Local Vorticity Research Articles

Manipulation of self-organized multi-vortical states in active magnetic roller suspensions

Ensembles of active magnetic colloids demonstrate complex collective behavior and self-organization when driven out of equilibrium by external magnetic fields. The interplay between magnetic and hydrodynamic interactions often result in spontaneous self-assembly and the emergence of localized vortices in ensembles of ferromagnetic rollers. We report experimental and computational study of the self-organized multi-vortical state in ensembles of magnetic rollers under the imposed external confining potential realized by patterned substrates. We explore the behavior of the system on a substrate patterned with shallow wells ordered in a lattice with square symmetry and lattice spacing smaller than the wells’ diameter. We demonstrate, that ensembles of active magnetic rollers evolve in response to changes in the geometry of the confining lattice from a globally correlated state characterized by anti-ferromagnetic vortex ordering to a state with rapidly changing particle flows and self-organized vortical states with a lattice constant larger than one of the confining pattern. Our experimental observations are accompanied by numerical simulations based on phenomenological coarse grained particle dynamics coupled to Navier–Stokes hydrodynamics in shallow water approximation. The reported results provide insights into the collective behavior of active magnetic rollers under confinement and suggest strategies for the manipulation of collective dynamic states in active magnetic liquids.

Experimental Measurements of Flow-Averaged Toroidal Vortices in Buoyancy-Dominated Rotating Cavities

Abstract The flow structures and heat transfer within rotating cavities of aero-engine axial compressors influence the thermal expansion of the rotor disks, and consequently the blade-tip clearances. To investigate the flow field at the bore and lower cavity region, experimental measurements have been acquired in an engine-representative test facility. Axial, tangential, and radial velocities were measured using a miniature five-hole probe at a range of axial and radial positions. Time-averaged results from 28 tests carried out at nondimensional parameters comparable to engine conditions: 1.3 × 104 ≤ Rez ≤ 8.2 × 104, 3.0 × 105 ≤ Reθ ≤ 3.2 × 106, 0.11 ≤ Ro ≤ 3.24, 0.14 ≤ βΔT ≤ 0.36 are presented in this paper. The axial and tangential velocity measurements conform to previous work, while the radial velocity component provides quantitative evidence of an asymmetric toroidal vortex in the cavity gap, biased toward the downstream disk. The vortex is characterized by the local vorticity and grows in strength and size as Rossby number increases above Ro = 0.34 to 1.63. The effect of βΔT on the vortex formation is negligible compared to the influence of the tangential Reynolds number as the local circulation is suppressed by the Coriolis forces at high rotational speeds. Both the tangential and radial velocity results suggest that as Ro is increased, the proportion of air that is radially ingested and expelled from a cavity decreases.

Partial tip air injection to extend the stall margin in an axial flow compressor with circumferential inlet distortion

As a typical non-axisymmetric inflow, circumferential pressure inlet distortion was experimentally investigated in an axial flow compressor. Based on the obvious decreasing trend of stall margin with the enhancement of distorted intensity, the stall mechanism under the condition of maximum distorted intensity, namely, 24.57 %, was studied in detailed. The casing static pressure over the rotor blade tip along the chord and circumferential direction were measured using a collection of dynamic transducers. Results show that under the circumferential inlet distortion condition, the pressure disturbance is always generated downstream from the distorted region along the rotational direction, and circumferentially propagates until it disappears in the upstream of the distorted region. With the continuous throttling, if the pressure disturbance that has not completely disappeared in the undistorted region enters the distorted region again, its energy will be enhanced, finally induces the stall. Using the above understanding as a foundation to apply partial tip air injection to suppress the disturbance caused by the circumferential inlet distortion, and resist its adverse effect on stall margin to ensure the safe operation of the compressor. It demonstrated that the tip air injection applied in the downstream of the distorted region can obtained the largest stall margin on the premise of the same injected momentum. For the strongest distortion case (DC (60) equals to 24.57 %), the injectors fixed downstream the distorted region can reduce the number and scale of the spike disturbances, suppress the local tip leakage vortex, and decrease the amplitude of the pressure disturbance energy, thus a maximum stall margin improvement of 3.18 % is obtained. However, tip air injection in the undistorted region cannot contribute the stall margin improvement that it leads to stronger tip leakage vortex and earlier stall inception. This study provides a guideline to design the non-axisymmetric tip air injection for circumferential inlet distortion with a help of injected mass flow and energy reduction.

