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NASA NTRS1991

Surface reaction and pore diffusion in flow-tube reactors

The interaction of gas diffusion with surface reaction in porous solids is discussed and applied specifically to heterogeneous rate measurements in flow-tube reactors. External diffusion to the outer surface of a reactive solid, internal diffusion within the pores, surface reaction, and laminar flow are considered. A procedure is developed to correct observed surface rate constants for the interaction of these processes. Measured surface areas and bulk densities are used to construct a semiempirical model for porous diffusion in vapor-formed HNO3-H2O ices which are used to simulate polar stratospheric cloud surfaces. The model is tested experimentally by varying the thickness of these ices from about 15 to 120 microns. The results are consistent with the model predictions and show that the HNO3-H2O ices used are highly porous, and the internal surface must be considered in calculating kinetic parameters from observed loss rates. The best fit of the data yields a tortuosity factor of 3.3 +/-1.1 for the ice substrates.

Keyser, Leon F.↗

DOE OSTI2024

Defect Production and Microstructural Feature Impact for Radiation Damage in Additively Manufactured 316 Stainless Steel

This milestone presents multi-scale modeling research results for additively manufactured 316 stainless steel. A combination of phase field, cluster dynamics, molecular dynamics, and density functional theory with machine learning is used, allowing for predictions of radiation-driven microstructural evolution in additively manufactured 316 stainless steel over a range of temperatures, damage rates, neutron spectra, and microstructures, and supporting the development of combined ion and neutron irradiation for material qualification. Informed by ion irradiation and neutron irradiation results across the Advanced Materials and Manufacturing Technologies program, we investigate the unique aspects of radiation-driven microstructure evolution in additively manufactured 316 stainless steel. In particular, we focus on understanding the impact of carbon concentration (varying, for example, between the 316L and 316H standards) on void formation; radiation-induced segregation at dislocation cells and grain boundaries; and the evolution of dislocation loops and network dislocation populations. We find that the unique characteristics of the additively manufactured microstructures must be accounted for in understanding the evolution of dislocation populations under thermal and irradiation conditions, such as the variation in sink strengths arising due to the variation in dislocation density. We also find that the radiation-induced segregation of Cr and Ni to grain boundaries and cell walls differs due to the differences in their defect sink biases. We also find that increasing the Ni content can slow vacancy diffusion, which may provide a mechanism for the observed reduction in transient swelling rate for austenitic Fe-Cr-Ni alloys with increasing Ni content. In addition, ion irradiations have shown that increasing carbon content in 316 SS results in a larger population of smaller voids, suggesting reduced vacancy diffusion. Our results show that the carbon content of additively manufactured 316 SS has a significant impact on the migration rate of defect clusters. The presence of carbon atoms results in carbon-vacancy trapping, significantly reducing the diffusion rate of vacancies. Carbon atoms may also be trapped near the surface of a void, which may reduce void growth by trapping vacancies that diffuse toward the void.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Representing methane emissions from wet tropical forest soils using microbial functional groups constrained by soil diffusivity

Tropical ecosystems contribute significantly to global emissions of methane (CH 4 ), and landscape topography influences the rate of CH 4 emissions from wet tropical forest soils. However, extreme events such as drought can alter normal topographic patterns of emissions. Here we explain the dynamics of CH 4 emissions during normal and drought conditions across a catena in the Luquillo Experimental Forest, Puerto Rico. Valley soils served as the major source of CH 4 emissions in a normal precipitation year (2016), but drought recovery in 2015 resulted in dramatic pulses in CH 4 emissions from all topographic positions. Geochemical parameters including (i) dissolved organic carbon (C), acetate, and soil pH and (ii) hydrological parameters like soil moisture and oxygen (O 2 ) concentrations varied across the catena. During the drought, soil moisture decreased in the slope and ridge, and O 2 concentrations increased in the valley. We simulated the dynamics of CH 4 emissions with the Microbial Model for Methane Dynamics-Dual Arrhenius and Michaelis–Menten (M3D-DAMM), which couples a microbial functional group CH 4 model with a diffusivity module for solute and gas transport within soil microsites. Contrasting patterns of soil moisture, O 2 , acetate, and associated changes in soil pH with topography regulated simulated CH 4 emissions, but emissions were also altered by rate-limited diffusion in soil microsites. Changes in simulated available substrate for CH 4 production (acetate, CO 2 , and H 2 ) and oxidation (O 2 and CH 4 ) increased the predicted biomass of methanotrophs during the drought event and methanogens during drought recovery, which in turn affected net emissions of CH 4 . A variance-based sensitivity analysis suggested that parameters related to aceticlastic methanogenesis and methanotrophy were most critical to simulate net CH 4 emissions. This study enhanced the predictive capability for CH 4 emissions associated with complex topography and drought in wet tropical forest soils.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1997

