Flux Closure Research Articles

Development and application of turbulent heat flux model for lead-bismuth eutectic based on deep learning

Existing turbulent heat flux (THF) closure models in Reynolds-averaged Navier–Stokes simulation of scalar transport are insufficient on accuracy for fluids with a low Prandtl number (Pr), such as lead–bismuth eutectic (LBE), especially under complex operating conditions like in heat exchangers of nuclear reactors. This paper aims to propose a THF model suitable for such conditions. Firstly, we established a high-fidelity database of forced convection flow past two tandem cylinders under a Reynolds number (Re) of 1 × 105 and various low Pr conditions by hybrid large eddy simulation and direct numerical simulation algorithm. Based on the database, a deep learning architecture was then built and trained to predict dimensionless THF. Finally, a posteriori test proved that the proposed THF model helps to improve the prediction performance for temperature fields and also performs well when extrapolated to cases of LBE past the tube bundles, especially under the case with large Peclet numbers.

A reduced kinetic method for investigating non-local ion heat transport in ideal multi-species plasmas

A reduced kinetic method (RKM) with a first-principles collision operator is introduced in a 1D2V planar geometry and implemented in a computationally inexpensive code to investigate non-local ion heat transport in multi-species plasmas. The RKM successfully reproduces local results for multi-species ion systems and the important features expected to arise due to non-local effects on the heat flux are captured. In addition to this, novel features associated with multi-species, as opposed to single species, cases are found. Effects of non-locality on the heat flux are investigated in mass and charge symmetric and asymmetric ion mixtures with temperature, pressure, and concentration gradients. In particular, the enthalpy flux associated with diffusion is found to be insensitive to sharp pressure and concentration gradients, increasing its significance in comparison to the conductive heat flux driven by temperature gradients in non-local scenarios. The RKM code can be used for investigating other kinetic and non-local effects in a broader plasma physics context. Due to its relatively low computational cost it can also serve as a practical non-local ion heat flux closure in hydrodynamic simulations or as a training tool for machine learning surrogates.

Electric-field-induced multiferroic topological solitons.

Topologically protected spin whirls in ferromagnets are foreseen as the cart-horse of solitonic information technologies. Nevertheless, the future of skyrmionics may rely on antiferromagnets due to their immunity to dipolar fields, straight motion along the driving force and ultrafast dynamics. While complex topological objects were recently discovered in intrinsic antiferromagnets, mastering their nucleation, stabilization and manipulation with energy-efficient means remains an outstanding challenge. Designing topological polar states in magnetoelectric antiferromagnetic multiferroics would allow one to electrically write, detect and erase topological antiferromagnetic entities. Here we stabilize ferroelectric centre states using a radial electric field in multiferroic BiFeO3 thin films. We show that such polar textures contain flux closures of antiferromagnetic spin cycloids, with distinct antiferromagnetic entities at their cores depending on the electric field polarity. By tuning the epitaxial strain, quadrants of canted antiferromagnetic domains can also be electrically designed. These results open the path to reconfigurable topological states in multiferroic antiferromagnets.

Low-noise inverse magnetoelectric magnetic field sensor

In the development of any type of magnetic field sensor based on magnetic films, special consideration must be given to the magnetic layer component. The presented work investigates the use of scalable flux closing magnetostrictive multilayers for inverse magnetoelectric sensors. In such a type of magnetic field sensor, highly sensitive AC and DC field detection relies on strong excitation of the incorporated magnetic layers by piezoelectrically driven cantilever oscillation at mechanical resonances. The provoked periodic flux change is influenced by the magnetic field to be measured and is picked up by a coil, which generates the measured output. The multilayered inverse magnetoelectric sensor is investigated with regard to linearity, noise behavior, and detection limit of DC and AC signals. A significant advancement for inverse magnetoelectric thin film sensors is demonstrated in this study. Using exchange bias stabilized magnetic multilayers with flux closure structures, detection limits are improved by an order of magnitude to less than 8 pT/Hz1/2 at 10 Hz and 18 pT/Hz1/2 at DC.

