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DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗

DOE OSTI2020

Experimental Investigation of Uranium Volatility during Vapor Condensation

The predictive models that describe the fate and transport of radioactive materials in the atmosphere following a nuclear incident (explosion or reactor accident) assume that uranium-bearing particulates would attain chemical equilibrium during vapor condensation. Here, we show that kinetically driven processes in a system of rapidly decreasing temperature can result in substantial deviations from chemical equilibrium. This can cause uranium to condense out in oxidation states (e.g., UO 3 vs UO 2 ) that have different vapor pressures, significantly affecting uranium transport. To demonstrate this, we synthesized uranium oxide nanoparticles using a flow reactor under controlled conditions of temperature, pressure, and oxygen concentration. The atomized chemical reactants passing through an inductively coupled plasma cool from ~5000 to 1000 K within milliseconds and form nanoparticles inside a flow reactor. The ex situ analysis of particulates by transmission electron microscopy revealed 2–10 nm crystallites of fcc-UO 2 or α-UO 3 depending on the amount of oxygen in the system. α-UO 3 is the least thermodynamically preferred polymorph of UO 3 . The absence of stable uranium oxides with intermediate stoichiometries (e.g., U 3 O 8 ) and sensitivity of the uranium oxidation states to local redox conditions highlight the importance of in situ measurements at high temperatures. Therefore, we developed a laser-based diagnostic to detect uranium oxide particles as they are formed inside the flow reactor. Our in situ measurements allowed us to quantify the changes in the number densities of the uranium oxide nanoparticles (e.g., UO 3 ) as a function of oxygen gas concentration. Our results indicate that uranium can prefer to be in metastable crystal forms (i.e., α-UO 3 ) that have higher vapor pressures than the refractory form (i.e., UO 2 ) depending on the oxygen abundance in the surrounding environment. This demonstrates that the equilibrium processes may not dominate during rapid condensation processes, and thus kinetic models are required to fully describe uranium transport subsequent to nuclear incidents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Microstructural changes and mass transport in cement-based materials: A modeling approach

Highlights: • Concept to relate microstructural changes, mass transport, and chemical reactions in cement-based materials is presented. • Multi-physics modeling approach utilizing an extended version of the PNP equation and the geochemical code IPHREEQC. • Case studies indicate significant changes in mass transport properties due to alterations in the microstructure. • Microstructural changes depend on exposure and interactions between chemical reactions, pore structure, and mass transport. A generic modeling framework is presented to relate microstructural changes, i.e. changes in the pore volume distribution and phase assemblage, and mass transport in cement-based materials. The modeling framework accounts for mass transport and chemical equilibrium between ions in the pore solution and solid hydrates by means of an extended version of the Poisson-Nernst-Planck equation, in which the chemical equilibrium is solved by the external geochemical code IPHREEQC. Results of numerical studies concerning carbonation and leaching of a cement-based material indicate significant changes in mass transport properties due to chemical reactions leading to alterations in the microstructure. The resulting highly non-linear (both spatial and temporal) microstructural changes are thereby depending on the exposure and indicate that interactions between chemical reactions, pore structure changes, and mass transport have to be accounted for as a whole.

36 MATERIALS SCIENCE↗

NASA NTRS1995

Hypersonic Aerodynamic Characteristics of a Proposed Single-Stage-To-Orbit Vehicle

The hypersonic aerodynamic characteristics of a winged body concept representing a candidate single- stage-to-orbit vehicle which features wing tip fin controllers and elevon/body flap control surfa'Fs are predicted at points along a nominal trajectory for Mach numbers from 5 to 27 and angles of attack from 19 to 32 degrees. Predictions are derived from surface properties based on flow solvers for inviscid and viscous, laminar flows acting as a perfect gas, as a gas in chemical equilibrium and as a gas in chemical non- equilibrium. At a Mach number of 22, the lateral aerodynamic characteristics of the vehicle are determined based on an inviscid analysis at side slip angles of 2 and 4 degrees and 32 degrees angle of attack; a viscous analysis was carried out to determine the effect of gas chemistry model on surface pressure and to determine the incremental aerodynamics for control surface deflections. The results show that the longitudinal pitch characteristics of the baseline configuration, i.e., zero control surface deflections, are significantly altered by real gas chemistry at angles of attack greater than 30 degrees and Mach numbers greater than 9; and, that aerodynamics derived from inviscid solutions are of sufficient accuracy for preliminary analysis. Also, it is shown that a Mach number of 22, the choice of gas chemistry model has a large impact on surface pressure levels at highly localized regions on the vehicle and that the vehicle can be trimmed at control surface deflections less than 11 degrees.