Flow-induced response and wake characteristics of a flexible splitter plate attached to a circular cylinder in laminar flow

This paper reported the numerical results of the flow past a flexible splitter plate attached to the rear of a rigid circular cylinder at a low Reynolds number of 160. The finite-volume method (FVM) in OpenFOAM-9 and the finite-element method (FEM) in deal.ii are utilized to solve the fluid and solid domains of the fluid–structure interaction (FSI) issue, respectively. The effects of the plate length L/D and normalized Young's modulus E* are examined. According to the equilibrium position and bending deformation order, five response modes are identified, including the symmetry-I, symmetry-II, symmetry-III, bifurcation-I, and bifurcation-II. The amplitude of the plate-tip is enhanced as the vortex shedding frequency approaches the natural frequency. Nevertheless, the bifurcation is observed between the symmetry-I and symmetry-II modes, where the vibration amplitude sharply drops. The number of local vortices occurring along the surface of flexible plate increases with the plate length, leading to more local negative pressure regions. Consequently, the higher mode response is excited. The greater shear stress occurs at the position of small curvature radius during the plate deformation. The 2S (a pair of vortices is alternately shed per cycle) vortex shedding mode is recognized in most cases. In contrast, the P + S (a pair of vortices shedding from one side and a single vortex shedding from the other side) mode is observed in the bifurcation-II mode with a relatively large amplitude. Due to the deflection, the wake flow becomes asymmetrical with a significant elongation of the recirculation region. Four interaction behaviors between the boundary layers and the plate are identified. The significant reduction of hydrodynamic forces is achieved when the flexible plate experiences the bifurcation.

Theoretical and numerical study on new evaluation criteria for longitudinal vortex enhanced heat transfer

The enhancement of heat transfer caused by longitudinal vortex phenomena has been a widely studied topic for a significant period in fluid mechanics and heat transfer. However, despite extensive efforts, the current understanding of longitudinal vortex flow and the involved physical mechanisms leading to enhanced heat transfer remains qualitative in nature. To unveil the physical mechanisms underlying the enhancement of convective heat transfer by longitudinal vortices, further quantitative research and in-depth discussions are necessary. By performing detailed derivations and proofs of the equations, this study aims to further understand the relationship between local vortex variations and heat transfer performance. The results indicate that the presence of longitudinal vortices alters the gradient of the convective term and ultimately leads to enhanced heat transfer performance. Based on the derived results, corresponding metrics have been proposed to quantitatively analyze the degree of heat transfer enhancement due to longitudinal vortices. This proposed quantitative analysis metric has been applied to evaluate the heat transfer performance of a cross-wavy primary surface heat exchanger, validating the reliability of the metrics. The research content and conclusions provide valuable insights for both theoretical investigations and practical engineering applications in the field of enhanced heat transfer.

Simultaneous emergence of active turbulence and odd viscosity in a colloidal chiral active system

Active fluids display collective phenomena such as active turbulence or odd viscosity, which refer to spontaneous complex and transverse flow. The simultaneous emergence of these seemingly separate phenomena is here reported in experiment for a chiral active fluid composed of a carpet of standing and spinning colloidal rods, and in simulations for synchronously rotating hard discs in a hydrodynamic explicit solvent. Experiments and simulations reveal that multi-scale eddies emerge, a hallmark of active turbulence, with a power-law decay of the kinetic-energy spectrum, a feature of self-similar dynamics. Moreover, the particles are dragged to the centre of the vortices, a telltale sign of odd viscosity. The weak compressibility of the system enables an explicit measurement of the odd viscosity in bulk via the relation between local vorticity and excess density. Our findings are relevant for the understanding of biological systems and for the design of microrobots with collective self-organized behavior.

