Planar Flow Research Articles

Lightweight Acquisition and Ranging of Flows in the Data Plane

As networks get more complex, the ability to track almost all the flows is becoming of paramount importance. This is because we can then detect transient events impacting only a subset of the traffic. Solutions for flow monitoring exist, but it is getting very difficult to produce accurate estimations for every <flowID,counter> tuple given the memory constraints of commodity programmable switches. Indeed, as networks grow in size, more flows have to be tracked, increasing the number of tuples to be recorded. At the same time, end-host virtualization requires more specific flowIDs, enlarging the memory cost for every single entry. Finally, the available memory resources have to be shared with other important functions as well (e.g., load balancing, forwarding, ACL). To address those issues, we present FlowLiDAR (Flow Lightweight Detection and Ranging), a new solution that is capable of tracking almost all the flows in the network while requiring only a modest amount of data plane memory, which is not dependent on the size of flowIDs. We implemented the scheme in P4, tested it using real traffic from ISPs, and compared it against four state-of-the-art solutions: FlowRadar, NZE, PR-sketch, and Elastic Sketch.

Resonant and nonresonant excitation of waves in a planar magnetosonic flow

AbstractForced propagation of perturbations in a magnetosonic wave are considered. The driving force may be caused by stimulated Mandelstam–Brillouin scattering of optic waves or by intense magnetosonic exciter. Some heating‐cooling function which takes into account radiative cooling and unspecified heating is taken into consideration, as well as nonlinearity of a medium. Both these factors make the excitation particular. The analytical and numerical evaluations reveal that forced oscillations differ essentially from the free propagation and depend on a number of dimensionless parameters such as the ratio of speed of exciter to the eigen speed of excited wave, the ratio of speed of an excited wave to its eigen speed, and the dimensionless magnitude of an exciter. Forced excitation is resonant if speed of an exciter coincides with the eigen speed of excited wave but may give rise to the excited perturbations with the speed different from the eigen one. The preliminary evaluations may be helpful for the controlled excitation of perturbations in natural and laboratory plasma systems and indication of the parameters of an exciter.

Well-Posedness of the Two-Dimensional Compressible Plasma-Vacuum Interface Problem

We consider the two-dimensional plasma-vacuum interface problem in ideal compressible magnetohydrodynamics (MHD). This is a hyperbolic-elliptic coupled system with a characteristic free boundary. In the plasma region the 2D planar flow is governed by the hyperbolic equations of ideal compressible MHD, while in the vacuum region the magnetic field obeys the elliptic system of pre-Maxwell dynamics. At the free interface moving with the velocity of plasma particles, the total pressure is continuous and the magnetic field on both sides is tangent to the boundary. The plasma-vacuum system is not isolated from the outside world, since it is driven by a given surface current which forces oscillations onto the system. We prove the local-in-time existence and uniqueness of solutions to this nonlinear free boundary problem, provided that at least one of the two magnetic fields, in the plasma or in the vacuum region, is non-zero at each point of the initial interface. The proof follows from the analysis of the linearized MHD equations in the plasma region and the elliptic system for the vacuum magnetic field, suitable tame estimates in Sobolev spaces for the full linearized problem, and a Nash–Moser iteration.

Nonlinear Asymptotic Stability and Transition Threshold for 2D Taylor–Couette Flows in Sobolev Spaces