Weilmuenster, K. James↗

NASA NTRS1993

Direct numerical simulation of turbulent H2-O2 combustion using reduced chemistry

Results of direct numerical simulations of hydrogen-oxygen combustion using a partial-equilibrium chemistry scheme in constant density, decaying, isotropic turbulence are reported. The simulations qualitatively reproduce many features of experimental results, such as superequilibrium radical species mole fractions, with temperature and major species mole fractions closer to chemical equilibrium. It was also observed that the peak reaction rates occur in narrow zones where the stoichiometric surface intersects regions of high scalar dissipation, as might be expected for combustion conditions close to chemical equilibrium. Another finding was that high OH mole fraction correspond more closely to the stoichiometric surface than to areas of high reaction rate for conditions of the simulations. Simulation results were compared to predictions of the Conditional Moment Closure model. This model was found to give good results for all quantities of interest when the conditionally averaged scalar dissipation was used in the prediction. When the nonconditioned average dissipation was used, the predictions compared well to the simulations for most of the species and temperature, but not for the reaction rate. The comparison would be expected to improve for higher Reynolds number flows, however.

Montgomery, Christopher J.↗

NASA NTRS1997

The Kinetic Nonequilibrium Processes in the Internal Flow and in the Plume of Subsonic and Supersonic Aircrafts

(1) Our results show that under combustion of thermal destruction products of n-C8H18, and other hydrocarbon fuels with air at the equivalent ratio -0.5 and less the chemical equilibrium is not realized at the exit plane of combustion chamber and in the gas turbine and nozzle for most of small components such as NO2, NO3, HNO, HNO2, HNO3, N(x)H(y), HO2, OH. The chemical equilibrium is not realized in the internal flow of ramjet hydrogen combustion engine too. So at the nozzle exit plane both of gas-turbine hydrocarbon combustion engine and of ramjet hydrogen combustion engine the relatively large values of concentration of such small components as NO3, HNO2, N2O, HNO3, HNO, NH, N2H, HO2, H2O2 may be realized. The exact definition of these component concentration as well as concentration of NO(x), OH, SO2, O, H, H2, H2O at the nozzle exit plane is very important for plume chemistry. (2) The results which were obtained for subsonic and hypersonic aircrafts indicate on the considerable change of the composition of the gas mixture along the plume. This change can be caused not only by the mixture of combustion products with the atmosphere air but by proceeding of whole complex of nonequilibrium photochemical reactions. The photodissociation processes begin to influence on the formation of the free atoms and radicals at flight altitude H greater than or equal to 18 km. Neglect of these processes can result in essential (up to 10(exp 4) times) mistakes of values gamma(sub OH), gamma(sub O), gamma(sub H), gamma(sub HSO3) and some products of CFC's disintegration. It was found that penetration of Cl-containing species from the atmosphere into the exhaust flow and its interaction with nitrogen oxides leads to essential increasing of the concentration of Cl, Cl2, ClO2, ClNO3, CH3Cl and sometimes HCl and the decreasing of ClO concentration by comparison with background values. The results of our analysis show that the plume aircraft with both hydrocarbon and hydrogen combustion engine may be source of various pollutant components such as HNO, HNO4,ClO2, CH3NO2, CH3NO3, CH2O, Cl, H2O2, but not only NO, NO2, HNO2, HNO3, N2O5, SO2, SO3, H2SO4 as it was supposed before.

