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At least 883 records · Page 49

Linear density drift instabilities in very low beta plasmas A different approach

This paper reports a study of the linear Vlasov electromagnetic dispersion equation for density drift instabilities in very low beta plasmas. A uniform magnetic field and a weak uniform density gradient are assumed. This paper differs from most other studies of this topic in three important ways: (1) no low frequency or long wavelength approximations are made, (2) no gauge condition is imposed and (3) a modification of the local approximation is used which is argued to be less arbitrary than the usual local approximation. Numerical solution of the resulting dispersion equation yields stabilization of the universal density drift instability at values of beta somewhat higher than those obtained from the local approximation, and near maximum growth shows no evidence of coupling between the universal and Alfven modes.

Gary, S. P.↗

Two time scale output feedback regulation for ill-conditioned systems

Issues pertaining to the well-posedness of a two time scale approach to the output feedback regulator design problem are examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. It is shown that, under mild assumptions, minimization of this cost leads to feedback gains providing a second-order approximation of optimal full system performance. A simplified approach to two time scale feedback design is also developed, in which gains are separately calculated to stabilize the slow and fast subsystem models. By exploiting the notion of combined control and observation spillover suppression, conditions are derived assuring that these gains will stabilize the full-order system. A sequential numerical algorithm is described which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. It is shown that the algorithm converges to a local minimum under nonrestrictive assumptions. This procedure is adapted to and demonstrated for the two time scale design formulations.

Calise, A. J.↗

Decoupled direct method for sensitivity analysis in combustion kinetics

An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.

Radhakrishnan, Krishnan↗

Stability with large step sizes for multistep discretizations of stiff ordinary differential equations

One-leg and multistep discretizations of variable-coefficient linear systems of ODEs having both slow and fast time scales are investigated analytically. The stability properties of these discretizations are obtained independent of ODE stiffness and compared. The results of numerical computations are presented in tables, and it is shown that for large step sizes the stability of one-leg methods is better than that of the corresponding linear multistep methods.

Majda, George↗

Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil

A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.

Hariharan, S. I.↗

Application of the boundary element method to transient heat conduction

An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.

Dargush, G. F.↗

Numerical simulation of shock-induced combustion/detonation in a premixed H2-air mixture using Navier-Stokes equations

A numerical study was conducted to address the structural stability of the oblique detonation wave. An attempt was made to isolate the structural instability predicted by Buckmaster's (1990) linear stability analysis. For this study a detailed viscous flowfield with finite-rate chemistry was computed past a 20-deg wedge. The finite-rate chemistry was modeled by using a seven-species and seven-reaction model. Instability modes were isolated by analyzing the Fourier power spectrum of the H2O mass fraction at selected sample stations. No unstable temporal modes with dominant frequency were isolated. It was concluded that the instability which is predicted by the Buckmaster work was a high-frequency low-amplitude phenomenon. For engineering purposes, the oblique detonation wave is a stable phenomenon as long as sufficient levels of overdrive are present.

Singh, D. J.↗

Conceptual design and structural analysis of the spectroscopy of the atmosphere using far infrared emission (SAFIRE) instrument

The conceptual design and structural analysis for the Spectroscopy of the Atmosphere using Far Infrared Emission (SAFIRE) Instrument are provided. SAFIRE, which is an international effort, is proposed for the Earth Observing Systems (EOS) program for atmospheric ozone studies. A concept was developed which meets mission requirements and is the product of numerous parametric studies and design/analysis iterations. Stiffness, thermal stability, and weight constraints led to a graphite/epoxy composite design for the optical bench and supporting struts. The structural configuration was determined by considering various mounting arrangements of the optical, cryo, and electronic components. Quasi-static, thermal, modal, and dynamic response analyses were performed, and the results are presented for the selected configuration.

Moses, Robert W.↗

Nonlinearly stable compact schemes for shock calculations

The applications of high-order, compact finite difference methods in shock calculations are discussed. The main concern is to define a local mean which will serve as a reference for introducing a local nonlinear limiting to control spurious numerical oscillations while maintaining the formal accuracy of the scheme. For scalar conservation laws, the resulting schemes can be proven total-variation stable in one space dimension and maximum-norm stable in multiple space dimensions. Numerical examples are shown to verify accuracy and stability of such schemes for problems containing shocks. These ideas can also be applied to other implicit schemes such as the continuous Galerkin finite element methods.

Cockburn, Bernardo↗

Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil

A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.

