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The variation of polar vortex intensity is a significant factor affecting the atmospheric conditions and weather in the Northern Hemisphere (NH) and even the world. However, previous studies on the prediction of polar vortex intensity are insufficient. This paper establishes a deep learning (DL) model for multi-day and long-time intensity prediction of the polar vortex. Focusing on the winter period with the strongest polar vortex intensity, geopotential height (GPH) data of NCEP from 1948 to 2020 at 50 hPa are used to construct the dataset of polar vortex anomaly distribution images and polar vortex intensity time series. Then, we propose a new convolution neural network with long short-term memory based on Gaussian smoothing (GSCNN-LSTM) model which can not only accurately predict the variation characteristics of polar vortex intensity from day to day, but also can produce a skillful forecast for lead times of up to 20 days. Moreover, the innovative GSCNN-LSTM model has better stability and skillful correlation prediction than the traditional and some advanced spatiotemporal sequence prediction models. The accuracy of the model suggests important implications that DL methods have good applicability in forecasting the nonlinear system and vortex spatial–temporal characteristics variation in the atmosphere.

This study is focused on the propagation behavior and attenuation characteristics of a planar incident shock wave when propagating through an array of perforated plates. Based on a density-based coupled explicit algorithm, combined with a third-order MUSCL scheme and the Roe averaged flux difference splitting method, the Navier–Stokes equations and the realizable k-ε turbulence model equations describing the air flow are numerically solved. The evolution of the dynamic wave and ring vortex systems is effectively captured and analyzed. The influence of incident shock Mach number, perforated-plate porosity, and plate number on the propagation and attenuation of the shock wave was studied by using pressure- and entropy-based attenuation rates. The results indicate that the reflection, diffraction, transmission, and interference behaviors of the leading shock wave and the superimposed effects due to the trailing secondary shock wave are the main reasons that cause the intensity of the leading shock wave to experience a complex process consisting of attenuation, local enhancement, attenuation, enhancement, and attenuation. The reflected shock interactions with transmitted shock induced ring vortices and jets lead to the deformation and local intensification of the shock wave. The formation of nearly steady jets following the array of perforated plates is attributed to the generation of an oscillation chamber for the inside dynamic wave system between two perforated plates. The vorticity diffusion, merging and splitting of vortex cores dissipate the wave energy. Furthermore, the leading transmitted shock wave attenuates more significantly whereas the reflected shock wave from the first plate of the array attenuates less significantly as the shock Mach number increases. The increase in the porosity weakens the suppression effects on the leading shock wave while increases the attenuation rate of the reflected shock wave. The first perforated plate in the array plays a major role in the attenuation of the shock wave.

The development of oil and gas resources is gradually transferring to the deep sea, and the hydrate plugging of submarine pipelines at high pressures and low temperatures is becoming an important problem to ensure the safety of pipeline operations. The swirl flow is a new method to expand the boundary of hydrate safe flow. Numerical simulation of the hydrate slurry flow characteristics in a horizontal pipeline by twisted band has been carried out, and the flow of CO2 hydrate slurry in low concentration has been simulated by the RSM and DPM models. The results show that the heat transfer efficiency is also related to Re and particle concentration. The velocity distribution has the form of symmetrical double peaks, and the peaks finally merge at the center of the pipeline. Vortexes firstly appear on both sides of the edge of the twisted band, and then move to the middle part of the twisted band. Finally, the vortex center almost coincides with the velocity center. The rotation direction of hydrate particles is the same as the twisted direction of the twisted band, twist rate (Y) is smaller, Re is larger, and the symmetric vortex lines merge farther away. The initial swirl number is mainly related to Y, but not Re. The swirl flow attenuates exponentially, and its attenuation rate is mainly related to Re, but not Y. Compared with ordinary pipelines, the swirl flow can obviously improve the transportation distance of hydrate slurry.

In order to explore the mechanism during the process of the non-synchronous vibration (NSV), the flow field formation development is investigated in this paper. Based on the fluid–structure interaction method, the vibration of rotor blades is found to be in the first bending mode with a non-integral order (4.6) of the rotation speed. Referring to the constant inter blade phase angle (IBPA), the appearances of frequency-locking and phase-locking can be identified for the NSV. A periodical instability flow emerges in the tip region with the mixture of separation vortex and tip leakage flow. Due to the nonlinearities of fluid and structure, the blade vibration exhibits a limit cycle oscillation (LCO) response. The separation vortex presenting a spiral structure propagates in the annulus, indicating a pattern as modal oscillation. A flow induced vibration is initiated by the spiral vortex in the tip. The large pressure oscillation caused by the movement of the spiral vortex is regarded as a main factor for the presented NSV. As the oscillation of blade loading occurs with blade rotating pass the disturbances, the intensity of the reverse leakage flow in adjacent channels also plays a crucial role in the blade vibration.

