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At least 253 records · Page 14

On the applicability of relativistic dispersion to auroral zone electron distributions

An examination is made to identify appropriate times to include weakly relativistic wave dispersion in calculations of auroral zone electron distributions. Two dispersion relations are examined. First, solutions are found for a ring distribution of particles around a cold ambient plasma. The solutions are found only for modes near the electron gyrofrequency. A trapped mode which is decoupled from the freely propagating R-X mode of cold plasmas is found to be the most unstable mode. Wave dispersion is examined with a spherically symmetric Dory-Guest-Harris (DGH) distribution, which describes a shell distribution that has a peak momentum larger than the thermal spread. The trapped mode is again found to be the most unstable. The analysis indicates it is beneficial to include relativistic effects whenever calculating auroral plasma distributions, and that a simple model will have sufficient accuracy.

Strangeway, R. J.↗

Compressible magnetic convection - Formulation and two-dimensional models

Details on a formulation and numerical solution of the equations of time-dependent magnetized convection are presented. Results on the transition between weak and strong magnetic fields where the highly nonlinear behavior commences are discussed, and the sensitivity of these results to the value of the magnetic resistivity, which can significantly influence the details of the interactions, is indicated. Consideration is given to the consequences of the findings for modeling stellar and solar magnetic fields.

Fox, Peter A.↗

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗

Capillary Corner Flows With Partial and Nonwetting Fluids

Capillary flow in containers or conduits with interior corners are common place in nature and industry. The majority of investigations addressing such flows solve the problem numerically in terms of a friction factor for flows along corners with contact angles below the Concus-Finn critical wetting condition for the particular conduit geometry of interest. This research effort provides missing numerical data for the flow resistance function F(sub i) for partially and nonwetting systems above the Concus-Finn condition. In such cases the fluid spontaneously de-wets the interior corner and often retracts into corner-bound drops. A banded numerical coefficient is desirable for further analysis and is achieved by careful selection of length scales x(sub s) and y(sub s) to nondimensionalize the problem. The optimal scaling is found to be identical to the wetting scaling, namely x(sub s) = H and y(sub s) = Htan (alpha), where H is the height from the corner to the free surface and a is the corner half-angle. Employing this scaling produces a relatively weakly varying flow resistance F(sub i) and for subsequent analyses is treated as a constant. Example solutions to steady and transient flow problems are provided that illustrate applications of this result.

Bolleddula, D. A.↗

Simultaneous solution for core magnetic field and fluid flow beneath an electrically conducting mantle

The effects of laterally homogeneous mantle electrical conductivity were included in steady, frozen-flux core surface flow estimation along with refinements in method and weighting. The refined method allows simultaneous solution for both the initial radial geomagnetic field component at the core-mantle boundary (CMB) and the sub-adjacent fluid motion; it also features Gauss' method for solving the non-linear inverse problem associated with steady motional induction. The tradeoff between spatial complexity of the derived flows and misfit to the weighted Definitive Geomagnetic Reference Field models (DGRF's) is studied for various mantle conductivity profiles. For simple flow and a fixed initial geomagnetic condition, a fairly high deep-mantle conductivity performs better than either insulating or weakly conducting profiles; however, a thin, very high conductivity layer at the base of the mantle performs almost as well. Simultaneous solution for both initial geomagnetic field and flow reduces the misfit per degree of freedom even more than does changing the mantle conductivity profile. Moreover, when both core field and flow are estimated, the performance of the solutions and the derived flows become insensitive to the conductivity profile.

Voorhies, Coerte V.↗

Kalman Orbit Optimized Loop Tracking

Under certain conditions of low signal power and/or high noise, there is insufficient signal to noise ratio (SNR) to close tracking loops with individual signals on orbiting Global Navigation Satellite System (GNSS) receivers. In addition, the processing power available from flight computers is not great enough to implement a conventional ultra-tight coupling tracking loop. This work provides a method to track GNSS signals at very low SNR without the penalty of requiring very high processor throughput to calculate the loop parameters. The Kalman Orbit-Optimized Loop (KOOL) tracking approach constitutes a filter with a dynamic model and using the aggregate of information from all tracked GNSS signals to close the tracking loop for each signal. For applications where there is not a good dynamic model, such as very low orbits where atmospheric drag models may not be adequate to achieve the required accuracy, aiding from an IMU (inertial measurement unit) or other sensor will be added. The KOOL approach is based on research JPL has done to allow signal recovery from weak and scintillating signals observed during the use of GPS signals for limb sounding of the Earth s atmosphere. That approach uses the onboard PVT (position, velocity, time) solution to generate predictions for the range, range rate, and acceleration of the low-SNR signal. The low- SNR signal data are captured by a directed open loop. KOOL builds on the previous open loop tracking by including feedback and observable generation from the weak-signal channels so that the MSR receiver will continue to track and provide PVT, range, and Doppler data, even when all channels have low SNR.

