Thermodynamics of the gray atmosphere. II - Unattainability of detailed balancing.
Unattainability of detailed balancing in thermodynamic equilibrium of gray atmosphere
GRAY GAS↗
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Detailed balance as a check on impact parameter calculations.
It is demonstrated numerically that detailed balance indeed is well satisfied in the multi-state impact parameter formulation of proton-hydrogen atom collisions. It is also demonstrated numerically that detailed balance is a much more sensitive test of computational accuracy than is the charge conservation test usually employed in such impact parameter calculations. It is suggested that detailed balance be used as a check on all impact parameter calculations. That even agreement with detailed balance may not be a sufficient test for accuracy of the results is pointed out.
Tai, H.↗
Forbidden lines of np/q/ ions. I - Detailed balance and line intensity ratios
The detailed balance equations are solved in the ground state terms of 37 ions of C, N, O, Ne, Mg, Si, S and Fe; atomic data for 235 transitions of these ions are tabulated, and 14 line ratios of q = 2,4 ions and eight line ratios of q = 3 ions are graphed. Forbidden emission lines of these ions are in the far and near UV, visible, and near and far IR regions of the spectrum. In addition, detailed calculations of the relative populations of the levels of the ground state are presented as a function of temperature and density.
Kafatos, M.↗
A far-wing line shape theory which satisfies the detailed balance principle
A far-wing theory in which the validity of the detailed balance principle is maintained in each step of the derivation is presented. The role of the total density matrix including the initial correlations is analyzed rigorously. By factoring out the rapidly varying terms in the complex-time development operator in the interaction representation, better approximate expressions can be obtained. As a result, the spectral density can be expressed in terms of the line-coupling functions in which two coupled lines are arranged symmetrically and whose frequency detunings are omega - 1/2(omega(sub ji) + omega (sub j'i'). Using the approximate values omega - omega(sub ji) results in expressions that do not satisfy the detailed balance principle. However, this principle remains satisfied for the symmetrized spectral density in which not only the coupled lines are arranged symmetrically, but also the initial and final states belonging to the same lines are arranged symmetrically as well.
Ma, Q.↗
The detailed balance requirement and general empirical formalisms for continuum absorption
Two general empirical formalisms are presented for the spectral density which take into account the deviations from the Lorentz line shape in the wing regions of resonance lines. These formalisms satisfy the detailed balance requirement. Empirical line shape functions, which are essential to provide the continuum absorption at different temperatures in various frequency regions for atmospheric transmission codes, can be obtained by fitting to experimental data.
Ma, Q.↗
An archetype hydrogen atmosphere problem
Populations for the first three bound states and the continuum of hydrogen are determined for an isothermal hydrostatic atmosphere at 20,000 K. The atmosphere is treated as optically thin in the Balmer and Paschen continua and illuminated by continuum radiation at these wavelengths with prescribed radiation temperatures. The atmosphere is optically thick in the 2-1, 3-1, 3-2 and c-1 transitions. Three stages of approximation are treated: (1) radiative detailed balance in the 2-1, 3-1 and 3-2 transitions, (2) radiative detailed balance in the 3-1 and 3-2 transitions, and (3) all transitions out of detailed balance. The solution of this problem is nontrivial and presents sufficient difficulty to have caused the failure of at least one rather standard technique. The problem is thus a good archetype against which new methods or new implementations of old methods may be tested.
Athay, R. G.↗
Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind
The PI (Cranmer) and Co-I (A. van Ballegooijen) made significant progress toward the goal of building a "unified model" of the dominant physical processes responsible for the acceleration of the solar wind. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a one-dimensional and time-independent model of plasma heating and acceleration. The accomplishments in the report period are thus divided into these two categories: 1a. Focused Study of Kinetic MHD Turbulence. We have developed a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. A turbulent cascade is one possible way of generating small-scale fluctuations (easy to dissipate/heat) from a pre-existing population of low-frequency Alfven waves (difficult to dissipate/heat). We modeled the cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, though, there is insufficient power to heat protons and heavy ions. The dominant oblique waves undergo Landau damping, which implies strong parallel electron heating. We thus investigated the nonlinear evolution of the electron velocity distributions (VDFs) into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere) which are an alternate means of heating protons via stochastic interactions similar to particle-particle collisions. 1b. Focused Study of the Multi-Mode Detailed Balance Formalism. The PI began to explore the feasibility of using the "weak turbulence," or detailed-balance theory of Tsytovich, Melrose, and others to encompass the relevant physics of the solar wind. This study did not go far, however, because if the "strong" MHD turbulence discussed above is a dominant player in the wind's acceleration region, this formalism is inherently not applicable to the corona. We will continue to study the various published approaches to the weak turbulence formalism, especially with an eye on ways to parameterize nonlinear wave reflection rates. 2. Building the Unified Model Code Architecture. We have begun developing the computational model of a time-steady open flux tube in the extended corona. The model will be "unified" in the sense that it will include (simultaneously for the first time) as many of the various proposed physical processes as possible, all on equal footing. To retain this generality, we have formulated the problem in two interconnected parts: a completely kinetic model for the particles, using the Monte Carlo approach, and a finite-difference approach for the self-consistent fluctuation spectra. The two codes are run sequentially and iteratively until complete consistency is achieved. The current version of the Monte Carlo code incorporates gravity, the zero-current electric field, magnetic mirroring, and collisions. The fluctuation code incorporates WKJ3 wave action conservation and the cascade/dissipation processes discussed above. The codes are being run for various test problems with known solutions. Planned additions to the codes include prescriptions for nonlinear wave steepening, kinetic velocity-space diffusion, and multi-mode coupling (including reflection and refraction).