Starik, Alexander M.↗

NASA NTRS1986

Observations of composition from Pioneer Venus

Long latitude distributions of atmospheric neutral hydrogen were derived at Venus for the period 1979 to 1980. In-situ measurements of H+, O+, O, and CO2 obtained from the ion and neutral mass spectrometers on the Pioneer Venus orbiter are combined with the appropriate chemical equilibrium relationship to determine the abundance of neutral hydrogen which is very difficult to measure directly. The measurements are all obtained below 165 km on the nightside and below 200 km on the dayside, based on evidence for chemical equilibrium prevailing up to those altitudes. During the period examined nearly three complete diurnal cycles were available and a comparison of the year-to-year variation in hydrogen content is made across the dawn region where the distributions of light gases are most pronounced. The dawn bulge in H (and also in He) which was reported from the first diurnal cycle by Brinton et al. is found to persist. Superimposed upon the diurnal variation are strong day-to-day variations in which n(H) changes by as much as a factor of five. Such variations are linked to pronounced changes in the ion and neutral composition which sometimes occur in association with solar wind disturbances passing the planet. The interaction of the solar wind and the planetary environment somehow results in large changes in the relative abundances and scale heights of the ion and neutral species, thus modifying the derived values of n(H). These variations in the ion distributions are not surprising owing to the strong dependence of the nightside ionization upon convection from the dayside and associated sensitivity of this convection to changes in solar wind pressure and interplanetary magnetic field variations. The variation exhibited by the neutrals, however, appears to require some other explanation owing to the limited momemtum transfer between the ions and neturals. Allowing for these short term perturbations, there appears to be no clear evidence for interannual variation in n(H) during the period examined, apparently consistent with the very small change in solar EUV flux over the same interval.

Taylor, H. A., Jr.↗

DOE OSTI2020

An Unusual Transmission Spectrum for the Sub-Saturn KELT-11b Suggestive of a Subsolar Water Abundance

We present an optical-to-infrared transmission spectrum of the inflated sub-Saturn KELT-11b measured with the Transiting Exoplanet Survey Satellite (TESS), the Hubble Space Telescope (HST) Wide Field Camera 3 G141 spectroscopic grism, and the Spitzer Space Telescope (Spitzer) at 3.6 μm, in addition to a Spitzer 4.5 μm secondary eclipse. The precise HST transmission spectrum notably reveals a low-amplitude water feature with an unusual shape. Based on free-retrieval analyses with varying molecular abundances, we find strong evidence for water absorption. Depending on model assumptions, we also find tentative evidence for other absorbers (HCN, TiO, and AlO). The retrieved water abundance is generally ≲0.1× solar (0.001–0.7× solar over a range of model assumptions), several orders of magnitude lower than expected from planet formation models based on the solar system metallicity trend. We also consider chemical-equilibrium and self-consistent 1D radiative-convective equilibrium model fits and find that they, too, prefer low metallicities ([M/H] ≲ -2, consistent with the free-retrieval results). However, all of the retrievals should be interpreted with some caution because they either require additional absorbers that are far out of chemical equilibrium to explain the shape of the spectrum or are simply poor fits to the data. Finally, we find that the Spitzer secondary eclipse is indicative of full heat redistribution from KELT-11b’s dayside to nightside, assuming a clear dayside. These potentially unusual results for KELT-11b’s composition are suggestive of new challenges on the horizon for atmosphere and formation models in the face of increasingly precise measurements of exoplanet spectra.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

An Unusual Transmission Spectrum for the Sub-Saturn KELT-11b Suggestive of a Subsolar Water Abundance

We present an optical-to-infrared transmission spectrum of the inflated sub-Saturn KELT-11b measured with the Transiting Exoplanet Survey Satellite (TESS), the Hubble Space Telescope (HST) Wide Field Camera 3 G141 spectroscopic grism, and the Spitzer Space Telescope (Spitzer) at 3.6 μm, in addition to a Spitzer 4.5 μm secondary eclipse. The precise HST transmission spectrum notably reveals a low-amplitude water feature with an unusual shape. Based on free-retrieval analyses with varying molecular abundances, we find strong evidence for water absorption. Depending on model assumptions, we also find tentative evidence for other absorbers (HCN, TiO, and AlO). The retrieved water abundance is generally ≲ 0.1× solar (0.001–0.7× solar over a range of model assumptions), several orders of magnitude lower than expected from planet formation models based on the solar system metallicity trend. We also consider chemical-equilibrium and self-consistent 1D radiative-convective equilibrium model fits and find that they, too, prefer low metallicities ([M/H] ≲ −2, consistent with the free-retrieval results). However, all of the retrievals should be interpreted with some caution because they either require additional absorbers that are far out of chemical equilibrium to explain the shape of the spectrum or are simply poor fits to the data. Finally, we find that the Spitzer secondary eclipse is indicative of full heat redistribution from KELT-11b's dayside to nightside, assuming a clear dayside. These potentially unusual results for KELT-11b's composition are suggestive of new challenges on the horizon for atmosphere and formation models in the face of increasingly precise measurements of exoplanet spectra.

