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NASA NTRS1978

A theoretical study of a laminar diffusion flame

Theoretical models of an axisymmetric laminar diffusion flame are discussed, with an emphasis on the behavior of such flames at increasing pressures. The flame-sheet or Burke-Schumann model (in terms of Bessel functions) and various boundary layer numerical solutions are presented and their results compared with experimental data. The most promising theoretical model combines the numerical flow field solution of the Patankar-Spalding computer code with the Pratt-Wormeck chemical reaction subroutine. The flame shapes for pressures of 1, 5, 10, 20, and 50 atmospheres were computed and agree remarkably well with experimental data. There is a noticeable shape change with pressure, believed to be a result of buoyancy effects. The chemical concentration profiles do not exhibit much dependence on pressure, a reflection of the fact that only one chemical mechanism was utilized at all pressures.

Frair, K. L.↗

NASA NTRS1997

Diffuse-Interface Methods in Fluid Mechanics

The authors review the development of diffuse-interface models of hydrodynamics and their application to a wide variety of interfacial phenomena. The authors discuss the issues involved in formulating diffuse-interface models for single-component and binary fluids. Recent applications and computations using these models are discussed in each case. Further, the authors address issues including sharp-interface analyses that relate these models to the classical free-boundary problem, related computational approaches to describe interfacial phenomena, and related approaches describing fully-miscible fluids.

SURFACE DIFFUSION↗

DOE OSTI2022

A Robust Numerical Treatment of Solid-Phase Diffusion in Pseudo Two-Dimensional Lithium-Ion Battery Models

Solid-phase diffusion in active materials of lithium-ion batteries significantly affects charging and safety-related behavior of lithium-ion batteries. Therefore, it is essential to develop an efficient and robust numerical algorithm for solving solid-phase diffusion equations in physics-based battery models. In this work, we discuss the origins of numerical instabilities that can occur when solving the solid-phase diffusion equations using iterative methods. Then, in order to resolve such issues, we propose a simple numerical treatment to the surface flux term of discretized solid-phase diffusion equations. To demonstrate its numerical robustness, the proposed method is implemented into a pseudo two-dimensional (P2D) physics-based battery model and simulations are conducted at wide ranges of operating conditions. Even with extremely poor initial guesses for the Li+ concentrations of the active materials, computations using the proposed method do not diverge and the their computational speeds are comparable to those with conventional initial guesses. Comprehensive tests of the proposed method are also performed with a dynamic current profile based on US06 driving profile and a multi-stage charging profile with very high initial C-rate (12C).

battery modeling↗

NASA NTRS1977

Cooling rate estimations based on kinetic modelling of Fe-Mg diffusion in olivine

A finite one-dimensional kinetic model was developed to estimate the cooling rates of lunar rocks. The model takes into consideration the compositional zonation of olivine and applies Buening and Buseck (1973) data on ion diffusion in olivine. Since the 'as-solidified' profile of a given olivine is not known, a step-function, with infinite gradient, is assumed; the position of this step is based on mass balance considerations of the measured compositional profile. A minimum cooling rate would be associated with the preservation of a given gradient. The linear cooling rates of lunar rocks 12002 and 15555 were estimated by use of the olivine cooling-rate indicator to be 10 C/day and 5 C/day, respectively. These values are lower than those obtained by dynamic crystallization studies (10-20 C/day).

Taylor, L. A.↗

DOE OSTI2018

Predicting Effective Diffusion Coefficients in Mudrocks Using a Fractal Model and Small-Angle Neutron Scattering Measurements

The determination of effective diffusion coefficients of gases or solutes in the water–saturated pore space of mudrocks is time consuming and technically challenging. Yet, reliable values of effective diffusion coefficients are important to predict migration of hydrocarbon gases in unconventional reservoirs, dissipation of (explosive) gases through clay barriers in radioactive waste repositories, mineral alteration of seals to geological CO 2 storage reservoirs and contaminant migration through aquitards. In this study, small angle and very small angle neutron scattering techniques have been utilized to determine a range of transport properties in mudrocks, including porosity, pore size distributions and surface and volume fractal dimensions of pores and grains, from which diffusive transport parameters can be estimated. Using a fractal model derived from Archie's Law, we calculate effective diffusion coefficients from these parameters and compare them to laboratory–derived effective diffusion coefficients for CO 2 , H 2 , CH 4 and HTO on either the same or related mudrock samples. The samples include Opalinus Shale from the underground laboratory in Mont Terri, Switzerland; Boom Clay from a core drilled in Mol, Belgium and a marine claystone cored in Utah, USA. The predicted values were compared to laboratory diffusion measurements. The measured and modeled diffusion coefficients show good agreement, differing generally by less than factor 5. Furthermore, neutron or X–ray scattering analysis is therefore proposed as a novel method for fast, accurate estimation of effective diffusion coefficients in mudrocks, together with simultaneous measurement of multiple transport parameters including porosity, pore size distributions and surface areas, important for (reactive) transport modelling.

