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NASA NTRS1993

Inertial Currents in Isotropic Plasma

The magnetospheric convection electric field contributes to Birkeland currents. The effects of the field are to polarize the plasma by displacing the bounce paths of the ions from those of electrons, to redistribute the pressure so that it is not constant along magnetic field lines, and to enhance the pressure gradient by the gradient of the bulk speed. Changes in the polarization charge during the convection of the plasma are neutralized by electrons in the form of field-aligned currents that close through the ionosphere. The pressure drives field-aligned currents through its gradient in the same manner as in quasi-static plasma, but with modifications that are important if the bulk speed is of the order of the ion thermal speed; the variations in the pressure along field lines are maintained by a weak parallel potential drop. These effects are described in terms of the field-aligned currents in steady state, isotropic, MED plasma. Solutions are developed by taking the MHD limit of two-fluid solutions and illustrated in the special case of Maxwellian plasma for which the temperature is constant along magnetic field lines. The expression for the Birkeland current density is a generalization of Vasyliunas' expression for the field-aligned current density in quasi-static plasma and provides a unifying expression when both pressure gradients and ion inertia operate simultaneously as sources of field-aligned currents. It contains a full account of different aspects of the ion flow (parallel and perpendicular velocity and vorticity) that contribute to the currents. Contributions of ion inertia to field-aligned currents will occur in regions of strong velocity shear, electric field reversal, or large gradients in the parallel velocity or number density, and may be important in the low-latitude boundary layer, plasma sheet boundary layer, and the inner edge region of the plasma sheet.

Heinemann, M.↗
NASA NTRS1985

Coronal temperatures, heating, and energy flow in a polar region of the sun at solar maximum

The profiles of resonantly scattered Lyman-alpha coronal radiation have been used to determine the hydrogen kinetic temperature from 1.5 to 4 solar radius from the center of the polar region of the corona observed in 1980 at solar maximum. Hydrogen temperatures derived from the line profiles were found to decrease with height from 1.2 million K at r = 1.5 solar radii to 600,000 K at r = 4 solar radius. Comparison of the measured kinetic temperatures with predictions from a semiempirical two-fluid model showed evidence of a small amount of heating or a nonthermal contribution to the motions of coronal protons between 1.5 and 4 solar radius. The widths of the profiles confirmed an upper limit of 110 + or - 15 km/s on the rms magnitude of the line-of-sight component of velocities between 1.5 and 4 solar radius. Density measurements obtained in situ in the solar wind in the ecliptic were used to locate the sources of low speed and high-speed winds in the polar region. An eclipse photograph of the corona at solar maximum is provided.

Withbroe, G. L.↗
NASA NTRS1986

Characterization of simulated small-droplet fuel sprays

A two-fluid pneumatic atomizer operating at relatively high liquid and gas pressures produced water sprays that simulated small-droplet clouds of liquid fuel for use in studying vaporization and fuel-air mixing effects on combustor performance and emissions. To characterize the sprays, a scattered-light scanning instrument was developed and measurements of volume median or volume mean diameter, D sub V.5, were correlated with D sub O, W sub w, and W sub n, i.e., orifice diameter, water, and nitrogen gas flow rates, respectively, to give the general expression: D sub v.5 approx. (D sub o sup 0.2) (W sub w sup m) (W sub n sup n), which yields D sub v.5 = 45 (D sub o sup 0.2) (W sub w sup 0.2) (W sub w sup - 1.2). Values of D sub o, W sub w, and W sub n are in centimeters and grams/second, respectively. Farther downstream at an axial distance of 6.7 cm, exponent m increased from 0.2 to 0.4 and exponent n decreased from -1.2 to -1.0 and at a distance of 25 cm downstream of the atomizer, n decreased to -0.8. The increase in exponent m and decrease in exponent n was attributed to a loss of very small droplets from the spray due primarily to vaporization and diffusion effects on clouds of small droplets traveling a distance of 25 cm.

Ingebo, R. D.↗
NASA NTRS1986

Characterization of simulated small-droplet fuel sprays

A two-fluid pneumatic atomizer operating at relatively high liquid and gas pressures produced water sprays that simulated small-droplet clouds of liquid fuel for use in studying vaporization and fuel-air mixing effects on combustor performance and emissions. To characterize the sprays, a scattered-light scanning instrument was developed and measurements of volume median or volume mean diameter, D sub V.5, were correlated with D sub O, W sub w, and W sub n, i.e., orifice diameter, water, and nitrogen gas flow rates, respectively, to give the general expression: D sub v.5 approx. (D sub O sup 0.2) (W sub w sup m) (W sub n sup n), which yields D sub v.5 = 45 (D sub o sup 0.2) (W sub w sup 0.2) (W sub w sup -1.2). Values of D sub 0, W sub w, and W sub n are in centimeters and grams/second, respectively. Farther downstream at an axial distance of 6.7 cm, exponent m increased from 0.2 to 0.4 and exponent n decreased from -1.2 to -1.0 and at a distance of 25 cm downstream of the atomizer, n decreased to -0.8. The increase in exponent m and decrease in exponent n was attributed to a loss of very small droplets from the spray due primarily to vaporization and diffusion effects on clouds of small droplets traveling a distance of 25 cm.