Ensemble-based analysis of heavy rainfall–snowfall associated with mesoscale precipitation bands within an extratropical cyclone over northeastern China

This paper investigates the key synoptic-scale factors that affected the forecasting of mesoscale rainfall and snowfall and their associated uncertainties in a heavy rain–snow event in northeastern China on 18–20 November 2020, using ensemble-based sensitivity analysis based on global ensemble forecasts from the European Centre for Medium-Range Weather Forecasts. The heavy precipitation event was attributed to an extratropical cyclone and experienced two stages, with the snowfall stage having a better precipitation forecast skill than the rainfall stage. The mesoscale rainfall and snowfall were caused by a mesoscale rainband over Liaoning Province and two mesoscale snowbands over Heilongjiang Province, respectively, and they showed some differences with respect to their forecast skill and related key synoptic-scale factors contributing to the precipitation centers. The precipitation amount in the two different stages was correlated significantly with the midlevel trough and sensitive to the location and intensity of the low-level vortex (surface cyclone), and particularly the low-level jets and the associated water vapor transport. However, some differences were confirmed in the two different stages: the weaker midlevel trough and accompanying weaker low-level temperature trough in the rainfall stage were related to increased precipitation because the midlevel trough was far away from the control area, while the stronger midlevel trough and accompanying stronger low-level temperature trough were associated with increased precipitation in the snowfall stage. In addition to the synoptic-scale low-level jet (SLLJ), the precipitation in the rainfall stage was also affected by a boundary layer jet (BLJ) over the ocean, while only SLLJs were present in the snowfall stage. The uncertainty of the precipitation forecast was derived mainly from the uncertainty in the strength and location of the SLLJs and BLJ. Notably, the intensity of northeasterly winds west of the low-level vortex may affect the predictability of heavy snowfall.

Fundamental, dipole, and vortex solitons in fractional nonlinear Schrödinger equation with a parity-time-symmetric periodic potential

We investigate the existence and stability of two-dimensional (2D) solitons in the framework of the nonlinear fractional Schrödinger equation (NLFSE) with focusing nonlinearity and a parity-time (PT) symmetric periodic potential. Numerical studies reveal that the fundamental, dipole, and localized vortex solitons exist in a semi-infinite band gap. The Lévy index (α) cannot change the phase transition point of the PT-symmetric periodic potential, but it affects the existence and stability of these solitons significantly. With the growth of the Lévy index, the stability regions become markedly wider for the fundamental, dipole solitons and vortex solitons with the topological charge of 2 (S=2). But for a unit topological charge (S=1), the vortex soliton cannot maintain its stability under the usual diffraction effect (α=2). The result shows that the fractional-order diffraction helps to stabilize the vortex solitons with S=1.

To the Theory of Decaying Turbulence

We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension d>2. This solution family is equivalent to a fractal curve in complex space Cd with random steps parametrized by N Ising variables σi=±1, in addition to a rational number pq and an integer winding number r, related by ∑σi=qr. This equivalence provides a dual theory describing a strong turbulent phase of the Navier-Stokes flow in Rd space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a quantum statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size N→∞ or its chemical potential μ→0. The system with fixed N has different asymptotics at odd and even N→∞, but the limit μ→0 is well defined. The energy dissipation rate is analytically calculated as a function of μ using methods of number theory. It grows as ν/μ2 in the continuum limit μ→0, leading to anomalous dissipation at μ∝ν→0. The same method is used to compute all the local vorticity distribution, which has no continuum limit but is renormalizable in the sense that infinities can be absorbed into the redefinition of the parameters. The small perturbation of the fixed manifold satisfies the linear equation we solved in a general form. This perturbation decays as t−λ, with a continuous spectrum of indexes λ in the local limit μ→0. The spectrum is determined by a resolvent, which is represented as an infinite product of 3⊗3 matrices depending of the element of the Euler ensemble.