Ten-moment fluid model with heat flux closure for gasdynamic flows

The gasdynamic 10-moment equations are revisited, applying a Chapman-Enskog type expansion to achieve the closure for heat flux. The resulting gradient-based closure performs favorably against previously employed closures in regions of shocks when compared to the kinetic results obtained from Direct Simulation Monte Carlo simulations. The 10-moment model can capture finite kinetic effects due to non-Maxwellian velocity distribution functions, as compared to the 5-moment Navier-Stokes equations, and remains hyperbolic-parabolic with real wave speeds under all initial conditions. Self-consistent kinetic boundary conditions are derived without consideration of a distinct Knudsen layer. The model is applied to a number of canonical gasdynamics problems in one and two dimensions such as steady normal and oblique shocks, as well as the Sod shock tube problem.

Kinetic plasma-sheath self-organization

The interaction between a plasma and a solid surface is studied in a (1D–1V) kinetic framework using a localized particle and convective energy source. Matching the quasineutral plasma region and sheath horizon is addressed in the fluid framework with a zero heat flux closure. It highlights non-polytropic nature of the physics of parallel transport. Shortfalls of this approach compared to a reference kinetic simulation highlight the importance of the heat flux as the measure of kinetic effects. Non-collisional closure and higher moment closure are used to determine the sound velocity. Within these frameworks, no gain in the fluid predictive capability is obtained. The kinetic constraint at the sheath horizon is discussed and modified to account for conditions that are actually met in simulations, namely quasineutrality with a small but finite charge density. Analyzing the distribution functions shows that collisional transfer is mandatory to achieve steady-state self-organization on the open field lines.

Analysis on bimodal complex permeability spectrum of a noise suppression sheet and single constituent flakes

In recent years, highly integrated active components inside small mobile communication devices have led to serious electromagnetic interference problems. The countermeasure to this problem is covering a noise source with a noise suppression sheet (NSS) which is composed of ferromagnetic flakes and polymers. The NSS absorbs effectively electromagnetic waves due to a large imaginary part of relative permeability μr″ at the specific frequency region. This function is attributed to the bimodal μr″ spectrum of NSS, but its physical origin has not been revealed so far. In this study, the bimodal μr″ spectrum of NSS has been analyzed and its physical mechanism has been discussed. The μr″ spectrum of a constituent single magnetic flake was measured by using a newly developed high-sensitivity permeability measurement system, which showed a bimodal spectrum quite similar to that of NSS. This fact indicates that the physical origin of the bimodal μr″ spectrum is attributed to the magnetization dynamics of each single constituent flake. After measuring the μr″ spectra of single flakes with various materials, such as Fe, Fe-Al, Fe-Co-V, and Fe-Si-Al alloys, these bimodal μr″ spectra were quantitatively explained by the magnetization dynamics of the flux closure states inside the flake. The magnetic domain structure of a single flake was observed by a micro-beam X-ray magnetic circular dichroism microscopy. The result confirmed that the segmented magnetic domains form the local flux closure states inside the flake.

Bowing to ferroelectric artificial flux closure.

Bowing to ferroelectric artificial flux closure.

Data-driven turbulence modelling of inherently unsteady flow in stratified water storage tanks

The flow and thermal characteristics of thermal stratification appears in a wide range of industrial applications related to energy storage. In a previous study (Xu et al. submitted to Flow, Turbulence and Combustion), it has been shown that linear closure models in unsteady Reynolds averaged Navier–Stokes (RANS) calculations are unable to accurately capture the transient flow and thermal characteristics occurring in stratified water storage tank configurations. In the current study, we extend a data-driven framework to develop turbulence and heat flux closures for a three-dimensional (3D) geometry of a stratified water storage tank, using data from a highly resolved large eddy simulation. The transient high-fidelity data set is partitioned into several time-intervals used for closure development and testing. In detail, we first present the model formulations for 3D buoyant flow. We then use the reference data to extract the most suitable input features, i.e. variables used to regress the data driven model. In order to reduce the complexity of the resulting models and accelerate the training process, a recursive basis function elimination is performed, using alignment of the different basis functions with the target turbulence stress and heat flux as metric. Using the identified features and the subsets of basis functions, novel closures are then developed using a symbolic regression framework, based on Gene Expression Programming (GEP). Models are developed either for each time interval or for all intervals at once. The different machine-learnt turbulence and heat-flux closure models are then tested for two different tank configurations where the thermal stratification is affected by positively/negatively buoyant jets within simple or complex three-dimensional geometries. It is demonstrated that the extended GEP-based data-driven turbulence modelling approach is able to create models that can accurately predict flow with inherent unsteadiness in three dimensional complex-geometry cases.

