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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Coronal roots of solar wind streams: 3-D MHD modeling

Weak (discontinuous) solutions of the 3-D MHD equations look like a promising tool to model the transonic solar wind with structural elements: current sheets, coronal plumes etc. Using the observational information about various coronal emissions one can include these structural elements into the 3-D MHD solar wind model by embedding the discontinuities of given type. Such 3-D MHD structured solar wind is calculated self-consistently: variants are examined via numerical experiments. In particular, the behavior of coronal plumes in the transonic solar wind flow, is modeled. The input information for numerical modeling (for example, the magnetic field map at the very base of the solar corona) can be adjusted so that fast stream arises over the center of the coronal hole, over the coronal hole boundaries and, even, over the region with closed magnetic topology. 3-D MHD equations have the analytical solution which can serve as a model of supersonic trans-alfvenic solar wind in the (5-20) solar radii heliocentric distance interval. The transverse, nonradial total (gas + magnetic field) pressure balance in the flow is the corner-stone of this solution. The solution describes the filamentation (ray-like structure of the solar corona) and streaming (formation of high-speed streams with velocities up to 800 km/sec) as a consequence of the magnetic field spatial inhomogeneous structure and trans-alfvenic character of the flow. The magnetic field works in the model as a 'controller' for the solar wind streaming and filamentation.

Pisanko, Yu. V.↗
DOE OSTI2025

Beam focusing and consequences for Doppler backscattering measurements

The phenomenon of focusing of microwave beams in a plasma near a turning-point caustic is discussed by exploiting the analytical solution to the Gaussian beam-tracing equations in the two-dimensional (2-D) linear-layer problem. The location of maximum beam focusing and the beam width at that location are studied in terms of the beam initial conditions. This focusing must be taken into account to interpret Doppler backscattering (DBS) measurements. We find that the filter function that characterises the scattering intensity contribution along the beam path through the plasma is inversely proportional to the beam width, predicting enhanced scattering from the beam focusing region. We show that the DBS signal enhancement for decreasing incident angles between the beam path and the density gradient is due to beam focusing and not due to forward scattering, as was originally proposed by (Gusakov et al., (Plasma Phys. Contr. Fusion, vol. 56, 2014, p. 0250092014, 2017); Plasma Phys. Rep. vol. 43(6), 2017, pp. 605–613). The analytic beam model is used to predict the measurement of the k y density-fluctuation wavenumber power spectrum via DBS, showing that, in an NSTX-inspired example, the spectral exponent of the turbulent, intermediate-to-high k y density-fluctuation spectrum might be quantitatively measurable via DBS, but not the spectral peak corresponding to the driving scale of the turbulent cascade.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

Understanding the Impact of Return-Current Losses on the X-Ray Emission from Solar Flares

I obtain and examine the implications of one-dimensional analytic solutions for return-current losses on an initially power-law distribution of energetic electrons with a sharp low-energy cutoff in flare plasma with classical (collisional) resistivity. These solutions show, for example, that return-current losses are not sensitive to plasma density, but are sensitive to plasma temperature and the low energy cutoff of the injected nonthermal electron distribution. A characteristic distance from the electron injection site, x(sub rc), is derived. At distances less than x(sub rc) the electron flux density is not reduced by return-current losses, but plasma heating can be substantial in this region, in the upper, coronal part of the flare loop. Before the electrons reach the collisional thick-target region of the flare loop, an injected power-law electron distribution with a low-energy cutoff maintains that structure, but with a flat energy distribution below the cutoff energy, which is now determined by the total potential drop experienced by the electrons. Modifications due to the presence of collisional losses are discussed. I compare these results with earlier analytical results and with more recent numerical simulations. Emslie's 1980 conjecture that there is a maximum integrated X-ray source brightness on the order of 10(exp -15) photons per square centimeter per second per square centimeter is examined. I find that this is not actually a maximum brightness and its value is parameter dependent, but it is nevertheless a valuable benchmark for identifying return-current losses in hard X-ray spectra. I discuss an observational approach to identifying return-current losses in flare data, including identification of a return-current "bump" in X-ray light curves at low photon energies.

