Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Conditional diffusion models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,711 records · Page 95
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Velocity and pressure characteristics of a model SSME high pressure fuel turbopump

Under the present effort an experiment rig has been constructed, an instrumentation package developed and a series of mean and rms velocity and pressure measurements made in a turbopump which modelled the first stage of the Space Shuttle Main Engine (SSME) High Pressure Fuel Turbopump. The rig was designed so as to allow initial experiments with a single configuration consisting of a bell-mouth inlet, a flight impeller, a vaneless diffuser and a volute. Allowance was made for components such as inlet guide vanes, exit guide vanes, downstream pumps, etc. to be added in future experiments. This flexibility will provide a clear baseline set of experiments and allow evaluation in later experiments of the effect of adding specific components upon the pump performance properties. The rotational speed of the impeller was varied between 4260 and 7680 rpm which covered the range of scaled SSME rotation speeds when due allowance is made for the differing stagnation temperature, model to full scale. The results at the inlet obtained with rotational speeds of 4260, 6084 and 7680 rpm showed that the axial velocity at the bell-mouth inlet remained roughly constant at 2.2 of the bulk velocity at the exit of the turbopump near the center of the inlet, but it decreased rapidly with increasing radius at all three speeds. Reverse flow occurred at a radius greater than 0.9 R for all three speeds and the maximum negative velocity reduced from 1.3 of the bulk velocity at the exit of the turbopump at 4260 rpm to 0.35 at 7680 rpm, suggesting that operating at a speed closer to the design condition of 8700 rpm improved the inlet characteristics. The reverse flow caused positive prerotation at the impeller inlet which was negligibly small near the center but reached 0.7 of the impeller speed at the outer annulus. The results in the diffuser and the volute obtained at 7680 rpm show that the hub and shroud walls of the diffuser were characterized by regions of transient reverse flow with negative revolution-averaged velocity of 8 percent of the maximum forward revolution-averaged velocity at the center of the diffuser passage near the shroud wall.

Tse, D. G-N.↗
NASA NTRS1981

Stability of a diffuse linear pinch with axial boundaries

A formulation of the stability behavior of a finite-length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end-boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of delta-W still admits a proper second-variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end-effect model to the stability of solar coronal loops.

Einaudi, G.↗
DOE OSTI2018

Efficient multistep arsenate removal onto magnetite modified fly ash

The modification of the fly ash (FA) by magnetite (M) was performed to obtain FAM adsorbent with improved adsorption efficiency for arsenate removal from water. The novel low cost adsorbents are characterized by liquid nitrogen porosimetry (BET), scanning electron microscopy (SEM), X-ray diffraction (XRD), Mössbauer spectroscopy (MB) and Fourier transform infrared (FTIR) spectroscopy. The optimal conditions and key factors influencing the adsorbent synthesis are assessed using the response surface method (RSM). The adsorption experiment was carried out in a batch system by varying the contact time, temperature, pH, and mass of the adsorbent. The adsorption capacity of the FAM adsorbent for As(V), calculated by Langmuir model, was 19.14 mg g−1. The thermodynamic parameters showed spontaneity of adsorption with low endothermic character. The kinetic data followed the pseudo-second-order kinetic model (PSO), and Weber-Morris model indicated intra-particle diffusion as rate limiting step. Alternative to low desorption capability of the FAM was found by five consecutive adsorption/magnetite precipitation processes which gave exhausted layered adsorbent with 65.78 mg g−1 capacity. This research also has shed light on the mechanism of As(V)-ion adsorption, presenting a promising solution for the valorization of a widely abundant industrial waste. © 2018 Elsevier Ltd.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Shear-induced aggregation or disaggregation in edible oils: Models, computer simulation, and USAXS measurements

