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All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Automated Euler and Navier-Stokes Database Generation for a Glide-Back Booster

The past two decades have seen a sustained increase in the use of high fidelity Computational Fluid Dynamics (CFD) in basic research, aircraft design, and the analysis of post-design issues. As the fidelity of a CFD method increases, the number of cases that can be readily and affordably computed greatly diminishes. However, computer speeds now exceed 2 GHz, hundreds of processors are currently available and more affordable, and advances in parallel CFD algorithms scale more readily with large numbers of processors. All of these factors make it feasible to compute thousands of high fidelity cases. However, there still remains the overwhelming task of monitoring the solution process. This paper presents an approach to automate the CFD solution process. A new software tool, AeroDB, is used to compute thousands of Euler and Navier-Stokes solutions for a 2nd generation glide-back booster in one week. The solution process exploits a common job-submission grid environment, the NASA Information Power Grid (IPG), using 13 computers located at 4 different geographical sites. Process automation and web-based access to a MySql database greatly reduces the user workload, removing much of the tedium and tendency for user input errors. The AeroDB framework is shown. The user submits/deletes jobs, monitors AeroDB's progress, and retrieves data and plots via a web portal. Once a job is in the database, a job launcher uses an IPG resource broker to decide which computers are best suited to run the job. Job/code requirements, the number of CPUs free on a remote system, and queue lengths are some of the parameters the broker takes into account. The Globus software provides secure services for user authentication, remote shell execution, and secure file transfers over an open network. AeroDB automatically decides when a job is completed. Currently, the Cart3D unstructured flow solver is used for the Euler equations, and the Overflow structured overset flow solver is used for the Navier-Stokes equations. Other codes can be readily included into the AeroDB framework.

Chaderjian, Neal M.↗
NASA NTRS2012

Development of the Packed Bed Reactor ISS Flight Experiment

Packed bed reactors are compact, require minimum power and maintenance to operate, and are highly reliable. These features make this technology a leading candidate as a potential unit operation in support of long duration human space exploration. On earth, this type of reactor accounts for approximately 80% of all the reactors used in the chemical process industry today. Development of this technology for space exploration is truly crosscutting with many other potential applications (e.g., in-situ chemical processing of planetary materials and transport of nutrients through soil). NASA is developing an ISS experiment to address this technology with particular focus on water reclamation and air revitalization. Earlier research and development efforts funded by NASA have resulted in two hydrodynamic models which require validation with appropriate instrumentation in an extended microgravity environment. The first model developed by Motil et al., (2003) is based on a modified Ergun equation. This model was demonstrated at moderate gas and liquid flow rates, but extension to the lower flow rates expected in many advanced life support systems must be validated. The other model, developed by Guo et al., (2004) is based on Darcy s (1856) law for two-phase flow. This model has been validated for a narrow range of flow parameters indirectly (without full instrumentation) and included test points where the flow was not fully developed. The flight experiment presented will be designed with removable test sections to test the hydrodynamic models. The experiment will provide flexibility to test additional beds with different types of packing in the future. One initial test bed is based on the VRA (Volatile Removal Assembly), a packed bed reactor currently on ISS whose behavior in micro-gravity is not fully understood. Improving the performance of this system through an accurate model will increase our ability to purify water in the space environment.

Patton, Martin O.↗
DOE OSTI2021

Enhancing Steam-Side Heat Transfer via Microdroplet Ejection using Inorganic Coatings