58 GEOSCIENCES↗

DOE OSTI2020

Using a coupled dispersion model to estimate depletion of a tritium oxide plume by a forest

Tritium processing facilities may release tritium oxide (HTO) to the atmosphere which poses potential health risks to exposed co-located workers and to offsite individuals. Most radiological consequence analyses determine HTO dose by applying Gaussian plume models to simulate the transport of HTO. Within these models, deposition velocity is used to assess the sum of all deposition processes acting on the plume. While this may account for vegetative and soil uptake or respiration processes, it may currently lack inclusion of the complex interactions within heterogeneous forested environments. In this complex morphology, dispersion patterns are significantly altered by changing flow regimes above and below the forest canopy and by the transfer of plume material across the canopy boundary. To determine the effects of a heterogeneous forest canopy on an airborne HTO plume, a Gaussian plume model coupled with an advection-diffusion plume model was applied to estimate transport in the free atmosphere above the forest and within the forest canopy and understory. During 2012, wind speed and wind direction measurements taken at 5 heights, ranging from 2-m to 28-m, on an instrumented meteorological tower located in a loblolly pine forest at the Department of Energy (DOE) Savannah River Site (SRS), near Aiken, SC. From these measurements, model predictions were made over a full spectrum of meteorological conditions. Deposition and resuspension velocities were calculated based on the model-predicted flux of plume material across the top of the forest canopy. Additionally, net deposition velocity of the plume material was calculated as the difference between the deposition and resuspension velocities. The 1st and 5th percentile net deposition velocities were estimated to be 0.7 cm s-1 and 1.2 cm s-1, respectively.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

DOE OSTI2022

Modeling of a 43 GHz microplasma within a photonic crystal

The electron density (n e ) and argon metastable density (1 s 5 ) of a 43GHz microplasma are obtained using the zero-dimensional plasma kinetics solver (ZDPlasKin®) for an incident power of 160 and 1000mW and argon pressures of 10–600Torr (1.3 ×10 3 to 8.0 × 10 4 Pa). These simulations are compared with previously published experimental data. To determine the self-consistent electric field in the modeled plasma, the three-dimensional millimeter wave fields are computed as a function of electron density using ANSYS EM19.2, HFSS®. This electromagnetic field model is coupled to ZDPlasKin such that any increase in the simulated plasma density correctly attenuates the simulated electric field within the microplasma. The electron density is found to be sensitive to argon gas temperature, so a two-zone temperature model was needed to obtain agreement with experimental measurements. The temperature in the central core of the microplasma was determined by a previous experimental study. That temperature was used as an input to the model for the simulation of volume recombination losses. The outer regions of the microplasma are assumed to be in equilibrium with the walls (300K). This second temperature was used in the model to determine diffusion losses. The modeled electron and metastable densities are of the order 10 20 and 10 18 m –3 , respectively. This is in good agreement with those measured experimentally as long as the two-zone temperature model is used. In the absence of a hot gas core, the modeled three-body recombination rates are excessive and the simulation severely under-predicts the electron density and over-estimates the metastable density. We conclude that the millimeter wave microplasma has a hot core (2500K at 600 Torr) that rarifies the argon gas and effectively reduces three-body recombination. Furthermore, this allows one to achieve high electron density on the order of 10 20 m –3 with only 100mW of wave power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

The isotopic composition of cosmic-ray beryllium and its implication for the cosmic ray's age

We report a new measurement of the cosmic-ray isotopic composition of beryllium in the low-energy range from 35 to 113 MeV per nucleon. This measurement was made using the High Energy Telescope of the CRS experiment on the Voyager 1 and 2 spacecraft during the time period from 1977 to 1991. In this overall time period of 14 years the average solar modulation level was about 500 MV. The cosmic-ray beryllium isotopes were completely separated with an average mass resolution sigma of 0.185 amu. The isotope fractions of Be-7, Be-9, and Be-10 obtained are 52.4 +/- 2.9%, 43.3 +/- 3.7%, and 4.3 +/- 1.5%, respectively. The measured cosmic-ray abundances of Be-7 and Be-9 are found to be in agreement with calculations based on standard Leaky-Box model for the interstellar propagation of cosmic-ray nuclei using the recent cross sections of the New Mexico-Saclay collaboration. From our observed ratio Be-10/Be = 4.3 +/- 1.5% we deduce an average interstellar density of about 0.28 (+0.14, -0.11) atoms/cu cm, and acosmic-ray lifetime for escape of 27 (+19, -9) x 10(exp 6) years. The surviving fraction of Be-10 is found to be 0.19 +/- 0.07. Modifications to the conclusions of the Leaky-Box model when a diffusion + convection halo model for propagation is used are also considered.