The effects of shear upon the aggregation of solid objects formed from solid triacylglycerols (TAGs) immersed in liquid TAG oils were modeled using Dissipative Particle Dynamics (DPD) and the predictions compared to experimental data using Ultra-Small Angle X-ray Scattering (USAXS). The solid components were represented by spheres interacting via attractive van der Waals forces and short range repulsive forces. A velocity was applied to the liquid particles nearest to the boundary, and Lees-Edwards boundary conditions were used to transmit this motion to non-boundary layers via dissipative interactions. The shear was created through the dissipative forces acting between liquid particles. Translational diffusion was simulated, and the Stokes-Einstein equation was used to relate DPD length and time scales to SI units for comparison with USAXS results. The SI values depended on how large the spherical particles were (250 nm vs. 25 nm). Aggregation was studied by (a) computing the Structure Function and (b) quantifying the number of pairs of solid spheres formed. Solid aggregation was found to be enhanced by low shear rates. As the shear rate was increased, a transition shear region was manifested in which aggregation was inhibited and shear banding was observed. Aggregation was inhibited, and eventually eliminated, by further increases in the shear rate. The magnitude of the transition region shear, $\dot{γ}_t$, depended on the size of the solid particles, which was confirmed experimentally.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Measurements of the electron energy distribution function in partially magnetized low temperature plasmas

While Langmuir probes (LPs) are relatively simple and inexpensive plasma diagnostics for the electron density, temperature, and the electron energy distribution function (EEDF), the interpretation of the measured current–voltage (I–V) characteristic is complicated considerably by the presence of a magnetic field. In regimes where the electron gyroradius is comparable to the probe radius, the electron flux to the probe surface is retarded by reduced mobility across field lines and can no longer be described by a thermal model. Predicting the current collected by the probe in these regimes requires accurate estimates of the plasma diffusion coefficients, which are usually difficult to obtain. In this work, we measure electron energy distribution functions in E×B plasmas with magnetized electrons and non-magnetized ions in argon and krypton gases, using both a LP and laser Thomson scattering (LTS) at various magnetic fields. Using the LTS measurements to provide a robust benchmark for comparison, we compare existing theories describing the flux to the probe under magnetized conditions. We find that even when the electron gyroradius associated with the effective electron temperature is small compared to the probe radius, the EEDF computed using classical probe theory is still robust at energies higher than the energy at which the gyroradius becomes larger than the probe size. For plasmas that are not strongly non-Maxwellian, we formulate a method to extract robust density and temperature measurements using physics-informed fitting techniques to analyze EEDFs computed using classical theory.

Devin, E. G. [Princeton Plasma Physics Laboratory ↗
DOE OSTI2016

THE EFFECTS OF GRAIN SIZE AND TEMPERATURE DISTRIBUTIONS ON THE FORMATION OF INTERSTELLAR ICE MANTLES

Computational models of interstellar gas-grain chemistry have historically adopted a single dust-grain size of 0.1 micron, assumed to be representative of the size distribution present in the interstellar medium. Here, we investigate the effects of a broad grain-size distribution on the chemistry of dust-grain surfaces and the subsequent build-up of molecular ices on the grains, using a three-phase gas-grain chemical model of a quiescent dark cloud. We include an explicit treatment of the grain temperatures, governed both by the visual extinction of the cloud and the size of each individual grain-size population. We find that the temperature difference plays a significant role in determining the total bulk ice composition across the grain-size distribution, while the effects of geometrical differences between size populations appear marginal. We also consider collapse from a diffuse to a dark cloud, allowing dust temperatures to fall. Under the initial diffuse conditions, small grains are too warm to promote grain-mantle build-up, with most ices forming on the mid-sized grains. As collapse proceeds, the more abundant, smallest grains cool and become the dominant ice carriers; the large population of small grains means that this ice is distributed across many grains, with perhaps no more than 40 monolayers of ice each (versus several hundred assuming a single grain size). This effect may be important for the subsequent processing and desorption of the ice during the hot-core phase of star formation, exposing a significant proportion of the ice to the gas phase, increasing the importance of ice-surface chemistry and surface–gas interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

The COS-Halos survey: origins of the highly ionized circumgalactic medium of star-forming galaxies