During condensation of water on a superhydrophobic nanostructured surfaces, droplets coalesce and jump (droplet ejection) due to the release of excess surface energy. Meticulously designed nanostructured surfaces or coatings capable of droplet ejection can enhance heat transfer performance by easy removal of droplets during condensation. In the present work, the capabilities of the Nelumbo droplet ejection coatings technology currently used in commercial heat exchangers are explored and optimized for materials and conditions relevant to steam condensers. Specifically, this includes (1) adapting and optimizing the procedures and chemistries to deposit droplet ejecting coatings on materials used in the steam condenser, (2) testing of the heat transfer, durability, and fouling of the fabricated coatings under a variety of steam condenser relevant conditions, and (3) modeling of the impact of droplet dynamics and interfacial properties on heat transfer in steam condensers. We experimentally demonstrated that at low supersaturation conditions (S~1.02), developed superhydrophobic nanostructured surface gives a 40% higher peak heat transfer flux and a 17% higher peak overall heat transfer coefficient (U) with droplet ejection mechanism compared to the dropwise condensation mechanism on the same nanostructured surface. Though the experimentally observed droplet ejection mechanism was short-lived (~3 min) due to the limitation of the chiller to maintain a constant supersaturation condition in fabricated steam condenser. And large variations in water inlet temperature (+ to - 2 degrees C) caused flooding of nanostructure (Wenzel state) at higher supersaturation (S > or = 1.12). This is an important finding because typical supersaturation levels in field operation are over 1.8 and as such, either the flooding potential for these materials should be improved or operation at lower supersaturation may be required to maximize heat transfer efficiency. If supersaturation conditions can be maintained reliably in the steam condenser in addition to droplet ejection mechanism during condensation, this could provide a potential 2% reduction in water flow rate which equates to a savings of over 3900 gallons of water per minute for a 500 MW steam turbine and over $0.3MM savings annually given a 0.02 cent marginal water withdrawal cost. It is also worth noting that these savings are based on improvement of droplet ejection coatings over coatings capable of performing consistent dropwise mechanism in in-field surface condensers. Savings due to the droplet ejections coatings when compared to bare substrates could be much higher. Additionally, the present work provides the importance of steam condenser operating conditions and insights into the challenges in modeling the condensing droplet dynamics on surfaces.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2023

Fluoride-Cooled High-Temperature Pebble-Bed Reactor Reference Plant Model

In this report we present work performed in Fiscal Year 2022 that demonstrates the modeling and simulation of a fully coupled neutronics thermal hydraulics reference plant model for a fluoride-cooled high-temperature pebble-bed reactor. The multiphysics model is developed on the Nuclear Regulatory Commission’s Comprehensive Reactor Analysis Bundle (BlueCRAB) available on the Idaho National Laboratory’s high-performance computer, which natively and seamlessly couples Griffin, Pronghorn, and the BISON Multiphysics Object-Oriented Simulation Environment based applications. Griffin provides reactor physics capabilities, including depletion to the equilibrium core, k-eigenvalue, adjoint, and transient. The unique direct equilibrium core capability in Griffin is based on a streamline methodology to spatially deplete the pebbles into burnup groups. Pronghorn solves the porous medium equations for the fluid regions and conduction in the solid regions and incorporates a fluidic diode model to simulate the transition from forced to natural convection during accident scenarios. MOOSE modules solves thermal conduction problems for the pebbles and tristructural isotropic in the pebble-bed core, thus providing the fuel and moderator spatial fields for each pebble burnup group. The neutronics feedback relies primarily on fuel, moderator, and reflector temperatures as as well as the FLiBe salt density. Here, we present results for the uncoupled equilibrium core and perform comparisons to equivalent Monte Carlo models. The power distributions and kinetic parameters obtained with Griffin are consistent with those computed with Griffin. We demonstrate a noticeable improvement with the use of discrete ordinates method (SN) transport. The coupled steady-state equilibrium core provides the initial condition for two time-dependent problems: a control rod withdrawal event and an unprotected loss of flow event. In both cases, the reactor design is self-stabilizing and the solutions are consistent with the expected physics. Although this model is prototypical regarding BlueCRAB’s capabilities, its results are consistent with published work by Kairos Power and other research entities. Significant improvements to the model are planned in future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1964

Three-dimension heat transfer program

An IBM 7094, three dimensional, heat transfer program for satellite application is discussed. The program may be applied to all phases of spacecraft life, from launch to orbital quasi-steady state. Launch phase heating includes inputs by radiation from the hot fairing and free molecule flow heating after nose cone ejection. Orbital heat fluxes are accounted for by direct sunlight, earth-reflected sunlight, and earth-emitted input to the satellite. Internal heat exchange by conduction and radiation is determined, provided the appropriate conductances, radiation view factors, and effective emittances are known. A simplified analysis of an active thermal controlled spacecraft is incorporated into the program. One or more surfaces may contain shutter systems which have optical properties specified as a function of shutter opening. The program evaluates the feasibility of any configuration based upon maintaining an internal component within its tolerable temperature limits. The program employs a matrix inversion subroutine (Gauss Elimination Method) to solve the heat balance equations.