Lukasiak, A.↗

NASA NTRS2009

Heat Transfer Modeling and Validation for Optically Thick Alumina Fibrous Insulation

Combined radiation/conduction heat transfer through unbonded alumina fibrous insulation was modeled using the diffusion approximation for modeling the radiation component of heat transfer in the optically thick insulation. The validity of the heat transfer model was investigated by comparison to previously reported experimental effective thermal conductivity data over the insulation density range of 24 to 96 kg/cu m, with a pressure range of 0.001 to 750 torr (0.1 to 101.3 x 10(exp 3) Pa), and test sample hot side temperature range of 530 to 1360 K. The model was further validated by comparison to thermal conductivity measurements using the transient step heating technique on an insulation sample at a density of 144 kg/cu m over a pressure range of 0.001 to 760 torr, and temperature range of 290 to 1090 K.

Daryabeigi, Kamran↗

DOE OSTI2023

Modeling of fission gas diffusion and release for Gd 2 O 3 doped UO 2

Uranium dioxide (UO 2 ) is the primary nuclear fuel in light water reactors, and its excess neutronic reactivity can be controlled by adding burnable absorbers, such as Gd 2 O 3 . This burnable absorber has a large neutron absorption cross-section, lowering the high reactivity of the reactor's initial fuel load. However, there needs to be more understanding of how added Gd 2 O 3 influences the properties of UO 2 under irradiation. To understand the behavior of defects and fission gas in the UO 2 /Gd 2 O 3 system under irradiation, we use cluster dynamics modeling supported by density functional theory calculations. First, we calculate the formation energies of Gd point and cluster defects, and evaluate the temperature-dependent defect concentrations using the defect formation energies and entropies. We show that Gd is soluble in UO 2 , introducing a negative charge in the system. Using this information, we adapted the cluster dynamics code Centipede to model the influence of Gd on U self-diffusion and Xe diffusion in UO 2 with 10 wt% Gd 2 O 3 . Also, we analyzed the Xe diffusion as a function of Gd 2 O 3 concentration, showing that the Xe diffusivity is decreased, which means that the athermal diffusivity due to electronic stopping persists at higher temperatures. In conclusion, the decrease in Xe diffusion means that more Xe stays in the matrix, decreasing the Xe release, and lowering its influence of fission gas release on the thermomechanical properties of UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1975

External field effects on diffusion and solidification derived from the free-volume model

Expressions for the diffusion coefficient and the solidification rate from the free-volume model of liquids developed by Turnbull and Cohen have been used to estimate the effects which microgravity and magnetic fields will have on these quantities. The mathematical formalism describing changes of the diffusion coefficient and the solidification rate is the same for both the microgravity and magnetic field cases, but the difference between the magnitudes of the two effects is quite large. The change in the two parameters is found to be less than .0001% for the microgravity case and on the order of 0.1 to 1.1% for the magnetic field case for four representative materials. The diffusion coefficient and the solidification rate are found to increase under the influence of an applied magnetic field, and this is in agreement with experimental observations.

Miller, R. I.↗

NASA NTRS1999

Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities

Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable underestimate of the extent of turbulent mixing and thus to an incorrect mixed layer depth. The predicted temperature and salinity profiles (vs. depth) are presented and compared with those of the Kolmogorov-Petruvsky-Piskunuv (KPP) model and Levitus data.

Canuto, V. M.↗

NASA NTRS1986

A three-dimensional axisymmetric calculation procedure for turbulent flows in a radial vaneless diffuser

An analytical model is proposed to calculate the three-dimensional axisymmetric turbulent flowfield in a radial vneless diffuser. The model assumes that the radial and tangential boundary layer profiles are approximated by power law profiles. Then, using the integrated radial and tangential momentum and continuity equations for the boundary layer and corresponding inviscid equations for the core flow, there results six ordinary differential equation in six unknowns which are easily solved using a Runge-Kutta technique. A model is also proposed for fully developed flow. The results using this technique were compared with the results from a three-dimensional viscous, axisymmetric duct code and with experimental data and good quantitative agreement was obtained.

Schumann, L. F.↗

NASA NTRS1972

A critical examination of the validity of simplified models for radiant heat transfer analysis.