Defeating depolarizing fields with artificial flux closure in ultrathin ferroelectrics

Material surfaces encompass structural and chemical discontinuities that often lead to the loss of the property of interest in so-called dead layers. It is particularly problematic in nanoscale oxide electronics, where the integration of strongly correlated materials into devices is obstructed by the thickness threshold required for the emergence of their functionality. Here we report the stabilization of ultrathin out-of-plane ferroelectricity in oxide heterostructures through the design of an artificial flux-closure architecture. Inserting an in-plane-polarized ferroelectric epitaxial buffer provides the continuity of polarization at the interface; despite its insulating nature, we observe the emergence of polarization in our out-of-plane-polarized model of ferroelectric BaTiO3 from the very first unit cell. In BiFeO3, the flux-closure approach stabilizes a 251° domain wall. Its unusual chirality is probably associated with the ferroelectric analogue to the Dzyaloshinskii–Moriya interaction. We, thus, see that in an adaptively engineered geometry, the depolarizing-field-screening properties of an insulator can even surpass those of a metal and be a source of functionality. This could be a useful insight on the road towards the next generation of oxide electronics.

Fingerprint of vortexlike flux closure in an isotropic Nd-Fe-B bulk magnet

Fingerprint of vortexlike flux closure in an isotropic Nd-Fe-B bulk magnet

Induction and Ferroelectric Switching of Flux Closure Domains in Strained PbTiO3 with Neural Network Quantum Molecular Dynamics.

We have developed an extension of the Neural Network Quantum Molecular Dynamics (NNQMD) simulation method to incorporate electric-field dynamics based on Born effective charge (BEC), called NNQMD-BEC. We first validate NNQMD-BEC for the switching mechanisms of archetypal ferroelectric PbTiO3 bulk crystal and 180° domain walls (DWs). NNQMD-BEC simulations correctly describe the nucleation-and-growth mechanism during DW switching. In triaxially strained PbTiO3 with strain conditions commonly seen in many superlattice configurations, we find that flux-closure texture can be induced with application of an electric field perpendicular to the original polarization direction. Upon field reversal, the flux-closure texture switches via a pair of transient vortices as the intermediate state, indicating an energy-efficient switching pathway. Our NNQMD-BEC method provides a theoretical guidance to study electro-mechano effects with existing machine learning force fields using a simple BEC extension, which will be relevant for engineering applications such as field-controlled switching in mechanically strained ferroelectric devices.

Magneto-structural characterization of different kinds of magnetic nanoparticles

Using well-established measurement techniques like transmission electron microscopy (TEM), dynamic light scattering (DLS), small and wide angle X-ray scattering (SAXS, WAXS), susceptometry, and magnetorelaxometry, the distribution of the physical and magnetic size (magnetic moments) and magnetic anisotropy of a variety of structurally different magnetic nanoparticle samples (MNPs) is analyzed and compared. A term which accounts for the presence of weak magnetic areas (WMAs) within the MNPs was introduced to the widespread analysis model for M(H) data, enabling a consistent interpretation of the data in most of the systems. A comparison of the size distributions as obtained for the physical and the magnetic diameter suggests a multidomain structure for three single core systems under investigation, in all probability evoked by the presence of a wustite phase, as identified by WAXS.Analyzing the relationship d < dm < dc between the average single core diameter d, the effective magnetic (domain) size dm and the cluster diameter dc quantitatively, two qualitatively different magnetic structures in multicore MNP (MCMNP) systems were identified: (i) The magnetic moments of single cores within the MCMNP of fluidMAG tend to build flux closure structures, driven by dipole–dipole interaction. (ii) The magnetic behavior of Resovist® was attributed to the presence of domain sizes of about 12 nm within MCMNP, exceeding the single core diameters of 5 nm. Thereby, WAXS revealed a bimodal crystallite size distribution suggesting a crystallite merging process within the MCMNP. The value of the effective magnetic moment of these MCMNP could be explained within the presented “random moment cluster model” (RMCM).We conclude that the combination of physical and magnetic structure parameters obtained from complementary measurement methods allows a reliable assessment of the magnetic structure of single and multicore MNPs.