In this paper, we investigate the stability of the 2-dimensional (2D) Taylor–Couette (TC) flow for the incompressible Navier–Stokes equations. The explicit form of velocity for 2D TC flow is given by u=(Ar+Br)(-sinθ,cosθ)T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u=(Ar+\\frac{B}{r})(-\\sin \ heta , \\cos \ heta )^T$$\\end{document} with (r,θ)∈[1,R]×S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(r, \ heta )\\in [1, R]\ imes \\mathbb {S}^1$$\\end{document} being an annulus and A, B being constants. Here, A, B encode the rotational effect and R is the ratio of the outer and inner radii of the annular region. Our focus is the long-term behavior of solutions around the steady 2D TC flow. While the laminar solution is known to be a global attractor for 2D channel flows and plane flows, it is unclear whether this is still true for rotating flows with curved geometries. In this article, we prove that the 2D Taylor–Couette flow is asymptotically stable, even at high Reynolds number (Re∼ν-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re\\sim \ u ^{-1}$$\\end{document}), with a sharp exponential decay rate of exp(-ν13|B|23R-2t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (-\ u ^{\\frac{1}{3}}|B|^{\\frac{2}{3}}R^{-2}t)$$\\end{document} as long as the initial perturbation is less than or equal to ν12|B|12R-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u ^\\frac{1}{2} |B|^{\\frac{1}{2}}R^{-2}$$\\end{document} in Sobolev space. The powers of ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} and B in this decay estimate are optimal. It is derived using the method of resolvent estimates and is commonly recognized as the enhanced dissipative effect. Compared to the Couette flow, the enhanced dissipation of the rotating Taylor–Couette flow not only depends on the Reynolds number but also reflects the rotational aspect via the rotational coefficient B. The larger the |B|, the faster the long-time dissipation takes effect. We also conduct space-time estimates describing inviscid-damping mechanism in our proof. To obtain these inviscid-damping estimates, we find and construct a new set of explicit orthonormal basis of the weighted eigenfunctions for the Laplace operators corresponding to the circular flows. These provide new insights into the mathematical understanding of the 2D Taylor–Couette flows.

Observing S-Matrix Pole Flow in Resonance Interplay

We provide an overview of experiments exploring resonances in the collision of ultracold clouds of atoms. Using a laser-based accelerator that capitalises on the energy resolution provided by the ultracold atomic setting, we unveil resonance phenomena such as Feshbach and shape resonances in their quintessential form by literally photographing the halo of outgoing scattered atoms. We exploit the tunability of magnetic Feshbach resonances to instigate an interplay between scattering resonances. By experimentally recording the scattering in a parameter space spanned by collision energy and magnetic field, we capture the imprint of the S-matrix pole flow in the complex energy plane. After revisiting experiments that place a Feshbach resonance in the proximity of a shape resonance and an anti-bound state, respectively, we discuss the possibility of using S-matrix pole interplay between two Feshbach resonances to create a bound-state-in-the-continuum.

Vortex shedding from bluff bodies: a conformal mapping approach

A model to calculate flow around bluff bodies of various geometries is presented. A conformal map between the plane of the bluff body and the plane of a unit circular cylinder is established by using a combination of Karman–Trefftz transformations and Fornberg’s method. Flow in the circle plane is calculated using the authors’ Hybrid Potential Flow (HPF) model and mapped back to the shape plane. By joining this calculated near-body flow with von Karman’s model for a vortex wake, forces due to vortex shedding and shedding frequencies are calculated. In this manner, a complete solution for the flow around bluff bodies of various geometries is established. Results for two shapes are presented, along with recommendations for further work.

Probing the Kinematic Signatures of Planet Formation in the Gas Disk of MWC 480

The disk around MWC 480 has shown multiple substructures in both dust and gas observations, possibly suggesting ongoing planet formation in situ. In this paper, we explore the gas kinematics of the MWC 480 disk by analyzing the archival Atacama Large Millimeter/submillimeter Array observations of 12CO (J = 2-1), 13CO (J = 2-1), and C18O (J = 2-1). By modeling the line-of-sight velocities, inferred from the Doppler shifts of the emission lines, we are able to decompose the three-dimensional (3D) velocity field of the disk into rotational, radial, and vertical components. Further analysis reveals the presence of large-scale gas flows in the (r, z) plane. Notably, we identify potential meridional flows across various heights as traced by all three CO isotopologues in the 80–120 au region, possibly associated with ongoing planet formation activities in this region. Moreover, we find upward flows near 200 au for all three CO isotopologues, which may point to the presence of disk winds.

A study of streamline geometries in subsonic and supersonic regions of compressible flow fields