Holman, Gordon D.↗
DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

Infiltration processes in fractured-porous media remain a crucial, yet not very well understood component of recharge and vulnerability assessment. Under partially-saturated conditions flows in fractures, percolating fracture networks, and fault zones contribute to the fastest spectrum of infiltration velocities via preferential pathways. Specifically, the partitioning dynamics at fracture intersections determine the magnitude of flow fragmentation into vertical and horizontal components and hence the bulk flow velocity and dispersion of fracture networks. In this work, we derive an approximate analytical solution for the partitioning process and validate it using smoothed particle hydrodynamics simulations. The developed transfer function is conceptually based on simulation results and laboratory experiments carried out in previous works. It allows to efficiently simulate flow through fracture networks with simple cubic structure and arbitrary number of fractures and aperture sizes via linear response theory and convolution of a given input signal. We derive a non-dimensional bulk flow velocity ($\widetilde{v}$) and dispersion coefficient ($\widetilde{D}$) to characterize fracture networks in terms of dimensionless horizontal and vertical time scales $\tau_m$ and $\tau_0$. The dispersion coefficient is shown to strongly depend on the horizontal time scale and converges towards a constant value of $0.08$ within reasonable fluid and geometrical parameter ranges, while the non-dimensional velocity exhibits a characteristic $\widetilde{v} \sim \tau_m^{-1/2}$ scaling. Given that hydraulic information is often only available at limited places within (fractured-porous) aquifer system, such as boreholes or springs, our study intends to provide a rudimentary analytical concept to potentially reconstruct internal fracture network geometries from external boundary information, e.g., the dispersive properties of discharge (groundwater level fluctuations).

42 ENGINEERING↗
NASA NTRS2024

Hyper Illumination of Exoplanets: Analytical and Numerical Approaches

This work describes the illumination of exoplanets whose orbits are close enough to their host star that the finite angular size of their host star causes hyper illumination, in which more than 50% of the planet receives light. Such exoplanets include the hot Jupiters KELT-9 b (64.5% illuminated) and Kepler-91 b (69.6% illuminated). We describe the geometry of three primary illumination zones: the fully illuminated zone, penumbral zone, and unilluminated zone. The integrals required to determine the incident radiation as a function of position from the substellar point on the exoplanet are explained and derived, and the analytical solution is presented within the fully illuminated zone. We find that the illumination predicted by our model is greater at the substellar point than the typical plane-parallel ray model used would suggest. In addition, it is greater within the region of the penumbral zone extending into the antistellar side of the exoplanet. Finally, we compare our model to that used in starry, an open-source software package used to create albedo maps. It appears that starry may be overestimating the illumination of closely orbiting exoplanets because the foreshortening of the area element of the host star is not included in its calculation.

Exoplanets↗
NASA NTRS1990

Damage states in laminated composite three-point bend specimens: An experimental-analytical correlation study

Damage states in laminated composites were studied by considering the model problem of a laminated beam subjected to three-point bending. A combination of experimental and theoretical research techniques was used to correlate the experimental results with the analytical stress distributions. The analytical solution procedure was based on the stress formulation approach of the mathematical theory of elasticity. The solution procedure is capable of calculating the ply-level stresses and beam displacements for any laminated beam of finite length using the generalized plane deformation or plane stress state assumption. Prior to conducting the experimental phase, the results from preliminary analyses were examined. Significant effects in the ply-level stress distributions were seen depending on the fiber orientation, aspect ratio, and whether or not a grouped or interspersed stacking sequence was used. The experimental investigation was conducted to determine the different damage modes in laminated three-point bend specimens. The test matrix consisted of three-point bend specimens of 0 deg unidirectional, cross-ply, and quasi-isotropic stacking sequences. The dependence of the damage initiation loads and ultimate failure loads were studied, and their relation to damage susceptibility and damage tolerance of the mean configuration was discussed. Damage modes were identified by visual inspection of the damaged specimens using an optical microscope. The four fundamental damage mechanisms identified were delaminations, matrix cracking, fiber breakage, and crushing. The correlation study between the experimental results and the analytical results were performed for the midspan deflection, indentation, damage modes, and damage susceptibility.