Bulk Growth of Wide Band Gap II-VI Compound Semiconductors by Physical Vapor Transport

The mechanism of physical vapor transport of II-VI semiconducting compounds was studied both theoretically, using a one-dimensional diffusion model, as well as experimentally. It was found that the vapor phase stoichiometry is critical in determining the vapor transport rate. The experimental heat treatment methods to control the vapor composition over the starting materials were investigated and the effectiveness of the heat treatments was confirmed by partial pressure measurements using an optical absorption technique. The effect of residual (foreign) gas on the transport rate was also studies theoretically by the diffusion model and confirmed experimentally by the measurements of total pressure and compositions of the residual gas. An in-situ dynamic technique for the transport rate measurements and a further extension of the technique that simultaneously measured the partial pressures and transport rates were performed and, for the first time, the experimentally determined mass fluxes were compared with those calculated, without any adjustable parameters, from the diffusion model. Using the information obtained from the experimental transport rate measurements as guideline high quality bulk crystal of wide band gap II-VI semiconductor were grown from the source materials which undergone the same heat treatment methods. The grown crystals were then extensively characterized with emphasis on the analysis of the crystalline structural defects.

Su, Ching-Hua↗

NASA NTRS1997

Bulk Growth of Wide Band Gap II-VI Compound Semiconductors by Physical Vapor Transport

Su, Ching-Hua↗

DOE OSTI2022

Single molecule tracking of bacterial cell surface cytochromes reveals dynamics that impact long-distance electron transport

Using a series of multiheme cytochromes, the metal-reducing bacterium Shewanella oneidensis MR-1 can perform extracellular electron transfer (EET) to respire redox-active surfaces, including minerals and electrodes outside the cell. While the role of multiheme cytochromes in transporting electrons across the cell wall is well established, these cytochromes were also recently found to facilitate long-distance (micrometer-scale) redox conduction along outer membranes and across multiple cells bridging electrodes. Recent studies proposed that long-distance conduction arises from the interplay of electron hopping and cytochrome diffusion, which allows collisions and electron exchange between cytochromes along membranes. However, the diffusive dynamics of the multiheme cytochromes have never been observed or quantified in vivo, making it difficult to assess their hypothesized contribution to the collision-exchange mechanism. Here, we use quantum dot labeling, total internal reflection fluorescence microscopy, and single-particle tracking to quantify the lateral diffusive dynamics of the outer membrane-associated decaheme cytochromes MtrC and OmcA, two key components of EET in S. oneidensis. We observe confined diffusion behavior for both quantum dot-labeled MtrC and OmcA along cell surfaces (diffusion coefficients D MtrC = 0.0192 ± 0.0018 µm 2 /s, D OmcA = 0.0125 ± 0.0024 µm 2 /s) and the membrane extensions thought to function as bacterial nanowires. We find that these dynamics can trace a path for electron transport via overlap of cytochrome trajectories, consistent with the long-distance conduction mechanism. The measured dynamics inform kinetic Monte Carlo simulations that combine direct electron hopping and redox molecule diffusion, revealing significant electron transport rates along cells and membrane nanowires.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Tuning the Kinetics of Zinc-Ion Insertion/Extraction in V 2 O 5 by In Situ Polyaniline Intercalation Enables Improved Aqueous Zinc-Ion Storage Performance

Rechargeable zinc-ion batteries (ZIBs) are emerging as a promising alternative for Li-ion batteries. However, the developed cathodes suffer from sluggish Zn 2+ diffusion kinetics, leading to poor rate capability and inadequate cycle life. Herein, an in situ polyaniline (PANI) intercalation strategy is developed to facilitate the Zn 2+ (de)intercalation kinetics in V 2 O 5 . In this way, a remarkably enlarged interlayer distance (13.90 Å) can be constructed alternatively between the V-O layers, offering expediting channels for facile Zn 2+ diffusion. Importantly, the electrostatic interactions between the Zn 2+ and the host O 2- , which is another key factor in hindering the Zn 2+ diffusion kinetics, can be effectively blocked by the unique π-conjugated structure of PANI. As a result, the PANI-intercalated V 2 O 5 exhibits a stable and highly reversible electrochemical reaction during repetitive Zn 2+ insertion and extraction, as demonstrated by in situ synchrotron X-ray diffraction and Raman studies. Further first-principles calculations clearly reveal a remarkably lowered binding energy between Zn 2+ and host O 2- , which explains the favorable kinetics in PANI-intercalated V 2 O 5 . Benefitting from the above, the overall electrochemical performance of PANI-intercalated V 2 O 5 electrode is remarkable improved, exhibiting excellent high rate capability of 197.1 mAh g -1 at current density of 20 A g -1 with capacity retention of 97.6% over 2000 cycles.