In order to explore the inducing factors and mechanism of the non-synchronous vibration, the flow field structure and its formation mechanism in the non-synchronous vibration state of a high speed turbocompressor are discussed in this paper, based on the fluid&ndash, structure interaction method. The predicted frequencies fBV (4.4EO), fAR (9.6EO) in the field have a good correspondence with the experimental data, which verify the reliability and accuracy of the numerical method. The results indicate that, under a deviation in the adjustment of inlet guide vane (IGV), the disturbances of pressure in the tip diffuse upstream and downstream, and maintain the corresponding relationship with the non-synchronous vibration frequency of the blade. An instability flow that developed at the tip region of 90% span emerged due to interactions among the incoming main flow, the axial separation backflow, and the tip leakage vortices. The separation vortices in the blade passage mixed up with the tip leakage flow reverse at the trailing edge of blade tip, presenting a spiral vortex structure which flows upstream to the leading edge of the adjacent blade. The disturbances of the spiral vortexes emerge to rotate at 54.5% of the rotor speed in the same rotating direction as a modal oscillation. The blade vibration in the turbocompressor is found to be related to the unsteadiness of the tip flow. The large pressure oscillation caused by the movement of the spiral vortex is regarded as the one of the main drivers for the non-synchronous vibration for the present turbocompressor, besides the deviation in the adjustment of IGV.

In order to protect the vulnerable turbine components from extreme high temperature, coolant flow is introduced from the compressor to the disk cavity, inevitably interacting with the main flow. This paper describes an experimental investigation of the interaction between the main flow and the purge flow in a low-speed turbine cascade with three purge flow rates, Cm = 0, Cm = 1%, and Cm = 2%. In order to study the effect of the interaction between the main flow and the purge flow on the secondary flows, a Rortex method developed by Liu Chaoquan is introduced to identify the vortex in the flow field. In the meantime, a method to calculate the mean entropy production rate based on the particle image velocimetry (PIV) result is adopted to investigate the flow loss. The PIV result indicates that the purge flow has a prominent impact on the flow field of the cascade passage, changing the velocity distribution that induces a local blockage area. The results of vortex identification show that the purge flow promotes the generation of the passage vortex near the suction side. In addition, the purge flow makes the passage vortex migrate to the tip wall direction, enlarging the region affected by the secondary flow. The mean entropy production (MEP) result shows that the flow loss is mainly caused by the passage vortex. The coincidence of the high-MEP region and the location of the passage vortex indicates that the purge flow increases the secondary flow loss by affecting the formation and the migration of the passage vortex.

To investigate the influence of the change of tip clearance size on the control effect of the endwall suction, the effects of endwall suction on the aerodynamic performance of the axial compressor cascade were studied numerically. Three tip clearance sizes of 0.5% h, 1.0% h, and 2.0% h (h is the blade height) were mainly considered. The results show that the endwall suction scheme whose coverage range was 8&ndash, 33% axial chord can reduce the leakage flow and improve the aerodynamic performance by directly influencing the structure of tip leakage vortex. The overall total pressure loss coefficients of the three clearance size schemes at 0&deg, angle of incidence with 0.4 inlet Mach number are reduced by about 10.3%, 10.8%, and 6.0%, respectively, at the suction flow rate of 0.7%. Under the same suction flow rate, the onset position of the tip leakage vortex of the cascade with small clearance is shifted from the 15% of the axial chord length of original to the 48% of the axial chord length, which with large clearance is nearly no changed. The leakage flow rate and the distance from the leakage vortex to the suction slot are the main reasons for the different control effect of the endwall suction under different tip clearance sizes. The difference of the spanwise distribution of flow field parameters may also cause the difference of flow control effect.