Starbuck, J. Michael↗
DOE OSTI2020

Coordinate parameterisation and spectral method optimisation for Beltrami field solver in stellarator geometry

The numerical solution of the stepped pressure equilibrium (Hudson et al 2012 Phys. Plasmas 19 112502) requires a fast and robust solver to obtain the Beltrami field in three-dimensional geometry such as stellarators. The spectral method implemented in the stepped pressure equilibrium code (SPEC) is efficient when the domain is a hollow torus, but ill-conditioning of the discretised linear equations occurs in the (solid) toroid due to the artificially singular coordinate parameterisation near the axis. Here, we propose an improved choice for the reference axis to prevent coordinates surfaces from overlapping. Then, we examine the parity and asymptotics of the magnetic vector potential near the axis and suggest the use of recombined and rescaled Zernike radial basis functions. The maximum relative error in the magnetic field of the Wendelstein 7-X geometry is shown to reach 10 –9 at high resolution in a series of convergence tests and benchmarks against the boundary integral equation solver for Taylor states. The new method is also reported to significantly improve the accuracy of multi-volume SPEC calculations. A comparison between free-boundary SPEC and the analytical Dommaschk potential is presented with higher-than-usual Fourier resolution. It is illustrated that we are able to resolve low amplitude current sheets when an interface is placed where there is no flux surface in the analytic solution. This was previously concealed because of insufficient numerical resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A new form of the Saint-Venant equations for variable topography

The solution stability of river models using the one-dimensional (1D) Saint-Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint-Venant equations to ensure smooth slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

An immersed interface method for microstructure-scale electrochemical battery models: numerical formulation and performance portable implementation

We present the numerical formulation, verification, and performance portable implementation of an immersed interface method for microstructure scale electrochemical modeling of batteries. The innovation in this approach is the resolution of chemical species and electrostatic potential discontinuities at active interfaces without the use of interface conforming unstructured grids. A unified formulation on Cartesian grids for all domains (electrodes and electrolyte) is used with interfacial flux conditions applied using volume fraction or “color” function gradients. We have developed one dimensional and two dimensional test cases with analytic solutions for electrochemical modeling using which we verified the consistency and accuracy of our scheme. Our solver is also validated against solutions from a macroscale model and an unstructured multi-subdomain solver for a full lithium ion cell. We then demonstrated the utility of our solver on an image-based complex battery electrode microstructure at high charging rate. Our technique also exhibits good scalability on distributed memory architectures using central processing units (CPU), with problem sizes up to 1.8 billion degrees of freedom and with 5400 ranks. Initial performance studies of our open-source performance portable solver showed about 70 times speed up using a graphics processing unit (GPU) compared to single compute core for a problem with 4 million cells.