The geometrical properties of streamlines, such as the curvatures, directions and positions, are studied in steady inviscid compressible flow fields via differential geometry theories and conservation laws. The influences of the streamline geometries on the flow speeds and pressures are also identified and discussed. By transforming the streamlines to fill the domain and satisfy the boundary conditions, a unified geometry-based solver, the streamline transformation method, is proposed for both subsonic and supersonic regions. The governing equations and boundary conditions along streamlines and shock waves are also derived. This method is verified by numerical results of three typical flow fields, including the subsonic channel flow, the supersonic downstream of attached shock waves and especially the subsonic/supersonic downstream of detached bow shock waves. Both two-dimensional planar and axisymmetric flow fields are considered. Compared with the results from computational fluid dynamics, good agreements are achieved by this method, while fewer computational resources, by an order of magnitude, are consumed. Features of these flow fields are also analysed from a geometrical perspective, such as flow speeds and pressures deviated by the wall curvatures, and three-dimensional effects in the after-shock flow fields. For a hyperbolic-shaped bow shock wave, the stand-off distances and the transitions from subsonic to supersonic regions are also discussed. As indicated by the accuracy, efficiency and applicability in a wide range of flow speeds, the streamline transformation method would be a potential candidate for the theoretical analysis and inverse design of high-speed flow fields, especially where the subsonic regions exist downstream of strong shock waves.

Unsteady behaviour and plane blade angle configurations' effects on pressure fluctuations and internal flow analysis in axial flow pumps

Pumps play a crucial role in various applications, and this study employs the CFD method to simulate the internal flow of an axial pump. Utilizing a three-dimensional model with real clearances, our investigation focuses on the pump's internal flow and pressure pulsation under diverse operating conditions. Specifically, we operated an axial pump at varying blade angles (30°, 45°, 60°, and 75°) to determine transient flow fields, aiming to identify both qualitative and quantitative characteristics. In line with current research practices, we present a comparison between numerical calculations and experimental results, revealing reasonable agreement. The simulation results highlight the influence of flow rate and plane blade angle on key parameters such as static pressure, dynamic pressure, total pressure, velocity magnitude fluctuations, and shear stress. Notably, pressure increases near or at the blade tip, and hydraulic flow becomes more evident under different blade angles and conditions. The highest pressure and velocity are observed on the blade with a 45-degree plane angle. These findings provide valuable insights for enhancing the hydraulic performance of axial pumps. To ascertain the model's accuracy and reliability, our research establishes a side-by-side comparison between numerical predictions and experimental data, demonstrating a satisfactory level of agreement. The CFD simulations yield critical insights into the pump's performance, emphasizing the profound sensitivity of parameters to variations in flow rate and blade angle, crucial for understanding and optimizing the pump's behavior.

Shear rate dependency on flowing granular biomass material

The commercialization of bioenergy has been significantly limited by various material handling issues due to the poor flowability of granular biomass materials. Addressing these issues demands a fundamental understanding of flow physics and robust models to predict the multi-regime flow behavior of biomass particles. In this study, we investigated the multi-regime flow behavior of loblolly pine chips, a widely used bioenergy feedstock, through combined experiments and simulations. A quasi-static hypoplastic model and a cross-regime Drucker–Prager (DP)-μ(I) model were utilized and validated against inclined plane flow experiments to understand the quasi-static and dense flow behavior of milled pine chips. The results show that along the inclined plane, loblolly pine chips mainly present in heap flow (varying thickness along the plane), and in plane flow (iso-thickness along the plane) only when the inclination closes to the material’s critical state internal friction angle. The results also show that the multi-regime DP-μ(I) model predicts a completely different velocity profile from the hypoplastic model. DP-μ(I) model can capture the flow behavior of pine chips in both flow regimes well but at the cost of extra parameter determination, and the shear-rate dependent rheology model can successfully capture the flow of elongated high-frictional particles. These findings advance the scientific understanding of the multi-regime flow behavior of granular biomass materials and shed light on formulating novel constitutive models to assist granular biomass handling in the bioenergy industry.

Bayesian inference of vorticity in unbounded flow from limited pressure measurements

We study the instantaneous inference of an unbounded planar flow from sparse noisy pressure measurements. The true flow field comprises one or more regularized point vortices of various strength and size. We interpret the true flow's measurements with a vortex estimator, also consisting of regularized vortices, and attempt to infer the positions and strengths of this estimator assuming little prior knowledge. The problem often has several possible solutions, many due to a variety of symmetries. To deal with this ill posedness and to quantify the uncertainty, we develop the vortex estimator in a Bayesian setting. We use Markov-chain Monte Carlo and a Gaussian mixture model to sample and categorize the probable vortex states in the posterior distribution, tailoring the prior to avoid spurious solutions. Through experiments with one or more true vortices, we reveal many aspects of the vortex inference problem. With fewer sensors than states, the estimator infers a manifold of equally possible states. Using one more sensor than states ensures that no cases of rank deficiency arise. Uncertainty grows rapidly with distance when a vortex lies outside of the vicinity of the sensors. Vortex size cannot be reliably inferred, but the position and strength of a larger vortex can be estimated with a much smaller one. In estimates of multiple vortices their individual signs are discernible because of the nonlinear coupling in the pressure. When the true vortex state is inferred from an estimator of fewer vortices, the estimate approximately aggregates the true vortices where possible.