Beyond the usual ferromagnetic and paramagnetic phases present in spin systems, the usual q-state clock model presents an intermediate vortex state when the number of possible orientations q for the system is greater than or equal to 5. Such vortex states give rise to the Berezinskii-Kosterlitz-Thouless (BKT) phase present up to the XY model in the limit q→∞. Based on information theory, we present here an analysis of the classical order parameters plus new short-range parameters defined here. Thus, we show that even using the first nearest neighbors spin-spin correlations only, it is possible to distinguish the two transitions presented by this system for q greater than or equal to 5. Moreover, the appearance at relatively low temperature and disappearance of the BKT phase at a rather fix higher temperature is univocally determined by the short-range interactions recognized by the information content of classical and new parameters.

The natural gas hydrate plugging problems in the mixed pipeline are becoming more and more serious. The hydrate plugging has gradually become an important problem to ensure the safety of pipeline operation. The deposition and heat transfer characteristics of natural gas hydrate particles in the spiral flow pipeline have been studied. The DPM model (discrete phase model) was used to simulate the motion of solid particles, which was used to simulate the complex spiral flow characteristics of hydrate in the pipeline with a long twisted band. The deposition and heat transfer characteristics of gas hydrate particles in the spiral flow pipeline were studied. The velocity distribution, pressure drop distribution, heat transfer characteristics, and particle settling characteristics in the pipeline were investigated. The numerical results showed that compared with the straight flow without a long twisted band, two obvious eddies are formed in the flow field with a long twisted band, and the velocities are maximum at the center of the vortices. Along the direction of the pipeline, the two vortices move toward the pipe wall from near the twisted band, which can effectively carry the hydrate particles deposited on the wall. With the same Reynolds number, the twisted rate was greater, the spiral strength was weaker, the tangential velocity was smaller, and the pressure drop was smaller. Therefore, the pressure loss can be reduced as much as possible with effect of the spiral flow. In a straight light flow, the Nusselt number is in a parabolic shape with the opening downwards. At the center of the pipe, the Nusselt number gradually decreased toward the pipe wall at the maximum, and at the near wall, the attenuation gradient of the Nu number was large. For spiral flow, the curve presented by the Nusselt number was a trough at the center of the pipe and a peak at 1/2 of the pipe diameter. With the reduction of twist rate, the Nusselt number becomes larger. Therefore, the spiral flow can make the temperature distribution more even and prevent the large temperature difference, resulting in the mass formation of hydrate particles in the pipeline wall. Spiral flow has a good carrying effect. Under the same condition, the spiral flow carried hydrate particles at a distance about 3–4 times farther than that of the straight flow.

The possibilities of applying the pure Lagrangian vortex methods of computational fluid dynamics to viscous incompressible flow simulations are considered in relation to various problem formulations. The modification of vortex methods&mdash, the Viscous Vortex Domain method&mdash, is used which is implemented in the VM2D code developed by the authors. Problems of flow simulation around airfoils with different shapes at various Reynolds numbers are considered: the Blasius problem, the flow around circular cylinders at different Reynolds numbers, the flow around a wing airfoil at the Reynolds numbers 104 and 105, the flow around two closely spaced circular cylinders and the flow around rectangular airfoils with a different chord to the thickness ratio. In addition, the problem of the internal flow modeling in the channel with a backward-facing step is considered. To store the results of the calculations, the POD technique is used, which, in addition, allows one to investigate the structure of the flow and obtain some additional information about the properties of flow regimes.

There are some inclined jet holes in the cooling structure of the leading edge region of gas turbine blades. In order to improve the cooling effect of traditional round holes, this paper proposes to replace the round holes with threaded holes, and studies the complex flow and heat transfer performance of the swirling impinging jet (SIJ) issuing from the 45&deg, threaded holes in the inclined condition by numerical simulation. The influencing factors include jet inclination angle &alpha, (45&deg, &ndash, 90&deg, ), jet-to-plate distance (H/d = 2, 4, 6), and Reynolds number (6000&ndash, 24,000). The results show that the inclination angle and jet-to-plate distance have a great influence on the size, shape, and position of vortices in the jet space, while the Reynolds number has little effect on the vortices. In the inclined state, the impinging cooling effect of the swirling impinging jet is better than that of the circular impinging jet (CIJ), both heat transfer coefficients will degrade significantly when the inclination angle is 45&deg, When the inclination angle is greater than 45&deg, compared with the round hole, the enhanced heat transfer region for the swirling jet is in the region of r/d &lt, 3, while both of the Nusselt numbers in the wall jet region are weak, with a value of just 20. At the same time, with the increasing of the inclination angle (&alpha, &gt, 45&deg, ), the average Nusselt number on target surface holds a constant value. Under the inclined conditions, the heat transfer coefficient on the target surface for the swirling jet is increased totally with the increasing of the Re, but when the Re is larger than 18,000, the rate of enhanced heat transfer gradually weakens.