Observation of Hidden Polar Phases and Flux Closure Domain Topology in Bi2WO6 Thin Films.

Topological textures of ferroelectric polarizations have promise as alternative devices for future information technology. A polarization rotation inevitably deviates from the stable orientation in axial ferroelectrics, but local energy losses compromise the global symmetry, resulting in a distorted shape of the topological vortex or inhibiting the vortex. Easy planar isotropy helps to promote rotating structures and, accordingly, to facilitate access to nontrivial textures. Here, we investigate the domain structure of an epitaxial thin film of bismuth tungsten oxide (Bi2WO6) grown on a (001) SrTiO3 substrate. By using angle-resolved piezoresponse force microscopy and scanning transmission electron microscopy, we find the existence of a hidden phase with ⟨100⟩-oriented ferroelectric polarizations in the middle of the four variant ⟨110⟩-oriented polarization domains, which assists in the formation of flux closure domains. The results suggest that this material is one step closer to becoming an isotropic two-dimensional polar material.

Three-dimensional tomographic imaging of the magnetization vector field using Fourier transform holography

The authors present a new tomographic technique, based on Fourier transform holography. It is a lensless imaging technique to retrieve the object of interest from its diffraction pattern in a single step of computation. A combination of dual-axis tomographic projections provides a 3D vectorial magnetic image of an 800-$n\phantom{\rule{0}{0ex}}m$-thick Fe/Gd multilayer in a 5-$\ensuremath{\mu}\phantom{\rule{0}{0ex}}m$-diameter field of view with a resolution of 80 $n\phantom{\rule{0}{0ex}}m$. The reconstruction reveals not only wormlike domains with magnetization pointing mostly out of plane, but also the subtle features of magnetic flux closure around the domain walls.

Comparison of a hybrid model and experimental measurements for a dielectric-coated coaxial ECR thruster

Electrostatic probe and thrust balance measurements of a coaxial electron-cyclotron-resonance plasma thruster with magnetic nozzle are compared against numerical simulations of the device that solve self-consistently the plasma transport problem with a hybrid particle-in-cell/fluid approach and the microwave electromagnetic fields using mixed finite elements. A simple phenomenological anomalous transport model similar to those used in Hall thruster modeling is applied. Reasonable average relative errors are reported on the ion current density (8.7%) and plasma density (12.8%) profiles along the plume. Good agreement is found in terms of relative errors on thruster performance parameters as the 90%-current divergence angle (0%–3%), utilization efficiency (3%–10%), peak ion energy (9%–15%), and energy efficiency (2%–17%). The comparison suggests that enhanced cross-field diffusion is present in the plasma. Differences in the experimental and numerical behavior of electron temperature point to the areas of the model that could be improved. These include the electron heat flux closure relation, which must correctly account for the axial electron cooling observed.

Thickness effect on ferroelectric domain formation in compressively strained K0.65Na0.35NbO3 epitaxial films