36 MATERIALS SCIENCE↗

NASA NTRS2001

Reaction Kernel Structure of a Slot Jet Diffusion Flame in Microgravity

Diffusion flame stabilization in normal earth gravity (1 g) has long been a fundamental research subject in combustion. Local flame-flow phenomena, including heat and species transport and chemical reactions, around the flame base in the vicinity of condensed surfaces control flame stabilization and fire spreading processes. Therefore, gravity plays an important role in the subject topic because buoyancy induces flow in the flame zone, thus increasing the convective (and diffusive) oxygen transport into the flame zone and, in turn, reaction rates. Recent computations show that a peak reactivity (heat-release or oxygen-consumption rate) spot, or reaction kernel, is formed in the flame base by back-diffusion and reactions of radical species in the incoming oxygen-abundant flow at relatively low temperatures (about 1550 K). Quasi-linear correlations were found between the peak heat-release or oxygen-consumption rate and the velocity at the reaction kernel for cases including both jet and flat-plate diffusion flames in airflow. The reaction kernel provides a stationary ignition source to incoming reactants, sustains combustion, and thus stabilizes the trailing diffusion flame. In a quiescent microgravity environment, no buoyancy-induced flow exits and thus purely diffusive transport controls the reaction rates. Flame stabilization mechanisms in such purely diffusion-controlled regime remain largely unstudied. Therefore, it will be a rigorous test for the reaction kernel correlation if it can be extended toward zero velocity conditions in the purely diffusion-controlled regime. The objectives of this study are to reveal the structure of the flame-stabilizing region of a two-dimensional (2D) laminar jet diffusion flame in microgravity and develop a unified diffusion flame stabilization mechanism. This paper reports the recent progress in the computation and experiment performed in microgravity.

Takahashi, F.↗

DOE OSTI2023

Ab Initio Simulations of Tritium Diffusion in Al-Rich Iron Aluminide Coating Phases

Surface coatings of steels used in extreme conditions and corrosive environments generally aim to provide protection and increased durability. In the case of tritium-producing burnable absorber rods (TPBARs) used in nuclear reactors, a 316 stainless steel has been coated with Al. Scanning transmission electron microscopy (STEM) characterization of the coating found three Al-rich (>60 atom % Al) iron aluminide alloys identified as hexagonal FeNiAl 5 , monoclinic Fe 4 Al 13 , and orthorhombic Fe 2 Al 5 . Density functional theory simulations using nudged elastic band have been performed to investigate the diffusion of interstitial tritium in each Al-rich iron aluminide phase. While FeNiAl 5 and Fe 4 Al 13 can be viewed as the stacking of two layers, the structural peculiarity of Fe 2 Al 5 is that channels of variable Al vacancy content are present along the c-axis. Therefore, three stoichiometries for Fe 2 Al x phase, namely, Fe 2 Al 4 , Fe 2 Al 5 , and Fe 2 Al 6 , have been considered to evaluate the impact of Al vacancy concentration on tritium diffusion behavior. Altogether, we found that at 600 K, tritium diffusion decreases from a faster rate in the channels of Fe 2 Al x phases (D T ≤ 10 –11 m 2 ·s –1 ) to Fe 4 Al 13 (D T ≈ 10–12 m2·s–1), and finally in FeNiAl5 (D T ≈ 10 –13 m 2 ·s –1 ). Here, we also find that interstitial tritium generally diffuses faster in Fe–Al coating phases than in the tritium breeding material γ-LiAlO 2 (D T ≈ 10 –14 m 2 ·s –1 ) but slightly slower than in 316 stainless steel (D T ≈ 10 –10 m 2 ·s –1 ).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1972

The effect of ambient pressure on the evaporation rate of materials

A simple expression is obtained using a diffusion model for the effect of ambient pressure on the outgassing or evaporation rate of materials. The correctness of the expression is demonstrated by comparing the estimates from this expression with actual weight loss measurements. It is shown that the rate of mass loss is governed by the ratio of mean free path to the characteristic dimension of the surface in question.