Cranmer, Steven R.↗
Hybrid Reduced Order Model for N2-N2 Interactions for Application to Dissociation and Energy Transfer Processes
Recent work in the aerothermodynamics community has focused on the development of reduced-order models for thermo-chemical non-equilibrium which avoid the restrictive assumptions of multi-temperature models and the prohibitive cost associated with State-to-State (StS) models. In the present work, this is accomplished by lumping energy states together and assuming groups of states are roughly in equilibrium. As a result, the non-equilibrium behavior of a gas can be captured at a reduced computational cost from a full StS simulation. In this work, we present a hybrid grouping model for studying energy transfer and dissociation in a mixture of nitrogen molecules due to N2-N2 reactions. This is accomplished by making use of a grouping strategy informed by data from the N2-N StS kinetic data. However, due to the massive computational cost associated with constructing StS data for the N2-N2 system, the kinetic data for the hybrid grouping model are calculated using the quasi-classical trajectory (QCT) method by sampling states for trajectory within the groups. This general framework is called the Maximum-Entropy Quasi-Classical Trajectory (ME-QCT) method. The primary challenge associated with this method is that rates for reverse grouped reactions cannot be obtained through detailed balance at a group level, due to the variation of group internal temperatures. To construct the full model for N2-N2 grouped kinetics using the ME-QCT method, detailed balance is invoked at the microscopic level, allowing for the calculation of the full kinetic data from QCT. Results will be presented using the full ME-QCT model for the N2-N2 system in an isothermal and isochoric reactor simulation. In addition, simple CFD test cases for a one-dimensional standing shock and for a quasi-one-dimensional nozzle will be used for demonstration of the ME-QCT method. This method allows for the calculation of non-equilibrium behavior for the N2-N2 system without the prohibitive cost of a full StS simulation. Moreover, it enables the construction of a unified model for the dissociating and recombining non-equilibrium flows.
nonequilibrium modeling↗
Force balance near an X line in a collisionless plasma
The suggestion by Dungey (1988) that the gyroviscosity associated with gradients of the off-diagonal elements of the electron pressure tensor can balance a reconnection electric field along a magnetic X line in a collisionless plasma is investigated. The detailed balance of forces in the vicinity of an X line is evaluated using a two-dimensional magnetic field model and a simple model for particle motion. The results show that the gyroviscosity can indeed provide the force required to balance a reconnection electric field in that region, so that neither collisions nor wave turbulence are necessary for reconnection. The results also show that there should not be a significant increase in current from electron acceleration very near an X line. Reasonable numerical estimates are obtained for conditions expected in the vicinity of the distant X line in the geomagnetic tail.
Lyons, L. R.↗
Method of balancing bladed gas turbine engine rotor
A balance ring (18) which is shrunk fit within each disk (12) of a rotor is selectively ground for detail balance. A plurality of openings (20) through the outer edge of the balance ring receive weights during the assembly balance of the rotor. A snap ring (42) retains the weights within the openings.
Novotny, Rudolph J.↗
Rotor balance system
A balance ring (18) which is shrunk fit within each disk (12) of a rotor is selectively ground for detail balance. A plurality of openings (20) through the outer edge of the balance ring receive weights during the asssembly balance of the rotor. A snap ring (42) retains the weights within the openings.
Novotny, Rudolph J.↗
Dynamics of face and annular seals with two-phase flow
A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. Some of the distinctive behavior characteristics of two phase seals are discussed, particularly their axial stability. The main conclusions are that seals with two phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction: calculations of stiffness coefficients, temperature and pressure distributions, and leakage rates for parallel and coned face seals. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two phase flow is described and documented. The analyses, results, and computer codes are summarized.