COMPUTER PROGRAM↗
NASA NTRS1990

Analysis of unsteady compressible viscous layers

The development of an analysis to predict the unsteady compressible flows in blade boundary layers and wakes is presented. The equations that govern the flows in these regions are transformed using an unsteady turbulent generalization of the Levy-Lees transformation. The transformed equations are solved using a finite difference technique in which the solution proceeds by marching in time and in the streamwise direction. Both laminar and turbulent flows are studied, the latter using algebraic turbulence and transition models. Laminar solutions for a flat plate are shown to approach classical asymptotic results for both high and low frequency unsteady motions. Turbulent flat-plate results are in qualitative agreement with previous predictions and measurements. Finally, the numerical technique is also applied to the stator and rotor of a low-speed turbine stage to determine unsteady effects on surface heating. The results compare reasonably well with measured heat transfer data and indicate that nonlinear effects have minimal impact on the mean and unsteady components of the flow.

Power, G. D.↗
DOE OSTI2024

Model-based optimization strategies for direct hydrogenation of carbon dioxide to dimethyl ether

Here, this study discusses model-based optimization strategies for CO 2 hydrogenation to dimethyl ether (DME) over aCuZnZr (CZZ) and ferrite (FER) mixed catalyst system in a packed-bed reactor configuration. A two-dimensional axisymmetric, nonisothermal packed-bed reactor model was developed using COMSOL Multiphysics 6.2 software. The model solves two-dimensional (radial and axial) heat and mass transport equations in the packed-bed and integrates intraparticle diffusion and heat transfer in a 1D approach. This powerful feature differs from a traditional porous media approach and takes into account any heat and mass transfer limitations that may exist. Analysis shows that the heat transfer limitations are negligible, but strong internal mass transfer limitations were observed at 10 ≤ WHSV ≤ 90 h -1 on the FER catalyst and at 240 °C. The optimum catalyst composition (i.e., mixing ratio) varies depending on the operating regime. The FER catalyst weight in the mixture can be as low as 5 wt.%, but the ideal composition de-pends on the internal mass transfer limitation and its relationship with the operating regime (i.e., weight hourly space velocity, temperature). A catalyst composition of 80 wt.% CZZ and 20 wt.% FER was suggested; this composition can provide high CO 2 conversion and DME production rates at a wide range of temperatures and flow rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Towards multi-fidelity deep learning of wind turbine wakes

We report engineering wake models that accurately predict wake in a computationally efficient manner are very important for tasks such as layout optimization and control of wind farms. In this paper, we explore an application of deep learning (DL) to learn the wake model from hierarchies of physics-based approaches ranging from analytical models to an approximate form of the Reynolds-averaged Navier-Stokes equations. We first illustrate the application of principal component analysis to obtain a lower-dimensional representation that allows a computationally tractable training and deployment of DL models. Then, the DL model is trained to learn the mapping from input parameter space to the principal components, which are then used to reconstruct the three-dimensional flow field. Additionally, we investigate a composite framework consisting of two neural networks to learn the correlation between low- and high-fidelity data with Gauss and curl models treated as proxies for low- and high-fidelity models, respectively. The prediction from both DL models matches well with the high-fidelity data with a maximum relative percentage error for the kinetic energy flux of <1%. This work opens up possibilities for data-efficient construction of surrogate models for wake prediction that can be used to study the influence of wind speed and yaw angles on wind farm power production.