Hariharan, S. I.↗

Designing reduced-order linear multivariable controllers using experimentally derived plant data

An iterative numerical algorithm for simultaneously improving multiple performance and stability robustness criteria for multivariable feedback systems is developed. The unsatisfied design criteria are improved by updating the free parameters of an initial, stabilizing controller's state-space matrices. Analytical expressions for the gradients of the design criteria are employed to determine a parameter correction that improves all of the feasible, unsatisfied design criteria at each iteration. A controller design is performed using the algorithm with experimentally derived data from a large space structure test facility. Experimental results of the controller's performance at the facility are presented.

Frazier, W. G.↗

Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

Liu, C.↗

Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness

The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.

Liu, Chaoqun↗

Temporal model of an optically pumped co-doped solid state laser

Currently, research is being conducted on the optical properties of materials associated with the development of solid state lasers in the two micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are attained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.

Wangler, T. G.↗

Transient nucleation in glasses

Nucleation rates in condensed systems are frequently not at their steady state values. Such time dependent (or transient) nucleation is most clearly observed in devitrification studies of metallic and silicate glasses. The origin of transient nucleation and its role in the formation and stability of desired phases and microstructures are discussed. Numerical models of nucleation in isothermal and nonisothermal situations, based on the coupled differential equations describing cluster evolution within the classical theory, are presented. The importance of transient nucleation in glass formation and crystallization is discussed.

Kelton, K. F.↗

Astrophysical Adaptation of Points, the Precision Optical Interferometer in Space

POINTS (Precision Optical INTerferometer in Space) would perform microarcsecond optical astrometric measurements from space, yielding submicroarcsecond astrometric results from the mission. It comprises a pair of independent Michelson stellar interferometers and a laser metrology system that measures both the critical starlight paths and the angle between the baselines. The instrument has two baselines of 2 m, each with two subapertures of 35 cm; by articulating the angle between the baselines, it observes targets separated by 87 to 93 deg. POINTS does global astrometry, i.e., it measures widely separated targets, which yields closure calibration, numerous bright reference stars, and absolute parallax. Simplicity, stability, and the mitigation of systematic error are the central design themes. The instrument has only three moving-part mechanisms, and only one of these must move with sub-milliradian precision; the other two can tolerate a precision of several tenths of a degree. Optical surfaces preceding the beamsplitter or its fold flat are interferometrically critical; on each side of the interferometer, there are only three such. Thus, light loss and wavefront distortion are minimized. POINTS represents a minimalistic design developed ab initio for space. Since it is intended for astrometry, and therefore does not require the u-v-plane coverage of an imaging, instrument, each interferometer need have only two subapertures. The design relies on articulation of the angle between the interferometers and body pointing to select targets; the observations are restricted to the 'instrument plane.' That plane, which is fixed in the pointed instrument, is defined by the sensitive direction for the two interferometers. Thus, there is no need for siderostats and moving delay lines, which would have added many precision mechanisms with rolling and sliding parts that would be required to function throughout the mission. Further, there is no need for a third interferometer, as is required when out-of-plane observations are made. An instrument for astrometry, unlike those for imaging, can be compact and yet scientifically productive. The POINTS instrument is compact and therefore requires no deployment of precision structures, has no low-frequency (i.e., under 100 Hz) vibration modes, and is relatively easy to control thermally. Because of its small size and mass, it is easily and quickly repointed between observations. Further, because of the low mass, it can be economically launched into high Earth orbit which, in conjunction with a solar shield, yields nearly unrestricted sky coverage and a stable thermal environment.

Reasenberg, Robert D.↗

Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition.

Tam, Christopher K. W.↗

Redox Interactions between Iron and Carbon in Planetary Mantles: Implications for Degassing and Melting Processes

Carbon stability in planetary mantles has been studied by numerous authors because it is thought to be the source of C-bearing atmospheres and of C-rich lavas observed at the planetary surface. In the Earth, carbonaceous peridotites and eclogites compositions have been experimentally studied at mantle conditions [1] [2] [3]. [4] showed that the fO2 variations observed in martian meteorites can be explained by polybaric graphite-CO-CO2 equilibria in the Martian mantle. Based on thermodynamic calculations [4] and [5] inferred that the stable form of carbon in the source regions of the Martian basalts should be graphite (and/or diamond), and equilibrium with melts would be a source of CO2 for the martian atmosphere. Considering the high content of iron in the Martian mantle (approx.18.0 wt% FeO; [6]), compared to Earth s mantle (8.0 wt% FeO; [7]) Fe/C redox interactions should be studied in more detail.

Martin, A.↗