Young, Lawrence E.↗

Enhancements to Program LAURA for computation of three-dimensional hypersonic flow

Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.

Gnoffo, Peter A.↗

On oscillatory flow over topography in a rotating fluid

Quasi-geostrophic beta-plane motion of a homogeneous liquid over topography is considered for situations in which there is a time-periodic forcing of a zonal current. Such an oscillatory current generates a topographic Rossby wave response that has a complicated, but periodic, temporal structure. The linear solution grows resonances at all integer values of the beta-parameter. The nonlinear analysis demonstrates that for weak friction and forcing, the resonances are bent and multiple equilibria of the time-dependent Rossby wave states are possible in certain parameter ranges. While the basic forced flow in the absence of topography has no time-mean, the nonlinear amplitude equations show that a mean retrograde (westward) Eulerian zonal flow is generated in the interactions of the forced flow with the topography.

Hart, J. E.↗

Nozomi Cis-Lunar Phase Orbit Determination

Japan's Institute of Space and Astronautical Science (ISAS) launched Nozomi, its first mission to the planet Mars using the newly developed M-V launch vehicle on July 3, 1998. Scientific objectives of the mission are to study the structure and dynamics of the Martian upper atmosphere and its interaction with the solar wind. Nozomi is a cooperative mission between ISAS and the National Aeronautics and Space Administration (NASA). The NASA contribution includes navigation and tracking services provided by the Jet Propulsion Laboratory (JPL). The spacecraft also serves as an engineering demonstration of basic technology for planetary exploration. One of the new technologies was a unique trajectory, developed by ISAS, which used solar gravitational perturbations at the weak stability boundary as an aid to achieve an Earth-Mars transfer orbit. This trajectory saves approximately 120 m/s of Delta V compared to direct hyperbolic insertion and is considered an enabling technology for the mission. Nozomi was the first spacecraft to employ this trajectory and provided on-orbit validation of the technique. The trajectory was achieved by initially placing the spacecraft in a highly elliptical cis-lunar phasing orbit. Six maneuvers were performed during this period to correct injection errors and target an outbound lunar swingby in September 1998. The gravity assist from the lunar swingby raised apogee to the vicinity of the weak stability boundary. After three more targeting maneuvers, Nozomi performed an inbound lunar swingby followed immediately by a powered Earth swingby in late December 1998. A 420 m/s Trans Mars Insertion (TMI) burn at the final Earth periapsis was intended to place the spacecraft on a heliocentric trajectory leading to Mars orbit insertion in October 1999. Orbit determination for Nozomi is performed in parallel by both ISAS and the Multi-Mission Navigation (MMNAV) group at JPL. This was an advantage for the mission because each group would generate solutions based on data collected from their respective tracking networks. Spacecraft events, such as sequence uplinks and maneuvers, were generally scheduled during passes at the Usuda tracking station in Japan. As a result, maneuver design and reconstruction was derived from MMNAV solutions based on JPL tracking data obtained immediately prior to or following maneuvers. Data was also exchanged between ISAS and MMNAV so orbit determination could be performed on joint data sets in support of critical targeting late in the cis-lunar phase. In this paper, information regarding the MMNAV orbit determination effort for the first six months of the mission is presented. The spacecraft trajectory is characterized first, followed by a discussion of the orbit determination estimation procedure and models. Results from selected orbit solutions are presented and compared against reconstructed trajectories. One area of emphasis in this paper is orbit determination in the vicinity of the weak stability boundary. Precise navigation was necessary to target the second lunar swingby and the powered Earth swingby. Delivery accuracy of 150 m was required for these critical encounters, but a number of factors contributed to the general degradation of orbit determination accuracy. This included the fact that the spacecraft was at apogee, at a range of 1.7 million km and moving at less than I km/sec perpendicular to the line of sight. Nozomi was also close to zero degrees declination where there are known limitations on orbit determination performance. Finally, S-band tracking data was acquired through the Nozomi backup low gain antenna. This antenna is offset from the axis of this spin stabilized spacecraft and superimposed large signatures in the Doppler and range data. These difficulties were overcome by combining long data arcs, spanning several maneuvers, with a high fidelity solar pressure model. The model included a physically accurate representation of the spacecraft structure and a high time resolution orientation model. Observation modeling included the removal of the spin induced Doppler bias, spin signature and per pass correction of range calibration errors applied for data leading up to critical events. As a result, all orbit determination goals were met. A second area of emphasis in this paper is the JPL tracking and orbit determination effort in support of the TMI maneuver. TMI occurred out of contact with ground stations and the JPL Goldstone tracking complex had the first pass following the bum. As a result, MMNAV had the responsibility to make a rapid assessment of the maneuver performance. MMNAV made the determination that a 100 m/s under bum had occurred and promptly informed ISAS via voice lines. ISAS immediately began preparations for a correction maneuver (TMIc), which had to be performed during the next Usuda pass. The near real time assessment by MMNAV provided accurate antenna frequency and pointing updates for the spacecraft acquisition at Usuda and the close coordination between the two agencies enabled the design and successful execution of the TMc maneuver. Propellant consumption during the correction burn dictated that the mission be redesigned. ISAS developed a new plan which adds 3 full solar orbits, two Earth swingbys and one lunar swingby with arrival at Mars in January 2004. The final Mars orbit will still enable the mission to achieve all of its science objectives.