The intent of shielding functions in delayed detached-eddy simulation methods (DDES) is to preserve the wall boundary layers as Reynolds-averaged Navier–Strokes (RANS) mode, avoiding possible modeled stress depletion (MSD) or even unphysical separation due to grid refinement. An entropy function fs is introduced to construct a DDES formulation for the k-ω shear stress transport (SST) model, whose performance is extensively examined on a range of attached and separated flows (flat-plate flow, circular cylinder flow, and supersonic cavity-ramp flow). Two more forms of shielding functions are also included for comparison: one that uses the blending function F2 of SST, the other which adopts the recalibrated shielding function fd_cor of the DDES version based on the Spalart-Allmaras (SA) model. In general, all of the shielding functions do not impair the vortex in fully separated flows. However, for flows including attached boundary layer, both F2 and the recalibrated fd_cor are found to be too conservative to resolve the unsteady flow content. On the other side, fs is proposed on the theory of energy dissipation and independent on from any particular turbulence model, showing the generic priority by properly balancing the need of reserving the RANS modeled regions for wall boundary layers and generating the unsteady turbulent structures in detached areas.

In this study; the Rayleigh–Benard convection model was established; and a great number of Benard cells with different numbered vortexes were acquired by numerical simulation. Additionally; the Benard cell with two vortexes; which appeared in the steady Benard fluid with a different Rayleigh number (abbreviated Ra); was found to display the primary characteristics of the system’s entropy production. It was found that two entropy productions; which are calculated using either linear theory or classical thermodynamic theory; are all basically consistent when the system can form a steady Benard flow in the proper range of the Rayleigh number’s parameters. Furthermore; in a steady Benard flow; the entropy productions of the system increase alongside the Ra parameters. It was also found that the difference between the two entropy productions is the driving force to drive the system to a steady state. Otherwise; through the distribution of the local entropy production of the Benard cell; two vortexes are clearly located where there is minimum local entropy production and in the borders around the cell’s areas of larger local entropy production.

Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler equations, as well as the quasi-geostrophic equations for either single-layer or two-layer flows. Optimal closure refers to a general method of reduction for Hamiltonian systems, in which macroscopic states are required to belong to a parametric family of distributions on phase space. In the case of point vortex ensembles, the macroscopic variables describe the spatially coarse-grained vorticity. Dynamical closure in terms of those macrostates is obtained by optimizing over paths in the parameter space of the reduced model subject to the constraints imposed by conserved quantities. This optimization minimizes a cost functional that quantifies the rate of information loss due to model reduction, meaning that an optimal path represents a macroscopic evolution that is most compatible with the microscopic dynamics in an information-theoretic sense. A near-equilibrium linearization of this method is used to derive dissipative equations for the low-order spatial moments of ensembles of point vortices in the plane. These severely reduced models describe the late-stage evolution of isolated coherent structures in two-dimensional and geostrophic turbulence. For single-layer dynamics, they approximate the relaxation of initially distorted structures toward axisymmetric equilibrium states. For two-layer dynamics, they predict the rate of energy transfer in baroclinically perturbed structures returning to stable barotropic states. Comparisons against direct numerical simulations of the fully-resolved many-vortex dynamics validate the predictive capacity of these reduced models.

Maximum entropy inference can be used to find equations for the critical currents (Jc) in a type II superconductor as a function of temperature, applied magnetic field, and angle of the applied field, θ or φ . This approach provides an understanding of how the macroscopic critical currents arise from averaging over different sources of vortex pinning. The dependence of critical currents on temperature and magnetic field can be derived with logarithmic constraints and accord with expressions which have been widely used with empirical justification since the first development of technical superconductors. In this paper we provide a physical interpretation of the constraints leading to the distributions for Jc(T) and Jc(B), and discuss the implications for experimental data analysis. We expand the maximum entropy analysis of angular Jc data to encompass samples which have correlated defects at arbitrary angles to the crystal axes giving both symmetric and asymmetric peaks and samples which show vortex channeling behavior. The distributions for angular data are derived using combinations of first, second or fourth order constraints on cot θ or cot φ . We discuss why these distributions apply whether or not correlated defects are aligned with the crystal axes and thereby provide a unified description of critical currents in superconductors. For J//B we discuss what the maximum entropy equations imply about the vortex geometry.