Hughes, William F.↗
Co2(nu2)-o Quenching Rate Coefficient Derived from Coincidental SABER-TIMED and Fort Collins Lidar Observations of the Mesosphere and Lower Thermosphere
Among the processes governing the energy balance in the mesosphere and lower thermosphere (MLT), the quenching of CO2(nu2) vibrational levels by collisions with O atoms plays an important role. However, there is a factor of 3-4 discrepancy between the laboratory measurements of the CO2-O quenching rate coefficient, k(sub VT),and its value estimated from the atmospheric observations. In this study, we retrieve k(sub VT) in the altitude region85-105 km from the coincident SABER/TIMED and Fort Collins sodium lidar observations by minimizing the difference between measured and simulated broadband limb 15 micron radiation. The averaged k(sub VT) value obtained in this work is 6.5 +/- 1.5 X 10(exp -12) cubic cm/s that is close to other estimates of this coefficient from the atmospheric observations.However, the retrieved k(sub VT) also shows altitude dependence and varies from 5.5 1 +/-1 10(exp -12) cubic cm/s at 90 km to 7.9 +/- 1.2 10(exp -12) cubic cm/s at 105 km. Obtained results demonstrate the deficiency in current non-LTE modeling of the atmospheric 15 micron radiation, based on the application of the CO2-O quenching and excitation rates, which are linked by the detailed balance relation. We discuss the possible model improvements, among them accounting for the interaction of the non-thermal oxygen atoms with CO2 molecules.
SABER/TIMED↗
Dynamics of face and annular seals with two-phase flow
A detailed study was made of face and annular seals under conditions where boiling, i.e., phase change of the leaking fluid, occurs within the seal. Many seals operate in this mode because of flashing due to pressure drop and/or heat input from frictional heating. High pressure, water pumps, industrial chemical pumps, and cryogenic pumps are mentioned as a few of many applications. The initial motivation was the LOX-GOX seals for the space shuttle main engine, but the study was expanded to include any face or annular seal where boiling occurs. Some of the distinctive behavior characteristics of two-phase seals were discussed, particularly their axial stability. While two-phase seals probably exhibit instability to disturbances of other degrees of freedom such as wobble, etc., under certain conditions, such analyses are too complex to be treated at present. Since an all liquid seal (with parallel faces) has a neutral axial stiffness curve, and is stabilized axially by convergent coning, other degrees of freedom stability analyses are necessary. However, the axial stability behavior of the two-phase seal is always a consideration no matter how well the seal is aligned and regardless of the speed. Hence, axial stability is thought of as the primary design consideration for two-phase seals and indeed the stability behavior under sub-cooling variations probably overshadows other concerns. The main thrust was the dynamic analysis of axial motion of two-phase face seals, principally the determination of axial stiffness, and the steady behavior of two-phase annular seals. The main conclusions are that seals with two-phase flow may be unstable if improperly balanced. Detailed theoretical analyses of low (laminar) and high (turbulent) leakage seals are presented along with computer codes, parametric studies, and in particular a simplified PC based code that allows for rapid performance prediction. A simplified combined computer code for the performance prediction over the laminar and turbulent ranges of a two-phase seal is described and documented. The analyses, results, and computer codes are summarized.
Hughes, William F.↗
Departures from LTE in the hydrogen lines of late B stars.
Atomic hydrogen departures from LTE computed for models of B star atmospheres, assuming detailed balance in hydrogen lines
Peterson, D. M.↗
Nonequilibrium boundary layer at a stagnation point for a hydrogen-helium stream over ablating graphite
The nonequilibrium axisymmetric stagnation point boundary layer over an ablating graphite surface is considered. The external stream is a high temperature mixture of hydrogen and helium. Variable thermodynamic and transport properties are assumed. Lennard-Jones potential model is used to calculate the transport coefficients of each species. Although the mixture rules for viscosity of the gas mixture are used, the weighting functions are more sophisticated than those commonly employed. For the conductivity of the mixture, generalized Wassiljewa coefficients are used. Seven species with 28 dissociation/recombination reactions are considered. Hansen's model for the dissociation rate constants is employed. The recombination rate constants are obtained by invoking detailed balance principles assisted by the JANAF thermodynamic data and the Hansen-Pearson thermodynamic data for C3.
Liu, T.-M.↗
Li production in alpha-alpha reactions
The cross section for Li-7 production in alpha-alpha reactions is shown to be increased by about a factor of 2 due to the excitation levels of Li-7 and Be-7 at 478 keV and 431 keV, respectively. The cross section for Li-6 production, however, remains the same as calculated on the basis of the detailed balance principle. The lines at 478 keV and 431 keV may link Li-7 production to feasible gamma-ray observations.
Kozlovsky, B.↗
Scattering of 4.5 eV electrons by ground /x 3 Sigma g minus/ state and metastable /a 1 Delta g/ oxygen molecules
The paper reports on differential and integral cross sections for scattering of 4.5 eV electrons by ground state (x 3 Sigma g minus) and metastable (a 1 Delta g) oxygen molecules in the -2.0 eV to plus 2.0 eV energy loss range. The cross section for the (a 1 Delta g to b 1 Sigma g plus) transition was found to be more than an order of magnitude larger than that of the excitation of the b state from the ground state. It was found that the principle of detailed balance can be applied to the rotationally unresolved inelastic and superelastic electronic transitions between the (x 3 Sigma g minus) and (a 1 Delta g) states, which indicates that for this transition one may neglect the very different rotational level structure of the two states in estimating superelastic cross section from inelastic data to an accuracy of about 15 per cent.
Hall, R. I.↗