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At least 73 records · Page 4

Convective instability when the temperature gradient and rotation vector are oblique to gravity. I - Fluids without diffusion

A linear stability analysis of fluid layers under uniform rotation (generally oblique to gravity) which possess both vertical and horizontal temperature gradients is made by considering ideal fluids without diffusion within a Boussinesq approximation. This simplified configuration is used to assess the preferred convective modes as a function of latitude on a planet like Jupiter. The tilted rotation vector introduces a preference for roll-like disturbances with north-south orientations, while the horizontal temperature gradient produces a thermal wind shear which favors convective rolls oriented parallel to the flow in an east-west direction. It is found that the horizontal temperature gradient needed to produce a preference for the axisymmetric or east-west rolls increases with an increasing rotation rate and a decreasing latitude. The parameter values for Jupiter are estimated with the use of a simple radiative convective model, indicating a preference for axisymmetric rolls at nearly all latitudes if the convection zone depth is greater than about 200 km below the one atmosphere pressure level and convective roll characteristics which contribute to an equatorial acceleration.

Hathaway, D. H.↗

Control of Meridional Flow by a Non-Uniform Rotational Magnetic Field

The diffusive mass transfer of species during crystal growth in vertical ampoules is significantly affected by fluid flow in the liquid mother phase (melt). For electrically conductive melts, an elegant way of remotely inducing and controlling this flow is by utilizing a uniform rotational magnetic field (RMF) in the transverse direction. It induces an azimuthal flow which tends to homogenize the thermal and solutal fields. The rotating field also reduces the diffusion boundary layer, stabilizes temperature fluctuations, and promotes better overall crystal growth. For moderate strengths of the applied magnetic field (2-20 m Tesla) with frequencies of up to 400 Hz, the induced secondary meridional flow becomes significant. It typically consists of one roll at the bottom of the liquid column and a second roll (vortex) at the top. The flow along the centerline (ampoule axis) is directed from the growing solid (interface) towards the liquid (melt). In case of convex interfaces (e.g. in floating zone crystal growth) such flow behavior is beneficial since it suppresses diffusion at the center. However, for concave interfaces (e.g. vertical Bridgman crystal growth) such a flow tends to exacerbate the situation in making the interface shape more concave. It would be beneficial to have some control of this meridional flow- for example, a single recirculating cell with controllable direction and flow magnitude will make this technique even more attractive for crystal growth. Such flow control is a possibility if a non-uniform PNE field is utilized for this purpose. Although this idea has been proposed earlier, it has not been conclusively demonstrated so far. In this work, we derive the governing equations for the fluid dynamics for such a system and obtain solutions for a few important cases. Results from parallel experimental measurements of fluid flow in a mercury column subjected to non-uniform RMF will also be presented.

Mazuruk, Konstantin↗

Active unsteady aerodynamic suppression of rotating stall in an incompressible flow centrifugal compressor with vaned diffuser

A mathematical model is developed to analyze the suppression of rotating stall in an incompressible flow centrifugal compressor with a vaned diffuser, thereby addressing the important need for centrifugal compressor rotating stall and surge control. In this model, the precursor to to instability is a weak rotating potential velocity perturbation in the inlet flow field that eventually develops into a finite disturbance. To suppress the growth of this potential disturbance, a rotating control vortical velocity disturbance is introduced into the impeller inlet flow. The effectiveness of this control is analyzed by matching the perturbation pressure in the compressor inlet and exit flow fields with a model for the unsteady behavior of the compressor. To demonstrate instability control, this model is then used to predict the control effectiveness for centrifugal compressor geometries based on a low speed research centrifugal compressor. These results indicate that reductions of 10 to 15 percent in the mean inlet flow coefficient at instability are possible with control waveforms of half the magnitude of the total disturbance at the inlet.

Lawless, Patrick B.↗

Li-7 abundances in halo stars: Testing stellar evolution models and the primordial Li-7 abundance

A large number of stellar evolution models with (Fe/H) = -2.3 and -3.3 have been calculated in order to determine the primordial Li-7 abundance and to test current stellar evolution models by a comparison to the extensive database of accurate Li abundances in extremely metal-poor halo stars observed by Thorburn (1994). Standard models with gray atmospheres do a very good job of fitting the observed Li abundances in stars hotter than approximately 5600 K. They predict a primordial. Li-7 abundance of log N(Li) = 2.24 +/- 0.03. Models which include microscopic diffusion predict a downward curvature in the Li-7 destruction isochrones at hot temperatures which is not present in the observations. Thus, the observations clearly rule out models which include uninhibited microscopic diffusion of Li-7 from the surface of the star. Rotational mixing inhibits the microscopic diffusion and the (Fe/H) = -2.28 stellar models which include both diffusion and rotational mixing provide an excellent match to the mean trend in T(sub eff) which is present in the observations. Both the plateau stars and the heavily depleted cool stars are well fit by these models. The rotational mixing leads to considerable Li-7 depletion in these models and the primordial Li-7 abundance inferred from these models is log N(Li) = 3.08 +/- 0.1. However, the (Fe/H) = -3.28 isochrones reveal problems with the combined models. These isochrones predict a trend of decreasing log N(Li) with increasing T(sub eff) which is not present in the observations. Possible causes for this discrepancy are discussed.