Knicole D. Colón↗

DOE OSTI2026

Quark flavor equilibration of the quark-gluon plasma

The early stage of a heavy-ion collision is marked by rapid entropy production and the transition from a gluon saturated initial condition to a plasma of quarks and gluons that evolves hydrodynamically. However, during the early times of the hydrodynamic evolution, the chemical composition of the QCD medium is still largely unknown. We present a study of quark chemical equilibration in the (Q)GP using a novel model of viscous hydrodynamic evolution in partial chemical equilibrium. Motivated by the success of gluon saturated initial condition models, we initialize the QCD medium as a completely gluon dominated state. Local quark production during the hydrodynamic phase is then simulated through the evolution of time-dependent fugacities for each independent quark flavor, with the timescales set as free parameters to compare different rates of equilibration. We present the results of complete heavy-ion collision simulations using this partial chemical equilibrium model, and show the effects on hadronic and electromagnetic observables. In particular, we show that the development of flow is sensitive to the equilibration timescale, providing an empirical way to probe the chemical equilibration of the QCD medium.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

CO and [C ii] line emission of molecular clouds: the impact of stellar feedback and non-equilibrium chemistry

We analyse synthetic 12 CO, 13 CO, and [C ii] emission maps of molecular cloud (MC) simulations from the SILCC-Zoom project. We present radiation, magnetohydrodynamic zoom-in simulations of individual clouds, both with and without radiative stellar feedback, forming in a turbulent multiphase interstellar medium following on-the-fly the evolution of e.g. H 2 , CO, and C + . We introduce a novel post-processing routine based on cloudy which accounts for higher ionization states of carbon due to stellar radiation in H ii regions. Synthetic emission maps of [C ii] in and around feedback bubbles show that the bubbles are largely devoid of [C ii], as recently found in observations, which we attribute to the further ionization of C+ into C 2+ . For both 12 CO and 13 CO, the cloud-averaged luminosity ratio, $L_\rm {CO}/L_\rm {[C\, \small {II}]}$, can neither be used as a reliable measure of the H 2 mass fraction nor of the evolutionary stage of the clouds. We note a relation between the $I_\rm {CO}/I_\rm {[C\, \small {II}]}$ intensity ratio and the H 2 mass fraction for individual pixels of our synthetic maps. The scatter, however, is too large to reliably infer the H 2 mass fraction. Finally, the assumption of chemical equilibrium overestimates H2 and CO masses by up to 150 and 50 per cent, respectively, and $L_\rm {CO}$ by up to 60 per cent. The masses of H and C + would be underestimated by 65 and 30 per cent, respectively, and $L_\rm {[C\, \small {II}]}$ by up to 35 per cent. Hence, the assumption of chemical equilibrium in MC simulations introduces intrinsic errors of a factor of 2 in chemical abundances, luminosities, and luminosity ratios.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2022