Examination of the directional effects of the simplified models by comparing the experimental data with the predictions based on simple and more detailed models for the radiation characteristics of surfaces. Analytical results indicate that the constant property diffuse and specular models do not yield the upper and lower bounds on local radiant heat flux. In general, the constant property specular analysis yields higher values of irradiation than the constant property diffuse analysis. A diffuse surface in the enclosure appears to destroy the effect of specularity of the other surfaces. Semigray and gray analyses predict the irradiation reasonably well provided that the directional properties and the specularity of the surfaces are taken into account. The uniform and nonuniform radiosity diffuse models are in satisfactory agreement with each other.

Toor, J. S.↗

NASA NTRS2002

Propagation of Secondary Antiprotons and Cosmic Rays in the Galaxy

Recent more accurate antiproton data obtained by the BESS team during the last solar minimum pose a challenge to conventional propagation models of cosmic rays. In particular, the diffusive reacceleration model, which matches well key secondary/primary isotope ratios in cosmic rays, fails to reproduce the secondary antiproton spectrum. Tuning both secondary/primary isotope ratios and antiprotons is possible, but requires artificial breaks in the diffusion coefficient and the injection spectrum of primaries. We will discuss some possibilities to overcome these difficulties in the propagation models. We will present new results of our calculation of CR propagation in the Galaxy using the GALPROP code.

Moskalenko, I. V.↗

DOE OSTI2022

Tools Assessing Performance (FY2022 Quarter 4 Report)

We were finally successful in acquiring TTU’s 200-meter tower data for the duration of the Isolated Building Wake Experiment (IBWE). This data will provide an independent measurement of the undisturbed wind profile including heights far above those that are typical of meteorological sensor networks. These measurements will characterize the mean and turbulence throughout the atmospheric surface layer, which will be particularly useful for validation of highfidelity computational fluid dynamics models. This dataset can be shared freely among the TAP team but not outside of it as TTU sells this data to the wind power industry. The journal article overview has been submitted to LANL’s publication review and will be submitted to the Journal of Wind Engineering and Industrial Aerodynamics once the review is complete. We are nearing completion on another two articles. The first discusses analyses of the evolution of the measurements of mean wind speed along the centerline of the building as a function of atmospheric stability. Rather than using individual time steps, all of the wind speed measurements are normalized using the upwind measurement at 2 building heights (H) and filtered by wind direction and atmospheric stability. The second discusses the development of the diffusive wake model and uses the averaged profiles from the first article to validate the behavior of the model. The portion of the section below on the diffusive wake model discussing comparisons with the averaged profiles, will be included in the validation section of this paper.

17 WIND ENERGY↗

DOE OSTI2025

A fluctuating hydrodynamics model for nanoscale surfactant-laden interfaces

A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a Cahn-Hilliard free energy density combined with incompressible, isothermal fluctuating hydrodynamics where dissipative fluxes include both deterministic and stochastic terms. The intermolecular parameters in the free energy are chosen such that one species acts as a partially miscible surfactant. From Laplace pressure measurements, we show that in this model the surface tension decreases linearly with surfactant concentration, leading to Marangoni convection for interfaces with concentration gradients. In the capillary wave spectrum for interfaces with and without surfactant, we find that for the former, the spectrum deviates significantly from classical capillary wave theory, presumably due to Gibbs elasticity. In non-equilibrium simulations of the Rayleigh-Plateau instability, deterministic simulations showed that the surfactant delays pinching of a fluid cylinder into droplets. However, stochastic simulations indicate that thermal fluctuations disrupt the surfactant's stabilizing effect. Similarly, the spreading of a patch of surfactant, driven by Marangoni convection, was found to be partially suppressed by thermal fluctuations.

Capillary waves↗

NASA NTRS1991

Lithium in halo stars - Constraining the effects of helium diffusion on globular cluster ages and cosmology

Stellar evolutionary models with diffusion are used to show that observations of lithium in extreme halo stars provide crucial constraints on the magnitude of the effects of helium diffusion. The flatness of the observed Li-T(eff) relation severely constrains diffusion Li isochrones, which tend to curve downward toward higher T(eff). It is argued that Li observations at the hot edge of the plateau are particularly important in constraining the effects of helium diffusion; yet, they are currently few in number. It is proposed that additional observations are required there, as well as below 5500 K, to define more securely the morphology of the halo Li abundances. Implications for the primordial Li abundance are considered. It is suggested that a conservative upper limit to the initial Li abundance, due to diffusive effects alone, is 2.35.

Deliyannis, Constantine P.↗