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At least 1,135 records · Page 63

DEMONSTRATION OF A DATA-DRIVEN PHYSICS-BASED APPROACH FOR COMPUTATIONALLY EFFICIENT CFD PREDICTION OF TWO-PHASE BUBBLY FLOW

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale physics-guided data-driven approach, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. By defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. In a demonstration case of two-phase bubbly flow, the DFNN model well captured and corrected the unphysical “peaks” in the velocity and void fraction profiles near the wall in the coarse-mesh configuration, even for extrapolative predictions. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.

42 ENGINEERING↗

CLASSY III. The Properties of Starburst-driven Warm Ionized Outflows

We report the results of analyses of galactic outflows in a sample of 45 low-redshift starburst galaxies in the COS Legacy Archive Spectroscopic SurveY (CLASSY), augmented by five additional similar starbursts with Cosmic Origins Spectrograph (COS) data. The outflows are traced by blueshifted absorption lines of metals spanning a wide range of ionization potential. The high quality and broad spectral coverage of CLASSY data enable us to disentangle the absorption due to the static interstellar medium (ISM) from that due to outflows. We further use different line multiplets and doublets to determine the covering fraction, column density, and ionization state as a function of velocity for each outflow. We measure the outflow's mean velocity and velocity width, and find that both correlate in a highly significant way with the star formation rate, galaxy mass, and circular velocity over ranges of four orders of magnitude for the first two properties. We also estimate outflow rates of metals, mass, momentum, and kinetic energy. We find that, at most, only about 20% of silicon created and ejected by supernovae in the starburst is carried out in the warm phase we observe. The outflows' mass-loading factor increases steeply and inversely with both circular and outflow velocity (log–log slope ~–1.6), and reaches ~10 for dwarf galaxies. We find that the outflows typically carry about 10%–100% of the momentum injected by massive stars and about 1%–20% of the kinetic energy. We show that these results place interesting constraints on, and new insights into, models and simulations of galactic winds.

79 ASTRONOMY AND ASTROPHYSICS↗

Computationally efficient CFD prediction of bubbly flow using physics-guided deep learning

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. In this work, by defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. In a demonstration case of two-phase bubbly flow, the DFNN model well captured and corrected the unphysical “peaks” in the velocity and void fraction profiles near the wall in the coarse-mesh configuration, even for extrapolative predictions. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Kinematic modeling of the Milky Way using the RAVE and GCS stellar surveys

We investigate the kinematic parameters of the Milky Way disk using the Radial Velocity Experiment (RAVE) and Geneva-Copenhagen Survey (GCS) stellar surveys. We do this by fitting a kinematic model to the data and taking the selection function of the data into account. For stars in the GCS we use all phase-space coordinates, but for RAVE stars we use only (ℓ, b, v {sub los}). Using the Markov Chain Monte Carlo technique, we investigate the full posterior distributions of the parameters given the data. We investigate the age-velocity dispersion relation for the three kinematic components (σ {sub R}, σ{sub φ}, σ {sub z}), the radial dependence of the velocity dispersions, the solar peculiar motion (U {sub ☉}, V {sub ☉}, W {sub ☉}), the circular speed Θ{sub 0} at the Sun, and the fall of mean azimuthal motion with height above the midplane. We confirm that the Besançon-style Gaussian model accurately fits the GCS data but fails to match the details of the more spatially extended RAVE survey. In particular, the Shu distribution function (DF) handles noncircular orbits more accurately and provides a better fit to the kinematic data. The Gaussian DF not only fits the data poorly but systematically underestimates the fall of velocity dispersion with radius. The radial scale length of the velocity dispersion profile of the thick disk was found to be smaller than that of the thin disk. We find that correlations exist between a number of parameters, which highlights the importance of doing joint fits. The large size of the RAVE survey allows us to get precise values for most parameters. However, large systematic uncertainties remain, especially in V {sub ☉} and Θ{sub 0}. We find that, for an extended sample of stars, Θ{sub 0} is underestimated by as much as 10% if the vertical dependence of the mean azimuthal motion is neglected. Using a simple model for vertical dependence of kinematics, we find that it is possible to match the Sgr A* proper motion without any need for V {sub ☉} being larger than that estimated locally by surveys like GCS.