25 ENERGY STORAGE↗
NASA NTRS1994

The hard X-ray emission spectra from accretion columns in intermediate polars

We consider the hard (greater than 2 keV) X-ray emission from accretion columns in an intermediate polar system, GK Per, using a simple settling solution. The rate of photon emission per logarithmic energy interval can be fitted with a power law, E(exp -gamma), with gamma approximately 2.0, in agreement with observations. This index is only weakly dependent on the mass accretion rate, dot-M, for dot-M in the range of a few times 10(exp 16-18) g/s. The peak energy of the photon spectra (after photoelectric absorption) is expected to be E(sub p) approximately (5 keV) gamma(exp -1/3) (N(sub H)/10(exp 23)/sq cm)(exp 1/3) where N(sub H) is the hydrogen column density along the line of sight. The observed spectra of GK Per and possibly of V1223 Sgr suggest N(sub H) approximately 10(exp 23)/sq cm. This large N(sub H) may be due to partially ionized preshock column material. Alternatively, we also consider absorption by the cool outer parts of an accretion disk. In this case the photoelectric absorption depth in the disk is a sensitive function of inclination. For GK Per the required inclination is approximately 83 deg. For mass accretion rates larger than a critical rate of approximately 10(exp 18) g/s, X-ray emission from the column accretion is significantly affected by radiation drag. Although the mass accretion rate increases dramatically during outbursts, the observed hard (greater than 2 keV) X-ray luminosity will not rise proportionately. The slope and peak energy of the outburst spectra are only weakly affected. We conclude that the observed X-ray spectra can be explained by this simple analytic solution and that the production of hard X-rays from the accretion shock at the magnetic poles in the intermediate polars is in general agreement with the observations. However, since the X-ray emission and absorption depend on the mass accretion rate in a complicated manner, observed hard X-ray luminosities (greater than 2 keV) are not a good indicator of the mass accretion rate in the X-ray emitting regions.

Yi, Insu↗
DOE OSTI2020

Dynamics of poly[n]catenane melts

Inspired by advances in the chemical synthesis of interlocking polymer architectures, extensive molecular dynamics simulations have been conducted to study the dynamical properties of poly[n]catenanes-polymers composed entirely of interlocking rings-in the melt state. Both the degree of polymerization (number of links) and the number of beads per ring are systematically varied, and the results are compared to linear and ring polymers. Herein, a simple Rouse-like model is presented, and its analytical solution suggests a decomposition of the dynamics into "ring-like" and "linear-like" regimes at short and long times, respectively. In agreement with this picture, multiple sub-diffusive regimes are observed in the monomer mean-squared-displacements even though interchain entanglement is not prevalent in the system. However, the Rouse-type model does not account for the topological effects of the mechanical bonds, which significantly alter the dynamics at intermediate length scales both within the rings and at the chain segment scales. The stress relaxation in the system is extremely rapid and may be conveniently separated into ring-like and linear-like contributions, again in agreement with the Rouse picture. However, the viscosity has a non-monotonic dependence on the ring size for long chains, which disagrees strongly with theoretical predictions. This unexpected observation cannot be explained in terms of chain disentanglement and is inconsistent with other measures of polymer relaxation. Possible mechanisms for this behavior are proposed and implications for materials design are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Tracking Radioactive Isotopes in HVAC and Application for Hot Cell Analyses - 20155

