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At least 523 records · Page 29

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NASA NTRS1972

Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown

A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.

Bossel, H. H.↗

NASA NTRS1995

Modeling and simulation of a turbulent far wake

Work continued on two projects which had been started during previous years. Both projects involve calculations of the subsonic, turbulent far wake of a two-dimensional object at a Reynolds number of 1000 (based on wake momentum thickness). This flow was used as a test case for direct comparison of various turbulence models and a direct numerical simulations (DNS) of this flow were undertaken. In the turbulence model comparison studies, for any particular model tested, a unique self-similar solution was obtained far enough downstream, regardless of inlet conditions. Furthermore, different turbulence models led to different far-wake equilibrium solutions. No turbulence model could correctly predict all features of the turbulent far wake. For example, the spreading rate and turbulent shear stresses were underpredicted by all the standard models (both two-equation and full Reynolds stress models). In cases where a more correct spreading rate was achieved, it was at the expense of the turbulent kinetic energy, which was overpredicted. In general, the Algebraic Dissipation Rate Model of Gatski and Speziale, 1992, when added to any of the standard models, improved the results dramatically. Also, full Reynolds stress closure models did a much better job at predicting the shapes of both the mean and turbulence profiles, but the spreading rate was not significantly improved over that predicted by the simpler two-equation models. There are two main conclusions from these studies: First, in a comparison such as this, it is not enough to compare just one parameter, like the spreading rate. A good prediction for one parameter does not necessarily imply good predictions for all parameters in a flow. Second, since no turbulence model could correctly predict the turbulent far wake, much of the important physics of turbulent free shear flows is apparently lost by the assumptions inherent in today's methods of turbulence modeling; turbulence models must be improved. Direct simulations of this flow were begun last year in order to provide a data base through which some of the deficiencies of the existing turbulence models could be identified. Quantities such as the pressure-strain correlation, turbulent diffusion, and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. During this summer, diagnostics codes were written which will calculate the parameters mentioned above, along with other single-point and multi-point statistics. The DNS calculations are still in progress at the time of this writing. When these calculations are complete, the diagnostics codes will be applied so that the results can aid turbulence modelers. In addition, the results will show whether or not there exists a universal equilibrium turbulent far wake, independent of initial conditions.

Cimbala, John M.↗

NASA NTRS1995

Forced Convection and Sedimentation Past a Flat Plate

The steady laminar flow of a well-mixed suspension of monodisperse solid spheres, convected steadily past a horizontal flat plate and sedimenting under the action of gravity, is examined. It is shown that, in the limit as Re approaches infinity and epsilon approaches 0, where Re is the bulk Reynolds number and epsilon is the ratio of the particle radius a to the characteristic length scale L, the analysis for determining the particle concentration profile has several aspects in common with that of obtaining the temperature profile in forced-convection heat transfer from a wall to a fluid stream moving at high Reynolds and Prandtl numbers. Specifically, it is found that the particle concentration remains uniform throughout the O(Re(exp -1/2)) thick Blasius boundary layer except for two O(epsilon(exp 2/3)) thin regions on either side of the plate, where the concentration profile becomes non-uniform owing to the presence of shear-induced particle diffusion which balances the particle flux due to convection and sedimentation. The system of equations within this concentration boundary layer admits a similarity solution near the leading edge of the plate, according to which the particle concentration along the top surface of the plate increases from its value in the free stream by an amount proportional to X(exp 5/6), with X measuring the distance along the plate, and decreases in a similar fashion along the underside. But, unlike the case of gravity settling on an inclined plate in the absence of a bulk flow at infinity considered earlier, here the concentration profile remains continuous everywhere. For values of X beyond the region near the leading edge, the particle concentration profile is obtained through the numerical solution of the relevant equations. It is found that, as predicted from the similarity solution, there exists a value of X at which the particle concentration along the top side of the plate attains its maximum value phi(sub m) and that, beyond this point, a stagnant sediment layer will form that grows steadily in time. This critical value of X is computed as a function of phi(sub s), the particle volume fraction in the free stream. In contrast, but again in conformity with the similarity solution, for values of X sufficiently far removed from the leading edge along the underside of the plate, a particle-free region is predicted to form adjacent to the plate. This model, with minor modifications, can be used to describe particle migration in other shear flows, as, for example, in the case of crossflow microfiltration.