Naumann, R. J.↗

NASA NTRS1995

Studies on Methanol Crossover in Liquid-Feed Direct Methanol Pem Fuel Cells

The performance of liquid feed direct methanol fuel cells using various types of Nafion membranes as the solid polymer electrolyte have been studied. The rate of fuel crossover and electrical performance has been measured for cells with Nafion membranes of various thicknesses and equivalent weights. The crossover rate is found to decrease with increasing thickness and applied current. The dependence of crossover rate on current density can be understood in terms of a simple linear diffusion model which suggests that the crossover rate can be influenced by the electrode structure in addition to the membrane. The studies suggest that Nafion EW 1500 is a very promising alternate to Nafion EW 1100 for direct methanol fuel cells.

Methanol Pem Fuel↗

DOE OSTI2024

Adsorption of terbium (III) on DGA and LN resins: Thermodynamics, isotherms, and kinetics

Two commercially available extraction chromatography (EXC) resins containing N,N,N’,N’-tetra-n-octyldiglycolamide (DGA Resin, Normal, 50 – 100 μm) and Bis(2-ethylhexyl) phosphate (LN Resin, 100 – 150 μm) were used as adsorbents to study fundamental adsorption properties such as thermodynamic values, equilibrium isotherms, and kinetic uptake models for terbium(III) adsorption. Weight distribution ratios (D w ) for terbium on DGA and LN resins were measured using a [ 160 Tb]Tb 3+ radiometric tracer in nitric acid as a function of acidity, temperature, initial analyte concentration, and equilibrium time. The D w values showed increasing binding affinity for DGA resin at high nitric acid concentrations and decreasing binding affinity for LN resins. Thermodynamic studies for DGA and LN resins revealed that the Gibbs free energy (ΔG) increased consistently with temperature. To model equilibrium data, increasingly higher parameter equilibrium isotherm models (Henry (1) < Langmuir, Freundlich (2) < Redlich-Peterson (3) < Fritz-Schluender (4)) were compared on their root mean squared errors (RMSE) and adjusted determination coefficients to determine the most applicable model. In all cases, the empirical four-parameter Fritz-Schluender isotherm demonstrated a superior fit. Similar comparisons for reaction-based kinetic models (Pseudo-first-order < Pseudo-second-order < Pseudo-n-order) revealed that the higher-order PNO model yielded a superior fit of kinetic data for both resins. Furthermore, in some cases, adsorption isotherms and kinetic models could also be modeled by a lower-order model with minimal change in error parameters. Weber-Morris plots revealed that two linear sections are observed for each resin, where the first linear segment is attributed to fast (film diffusion) adsorption of terbium, followed by slower intraparticle diffusion of terbium through the pores as the rate-limiting step. Based on the Weber-Morris plot, both film and intraparticle diffusion are involved in controlling the kinetic rate of adsorption for DGA and LN resins.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2020

Radiation-Induced Effects on the Extraction Properties of Hexa-n-octylnitrilo-triacetamide (HONTA) Complexes of Americium and Europium