Inferring the Interstellar Magnetic Field Direction from Energetic Neutral Atom Observations of the Heliotail

Determining the magnitude and direction of the interstellar magnetic field (B ISM) is a long-standing problem. To date, some methods to infer the direction and magnitude have utilized best-fit models to the positions of the termination shock and heliopause measured by Voyager 1 and 2. Other models use the circularity of the Interstellar Boundary Explorer (IBEX) ribbon assuming a secondary energetic neutral atom (ENA) mechanism. Previous studies have revealed that the B ISM organizes the orientation of the heliotail with respect to the solar meridian. Here we propose a new way to infer the direction of the B ISM based on ENA observations of the heliotail. IBEX observations of the heliotail have revealed high-latitude lobes of enhanced ENA flux at energies >2 keV. Analyses showed that the high-latitude lobes are nearly aligned with the solar meridian, while also exhibiting a rotation with solar cycle. We show, using steady-state solar wind conditions, that the inclination of the lobes reproduced with commonly used values for the angle (α BV ) between B ISM and the interstellar flow in the hydrogen deflection plane (40° < α BV < 60°) is inconsistent with the IBEX ENA observations. We report that 0° < α BV < 20° best replicates the heliotail lobe inclinations observed by IBEX. Additionally, our model results indicate that the variation of the solar magnetic field magnitude with solar cycle causes the longitudinal rotation of the lobes observed by IBEX by affecting the inclination of the lobes.

Development of additively manufactured cryogenic heat exchangers for hydrogen-electric aircraft propulsion

Storage of liquid hydrogen at low pressures and temperatures is advantageous in terms of overall system weight compared to high-pressure gas storage at room temperature [1]. The weight penalty for insulation of cryogenic media is typically outperforming the combined weight and volume penalty of high-pressure storage [2] [3]. For aviation applications, where light-weight and compact design is key, it is, therefore, preferred to store the propellant as liquid. In the context of hydrogen, this implies storage of the liquid between 20K and 30K, depending on tank pressure. As the fuel cell, which converts chemical energy to electrical energy, requires the hydrogen to be provided at temperatures well above the freezing level of water, hydrogen extracted from the tank must be thermally conditioned, to comply with applicable requirements [4] [5].In the presented work, a liquid hydrogen and fuel cell based electrical propulsion system for aircraft is developed, which incorporates several novel technologies and non-trivial operating conditions [6]. One major focus is the utilization of additive manufacturing enabling advanced geometric designs to enhance performance and reduce weight. However, the influence of hydrogen and cryogenic operating conditions on thermal and mechanical properties of additively manufactured materials must be assessed and accounted for in the design process.The underlying architecture of the investigated hydrogen-electric aircraft powertrain incorporates several heat exchangers with different purposes. One of the heat exchangers is tasked with transfer of heat from a liquid coolant cycle to the gaseous hydrogen in order to rise its temperature to the working level of the fuel cell (>300K). The design of the heat exchanger is based on empirical formulae for cylindrical tube bundles (pins), which enhance heat transfer on the gas side. Alternating flow planes of gaseous hydrogen and liquid coolant media are stacked to reach a number of units, which generate the desired heat transfer rates and keep the pressure loss due to friction below the defined limit. The particular arrangement of rows, columns, pin diameter or distances between individual pins is optimized to arrive at the minimum structural mass, while satisfying heat transfer and pressure drop requirements. Boundaries for this parameter optimization may originate from manufacturing limitations, like the minimum thickness of fine structures impacting the reliability of the manufacturing process. Therefore, accompanying manufacturing tests are required, to feed the optimizer with meaningful limits.After the initial optimization, computational fluid dynamics (CFD) analysis confirms the performance of the entire heat exchanger, including the intake and outflow manifold. Lastly, the lower limits of wall thicknesses may be defined by either the manufacturability in the 3d-printer or the differential pressure across the wall causing material stress. Therefore, mechanical analysis is performed, to confirm that the manufacturing limit is the actual driving limit for the minimum wall thickness.Comparison of results of the analytical method with CFD show very good agreement with deviations of average media temperature at the heat exchanger exit of less than 3% for relevant conditions. The pressure drop results deviate predictably in the order of 50%, which can be accounted for with a correction factor. CFD analysis of the entire heat exchanger shows good agreement of the flow properties in the heat exchanger core, but also demonstrate that the intake (from pipe flow into heat exchanger core) and outflow plena can contribute significantly to the overall pressure drop, depending on flow conditions and geometry.This presentation summarizes the entire development process of a heat exchanger starting with the requirements derivation based on a system analysis, via the initial design optimization based on empirical coupled thermal and fluid mechanical formulae to CFD and mechanical strength analysis of the detailed design. Close attention is paid on the additional degrees of freedom and restrictions in design gained by additive manufacturing as well as the impact of the manufacturing method on material properties especially in the context of cryogenic hydrogen.

