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At least 685 records · Page 38
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NASA NTRS1984

Fast algorithms for combustion kinetics calculations: A comparison

To identify the fastest algorithm currently available for the numerical integration of chemical kinetic rate equations, several algorithms were examined. Findings to date are summarized. The algorithms examined include two general-purpose codes EPISODE and LSODE and three special-purpose (for chemical kinetic calculations) codes CHEMEQ, CRK1D, and GCKP84. In addition, an explicit Runge-Kutta-Merson differential equation solver (IMSL Routine DASCRU) is used to illustrate the problems associated with integrating chemical kinetic rate equations by a classical method. Algorithms were applied to two test problems drawn from combustion kinetics. These problems included all three combustion regimes: induction, heat release and equilibration. Variations of the temperature and species mole fraction are given with time for test problems 1 and 2, respectively. Both test problems were integrated over a time interval of 1 ms in order to obtain near-equilibration of all species and temperature. Of the codes examined in this study, only CREK1D and GCDP84 were written explicitly for integrating exothermic, non-isothermal combustion rate equations. These therefore have built-in procedures for calculating the temperature.

Radhakrishnan, K.↗
NASA NTRS1984

Dynamics analysis of electrodynamic satellite tethers. Equations of motion and numerical solution algorithms for the tether

The equations of motion are developed for a perfectly flexible, inelastic tether with a satellite at its extremity. The tether is attached to a space vehicle in orbit. The tether is allowed to possess electrical conductivity. A numerical solution algorithm to provide the motion of the tether and satellite system is presented. The resulting differential equations can be solved by various existing standard numerical integration computer programs. The resulting differential equations allow the introduction of approximations that can lead to analytical, approximate general solutions. The differential equations allow more dynamical insight of the motion.

Nacozy, P. E.↗
NASA NTRS1984

GCKP84--General Chemical Kinetics Code for Gas-Phase Flow and Batch Processes Including Heat Transfer Effects

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

David A Bittker↗
NASA NTRS1984

Accuracy of Three Dimensional Solid Finite Elements

The results of a study to determine the accuracy of the three dimensional solid elements available in NASTRAN for predicting displacements is presented. Of particular interest in the study is determining how to effectively use solid elements in analyzing thick optical mirrors, as might exist in a large telescope. Surface deformations due to thermal and gravity loading can be significant contributors to the determination of the overall optical quality of a telescope. The study investigates most of the solid elements currently available in either COSMIC or MSC NASTRAN. Error bounds as a function of mesh refinement and element aspect ratios are addressed. It is shown that the MSC solid elements are, in general, more accurate than their COSMIC NASTRAN counterparts due to the specialized numerical integration used. In addition, the MSC elements appear to be more economical to use on the DEC VAX 11/780 computer.

Case, W. R.↗
NASA NTRS1983

Chaotic behavior and the origin of the 3/1 Kirkwood gap

The sudden eccentricity increases discovered by Wisdom (1982) are reproduced in numerical integrations of the planar ecliptic restricted three-body problem, verifying that this phenomenon is real. Mapping derivations are qualitatively reviewed and the maximum Liapunov characteristic exponent and its importance for determining the character of a trajectory are explained. The results of a number of calculations of this exponent using the differential equations for the unaveraged three-body problem are shown and compared to equivalent calculations using a mapping. In all cases the two approaches agree whether the orbits are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the 3/1 commensurability, both in the planar-ecliptic problem and in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the 3/1 Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.

Wisdom, J.↗
NASA NTRS1983

A mechanism for plasma waves at the harmonics of the plasma frequency in the electron foreshock boundary

A bump-on-tail unstable reduced velocity distribution, constructed from data obtained at the upstream boundary of the electron foreshock by the GSFC electron spectrometer experiment on the ISEE-1 satellite, is used as the initial plasma state for a numerical integration of the 1D-Vlasov-Maxwell system of equations. The integration is carried through the growth of the instability, beyond its saturation, and well into the stabilized plasma regime. A power spectrum computed for the electric field of the stabilized plasma is dominated by a narrow peak at the Bohm-Gross frequency of the unstable field mode but also contains significant power at the harmonics of the Bohm-Gross frequency. The harmonic power is in sharp peaks which are split into closely spaced doublets. The fundamental peak at the Bohm-Gross frequency is split into a closely spaced triplet. The mechanism for excitation of the second harmonic is shown to be second order wave-wave coupling. Previously announced in STAR as N83-17315

Klimas, A. J.↗
NASA NTRS1983

The wake model for azimuthal brightness variations in Saturn's A-ring

A dynamical model offering a possible explanation for azimuthal brightness variations in Saturn's ring A is considered. The orbits of ring particles encountering a massive moonlet (radius = about 100 m) are integrated numerically. It is seen that a density wake is produced if the random velocities of the ring particles are much smaller than 1 cm/s.