The candidate An(III)/Ln(III) separation ligand hexa-n-octylnitrilo-triacetamide (HONTA) was irradiated under envisioned SELECT (Solvent Extraction from Liquid waste using Extractants of CHON-type for Transmutation) process conditions (n-dodecane/0.1 M HNO 3 ) using a solvent test loop in conjunction with cobalt-60 gamma irradiation. The extent of HONTA radiolysis and complimentary degradation product formation was quantified by HPLC-ESI-MS/MS. Further, the impact of HONTA radiolysis on process performance was evaluated by measuring the change in 243 Am and 154 Eu distribution ratios as a function of absorbed gamma dose. HONTA was found to decay exponentially with increasing dose, affording a dose coefficient of d = (4.48 ± 0.19) × 10 –3 kGy –1 . Multiple degradation products were detected by HPLC-ESI-MS/MS with dioctylamine being the dominant quantifiable species. Both 243 Am and 154 Eu distribution ratios exhibited an induction period of ~70 kGy for extraction (0.1 M HNO 3 ) and back-extraction (4.0 M HNO 3 ) conditions, after which both values decreased with absorbed dose. The decrease in distribution ratios was attributed to a combination of the destruction of HONTA and ingrowth of dioctylamine, which is capable of interfering in metal ion complexation. Furthermore, the loss of HONTA with absorbed gamma dose was predominantly attributed to its reaction with the n-dodecane radical cation (R˙ + ). These R˙ + reaction kinetics were measured for HONTA and its 241 Am and 154 Eu complexes using picosecond pulsed electron radiolysis techniques. All three second-order rate coefficients (k) were essentially diffusion limited in n-dodecane indicating a significant reaction pathway: k(HONTA + R˙ + ) = (7.6 ± 0.8) × 10 9 M –1 s –1 , k(Am(HONTA) 2 + R˙ + ) = (7.1 ± 0.7) × 10 10 M –1 s –1 , and k(Eu(HONTA) 2 + R˙ + ) = (9.5 ± 0.5) × 10 10 M –1 s –1 . HONTA-metal ion complexation afforded an order-of-magnitude increase in rate coefficient. Additional nanosecond time-resolved measurements showed that both direct and indirect HONTA radiolysis yielded the short-lived (< 100 ns) HONTA radical cation and a second long-lived (µs) species identified as the HONTA triplet excited state. The latter was confirmed by a series of oxygen quenching picosecond pulsed electron measurements, affording a quenching rate coefficient of k( 3 [HONTA]* + O 2 ) = 2.2 × 10 8 M –1 s –1 . Overall, both the HONTA radical cation and triplet excited state are important precursors to the suite of measured HONTA degradation products.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

NASA NTRS1973

Condensed phase details in the time-independent combustion of AP/composite propellants

The problem of nonmetallized ammonium perchlorate (AP)/composite propellant combustion is studied with the aim of coherently interpreting apparently diverse experimental data. Three fundamental hypotheses are introduced: the extent of propellant degradation at the vaporization step has to be specified through a scientific criterion; condensed phase degradation of AP to vaporizable fragments is the overall rate-limiting reaction; the rate of combustion in the gas phase is controlled by diffusive-mixing processes. Theoretical predictions of the regression rates of AP are seen to match well with experimental observations. Theoretical curves of regression rate are presented for a typical composite propellant. It is seen through analyses that either of the two familiar models for the gas phase (flame sheet approximation and uniform combustion) describes the general behavior adequately, hence de-emphasizing the role of gas phase details in propellant combustion.

Kumar, R. N.↗

NASA NTRS1995

Finite Element Analysis of Poroelastic Composites Undergoing Thermal and Gas Diffusion

A theory for time-dependent thermal and gas diffusion in mechanically time-rate-independent anisotropic poroelastic composites has been developed. This theory advances previous work by the latter two authors by providing for critical transverse shear through a three-dimensional axisymmetric formulation and using it in a new hypothesis for determining the Biot fluid pressure-solid stress coupling factor. The derived governing equations couple material deformation with temperature and internal pore pressure and more strongly couple gas diffusion and heat transfer than the previous theory. Hence the theory accounts for the interactions between conductive heat transfer in the porous body and convective heat carried by the mass flux through the pores. The Bubnov Galerkin finite element method is applied to the governing equations to transform them into a semidiscrete finite element system. A numerical procedure is developed to solve the coupled equations in the space and time domains. The method is used to simulate two high temperature tests involving thermal-chemical decomposition of carbon-phenolic composites. In comparison with measured data, the results are accurate. Moreover unlike previous work, for a single set of poroelastic parameters, they are consistent with two measurements in a restrained thermal growth test.

Salamon, N. J.↗

DOE OSTI2021

Loss and Isotopic Fractionation of Alkali Elements during Diffusion-Limited Evaporation from Molten Silicate: Theory and Experiments