79 ASTRONOMY AND ASTROPHYSICS↗

Rolling hills on the core-mantle boundary

Recent results suggest that an iron-rich oxide may have fractionally crystallized from a primordial magma ocean and settled on the core–mantle boundary (CMB). Based on experimental results, the presence of only a few percent of Fe-rich oxide could slow seismic waves down by several percent. This heavy layer can become highly undulating as predicted from dynamic modeling but can remain as a distinct structure with uniform velocity reductions. Here, we use the large USArray seismic network to search for such structures. Strong constraints on D" are provided by the core-phase SKS where it bifurcates, containing a short segment of P-wave diffractions (P d ) when crossing the CMB, called SKS d . Synthetics from models with moderate velocity drops (less than 10%) involving a layer with variable thickness, perhaps a composite of sharp small structures, with strong variation in thickness can explain both the observed SKS d waveforms and large scatter in differential times between SKKS and SKS. A smooth 3D image is obtained from inverting SKS d waveforms displaying rolling-hills with elongated dome-like structures sitting on the CMB. The most prominent one has an 80-km height, ~8° length, and ~4° width, thus adding still more structural complexity to the lower mantle. We suggest that these results can be explained by a dynamically-stabilized material containing small amounts (~5%) iron-rich (Mg,Fe)O providing a self-consistent physical interpretation.

Sun, Daoyuan↗

THE COSMIC EVOLUTION OF MASSIVE BLACK HOLES AND GALAXY SPHEROIDS: GLOBAL CONSTRAINTS AT REDSHIFT z {approx}< 1.2

We study observational constraints on the cosmic evolution of the relationships between massive black hole (MBH) mass (M{sub .}) and stellar mass (M{sub *,sph}; or velocity dispersion {sigma}) of a host galaxy/spheroid. Assuming that the M{sub .}-M{sub *,sph} (or M{sub .}-{sigma}) relation evolves with redshift as {proportional_to}(1 + z){sup {Gamma}}, the MBH mass density can be obtained from either the observationally determined galaxy stellar mass functions or velocity dispersion distribution functions over redshift z {approx} 0-1.2 for any given {Gamma}. The MBH mass density at different redshifts can also be inferred from the luminosity function of QSOs/active galactic nuclei (AGNs) provided the radiative efficiency {epsilon} is known. By matching the MBH density inferred from galaxies to that obtained from QSOs/AGNs, we find that {Gamma} = 0.64{sup +0.27}{sub -0.29} for the M{sub .}-M{sub *,sph} relation and {Gamma} = -0.21{sup +0.28}{sub -0.33} for the M{sub .}-{sigma} relation, and {epsilon} = 0.11{sup +0.04}{sub -0.03}. Our results suggest that MBH mass growth precedes bulge mass growth but that the galaxy velocity dispersion does not increase with the mass growth of the bulge after nuclear activity is quenched, which is roughly consistent with the two-phase galaxy formation scenario proposed by Oser et al. in which a galaxy roughly doubles its mass after z = 1 due to accretion and minor mergers while its velocity dispersion drops slightly.