The total contribution of diffuse halo gas to the galaxy baryon budget strongly depends on its dominant ionization state. In this paper, we address the physical conditions in the highly ionized circumgalactic medium (CGM) traced by O VI absorption lines observed in COS-Halos spectra. We analyze the observed ionic column densities, absorption-line widths and relative velocities, along with the ratios of N V/O VI for 39 fitted Voigt profile components of O vi. We compare these quantities with the predictions given by a wide range of ionization models. Photoionization models that include only extragalactic UV background radiation are ruled out; conservatively, the upper limits to N V/O VI and measurements of N{sub OVI} imply unphysically large path lengths ≳100 kpc. Furthermore, very broad O VI absorption (b > 40 km s{sup −1}) is a defining characteristic of the CGM of star-forming L* galaxies. We highlight two possible origins for the bulk of the observed O VI: (1) highly structured gas clouds photoionized primarily by local high-energy sources or (2) gas radiatively cooling on large scales behind a supersonic wind. Approximately 20% of circumgalactic O vi does not align with any low-ionization state gas within ±50 km s{sup −1} and is found only in halos with M{sub halo} < 10{sup 12} M{sub ⊙}. We suggest that this type of unmatched O vi absorption traces the hot corona itself at a characteristic temperature of 10{sup 5.5} K. We discuss the implications of these very distinct physical origins for the dynamical state, gas cooling rates, and total baryonic content of L* gaseous halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Effect of Radiation on Chromospheric Magnetic Reconnection: Reactive and Collisional Multi-fluid Simulations

We study magnetic reconnection under chromospheric conditions in five different ionization levels from 0.5% to 50% using a self-consistent two-fluid (ions + neutrals) model that accounts for compressibility, collisional effects, chemical inequilibrium, and anisotropic heat conduction. Results with and without radiation are compared, using two models for the radiative losses: an optically thin radiation loss function, and an approximation of the radiative losses of a plasma with photospheric abundances. The results without radiation show that reconnection occurs faster for the weakly ionized cases as a result of the effect of ambipolar diffusion and fast recombination. The tearing mode instability appears earlier in the low ionized cases and grows rapidly. We find that radiative losses have a stronger effect than was found in previous results as the cooling changes the plasma pressure and the concentration of ions inside the current sheet. This affects the ambipolar diffusion and the chemical equilibrium, resulting in thin current sheets and enhanced reconnection. The results quantify this complex nonlinear interaction by showing that a strong cooling produces faster reconnections than have been found in models without radiation. The results accounting for radiation show timescales and outflows comparable to spicules and chromospheric jets.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

Effects of confinement on partially premixed flames

Partially premixed combustion is an intermediate regime between the limiting cases of premixed and nonpremixed combustion. Although combustion problems are generally approached from one of these two limiting cases, there are many practical situations where flames cannot be considered as purely premixed or nonpremixed, and thus the partially premixed approach must be used. In partially premixed combustion, mechanisms from the premixed and nonpremixed regimes can coexist, and as a result some interesting new phenomena can arise. One such phenomenon is the flame stabilization in laminar mixing layers by triple flames. One of the first observations of triple flames was made by Phillips (1965), who investigated a triple flame propagating in a methane mixing layer. Kioni et al. (1993) also examined triple flames both experimentally and numerically. There have also been numerous analytical studies on the shape and propagation of triple flames under various assumptions by Dold (1989), Dold et al. (1991), and Hartley and Dold (1991). In terms of modeling, Muller et al. (1994) have combined the flamelet formulations for premixed and nonpremixed combustion in order to treat lifted diffusion flames. One common feature in the analytical and numerical studies mentioned above is the assumption of zero heat release, which is necessary to make the problem tractable. The effect of heat release on triple flames was investigated by Ruetsch et al. (1995), where for the unconfined case, flame speeds larger than their premixed counterparts were found. One of the most important practical situations in which these conditions arise is in lifted turbulent jet diffusion flames. At a critical velocity the burning zone of a fuel jet lifts off from the nozzle, moves to increasing distances as the jet velocity increases, and finally blows off. The mechanisms that control these phenomena, i.e. that determine the stability of these flames, are still not understood. In addition to regions where diffusion flame stabilization takes place, partially premixed conditions also exist during the ignition process in nonpremixed systems. Numerical simulations by Reveillon et al. (1994) of the ignition process in a weakly stirred mixture of fuel and oxidizer show that triple flames propagate along lines of stoichiometric mixture fraction throughout the fluid. In addition, Peters (1994) notes that NO(x) emissions are likely to be large in such transient cases, and therefore an understanding of triple flames can provide information concerning pollutant formation. This study extends the work previously done and examines the effects of lateral confinement on partially premixed flames. Once again, we study both the flame structure and propagation.