Ingebo, R. D.↗
NASA NTRS1992

Effect of vaporization on cryogenic spray dropsize measurement

The fluid mechanics of multi-phase flow breakup of liquid nitrogen, LN2, jets injected into sonic velocity nitrogen gasflow, was experimentally investigated. A scattered-light scanning instrument was used to measure the characteristic dropsize, D(sub v.5), of LN2 sprays and to determine the effect of droplet vaporization on experimental dropsize measurements. Under sonic gas-velocity conditions, liquid-jet breakup occurred in the regime of aerodynamic stripping. As a result, the following correlation of volume-median drop diameter, D(sub v.5), with atomizing gas flowrate, W(sub g), was derived for two-fluid atomizers; with atomizing gas flowrate, W(sub g), was derived for two-fluid atomizers; (D(sub v.5))(exp -1) = k(sub c)(W(sub g))(sup n), where proportionally constant k(sub c) and exponent n are functions of droplet vaporization rate. Partially vaporized sprays were investigated and it was found that n = 1.11, which is considerably less than the value of 1.33 that is predicted by atomization theory. This was attributed to the evaporative loss of very small droplets. As a result, the following expression was obtained experimentally: (D(sub v.5e))(exp -1) = 301(W(sub g))(sup 1.11). Values of D(sub v.5), that existed prior to partial vaporization of the LN2 sprays, were calculated and the following expression was derived for originally unvaporized LN2 sprays: (D(sub v.5))(exp -1) = 285(W(sub g))(sup 1.33). This expression agrees well with atomization theory that predicts n = 1.33, for liquid jet breakup in high-velocity gasflow.

Ingebo, Robert D.↗
NASA NTRS1993

Effect of vaporization on cryogenic spray dropsize measurement

The fluid mechanics of multi-phase flow breakup of liquid nitrogen, LN2, jets injected into sonic velocity nitrogen gasflow, was experimentally investigated. A scattered-light scanning instrument was used to measure the characteristic dropsize, D(sub v.5), of LN2 sprays and to determine the effect of droplet vaporization on experimental dropsize measurements. Under sonic gas-velocity conditions, liquid-jet breakup occurred in the regime of aerodynamic stripping. As a result, the following correlation of volume-median drop diameter, D(sub v.5), with atomizing gas flowrate, W(sub g), was derived for two-fluid atomizers: (D(sub v.5)) (exp -1) = k(sub c) (W(sub g)) (sup n), where proportionally constant k(sub c) and exponent n are functions of droplet vaporization rate. Partially vaporized sprays were investigated and it was found that n = 1.11, which is considerably less than the value of 1.33 that is predicted by atomization theory. This was attributed to the evaporative loss of very small droplets. As a result, the following expression was obtained experimentally: (D(sub v.5e)) (exp -1) = 301 (W(sub g)) (sub 1.11). Values of D(sub v.5), that existed prior to partial vaporization of the LN2 sprays, were calculated and the following expression was derived for originally unvaporized LN2 sprays: (D(sub v.5)) (exp -1) = 285 (W(sub g)) (sub 1.33). This expression agrees well with atomization theory that predicts n = 1.33, for liquid jet breakup in high-velocity gasflow.

Ingebo, Robert D.↗
NASA NTRS1993

Particle injection and the structure of energetic-particle-modified shocks

A macroscopic 'self-consistent' nonlinear two-fluid model is developed for energetic-particle-modeled shocks. The model incorporates particle exchange between a thermal gas and an energetic population via a 'thermal leakage' mechanism. In the model, injection is regarded as a process whereby particles in the cooler thermal core of a total particle distribution are energized sufficiently to cross a 'momentum boundary' into the wings of the distribution. Particles in the wings are identified as 'energetic particles' or 'cosmic rays' and are assumed to propagate according to the diffusive transport equation of cosmic ray theory. Thermal particles are energized either as a result of adiabatic compression in a decelerating flow or directly via anomalous heating within a subshock. It is shown that the nature and model of particle injection directly affects the nature and dynamics of the shock, and hence the efficiency of particle acceleration, and that the shock itself regulates particle injection dynamically.

