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Edge-defined, film-fed growth process allows both tubular shapes and single crystallinity to be achieved. Beta alumina in single crystal form makes possible membranes with improved conductivities. Single crystal membranes also eliminate problems associated with electrical short circuiting of membrane due to possible sodium metal diffusion.
The NASA/MSFC multilayer diffusion models are discribed which are used in applying meteorological information to the estimation of toxic fuel hazards resulting from the launch of rocket vehicle and from accidental cold spills and leaks of toxic fuels. Background information, definitions of terms, description of the multilayer concept are presented along with formulas for determining the buoyant rise of hot exhaust clouds or plumes from conflagrations, and descriptions of the multilayer diffusion models. A brief description of the computer program is given, and sample problems and their solutions are included. Derivations of the cloud rise formulas, users instructions, and computer program output lists are also included.
A rational approach to the correlation of boundary layer mass transport rates, applicable to many commonly encountered laminar flow conditions with thermal diffusion and/or variable properties, is outlined. The correlation scheme builds upon already available constant property blowing/suction solutions by introducing appropriate correction factors to account for the additional ('pseudo' blowing and source) effects identified with variable properties and thermal diffusion. Applications of the scheme to the particular laminar boundary layer mass transfer problems considered herein (alkali and transition metal compound vapor transport) indicates satisfactory accuracy up to effective blowing factors equivalent to about one third of the 'blow off' value. As a useful by-product of the variable property correlation, we extend the heat-mass transfer analogy, for a wide range of Lewis numbers, to include variable property effects.
Although there is growing observational and theoretical evidence for many disk-shaped objects of astrophysical interest, spherical geometry is assumed in most radiative transfer models. Recently we generalized the quasi-diffusion method developed by Leung (1975, 1976) for spherical geometry to solve the problem of scattering, absorption, and reemission by dust grains in a medium of disk geometry. The method is applicable to a variety of astronomical sources whose dynamics are angular-momentum dominated and hence not accurately treated by spherical geometry, e.g., protoplanetary nebulae, circumstellar disks, bipolar-flow molecular clouds, accretion disks and disk galaxies. Using this technique and realistic grain opacities we construct theoretical models to determine self-consistently the dust temperature distribution and infrared emission from disk-shaped, quiescent dark globules heated externally by the intersteller radiation field. The effects of the following parameters on the temperature structure and the emergent spectrum are studied: grain type (graphite and silicate), optical depth, density inhomogeneity, and degree of disk flattening. The disk models are characterized by an aspect ratio and an optical depth at 0.55 microns. For inhomogeneous models, a gaussian density distribution is assumed such that the ratio of central to surface density is 100. To study the effects of source geometry, we also compare results for models with spherical and disk geometry. In this case both models have the same radius and central optical depth, the disk models having a 1:1 aspect ratio. While the dust temperature distributions in the two cases are very similar, the emergent flux for the disk model depends sensitively on the viewing angle. For clouds which are unresolved, one would expect, since the thermal emission is isotropic in the neighborhood of an emitting grain, and since the emission (in the far infrared) is optically thin, that the emergent flux spectrum should be characteristic only of the dust temperature, and independent of viewing angle. However, because of the lack of complete symmetry and the resulting radiation anisotropy, this is found not to be the case for the disk models. Angle is that it implies a large uncertainty in estimating the radiation dust mass.
This paper describes a method, called CONDIF, which retains the essential nature of the central difference scheme (CDS) but eliminates the over- and under-shoots. It modifies the CDS by introducing a controlled amount of numerical diffusion based on local gradients. The results obtained for a number of test problems show that the CONDIF is significantly more accurate than the hybrid scheme when the Peclet number is very high and the flow is at large angles to the grid. In the worst case, it yields results similar to those of the hybrid scheme. Though the CONDIF is unconditionally stable, under some conditions the rate of convergence deteriorates as the grid Peclet number is increased. Efforts are currently underway to develop a faster converging variation of CONDIF.
The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is considered. The domain identification treated is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficiency of the theoretical ideas are reported.
Report discusses use of explicit exponential finite-difference technique to solve various diffusion-type partial differential equations. Study extends technique to transient-heat-transfer problems in one dimensional cylindrical coordinates and two and three dimensional Cartesian coordinates and to some nonlinear problems in one or two Cartesian coordinates.
The effects of gravity level elevation in a centrifuge on the onset of salt finger convection in a double-diffusive system are examined. It is shown that the steady onset of salt finger convection in a double-diffusive layer is exactly analogous to the small-gap Taylor-Couette problem. The results presented by Chandrasekhar (1961) for the Taylor-Couette problem are extended to cover a wider range of application in the present case.
Techniques used to explain the nature of the optical effects of clouds on the light produced by lightning include a Monte Carlo simulation, an equivalent medium approach, and methods based on Boltzmann transport theory. A cuboidal cloud has been considered using transform methods and a diffusion approximation. Many simplifying assumptions have been used by authors to make this problem tractable. In this report, the cloud will have a spherical shape and its interior will consist of a uniform distribution of identical spherical water droplets. The source will be modeled as a Hertz dipole, electric or magnetic, inside or outside the cloud. An impulsive source is used. Superposition may be employed to obtain a sinusoid within an envelope which describes a lightning event. The problem is investigated by transforming to the frequency domain, obtaining Green's functions, and then using the Cagniard-DeHoop method to symbolically recover the time domain solution.