Obtaining Vortex Formation in Blood Flow by Particle Tracking: Echo-PV Methods and Computer Simulation

Micrometer-sized particles are widely introduced as fluid flow markers in experimental studies of convective flows. The tracks of such particles demonstrate a high contrast in the optical range and well illustrate the direction of fluid flow at local vortices. This study addresses the theoretical justification on the use of large particles for obtaining vortex phenomena and its characterization in stenotic arteries by the Echo Particle Velocimetry method. Calcite particles with an average diameter of 0.15 mm were chosen as a marker of streamlines using a medical ultrasound device. The Euler–Euler model of particle motion was applied to simulate the mechanical behavior of calcite particles and 20 µm aluminum particles. The accuracy of flow measurement at vortex regions was evaluated by computational fluid dynamics methods. The simulation results of vortex zone formation obtained by Azuma and Fukushima (1976) for aluminum particles with the use of the optical velocimetry method and calcite particles were compared. An error in determining the size of the vortex zone behind of stenosis does not exceed 5%. We concluded that the application of large-size particles for the needs of in vitro studies of local hemodynamics is possible.

The Role of Subtropical Rossby Waves in Amplifying the Divergent Circulation of the Madden–Julian Oscillation

Abstract The composite structure of the Madden–Julian oscillation (MJO) has long been known to feature pronounced Rossby gyres in the subtropical upper troposphere, whose existence can be interpreted as the forced response to convective heating anomalies in the presence of a subtropical westerly jet. The question of interest here is whether these forced gyre circulations have any subsequent effects on divergence patterns in the tropics and the Kelvin-mode component of the MJO. A nonlinear spherical shallow water model is used to investigate how the introduction of different background jet profiles affects the model’s steady-state response to an imposed MJO-like stationary thermal forcing. Results show that a stronger jet leads to a stronger Kelvin-mode response in the tropics up to a critical jet speed, along with stronger divergence anomalies in the vicinity of the forcing. To understand this behavior, additional calculations are performed in which a localized vorticity forcing is imposed in the extratropics, without any thermal forcing in the tropics. The response is once again seen to include pronounced equatorial Kelvin waves, provided the jet is of sufficient amplitude. A detailed analysis of the vorticity budget reveals that the zonal-mean zonal wind shear plays a key role in amplifying the Kelvin-mode divergent winds near the equator, with the effects of nonlinearities being of negligible importance. These results help to explain why the MJO tends to be strongest during boreal winter when the Indo-Pacific jet is typically at its strongest. Significance Statement The MJO is a planetary-scale convectively coupled equatorial disturbance that serves as a primary source of atmospheric predictability on intraseasonal time scales (30–90 days). Due to its dominance and spontaneous recurrence, the MJO has a significant global impact, influencing hurricanes in the tropics, storm tracks, and atmosphere blocking events in the midlatitudes, and even weather systems near the poles. Despite steady improvements in subseasonal-to-seasonal (S2S) forecast models, the MJO prediction skill has still not reached its maximum potential. The root of this challenge is partly due to our lack of understanding of how the MJO interacts with the background mean flow. In this work, we use a simple one-layer atmospheric model with idealized heating and vorticity sources to understand the impact of the subtropical jet on the MJO amplitude and its horizontal structure.

Kelvin–Helmholtz Instability “Tube” and “Knot” Dynamics. Part I: Expanding Observational Evidence of Occurrence and Environmental Influences