Pelekasis, Nikolaos A.↗

NASA NTRS2008

The Stationary Condensation and Radial Outflow of a Liquid Film on a Horizontal Disk

The application of capillary screen liquid acquisition devices to space-based cryogenic propulsion systems is expected to necessitate thermodynamic conditioning in order to stabilize surface tension retention characteristics. The present results have been obtained in the framework of the research of low gravity condensation-flow processes for conditioning cryogenic liquid acquisition devices. The following system is studied: On the top of a subcooled horizontal disk, a liquid film condenses from the ambient saturated vapor. The liquid is forcedly removed at the disk edge, and there is an outward radial flow of the film. Stationary regimes of the flow are uncovered such that (i) the gravity is negligible, being eclipsed by the capillary forces; (ii) the film thickness is everywhere much smaller than the disk radius; and (iii) the slow-flow lubrication approximation is valid. A nonlinear differential equation for the film thickness as a function of the radial coordinate is obtained. The (two-dimensional) fields of velocities, temperature and pressure in the film are explicitly determined by the radial profile of its thickness. The equilibrium is controlled by two parameters: (i) the vapor-disk difference of temperatures and (ii) the liquid exhaust rate. For the flow regimes with a nearly uniform film thickness, the governing equation linearizes, and the film interface is analytically predicted to have a concave-up quartic parabola profile. Thus, perhaps counter-intuitively, the liquid film is thicker at the edge and thinner at the center of the disk.

Bolshinskiy, Leonid↗

NASA NTRS1994

Electric currents in the subsolar region of the Venus lower ionosphere

The ion and electron momentum equations, along with Ampere's law, are solved for the ion and electron drift velocities and the electric field in the subsolar Venus ionosphere, assuming a partially ionized gas and a single ion species having the ion mean mass. All collision terms among the ions, electrons and neutral particles are retained in the equations. A general expression for the evolution of the magnetic field is derived and compared with earlier expressions. Subsolar region data in the altitude range 150-300 km from the Pioneer Venus Orbiter are used to calculate altitude profiles of the components of the current due to the electric field, gradients of pressure, and gravity. Altitude profiles of the ion and electron velocities as well as the electric field, electrodynamic heating, and the energy density are determined. Only orbits having a complete set of measured plasma temperatures and densities, neutral densities, and magnetic field were considered for analysis; the results are shown only for orbit 202. The vertical velocity at altitudes above 220 km is upgoing for orbit 202. This result is consistent with observations of molecular ions at high altitudes and of plasma flow to the nightside, both of which require upward velocity of ions from the dayside ionosphere. Above about 230 km the momentum equations are extremely sensitive to the altitude profiles of density, temperature, and magnetic field.

Cole, K. D.↗

NASA NTRS1989

Acoustical effects of a large ridge on low-frequency sound propagation in stationary and moving atmospheres

The effects of a ridge on a low-frequency acoustic propagation in quiescent and windy atmospheres are investigated using a parabolic approximation. A logarithmic wind-speed profile, commonly employed to model atmospheric wind currents, is modified and used to model two-dimensional atmospheric flow over a triangularly-shaped hill. The parabolic equation is solved using an implicit finite-difference algorithm. Several examples are examined to determine the combined effects of source-ridge distance, ridge dimensions, wind-speed profile, and CW source frequency on the received acoustic field.

Robertson, J. S.↗

DOE OSTI2020

Solitary wave solutions of the 2+1 and 3+1 dimensional nonlinear Dirac equation constrained to planar and space curves

Here, we study the effect of curvature and torsion on the solitons of the nonlinear Dirac equation considered on planar and space curves. Since the spin connection is zero for the curves considered here, the arc variable provides a natural setting to understand the role of curvature. We obtain for various curves in two and three dimensions the transformation of the Dirac equation to the 1 + 1 dimensional flat space Dirac equation written in terms of the arc length. Depending on the curvature, the soliton profile either narrows or expands. Our results may be applicable to yet-to-be-synthesized curved quasi-one dimensional Bose condensates.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

