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NASA NTRS1993

On the tidal interaction between protostellar disks and companions

Formation of protoplanets and binary stars in a protostellar disk modifies the structure of the disk. Through tidal interactions, energy and angular momentum are transferred between the disk and protostellar or protoplanetary companion. We summarize recent progress in theoretical investigations of the disk-companion tidal interaction. We show that low-mass protoplanets excite density waves at their Lindblad resonances and that these waves are likely to be dissipated locally. When a protoplanet acquires sufficient mass, its tidal torque induces the formation of a gap in the vicinity of its orbit. Gap formation leads to the termination of protoplanetary growth by accretion. For proto-Jupiter to attain its present mass, we require that (1) the primordial solar nebula is heated by viscous dissipation; (2) the viscous evolution time scale of the nebula is comparable to the age of typical T Tauri stars with circumstellar disks; and (3) the mass distribution in the nebula is comparable to that estimated from a minimum-mass nebula model.

Lin, D. N. C.↗

NASA NTRS1993

Collective effects of temperature gradients and gravity on droplet coalescence

The interaction and coalescence of small spherical drops in dilute, homogeneous dispersions are considered theoretically under conditions, where drop motion results from gravity settling and thermocapillary migration acting simultaneously. A trajectory analysis is used to predict pairwise collision rates, and population dynamics equations are solved to predict the time evolution of the droplet size distribution. The rate of droplet collisions and growth may be reduced dramatically by antiparallel alignment of the gravitational and thermocapillary velocities. For such antiparallel alignment with the gravitational relative velocity exceeding the thermocapillary relative velocity for two widely separated drops, there is a 'collision-forbidden region' in parameter space. This occurs because the gravitational relative velocity decays more rapidly with decreasing separation distance between the drops than does the thermocapillary relative velocity, and so the resultant relative velocity along the line-of-centers from these two sources combined becomes zero at a finite separation and the drops are unable to collide. As a result, small drops which initially collide and coalesce due to thermocapillary motion will only grow until they reach a critical size for which the oppositely directed gravitational motion balances the thermocapillary motion.

Zhang, Xiaoguang↗

NASA NTRS1993

Navier-Stokes calculations for vortex rings in an unbounded domain

A computational code for the vorticity-potential method is developed for a three-dimensional bounded vorticity field. The evaluation of the boundary data for the vector potential in the code is improved so that the numerical solution simulates that in an unbounded domain to a high order. The time evolution of two vortex rings and that of an elliptic ring are investigated with this code. The cut-and-connect phenomena of vortex rings are successfully captured. The results are compared with those of asymptotic theory and the experiment. They also highlight the need for additional theoretical and numerical investigations.

Ishii, Katsuya↗

NASA NTRS1993

Energy considerations in computational aeroacoustics

A finite-volume multistage time-stepping Euler code is used to investigate the use of CFD algorithms for the direct calculation of acoustics. The 2D compressible inviscid flow about an accelerating or decelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder to the fluid, as the cylinder is moved from rest to some nonnegligible velocity, is clearly seen. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy contained in the local aerodynamic field. Systematic variation of the cylinder acceleration shows that the radiated acoustic energy depends strongly upon the rate of acceleration or deceleration. The computational grid has a large effect on the ratio of acoustic energy to nonphysical entropy associated energy, while the role of the explicit artificial viscosity seems to be of second order. The entropy term was nearly negligible in all cases the cylinder was started slowly.

Brentner, Kenneth S.↗

NASA NTRS1992

A numerical model including PID control of a multizone crystal growth furnace

This paper presents a 2D axisymmetric combined conduction and radiation model of a multizone crystal growth furnace. The model is based on a programmable multizone furnace (PMZF) designed and built at NASA Lewis Research Center for growing high quality semiconductor crystals. A novel feature of this model is a control algorithm which automatically adjusts the power in any number of independently controlled heaters to establish the desired crystal temperatures in the furnace model. The control algorithm eliminates the need for numerous trial and error runs previously required to obtain the same results. The finite element code, FIDAP, used to develop the furnace model, was modified to directly incorporate the control algorithm. This algorithm, which presently uses PID control, and the associated heat transfer model are briefly discussed. Together, they have been used to predict the heater power distributions for a variety of furnace configurations and desired temperature profiles. Examples are included to demonstrate the effectiveness of the PID controlled model in establishing isothermal, Bridgman, and other complicated temperature profies in the sample. Finally, an example is given to show how the algorithm can be used to change the desired profile with time according to a prescribed temperature-time evolution.