Abstract Multiple recent observations in the mesosphere have revealed large-scale Kelvin–Helmholtz instabilities (KHI) exhibiting diverse spatial features and temporal evolutions. The first event reported by Hecht et al. exhibited multiple features resembling those seen to arise in early laboratory shear-flow studies described as “tube” and “knot” (T&K) dynamics by Thorpe. The potential importance of T&K dynamics in the atmosphere, and in the oceans and other stratified and sheared fluids, is due to their accelerated turbulence transitions and elevated energy dissipation rates relative to KHI turbulence transitions occurring in their absence. Motivated by these studies, we survey recent observational evidence of multiscale Kelvin–Helmholtz instabilities throughout the atmosphere, many features of which closely resemble T&K dynamics observed in the laboratory and idealized initial modeling. These efforts will guide further modeling assessing the potential importance of these T&K dynamics in turbulence generation, energy dissipation, and mixing throughout the atmosphere and other fluids. We expect these dynamics to have implications for parameterizing mixing and transport in stratified shear flows in the atmosphere and oceans that have not been considered to date. Companion papers describe results of a multiscale gravity wave direct numerical simulation (DNS) that serendipitously exhibits a number of KHI T&K events and an idealized multiscale DNS of KHI T&K dynamics without gravity wave influences. Significance Statement Kelvin–Helmholtz instabilities (KHI) occur throughout the atmosphere and induce turbulence and mixing that need to be represented in weather prediction and other models of the atmosphere and oceans. This paper documents recent atmospheric evidence for widespread, more intense, features of KHI dynamics that arise where KH billows are initially discontinuous, misaligned, or varying along their axes. These features initiate strong local vortex interactions described as “tubes” and “knots” in early laboratory experiments, suggested by, but not recognized in, earlier atmospheric and oceanic profiling, and only recently confirmed in newer, high-resolution atmospheric imaging and idealized modeling to date.

Highly localized continuous wave optical vortex with controllable orbital angular momentum orientation and topological charge.

We report an approach to simultaneously control orbital angular momentum (OAM) orientation and topological charge in highly localized optical vortices by employing a 4π focusing system. The required continuous wave illumination field in the pupil planes is derived by superimposing the radiation pattern of only one dipole placed at the focal point of the high numerical aperture lens and the corresponding tailored spiral phase factor. The topological charge and OAM orientation of the obtained focused fields are quantitatively evaluated based on the focal field distributions calculated by the Richards-Wolf vector diffraction integration theory. Results show that the OAM of the generated optical vortices can be tailored by changing the oscillation orientation of the mimic dipole and the topological charge of the superimposed spiral phase term. The presented method may find potential applications in optical trapping, optical tweezers, light-matter interaction, etc.

Investigation on energy dissipation mechanism in a double-suction centrifugal pump based on Rortex and enstrophy

Since double-suction centrifugal pumps consume quantities of energy, revealing critical factors for energy dissipation is helpful for energy-saving design. This study aims to investigate the relationship between energy dissipation and vortex based on Rortex method in a double-suction centrifugal pump. Detached eddy simulation was applied to obtain the flow field. Enstrophy was used to present the strength of the local rigid vortex and shear. The results indicate that the local shear dominates energy dissipation in the pump. Owing to jet flows, the energy loss on blade leading edges (LE) and trailing edges (TE) were 102-103 times that of the middle region at 0.4Qd and ten times at 1.4Qd. The energy dissipation on pressure sides (PS) was ten times greater than that on suction sides (SS) at the TE, while flow separation at the middle of SS caused by wake flow increased energy dissipation to nearly ten times that of PS. Jet-wake flow near volute inlet was the dominant factor for energy dissipation at part-load, while separation flows in volute discharge was more significant at overload. The induced high local shear strength was responsible for energy dissipation. Therefore, reducing local shear is a potential energy-saving approach in pumps.

Cyclic Analysis of In-Cylinder Vortex Interactions Based on Data-Driven Detection and Characterization Framework