Ruetsch, G. R.↗
NASA NTRS1997

Effects of Fuel Preheat on Soot Formation in Microgravity Laminar Diffusion Flames

Nonbuoyant flames offer themselves as an attractive and promising platform to gain a better understanding of soot mechanisms. The effects of buoyancy can be eliminated temporarily in drop towers which sustain brief intervals of reduced gravity-typically lower than 10(exp -3)g- extending up to several seconds at a time. Microgravity facilities have been employed to show that nonbuoyant flames are longer, wider and sootier than their normal-gravity counterparts. Sunderland et al. recently verified the existence of smoke point in laminar nonbuoyant flames. As reported, microgravity flames operating above their smoke point displayed a blunt tip and much broader soot-containing regimes in comparison to their buoyant counterparts. Mortazavi et al. established that residence times in microgravity laminar jet diffusion flames with Re=0(100) tend to be proportional to burner diameter and inversely proportional to burner exit velocity. This offers the capability to alter residence times in nonbuoyant laminar jet diffusion flames when varying the burner exit diameters and velocities. Megaridis et al. presented a quantitative definition of the soot-field structure within laminar microgravity jet diffusion flames which operated well above their smoke point. The experimental methodology involved a full-field laser-light extinction technique and jet diffusion flames of nitrogen-diluted (50% vol.) acetylene fuel burning in quiescent air at atmospheric pressure. The work was conducted at the 2.2s drop tower of the NASA Lewis Research Center (NASA-LeRC). Parallel work on 1-g flames was also presented in (6) to facilitate comparisons on the effect of gravity on the soot fields. As reported, the soot spatial distributions in 0-g flames did not change in a detectable manner after 1s within a typical 2.2s experiment. During that period, the soot field was shown to sustain a pronounced annular structure throughout the luminous nonbuoyant-flame zone. The maximum soot volume fraction measured at 0-g was nearly a factor of two higher than that at 1-g, thus confirming the enhanced sooting tendency of nonbuoyant flames. Greenberg and Ku presented a similar study and reported trends that matched those of for the 50% (vol.) nitrogen-diluted acetylene fuel. Furthermore, they examined pure acetylene flames and reported similar trends with respect to the influence of gravity on maximum soot volume fractions and flame cross-section-averaged soot loadings. Both studies clearly demonstrated the improved spatial resolution of microgravity flames compared to their normal-gravity counterparts. The current study evaluates the influence of moderate fuel preheat on soot formation within 0-g laminar gas jet diffusion flames. While fuel temperature variations have little influence on residence times in 1-g, they have a much more significant effect in 0-g. The primary objective of this program is to quantify this effect and its consequences on sooting by comparing soot volume fraction distributions under preheated and unpreheated-fuel conditions. Furthermore, the current work aims at expanding the limited soot database available for nonbuoyant flames. Soot fields in such flames can be used to perform additional tests of recently developed soot sub-models which have the potential to become powerful predicting tools in combustion design.

Konsur, Bogdan↗
DOE OSTI2018

On the importance of the heat and mass transfer resistances in internally-cooled liquid desiccant dehumidifiers and regenerators

Liquid desiccant heat and mass exchangers are a promising technology for efficient humidity control in buildings. Many researchers have investigated these exchangers, often using numerical models to predict their performance. However, there is a lack of information in the literature on the magnitude of the heat and mass transfer resistances, both for the dehumidifier (which absorbs moisture from the air) and the regenerator (which heats the liquid desiccant to re-concentrate it). This article focuses on internally-cooled, 3-fluid exchangers in a parallel plate geometry. Water heats or cools a desiccant across a plate, and the desiccant absorbs or releases water into an airstream through a membrane. A sensitivity analysis was used to estimate the importance of each of the heat and mass transfer resistances (air, membrane, desiccant, plate, water), and how it changes with different design geometries. The results show that, for most designs, the latent and sensible heat transfer of the dehumidifier is dominated by the air mass transfer resistance and air heat transfer resistance, respectively. The air mass transfer resistance is also important for the regenerator, but much less so; the change in the desiccant equilibrium humidity ratio due to a change in either temperature or desiccant mass fraction is much higher at the regenerator's higher temperatures. This increases the importance of (1) getting heat from the water to the desiccant/membrane interface, and (2) diffusing salt ions quickly away from the desiccant/membrane interface. The membrane heat transfer and water heat transfer resistances were found to be the least important. These results can help inform decisions about what simplifying assumptions to make in numerical models, and can also help in designing these exchangers by understanding which resistances are most important.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Effects of elastic softening and helium accumulation kinetics on surface morphological evolution of plasma-facing tungsten