Panzarella, Charles H.↗

NASA NTRS1993

Mixing in a stratified shear flow: Energetics and sampling

Direct numerical simulations of the time evolution of homogeneous stably stratified shear flows have been performed for Richardson numbers from 0 to 1 and for Prandtl numbers between 0.1 and 2. The results indicate that mixing efficiency R(sub f) varies with turbulent Froude number in a manner consistent with laboratory experiments performed with Prandtl numbers of 0.7 and 700. However, unlike the laboratory results, for a particular Froude number, the simulations do not show a clear dependence on the magnitude of R(sub f) on Pr. The observed maximum value of R(sub f) is 0.25. When averaged over vertical length scales of an order of magnitude greater than either the overturning or Ozmidov scales of the flow, the simulations indicate that the dissipation rate epsilon is only weakly lognormally distributed with an intermittency of about 0.01 whereas estimated values in the ocean are 3 to 7.

Ivey, G. N.↗

NASA NTRS1993

On the large eddy simulation of turbulent flows in complex geometry

Application of the method of Large Eddy Simulation (LES) to a turbulent flow consists of three separate steps. First, a filtering operation is performed on the Navier-Stokes equations to remove the small spatial scales. The resulting equations that describe the space time evolution of the 'large eddies' contain the subgrid-scale (sgs) stress tensor that describes the effect of the unresolved small scales on the resolved scales. The second step is the replacement of the sgs stress tensor by some expression involving the large scales - this is the problem of 'subgrid-scale modeling'. The final step is the numerical simulation of the resulting 'closed' equations for the large scale fields on a grid small enough to resolve the smallest of the large eddies, but still much larger than the fine scale structures at the Kolmogorov length. In dividing a turbulent flow field into 'large' and 'small' eddies, one presumes that a cut-off length delta can be sensibly chosen such that all fluctuations on a scale larger than delta are 'large eddies' and the remainder constitute the 'small scale' fluctuations. Typically, delta would be a length scale characterizing the smallest structures of interest in the flow. In an inhomogeneous flow, the 'sensible choice' for delta may vary significantly over the flow domain. For example, in a wall bounded turbulent flow, most statistical averages of interest vary much more rapidly with position near the wall than far away from it. Further, there are dynamically important organized structures near the wall on a scale much smaller than the boundary layer thickness. Therefore, the minimum size of eddies that need to be resolved is smaller near the wall. In general, for the LES of inhomogeneous flows, the width of the filtering kernel delta must be considered to be a function of position. If a filtering operation with a nonuniform filter width is performed on the Navier-Stokes equations, one does not in general get the standard large eddy equations. The complication is caused by the fact that a filtering operation with a nonuniform filter width in general does not commute with the operation of differentiation. This is one of the issues that we have looked at in detail as it is basic to any attempt at applying LES to complex geometry flows. Our principal findings are summarized.

Ghosal, Sandip↗

NASA NTRS1991

Excited state dynamics of thulium ions in yttrium aluminum garnets

The processes that take place in the excited states of a trivalent Thulium (Tm) ion in an Yttrium Aluminum Garnet (YAG) crystal, being relevant to the use of this system for laser applications, have been the object of several studies. We have reexamined this system focusing our attention on the dynamics of Tm following its excitation in the H-3(sub 4) level. Under these conditions the system relaxes through a cross-relaxation process. H-3(sub 4) yields F-3(sub 4), H-3(sub 6) yields F-3(sub 4), whose rate depends upon both the concentration of the Tm ion and the temperature of the crystal. The excitation spectrum obtained by monitoring the 1.8 micron emission of Tm (due to the F-3(sub 4) yields H-3(sub 6) transition) indicates an increase in the contribution to this emission from the H-3(sub 4) level relative to the H-3(sub 5) level as the Tm concentration increases; this shows the increased role played by the H-3(sub 4) level in pumping the infrared emission. Correspondingly, the duration of the luminescence originating in the H-3(sub 4) level is shortened as the concentration of Tm increases. The concentration quenching of this lifetime can be fit to a model which assumes that the cross-relaxation is due to a dipole-dipole interaction; from this fit, the intrinsic Tm lifetime in the absence of cross relaxation can be derived. We have used this lifetime to calculate the rate of the cross-relaxation process. We have evaluated this rate as a function of the temperature and found it to be fastest at 77 K. We have also calculated the microscopic interaction parameters for the cross-relaxation process by using two independent experimental features: (1) the time evolution of the emission from the H-3(sub 4) level; and (2) the spectral overlap between the H-3(sub 4) yields F-3(sub 4) emission and the H-3(sub 6) yields F-3(sub 4) absorption. We have also considered the migration of excitation among the Tm ions in the F-3(sub 4) level and calculated the relevant microparameter by the use of the relevant spectral overlap. The data are consistent with the model in which the Tm ions, once excited into the H-3(sub 4) level decay by cross-relaxation to the F-3(sub 4), and then transfer rapidly their energy to other Tm ions.