Abstract The complex vortex flow interactions are critical to affect the fuel–air mixing and combustion stability in direct-injection engine. However, due to the strong cyclic variations inside engine, the multiscale swirl flow characteristics with cyclic details are difficult to be sufficiently revealed. Therefore, a vortex detection and characterization framework, including physical and data-driven methods, is implemented to elucidate the cyclic vortex interaction process. In this study, a high-speed time-resolved particle image velocimetry is applied to record the spatiotemporal flow behavior under three different swirl ratio conditions. First, the presence of vortex motion is detected at each crank angle for each engine cycle. Results show that the vortex interaction processes under different swirl ratio conditions exhibit distinctive characteristics. The presence of multiple vortices and their interactions are found to trigger dramatic changes and variations in swirl flow behavior. Then, the individual-cycle analysis of the vortex interaction effects on flow characteristics is conducted. The vortex characteristics including vortex location, strength, and size are examined with cyclic detail using data-driven unsupervised clustering. Results indicate that the vortex merging is the main source inducing the vortex characteristics variations. Furthermore, the occurrence and duration of the vortex merging process are found to be closely related to the intake swirl ratio and valve lift profile. Increased swirl ratio and valve lift cause vortex to merge earlier and reduce the merging duration. This finding provides a potential idea to alleviate the cyclic variation issue by controlling the vortex merging process.

A parameter-free LES model for anisotropic mesh adaptivity

Balancing accuracy and computational cost is a challenge in the modelling of turbulent flows. A widely used method for turbulence modelling is large–eddy simulation (LES). LES allows one to describe large scale flow features at a reasonable computational cost compared to the more accurate direct numerical simulation (DNS), making it a popular choice for engineering applications. One strategy to balance accuracy and cost with LES is through the use of mesh adaptivity, which allows the degrees of freedom in a problem to be reduced by changing spatial discretisation. However, mesh adaptivity can affect accuracy when using the standard Smagorinsky LES model with an implicit filter, considering that the parameter Cs is highly dependent on the filter width, which depends on mesh resolution. This work is aimed to develop an LES model that does not require any user–defined parameters and is suitable for mesh adaptivity with implicit filter. In this study we introduce a parameter–free LES model incorporating an anisotropic eddy–viscosity formulation combined with anisotropic mesh adaptivity. In our model, the parameter Cs in the eddy–viscosity formulation of the Smagorinsky model, is replaced by a function that evaluates the relative location of turbulence fluctuations in each element with respect to the turbulence spectrum inertial range. The anisotropic formulation of the eddy–viscosity allows for the application of an appropriate filter width in different directions, improving accuracy. Additionally, the mesh adaptivity algorithm assesses the local turbulence fluctuations via local Reynolds number and vortex identification criteria. This assessment leads to the refinement of regions with higher turbulence fluctuations down to the smallest scale limit in the inertial range in the corresponding direction, and also leads to the coarsening of regions without turbulence fluctuation up to largest scale limit in the inertial range. This method is tested using a flow past a sphere test case. The results are compared both qualitatively and quantitatively to results obtained with the standard Smagorinsky model, and demonstrate the better performance of our method with lower computational cost. This allows us to simulate large Reynolds number cases and compare our quantitative results to experimental results found in the literature, emphasising that our method produces good results at reasonable computational cost.

Experimental and numerical study on explosion behavior of hydrogen-air mixture in an obstructed closed chamber

The flame evolution, flame front speed and pressure dynamics are investigated through experimental and simulation analysis. The effects of the obstacle on velocity vector field and vorticity field are analyzed. The results indicate that a rise in blockage ratio causes a rapid rise in flame front speed. The turbulent combustion, flame backflow, and overpressure are significantly enhanced as obstacle distance and blockage ratio increase. The jet flame results in a surge in flame front speed, and a momentary increase in pressure rise. The flame-vortex interaction causes strong turbulent combustion and a rapid overpressure increase. The overpressure displays regular periodic fluctuations and high-frequency oscillations with high amplitudes, which can be attributed to the dynamic and impulsive responses. The vortex results in the formation of a curled flame with high localized vorticity. The backflow flame, exhibiting an extremely high vorticity magnitude, is induced by the overall pressure gradient and flow field recirculation.

