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At least 1,153 records · Page 64

Phase field-volumetric lattice Boltzmann model of ion uptake in porous nuclear waste form materials under continuous flow

The flow field within the mesopores of sorbent particles plays a crucial role in radionuclide diffusion and ion uptake kinetics, thus, impacting the overall performance of porous nuclear waste form materials. To fundamentally understand the influence of microstructures and material properties on the radionuclide absorption and retention processes requires a coupled multi-physics model that considers the advection and diffusion within the flow field, the reaction at liquid-solid interfaces, and finally, the solid-state diffusion within a complex nanoporous medium. Here, this study employs the volumetric lattice Boltzmann method (VLBM) to accurately and efficiently calculate the steady state velocity field inside the mesopores of sorbent particles. The obtained velocity field is then utilized to calculate the advection of ions in the steady flow. A phase field (PF) model of ion uptake is used to describe the reaction occurring at the solid-liquid interface and diffusion inside the porous medium. The integrated PF-VLBM model is verified in terms of the mass conservation and numerical efficiency and validated qualitatively with experimental observation data. Then, it is applied to study the influence of thermodynamic and kinetic properties, as well as flow field conditions on the ion uptake kinetics. The numerical results demonstrate that the ion uptake kinetics in porous particles has three distinct stages, which is in agreement with the observations in continuous flow experiments. In the first stage, the kinetics is predominantly controlled by the flow field and ion diffusivity in the liquid phase. The kinetics in the second stage is primarily governed by ion diffusivity in the solid phase. In the third stage the system reaches a dynamic equilibrium with a net zero uptake flux at the interface. It is also found that porous structures significantly affect the efficiency and capacity of ion uptake. The simulation results can help to understand the physics behind the observed ion uptake kinetics in experiments and to facilitate the development of constitutive equations that can account for heterogeneous microstructures in engineering performance codes.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

The Binary Dwarf Carbon Star SDSS J125017.90+252427.6

Even though dwarf carbon (dC) stars are universally thought to be binaries in order to explain the presence of C 2 in their spectra while still near main-sequence luminosity, direct observational evidence for their binarity is remarkably scarce. In this work, we introduce the detection of a 2.92 day periodicity in both the photometry and radial velocity of SDSS J125017.90+252427.6, an r = 16.4 dC star. This is the first photometric binary dC, and only the second dC spectroscopic binary. The relative phase of the photometric period to the spectroscopic observations suggests that the photometric variations are a reflection effect due to heating from an unseen companion. The observed radial velocity amplitude of the dC component ( K = 98.8 ± 10.7 km s -1 ) is consistent with a white dwarf companion, presumably the evolved star that earlier donated the carbon to the dC, although substantial orbital evolution must have occurred. Large synoptic photometric surveys such as the Palomar Transient Factory, which was used for this work, may prove useful for identifying binaries among the shorter-period dC stars.

79 ASTRONOMY AND ASTROPHYSICS↗

Particle in cell simulations of Buneman instability of a current-driven plasma with q-nonextensive electron velocity distribution

The nonlinear evolution of low frequency Buneman instability in an unmagnetized current-driven plasma with q-nonextensive electron velocity distribution is investigated using particle in cell simulation. Simulation results show that the generation of electron phase space holes and the counter-streaming current induced in the plasma strongly depend on the q-parameter. It is found that by increasing the nonextensive parameter, the distribution of electron density becomes highly peaked. This density steepening or grating-like pattern occurs at the saturation time. In addition, a generalized dispersion relation is obtained using the kinetic theory. Analysis of the dispersion relation and the temporal evolution of the electric field energy density reveal that the growth rate of instability increases by increasing the q-parameter. Finally, the results of Maxwellian and q-nonextensive velocity distributions have been compared and discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Developing a Consistent Travel-Time Framework for Comparing Three-Dimensional Velocity Models for Seismic Location Accuracy