Based on a continuous-domain model, capable of accessing the spatiotemporal scales relevant to fuzz formation on the surface of plasma-facing component (PFC) tungsten, we report self-consistent simulation results that elucidate the effects of elastic softening and helium (He) accumulation kinetics on the surface morphological response of PFC tungsten. The model accounts for the softening of the elastic moduli in the near-surface region of PFC tungsten, including both thermal softening at high temperature and softening due to He accumulation upon He implantation. The dependence of the elastic moduli on the He content follows an exponential scaling relation predicted by molecular-dynamics simulations, while the He content in the near-surface region of PFC tungsten evolves according to a first-order saturation kinetics, consistent with experimental and simulation results reported in the literature. We establish that this elastic softening accelerates both nanotendril growth on the PFC surface and the onset of fuzz formation. We also explore the role of the rate of He accumulation to a saturation level in the near-surface region of irradiated tungsten in the onset of fuzz formation. For PFC tungsten surfaces such as W(110) where, under typical irradiation conditions, the characteristic time scale for stress-driven surface diffusion is comparable to the characteristic time scale for He accumulation, we find that accelerating the rate of He accumulation accelerates the growth rate of nanotendrils emanating from the surface. Additionally, we present a systematic parametric study of the PFC surface morphological response to explore its dependence on the He accumulation kinetics that is controlled by the irradiation conditions for low-energy implantation. Finally, we introduce an incubation time for nanotendril growth on the PFC surface, a concept equivalent to that of incubation fluence discussed in the literature, to predict and explain the minimum exposure time required to observe fuzz formation on PFC tungsten surfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Topology optimization for the full-cell design of porous electrodes in electrochemical energy storage devices

In this paper, we introduce a density-based topology optimization framework to design porous electrodes for maximum energy storage. We simulate the full cell with a model that incorporates electronic potential, ionic potential, and electrolyte concentration. The system consists of three materials, namely pure liquid electrolyte and the porous solids of the anode and cathode, for which we determine the optimal placement. We use separate electronic potentials to model each electrode, which allows interdigitated designs. As a result, a penalization is required to ensure that the anode and cathode do not touch, i.e., causing a short circuit. We compare multiple 2D designs generated for different fixed conditions, e.g. material properties. A 3D design with complex channel and interlocked structure is also created. All optimized designs are far superior to the traditional monolithic electrode design with respect to energy storage metrics. We observe up to a 750% increase in energy storage for cases with slow effective ionic diffusion within the porous electrode.

25 ENERGY STORAGE↗
DOE OSTI2021

Modeling of High-Temperature Corrosion of Zirconium Alloys Using the eXtended Finite Element Method (X-FEM)

Oxidation modeling in modern nuclear fuel performance codes is currently limited by the lack of coupling with mechanics, thus preventing proper description of how high-temperature oxidation impacts mechanical properties. This is mostly due to the fact that the finite difference formalism adopted in corrosion models is incompatible with the direct coupling with mechanics in the finite element modeling employed in modern nuclear fuel performance codes. In this study, a physically based zirconium alloy corrosion model called the Coupled-Current Charge Compensation (C4) model, which was initially developed for operating temperature conditions, has been updated to include high-temperature corrosion in order to provide additional critical information (e.g., oxygen concentration profile) under loss-of-coolant accident (LOCA) conditions—information lacking in existing empirical models. The C4 model was implemented in the MOOSE finite-element framework developed at Idaho National Laboratory, enabling it to be used in the BISON nuclear fuel performance code based on the MOOSE framework. To precisely track the different interfaces at a relatively low computational cost, the eXtended Finite Element Method (X-FEM) was applied in MOOSE. The model’s results were compared to those of existing empirical models as well as metallographic analysis of high-temperature oxidized Zircaloy-4 coupons. Oxygen diffusivities in the a and ß phases resulting from this comparison closely agree with those found in the literature. The C4 model implemented with X-FEM in MOOSE now has the capability to accurately predict oxide, oxygen-stabilized a, and prior ß phase layer growth kinetics under isothermal exposure at high temperature (1000–1500°C). Furthermore, in contrast with the empirical models, the C4 model accounts for the finite thickness of the fuel cladding. It can predict the oxygen concentration profile evolution through the whole cladding, enabling evaluation of the remaining ductile thickness—a crucial variable for modeling the mechanical behavior of the fuel cladding under LOCA. Furthermore, this implementation allows direct coupling with mechanics, at a low computing cost, using finite-element-based nuclear fuel performance codes such as BISON.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Computational framework for modeling membrane processes without process and solution property simplifications