Chaboyer, Brian↗

Mass diffusion in a self-confined rotating flow

The effectiveness of fluid containment near an interior stagnation point and within a self-confined stagnation region is determined by numerically solving the species conservation equation for a bi-component mixture. The flow geometry is that of a swirling fluid stream containing a stationary eddy on the axis of rotation. The base flow is axisymmetric, and the Reynolds number is equal to 50. Schmidt numbers range from 0.1 to 10.

Torrance, K. E.↗

Simulations of magnetic-flux transport in solar active regions

The evolution of several observed solar active regions is simulated by solving a transport equation for magnetic flux at the photosphere. The rates of rotation, meridional flow, and diffusion of the flux are determined self-consistently in the calculations. The findings are in good quantitative agreement with previous measures of the rotation rate and diffusion constant associated with photospheric magnetic fields. Although the meridional velocities are consistent in direction and magnitude with recently reported poleward flows, relatively large uncertainties in the velocity determinations make this result inconclusive.

Devore, C. R.↗

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

The gravitational collapse and fragmentation of centrally condensed molecular cloud cores are investigated using a new hydrodynamical code. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a 3D Cartesian grid. Two initial power-law density profiles, rho varies as r exp -1 and rho varies as r exp -2, are considered, as well as two initial density perturbations in the azimuthal coordinate theta, rho-i - rho(1 + a cos 2theta) where a = 0.1 and 0.5. Fragmentation is found to be possible in these centrally condensed cores if the initial conditions also include differential rotation. Models which collapse with initial uniform rotation do not produce fragments. If molecular cloud cores are indeed centrally condensed, as suggested by observations of star-forming regions and by studies of ambipolar diffusion, then differential rotation may be a mechanism for producing binary protostars during gravitational collapse.

Myhill, Elizabeth A.↗

The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.

Schlesinger, R. E.↗

S-NPP VIIRS Solar Diffuser Degradation at the View Direction of the Rotating Telescope Assembly

S-NPP VIIRS has been on-orbit for more than nine years since it was launched on October28th,2011. The VIIRS reflective solar bands (RSBs) are calibrated on-orbit primarily by an onboard solar diffuser (SD). The SD on-orbit degradation is tracked by an onboard SD stability monitor(SDSM). The VIIRS RSBs view the SD through a rotating telescope assembly (RTA). The RTA views the SD from a direction that is quite different from that of the SDSM. It has been shown that the SD degrades non-uniformly with respect to the incident and outgoing directions, especially at the short wavelengths. Thus, the SDSM calibration cannot provide an accurate SD degradation estimation for the view direction of the RTA, resulting in long-term drifts in the calibration coefficients derived from the SD and SDSM calibration. S-NPP VIIRS has been scheduled to view the Moon approximately monthly since its launch. The lunar observations can provide accurate long-term trends for the RSB calibration coefficients since the lunar surface reflectance is quite stable. By comparing the SD and lunar calibration results, we can obtain the SD degradation differences at the view directions of the SDSM and RTA and derive the SD degradation at the view direction of the RTA. Moreover, we can also derive the SD degradation in the short-wave infrared (SWIR) spectral range, wherein the SDSM cannot track the SD degradation. In this paper, we will derive the SD degradation for the view direction of the RTA from the SD, SDSM, and lunar calibrations from the visible to SWIR spectral range. We will also simulate the SD degradation with analytical models and compare their performances.

SNPP VIIRS↗

Vortex Generators in a Streamline-Traced, External-Compression Supersonic Inlet

Vortex generators within a streamline-traced, external-compression supersonic inlet for Mach 1.66 were investigated to determine their ability to increase total pressure recovery and reduce total pressure distortion. The vortex generators studied were rectangular vanes arranged in counter-rotating and co-rotating arrays. The vane geometric factors of interest included height, length, spacing, angle-of-incidence, and positions upstream and downstream of the inlet terminal shock. The flow through the inlet was simulated numerically through the solution of the steady-state, Reynolds-averaged Navier-Stokes equations on multi-block, structured grids using the Wind-US flow solver. The vanes were simulated using a vortex generator model. The inlet performance was characterized by the inlet total pressure recovery and the radial and circumferential total pressure distortion indices at the engine face. Design of experiments and statistical analysis methods were applied to quantify the effect of the geometric factors of the vanes and search for optimal vane arrays. Co-rotating vane arrays with negative angles-of-incidence positioned on the supersonic diffuser were effective in sweeping low-momentum flow from the top toward the sides of the subsonic diffuser. This distributed the low-momentum flow more evenly about the circumference of the subsonic diffuser and reduced distortion. Co-rotating vane arrays with negative angles-of-incidence or counter-rotating vane arrays positioned downstream of the terminal shock were effective in mixing higher-momentum flow with lower-momentum flow to increase recovery and decrease distortion. A strategy of combining a co-rotating vane array on the supersonic diffuser with a counter-rotating vane array on the subsonic diffuser was effective in increasing recovery and reducing distortion.