Design of Hypervelocity Flow Generator (HFG) and Its Diagnostics

Ground facilities for hypersonic research are a key element for successful development of aerodynamically proven hypervelocity vehicles. Design concepts and diagnostics of a hypervelocity flow generator (HFG) were made as a test platform for hypersonic/hypervelocity spacecraft models at the NASA Langley Research Center. The HFG is a hypersonic flow field generator using optically heated gas which is blown into an 80 cu m vacuum chamber. The vacuum chamber is kept at a stable vacuum pressure with a combination of three large vacuum pumps, while the HFG is in the test mode. The HFG provides a relatively small test section with approximately a 20 cm window. This facility was designed to generate 2.45 km/sec of flow speed, and potentially generate a continuous flow with the nozzle and vacuum system. The window in test section provides a direct view of the shock wave around a model in order to measure temperature, pressure, and density profile within the shock layer. One of the key test goals under this project is to understand why the emission spectra from the standing shockwave plasma predicted by Lora-Loran codes are significantly different from the measured emission spectra from the Flight Investigation Reentry Environment (FIRE II) Flight. The correct estimate of the thermal loading on the leading edge of hypersonic vehicles greatly affects the aerodynamic design, the material selection for the vehicle, and the cooling requirement and can be obtained by the precise modeling of emission spectra from shockwave plasma. However, the estimation of thermal loading is not an easy task due to complex non-equilibrium radiative process within high temperature shock layers that still falls into a category of cold plasma. Direct flight experiments are the most desirable, but not a cost-effective approach. Analysis by computational fluid dynamics (CFD) offers many test flexibilities. However, the CFD codes must be fully tested and validated with experimental data before the codes are effectively used for practical design. Large discrepancies between experiments and codes appear in hypersonic/hypervelocity flow regimes at high altitudes of 60 km ~ 90 km. This HFG facility offers some important parameters for CFD code validation, such as collision cross-sections, relaxation times, reaction rate coefficients and transportation coefficients. The HFG test facility is based on the ejection flow of high temperature gas heated over to 3500 K through a nozzle. The tungsten gas chamber of the HFG is heated up to a desired temperature by a 60 kW optical power beam source. This system consists of an optical power source, a thermal chamber, an expansion nozzle, a test section, and an 80 cu m vacuum tank. 60 kW optical input power is obtained from the 150 kW Vortek arc lamp system (by Vortek Industries, Vancouver, Canada). This optical beam is focused to heat the gas chamber within which a flow media is heated. The maximum achievable temperature of the flow medium reached approximately 3500 K or even higher but is limited by the melting point of the chamber material used. The exhaust velocity through the nozzle was determined by the stagnation temperature and the molecular weight of the working medium at the test section. To provide design parameters, a NASA Chemical Equilibrium with Application (CEA) computer program is used for the simulation of aerothermal data. This CEA program can calculate chemical equilibrium and properties of complex mixtures using shock tube parameters. For nitrogen gas at 2666 K stagnation temperature, the maximum achievable velocity at the test section is approximately 2.45 km/sec which is within the range of the thermal velocity of 8000 K shock layer. Based on the calculation through the CEA program, the design parameters of a HFG were determined and implemented for the test section that includes an expansion nozzle. The installed test section of the experimental facility can sustain a condition of a re-entry vehicle from the Space at an altitude of 60-90 km. After installation of the HFG, the system was fully tested and its operational parameters were measured. An 80 cu m vacuum chamber of HFG was set at 1 torr level to keep a stable downstream condition. The pumping time to reach the minimum vacuum pressure (~ 1 torr) at the test chamber from atmospheric pressure was approximately an hour using Kinney (MBV-14000/MB -1600/KT-300) and Stokes (Model 1772 and 412) pumps. Such a setup condition allowed a continued stable operation of the HFG experiment with flowrates through 1-, 3-, or 5-mm diameters of nozzle throat. The flow characteristics of the HFG for various operating conditions were performed using a focused Schlieren method. At 0.8 torr chamber pressure, a barrel shock was observed at the test section. With a sphere obstacle of 12 mm diameter in the flow, a bow shock (~ 2-mm thickness) was observed by a focused Schlieren visualization method.

Hypervelocity flow↗

NASA NTRS1990

The chemical effects of the Martian environment on power system component materials: A theoretical approach

In the foreseeable future, an expedition may be undertaken to explore the planet Mars. Some of the power source options being considered for such a mission are photovoltaics, regenerative fuel cells and nuclear reactors. In addition to electrical power requirements, environmental conditions en route to Mars, in the planetary orbit and on the Martian surface must be simulated and studied in order to anticipate and solve potential problems. Space power systems components such as photovoltaic arrays, radiators, and solar concentrators may be vulnerable to degradation in the Martian environment. Natural characteristics of Mars which may pose a threat to surface power systems include high velocity winds, dust, ultraviolet radiation, large daily variation in temperature, reaction to components of the soil, atmosphere and atmospheric condensates as well as synergistic combinations. Most of the current knowledge of the characteristics of the Martian atmosphere and soil composition was obtained from the Viking 1 and 2 missions in 1976. A theoretical study is presented which was used to assess the effects of the Martian atmospheric conditions on the power systems components. A computer program written at NASA-Lewis for combustion research that uses a free energy minimization technique was used to calculate chemical equilibrium for assigned thermodynamic states of temperature and pressure. The power system component materials selected for this study include: silicon dioxide, silicon, carbon, copper, and titanium. Combinations of environments and materials considered include: (1) Mars atmosphere with power surface material, (2) Mars atmosphere and dust component with power surface material, and (3) Mars atmosphere and hydrogen peroxide or superoxide or superoxide with power system material. The chemical equilibrium calculations were performed at a composition ratio (oxidant to reactant) of 100. The temperature for the silicon dioxide material and silicon, which simulate photovoltaic cells, were 300 and 400 K; for carbon, copper and titanium, which simulate radiator surfaces, 300, 500, and 1000 K. All of the systems were evaluated at pressures of 700, 800, and 900 Pa, which stimulate the Martian atmosphere.