The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics.
Near-field and far-field noise surveys were made of the supersonic The exhaust jet of the Langley 9- by 6-foot thermal structures tunnel. The jet had a thrust rating of approximately 475,000 pounds. The sound power radiated was found to be about 3.6 x 10(exp 6) watts, and on an acoustical-mechanical efficiency basis this value is in reasonable agreement with data for smaller supersonic jets and for rocket engines of other investigations. Octave-band analyses of the near-field noise show that the maximum sound pressure levels in the low-frequency bands are greatest downstream, whereas maximum sound pressure levels in the high-frequency bands were greatest near the jet exit. A comparison of near-field noise measurements is made with data previously obtained for rocket engines. Noise survey measurements of the original jet are compared with similar data obtained after the addition of a 97-foot-long exit diffuser section, and an example of the application of this facility to the problem of acoustic environmental testing of a large space capsule is cited.
High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.
The candle flame in both normal and microgravity is non-propagating. In microgravity, however, the candle flame is also non-convective where (excepting Stefan flow) pure diffusion is the only transport mode. It also shares many characteristics with another classical problem, that of isolated droplet combustion. Given their qualitatively similar flame shapes and the required heat feedback to condensed-phase fuels, the gas-phase flow and temperature fields should be relatively similar for a droplet and a candle in reduced gravity. Unless the droplet diameter is maintained somehow through non-intrusive replenishment of fuel, the quasi-steady burning characteristics of a droplet can be maintained for only a few seconds. In contrast, the candle flame in microgravity may achieve a nearly steady state over a much longer time and is therefore ideal for examining a number of combustion-related phenomena. In this paper, we examine candle flame behavior in both short-duration and long-duration, quiescent, microgravity environments. Interest in this type of flame, especially 'candle flames in weightlessness', is demonstrated by very frequent public inquiries. The question is usually posed as 'will a candle flame burn in zero gravity', or, 'will a candle burn indefinitely (or steadily) in zero gravity in a large volume of quiescent air'. Intuitive speculation suggests to some that, in the absence of buoyancy, the accumulation of products in the vicinity of the flame will cause flame extinction. The classical theory for droplet combustion with its spherically-shaped diffusion flame, however, shows that steady combustion is possible in the absence of buoyancy if the chemical kinetics are fast enough. Previous experimental studies of candle flames in reduced and microgravity environments showed the flame could survive for at least 5 seconds, but did not reach a steady state in the available test time.
This paper presents the experimental and theoretical results for expanding methane and ethylene diffusion flames in microgravity. A small porous sphere made from a low-density and low-heat-capacity insulating material was used to uniformly supply fuel at a constant rate to the expanding diffusion flame. A theoretical model which includes soot and gas radiation is formulated but only the problem pertaining to the transient expansion of the flame is solved by assuming constant pressure infinitely fast one-step ideal gas reaction and unity Lewis number. This is a first step toward quantifying the effect of soot and gas radiation on these flames. The theoretically calculated expansion rate is in good agreement with the experimental results. Both experimental and theoretical results show that as the flame radius increases, the flame expansion process becomes diffusion controlled and the flame radius grows as gamma t. Theoretical calculations also show that for a constant fuel mass injection rate a quasi-steady state is developed in the region surrounded by the flame and the mass flow rate at any location inside this region equals the mass injection rate.
Over the past five years we have used our extensive CO surveys of the Galaxy and M31 in conjunction with spacecraft observations to address central problems in galactic structure and the astrophysics of molecular clouds. These problems included the nature of the molecular ring and its relation to the spiral arms and central bar, the cosmic ray distribution, the origin of the diffuse X-ray background, the distribution and properties of x-ray sources and supernova remnants, and the Galactic stellar mass distribution. For many of these problems, the nearby spiral M31 provided an important complementary perspective.
Over the course of this grant we used various spacecraft surveys of the Galaxy and M31 in conjunction with our extensive CO spectral line surveys to address central problems in galactic structure and the astrophysics of molecular clouds. These problems included the nature of the molecular ring and its relation to the spiral arms and central bar, the cosmic ray distribution, the origin of the diffuse X-ray background, the distribution and properties of x-ray sources and supernova remnants, and the Galactic stellar mass distribution. For many of these problems, the nearby spiral M31 provided an important complementary perspective. Our CO surveys of GMCs (Galactic Molecular Clouds) were crucial for interpreting Galactic continuum surveys from satellites such as GRO (Gamma Ray Observatory), ROSAT (Roentgen Satellite), IRAS (Infrared Astronomy Satellite), and COBE (Cosmic Background Explorer Satellite) because they provided the missing dimension of velocity or kinematic distance. GMCs are a well-defined and widespread population of objects whose velocities we could readily measure throughout the Galaxy. Through various emission and absorption mechanisms involving their gas, dust, or associated Population I objects, GMCs modulate the galactic emission in virtually every major wavelength band. Furthermore, the visibility. of GMCs at so many wavelengths provided various methods of resolving the kinematic distance ambiguity for these objects in the inner Galaxy. Summaries of our accomplishments in each of the major wavelength bands discussed in our original proposal are given