79 ASTRONOMY AND ASTROPHYSICS↗

SN 2013ej: A type IIL supernova with weak signs of interaction

We present optical photometric and spectroscopic observations of SN 2013ej. It is one of the brightest Type II supernovae (SNe II) exploded in a nearby (∼10 Mpc) galaxy, NGC 628. The light-curve characteristics are similar to SNe II, but with a relatively shorter (∼85 days) and steeper (∼1.7 mag (100 days){sup −1} in V) plateau phase. The SN shows a large drop of 2.4 mag in V-band brightness during the plateau-to-nebular transition. The absolute ultraviolet (UV) light curves are identical to SN 2012aw, showing a similar UV-plateau trend extending up to 85 days. The radioactive {sup 56}Ni mass estimated from the tail luminosity is 0.02 M{sub ⊙}, which is significantly lower than typical SNe IIP. The characteristics of spectral features and evolution of line velocities indicate that SN 2013ej is a Type II event. However, light-curve characteristics and some spectroscopic features provide strong support in classifying it as a Type IIL event. A detailed synow modeling of spectra indicates the presence of some high-velocity components in Hα and Hβ profiles, implying a possible ejecta–circumstellar medium interaction. The nebular phase spectrum shows an unusual notch in the Hα emission, which may indicate bipolar distribution of {sup 56}Ni. Modeling of the bolometric light curve yields a progenitor mass of ∼14 M{sub ⊙} and a radius of ∼450 R{sub ⊙}, with a total explosion energy of ∼2.3×10{sup 51} erg.

79 ASTRONOMY AND ASTROPHYSICS↗

Nonlinear transport, dynamic ordering, and clustering for driven skyrmions on random pinning

Using numerical simulations, we examine the nonlinear dynamics of skyrmions driven over random pinning. For weak pinning, the skyrmions depin elastically, retaining sixfold ordering; however, at the onset of motion there is a dip in the magnitude of the structure factor peaks due to a decrease in positional ordering, indicating that the depinning transition can be detected using the structure factor even within the elastic depinning regime. At higher drives, the moving skyrmion lattice regains full ordering. For increasing pinning strength, we find a transition from elastic to plastic depinning that is accompanied by a sharp increase in the depinning threshold due to the proliferation of topological defects, similar to the peak effect found at the elastic to plastic depinning transition in superconducting vortex systems. For strong pinning and strong Magnus force, the skyrmions in the moving phase can form a strongly clustered or phase-separated state with highly modulated skyrmion density, similar to that recently observed in continuum-based simulations for strong disorder. As the Magnus force is decreased, the density phase-separated state crosses over to a dynamically phase-separated state with uniform density but with flow localized in bands of motion, while in the strongly damped limit, both types of phase-separated states are lost. In the strong pinning limit, we find highly nonlinear velocity-force curves in the transverse and longitudinal directions, along with distinct regions of negative differential conductivity in the plastic flow regime. The negative differential conductivity is absent in the overdamped limit. In conclusion, the Magnus force is responsible for both the negative differential conductivity and the clustering effects since it causes faster moving skyrmions to partially rotate around slower moving or pinned skyrmions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Sommerfeld-enhanced J -factors for dwarf spheroidal galaxies

For models where dark matter annihilation is Sommerfeld-enhanced, the annihilation cross section increases at low relative velocities. Dwarf spheroidal galaxies (dSphs) have low characteristic dark matter particle velocities and are thus ideal candidates to study such models. Here, we model the dark matter phase space of dSphs as isotropic and spherically-symmetric, and determine the J-factors for several of the most important targets for indirect dark matter searches. For Navarro-Frenk-White density profiles, we quantify the scatter in the J-factor arising from the astrophysical uncertainty in the dark matter potential. We show that, in Sommerfeld-enhanced models, the ordering of the most promising dSphs may be different relative to the standard case of velocity-independent cross sections. This result can have important implications for derived upper limits on the annihilation cross section, or on possible signals, from dSphs

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Experimental investigation of turbulent wake flows in a helically wrapped rod bundle in presence of localized blockages

