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NASA NTRS1993

Size distribution of interplanetary iron and stony particles related with deep-sea spherules

To study origin and evolution of the interplanetary dust, it is very important to investigate the size distribution. Here the changes of the size distributions of meteoroid particles due to the ablative effects during atmospheric entry were investigated by numerical computer simulation. Using the results, the pre-atmospheric size distributions of the interplanetary dust particles could be estimated from that of ablated spherules taken from deep-sea sediments. We are now analyzing deep-sea spherules from some aspects and examining if we could get any information about the interplanetary dust.

Matsuzaki, H.↗

NASA NTRS1993

An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems

It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.

Cwik, T.↗

NASA NTRS1993

Multigrid schemes for viscous hypersonic flows

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).

Swanson, R. C.↗

NASA NTRS1994

Superfluid helium sloshing dynamics induced oscillations and fluctuations of angular momentum, force and moment actuated on spacecraft driven by gravity gradient or jitter acceleration associated with slew motion

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by the gravity gradient and jitter accelerations associated with slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) for slew motion which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid-vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers have also been derived. Examples are also given for cases applicable to the AXAF-S spacecraft sloshing dynamics associated with slew motion.

Hung, R. J.↗

NASA NTRS1994

Generation of gear tooth surfaces by application of CNC machines

This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.

Litvin, F. L.↗

NASA NTRS1994

Numerical studies of the surface tension effect of cryogenic liquid helium

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose of performing scientific observation during the normal spacecraft operation is investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics has been based on the non-inertia frame spacecraft bound coordinate, and solve time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers, have been derived.

Hung, R. J.↗

NASA NTRS1994

A three-dimensional structured/unstructured hybrid Navier-Stokes method for turbine blade rows

A three-dimensional viscous structured/unstructured hybrid scheme has been developed for numerical computation of high Reynolds number turbomachinery flows. The procedure allows an efficient structured solver to be employed in the densely clustered, high aspect-ratio grid around the viscous regions near solid surfaces, while employing an unstructured solver elsewhere in the flow domain to add flexibility in mesh generation. Test results for an inviscid flow over an external transonic wing and a Navier-Stokes flow for an internal annular cascade are presented.

Tsung, F.-L.↗

NASA NTRS1995

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗

NASA NTRS1995

Application of low dissipation and dispersion Runge-Kutta schemes to benchmark problems in computational aeroacoustics

We investigate accurate and efficient time advancing methods for computational aeroacoustics, where non-dissipative and non-dispersive properties are of critical importance. Our analysis pertains to the application of Runge-Kutta methods to high-order finite difference discretization. In many CFD applications, multi-stage Runge-Kutta schemes have often been favored for their low storage requirements and relatively large stability limits. For computing acoustic waves, however, the stability consideration alone is not sufficient, since the Runge-Kutta schemes entail both dissipation and dispersion errors. The time step is now limited by the tolerable dissipation and dispersion errors in the computation. In the present paper, it is shown that if the traditional Runge-Kutta schemes are used for time advancing in acoustic problems, time steps greatly smaller than that allowed by the stability limit are necessary. Low Dissipation and Dispersion Runge-Kutta (LDDRK) schemes are proposed, based on an optimization that minimizes the dissipation and dispersion errors for wave propagation. Optimizations of both single-step and two-step alternating schemes are considered. The proposed LDDRK schemes are remarkably more efficient than the classical Runge-Kutta schemes for acoustic computations. Numerical results of each Category of the Benchmark Problems are presented. Moreover, low storage implementations of the optimized schemes are discussed. Special issues of implementing numerical boundary conditions in the LDDRK schemes are also addressed.

Hu, F. Q.↗

NASA NTRS1994

Capillary surfaces in a wedge: Differing contact angles

The possible zero-gravity equilibrium configurations of capillary surfaces u(x, y) in cylindrical containers whose sections are (wedge) domains with corners are investigated mathematically, for the case in which the contact angles on the two sides of the wedge may differ. In such a situation the behavior can depart in significant qualitative ways from that for which the contact angles on the two sides are the same. Conditions are described under which such qualitative changes must occur. Numerically computed surfaces are depicted to indicate the behavior.