Armagan, G.↗

NASA NTRS1994

Observational constraints on black hole accretion disks

We review the empirical constraints on accretion disk models of stellar-mass black holes based on recent multiwavelength observational results. In addition to time-averaged emission spectra, the time evolutions of the intensity and spectrum provide critical information about the structure, stability, and dynamics of the disk. Using the basic thermal Keplerian disk paradigm, we consider in particular generalizations of the standard optically thin disk models needed to accommodate the extremely rich variety of dynamical phenomena exhibited by black hole candidates ranging from flares of electron-positron annihilations and quasiperiodic oscillations in the X-ray intensity to X-ray novae activity. These in turn provide probes of the disk structure and global geometry. The goal is to construct a single unified framework to interpret a large variety of black hole phenomena. This paper will concentrate on the interface between basic theory and observational data modeling.

Liang, Edison P.↗

NASA NTRS1994

On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate

The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.

Webb, J. C.↗

NASA NTRS1993

Simulated orbiter lift-off acceleration - A stochastic model

A simple procedure for generating synthetic orbiter liftoff acceleration is described. This stochastic method is based on a filtered white noise model which accounts for the nonstationary time evolution of amplitude and frequency content of orbiter lift-off accelerations. The example of Space Transportation System STS-41 Z-acceleration is carefully examined, and the corresponding synthetic orbiter lift-off accelerations model was developed. It is shown that the resulting simulated accelerations preserve significant properties of the original record. Statistically based acceleration response spectra curves for the simulated orbiter lift-off excitations are also evaluated and the results are compared with those for the actual flight data.

Lee-Glauser, Gina↗

NASA NTRS1993

An introduction to wavelet analysis in oceanography and meteorology - With application to the dispersion of Yanai waves

Wavelet analysis is a relatively new technique that is an important addition to standard signal analysis methods. Unlike Fourier analysis that yields an average amplitude and phase for each harmonic in a dataset, the wavelet transform produces an instantaneous estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time-dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. By studying the dispersion of Yanai waves in a reduced gravity equatorial model, the usefulness of the transform is demonstrated. The group velocity is measured directly over a finite range of wavenumbers by examining the time evolution of the transform. The results agree well with linear theory at higher wavenumber but the measured group velocity is reduced at lower wavenumbers, possibly due to interaction with the basin boundaries.

Meyers, Steven D.↗

NASA NTRS1994

Ignition dynamics of a laminar diffusion flame in the field of a vortex embedded in a shear flow

The role of streamwise-spanwise vorticity interactions that occur in turbulent shear flows on flame/vortex interactions is examined by means of asymptotic analysis and numerical simulation in the limit of small Mach number. An idealized model is employed to describe the interaction process. The model consists of a one-step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are then allowed to mix and react in the presence of a streamwise vortex embedded in a shear flow. It is found that the interaction of the streamwise vortex with shear gives rise to small-scale velocity oscillations which increase in magnitude with shear strength. These oscillations give rise to regions of strong temperature gradients via viscous heating, which can lead to multiple ignition points and substantially decrease ignition times. The evolution in time of the temperature and mass-fraction fields is followed, and emphasis is placed on the ignition time and structure as a function of vortex and shear strength.