Karttunen, H.↗
NASA NTRS1984

A parametric study of the effect of inlet lip shape upon the radiated sound field

Far field sound radiation predictions for four different axisymmetric inlet lips excited by different tangential acoustic modes at several cut-off ratios are presented. These results were obtained by numerical integration of a special cylindrically symmetric integral representation of the external solutions of the Helmholtz equation which yields unique solutions at all wave numbers. The paper presents plots which detail the dependence of the relative SPL (dB) in the field upon the engine inlet lip shape, the modal input, and the cut-off ratio. Examination of these data indicate that: (1) as the inlet lip becomes larger the predominant acoustic radiation peak in the field becomes narrower and moves towards the centerline of the inlet; (2) as the order of the tangential acoustic mode of the driver increases the radiated sound peak again becomes narrower but moves away from the inlet centerline; and (3) as the cut-off ratio is increased for a specific tangential acoustic mode the predominant radiation peak becomes narrower and moves towards the centerline of the inlet.

Meyer, W. L.↗
NASA NTRS1983

Manipulator interactive design with interconnected flexible elements

This paper describes the development of an analysis tool for the interactive design of control systems for manipulators and similar electro-mechanical systems amenable to representation as structures in a topological chain. The chain consists of a series of elastic bodies subject to small deformations and arbitrary displacements. The bodies are connected by hinges which permit kinematic constraints, control, or relative motion with six degrees of freedom. The equations of motion for the chain configuration are derived via Kane's method, extended for application to interconnected flexible bodies with time-varying boundary conditions. A corresponding set of modal coordinates has been selected. The motion equations are imbedded within a simulation that transforms the vector-dyadic equations into scalar form for numerical integration. The simulation also includes a linear, time-invariant controler specified in transfer function format and a set of sensors and actuators that interface between the structure and controller. The simulation is driven by an interactive set-up program resulting in an easy-to-use analysis tool.

Singh, R. P.↗
NASA NTRS1984

Dynamics of two-phase face seals

An analytic study is presented of the effects of phase change on load support for parallel and tapered face seals. Consideration is given to an adiabatic model for low Reynolds number flow. Numerical integration is carried out of the descriptive fluid equations, giving the opening force due to fluid film pressure. The loci of steady-state solutions are then plotted for water to provide curves of load support as a function of film thickness. For axial excursions of the seal rings, a quasi-steady transient analysis is made. It is found that the load support generated by fluid pressure can be multivalued for a given film thickness. Another finding is that axial disturbances of the seal rings may lead to sudden drops in load support generated by fluid pressure with three possible results. The first is that sufficient damping may permit the seal to return to the previous equilibrium operating position. The second is that the seal may collapse to an equilibrium position of smaller film thickness where face contact is more likely and a significantly higher operating temperature is assured. The third is that a limit cycle of self-sustained oscillation in the axial direction may occur if damping is sufficiently low.

Beeler, R. M.↗
NASA NTRS1984

A hydromagnetic model of corotating conductive solar wind streams

Under the assumption of quasi-azimuthal symmetry the governing equations of a steady hydromagnetic flow in a thermally conductive flux tube possess six invariants. Four of them represent constancy of mass efflux, energy efflux, angular momentum efflux and magnetic flux. Based on the entropy equation we obtain useful approximation in explicit expressions for the two remaining invariants. One of them provides the constraint which determines the compatible heat flux to ensure a vanishing pressure at infinity. Thus, the admissible solution that represents a corotating solar wind stream in terms of specified interplanetary condition can be calculated by an algebraic method, without the necessity of numerical integration. A two-point relationship is then derived, which correlates the solar wind properties at two separated interplanetary sites measured at two properly separated instants. This relationship may be applied to observational data from spacecraft and earth-bound satellites to discern the corotation feature in the solar wind.