Abstract Location algorithms have historically relied on simple, one-dimensional (1D) velocity models for fast seismic event locations. 1D models are generally used as travel-time lookup tables, one for each seismic phase, with travel-times pre-calculated for event distance and depth. These travel-time lookup tables are extremely fast to use and this fast computational speed makes them the preferred type of velocity model for operational needs. Higher-dimensional (i.e., three-dimensional—3D) seismic velocity models are becoming readily available and provide more accurate event locations over 1D models. The computational requirements of these 3D models tend to make their operational use prohibitive. Additionally, comparing location accuracy for 3D seismic velocity models tends to be problematic, as each model is determined using different ray-tracing algorithms. Attempting to use a different algorithm than the one used to develop a model usually results in poor travel-time prediction. We demonstrate and test a framework to create first-P and first-S 3D travel-time correction surfaces using an open-source framework ( PCalc + GeoTess , https://www.sandia.gov/salsa3d/software/geotess ) that easily stores 3D travel-time and uncertainty data. This framework produces fast travel-time and uncertainty predictions and overcomes the ray-tracing algorithm hurdle because the lookup tables can be generated using the exact ray-tracing algorithm that is preferred for a model.

3D velocity models↗

Chandra X-ray spectroscopy of focused wind in the Cygnus X-1 system: II. The non-dip spectrum in the low/hard state – modulations with orbital phase

Accretion onto the black hole in the system HDE 226868/Cygnus X-1 is powered by the strong line-driven stellar wind of the O-type donor star. We study the X-ray properties of the stellar wind in the hard state of Cyg X-1, as determined using data from the Chandra High Energy Transmission Gratings. Large density and temperature inhomogeneities are present in the wind, with a fraction of the wind consisting of clumps of matter with higher density and lower temperature embedded in a photoionized gas. Absorption dips observed in the light curve are believed to be caused by these clumps. This work concentrates on the non-dip spectra as a function of orbital phase. The spectra show lines of H-like and He-like ions of S, Si, Na, Mg, Al, and highly ionized Fe (Fe xvii–Fe xxiv). We measure velocity shifts, column densities, and thermal broadening of the line series. The excellent quality of these five observations allows us to investigate the orbital phase-dependence of these parameters. We show that the absorber is located close to the black hole. Doppler shifted lines point at a complex wind structure in this region, while emission lines seen in some observations are from a denser medium than the absorber. Here, the observed line profiles are phase-dependent. Their shapes vary from pure, symmetric absorption at the superior conjunction to P Cygni profiles at the inferior conjunction of the black hole.

79 ASTRONOMY AND ASTROPHYSICS↗

Interface tracking simulations of bubbly flows in PWR relevant geometries

[en] Highlights: • Simulations were performed for turbulent bubbly flows in PWR subchannel geometry. • Liquid turbulence is fully resolved by direct numerical simulation approach. • Bubble behavior is captured using level-set interface tracking method. • Time-averaged single- and two-phase turbulent flow statistical quantities are obtained. - Abstract: The advances in high performance computing (HPC) have allowed direct numerical simulation (DNS) approach coupled with interface tracking methods (ITM) to perform high fidelity simulations of turbulent bubbly flows in various complex geometries. In this work, we have chosen the geometry of the pressurized water reactor (PWR) core subchannel to perform a set of interface tracking simulations (ITS) with fully resolved liquid turbulence. The presented research utilizes a massively parallel finite-element based code, PHASTA, for the subchannel geometry simulations of bubbly flow turbulence. The main objective for this research is to demonstrate the ITS capabilities in gaining new insight into bubble/turbulence interactions and assisting the development of improved closure laws for multiphase computational fluid dynamics (M-CFD). Both single- and two-phase turbulent flows were studied within a single PWR subchannel. The analysis of numerical results includes the mean gas and liquid velocity profiles, void fraction distribution and turbulent kinetic energy profiles. Two sets of flow rates and bubble sizes were used in the simulations. The chosen flow rates corresponded to the Reynolds numbers of 29,079 and 80,775 based on channel hydraulic diameter (D_h) and mean velocity. The finite element unstructured grids utilized for these simulations include 53.8 million and 1.11 billion elements, respectively. This has allowed to fully resolve all the turbulence scales and the deformable interfaces of individual bubbles. For the two-phase flow simulations, a 1% bubble volume fraction was used which resulted in 17 bubbles in the smaller case and 262 bubbles in the larger case. In the larger simulation case the size of the resolved bubbles is 0.65 mm in diameter, and the bulk mesh cell size is about 30 microns. Those large-scale simulations provide new level of details previously unavailable and were enabled by the excellent scaling performance of our two-phase flow solver and access to the state-of-the-art supercomputing resources. The presented simulations used up to 256 thousand processing threads on the IBM BG/Q supercomputer “Mira” (Argonne National Laboratory).