In nuclear sodium fast reactors, bundles of rods are tightly packed into a triangular lattice, enclosed in a hexagonal duct, and each pin is spirally wrapped with a thin wire. Flow blockages can potentially impact the local flow characteristics and heat transfer mechanisms in the bundle due to its small subchannel size. The effects of the blockage on the flow structures and heat transfer mechanisms are important aspects that require an accurate investigation. In this study, the flow-field characteristics in the vicinity of a blockage located in the exterior subchannel of rod bundles with helically wrapped wires were experimentally investigated. The velocity fields in the exterior subchannel were acquired by applying matched-index-of-refraction and time-resolved particle image velocimetry (TR-PIV) techniques for Reynolds numbers of Re 1 = 4000 and Re 2 = 17 000, i.e., equivalent to Rew 1 = 19 600 and Rew 2 = 83 200, respectively, based on the blockage width. The results from the TR-PIV measurements revealed an arch-shaped vortex with a large flow recirculation and a pair of counter-rotating vortices in the wake region downstream of the blockage, which is commonly observed in the wake flow of bluff bodies. The relative lateral distance and angle between the two vortices decreased when the Reynolds numbers increased. Profiles of maximum turbulence intensity along the shear layers illustrated the transition process including the growth, peak, and decay along the flow direction. From the spectral analysis of the turbulent velocities extracted at points along the shear layer, the Strouhal numbers ( St ) representing the vortex shedding frequency were found to be St = 0.25 and St = 0.56 for the left and right shear layers, respectively. Characteristics of shear layers generated by the blockage in the exterior subchannel were investigated via the two-point cross correlation of fluctuating velocities. The patiotemporal cross correlations of turbulent velocities, computed at points in the region where the left shear layer exhibited rolling effects and vortex breakdowns, were considerably wider and longer. The convection velocity U c was estimated to be ~0.82 U m to 0.93 U m . Proper orthogonal decomposition (POD) analysis was applied to the instantaneous velocity fields to extract the statistically dominant flow structures. It was found that POD modes 2–3 and 4–5 formed the pair modes when the corresponding POD temporal coefficients depicted sinusoidal shapes and exhibited nearly circular orbits in the phase space. Spectral analysis of the POD temporal coefficients confirmed the vortex shedding frequencies detected in the analysis of turbulent velocities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Nonequilibrium phases and segregation for skyrmions on periodic pinning arrays

Using particle-based simulations, we examine the collective dynamics of skyrmions interacting with periodic pinning arrays, focusing on the impact of the Magnus force on the sliding phases. As a function of increasing pinning strength, we find a series of distinct dynamical phases, including an interstitial flow phase, a moving disordered state, a moving crystal, and a segregated cluster state. The transitions between these states produce signatures in the skyrmion lattice structure, the skyrmion Hall angle, the velocity fluctuation distributions, and the velocity-force curves. The moving clustered state is similar to the segregated state recently observed in continuum-based simulations with strong quenched disorder. The segregation arises from the drive dependence of the skyrmion Hall angle, and appears in the strong pinning limit when the skyrmions have nonuniform velocities, causing different portions of the sample to have different effective skyrmion Hall angles. As a result, we map the evolution of the dynamic phases as a function of the system density, the ratio of the Magnus force to the dissipative term, and the ratio of the number of skyrmions to the number of pinning sites.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A Study of Turbulence-Driven Inward Momentum Flux & Construction of a Difference Scheme for Fokker-Planck-Landau Operator

Momentum transport driven by microinstability is studied via analytic theories, gyrokinetic simulations, and experimental data analysis. A scenario for rotation profile evolution is constructed based on experimental observation that parallel flow initiates at edge region and penetrates into core region of tokamak [1]. In particular, turbulent diffusion and inward convective pinch are studied according to this scenario. For study of convective momentum pinch, toroidal ion temperature gradient mode near marginal stability is examined in kinetic limit. It is found from quasilinear estimation that the inward turbulent equipartition momentum pinch remains as the most robust part of pinch. In addition, it is found that ion temperature gradient driven momentum pinch is inward for typical parameters, while ion density gradient driven momentum pinch is outward. It is shown by theoretical formulas and experimental data analysis that momentum pinch velocity is sensitive to the electron to ion temperature ratio. For study of diffusive momentum transport, parallel shear flow instability is studied in fluid limit. Diffusion coefficient using mixing length estimate from nonlocal theory reveals that it has a strong dependence on the parallel flow shear and is mainly carried by fluctuations in short wavelength regime. Gyrokinetic simulation of collisionless parallel shear flow instability shows that the analytic prediction of diffusion coefficient is comparable to numerical values in the linear phase of the simulations. In the nonlinear phase, fluctuation energy gets transferred to the long wavelength regime. A two-dimensional, uniform velocity-grid based solver for the nonlinear Fokker-Planck-Landau (FPL) collision operator has been developed in the limit of strong magnetic field. The conservative and entropy increasing semidiscretized numerical scheme for the isotropic FPL equation by C. Buet et al. (2002) has been extended to 2D velocity space. A Picard fixed point method is used for semi-implicit time advance. One time evaluation of interpolation coefficients for probability distribution function is introduced so that numerical equilibrium is achieved with Maxwellian. However, positivity property is sacrificed at the saving of computational costs. In addition, a highly practical method is suggested to apply the velocity-grid based collision solver to particle-in-cell code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Long-lifetime ice particles in mixed-phase stratiform clouds: Quasi-steady and recycled growth