Yeh, T.↗
NASA NTRS1984

Response of small amplitude slosh to time-dependent effective gravity

Small amplitude, linearized wave theory is used to derive a differential equation for the sloshing wave height under conditions in which a sloshing liquid drains out of a tank of circular but variable cross sectional area, allowing for changes of effective gravity with time. A few illustrative examples are given in which analytical results can be displayed and interpreted. Numerical integrations are presented for various examples of interest with respect to slosh behavior in the bottom dome of the Space Shuttle External Tank during thrust termination, particularly as this bears on scavenging of cryogens.

Traugott, S. C.↗
NASA NTRS1984

Thermal evaporation of spherical clouds - Effects of viscous stresses

The thermal evaporation of a cold spherical cloud embedded in hot gas is analyzed, including the effects of viscous stresses as well as 'saturation' of the conductive heat flux, for the case of equal electron and ion temperatures. The relevant transport properties for an H-He plasma are discussed, including the modification of these transport coefficients when temperature or velocity gradients become large. The fluid-dynamical equations for steady spherical evaporation are given and cast into dimensinless form. Numerical integration of these equations and the results are discussed, emphasizing the novel features of the viscous solutions, astrophysical implications, and uncertainties in the physics.

Giuliani, J. L., Jr.↗
NASA NTRS1984

The overshoot region at the bottom of the solar convection zone

The extent and thermal stratification of the region of convective overshoot underneath the convection zone of the sun are investigated. The phenomenon of convective overshoot in general is discussed, and some of the modal and model approaches to studying it are briefly reviewed. A detailed theoretical description of the motion of plumes in a stably stratified medium is given, leading to a 'derivation' of the plume equations from the hydrodynamic equations. Entrainment is discussed, and it is shown how the plume equations can be used to compute convective overshoot in the sun. The limitations of the plume model are addressed, arguing that a thin boundary layer must exist which separates convective and radiative regions. The results of numerical integrations of the plume equations, as applied to the region of convective overshoot underneath the solar convective zone, are discussed.

Schmitt, J. H. M. M.↗
NASA NTRS1985

Analyses of Multishaft Rotor-Bearing Response

Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).

Nelson, H. D.↗
NASA NTRS1984

Strong Langmuir turbulence

Beam-excited Langmuir turbulence in the solar wind is discussed and the criteria for wave-particle, three-wave and strong turbulence interactions are explained. The results of a numerical integration of the Zakharov equations are presented which describe the strong turbulence saturation of a weak (low-density) high energy, bump-on-tail beam instability.

Goldman, M. V.↗
NASA NTRS1984

Capture of planetesimals into a circumterrestrial swarm

The lunar origin model considered involves processing of protolunar material through a circumterrestrial swarm of particles. Once such a swarm has formed, it can gain mass by capturing infalling planetesimals and ejecta from giant impacts on the Earth, although the angular momentum supply from these sources remains a problem. Examined is the first stage of formation of a geocentric swarm by capture of planetesimals from initialy heliocentric orbits. The only plausible capture mechanism that is not dependent on very low approach velocities is the mutual collision of planetesimals passing within Earth's sphere of influence. This capture scenario was tested directly by many body numerical integration of planetesimal orbits in near Earth space. Results agree that the systematic contribution of angular momentum is insufficient to maintain an orbiting swarm under heavy bombardment. Thus, a circumterrestrial swarm can be formed rather easily, but is hard to sustain because the mean net angular momentum of a many body swarm is small.

Weidenschilling, S. J.↗
NASA NTRS1984

Analysis for leakage and rotordynamic coefficients of surface roughened tapered annular gas seals

In order to soften the effects of rub, the smooth stators of turbine gas seals are sometimes replaced by a honeycomb surface. This deliberately roughened stator and smooth rotor combination retards the seal leakage and may lead to enhanced rotor stability. However, many factors determine the rotordynamic coefficients and little is known as to the effectiveness of these honeycomb seals under various changes in the independent seal parameters. An analytical-computational method to solve for the rotordynamic coefficients of this type of compressible-flow seal is developed. The governing equations for surface roughned tapered annular gas seals are based on a modified Hirs' turbulent bulk flow model. A perturbation analysis is employed to develop zeroth and first-order perturbation equations. These equations are numerically integrated to solve for the leakage, pressure, density, and velocity for small motion of the shaft about the centered position. The resulting pressure distribution is then integrated to find the corresponding rotor-dynamic coefficients.

Nelson, C. C.↗