In recent years, the surge in the number of isotope production facilities under design has increased the need to analyze isotope migration in facility Heating, Ventilation, and Air Conditioning (HVAC) during normal operations and accident scenarios. These facilities are used to produce isotopes for medical, security, and industrial applications and as such are subject to license and regulatory requirements 10CFR20, 10CFR30, 10CFR50, and 10CFR70. GOTHIC, a general-purpose thermal-hydraulics software package, includes the ability to model isotopic tracers, radioactive decay and isotope migration as well as HEPA and charcoal filters for isotope retention. A GOTHIC model was developed by Zachry Nuclear Engineering (ZNE) to examine the effect of negative room pressure, HEPA filtration, and HVAC fluctuations on radiation areas, hot cells and gloveboxes. Radioactive tracers were used to simulate the concentration of spills within contaminated areas, track the migration of isotopes of interest, and determine the isotopic retention and buildup on facility HEPA filters. A variety of isotopes with concern to dose (e.g., Kr-85, Sr-90, I-131, etc.), including their decay and progeny, are included in the analysis. Negative pressures are maintained in the regions of interest by a representative central HVAC system equipped with a volumetric fan that exhausts to the environment after a series of isolation valves and HEPA filters. GOTHIC is an industry trusted tool for providing engineering solutions for a variety of applications, including fission product tracking, aerosol and particulate transport and ventilation assessments. The software provides an integrated analysis environment that includes a graphical user interface (GUI) for constructing analysis models, a numerical solver that includes parallel processing capabilities and a post-processor for evaluating simulation results. It solves the conservation equations for mass, momentum and energy for multicomponent, multi-phase flow in lumped parameter and multi-dimensional geometries (1, 2, or full 3D), including the effects of turbulence, diffusion and buoyancy. It has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B and applicable portions of ASME NQA-1 since 1995. GOTHIC has been used for assessing both forced and natural convection conditions for a wide range of applications, including: - Tracking concentration of hazardous gases and chemicals for habitability and safety assessments - Determining ventilation and filtration requirements and optimizing location and arrangement of these systems - Room heat-up, including diverse and Flexible coping strategies for Extended Loss of AC Power (FLEX/ELAP) - Equipment Qualification (EQ) A distinctive feature of GOTHIC is the ability to track many different fields/substances in a simulation, including user defined tracer elements, in the liquid, vapor and droplet fields as well as surfaces and filters. This capability allows GOTHIC to model fission product transport and release or the removal of particulates or harmful toxins from exhaust gases using a spray scrubber or other types of filtration systems. GOTHIC also includes models for engineered equipment, such as fans, filters, charcoal filters, dryers/demisters, dampers, etc. The aerosols and other filtered material are removed or accumulated in these components. The range of aerosol and radiological applications that GOTHIC has been used for includes: - Source Term: Primary Coolant (Equilibrium) Activity; Non-Water Coolant Source/Leakage. - Conditions for Iodine Re-evolution: Sump/Suppression Pool Conditions and pH; - RWST Conditions and pH. - Isotope Removal Mechanisms: Containment Sprayed and Unsprayed Region Mixing; Charcoal Filter Heating due to Iodine decay. - Radionuclide Transport and Decay: Post-LOCA Release in containment; Transport between connected Compartments and vent systems; Groundwater transport of radionuclides. - Non-Newtonian Fluid modeling for sludge, waste tanks, etc. ADAMS ML071581053 (titled 'Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications') poses guidelines for applying single phase CFD codes in nuclear reactor safety problems and GOTHIC is listed as a 'tool for 3D flows' and 'dispersal and deposition of radionuclides.' The Nuclear Quality Assurance (NQA) pedigree of GOTHIC is an important aspect for applications in the nuclear industry. The fundamental tracer models (convective transport, molecular and turbulent diffusion, removal mechanisms, etc.) have been verified using analytical solutions and validated against applicable separate effects tests. Also, GOTHIC has been benchmarked to many integrated effects tests, including Phebus FP (Fission Product). GOTHIC gives good agreement for the buildup and decay of fission products in Phebus Test 3. The model developed by ZNE demonstrates GOTHIC's applicability and acceptability for use in analyzing the migration and retention of radioactive isotopes and their progeny in normal operation and accident scenario analyses for isotope production facilities, hot cells, and gloveboxes. The tracer activities calculated by GOTHIC can then be used in downstream radiation transport and shielding codes like RADTRAD-NAI{sup C}, MCNP{sup R}, and MicroShield{sup R} to determine on-site and of-site doses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

A phased workflow to define permit‐ready locations for large volume CO 2 injection and storage