Zank, G. P.↗
DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1993

Three-dimensional solidification and melting using magnetic field control

A new two-fluid mathematical model for fully three dimensional steady solidification under the influence of an arbitrary acceleration vector and with or without an arbitrary externally applied steady magnetic field have been formulated and integrated numerically. The model includes Joule heating and allows for separate temperature dependent physical properties within the melt and the solid. Latent heat of phase change during melting/solidification was incorporated using an enthalpy method. Mushy region was automatically captured by varying viscosity orders of magnitude between liquidus and solidus temperature. Computational results were obtained for silicon melt solidification in a parallelepiped container cooled from above and from a side. The results confirm that the magnetic field has a profound influence on the solidifying melt flow field thus changing convective heat transfer through the boundaries and the amount and shape of the solid accrued. This suggests that development of a quick-response algorithm for active control of three dimensional solidification is feasible since it would require low strength magnetic fields.

Dulikravich, George S.↗
NASA NTRS1977

A reexamination of two-fluid solar wind models

The two-fluid solar-wind equations have been solved by a method which is approximately 50 times faster than any previously developed, through the use of asymptotic expansions which are self-consistently iterated upon to find a solution that passes through the critical point. The energy assumptions in two-fluid solar-wind models are reexamined, and the conclusions are as follows: (1) proton thermal conduction may not be neglected, (2) the Coulomb logarithm must be calculated as a function of radius, and (3) the electron and proton temperatures at the base need not be equal, even when the time scale for energy exchange between the species is an order of magnitude smaller than the expansion time at the base. It is possible to reproduce reasonable quiet-time solar-wind parameters at 1 AU, but only if the proton temperature is approximately twice the electron temperature at 1 solar radius. This may indicate that extended proton heating is important in the outer solar corona. Winds with velocities at 1 AU of 450 km/s are generated without nonthermal energy deposition but require high proton temperatures as well as very low densities at the base. Higher-velocity solutions are not possible in a spherically symmetric geometry for reasonable particle fluxes at 1 AU, and it is suggested that these higher-velocity states probably require additional heating, acceleration mechanisms, or nonradial flow.

Nerney, S.↗
NASA NTRS1995

Time-dependent simulation of oblique MHD cosmic-ray shocks using the two-fluid model

Using a new, second-order accurate numerical method we present dynamical simulations of oblique MHD cosmic-ray (CR)-modified plane shock evolution. Most of the calculations are done with a two-fluid model for diffusive shock acceleration, but we provide also comparisons between a typical shock computed that way against calculations carried out using the more complete, momentum-dependent, diffusion-advection equation. We also illustrate a test showing that these simulations evolve to dynamical equilibria consistent with previously published steady state analytic calculations for such shocks. In order to improve understanding of the dynamical role of magnetic fields in shocks modified by CR pressure we have explored for time asymptotic states the parameter space of upstream fast mode Mach number, M(sub f), and plasma beta. We compile the results into maps of dynamical steady state CR acceleration efficiency, epsilon(sub c). We have run simulations using constant, and nonisotropic, obliquity (and hence spatially) dependent forms of the diffusion coefficient kappa. Comparison of the results shows that while the final steady states achieved are the same in each case, the history of CR-MHD shocks can be strongly modified by variations in kappa and, therefore, in the acceleration timescale. Also, the coupling of CR and MHD in low beta, oblique shocks substantially influences the transient density spike that forms in strongly CR-modified shocks. We find that inside the density spike a MHD slow mode wave can be generated that eventually steepens into a shock. A strong layer develops within the density spike, driven by MHD stresses. We conjecture that currents in the shear layer could, in nonplanar flows, results in enhanced particle accretion through drift acceleration.

Frank, Adam↗
DOE OSTI2025

Combined Influence of Rotation and Scrape-Off Layer Drifts on Recycling Asymmetries in Tokamak Plasmas

Coupled 2D fluid-kinetic simulations of a DIII-D high confinement tokamak plasma show that plasma rotation coupled with drift effects near the plasma edge play a significant role in the creation of the observed poloidal distribution of neutrals. It is observed that including either drift or rotation effects enhances particle flux at the inner target in the case of ion 𝐵×∇𝐵 drift toward the 𝑋-point. However, the particle flux asymmetry is significantly higher with the combination of drifts and rotation than either effect alone. The heightened particle flux asymmetry allows for improved simulation of the strong in-out asymmetry of the Lyman-𝛼 brightness profiles measured in the experiment. Enhancement of radial transport of parallel momentum changes the upstream scrape-off layer flow pattern, increasing the fraction of deuterium flux that reaches the inboard divertor entrance while lowering that which arrives at the outboard. In conclusion, this Letter indicates that by combining drifts, rotation, and viscous coupling, existing boundary plasma models can achieve a satisfactory agreement with experimentally measured neutral asymmetries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Filament extension atomizers: A study of integration potential into spray dryers for high-viscosity and non-Newtonian fluids