Nuclear Science & Technology↗

OBSERVATIONAL EVIDENCE OF ELECTRON-DRIVEN EVAPORATION IN TWO SOLAR FLARES

We have explored the relationship between hard X-ray (HXR) emissions and Doppler velocities caused by the chromospheric evaporation in two X1.6 class solar flares on 2014 September 10 and October 22, respectively. Both events display double ribbons and the Interface Region Imaging Spectrograph slit is fixed on one of their ribbons from the flare onset. The explosive evaporations are detected in these two flares. The coronal line of Fe xxi 1354.09 Å shows blueshifts, but the chromospheric line of C i 1354.29 Å shows redshifts during the impulsive phase. The chromospheric evaporation tends to appear at the front of the flare ribbon. Both Fe xxi and C i display their Doppler velocities with an “increase-peak-decrease” pattern that is well related to the “rising-maximum-decay” phase of HXR emissions. Such anti-correlation between HXR emissions and Fe xxi Doppler shifts and correlation with C i Doppler shifts indicate the electron-driven evaporation in these two flares.

79 ASTRONOMY AND ASTROPHYSICS↗

High-resolution time-resolved experiments on mixing and entrainment of buoyant jets in stratified environments

Fluid jets interacting with a stratified layer play an important role in the safety of several reactor designs. In the containment of nuclear power plants, fluid jets dominate the transport and mixing of gaseous species and consequent hydrogen distribution in case of a severe accident. The mixing phenomena in the containment are driven by buoyant high-momentum injections (jets) and low momentum injection plumes. Mixing near the postulated break is initially dominated by high flow velocities. Plumes with moderate flow velocities are instead relevant in the break compartment during the long-term pressurization phase, or in any of the apertures between two connected compartments if the mass flows are sufficiently high and the density differences between efflux and ambient are sufficiently low. Phenomena of interest include free plumes (as produced by the efflux from the break compartment in a larger room or directly from a break flow), wall plumes (such those produced by low mass flows through inter-compartment apertures), and propagating stratification fronts in the ambient (for any stably stratified conditions). These phenomena have been highly ranked about nuclear reactor design, especially regarding of safety protocols. During a Pressurized Thermal Shock (PTS) scenario, the interaction between the cold ECCS injection plume and the stratified fluid present in the cold (or hot) leg is important in order to determine the temperature at the time-dependent temperature at the inlet of the reactor pressure vessel (RPV) and the potential to cause a thermal shock on the RPV wall. In sodium-cooled fast reactors (SFRs), core channels are typically hydro-dynamically isolated so that there exists a considerable temperature variation at the exit of adjacent fuel assemblies. All the above phenomena are characterized by the interaction of buoyant jets with the stratified flow. In stratified layers baroclinic forces create significant redistribution of turbulent kinetic energy and scales, which leads to anisotropy. This important physical phenomenon is highly three dimensional and is challenging to capture even with high-fidelity CFD simulations, due in part to lack of sufficiently resolved validation data. Furthermore, the experimental data available in the open literature do not feature the level of fidelity needed for an extensive validation of turbulence models in lower order CFD. To shed new lights into the crucial phenomena object of the present research project, it was proposed to conduct coordinated experiments and simulations at the University of Michigan and the George Washington University. The project has resulted in an experimental database of high-resolution time-resolved measurements of jets in uniform and stratified environments. The novel experimental data will be used to validate computational fluid dynamic (CFD) codes, including both Large Eddy Simulations (LES) and unsteady Reynolds-averaged Navier-Stokes equations (URANS) methodologies. In the Experimental and Multiphase flow (ECMF) laboratory at Univerisity of Michigan, we built two experimental facilities to investigate also the effect of scaling. The first facility, DESTROJER (DEnsity Stratified Turbulent ROund free Jet ExpeRiment), featuring a contoured jet nozzle with a diameter of D=12.7mm and a 1m×1m×1m cubic tank, which is made of acrylic glass for optical access. The ratio between the tank width and the nozzle diameter is equal to 78, which ensures that there is no direct interaction between the jet and the side walls. A second, modular experimental facility, features three different tank sizes of size 10×10×30, 20×20×30, 30×30×30 cm3 respectively (all tanks have the same height of 30 cm), and a jet diameter of 2mm. For the modular facility, tank-to-nozzle ratio of 50, 100, and 150 are obtained respectively. Experiments with different-density jet impactions and sharp interface with a density difference of 3.16% In the Laboratory at George Washington University, complementary experiments have been carried out at a facility featuring the same dimensions as DESTROYER. Experiments with different jet diameters have been carried out as well. High-resolution time-resolved measurements have been performed at all facilities using high-speed particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). In this way, simultaneous measurements of velocity and density fields have been carried out. At the University of Michigan, wire-mesh sensors have been designed and built to gather high-resolution, time-dependent data of the stratified front in the tank. These measurements are important to provide accurate initial conditions for the CFD simulations. An important outcome of the project has been the development of novel techniques to achieve refractive index matching (RIM) of acqueous solutions with high density differences. RIM is crucial if optical techniques such as PIV are used to measure velocity fields. Previous to this project, experiments up to 3% density difference had been reported in the literature. With the methodology developed in this project, we have been able to push the envelop to density differences up to 9%. The experiments have been used to validate Reynolds Averaged Navier-Stokes (RANS) turbulence models and Large Eddy Simulations (LES) models. Both NEK5000 and the commercial CFD code STAR-CCM+ have been used. The experimental data will be made available to the community through the NE-KAMS databasehave been successfully conducted in the scaled facility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