Revisiting the frozen gust assumption through the aeroacoustic scattering of wavepackets by a semi-infinite plate

This paper presents an analytic solution for the aerodynamic noise generated by a traveling wavepacket passing near the edge of a rigid semi-infinite flat plate. The solution is derived in the time domain for a wavepacket of either constant or spatially-varying wavenumber, for which novel closed-form expressions are obtained for the incident and scattered sound fields. The case of a varying wavepacket constitutes a surrogate model for turbulent flow distortions caused by the edge region and its geometry. This modeling approach permits a relaxation of the frozen gust assumption that is commonly used in the analytical prediction of trailing-edge noise, whereby the local vorticity is assumed to be unaffected by the edge. Our results shed light on the role that spatial variations of the vortical field near the trailing edge have on the incident and scattered sound contributions to the acoustic far field. In particular, we find that the wavenumber modification has a significant effect on the incident field but not on the scattered field amplitude. However, the phase difference between the incident and scattered fields depends strongly on the spatial variation in the wavepacket wavenumber, which leads to a variation in the sound level and directivity of the total pressure field.

Simulation of gas dynamics of oxygen flow and hydrodynamics of cooling water flow in tuyere tips with tangential optimized nozzles and results of their pilot tests.

The blowing mode largely determines the technical and economic indicators of BOF smelting, which was confirmed during the technological audit of the BOF shop of Azovstal Iron and Steel Works, carried out in 2021. It was found that the blowing mode of the process using an oxygen lance of the basic design was noticeably shifted from the optimal one in the direction of “hard” blowing. In a significant number of melts this led to an increase in the specific consumption of metal sheets, deterioration of lime assimilation by slag, dephosphorization and desulphurization of the metal. Taking into account that adjustment of the blowing mode by changing the working height of blowing and oxygen consumption did not provide a stable positive result, changes were made in the design of the tuyere tip. The design of the head with tangential arrangement of nozzles is proposed to “soften” the blowing of melts. The advantages and dis-advantages of oxygen lances of this type are considered. Numerical modeling of the gas dynamics of the oxygen flow and the hydrodynamics of the flow of cooling water in a tip with a tangential arrangement of nozzles has been per-formed. On the basis of simulation results, two variants of an improved design of the tips of 350-t LD converters with five (variant 1) and four (variant 2) main peripheral tangentially oriented nozzles and a central nozzle of lower throughput were developed to use them mainly in the second and first periods of the campaign according to the lining of the converters, respectively. It is shown that the design parameters of the nozzle blocks provide an oxygen jet outflow regime close to the design one in the main range of oxygen operating flow rates and a “non-separated” outflow regime with a decrease in the off-design ratio down to 0.8. The design parameters of the cooling system provide both an acceptable loss of water pressure in the head (0.9 MPa), the absence of local low-speed vortex zones of water, and a fairly high average coolant flow rate along the most heat-stressed (the lower) surface of the tip (about 4.5 m/s). As a result of industrial testing of a pilot batch of experimental heads with five main peripheral tangentially oriented nozzles, manufactured at the plant’s own repair and mechanical base, an increase in the resistance of copper tips was found to be 1.2 times, the resistance of lances to removal for cleaning from accretion was found to be 6.8 times, reduction in the specific consumption of metal charge by 0.9–5.6 kg/t, an increase in the dephosphorization and desulfurization coefficients of metal in the converter by 0.7–1.5 and 1.3–3.2%, respectively.

Polariton vortex Chern insulator [Invited

We propose a vortex Chern insulator, motivated by recent experimental demonstrations on programmable arrangements of cavity polariton vortices by [S. Alyatkin et al., arXiv, ArXiv:2207.01850 (2022)10.48550/arXiv.2207.01850 ] and [J. Wang et al, Natl. Sci. Rev. 10, Nwac096 (2022)10.1093/nsr/nwac096]. In the absence of any external fields, time-reversal symmetry is spontaneously broken through polariton condensation into structured arrangements of localized co-rotating vortices. We characterize the response of the rotating condensate lattice by calculating the spectrum of Bogoliubov elementary excitations and observe the crossing of edge-states, of opposite vorticity, connecting bands with opposite Chern numbers. The emergent topologically nontrivial energy gap stems from inherent vortex anisotropic polariton-polariton interactions and does not require any spin-orbit coupling, external magnetic fields, or elliptically polarized pump fields.