Results for “Conditional diffusion models” — Page 19

NASA NTRS1984

Calculation of vaporization rates assuming various rate determining steps: Application to the resistojet

The various steps that could control the vaporization rate of a material are discussed. These steps include the actual vaporization, flow rate of matrix gas, chemical reaction, gas diffusion, and solid state diffusion. The applicable equations have been collected from diverse appropriate sources, and their use is explained. Rate equations are derived for conditions where more than one step is rate controlling. Calculations are made for two model materials: rhenium which vaporizes congruently, and tantalum carbide which vaporizes incongruently. The case of vaporization under thermal gradient conditions is also treated. The existence of a thermal gradient in the resistojet means that the vaporization rate of a material may be only one thousandth of that predicted under isothermal conditions. Calculations show that rhenium might have a 100,000 hr lifetime at temperature in a 2500 C resistojet. Tantalum carbide would have a life of only 660 sec under similar conditions.

May, C. E.↗

NASA NTRS1982

A model of Martian slope winds - Implications for eolian transport

Observations of dark Martian wind streaks not associated with visible topographic points of origin (coalesced dark streaks) show these features to favor regions with slopes of 1-10 deg. To investigate the circulation over such slopes, a Boussinesq fluid is adopted and a constant eddy diffusivity parameterization is assumed for small-scale mixing. The equations of motion are scaled to determine the range of slopes over which a strong local circulation due to slope winds can exist. For nighttime conditions, the estimated range compares well with the observed range of slopes favored by coalesced dark streaks. For daytime conditions, the slope wind solution is not valid. A simple one-dimensional analytic model is solved to determine friction velocities and velocity and temperature profiles. For reasonable choices of the input parameters, friction velocities and wind velocities suggestive of active downslope eolian transport on slopes of 1-10 deg are found. Friction velocities are largest over surfaces with low thermal inertia and large roughness length.

Magalhaes, J.↗

NASA NTRS1986

Modeling of ion acceleration through drift and diffusion at interplanetary shocks

A test particle simulation designed to model ion acceleration through drift and diffusion at interplanetary shocks is described. The technique consists of integrating along exact particle orbits in a system where the angle between the shock normal and mean upstream magnetic field, the level of magnetic fluctuations, and the energy of injected particles can assume a range of values. The technique makes it possible to study time-dependent shock acceleration under conditions not amenable to analytical techniques. To illustrate the capability of the numerical model, proton acceleration was considered under conditions appropriate for interplanetary shocks at 1 AU, including large-amplitude transverse magnetic fluctuations derived from power spectra of both ambient and shock-associated MHD waves.

Decker, R. B.↗

NASA NTRS1977

Gravitational effects on chemically reacting laminar boundary layer flows over a horizontal flat plate

A theoretical study of the chemically reacting laminar boundary layer flow over a horizontal flat plate with gravitationally induced buoyant force is presented. A diffusion flame sheet model was used to describe the combustion process. The effects of gravity on the purely force convection flow can be characterized by a dimensionless coordinate quantity, which is involved in the generation of the governing equations. A numerical solution of the zero and first order governing equations subject to the appropriate physical boundary conditions was obtained. It is shown that the cross stream buoyancy induced body force acts effectively to produce a streamwise pressure gradient in the fluid adjacent to the plate surface. It is concluded that buoyancy plays an important role in boundary layer diffusion flames.

Lavid, M.↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS2010

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

Allgood, Daniel C.↗

NASA NTRS2012

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Pohorille, Andrew↗

NASA NTRS1979

Diffusion approximation for large absorption in radiative transfer

A new diffusion model is developed for radiative transfer in particulate media. It includes the effects of higher Legendre moments while avoiding the mathematical complexities of solving multiple coupled differential moment equations and satisfying higher-order boundary conditions. The method accurately extrapolates the conventional Eddington approximation to problems involving large absorption. Although the simplifying assumptions limit the model to nonbeam incidence and spatial homogeneity of the scattering material, they are nonrestrictive with regard to the size and shape of the medium, the character of background reflections, and the type of phase function.

Meador, W. E.↗

NASA NTRS1985

Coupled low-energy - ring current plasma diffusion in the Jovian magnetosphere

The outwardly diffusing Iogenic plasma and the simultaneously inwardly diffusing ring current plasma in the Jovian magnetosphere are described using a coupled diffusion model which incorporates the effects of the pressure gradient of the ring current into the cross-L diffusion coefficient. The coupled diffusion coefficient is derived by calculating the total energy available to drive the diffusion process. The condition is imposed that the diffusion coefficient takes on a local minimum value at some point in the region L = 7-8, at which point the gradient of the Io plasma density is specified as ramp value given by Siscoe et al. (1981). The hypothesis that the pressure gradient of the ring current causes the diminution of radial plasma transport is tested, and solution profiles for the Iogenic and ring current plasma densities are obtained which imply that the Io plasma ramp is caused by a high-density, low-energy component of the ring current hitherto unobserved directly.