Lagrangian ice particle tracking is applied in both a 3-D time dependent velocity field produced by a Large Eddy Simulation cloud model and in a 2-D idealized field. It is found that more than 10% of ice particles have lifetimes longer than 1.5 hours, much longer than the large eddy turnover time or the time for a crystal to fall through the depth of a non-turbulent cloud. An analysis of trajectories in a 2-D idealized field shows that there are two types of long lifetime ice particles: quasi-steady and recycled growth. For quasi-steady growth, ice particles are suspended in the updraft velocity region for a long time. For recycled growth, ice particles are trapped in the large-eddy structures, and whether ice particles grow or evaporate depends on the ice relative humidity profile within the boundary layer. Some ice particles can grow after each cycle in the trapping region, until they are too large to be trapped, and thus have long lifetimes. Here, the relative contribution of the recycled ice particles to the cloud mean ice water content depends on both the dynamic and thermodynamic properties of the mixing layer. In particular, the total ice water content of a mixed phase cloud in a decoupled boundary layer can be much larger than that in a fully coupled boundary layer.

54 ENVIRONMENTAL SCIENCES↗

Single–Well Injection–Drift Test to Estimate Groundwater Velocity

A simple algebraic equation is presented here to estimate the magnitude of groundwater velocity based on data from a single-well injection-drift test thereby eliminating the time-consuming and costly extraction phase. A volume of tracer-amended water was injected by forced-gradient into a single well followed by monitoring of the conservative solute tracers under natural-gradient conditions as their upgradient portions drifted back through the well. The breakthrough curve data from the single well during the drift phase was analyzed to determine the mean travel times of the tracers. The estimated mean upgradient travel distance back through the single well and the mean travel times of the tracers were used in a simple algebraic equation to estimate groundwater velocity. The groundwater velocity based on the single-well injection-drift test was estimated to be approximately 0.64 ft per day. Two transects of observation wells were used to monitor the natural-gradient tracer transport downgradient of the injection well. The one-dimensional, or dual-well, transport of the tracer from the injection well to the nearest downgradient observation well indicated that the groundwater velocity was 0.55 ft per day. The two-dimensional, or multi-well, transport of the center of mass of the tracers indicated that the groundwater velocity was 0.60 ft per day; the dual- and multi-well results were in excellent agreement with those from the single-well and validated the simple algebraic equation. In conclusion, the new single-well method presented here is relatively simple, rapid, and does not require an extraction phase.

54 ENVIRONMENTAL SCIENCES↗

A MODEL ATMOSPHERE ANALYSIS OF ALPHA AURIGAE A

This work presents the first quantitative composite model atmosphere analysis of Capella, the brightest near-equal-mass spectroscopic binary and principal star of the constellation Auriga. Its high-resolution spectrum leads to a slightly metal-rich object at [Fe/H] = +0.05 {+-} 0.08 dex. In line with its young age and its kinematics, this consistently associates Capella with the Hyades moving group. The measured projected rotational velocities, vsin i{sub Aa} = 3.5 {+-} 0.8 km s{sup -1} and vsin i{sub Ab} = 35.4 {+-} 3.2 km s{sup -1}, both agree with rotational and orbital coplanarity and synchronous orbital rotation for the Aa component. At an orbital period P = 104 d the primary's bound rotation together with the almost zero orbital eccentricity are both key characteristics of this binary and clearly imply that the Aa component must have passed the tip of the giant branch. Whether in that phase Capella also became a mass transfer system remains inconclusive at present, though the high rotational velocity of the less evolved Hertzsprung gap secondary and the very diverse lithium abundances of both its components render this a plausible case.