17 WIND ENERGY↗
NASA NTRS2003

Mechanisms for the Crystallization of ZBLAN

The objective of this ground based study is to test the hypothesis that shear thinning (the non-Newtonian response of viscosity to shear rate) is a viable mechanism to explain the observation of enhanced glass formation in numerous low-g experiments. In 1-g, fluid motion results from buoyancy forces and surface tension driven convection. This fluid flow will introduce shear in undercooled liquids in 1-g. In low-g it is known that fluid flows are greatly reduced so that the shear rate in fluids can be extremely low. It is believed that some fluids may have weak structure in the absence of flow. Very small shear rates could cause this structure to collapse in response to shear resulting in a lowering of the viscosity of the fluid. The hypothesis of this research is that: Shear thinning in undercooled liquids decreases the viscosity, increasing the rate of nucleation and crystallization of glass forming melts. Shear in the melt can be reduced in low-g, thus enhancing undercooling and glass formation. The viscosity of a model glass (lithium di-silicate, L2S) often used for crystallization studies has been measured at very low shear rates using a dynamic mechanical thermal analyzer. Our results are consistent with increasing viscosity with a lowering of shear rates. The viscosity of L2S may vary as much as an order of magnitude depending on the shear rate in the temperature region of maximum nucleation and crystal growth. Classical equations for nucleation and crystal growth rates, are inversely related to the viscosity and viscosity to the third power respectively. An order of magnitude variation in viscosity (with shear) at a given temperature would have dramatic effects on glass crystallization Crystallization studies with the heavy metal fluoride glass ZBLAN (ZrF2-BaF2-LaF3-AlF3-NaF) to examine the effect of shear on crystallization are being initiated. Samples are to be melted and quenched under quiescent conditions at different shear rates to determine the effect on crystallization. The results from this study are expected to advance the current scientific understanding of glass formation in low-g and glass crystallization under glass molding conditions and will improve the scientific understanding of technological processes such as fiber pulling, bulk amorphous alloys, and glass fabrication processes.

Ethridge, Edwin C.↗
NASA NTRS2015

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.

Orr, Jeb S.↗
DOE OSTI2021

Revisiting Theoretical Limits for One Degree-of-Freedom Wave Energy Converters

This work revisits the theoretical limits of one degree-of-freedom wave energy converters (WECs). This work considers the floating sphere used in the OES Task 10 WEC modeling and verification effort for analysis. Analytical equations are derived to determine bounds on displacement amplitude, time-averaged power (TAP), and power-take-off (PTO) force. A unique result found shows that the TAP absorbed by a WEC can be defined solely by the inertial properties and radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force was derived that provides lower and upper bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression only provides a lower bound, as there is theoretically no upper bound. These bounds assist in comparing the performance of the floating sphere if it were to extract energy using surge or heave motion. The analysis shows because of differences in hydrodynamic coefficients for each oscillating mode, there are different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on TAP while utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate TAP with a nonideal PTO is modified by the electrical conversion efficiency and the ratio of the PTO spring and damping coefficients. Furthermore, the PTO spring and damping coefficients were separated in the expression, allowing for limits to be set on the PTO coefficients to ensure net power generation.