Summers, D.↗

NASA NTRS1990

DSMC calculations for the double ellipse

The direct simulation Monte Carlo (DSMC) method involves the simultaneous computation of the trajectories of thousands of simulated molecules in simulated physical space. Rarefied flow about the double ellipse for test case 6.4.1 has been calculated with the DSMC method of Bird. The gas is assumed to be nonreacting nitrogen flowing at a 30 degree incidence with respect to the body axis, and for the surface boundary conditions, the wall is assumed to be diffuse with full thermal accommodation and at a constant wall temperature of 620 K. A parametric study is presented that considers the effect of variations of computational domain, gas model, cell size, and freestream density on surface quantities.

Moss, James N.↗

NASA NTRS1990

Three-dimensional modelling of horizontal chemical vapor deposition. I - MOCVD at atmospheric pressure

A systematic numerical study of the MOCVD of GaAs from trimethylgallium and arsine in hydrogen or nitrogen carrier gas at atmospheric pressure is reported. Three-dimensional effects are explored for CVD reactors with large and small cross-sectional aspect ratios, and the effects on growth rate uniformity of tilting the susceptor are investigated for various input flow rates. It is found that, for light carrier gases, thermal diffusion must be included in the model. Buoyancy-driven three-dimensional flow effects can greatly influence the growth rate distribution through the reactor. The importance of the proper design of the lateral thermal boundary conditions for obtaining layers of uniform thickness is emphasized.

Ouazzani, Jalil↗

NASA NTRS2001

Characteristics of Non-Premixed Turbulent Flames in Microgravity

This project is concerned with the characteristics of turbulent hydrocarbon (primarily propane) gas-jet diffusion flames in microgravity. A microgravity environment provides the opportunity to study the structure of turbulent diffusion flames under momentum-dominated conditions (large Froude number) at moderate Reynolds number which is a combination not achievable in normal gravity. This paper summarizes progress made since the last workshop. Primarily, the features of flame radiation from microgravity turbulent jet diffusion flames in a reduced gravity environment are described. Tests were conducted for non-premixed, nitrogen diluted propane flames burning in quiescent air in the NASA Glenn 5.18 Second Zero Gravity Facility. Measured flame radiation from wedge-shaped, axial slices of the flame are compared for microgravity and normal gravity flames. Results from numerical computations of the flame using a k-e model for the turbulence are also presented to show the effects of flame radiation on the thermal field. Flame radiation is an important quantity that is impacted by buoyancy as has been shown in previous studies by the authors and also by Urban et al. It was found that jet diffusion flames burning under microgravity conditions have significantly higher radiative loss (about five to seven times higher) compared to their normal gravity counterparts because of larger flame size in microgravity and larger convective heat loss fraction from the flame in normal gravity. These studies, however, were confined to laminar flames. For the case of turbulent flames, the flame radiation is a function of time and both the time-averaged and time-dependent components are of interest. In this paper, attention is focused primarily on the time-averaged level of the radiation but the turbulent structure of the flame is also assessed from considerations of the radiation power spectra.

Hegde, U.↗

NASA NTRS1973

Study of liquid-solid transition for materials processing in space. Analysis of field effects on dense liquid materials

The behavior of dense liquids near the solidification point under the influence of magnetic fields or near-zero gravity conditions were analyzed within the framework of existing liquid state models and classical field theory. The dynamic body forces which are an effect of the magnetic field on liquids are discussed. It is concluded that both magnetic fields and low gravity conditions produce an increase in the diffusion coefficient which result in an increased growth rate of crystals, and time varying magnetic fields induce eddy currents in the liquid which produce body forces and tend to disrupt convection.

