One-dimensional Steady-state Model Research Articles

Galactic fountains and extended H I disks

view Abstract Citations (49) References (44) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Galactic Fountains and Extended H i Disks Corbelli, E. ; Salpeter, E. E. Abstract Some of the hot material, ejected into the galactic halo by the more violent supernova events, can rise many kiloparsecs and then start cooling radiatively and falling back toward the outer part of the galactic plane (distances from the center >~20 kpc). Depending upon the temperature and mass-flow rate initiated by such an "outer galactic fountain," the dynamic hot downward flow can form an extended H I disk or shape and evaporate a preexisting one. These downward flows have been studied, using a one-dimensional steady state model which includes an extragalactic flux of soft X-rays but omits electron heat conduction. The pressure profile and column densities of H II and warm H I are given as functions of the injection temperature T_i_ and of the mass-flow rate. A small fraction of the total supernova energy release, if channeled into an outer galactic fountain with T_i_ ~ 2 or 3 x 10^6^ K, can form cool extended disks. A corona with T_i_ ~ 5-7 x 10^6^ K is more likely to evaporate and shrink a preexisting H I disk. If disk galaxies were formed with appreciably larger disks than now, as suggested by one type of quasar absorption lines, the subsequent shrinkage may have been caused by stronger hot fountains in young galaxies. Weak present-day fountains can also be effective in compressing an outer H I disk and, possibly, in giving it a sharp edge. Publication: The Astrophysical Journal Pub Date: March 1988 DOI: 10.1086/166116 Bibcode: 1988ApJ...326..551C Keywords: Cosmic Gases; Disk Galaxies; Ejecta; H I Regions; Spiral Galaxies; Absorption Spectra; Astronomical Models; Conductive Heat Transfer; High Temperature Gases; Quasars; Steady Flow; Thermal Stability; Astrophysics; GALAXIES: INTERNAL MOTIONS; GALAXIES: STRUCTURE; HYDRODYNAMICS; RADIO SOURCES: 21 CM RADIATION full text sources ADS |

Spontaneous combustion of coal stockpiles - an unusual chemical reaction engineering problem

Spontaneous combustion of stockpiled coal occurs because of reaction between atmospheric gases and coal, and causes pollution, as well as the potential loss of all or part of the stockpile. The stockpile may be viewed as a chemical reactor, and chemical engineering methods may be used to analyse and understand this problem. The analysis is complicated by the fact that coal stockpiles in general possess little or no symmetry. In addition, it has been shown that the flow in coal stockpiles is mainly due to natural convection, which makes the problem rather different to those traditionally analysed in the chemical reaction engineering literature. In order that a realistic model of this phenomenon be formulated, it is necessary to derive mass, momentum and energy balance equations. The various models that have been used to describe this phenomenon are discussed, starting with simple steady-state one-dimensional models, and culminating in a three-dimensional formulation. The simple one-dimensional model gives valuable insights into the behaviour of stockpiled coal. The solution of the more realistic model, using finite element techniques, is described. The models are compared in the light of the assumptions made in their derivation. Finally the practical implications of the work are discussed.

One-dimensional steady-state model for damage by vaporization and liquid expulsion due to laser-material interaction

A one-dimensional steady-state model describing the damage caused by materials removal by vaporization and liquid expulsion due to laser-material interaction is developed and presented. When vaporization occurs, there exists a discontinuity across the Knudsen layer of a few molecular mean free paths. This discontinuity is modeled by a Mott–Smith-type solution. The vaporization process creates a recoil pressure that pushes the vapor away from the target and expels the liquid. The materials are, therefore, removed in both vapor and liquid phases. The materials-removal rates are incorporated in the moving boundary immobilization transformation. The vapor phase is assumed to be optically thin so that its absorption of the high-energy beam is negligible. Closed-form analytical solutions are obtained and presented. The effect of heat-source power on removal rates, vaporization rate, liquid-expulsion rate, surface temperature, and Mach number are presented and discussed. Results are obtained for three different materials: aluminum, superalloy, and titanium.