16 TIDAL AND WAVE POWER↗
NASA NTRS2004

Buoyancy Effects on Flow Structure and Instability of Low-Density Gas Jets

A low-density gas jet injected into a high-density ambient gas is known to exhibit self-excited global oscillations accompanied by large vortical structures interacting with the flow field. The primary objective of the proposed research is to study buoyancy effects on the origin and nature of the flow instability and structure in the near-field of low-density gas jets. Quantitative rainbow schlieren deflectometry, Computational fluid dynamics (CFD) and Linear stability analysis were the techniques employed to scale the buoyancy effects. The formation and evolution of vortices and scalar structure of the flow field are investigated in buoyant helium jets discharged from a vertical tube into quiescent air. Oscillations at identical frequency were observed throughout the flow field. The evolving flow structure is described by helium mole percentage contours during an oscillation cycle. Instantaneous, mean, and RMS concentration profiles are presented to describe interactions of the vortex with the jet flow. Oscillations in a narrow wake region near the jet exit are shown to spread through the jet core near the downstream location of the vortex formation. The effects of jet Richardson number on characteristics of vortex and flow field are investigated and discussed. The laminar, axisymmetric, unsteady jet flow of helium injected into air was simulated using CFD. Global oscillations were observed in the flow field. The computed oscillation frequency agreed qualitatively with the experimentally measured frequency. Contours of helium concentration, vorticity and velocity provided information about the evolution and propagation of vortices in the oscillating flow field. Buoyancy effects on the instability mode were evaluated by rainbow schlieren flow visualization and concentration measurements in the near-field of self-excited helium jets undergoing gravitational change in the microgravity environment of 2.2s drop tower at NASA John H. Glenn Research Center. The jet Reynolds number was varied from 200 to 1500 and jet Richardson number was varied from 0.72 to 0.002. Power spectra plots generated from Fast Fourier Transform (FFT) analysis of angular deflection data acquired at a temporal resolution of 1000Hz reveal substantial damping of the oscillation amplitude in microgravity at low Richardson numbers (~0.002). Quantitative concentration data in the form of spatial and temporal evolutions of the instability data in Earth gravity and microgravity reveal significant variations in the jet flow structure upon removal of buoyancy forces. Radial variation of the frequency spectra and time traces of helium concentration revealed the importance of gravitational effects in the jet shear layer region. Linear temporal and spatio-temporal stability analyses of a low-density round gas jet injected into a high-density ambient gas were performed by assuming hyper-tan mean velocity and density profiles. The flow was assumed to be non parallel. Viscous and diffusive effects were ignored. The mean flow parameters were represented as the sum of the mean value and a small normal-mode fluctuation. A second order differential equation governing the pressure disturbance amplitude was derived from the basic conservation equations. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the temporal and spatio-temporal results were delineated. A decrease in the density ratio (ratio of the density of the jet to the density of the ambient gas) resulted in an increase in the temporal amplification rate of the disturbances. The temporal growth rate of the disturbances increased as the Froude number was reduced. The spatio-temporal analysis performed to determine the absolute instability characteristics of the jet yield positive absolute temporal growth rates at all Fr and different axial locations. As buoyancy was removed (Fr . 8), the previously existing absolute instability disappeared at all locations establhing buoyancy as the primary instability mechanism in self-excited low-density jets.

Pasumarthi, Kasyap Sriramachandra↗
NASA NTRSDate not supplied

Variety in the Variability of Accreting Supermassive Binary Black Holes

Accreting supermassive binary black holes are key multi-messenger sources for LISA, yet are challenging to simulate realistically as solving the radiation magnetohydrodynamics (MHD) equations over the full dynamic spatio-temporal range of the problem is computationally infeasible at present. We report on our collaboration's progress simulating these systems using general relativistic MHD simulations and dynamic GR. In order to cover a larger temporal range in one set of simulations, we constrain our view to the circumbinary disk region and measure the effects binary mass ratio, accretion disk size, and black hole spin have on the structure and variability of the accretion flow. We particularly emphasize how these parameters influence the overdensity feature, which orbits the binary near the edge of the cavity, since it is responsible for most of the electromagnetic emission's variability and variability is a key signature of a system being a binary. Extending to smaller length scales, we will report on simulations following accretion all the down to the event horizons so that we can begin to investigate how black hole spin affects mini-disk dynamics, accretion rate, and jet power.