Concus, Paul↗

NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem

We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.

Shu, Frank H.↗

NASA NTRS1994

Multipole moments of stellar oscillation modes

The oscillating mass 2(exp l)-pole moment, M(sub nl), of a star in a given (normalized) oscillation mode determines the energy that can be absorbed by the mode in a tidal interaction and the power radiated by the mode in gravitational waves, both of which are proportional to (absolute value of M(sub nl))(exp 2). The coefficients in the expansion of the vector fields del(r(exp l)Y(sub lm)(theta, phi)) in terms of the displacement fields of modes of given l and m are proportional to M(sub nl). This expansion leads to a sum rule sum over n(absolute value of M(sub nl))(exp 2) = constant. For stars of weak to moderate central condensation (such as neutron stars), the f-mode is well approximated by the vector field being expanded, and therefore it takes the lion's share of the sum. Thus the multipole moments of all other modes must be small. In there numerical evaluation, it is necessary to know the shape of the eigenfunctions quite precisly, since a small f-mode contamination can significantly increase the obtained values. This contamination occurs in some `hybrid' numerical computations of neutron star oscillations with relativistic equilibrium stars and Newtonian dynamics (e.g., McDermott et al. 1988). In this case, it is due to a slight inconsistency in the models and leads to a large overestimate of the power radiated in gravitational waves by modes other than the f-mode, although their oscillation periods are nearly unaffected.

Reisenegger, Andreas↗

NASA NTRS1994

Sloshing dynamics modulated angular momentum fluctuations actuated by gravity gradient acceleration associated with spacecraft slew motion

The mathematical formulation of orbital spacecraft sloshing dynamics for a partially filled cryogenic superfluid liquid helium II in a dewar container actuated by the gravity gradient acceleration associated with slew motion is studied. The Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) spacecraft is chosen as a practical example in this study. Explicit mathematical expressions which manage orbital galaxy gradient acceleration with slew motion which is acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics is based on the non-inertia frame spacecraft bound coordinates and the solution of time-dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. This study discloses the capillary effect of sloshing dynamics governed liquid-vapor interface fluctuations, angular momentum and moment fluctuations of fluid system, and also buble mass center fluctuations driven by the gravity gradient acceleration associated with slew motion which affects the stability of the orbital spacecraft fluid system in a microgravity environment.

Hung, R. J.↗

NASA NTRS1995

The effect of plasma heating on sublimation-driven flow in Io's atmosphere

The atmospheric flow on Io is numerically computed in a flat 2-D axisymmetric geometry for a sublimation atmosphere on the trailing hemisphere subjected to plasma bombardment, UV heating, and IR cooling. Calculations are performed for subsolar vapor pressures of approximately 6.5 x 10(exp -3) Pa (approximately 3 x 10(exp 18) SO2/sq cm) and 6.8 x 10(exp -4) Pa (approximately 4 x 10(exp 17) SO2/sq cm); the latter approximates the vapor pressure of F. P. Fanale et al. (1982). The amount of plasma energy deposited in the atmosphere is 20% of the plasma flow energy due to corotation (J. A. Linker et al., 1988). It is found that plasma heating significantly inflates the upper atmosphere, increasing both the exobase altitude and the amount of surface covered by more than an exospheric column of gas. This in turn controls the supply of the Io plasma torus (M. A. McGrath and R. E. Johnson, 1987). The horizontal flow of mass and energy is also important in determining the exobase altitude; and it is shown that IR cooling can be important, although our use of the equilibrium, cool-to-space approximation for a pure SO2 gas (E. Lellouch et al., 1992) may overestimate this effect. The calculated exobase altitudes are somewhat lower than those suggested by McGrath and Johnson (1987) for supplying the torus, indicating the details of the plasma energy deposition and sputter ejection rate near the exobase, as well as the IR emission from this region need to be examined. In addition, the molecules sublimed (or sputtered) from the surface are transported to the exobase in times short compared to the molecular photodissociation time. Therefore, the exobase is dominated by molecular species and the exobase is supplied by a small region of the surface.