Miller, R. I.↗

NASA NTRS1984

A model of the radiative properties of the El Chichon stratospheric aerosol layer

An accurate multiple-scattering model has been employed to examine the effect of an aerosol layer at 25 mb, corresponding to the El Chichon observations, on the reflection, transmission and absorption of radiation by the stratosphere as a function of latitude, optical thickness and aerosol size distribution. Results are presented and parameterized for each of two wavelength intervals in the shortwave region and 17 wavelength intervals in the longwave region for three models of the aerosol size distribution. They include one model representing the unperturbed stratospheric aerosol plus two models based on measurements of the El Chichon aerosol size distribution. In addition to models of the radiative properties of the aerosol layer, a simple model of the latitudinal distribution of aerosol optical thickness as a function of time is developed, based on diffusive transport in latitude and exponential decay in time. These parameterizations for solar and infrared radiation, together with the dispersion model, permit climate models to account for the evolution of an aerosol size distribution from post-volcanic conditions to background conditions.

King, M. D.↗

NASA NTRS1989

Investigation of the Saturn dust environment from the analysis of energetic charged particle measurements

In order to assist the Cassini project in evaluating risks of collisions with particulate matter in the rotational equatorial plane, available Pioneer 11 and Voyager energetic charged particle data were reinvestigated to constrain the column mass density of absorbing material within several radial ranges. Within the orbit of Mimas, CRAND proton phase space densities maximize near 2.67 R sub s and exhibit secondary maximum at 2.43 R sub s. From the condition that sources must exceed losses near these maxima and using available theoretical models for CRAND proton production rates, upper bounds on the column mass density at these two radial locations are calculated. Detailed fits of radial diffusion models to the observed flux maxima yield somewhat more restrictive upper limits. The upper limits compare to a lower limit on the column mass density, estimated from previous model calculations by Van Allen. Aside from continuous rings, longitudinally limited, low optical depth clouds of particulates may exist in orbit with several of the inner satellites including Mimas and Enceladus. A brief review of Voyager energetic particle microsignatures that suggest the presence of material co-orbiting with these two satellites is presented. Finally, Pioneer 11 and Voyager measurements of low energy electron fluxes exhibit minima near the location of the tenuous E Ring centered on approx. 4 R sub s. Pioneer 11 pitch angle distributions appear to support the possibility that direct absorption by Ring E particulates produced the observed flux decreases.

Hood, L. L.↗

NASA NTRS1976

Modeling of three-dimensional mixing and reacting ducted flows

A computer code, based upon a finite element solution algorithm, was developed to solve the governing equations for three-dimensional, reacting boundary region, and constant area ducted flow fields. Effective diffusion coefficients are employed to allow analyses of turbulent, transitional or laminar flows. The code was used to investigate mixing and reacting hydrogen jets injected from multiple orifices, transverse and parallel to a supersonic air stream. Computational results provide a three-dimensional description of velocity, temperature, and species-concentration fields downstream of injection. Experimental data for eight cases covering different injection conditions and geometries were modeled using mixing length theory (MLT). These results were used as a baseline for examining the relative merits of other mixing models. Calculations were made using a two-equation turbulence model (k+d) and comparisons were made between experiment and mixing length theory predictions. The k+d model shows only a slight improvement in predictive capability over MLT. Results of an examination of the effect of tensorial transport coefficients on mass and momentum field distribution are also presented. Solutions demonstrating the ability of the code to model ducted flows and parallel strut injection are presented and discussed.

Zelazny, S. W.↗

NASA NTRS1979

Particle deposition due to turbulent diffusion in the upper respiratory system

Aerosol deposition in the upper respiratory system (trachea to segmental bronchi) is considered and the importance of turbulent diffusion as a deposition mechanism is evaluated. It is demonstrated that for large particles (diameter greater than about 5 microns), turbulent diffusion is the dominant deposition mechanism in the trachea. Conditions under which turbulent diffusion may be important in successive generations of the pulmonary system are determined. The probability of particle deposition is compared with probabilities of deposition, as determined by the equations generally used in regional deposition models. The analysis is theoretical; no new experimental data is presented.

Hamill, P.↗

NASA NTRS1992

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

The gravitational collapse and fragmentation of centrally condensed molecular cloud cores are investigated using a new hydrodynamical code. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a 3D Cartesian grid. Two initial power-law density profiles, rho varies as r exp -1 and rho varies as r exp -2, are considered, as well as two initial density perturbations in the azimuthal coordinate theta, rho-i - rho(1 + a cos 2theta) where a = 0.1 and 0.5. Fragmentation is found to be possible in these centrally condensed cores if the initial conditions also include differential rotation. Models which collapse with initial uniform rotation do not produce fragments. If molecular cloud cores are indeed centrally condensed, as suggested by observations of star-forming regions and by studies of ambipolar diffusion, then differential rotation may be a mechanism for producing binary protostars during gravitational collapse.

Myhill, Elizabeth A.↗