Scott C Noble↗
DOE OSTI2020

AGC-4 Experiment Irradiation Monitoring Data Qualification Final Report

The Graphite Technology Development Program ran a series of six experiments to quantify the effects of irradiation on nuclear grade graphite. This report focuses on the fourth experiment, Advanced Graphite Creep 4 (AGC 4). The Advanced Reactor Development (ARD) Technology Development Office (TDO) Program for research and development activities require documentation of qualified monitoring data to design and license the first high-temperature reactor nuclear plant. Qualified data meets the requirements for use as described in the experiment planning and quality assurance documents. Failed data do not meet the requirements and provide no useable information. Trend data may not meet all requirements but still provide some useable information. Use of Trend data requires assessment of how any deficiencies affect a particular use of the data. AGC-4 began with Advanced Test Reactor (ATR) Cycle 157D on May 30, 2015. After irradiating the graphite for two cycles, the capsule was removed from the reactor after ATR Cycle 158A, which ended on January 2, 2016, due to interference with another experiment. Irradiation was resumed with Cycle 162A on October 7, 2017 after the interfering experiment was removed from the reactor. AGC-4 irradiation completed by the end of Cycle 166B on January 10, 2020. Between Cycles 162A and 166B, AGC-4 capsule was removed from the reactor core during two Powered Axial Locator Mechanism (PALM) Cycles 163A and 165A to avoid overheating. All thermocouples (TCs) have functioned throughout the AGC-4 experiment. A total of 9,256,184 out of all 11,167,213 temperature records (or 82.9%) are Qualified for use by the ARD Program and 1,911,029 missing values are Failed. Argon, helium, and total gas flow data were within expected ranges, except only eight out-of-range values occurred during outages. A total of 21,240,627 out of all 22,288,5103 gas flow rates (or 92.8%) are Qualified for use by the ARD Program and 1,644,476 are Failed records mostly due to missing values. Discharge gas line moisture values were consistently low during full ATR power, except for 162B, when moisture content was increasing to more than 200 ppmv by the end of this cycle. During outages, moisture content reached as high as 700 ppmv. 1,089,941 out of a total of 1,107,331 moisture values (or 98.4%) are within the measurement range of the instrument and are Qualified for use by the ARD Program and 17,390 missing moisture values are Failed. Graphite creep specimens were subjected to one of three loads: 393, 491, or 589 lbf. For a brief period during Cycle 157D between 12:19 on June 2, 2015, and 08:23 on June 11, 2015, the load cells were wired incorrectly, resulting in missing stack load data. Missing stack loads were estimated from measured ram pressures using regression equations developed from the existing data from Cycle 157D. Estimated stack loads during this period are considered to be an accurate representation of actual load applied to the stacks. These loads deviate slightly from the planned loads. This deviation does not prevent the data from being Qualified for use but must be taken into account when analyzing the effect of load on creep. 6,095,728 out of a total of 6,403,985 moisture values (or 95.2%) are within the measurement range of the instrument and are Qualified for use by the ARD Program and 308,257 missing load values are Failed. Stack displacement increased consistently throughout the eight cycles, with total displacement reached highest value of 2.4 in by the end of irradiation. During ATR outages, a set of pneumatic rams raised the stacks of graphite creep specimens to ensure the specimens were not stuck within the test train. This stack raising was performed seven times throughout irradiation. All stacks were raised successfully each time. 4,744,974 out of a total of 6,094,513 displacement values (or 77.9%) are within the measurement range of the instrument and are Qualified for use by the ARD Program and 1,349,539 displacement values are Failed mostly due to missing values. Analyses were conducted on correlations between TCs to look for trends and step changes that might indicate instrument degradation or failure. Correlation analysis was used to identify instances when TCs form short circuits, referred to as virtual junctions, which result in TCs reporting temperatures from some location in the capsule other than the location where they were intended to read. No evidence of virtual junctions was found. Analyses were also conducted on control charts of temperature differences of between two TCs, which are expected to behave consistently throughout the entire irradiation period. Upward or downward trend over time indicates at least one TC in the pair was drifted. Examining control charts for all 66 possible pairs out of twelve TCs installed in the AGC-4 capsules reveal no clear drift failures occurred, except unstable behavior of two TCs in Zone 3, TC-7 and TC-8, over irradiation time. In conclus