79 ASTRONOMY AND ASTROPHYSICS↗

DIRECT OBSERVATIONS OF MAGNETIC RECONNECTION OUTFLOW AND CME TRIGGERING IN A SMALL ERUPTING SOLAR PROMINENCE

We examine a small prominence eruption that occurred on 2014 May 1 at 01:35 UT and was observed by the Interface Region Imaging Spectrometer (IRIS) and the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory. Pre- and post-eruption images were taken by the X-ray Telescope (XRT) on Hinode. Pre-eruption, a dome-like structure exists above the prominence, as demarcated by coronal rain. As the eruption progresses, we find evidence for reconnection between the prominence magnetic field and the overlying field. Fast flows are seen in AIA and IRIS, indicating reconnection outflows. Plane-of-sky flows of 300 km s{sup −1} are observed in the AIA 171 A channel along a potentially reconnected field line. IRIS detects intermittent fast line of sight flows of 200 km s{sup −1} coincident with the AIA flows. Differential emission measure calculations show heating at the origin of the fast flows. Post-eruption XRT images show hot loops probably due to reconfiguration of magnetic fields during the eruption and subsequent heating of plasma in these loops. Although there is evidence for reconnection above the prominence during the eruption, high spatial resolution images from IRIS reveal potential reconnection sites below the prominence. A height–time analysis of the erupting prominence shows a slow initial rise with a velocity of 0.4 km s{sup −1} followed by a rapid acceleration with a final velocity of 250 km s{sup −1}. Brightenings in IRIS during the transition between these two phases indicate the eruption trigger for the fast part of the eruption is likely a tether-cutting mechanism rather than a break-out mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗

Stability of Fe-bearing hydrous phases and element partitioning in the system MgO–Al 2 O 3 –Fe 2 O 3 –SiO 2 –H 2 O in Earth’s lowermost mantle

We performed high pressure–temperature ( P-T ) experiments on a model composition of hydrous subducted slabs in the MgO–Al 2 O 3 –Fe 2 O 3 –SiO 2 –H 2 O system using laser-heated diamond anvil cells. The phase assemblages were characterized combining in-situ synchrotron X-ray diffraction and ex-situ transmission electron microscope techniques. The hydrous δ-phase AlOOH–FeOOH–MgSiO 2 (OH) 2 –SiO 2 coexists with bridgmanite (Bdg), post-perovskite (pPv), or both in a broad P-T range of 104–126 GPa and 1750–2500 K. The hydrous pyrite-type FeOOHx phase was observed in-situ over a P-T range of 112–123 GPa and 1750–2300 K, coexisting with the pPv phase. Chemical analysis on recovered samples showed that considerable amount of Fe 2 O 2 (OH) 2 (8–13 mol%) and SiO 2 (9–13 mol%) in the δ-phase does not reduce its thermal stability compared to the Al-endmember, indicating that the Fe-bearing δ-phase can transport water to the lowermost mantle along the mantle geotherm. In this hydrous system, we observed that Al depletion in both the Bdg and pPv phases can significantly reduce the width of the Bdg to pPv transition in contrast to a wide two-phase coexistence region in a dry Al-rich system. Meanwhile, the Fe enrichment in the pPv phase relative to the coexisting Bdg phase lowers the transition pressure to the depth of the D" discontinuity. Accordingly, the depth and thickness of the Bdg to pPv transition in subducted basaltic crustal materials can explain the seismically detected D" discontinuity. Partial melting could be triggered by dehydration of the Fe-bearing hydrous phases due to a steep temperature gradient at the core mantle boundary (CMB), and therefore the ultralow-velocity zones (ULVZs) might be the regions where partial melting occurs at the lowermost mantle.

58 GEOSCIENCES↗

A consistent and conservative Phase-Field method for multiphase incompressible flows

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

97 MATHEMATICS AND COMPUTING↗