Filament extension atomizers (FEAs) are an emerging class of spray nozzles designed to atomize high-viscosity and non-Newtonian fluids that are challenging for conventional pressure or two-fluid nozzles. In this study, we investigate the influence of roller geometry, surface velocity, roller material, and fluid rheology on the atomization performance of FEA systems using concentrated whey protein suspensions (50–70 wt. %). Extensional and shear rheology experiments, along with high-speed imaging and particle image velocimetry, reveal that filament breakup dynamics are governed by competition between inertial, capillary, and viscoelastic stresses. High roller rotational velocity leads to narrower spray cones, contradicting rheology experiments and suggests a significant inertial contribution to filament breakup. Smaller rollers operating at the same rotational velocity led to broader spray cones consistent with expectations. An FEA nozzle was integrated into a conventional dryer producing particles in the 100 μm range. Results suggest that FEA technology enables atomization of highly viscous fluids at industrially relevant spray cone angles similar to those generated by pressure nozzles, offering a pathway to improve energy efficiency in spray drying by enabling higher solids loading feedstocks. Furthermore, these insights provide critical guidance for optimizing FEA nozzle designs and process parameters across a range of applications.

Energy efficiency↗
NASA NTRS1973

Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

Pai, S. I.↗
NASA NTRS1982

Statistical mechanics of dilute liquid mixtures of He3 in He4

The Woo-Tan-Massey quantum-mechanical theory of dilute mixtures of He-3 in liquid He-4 is extended to incorporate superfluid flow. Then statistical-mechanical principles are employed to find explicit formulas for thermodyanmic and hydrodynamic properties of mixtures, such as internal energy, free energy, entropy, pressure, chemical potential, and normal-fluid and superfluid densities. This paper is the first in a planned series that applies methods originally developed for pure liquid He-4 to dilute mixtures as a means of establishing a comprehensive theory that includes a theoretical bridge between a microscopic description of the mixtures and a hydrodynamic two-fluid model. Ultimately effects of applied electric and magnetic fields on dilute solutions are also planned to be treated.

Jackson, H. W.↗
NASA NTRS1989

Numerical simulation of forced convection in a two fluid layered system in a floating zone configuration

Forced convection due to rotational effects has been numerically studied in a stable two-fluid layered system in which the lighter fluid occupies the upper portion of the computational and physical domain. Results are presented for three different fluid height combinations for conditions prevailing in a microgravity environment. It is found that the heavier fluid tends to dominate the flow field, and that equal corotation and counterrotation cases produce nearly identical behavior in the flow and thermal fields.

Ramachandran, N.↗
NASA NTRS1994

Analysis of phase distribution phenomena in microgravity environments

The purpose of the research presented in this paper is to demonstrate the ability of multidimensional two-fluid models for bubbly two-phase flow to accurately predict lateral phase distribution phenomena in microgravity environments. If successful, this research should provide NASA with mechanistically-based analytical methods which can be used for multiphase space system design and evaluation, and should be the basis for future shuttle experiments for model verification.

Lahey, Richard T., Jr.↗
NASA NTRS1994

Local shear instabilities in weakly ionized, weakly magnetized disks

We extend the analysis of axisymmetric magnetic shear instabilities from ideal magnetohydrodynamic (MHD) flows to weakly ionized plasmas with coupling between ions and neutrals caused by collisions, ionization, and recombination. As part of the analysis, we derive the single-fluid MHD dispersion relation without invoking the Boussinesq approximation. This work expands the range of applications of these instabilities from fully ionized accretion disks to molecular disks in galaxies and, with somewhat more uncertainty, to protostellar disks. Instability generally requires the angular velocity to decrease outward, the magnetic field strengths to be subthermal, and the ions and neutrals to be sufficiently well coupled. If ionization and recombination processes can be neglected on an orbital timescale, adequate coupling is achieved when the collision frequency of a given neutral with the ions exceeds the local epicyclic freqency. When ionization equilibrium is maintained on an orbital timescale, a new feature is present in the disk dynamics: in contrast to a single-fluid system, subthermal azimuthal fields can affect the axisymmetric stability of weakly ionized two-fluid systems. We discuss the underlying causes for this behavior. Azimuthal fields tend to be stabilizing under these circumstances, and good coupling between the neutrals and ions requires the collision frequency to exceed the epicyclic frequency by a potentially large secant factor related to the magnetic field geometry. When the instability is present, subthermal azimuthal fields may also reduce the growth rate unless the collision frequency is high, but this is important only if the field strengths are very subthermal and/or the azimuthal field is the dominant field component. We briefly discuss our results in the context of the Galactic center circumnuclear disk, and suggest that the shear instability might be present there, and be responsible for the observed turbulent motions.

Blaes, Omer M.↗