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1994

Asymptotic domination of cold relativistic MHD winds by kinetic energy flux

We study the conditions which lead to the conversion of most Poynting flux into kinetic energy flux in cold, relativistic hydromagnetic winds. It is shown that plasma acceleration along a precisely radial flow is extremely inefficient due to the near cancellation of the toroidal magnetic pressure and tension forces. However, if the flux tubes in a flow diverge even slightly faster than radially, the fast magnetosonic point moves inward from infinity to a few times the light cylinder radius. Once the flow becomes supermagnetosonic, further divergence of the flux tubes beyond the fast point can accelerate the flow via the 'magnetic nozzle' effect, thereby further converting Poynting flux to kinetic energy flux. We show that the Grad-Shafranov equation admits a generic family of kinetic energy-dominated asymptotic wind solutions with finite total magnetic flux. The Poynting flux in these solutions vanishes logarithmically with distance. The way in which the flux surfaces are nested within the flow depends only on the ratio of angular velocity to poliodal 4-velocity as a function of magnetic flux. Radial variations in flow structure can be expressed in terms of a pressure boundary condition on the outermost flux surface, provided that no external toriodal field surrounds the flow. For a special case, we show explicitly how the flux surfaces merge gradually to their asymptotes. For flows confined by an external medium of pressure decreasing to zero at infinity we show that, depending on how fast the ambient pressure declines, the final flow state could be either a collimated jet or a wind that fills the entire space. We discuss the astrophysical implications of our results for jets from active galactic nuclei and for free pulsar winds such as that believed to power the Crab Nebula.

Begelman, Mitchell C.↗
NASA NTRS2015

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

Orr, Jeb S.↗
NASA NTRS1994

Green's formula and variational principles for cosmic-ray transport with application to rotating and shearing flows

Green's theorem and Green's formula for the diffusive cosmic-ray transport equation in relativistic flows are derived. Green's formula gives the solution of the transport equation in terms of the Green's function of the adjoint transport equation, and in terms of distributed sources throughout the region R of interest, plus terms involving the particle intensity and streaming on the boundary. The adjoint transport equation describes the time-reversed particle transport. An Euler-Lagrange variational principle is then obtained for both the mean scattering frame distribution function f, and its adjoint f(dagger). Variations of the variational functional with respect to f(dagger) yield the transport equation, whereas variations of f yield the adjoint transport equation. The variational principle, when combined with Noether's theorem, yields the conservation law associated with Green's theorem. An investigation of the transport equation for steady, azimuthal, rotating flows suggests the introduction of a new independent variable H to replace the comoving frame momentum variable p'. For the case of rigid rotating flows, H is conserved and is shown to be analogous to the Hamiltonian for a bead on a rigidly rotating wire. The variable H corresponds to a balance between the centrifugal force and the particle inertia in the rotating frame. The physical interpretation of H includes a discussion of nonrelativistic and special relativistic rotating flows as well as the cases of aziuthal, differentially rotating flows about Schwarzs-child and Kerr black holes. Green's formula is then applied to the problem of the acceleration of ultra-high-energy cosmic rays by galactic rotation. The model for galactic rotation assumes an angular velocity law Omega = Omega(sub 0)(omega(sub 0)/omega), where omega denotes radial distance from the axis of rotation. Green's functions for the galactic rotation problem are used to investigate the spectrum of accelerated particles arising from monoenergetic and truncated power-law sources. We conclude that it is possible to accelerate particles beyond the knee by galactic rotation, but not in sufficient number to adequately explain the observed spectrum.

Webb, G. M.↗
DOE OSTI2020

Revisiting Theoretical Limits for One-Degree-of-Freedom Wave Energy Converters: Preprint

This work revisits the theoretical limits of one-degree of freedom wave energy converters (WECs). This paper considers the floating sphere used in the Ocean Energy Systems (OES) Task 10 Wave Energy Converter modeling and verification effort for analysis. Analytical equations are derived to determine bounds on the motion amplitude, time-averaged power, and power take-off (PTO) force. A unique result was found that shows the time-averaged power absorbed by a WEC can be defined solely by the inertial properties and the radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force amplitude was derived which has provided upper and lower bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression can only provide a lower bound as there is theoretically no upper bound. These bounds are used to compare the performance of a floating sphere if it were to extract energy using surge or heave motion. The analysis shows that because of the differences in hydrodynamic coefficients of each oscillating mode there will be different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on power absorption while also utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate the time-averaged power with a nonideal PTO is modified by the mechanical-to-electrical efficiency and the ratio of the PTO spring and damping coefficients. These were separated in the expression which allows for limits to be set on the possible values of PTO coefficients to ensure a net flow of power to the grid.

50 EE - Wind and Water Power Program - Water (EE-4↗