In this paper, the influence of thickness in epitaxial ${\mathrm{K}}_{0.65}{\mathrm{Na}}_{0.35}{\mathrm{NbO}}_{3}$ ferroelectric thin films grown on a (110) ${\mathrm{TbScO}}_{3}$ substrate was systematically studied. Detailed atomic force microscopy revealed a complex change in growth mode with increasing film thickness, with the surface roughness remaining 0.30 nm throughout. By combining piezoresponse force microscopy and high-resolution x-ray diffraction, the occurrence of 90\ifmmode^\circ\else\textdegree\fi{} stripe domains was demonstrated for the films with a thickness of \ensuremath{\ge}11 nm, while the domain periodicity is in good agreement with Kittel's law. Furthermore, up to the thickness of 93 nm, elastic strain relaxation induced by the formation of ferroelectric domains was observed, whereas plastic strain relaxation plays only a minor role. As the film thickness increases, three successive phases of ferroelectric domains were observed: (i) irregularly arranged orthorhombic $c$ domains in the thinnest film, (ii) periodically arranged 90\ifmmode^\circ\else\textdegree\fi{} monoclinic ${M}_{C}$ domains up to a thickness of 25 nm, and (iii) a flux closure vortexlike structure in thicker films to achieve the lowest equilibrium energy. These results demonstrate the importance of understanding the lattice relaxation mechanism for intentional tuning of ferroelectric thin film properties.

Assessment of turbulent heat flux models for URANS simulations of turbulent buoyant flows in ROCOM tests

Turbulent mixing in buoyant flows is an essential mechanism involved in many scenarios related to nuclear safety in nuclear power plants. Comprehensive understanding and accurate predictions of turbulent buoyant flows in the reactor are of crucial importance, due to the function of mitigating the potential detrimental consequences during postulated accidents. The present study uses URANS methodology to investigate the buoyancy-influenced flows in the reactor pressure vessel under the main steam line break accident scenarios. With a particular focus on the influence of turbulent heat flux closure models, various combinations of two turbulence models and three turbulent heat flux models are utilized for the numerical simulations of three ROCOM tests which have different characteristic features in terms of the flow rate and fluid density difference between loops. The simulation results are compared with experimental measurements of the so-called mixing scalar in the downcomer and at the core inlet. The study shows that the anisotropic turbulent heat flux models are able to improve the accuracy of the predictions under conditions of strong buoyancy whilst in the weak buoyancy case, a major role is played by the selected turbulence models with essentially a negligible influence of the turbulent heat flux closure models.

Improved Surface Mass Balance Closure in Ocean Hindcast Simulations

AbstractForced global ocean/sea‐ice hindcast simulations are subject to persistent surface mass flux estimation biases, for example, configurations with an explicit‐free surface may not take into account the seasonal storage of water on land when constraining sea level. We present a physically motivated surface mass flux closure, that results in: reduced watermass drift from initialization; improved Atlantic meridional overturning cirulation intensity; and more realistic rates of ocean heat uptake, in simulations using global ocean/sea‐ice/land (MOM6/SIS2/LM3) model configurations, forced with atmospheric reanalysis data. In addition to accounting for the land storage, the area‐integrated subpolar‐to‐polar (40°–90°N/S) surface mass fluxes are constrained, using a climatological estimate derived from the the CMIP6 historical ensemble, which helps to further improve hindcast performance. Simulations using MERRA‐2 and JRA55‐do forcing, subject to identical hydrologic constraints, exhibit similar reductions in drift.

Geometric Control of Domain Structure Stability in Ferroelectric Nanotubes

AbstractFerroelectric nanotubes offer intriguing opportunities for stabilizing exotic polarization domains and achieving new or enhanced functionalities by tailoring the complex interplay among the geometry, surface effects, crystal symmetry, and more. Here, phase‐field simulations to predict the room‐temperature equilibrium polarization domain structure in (001)pc PbZr0.52Ti0.48O3 (PZT) nanotubes are used (pseudocubic (pc)). The simulations incorporate the influence of surface‐tension‐induced strains, which have been ignored in existing computational studies. It is found that (001)pc PZT nanotubes can host a unique class of topological polarization domain structures comprising non‐planar flux‐closures and anti‐flux‐closures that are inaccessible with ferroelectrics of planar geometry (e.g., thin‐films, nanodots). It is shown that surface‐tension‐induced strain is significantly enhanced in thin‐walled nanotubes and thereby can lead to noticeable modulation of the flux closures. Domain stability map as a function of the nanotube wall thickness and height is established. The results provide a basis for geometrical engineering of domain structures and associated functional (e.g., piezoelectric, electrocaloric) responses in ferroelectric nanotubes.