6300 A quantum efficiency of the recombination mechanism in the night-time F layer.

Simultaneous airglow and electron content measurements made at Hawaii are used to infer the number of 6300 and 6364 A quanta produced per electron lost in the nighttime F layer of the ionosphere. The equation of continuity of electrons is then solved numerically to obtain the electron density profile, and the amount of quenching is estimated. This leads to the number of excitations of O(super-1 D) per O2(+) recombination (epsilon). We find, for an exospheric temperature of 1100 K, epsilon is equal to 1.1 plus or minus 0.6, in good agreement with Zipf's laboratory measurement at 300 K.

Brown, W. E.↗

NASA NTRS1974

The development of jet mixing toward the asymptotic similar solution

An analytic study of the development of an initially nonsimilar jet mixing velocity profile toward the final asymptotic, similar solution, is made. The corresponding incompressible boundary layer equations are solved for each of the streams above and below the dividing streamline by using Meksyn's asymptotic method of integration. The behavior of this flow development toward the final similar solution, as influenced by the initial condition, is properly described and discussed.

Brink, D. F.↗

NASA NTRS1976

A study of efficiency in low resistivity silicon solar cells

A general device-analysis program has been utilized to study the efficiency of silicon solar cells. The analysis is applied to specific geometries of both n(+)-p and n(+)-p-p(+) solar cells, and involves a numerical solution of the basic transport and continuity equations. This approach allows solutions that are free of typical limiting assumptions involved in solving the device equations as well as solutions relating to lifetime, mobility variations, and diffused-region profiles. The analysis includes available empirical information on diffusion length, mobility, and lifetime as a function of doping, as well as a Gaussian profile for the diffused region. Results are presented which illustrate the limitations of efficiency as a function of doping. It is found that the maximum efficiencies for both types of cell converge at lower resistivities to around 16% with air-mass-zero radiation and a single-layer absorbing-SiO antireflecting film. It is also found that the minority-carrier lifetime, both in the n(+) surface and p-type bulk regions, presents serious limitations to conversion efficiency, particularly in the low-resistivity cells.

Dunbar, P. M.↗

NASA NTRS1978

Analysis of stellar occultation data - Effects of photon noise and initial conditions

An occultation light curve can be analyzed to provide information about a planetary atmosphere. Temperature, pressure, and number density profiles for the atmosphere of Mars are derived from a series of boundary layer equations, which invert equal increments of altitude (as opposed to time) in order to predict the noise quality of the occultation. Numerical results are given for a noisy isothermal light curve, with special attention to error analysis.

French, R. G.↗

NASA NTRS1983

Numerical simulation of an electrothermal deicer pad

A numerical simulation is developed to investigate the removal of ice from composite aircraft blades by means of electrothermal deicing. The model considers one dimensional, unsteady state heat transfer in the composite blade-ice body. The heat conduction equations are approximated by using the Crank-Nicolson finite difference scheme, and the phase change in the ice layer is handled using the Enthalpy method. To solve the system of equations which result, Gauss-Seidel iteration is used. The simulation computes the temperature profile in the composite blade-ice body, as well as the movement of the ice-water interface, as a function of time. This information can be used to evaluate deicer performance. The simulation can also be used to solve a variety of other heat conduction problems involving composite bodies.

Marano, J. J.↗

NASA NTRS1982

A time-dependent ice sheet model - Preliminary results

A numerical model of ice sheet flow is developed, and preliminary results are described. This model includes vertical resolution of temperature, stress, and strain rate which represents a considerable improvement over previous vertically averaged ice sheet models. The model follows the flow of ice along a flow line within an ice sheet drainage basin. Longitudinal stresses and basal sliding are included. Basal sliding is dependent on the base shear stress and a specified distribution of basal water pressure. The numerical methods used to solve the coupled set of stress and velocity equations for the static and time-evolutionary cases are discussed. A steady state profile simulating an ice stream is calculated for a particular set of input parameters, and changes in the profile are examined for different choices of parameters. Preliminary studies of response behavior are completed using a simplified ice sheet geometry with a fixed terminus or grounding line. The results of these studies illustrate ice sheet thinning in response to a lowered sea level or to a reduction in the extent of ice rises (or pinning points) within ice shelves.