Perez-Davis, Marla E.↗

NASA NTRS1971

Thermodynamic properties and theoretical rocket performance of hydrogen to 100,000 K and 1.01325 x 10 to the 8th power N/sq m

The composition and thermodynamic properties were calculated for 100 to 110,000 K and 1.01325 x 10 to the 2nd power to 1.01325 x 10 to the 8th power N/sq m for chemical equilibrium in the Debye-Huckel and ideal-gas approximations. Quantities obtained were the concentrations of hydrogen atoms, protons, free electrons, hydrogen molecules, negative hydrogen ions, hydrogen diatomic molecular ions, and hydrogen triatomic molecular ions, and the enthalpy, entropy, average molecular weight, specific heat at constant pressure, density, and isentropic exponent. Electronically excited states of H and H2 were included. Choked, isentropic, one-dimensional nozzle flow with shifting chemical equilibrium was calculated to the Debye-Huckel and ideal-gas approximations for stagnation temperatures from 2500 to 100,000 K. The mass flow per unit throat area and the sonic flow factor were obtained. The pressure ratio, temperature, velocity, and ideal and vacuum specific impulses at the throat and for pressure ratios as low as 0.000001 downstream were found. For high temperatures at pressures approaching 1.01325 x 10 to the 8th power N/sq m, the ideal-gas approximation was found to be inadequate for calculations of composition, precise thermodynamic properties, and precise nozzle flow. The greatest discrepancy in nozzle flow occurred in the exit temperature, which was as much as 21 percent higher when the Debye-Huckel approximation was used.

Patch, R. W.↗

NASA NTRS2003

Internal Flow Thermal/Fluid Modeling of STS-107 Port Wing in Support of the Columbia Accident Investigation Board

As part of the aero-thermodynamics team supporting the Columbia Accident Investigation Board (CAB), the Marshall Space Flight Center was asked to perform engineering analyses of internal flows in the port wing. The aero-thermodynamics team was split into internal flow and external flow teams with the support being divided between shorter timeframe engineering methods and more complex computational fluid dynamics. In order to gain a rough order of magnitude type of knowledge of the internal flow in the port wing for various breach locations and sizes (as theorized by the CAB to have caused the Columbia re-entry failure), a bulk venting model was required to input boundary flow rates and pressures to the computational fluid dynamics (CFD) analyses. This paper summarizes the modeling that was done by MSFC in Thermal Desktop. A venting model of the entire Orbiter was constructed in FloCAD based on Rockwell International s flight substantiation analyses and the STS-107 reentry trajectory. Chemical equilibrium air thermodynamic properties were generated for SINDA/FLUINT s fluid property routines from a code provided by Langley Research Center. In parallel, a simplified thermal mathematical model of the port wing, including the Thermal Protection System (TPS), was based on more detailed Shuttle re-entry modeling previously done by the Dryden Flight Research Center. Once the venting model was coupled with the thermal model of the wing structure with chemical equilibrium air properties, various breach scenarios were assessed in support of the aero-thermodynamics team. The construction of the coupled model and results are presented herein.

