T. C.↗

Thermosolutal convection during directional solidification

During solidification of a binary alloy at constant velocity vertically upward, thermosolutal convection can occur if the solute rejected at the crystal-melt interface decreases the density of the melt. We assume that the crystal-melt interface remains planar and that the flow field is periodic in the horizontal direction. The time-dependent nonlinear differential equations for fluid flow, concentration, and temperature are solved numerically in two spatial dimensions for small Prandtl numbers and moderately large Schmidt numbers. For slow solidification velocities, the thermal field has an important stabilizing influence: near the onset of instability the flow is confined to the vicinity of the crystal-melt interface. Further, for slow velocities, as the concentration increases, the horizontal wavelength of the flow decreases rapidly - a phenomenon also indicated by linear stability analysis. The lateral inhomogeneity in solute concentration due to convection is obtained from the calculations. For a narrow range of solutal Rayleigh numbers and wavelengths, the flow is periodic in time.

Mcfadden, G. B.↗