Accurately modeling membrane processes is critical to evaluating novel process configurations, designing scalable membrane systems, informing process cost estimates, and directing future research. Most membrane process models trade accuracy for computational efficiency by employing simplified approximations of the process (i.e. no salt flux, no pressure drop) and solution properties (i.e. ideal solution, and constant density, viscosity, and diffusivity). Our report introduces a detailed one-dimensional finite difference model for evaluating membrane processes that avoids these common simplifications. We apply this model to quantify the error introduced by these simplifications for case studies of reverse osmosis, osmotically assisted reverse osmosis, forward osmosis, and pressure retarded osmosis. While the magnitude of error introduced by these simplifications is reliant on the case study parameters and specifications, we find that existing model formulations can underestimate or overestimate average water flux by nearly 50% for some membrane processes operating under standard conditions. Lastly we investigate the error introduced by simplified inlet-outlet models that do not solve the governing system of differential equations, and we assess the accuracy of novel inlet-outlet formulations that use a log and geometric mean, instead of the typical arithmetic mean, to represent non-linear water flux profiles.

42 ENGINEERING↗
DOE OSTI2016

IceCube constraints on fast-spinning pulsars as high-energy neutrino sources

Relativistic winds of fast-spinning pulsars have been proposed as a potential site for cosmic-ray acceleration from very high energies (VHE) to ultrahigh energies (UHE). We re-examine conditions for high-energy neutrino production, considering the interaction of accelerated particles with baryons of the expanding supernova ejecta and the radiation fields in the wind nebula. We make use of the current IceCube sensitivity in diffusive high-energy neutrino background, in order to constrain the parameter space of the most extreme neutron stars as sources of VHE and UHE cosmic rays. We demonstrate that the current non-observation of 10{sup 18} eV neutrinos put stringent constraints on the pulsar scenario. For a given model, birthrates, ejecta mass and acceleration efficiency of the magnetar sources can be constrained. When we assume a proton cosmic ray composition and spherical supernovae ejecta, we find that the IceCube limits almost exclude their significant contribution to the observed UHE cosmic-ray flux. Furthermore, we consider scenarios where a fraction of cosmic rays can escape from jet-like structures piercing the ejecta, without significant interactions. Such scenarios would enable the production of UHE cosmic rays and help remove the tension between their EeV neutrino production and the observational data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Extension of the PINN diffusion model to k-eigenvalue problems

This paper extends our recent work on the Physics-Informed Neural Networks (PINN) approach for the fixed source diffusion models and applies it to the diffusion theory based k-eigenvalue problems. To make the PINN equitable for the eigenvalue problems, we introduce a novel integral regularization term to the loss function in the framework, and allow the direct inference of the principal eigenvalue and the associated eigenfunction. The regularization term enforces a pre-defined value on the integration of the model predictions, and this value can be directly related to a physical property of the system. We also introduce an additional learnable parameter to approximate the principal eigenvalue. As a proof of principle, we solve the one-group two-dimensional k-eigenvalue neutron diffusion equation in this work. We then provide two numerical examples to demonstrate the applicability of the PINN approach. In each example, we solve the k-eigenvalue diffusion equation in a multi-region configuration constrained with a set of Robin boundary conditions for generality. We use a FEM solution based on the power-iteration method to verify the results of the PINN solution. The results showed relative percentage error in the predicted eigenvalue of about 0.77% and about 1.2% for example 1 and example 2, respectively. The mean absolute error in the predicted flux for example 1 is ∼ 0.002 and for example 2 is ∼ 0.0024. These results indicate some preliminary successes of the PINN application to k-eigenvalue problems. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