Moderately volatile elements (MVEs) are variably depleted in planetary bodies, reflecting the imprints of nebular and planetary processes. Among MVEs, Na, K, and Rb are excellent tracers for unraveling the history of MVE depletion in planetary bodies because they have similar geochemical behaviors but can be chemically fractionated by evaporation and condensation processes. Furthermore, K and Rb are amenable to high-precision isotopic analyses, which can help constrain the conditions of evaporation and condensation. To quantitatively understand why Na, K, and Rb are depleted in planetary bodies, we have carried out vacuum evaporation experiments from basaltic melt at 1200 and 1400 °C to study their evaporation kinetics and isotopic fractionations. We chose this composition because it is relevant to evaporation from small differentiated planetesimals. The Rb isotopic compositions of the evaporation residues were measured by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS), and the K isotopic compositions were measured along profiles across the residues by secondary ion mass spectrometry (SIMS). In the 1400 °C run products, we found that the concentrations of both K and Rb in the run products decreased from core to rim, which was accompanied by a heavy K isotope enrichment near the surface. This indicates that, in this run, evaporation was limited by diffusion. To use those data quantitatively, we derive analytical equations that describe the evaporation rate and isotopic fractionation associated with diffusion-limited evaporation from a sphere, slab, and cylinder in transient and quasi-steady state regimes. This model is used to tease out the roles that diffusive transport in the melt and evaporation at the melt/gas interface play in setting the elemental depletion and isotopic composition of the residue. Under our experimental conditions, volatility decreases in the order of Na, Rb, and K. Using our experimental results in a thermodynamic model, we have estimated the product γΓ of activity coefficients × evaporation coefficients of Na, Rb, and K. The measured isotopic compositions of the residues are well explained using Rayleigh distillations, whereby the relative volatilities of K and Rb isotopes are given by the square root of their masses. We use our results and previously published data to predict how K and Rb could have been lost as a function of temperature, melt composition, oxygen fugacity, and saturation degree relevant to Vesta’s building blocks. We find that the K and Rb depletions, K/Rb elemental fractionation, and δ 41 K and δ 87 Rb isotopic fractionations of Vesta (as sampled by howardite-eucrite-diogenite (HED) meteorites) are best explained by evaporation of submillimeter size objects for 0.1-10 years at moderate temperatures (~1050 °C) in a medium ~98.8% saturated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1990

Solubility and diffusion of hydrogen in IN-100 and Waspaloy

The solubility of hydrogen, at a fixed hydrogen pressure, was measured in two different heat treatment conditions in both IN-100 and Waspaloy by equilibrium and analysis. The diffusion coefficients were determined by measuring the rate of hydrogen evolution in a vacuum. Hydrogen evolution appeared to be a diffusion-controlled process in all cases. For hydrogen diffusion in Waspaloy, Delta H was 38.5 kJ and D0 was 2.6 x 10 to the -7th sq/s. For IN-100, Delta H was 68.2 kJ and D0 was 59 x 10 to the -7th sq/s. The values for Waspaloy are close to those for pure nickel. The values for IN-100 are more similar to high nickel alloys that show trapping or surface layer impedance.

Khan, A. S.↗

NASA NTRS2013

Uncertainty Determination for Aeroheating in Uranus and Saturn Probe Entries by the Monte Carlo Method

The 2013-2022 Decaedal survey for planetary exploration has identified probe missions to Uranus and Saturn as high priorities. This work endeavors to examine the uncertainty for determining aeroheating in such entry environments. Representative entry trajectories are constructed using the TRAJ software. Flowfields at selected points on the trajectories are then computed using the Data Parallel Line Relaxation (DPLR) Computational Fluid Dynamics Code. A Monte Carlo study is performed on the DPLR input parameters to determine the uncertainty in the predicted aeroheating, and correlation coefficients are examined to identify which input parameters show the most influence on the uncertainty. A review of the present best practices for input parameters (e.g. transport coefficient and vibrational relaxation time) is also conducted. It is found that the 2(sigma) - uncertainty for heating on Uranus entry is no more than 2.1%, assuming an equilibrium catalytic wall, with the uncertainty being determined primarily by diffusion and H(sub 2) recombination rate within the boundary layer. However, if the wall is assumed to be partially or non-catalytic, this uncertainty may increase to as large as 18%. The catalytic wall model can contribute over 3x change in heat flux and a 20% variation in film coefficient. Therefore, coupled material response/fluid dynamic models are recommended for this problem. It was also found that much of this variability is artificially suppressed when a constant Schmidt number approach is implemented. Because the boundary layer is reacting, it is necessary to employ self-consistent effective binary diffusion to obtain a correct thermal transport solution. For Saturn entries, the 2(sigma) - uncertainty for convective heating was less than 3.7%. The major uncertainty driver was dependent on shock temperature/velocity, changing from boundary layer thermal conductivity to diffusivity and then to shock layer ionization rate as velocity increases. While radiative heating for Uranus entry was negligible, the nominal solution for Saturn computed up to 20% radiative heating at the highest velocity examined. The radiative heating followed a non-normal distribution, with up to a 3x variation in magnitude. This uncertainty is driven by the H(sub 2) dissociation rate, as H(sub 2) that persists in the hot non-equilibrium zone contributes significantly to radiation.

Palmer, Grant↗