Ryne, Mark↗

Implicit multigrid Euler solutions with symmetric Total-Variation-Diminishing dissipation

A symmetric Total-Variation-Diminishing (TVD) formulation of the numerical dissipation terms has been incorporated into a diagonalized alternating direction implicit multigrid algorithm to solve the Euler equations of inviscid compressible flow. The new treatment of the dissipation makes is possible to capture both very strong and very weak shocks, virtually without oscillation for the steady flows of interest here. In addition, the TVD constraint fixes one of the two previously arbitrary constants in the formulation of the dissipation, and results in both converged solutions and convergence rates which are relatively insensitive to the choice of the remaining dissipation parameter.

Caughey, David A.↗

Computer experiments on the structure and dynamics of spiral galaxies

The evolution of an initially balanced rotating disk of stars with an initial velocity dispersion given by Toomre's local criterion was investigated by means of a computer model for isolated disks of stars. It was found that the disk is unstable against very large scale modes. A stable axisymmetric disk with a velocity dispersion much larger than that given by Toomre's criterion was generated. The final mass distribution for the disk gives a high density central core and a disk population of stars that is closely approximated by an exponential variation. Various methods and rates of cooling the hot axisymmetric disks were investigated. It was found that the cooling resulted in the development of two-arm spiral structures which persisted as long as cooling continued. An experiment was performed to induce spiral structure in a galaxy by means of the close passage of a companion galaxy. Parameters similar to those expected for M51 and its companion were used. It was found that because of the high velocity dispersion of the disturbed disk galaxy, only a weak two-arm spiral structure appeared. The evolution of a uniformly rotating disk galaxy which is a stationary solution of the collisionless Boltzmann equation was investigated for various values of the initial rms velocity dispersion. It was found that the disk becomes stable at a value of the velocity dispersion predicted by theory.

Hohl, F.↗

Turbulence and deterministic chaos

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.