computational fluid dynamics↗

Lateral fluid forces acting on a whirling centrifugal impeller in vaneless and vaned diffuser

Fluid forces on a rotating centrifugal impeller in whirling motion were studied. A two dimensional impeller installed in a parallel-walled vaneless and vaned diffuser whirled on a circular orbit with various positive and negative angular velocities. It is shown that the fluid forces exert a damping effect on the rotor in most operating conditions, but become excitatory when the impeller operates at very low partial discharge while rotating far faster than the whirl speed. The fluid forces were expressed in terms of mass, damping and stiffness matrices. Impellers with the same geometry and whirl condition are calculated. Quantitative agreement is obtained especially in positive whirl.

Ohashi, H.↗

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING↗

Confinement-Driven Heterogeneous Benzene Crystallization in Silica Nanopores

Nanoconfinement alters the thermodynamics, dynamics, and kinetics of fluids hosted in nanoscale solid nanopores to an extent that depends on the characteristics of the confining space and the chemistry of the confined fluids. Confinement-induced alterations in the phase behavior of confined energetic fluids under high pressure or low temperature are highly relevant to subsurface and subsea phenomena such as fluid flow in porous media, hydrate formation and dissociation, and gas storage capacity. Although extensive efforts have been directed toward understanding the phase behavior of confined fluids, the role of solid-liquid interfaces in the phase transitions of organic liquids has not been resolved yet. Here, we explore the onset and growth of benzene crystallization confined in 6 nm sized SBA-15 silica nanopores in the temperature range 300-200 K using in situ extended range small-angle and wide-angle X-ray scattering (SAXS/WAXS) measurements and atomistic classical molecular dynamics (MD) simulations. The crystallization onset of confined benzene depresses to 265 K compared to the freezing point of bulk benzene ( ~278 K), followed by the continuous growth of the emerged crystals in the pore space with complete crystallization at 200 K. The orientation of the emerged benzene crystals is dominated by parallel (π-π stacking) and perpendicular (T-shape stacking) orientations along the cylindrical pore radius and pore length, respectively. The onset of benzene crystals occurs heterogeneously on the pore surface and grows continuously toward the pore center. Further, confined benzene undergoes a dynamical crossover from fragile to strong dynamics behavior, inferred from the rotational and translational diffusion. The insights provided by this study have significant implications for the phase transitions of confined organic liquids that are relevant to a wide range of applications in the biological, geological, environmental, and chemical fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetohydrodynamic Control of Interfacial Degradation in Lithium-Ion Batteries for Fast Charging Applications

Interfacial anodic degradation in graphitic materials under fast charging conditions causes severe performance loss and safety hazard in lithium ion batteries. We present a novel method for minimizing the growth of these aging mechanism by application of an external magnetic field. Under magnetic field, paramagnetic lithium ions experience a magnetohydrodynamic force, which rotates the perpendicularly diffusing species and homogenizes the ionic transport. This phenomenon minimizes the overpotential hotspots at the anode/separator interface, consequently reducing SEI growth, lithium plating, and interfacial fracture. In situ electrochemical measurements indicate an improvement in capacity for lithium cobalt oxide/graphite pouch cell (20 mAh) charged from 1–5 C under an applied field of 1.8 kG, with a maximum capacity gain of 22% at 5C. Post-mortem FE-SEM and EDS mapping shows that samples charged with magnetic field have a reduced lithium deposition at 3C and a complete suppression of interfacial fracture at 5C. At 5C, a 24% reduction in the lithium content is observed by performing XPS on the anodic interfacial film. Finally, fast charging performance under variable magnetic field strengths indicate a saturation behavior in capacity at high fields (>2 kG), thereby limiting the field and consequent energy requirements to obtain maximum capacity gain under extreme conditions.

electromagnetism↗

Two-dimensional turbulence

The theory of two-dimensional turbulence is reviewed and unified, and some hydrodynamic and plasma applications are considered. The topics covered include some equations of incompressible hydrodynamics, absolute statistical equilibrium, spectral transport of energy and enstrophy, turbulence on the surface of a rotating sphere, turbulent diffusion, MHD turbulence, and two-dimensional superflow. Finally, an attempt is made to assess the status and future of the principal research topics which have been discussed.

Kraichnan, R. H.↗