Sharp, John R.↗

NASA NTRS2016

An Iron-Rain Model for Core Formation on Asteroid 4 Vesta

Asteroid 4 Vesta is differentiated into a crust, mantle, and core, as demonstrated by studies of the eucrite and diogenite meteorites and by data from NASA's Dawn spacecraft. Most models for the differentiation and thermal evolution of Vesta assume that the metal phase completely melts within 20 degrees of the eutectic temperature, well before the onset of silicate melting. In such a model, core formation initially happens by Darcy flow, but this is an inefficient process for liquid metal and solid silicate. However, the likely chemical composition of Vesta, similar to H chondrites with perhaps some CM or CV chondrite, has 13-16 weight percent S. For such compositions, metal-sulfide melting will not be complete until a temperature of at least 1350 degrees Centigrade. The silicate solidus for Vesta's composition is between 1100 and 1150 degrees Centigrade, and thus metal and silicate melting must have substantially overlapped in time on Vesta. In this chemically and physically more likely view of Vesta's evolution, metal sulfide drops will sink by Stokes flow through the partially molten silicate magma ocean in a process that can be envisioned as "iron rain". Measurements of eucrites show that moderately siderophile elements such as Ni, Mo, and W reached chemical equilibrium between the metal and silicate phases, which is an important test for any Vesta differentiation model. The equilibration time is a function of the initial metal grain size, which we take to be 25-45 microns based on recent measurements of H6 chondrites. For these sizes and reasonable silicate magma viscosities, equilibration occurs after a fall distance of just a few meters through the magma ocean. Although metal drops may grow in size by merger with other drops, which increases their settling velocities and decreases the total core formation time, the short equilibration distance ensures that the moderately siderophile elements will reach chemical equilibrium between metal and silicate before metal drop merger becomes important. In this model, there must be at least 30 percent melting of the silicate phase when metal melting is complete, corresponding to a crust thickness of at least 30 kilometers on Vesta, consistent with Dawn gravity observations. Greater degrees of silicate melting and a correspondingly thicker crust are possible if Vesta accreted sufficiently rapidly.

Kiefer, Walter S.↗

NASA NTRS1988

Experimental verification of the thermodynamic properties for a jet-A fuel

Thermodynamic properties for a Jet-A fuel were determined by Shell Development Company in 1970 under a contract for NASA Lewis Research Center. The polynomial fit necessary to include Jet-A fuel (liquid and gaseous phases) in the library of thermodynamic properties of the NASA Lewis Chemical Equilibrium Program is calculated. To verify the thermodynamic data, the temperatures of mixtures of liquid Jet-A injected into a hot nitrogen stream were experimentally measured and compared to those calculated by the program. Iso-octane, a fuel for which the thermodynamic properties are well known, was used as a standard to calibrate the apparatus. The measured temperatures for the iso-octane/nitrogen mixtures reproduced the calculated temperatures except for a small loss due to the non-adiabatic behavior of the apparatus. The measurements for Jet-A were corrected for this heat loss and showed excellent agreement with the calculated temperatures. These experiments show that this process can be adequately described by the thermodynamic properties fitted for the Chemical Equilibrium Program.

Graciasalcedo, Carmen M.↗

NASA NTRS1994

Collisional-Radiative Nonequilibrium and Precursor Effects in a Nitrogen Shock Wave

Improvements to a plasma code with a Collisional-Radiative (CR) non-equilibrium model are made, allowing for a more accurate description of the physical processes. The code allows for non-Boltzmann distributions of the electronic excited states by convecting separately each excited state, as a pseudo-specie. Each molecular state has also its own vibrational temperature, while a global rotational temperature is assumed. The free electron temperature is different from those of the excited states, and the electron heat conduction is also included. The CR model also uses a unique coupling between chemistry and vibrational energy (C-V coupling), which is fully coherent, and has the property of establishing thermal equilibrium as well as chemical equilibrium, on its own. We have also included a coupling between electronic excitations and vibrational energy (X-V coupling), which can have a strong influence on the vibrational temperature of some states. The recent improvements include the multi- temperature dependence of the chemical rates for associative ionization, as well as the estimation of the internal energies transferred during this process. Additionally, the distribution of energy into different translational modes (electron and heavy particles) is now correctly modeled. This provides a very rapid heating mechanism for the free electrons, since it is found that the electrons are generated with an average thermal energy of the same order as the heavy particle translational energy. This effect was observed by Gorelov et al in a recent paper, and lead to pronounced peaks in electron temperature immediately behind the shock. We will attempt ro reproduce this phenomenon. The last modification concerns the inclusion of the radiative terms into the calculations, thus enabling us to observe the effect of radiative losses and radiation transport. Preliminary tests have shown that the radiative losses are not negligible, i.e. the shock velocity drops when the radiative emission is included. In addition, we have observed some precursor excitation and ionization phenomena. These may be important at high shock velocities, and this will be investigated in detail. Precursor phenomena were also observed (in air) by Gorelov et al, and our results (for pure nitrogen) will be qualitatively compared with theirs.

Cambier, Jean-Luc↗