The thermal modeling of integrated-circuit device packages

Heat elimination from power integrated-circuit packages represents an ever present problem due to the highdegree of dissipation of energy emitted from high-voltage devices. An important consideration in the removal of large quantities of heat is the choice of material for the heat sink and its geometric configuration. The amount of copper used as a heat sink is limited by economic factors. An engineering model has been developed to estimate the dimensions of the heat sink based on a simple one-dimensional multilayer steady-state heat transport model. The model shows that the transport of energy from the heat sink to the ambient is a weak function of the thickness. On the other hand, the areal dimensions play a major role in the efficiency of heat transfer across the surface. Beyond a ratio of 4 (length/ width), efficiency of heat transport is not measurably increased. A transient analysis was included to see if time dependencies influenced the progress of heat flow.

Theory of the Hollow Cathode Glow Discharge

A theory of the hollow cathode glow discharge based on the two-temperature electron model is developed. The following two interdependent mechanisms are consistently taken into account: the creation of ions and excited atoms due to electron collisions in the discharge and the emission of secondary electrons on the cathode surface due to ions and ultraviolet photons. Trapped electrons in the hollow are also considered. Numerical calculations are made for helium gas in a cylindrical hollow cathode whose inner diameter and length are 10 and 32 mm, respectively, on the basis of a onedimensional steady state model. Voltage-current relations are obtained at gas pressures of 0.13, 0.27 and 0.40 kPa. Population densities of 64 excited atomic levels are determined as a function of the radial distance r as well as the densities of the ions and electrons.

On the mechanisms of downdraft maintenance in cumulonimbus clouds

The mechanisms of maintenance of cold steady downdraft in convective clouds have been investigated in numerical experiments using a one-dimensional steady-state model of the updraft-downdraft interaction. It was found that evaporation of cloud water entrained from the updraft in the presence of dry air entrained from the environment may in certain circumstances provide cooling sufficient for development and persistence of a quasisteady downdraft in the middle part of a cumulonimbus cloud. This effect may be essentially enhanced if the equivalent-potential temperature, θ e , has a distinct minimum in the middle troposphere. DOI: 10.1111/j.1600-0870.1987.tb00307.x

A multi-phase model for plumes in powder injection refining processes

A one-dimensional steady-state model for momentum transfer in ascending gas-liquid-powder plumes has been developed for conditions relevant to powder injection refining processes. Inter-phase transport of momentum permits the calculation of the volume fraction and velocity of the gas, liquid, and solid phases as they rise in the melt. The effects of plume geometry, initial conditions, density of the phases, head of liquid, bubble size, and powder loading and properties are assessed. Liquid velocities in gas-only injection into water compare favorably with available experimental data. Significantly lower liquid velocities are predicted in liquid metals. At solids loadings used in commercial powder injection stations, the powder is expected to have only a small effect on liquid velocity. For wire injection conditions with little gas release, liquid velocities are considerably smaller.

Predictions by Two One-Dimensional Cloud Models: A Comparison

Abstract Two one-dimensional steady-state models of cumulus convection in common use in weather modification research, the NOAA Experimental Meteorology Branch model (EMB) and the Great Plains Cumulus Model (GPCM), differ in their formulations in several ways. Some of the differences arise from the conceptualization of the convective phenomenon which is modeled in each and some from the physical parameterizations utilized. Predictions of cloud top and dynamic modification potential (seedability) by the two models for 57 midday radiosondes in the Midwest, differed significantly, with the EMB values consistently higher. GPCM simulations provided a better overall estimate of observed radar echo tops, while EMB consistently overestimated, by largest amounts when tops were below 12 km. Study of the impact of temporal and/or spatial separation between sounding and cloud area emphasizes the need, in the Midwest, to consider factors other than thermodynamic stratification (e.g. forced lifting, convergence) on the...