In Situ X-ray Diffraction of High Density Polyethylene During Dynamic Compression: Polymer Chain Compression and Phase Transformations

Polymers are widely implemented materials often used for safety and security in our daily lives. However, we do not have a thorough understanding of the phase transformations of these materials when exposed to extreme condition, high strain rate, events. To study polymers in these severe environments, we performed plate impact experiments that impart a one-dimensional shock wave, at high pressures and temperatures, to observe the materials response. Generally, velocimetry is the experimental diagnostic used to capture the movement of high velocity interfaces to then calculate the mechanical variables associated with shock compression. However, when a material undergoes a phase transition, such as between two crystalline phases or melting to decomposition during shock compression, velocimetry does not explicitly indicate what structural change occurred. At the Dynamic Compression Sector at the Advanced Photon Source gas gun driven compression has been paired with x-ray diffraction, providing the ability to study both the shock parameters and structural changes concurrently. We explored high density polyethylene (HDPE) both on its reactants Hugoniot (<10.12 GPa) and within its transition region (24.3 GPa) where HDPE is hypothesized to decompose from reactants to products. With x-ray diffraction we observed both polymer chain compression and crystal structure reorientation from orthorhombic to monoclinic above 6 GPa, as well as either a possible phase change or chemical decomposition at 24.3 GPa. With these experiments we were able to determine the crystalline and amorphous Hugoniot loci at pressures below the polymer transition region.

36 MATERIALS SCIENCE↗

High-Pressure $γ$-CaMgSi 2 O 6 : Does Penta-Coordinated Silicon Exist in the Earth's Mantle?

We report in situ X-ray diffraction experiments with natural Fe- and Al- bearing diopside single crystals and density functional theory (DFT) calculations on diopside end-member composition indicate the existence of a new high-pressure γ-diopside polymorph with rare penta-coordinated silicon. On compression $α$-diopside transforms to the $γ$-phase at ~50 GPa, which in turn, on decompression is observed to convert to the known $β$-phase below 47 GPa. The new $γ$-diopside polymorph constitutes another recent example of penta-coordinated silicon ( V Si) in overcompressed metastable crystalline silicates, suggesting that V Si may exist in the transition zone and the uppermost lower mantle in appreciable quantities, not only in silicate glass and melts but also in crystalline phases contained in the coldest parts of subducted stagnant slabs. V Si may have significant influences on buoyancy, wave velocity anomalies, deformation mechanisms, chemical reactivity of silicate rocks, and seismicity within the slab.