Generating periodic vortex pairs using flexible structures

In fluid dynamics, a planar starting flow through a narrow slit gives rise to a distinctive fluid mass in the form of counter-rotating vortex pairs, which do not undergo any propulsive detachment, known as ‘pinch-off’, from the tip-attached fluid layer. Our study envisions instigating the ‘pinch-off’ phenomenon in these vortex pairs using flexible plates as the slit edges to enhance momentum transport and self-propagation. In this study, considering a flow evolution model, we show that the growth rate of such ejected vortex pair scales as proportional to the square root of time. Using flexible plates to form the slit, we unearth a critical plate flexibility case with the Cauchy number, Ca=0.01, which induces a ‘pinch-off’ of the resultant vortex pair, a phenomenon absent in the case of rigid plates. We observe a train of vortex pairs generating one after the other, and the time period closely matches the plates’ oscillation period as the plates’ oscillation frequency locks-in with the shedding frequency of the vortex pairs. The streamwise speed of the leading vortex pair varies non-monotonically with Ca, showing an increase in the speed up to Ca≈0.04, and thereafter decreased speed due to upstream propagation of small-sized vortices. The new insights into inducing and controlling vortex pair behaviours pave the way for innovative applications in fluid transport and advanced flow manipulation techniques.

Analytical solution of the Poiseuille flow of a De Kee viscoplastic fluid

We provide an explicit analytical solution of the planar Poiseuille flow of a viscoplastic fluid governed by the constitutive equation proposed by De Kee and Turcotte (1980). Formulae for the velocity and the flow rate are derived, making use of the Lambert W function. It is shown that a solution does not always exist because the flow curve is bounded from above and hence the rheological model can accommodate stresses only up to a certain limit. In fact, the flow curve reaches a peak at a critical shear rate, beyond which it exhibits a negative slope, giving rise to unstable solutions.

Dynamics of meniscus-bound particle clusters in extensional flow

Capillary suspensions are three-phase mixtures containing a solid particulate phase, a continuous liquid phase, and a second immiscible liquid forming capillary bridges between particles. Capillary suspensions are encountered in a wide array of applications including 3D printing, porous materials, and food formulations, but despite recent progress, the micromechanics of particle clusters in flow is not fully understood. In this work, we study the dynamics of meniscus-bound particle clusters in planar extensional flow using a Stokes trap, which is an automated flow control technique that allows for precise manipulation of freely suspended particles or particle clusters in flow. Focusing on the case of a two-particle doublet, we use a combination of experiments and analytical modeling to understand how particle clusters rearrange, deform, and ultimately break up in extensional flow. The time required for cluster breakup is quantified as a function of capillary number Ca and meniscus volume V. Importantly, a critical capillary number Cacrit for cluster breakup is determined using a combination of experiments and modeling. Cluster relaxation experiments are also performed by deforming particle clusters in flow, followed by flow cessation prior to breakup and observing cluster relaxation dynamics under zero-flow conditions. In all cases, experiments are complemented by an analytical model that accounts for capillary forces, lubrication forces, hydrodynamic drag forces, and hydrodynamic interactions acting on the particles. Results from the analytical models are found to be in good agreement with experiments. Overall, this work provides a new quantitative understanding of the deformation dynamics of capillary clusters in extensional flow.