Water Quality Modelling of the River Rhine and Its Tributaries in Relation to Sanitation Strategies

Water quality modelling techniques havebeen used to evaluate and predict the influence of taken, projected and potential sanitation measures for domestic and industrial wastewater loads in the River Rhine drainage area. 15Because of serious eutrophication problems in the Dutch fresh water lakes, that are fed by the River Rhine, special attention is given to the quantification of sanitation measures that can reduce the nutrient concentrations. As a base for modelling the River Rhine water quality, a one-dimensional steady-state model MODQUAL (a modified version of the QUAL-II model) has been developed and applied on the riversystem downstream of Lake Constance, including the main tributaries Neckar, Main and Mosel and the Dutch branches IJssel, Lek and Waal. It is shown that the development of wasteloads and the introduction of biological (secondary) treatment since 1973, has resulted in a significant improvement of water quality components as DO, B0D5, COD, Kjeldahl-N and NH4-N. The influences of tertiary treatment directed on nitrogen or phosphorus removal and the introduction of phosphate-free detergents are quantified for various hydrological conditions.

The oxidation of isoprene in the troposphere: Mechanism and model calculations

A chemical mechanism describing the oxidation of isoprene by OH and O 3 in the troposphere has been developed and incorporated into a one-dimensional steady-state photochemical model. Calculations have been performed for continental conditions at two latitudes, 15°N and 45°N. At 45°N latitude, the effects of anthropogenic hydrocarbon emissions on the vertical profiles of NO x (NO + NO 2) and HNO 3 overshadow the effects of isoprene emissions; at 15°N, the reduced anthropogenic emissions and the increased isoprene emissions produce increases of 26 and 4% in the column contents of NO x and HNO 3, respectively. The integrated columns of CO at 45°N and 15°N latitude increased by 10 and 31 %, respectively, when isoprene chemistry was included, but these increases are much smaller than those that would have been obtained if all the carbon in isoprene had been photochemically transformed into CO. It appears that the fate of a significant quantity of isoprene is in the formation of longer carbon-chain (R > CH 3) oxygenated organic species. The longer carbon-chain alkylhydroperoxides and alkylperoxyacids appear to be important free radical sinks in the tropics given the lower NO x concentrations generally found in the tropics.

THREE‐PHASE FLOW OF FLASHING NON‐NEWTONIAN COAL SLURRY‐GAS MIXTURES THROUGH A CONDUIT*

To develop design procedures for predictin pressure drops in conduits carrying three-phase flashing flows, a model has been developed at Oak Ridge National Laboratory (ORNL) that is based on the current state of the art. This model has been tailored to consider coal liquids with gases and solids present. The investigation has examimed the fluid dynamics in the let-down valve area of a coal liquefaction plant by assuming a one-dimensional steady-state model. The coal liquids are modeled as a mixture of pseudocomponents in an approach similar to that used by the petroleum industry. Boiling points are chosen to characterize pseudocomponent fractions. Previous studies at ORNL have shown that, for a mixture of hydrogen gas, methane, and a coal-derived liquid, empirical correlations by Wilson and coworkers best predict critical pressures, temperatures, and acentric factors for the pseudocomponents. These properties are needed to perform flash calculations that use the Redlich-Kwong-Soave equation of state and a modified Grayson-Streed method. Reasonable agreement was found between experimental results and the theoretical flash calculations. Energy and mass balances used in the flash calculations interact with a momentum balance to obtain the pressure drop and gas-to-slurry ratio for each interval of length along the flow path. Sincemore » there is a possibility of choked flow at each interval of flow length, a calculation of critical flow velocity is also made.« less