58 GEOSCIENCES↗

A hybrid discrete bubble-lattice Boltzmann–discrete element model for gas-charged sediments

In this paper, we present a hybrid discrete bubble-lattice Boltzmann–discrete element modelling framework for simulating gas-charged sediments, especially in the seabed. A discrete bubble model proposed in chemical engineering is adapted in the coupled discrete element/lattice Boltzmann method to model the migration of gas bubbles in saturated sediments involving interactions between gas bubbles and fluid/solid phases. Surface tension is introduced into the discrete bubble model in this work, so that it can handle the complex gas–fluid–solid interface. The lattice Boltzmann and discrete element methods are, respectively, employed to simulate fluid flows and mechanical behaviours of sediments. A velocity interpolation-based immerse boundary method is utilised to resolve the coupling between the fluid flow and the solid/gas phase. The proposed technique is preliminarily validated using simulations of bubble migration in fluids, which is followed by high-resolution investigations of the transport of a gas bubble in seabed sediments. Lastly, it is demonstrated that this hybrid method can reproduce, to a certain degree, the characters of bubbles moving in seabed sediment tests.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Imaging observation of quasi-periodic disturbances' amplitudes increasing with height in the polar region of the solar corona

At present, there have been few extreme ultraviolet (EUV) imaging observations of spatial variations of the density perturbations due to the slow magnetoacoustic waves (SMWs) propagating along the solar coronal magnetic fields. In this paper, we present such observations taken from the polar region of the corona with the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory and investigate the amplitude of quasi-periodic propagating disturbances that increase with height in the lower corona (0-9 Mm over the solar limb). We statistically determined the following parameters associated with the disturbances: pressure scale height, period, and wavelength in AIA 171 Å, 193 Å, and 211 Å channels. The scale height and wavelength are dependent of temperature, while the period is independent of temperature. The acoustic velocities inferred from the scale height highly correlate with the ratios of wavelength to period, i.e., phase speeds. They provide evidence that the propagating disturbances in the lower corona are likely SMWs and the spatial variations in EUV intensity in the polar region likely reflects the density compressional effect by the propagating SMWs.

79 ASTRONOMY AND ASTROPHYSICS↗

Laning transitions in pattern-forming driven binary systems with competing interactions

A binary system of particles that move in opposite directions under an applied field can exhibit disordered states as well as laned states where the particles organize into oppositely moving high-mobility lanes to reduce collisions. Previous studies of laning transitions generally focused on particles with purely repulsive interactions. Here, in this study, we examine laning transitions for oppositely moving pattern-forming systems of particles with competing attractive and repulsive interactions, which in equilibrium form crystal, stripe, and bubble states. In addition to multiple types of laned states, we find jammed crystals, stripes, and bubbles, and generally observe a much richer variety of phases compared to the purely repulsive system. In the stripe-forming regime, the system can dynamically reorder into oppositely moving stripes that are aligned in the direction of the drive. The bubble phase can produce strongly polarized jammed states of elongated bubbles where particles in the individual bubbles segregate to opposite sides of the bubbles. We also find disordered states, segregated laned bubble states where the bubbles pass each other in lanes, and segregated bubbles that move through one another. In the compact bubble regime, we obtain a plastic bubble state in which the oppositely driven particles remain trapped in the bubbles but the bubbles move past each other at a slow velocity due to a net imbalance in the bubble population. At higher drives, individual particles begin to jump from bubble to bubble. We show that the different phases and the transitions between them produce signatures in the velocity-force and differential mobility curves. We demonstrate that the force for escaping from the jammed state is nonmonotonic, with stripes exhibiting the lowest unjamming force.