Abstract To‐date, only two UIC Class VI permits have been issued by the US Environmental Protection Agency. We illustrate a four‐phase workflow to first identify regional storage resources and then down‐select sites to yield permit‐ready locations that can accept and store large volumes of CO 2 . Specific permit requirements should guide objectives and define deliverables of respective workflow phases. In the first phase we used available regional data and screened structure and injection zones to locate resources that match CO 2 volumes planned to be captured. Available data were also used to assess presence and depth of usable groundwater, the key resource being protected via permitting. We then used advanced, closed‐form, analytical solutions (EASiTool) to estimate CO 2 injectivity into each hydrologically connected injection compartment. In the second phase we acquired and conditioned additional wireline logs and leased available seismic datasets. We interpreted the depositional systems from wireline well‐log character and mapped sandbody geometry to interpolate injection and confining‐zone distribution. Using available data, we mapped faults and locations of freshwater and overpressure (or other capacity‐limiting geologic parameters) in more detail. In the third phase, we used the augmented geologic data to develop a static model for the selected area, extracted the areas of highest interest, and generated and ran dynamic (flow) models. In a fourth phase, we reduced major uncertainties identified in earlier phases. Our case study indicates that to complete preparation of a permit application requires (1) improved lithologic characterization information (thicknesses and horizontal and vertical connectivity) and (2) better definition of poorly defined local faults. © 2023 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

58 GEOSCIENCES↗
DOE OSTI2023

Revisiting the empirical particle-fluid coupling model used in DEM-CFD by high-resolution DEM-LBM-IMB simulations: A 2D perspective

The work investigates the applicability of the unresolved Computational Fluid Dynamics and Discrete Element Method (CFDDEM) technique based on empirical equations for fluid-particle coupling. We first carry out a series of representative volume element simulations using the high-resolution particle-resolved Lattice Boltzmann method and Discrete Element Method (LBMDEM) coupled by an Immersed Moving Boundary (IMB) scheme. Then, we compare the results obtained by both LBMDEM and empirical equations used in unresolved CFDDEM with analytical solutions. It is found that the existing empirical equations used in solving fluid-particle interactions in 2D CFDDEM fail to accurately calculate the hydrodynamic force applied to solid particles. The underlying reason is that the existing empirical models are obtained based on 3D experimental results and thus are not applicable to 2D problems. Based on the simulation results, a new drag coefficient model is then proposed. The estimated drag forces using the new model are compared favourably with the simulated ones, indicating the good performance of the proposed model.

42 ENGINEERING↗
DOE OSTI2023

Implementation and verification of a user-defined element (UEL) for coupled thermal-hydraulic-mechanical-chemical (THMC) processes in saturated geological media

Efficient and accurate modeling of the coupled thermal-hydraulic-mechanical-chemical (THMC) processes in various rock formations is indispensable for designing energy geo-structures such as underground repositories for high-level nuclear wastes. Here, this work focuses on developing and verifying an implicit finite element solver for generic coupled THMC problems in geological settings. Starting from the mass, momentum, and energy balance laws, a specialized set of governing equations and a thermoporoelastic constitutive model is derived. This system is then solved by an implicit finite element (FE) scheme. Specifically, the residuals and the Jacobians are scripted in a user-defined element (UEL) subroutine which is then combined with the general-purpose FE software Abaqus Standard to solve initial-boundary value problems. Considering the complexity of the system, the UEL development follows a stepwise manner by first solving the coupled hydraulic-mechanical (HM) and thermal-hydraulic-mechanical (THM) equations before moving on to the full THMC problem. Each implementation step consists of at least one verification test by comparing computed results with closed-form analytical solutions to ensure that the various coupling effects are correctly realized. To demonstrate the robustness of the algorithm and to validate the UEL, a three-dimensional case study is performed with reference to the in-situ heating test of ATLAS at Belgium in 1980s. A hypothetical radionuclide leakage event is then simulated by activating the chemical-concentration degree of freedom and prescribing a constant high concentration at the heater's surface. The model predicts a limited contaminated regime after six years considering both diffusion and advection effects on species transport.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

A phase-field model for hydraulic fracture nucleation and propagation in porous media

Many geo-engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase-field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy-based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase-field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase-field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. In conclusion, the comparison of numerical results for two-dimensional test cases with existing analytical solutions demonstrates that the proposed phase-field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three-dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media

Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi-analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane-wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near-field) with that of the exterior region (far-field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two-dimensional unbounded domains.

42 ENGINEERING↗