Theory of Equilibrium Temperatures in Radiative-Turbulent Atmospheres

We have developed a thermodynamic model for the determination of the temperature profile based on the balance of radiative and turbulent fluxes. In the context of a one-dimensional case, we show that the temperature field is governed by a first-order differential-integro equation involving temperature to the fourth power. In conjunction with the temperature profile determination, parameterization programs for the transfer of broadband thermal infrared and solar fluxes in inhomogeneous atmospheres are developed. In addition, the vertical transport is parameterized using a first-order closure scheme with the eddy thermal diffusion coefficients derived either from known theories or from available data. By virtue of an efficient perturbation technique devised for the solution of the thermal equilibrium temperature, we show that the simulated temperatures compare well with those of a standard atmosphere employing climatological water vapor, ozone and cloud profiles. Simulations using the steady-state one-dimensional model also reveal that high clouds will produce warming everywhere in the atmosphere whereas middle and low clouds will generate cooling as noted by several previous investigators, Moreover, extension of the model to a two-dimensional case is accomplished by incorporating empirical data for the horizontal heat transport. Simulated temperature profiles for the tropics (0–30°) and midlatitude (30–60°) compare closely with the climatological data except in the vicinity of the tropopause. For the subarctic case (60–90°), simulated temperatures are colder than the climatological values within about 5 K in the troposphere. Finally, two-dimensional heat budget analyses reveal that there is a slight gain of energy in the tropical region of the Northern Hemisphere.

Mathematical modeling of combustion and gasification of a wet coal slab—II: Mode of combustion, steady state multiplicities and extinction

The previous one-dimensional steady state model for gasification of wet coal is extended to include both homogeneous and heterogeneous combustion. The conditions under which the flame separates from the coal surface are presented and it is shown that these conditions are functions of the properties of the coal and the ambient gas. It is also shown that for a given bulk gas temperature, there is a limiting bulk oxygen concentration for combustion. Above the limiting bulk gas oxygen concentration, two possible solutions were found: the flame located at the char surface (heterogeneous combustion) and the flame located in the ash layer or in the gas film (homogeneous combustion). The heterogeneous combustion is shown to be unstable while the homogeneous combustion, which has been observed experimentally, is shown to be stable. The global rates, the mode of combustion, the multiplicity of steady state solution and the flame extinction points are discussed as a function of ambient gas temperature, ash layer thickness, coal moisture content and film transport coefficients.

Stable Isotopes in Hailstones. Part I: The Isotopic Cloud Model

Abstract Equations describing the isotopic balance between five water species (vapor, cloud water, rainwater, cloud ice and graupel)have been incorporated into a one-dimensional steady-state cloud model. The isotope contents of the various water substances were calculated as a function of height. From these profiles, the isotopic concentration δH of the water accreted by hailstones growing in this model cloud is determined. The results are compared with those obtained from the adiabatic model (δAM). The differences are substantial. A sensitivity study shows that the δH profiles for two different soundings are dependent on the changes in the droplet-size distributions, which influence the conversion of cloud water to rainwater, and, to a lesser degree, on entrainment. If a reasonable concentration of raindrops is allowed, the results are remarkably stable if all the other adjustable parameters are varied. The application of the model to isotopic data of hailstones and its comparison with the adiabatic mode...

Analysis of salinity profiles in lateritic soils of south-western Australia

Salinity profiles in deeply weathered lateritic soils of south-western Australia frequently exhibit very high concentrations in the unsaturated zone above a less saline water table. A one-dimensional steady-state model using the simultaneous mass balance equations for water and solute is used to predict salt profiles which are compared with those observed. The model assumes input of salt in rainfall and water uptake by plants. Model parameters imply magnitudes of transpiration, water flux rates and possible mechanisms for water movement to the saturated zone. Some salt profiles cannot be accounted for with the steady-state model. In some cases there appears to be an injection of low salinity water at depth which could occur by movement through preferred pathways from the soil surface. In other cases the probable explanation is that the profiles are accumulating salts under the present hydrologic regime.