Bindschadler, R. A.↗

NASA NTRS1982

Flux-vector splitting for the Euler equations

Flux-vector splitting is shown to be the simplest way of implementing upwind differencing for the full or isenthalpic Euler equations combined with the ideal-gas law. The scheme presented produces steady shock profiles with two interior zones. A disadvantage in using flux-vector splitting is that it leads to numerical diffusion of a contact discontinuity at rest. This diffusion, however, can be removed, and present research is aimed at achieving this with minimal computational effort.

Van Leer, B.↗

NASA NTRS1984

Effect of growth parameters on compositional variations in directionally solidified HgCdTe alloys

A series of Hg(1-x)Cd(x)Te alloy crystals was grown by directional solidification with compositions ranging from x = 0.2 to x = 0.4. The measured axial compositional profiles were interpreted in terms of an exact numerical solution of the appropriate diffusion equation that takes into account both the variations of the segregation coefficient and solidification rate with composition. The solutions for all growth rates agree generally well with the experimental data, and confirm earlier observations that employed approximate analytical solutions. The effective mass diffusion coefficients showed no significant composition or melt temperature dependence. Slightly higher diffusion coefficients were obtained, however, for the highest growth rates.

Szofran, F. R.↗

NASA NTRS1989

A new rotational relaxation model for use in hypersonic computational fluid dynamics

The theoretical basis for the Landau-Teller equation commonly used to model rotational nonequilibrium is reviewed. Several assumptions underlying this model are indicated to be unrealistic for rarefied hypersonic flow. A new rotational nonequilibrium model based on recent measurements up to 2000K of quantum state transition rates is presented. The new model is applied to the continuum study of normal shock wave structure using both the Burnett equations and a simplified nonlinear constitutive relation. Comparisons are made between shock wave temperature profiles generated from the new model and those generated using the Landau-Teller model. Comparisons of shock reciprocal thicknesses between experimental data for nitrogen and continuum solutions using both rotational models are made. The new rotational model agrees well with experiment up to Mach 6, and under predicts shock thickness at higher Mach numbers. The Landau-Teller model agrees well with experimental shock thickness up to Mach 3, and over predicts the thickness at higher Mach numbers. A modification to the rotational collision number in the Landau-Teller model is found to give results which agree with experimental shock thicknesses at all Mach numbers up to 11.

Chapman, Dean E.↗

NASA NTRS1991

High-resolution threshold photoionization of N2O

Pulsed field ionization (PFI) has been used in conjunction with a coherent VUV source to obtain high-resolution threshold photoelectron spectra for the (000), (010), (020), and (100) vibrational states of the N2O(+) cation. Simulations for the rotational profiles of each vibronic level were obtained by fitting the Buckingham-Orr-Sichel equations using accurate spectroscopic constants for the ground states of the neutral and the ion. The relative branch intensities are interpreted in terms of the partial waves of the outgoing photoelectron to which the ionic core is coupled and in terms of the angular momentum transferred to the core.

Wiedmann, R. T.↗

NASA NTRS1993

An evaluation of the National Meteorological Center weekly hindcast of upper-ocean temperature along the eastern Pacific equator in January 1992

The upper-ocean temperature distribution along the Pacific equator from 139 to 103 deg W was observed in January 1992 with temperature profiles recorded from a ship and inferred from an ocean general circulation model calculation involving data assimilation (i.e., hindcast). An El Nino episode was in progress. The l00-m-thick mixed layer depth, the mixed-layer temperature, and the depth-averaged temperature below the thermocline were similar in both data products. Considerable differences occurred in the representation of the 15-25 C thermocline, such as the depth-averaged temperatures above and below the 20 C isotherm, the east-west slope of the 20 C isotherm, and a 1000-km-wide depression. The longitudinal-averaged root-mean-square difference between the hindcast and observed depths of the center of the thermocline was 17 m. Most of the disparities could be attributed to a high wavenumber transient event that the model-based assimilation system was not intended to resolve.

Halpern, David↗