Optimal wall shapes and flows for steady planar convection

We compute steady planar incompressible flows and wall shapes that maximize the rate of heat transfer ( $Nu$ ) between hot and cold walls, for a given rate of viscous dissipation by the flow ( $Pe^2$ ), with no-slip boundary conditions at the walls. In the case of no flow, we show theoretically that the optimal walls are flat and horizontal, at the minimum separation distance. We use a decoupled approximation to show that flat walls remain optimal up to a critical non-zero flow magnitude. Beyond this value, our computed optimal flows and wall shapes converge to a set of forms that are invariant except for a $Pe^{-1/3}$ scaling of horizontal lengths. The corresponding rate of heat transfer $Nu \sim Pe^{2/3}$ . We show that these scalings result from flows at the interface between the diffusion-dominated and convection-dominated regimes. We also show that the separation distance of the walls remains at its minimum value at large $Pe$ .

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

Effect of wheel speed on the microstructure and magnetic properties of Fe-3.0 wt %Si non-oriented silicon steel ultra-thin ribbons prepared by planar flow casting

Using the planar flow casting method to prepare ultra-thin silicon steel ribbons is an eco-friendly and efficient production method. However, the poor wettability between silicon steel and copper result in difficulties in formability by planar flow casting, which limits its application in production of silicon steel ultra-thin ribbons. The process parameters of planar flow casting are the key factors affecting the formability and magnetic properties of non-oriented silicon steel ribbons, in which the wheel speed determines the solidification rate of the silicon steel melt, which has an important influence on the surface quality and magnetic properties of silicon steel ultra-thin ribbons. Therefore, in this paper, the effect of wheel speed on microstructures and magnetic properties of Fe-3.0 wt %Si alloy are systematically investigated. The results indicate that as the wheel speed increases, the grain size and thickness gradually decrease. When the wheel speed is between 10 and 15 m/s, the surface of the ribbons is relatively flat. As the wheel speed increases, the surface quality of ribbons gradually deteriorates. The ribbons were in fragment with the wheel speed of 35 m/s. Compared with the ribbons before annealing, the magnetic induction B50 increased significantly and the iron losses P1.0/400 decreased sharply at 400 Hz after annealing. The magnetic induction of the ribbons after annealing with the wheel speed of 10 m/s reaches to 1.628 T as the wheel speed is 10 m/s with the corresponding iron loss is 16.171 W/kg. The lower lamination factor and micropores of the ribbons may cause the poorer magnetic properties.

Turbulent/non-turbulent interface of the turbulent boundary-layer over a spanwise-heterogeneous converging/diverging riblets rough wall

Turbulent boundary layer (TBL) flows over various spanwise-heterogeneous rough walls exhibit spanwise variations in turbulence statistics, implying modifications of the turbulent/non-turbulent interface (T/NTI). In this work, based on the datasets of TBL flows over a spanwise-alternating converging/diverging riblets wall, we investigate behavior of T/NTI, properties of ‘bubble’ and ‘drop’ that are associated with T/NTI, as well as connections between T/NTI and large-scale structures within the boundary layer. The flow datasets were obtained through stereoscopic particle image velocimetry measurements on the cross-stream plane of the TBL flow at a Reynolds number Reθ = 1.3 × 104. The T/NTI and associated ‘bubble’ and ‘drop’ are identified using a kinetic energy criterion, while the large-scale structures by a streak detection algorithm. It is observed that the T/NTI height and the occurrence of ‘bubble’ and ‘drop’ display a spanwise-heterogeneous feature, with lower T/NTI height and higher occurrence probability of ‘bubble’ over the diverging section of riblets than over the converging section of riblets. Results of conditional average show that the ‘bubble’ is associated with positive streamwise fluctuations, common-down flow and a pair of counter-rotating streamwise vortices, while the ‘drop’ with negative streamwise fluctuation, common-up flow and a pair of counter-rotating streamwise vortices. Probability density functions of the ‘bubble’ size and fractal dimensions of the T/NTI are found similar for both the riblets and smooth wall flows. Furthermore, it is observed that the large-scale low-speed structures occurring preferentially over the converging section of riblets play a role in elevating T/NTI while the large-scale high-speed ones over the diverging section of riblets lowering down T/NTI.