Natural Variability of Thermodynamic Features Affecting Convective Cloud Growth and Dynamic Seeding: A Comparative Summary of Three High Plain Sites from 1975 to 1977

Abstract A statistical summary of the thermodynamic features generally thought to be relevant to convective cloud development and the dynamic seeding hypothesis, as diagnosed by a one-dimensional steady-state model, has been compiled for selected locations on the High Plains. The summary is based primarily on rawinsonde data collected at Miles City, Montana, Goodland, Kansas, and Big Spring, Texas during the summer months from 1975 to 1977, as part of the High Plains Cooperative Program (HIPLEX). Data were stratified according to the occurrence or non-occurrence of convective clouds and, when clouds occurred, according to cloud type as seen in geosynchronous satellite imagery. Geographic comparisons are presented showing significant variations from north to south over the High Plains, the most intense convection occurring in the central and southern plains and the least intense in the north. Large annual variations were noted in mean values of thermodynamic features at each site between the three summers....

Cold downdrafts in cumulonimbus clouds

The mechanism of maintenance of cold steady downdrafts in convective clouds is investigated in a numerical experiment using a one-dimensional steady state model of the updraft-downdraft interaction. It is established that usually the downdraft cannot be effectively chilled unless it is fed with small droplets from the updraft by at least two simultaneously acting mechanisms: entrainment of the updraft air and fallout of drizzle-size droplets through the inclined updraft-downdraft interface. DOI: 10.1111/j.2153-3490.1980.tb00978.x

Parameterization of Convective Effects on the Momentum and Vorticity Budgets of Synoptic-Scale Atlantic Tropical Waves

Abstract Dynamic budgets of an average synoptic-scale wave have been made by Stevens (1979) from GARP Atlantic Tropical Experiment Phase III B- and A/B-scale data composited by Thompson et al. (1979). In the present study the apparent sources of momentum and vorticity, computed from the large-scale budgets, are compared with parameterized sources from independently derived cumulus mass fluxes and one-dimensional steady-state cloud models. The cloud models include spectral and bulk, as well as single-cloud models. The cumulus mass fluxes are determined from a thermodynamic budget analysis of Johnson (1 978). A simple single-cloud model is found to adequately account for the net effect of the cumulus transport and production of vorticity. The one-dimensional cloud models, however, do not account for the apparent momentum source in the upper troposphere. An evaluation is made of the sensitivity of the results to the assumed cloud-base vorticity and radiative heating rate. The limitations of the simple cloud ...

The evolution and variability of atmospheric ozone over geological time

The rise of atmospheric O 3 as a function of the evolution of O 2 has been investigated using a one-dimensional steady-state photochemical model based on the chemistry and photochemistry of O x (O 3, O, O( 1D)), N 2O, NO x (NO, NO 2, HNO 3), H 2O, and HO x (H, OH, HO 2, H 2O 2) including the effect of vertical eddy transport on the species distribution. The total O 3 column density was found to maximize for an O 2 level of 10 −1 present atmospheric level (PAL) and exceeded the present total O 3 column by about 40%. For that level of O 2, surface and tropospheric O 3 densities exceeded those of the present atmosphere by about an order of magnitude. Surface and tropospheric OH densities of the paleoatmosphere exceeded those of the present atmosphere by orders of magnitude. We also found that in the O 2-deficient paleoatmosphere, N 2O (even at present atmospheric levels) produces much less NO x than it does in the present atmosphere.

Gasdynamic modeling and computational accuracy

The study of the behavior of computational solutions of Burgers' equation at large mesh Reynolds numbers ReΔx is extended to a one-dimensional steady-state model gasdynamic system with downstream extrapolation conditions. The oscillations generally present in computed results at large ReΔx can be minimized by choosing a particular formally second-order accurate, conservative discretization of the nonlinear terms ( ϱu) x and ( ϱu 2) x in the continuity and momentum equations. This minimally oscillatory solution has small pointwise error even at large ReΔx. It is seen that smoothness by itself may not guarantee computational accuracy, and that overly refined spatial meshes may lead to large errors. Results from a realistic two-dimensional computation showing some qualitative agreement with the present conclusions are given.