Macaraeg, Michele G.↗

NASA NTRS1994

Coagulation algorithms with size binning

The Smoluchowski equation describes the time evolution of an aerosol particle size distribution due to aggregation or coagulation. Any algorithm for computerized solution of this equation requires a scheme for describing the continuum of aerosol particle sizes as a discrete set. One standard form of the Smoluchowski equation accomplishes this by restricting the particle sizes to integer multiples of a basic unit particle size (the monomer size). This can be inefficient when particle concentrations over a large range of particle sizes must be calculated. Two algorithms employing a geometric size binning convention are examined: the first assumes that the aerosol particle concentration as a function of size can be considered constant within each size bin; the second approximates the concentration as a linear function of particle size within each size bin. The output of each algorithm is compared to an analytical solution in a special case of the Smoluchowski equation for which an exact solution is known . The range of parameters more appropriate for each algorithm is examined.

Statton, David M.↗

NASA NTRS1994

A note on two-dimensional asymptotic magnetotail equilibria

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two-dimensional, at least in an asymptotic sense (B(sub z)/B (sub x)) = epsilon much less than 1. The necessary two-dimensionality is described by a rather arbitrary function f(x). We utilize the free function f(x) to construct two-dimensional magnetotail equilibria are 'equivalent' to current sheets in empirical three-dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two-dimensional MHD equilibria reflect some of the realistic, observation-based, aspects of three-dimensional models. For high Kp values the three-dimensional models do not fit the asymptotic MHD equlibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.

Voigt, Gerd-Hannes↗

NASA NTRS1994

Hard X-rays from SN 1993J

The Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Observatory observed SN 1993J during three intervals centered approximately 12, 30, and 108 days after its outburst. Hard X-ray emission was detected in the first two of these intervals. No emission was seen in the third observation or in two earlier observations in 1991 and 1992. The coincidence of the observed excess with the outburst of SN 1993J and the consistency of the spectra and time evolution with those seen at lower energies by ROSAT and ASCA (Astro-D) argue that the observed emission is indeed from SN 1993J. It is probably due to the interaction of the fast supernova ejecta with circumstellar material. The luminosity, 5 x 10(exp 40) ergs/sec (50-150 keV) in the first interval, is significantly larger than predicted. Extrapolating the spectrum to a few keV accounts for most or all of the observed emission at low energy. The observed high temperature, 10(exp 9) K, is easily obtained in the shocked circumstellar matter, but a surprisingly high density is required there to give the observed luminosity, and little or no additional X-ray emission from denser shocked supernova ejecta is allowed. The hard emission might also be explained in terms of the shocked supernova ejecta itself with unexpectedly high temperature.

Leising, M. D.↗

NASA NTRS1994

Quasi-biennial oscillations of ozone and diabatic circulation in the equatorial stratosphere

The quasi-biennial oscillation (QBO) in ozone in the equatorial stratosphere is obtained by analyzing the Stratospheric Aerosol and Gas Experiment (SAGE) data from 1984 to 1989. The phase of the ozone QBO in the lower stratosphere is found to precede the zonal wind QBO by several months as opposed to the theoretically expected in-phase relationship between the two. A mechanistic model is developed to explore possible reasons for this disagreement. The model is capable of simulating the actual time evolution of the ozone QBO by introducing the observed zonal wind profile as input. The modeled results confirm the conventional view that the ozone QBO is generated by the vertical ozone advection that is driven to maintain the temperature structure against radiative damping. However, a series of experiments emphasizes the importance of the feedback of the ozone QBO to the diabatic heating through the absorption of solar radiation. Due to this effect, the phase of the ozone QBO shifts up to a quarter cycle ahead and approaches that of the temperature QBO. Because of this inphase relationship, the feedback of the ozone QBO to the diabatic heating acts to compensate for the radiative damping of the temperature structure, thus reducing the magnitude of the induced diabatic circulation. Because the reduction of the magnitude of the vertical motion facilitates downward transport of easterly momentum by the mean flow, this feedback process can help to resolve the insufficiency of the easterly momentum in driving the dynamical QBO in general circulation models (GCMs). It should be emphasized that more sophisticated models that allow for full interaction between the chemical species and radiative and dynamical processes should be developed to improve our understanding of both dynamical and ozone QBOs.

Hasebe, Fumio↗

NASA NTRS1994

Time-dependent simulation of cosmic-ray shocks, including Alfven transport

Time evolution of plane, cosmic-ray modified shocks has been simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven-wave energy transport equations. Nonlinear feedback from the cosmic rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier, Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the timescale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.

Jones, T. W.↗