36 MATERIALS SCIENCE↗

Large Eddy Simulation of turbulent flow in rod bundle with spacer grids

Pressurized water nuclear reactor fuel assemblies are made of fuel rods held by spacer grids, which are the core components of the nuclear power plants. Hot fuel rods are cooled by the coolant water flow, and the spacer grids with mixing vanes distort the mainstream, producing the swirling flow which can enhance the heat transfer to improve CHF (Critical Heat Flux). Heat transfer between fuel rods and coolant is a crucial part of thermal-hydraulic analysis. For the purpose to improve the thermal hydraulic performance of the fuel assemblies, many experiments have been conducted to understand the flow structures and three-dimensional behaviors of the turbulence in the rod bundle sub-channels and then to optimize the design of the spacer grid. In the experimental work, which requires lots of efforts to get reliable data, LDA (Laser Doppler Anemometry) and PIV (Particle Image Velocimetry) are generally used to measure the velocity profile and turbulent intensity in the sub-channels. Computational Fluid Dynamics (CFD) is another useful way to study the characteristics of the detailed flow condition and heat transfer phenomena in the subchannels. The main issue of the single-phase CFD is to accurately predict the flow and turbulence characteristics. RANS method is generally used to simulate the induced lateral velocity and the heat transfer process. With the development of computer technology, some more precise but previously time-consuming turbulent models, such as LES (Large Eddy Simulation), are gradually used for the simulation of rod bundle flow with current advanced CPU resources. Ikeno and Kajishima explained the decay of swirling turbulent flow in the rod bundle using LES method. Benhamadouche acquired the turbulence induced forces on the central rod of the rod bundle through performing the LES of the flow downstream the spacer grid. Chang and Tavoularis conducted hybrid simulations with SAS SST and LES of a 5 x 5 rod bundle, and several vortices were identified in the vicinity of the vanes and the generation mechanisms, evolution progress and influence on the velocities of these vortices were clarified. In the paper we present CFD simulations of turbulent flow in rod bundle sub-channels with spacer grids of two different experiments. One is MATiS-H benchmark experiment with scaled spacer grids, which is conducted by KAERI, and is used as a CFD benchmark test, and the other is a 5 x 5 rod bundle with typical spacer grids using PIV technology, with the cooperation of Harbin Engineering University. The main objectives of the calculations are to validate LES methodology by the benchmark experiments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Ultimate response time of high electron mobility transistors

We present theoretical studies of the response time of the two-dimensional gated electron gas to femtosecond pulses. Our hydrodynamic simulations show that the device response to a short pulse or a step-function signal is either smooth or oscillating time-decay at low and high mobility, μ, values, respectively. At small gate voltage swings, U{sub 0} = U{sub g} − U{sub th}, where U{sub g} is the gate voltage and U{sub th} is the threshold voltage, such that μU{sub 0}/L < v{sub s}, where L is the channel length and v{sub s} is the effective electron saturation velocity, the decay time in the low mobility samples is on the order of L{sup 2}/(μU{sub 0}), in agreement with the analytical drift model. However, the decay is preceded by a delay time on the order of L/s, where s is the plasma wave velocity. This delay is the ballistic transport signature in collision-dominated devices, which becomes important during very short time periods. In the high mobility devices, the period of the decaying oscillations is on the order of the plasma wave velocity transit time. Our analysis shows that short channel field effect transistors operating in the plasmonic regime can meet the requirements for applications as terahertz detectors, mixers, delay lines, and phase shifters in ultra high-speed wireless communication circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Utah FORGE - Development of a Reservoir Seismic Velocity Model and Seismic Resolution Study

This is data from and a final report on the development of a 3D velocity model for the larger FORGE area and on the seismic resolution in the stimulated fracture volume at the bottom of well 16A-32. The velocity model was developed using RMS velocities of the seismic reflection survey and seismic velocity logs from borehole measurements as an input model. To improve the accuracy of the model in the shallow subsurface, travel times phase arrivals of the direct propagating P-waves were determined from the seismic reflection data, using PhaseNet, a deep-neural-network-based seismic arrival time picking method. The travel times were subsequently inverted using the input velocity model. The seismic resolution study used borehole and surface seismic sensors as well as the seismicity observed during the April 2022 stimulation experiment to estimate the seismic resolution in the activated fracture reservoir. The data contain a 3D P- and S-wave velocity model for the larger FORGE area.

15 GEOTHERMAL ENERGY↗

Scaling laws for two-dimensional dendritic crystal growth in a narrow channel

Here, we investigate analytically and computationally the dynamics of two-dimensional needle crystal growth from the melt in a narrow channel. Our analytical theory predicts that, in the low supersaturation limit, the growth velocity $\textit{V}$ decreases in time $\textit{t}$ as a power law $V ~t^{–2/3}$, which we validate by phase-field and dendritic-needle-network simulations. Simulations further reveal that, above a critical channel width $Λ ≈ 5l_D$, where $l_D$ is the diffusion length, needle crystals grow with a constant $V < V_s$, where $V_s$ is the free-growth needle crystal velocity, and approaches $V_s$ in the limit $Λ \gg l_D$.

36 MATERIALS SCIENCE↗

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