Wong, Mau C.↗

NASA NTRS1995

Improved Method Of Bending Concentric Pipes

Proposed method for bending two concentric pipes simultaneously while maintaining void between them replaces present tedious, messy, and labor-intensive method. Array of rubber tubes inserted in gap between concentric pipes. Tubes then inflated with relatively incompressible liquid to fill gap. Enables bending to be done faster and more cleanly, and amenable to automation of significant portion of bending process on computer numerically controlled (CNC) tube-bending machinery.

Schroeder, James E.↗

NASA NTRS1995

Material processing of convection-driven flow field and temperature distribution under oblique gravity

A set of mathematical formulation is adopted to study vapor deposition from source materials driven by heat transfer process under normal and oblique directions of gravitational acceleration with extremely low pressure environment of 10(exp -2) mm Hg. A series of time animation of the initiation and development of flow and temperature profiles during the course of vapor deposition has been obtained through the numerical computation. Computations show that the process of vapor deposition has been accomplished by the transfer of vapor through a fairly complicated flow pattern of recirculation under normal direction gravitational acceleration. It is obvious that there is no way to produce a homogeneous thin crystalline films with fine grains under such a complicated flow pattern of recirculation with a non-uniform temperature distribution under normal direction gravitational acceleration. There is no vapor deposition due to a stably stratified medium without convection for reverse normal direction gravitational acceleration. Vapor deposition under oblique direction gravitational acceleration introduces a reduced gravitational acceleration in vertical direction which is favorable to produce a homogeneous thin crystalline films. However, oblique direction gravitational acceleration also induces an unfavorable gravitational acceleration along horizontal direction which is responsible to initiate a complicated flow pattern of recirculation. In other words, it is necessary to carry out vapor deposition under a reduced gravity in the future space shuttle experiments with extremely low pressure environment to process vapor deposition with a homogeneous crystalline films with fine grains. Fluid mechanics simulation can be used as a tool to suggest most optimistic way of experiment with best setup to achieve the goal of processing best nonlinear optical materials.

Hung, R. J.↗

NASA NTRS1995

On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer

Recently, Berenger introduced a Perfectly Matched Layer (PML) technique for absorbing electromagnetic waves. In the present paper, a perfectly matched layer is proposed for absorbing out-going two-dimensional waves in a uniform mean flow, generated by linearized Euler equations. It is well known that the linearized Euler equations support acoustic waves, which travel with the speed of sound relative to the mean flow, and vorticity and entropy waves, which travel with the mean flow. The PML equations to be used at a region adjacent to the artificial boundary for absorbing these linear waves are defined. Plane waves solutions to the PML equations are developed and wave propagation and absorption properties are given. It is shown that the theoretical reflection coefficients at an interface between the Euler and PML domains are zero, independent of the angle of incidence and frequency of the waves. As such, the present study points out a possible alternative approach for absorbing out-going waves of the Euler equations with little or no reflection in computation. Numerical examples that demonstrate the validity of the proposed PML equations are also presented.

Hu, Fang Q.↗

NASA NTRS1995

Studies of droplet burning and extinction

A project on droplet combustion, pursued jointly with F. L. Dryer of Princeton University, has now been in progress for many years. The project involves experiments on the burning of single droplets in various atmospheres, mainly at normal atmospheric pressure and below, performed in drop towers and designed to be performed aboard space-based platforms such as the Space Shuttle or the Space Station and currently manifest for Spacelab in the MSL-1 flight of the Space Shuttle in April of 1997. It also involves numerical computations on droplet burning, performed mainly at Princeton, and asymptotic analyses of droplet burning, performed mainly at UCSD. The focus of the studies rests primarily on time-dependent droplet-burning characteristics and on extinction phenomena. The presentation to be given here concerns the recent research on application of asymptotic methods to investigation of the flame structure and extinction of alcohol droplets. These theoretical studies are relevant to the second of the proposed space-flight tests and are currently investigating the extent to which combustion of alcohols can be described by four-step reduced chemistry similar to that which has achieved a good degree of success for alkane flames. These studies have progressed to a point at which a number of definite conclusions can now be stated. These conclusions and the reasoning that led to them are outlined.

Williams, F. A.↗