Deissler, Robert G.↗

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Shortis, Trudi A.↗

Enhancing Adhesion: Relative Merits of Different Approaches

Adhesive performance is improved mainly by manipulation of the bimaterials interface zone, which is only a few molecules thick. There are three approaches to enhancement of interfacial adhesion at the molecular level. They are 1) changing the nonchemically bonded interactions across the interface from weak ones to strong ones, 2) making the true interfacial area much larger than the simple geometric area, and 3) inducing chemical bonding between the two materials forming the interface. Our goal this summer was to question some of the built-in assumptions contained within these approaches and to determine the most promising approach, both theoretically and practically, for enhancing adhesion in NASA structures. Our computations revealed that all three of these approaches have, in theory, the potential to enhance molecular adhesion approximately ten-fold. Experiments, however, revealed that this excellent level of enhancement is not likely to be reached in practice. Each approach was found to be severely limited by practical problems. In addition, some of the built-in assumptions associated with these approaches were found to be insufficient or inadequate. The first approach, changing the nonchemically bonded interactions from weak to strong, Is an example of one containing inadequate assumptions. The extensive literature on intermolecular interactions, based on solution studies, shows that certain functional group pairs interact much more strongly than others. It has always been assumed that these data can be reliably extended to systems where only one member of the pair is in solution and the other Is contained in a solid surface. Our experiments this summer demonstrated that solution data do not adequately predict the strength of functional group interaction at the solid-liquid interface. Furthermore, the strong solvents needed to dissolve the monomers or polymers to which the functional groups of interest are attached compete successfully with the solid surface for the functional group. As a result, functional groups in solution cannot pair with the complementary groups in the solid surface, and the expected enhancement of nonchemically bonded interactions is not realized. The second approach, increasing the true interfacial area, is an example of one containing inadequate assumptions and suffering from numerous practical problems. First, practitioners have assumed that material removal, such as bead blasting or etching, increases true surface area (and therefore interfacial area) in a meaningful way. Our geometric analysis demonstrated that removal methods increase area by a factor of two at most. To increase interfacial area by an order of magnitude or more. a thin layer of high porosity must be added to the substrate surface prior to application of the adhesive phase. Consistent with this finding, we attempted to create a thin layer of rigid, highly porous glass on the surface of our smooth glass substrate by means of sol-gel technology. We were unable to surmount a wide variety of practical problems and obtained only collapsed, nonporous layers. Thus this approach, appealing in principle, would require long term development and is not promising in the near term. The third approach, inducing chemical bonding at the interface, is an example of one having neither inadequate assumptions nor insurmountable practical problems. When silicate glass is the substrate, there are only a few chemical reactions that can be successfully conducted to create these chemical bonds, and these reactions usually involve silicon-containing reagents. We compared the silazane reagents to the silane reagents and found through experiment that the silazanes react with the glass surface much more readily, and under milder conditions, than the silanes. The functional groups attached to the glass surface by silazane reactions were not able to be removed by solvent extraction, elevated temperature exposure, or mechanical action. This clearly indicates that the formation of chemical bonds at the interface is the most effective approach for enhancing molecular adhesion.

Penn, L. S.↗

Courant Number and Mach Number Insensitive CE/SE Euler Solvers

It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.

Chang, Sin-Chung↗

Parasitic instabilities in magnetized, differentially rotating disks

Velikhov, Chandrasekhar, Balbus & Hawley have discovered a MHD instability of differentially rotating fluids that may explain the effective viscosity of accretion disks. If the unperturbed magnetic energy density is much less than the gas pressure, this `magnetorotational' instability (MRI) arises on small scales and is approximately incompressible. If the unperturbed field is suffiently, strong, the MRI is suppressed. We therefore ask whether the MRI mechanism can amplify even very weak initial fields until they reach equipartition with the gas pressure. We show that in the total incompressible limit, the MRI modes are exact solutions of the nonlinear fluid equations, even if the perturbed magnetic field is much larger than the unperturbed field. Also, we present a new exact solution in the opposite limit that the magnetic pressure is much larger than that of the gas. On the other hand, we show that the incompressible MRI modes are themselves subject to parasitic instabilities with instantaneous growth rates proportional to the MRI amplitude. Some of the parasitic instabilities are of the Kelvin-Helmholtz type, while others are less familiar. The eigenfunctions of the latter group suggest that they may promote rapid reconnection of the MRI field. Thus, parasitic modes may stop MRI growth at subequipartition amplitudes if it developes from a sufficiently weak initital field.

Goodman, Jeremy↗

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Hall, P.↗

Decoupled predictions of radiative heating in air using a particle simulation method

A particle simulation technique with decoupled radiation is used to estimate the radiative emission along the stagnation streamline and the radiative heating at the stagnation point of a blunt-nosed vehicle entering the earth's atmosphere at hypersonic speed. The direct simulation Monte Carlo (DSMC) method is used to compute the fluid mechanics of the weakly ionized flow. The radiative emission is computed using the NEQAIR computer code with the radiation decoupled from the flowfield solution. It is concluded that the new models make it possible to decrease the predicted total radiative heating at the stagnation point of the vehicle by a factor of 15. A comparison of the DSMC approach with a continuum flow model shows that the total predicted radiative heating estimates agree within a factor of 2.

Boyd, Iain D.↗