This article presents a comparison of the entropy production in a laminar and transitional boundary layer flow with the spectral entropy produced in a region of instability induced by an imposed periodic disturbance. The objective of the study is exploratory in nature by computing a boundary-layer environment with well-established computer techniques and comparing the predictions of the maximum rate of entropy production in the wall shear layer with the deterministic prediction of the spectral entropy growth within an inceptive instability in the inner region of the upstream boundary-layer flow. The deterministic values of the spectral entropy within the instability are brought into agreement with the computed rate of entropy production inversely along the shear flow with the assumption that the instability is of a span-wise vortex form and that the spectral entropy components are transported into the wall shear layer by vortex down sweep and are processed into thermodynamic entropy in the boundary-layer wall region.

Energy and exergy characteristics of a square cylinder (SC) in confined flow are investigated computationally by numerically handling the steady-state continuity, Navier-Stokes and energy equations in the Reynolds number range of Re = 10–50, where the blockage ratio (β = B/H) is kept constant at the high level of β = 0.8. Computations indicated for the upstream region that, the mean non-dimensional streamwise (u/Uo) and spanwise (v/Uo) velocities attain the values of u/Uo = 0.840®0.879 and v/Uo = 0.236®0.386 (Re = 10®50) on the front-surface of the SC, implying that Reynolds number and blockage have stronger impact on the spanwise momentum activity. It is determined that flows with high Reynolds number interact with the front-surface of the SC developing thinner thermal boundary layers and greater temperature gradients, which promotes the thermal entropy generation values as well. The strict guidance of the throat, not only resulted in the fully developed flow character, but also imposed additional cooling, such that the analysis pointed out the drop of duct wall (y = 0.025 m) non-dimensional temperature values (ζ) from ζ = 0.387®0.926 (Re = 10®50) at xth = 0 mm to ζ = 0.002®0.266 at xth = 40 mm. In the downstream region, spanwise thermal disturbances are evaluated to be most inspectable in the vortex driven region, where the temperature values show decrease trends in the spanwise direction. In the corresponding domain, exergy destruction is determined to grow with Reynolds number and decrease in the streamwise direction (xds = 0®10 mm). Besides, asymmetric entropy distributions as well were recorded due to the comprehensive mixing caused by the vortex system.

The corner separation in the high-loaded compressors deteriorates the aerodynamics and reduces the stable operating range. The flow pattern is further complicated with the interaction between the aperiodic corner separation and the periodically wake-shedding vortices. Accurate prediction of the corner separation is a challenge for the Reynolds-Averaged Navier–Stokes (RANS) method, which is based on the linear eddy-viscosity formulation. In the current work, the corner separation is investigated with the Delayed Detached Eddy Simulation (DDES) approach. DDES results agree well with the experiment and are systematically better than the RANS results, especially in the corner region where massive separation occurs. The accurate results from DDES provide a solid foundation for mechanism study. The flow structures and the distribution of Reynolds stress help reveal the process of corner separation and its interaction with the wake vortices. Before massive corner separation occurs, the hairpin-like vortex develops. The appearance of the hairpin-like vortex could be a signal of large-scale corner separation. The strong interaction between corner separation and wake vortices significantly enhances the turbulence intensity. Based on these analyses, entropy analysis is conducted from two aspects to study the losses. One aspect is the time-averaged entropy analysis, and the other is the instantaneous entropy analysis. It is found that the interaction between the passage vortex and wake vortex yields remarkable viscous losses over the 0–12% span when the corner separation has not yet been triggered; however, when the corner separation occurs, an enlarged region covering the 0–30% span is affected, and it is due to the interaction between the corner separation and wake vortices. The detailed coherent structures, local losses information and turbulence characteristics presented can provide guidance for the corner separation control and better design.

This article presents the computation of a set of control parameters for the deterministic prediction of laminar boundary-layer instabilities induced by an imposed unsteady shock interaction. The objective of the study is exploratory in nature by computing a supersonic flight environment for flow over a blunt body and the deterministic prediction of the spectral entropy rates for the boundary layer subjected to an unsteady pressure disturbance. The deterministic values for the spectral entropy rate within the instabilities are determined for each control parameter. Computational results imply that the instabilities are of a span-wise vortex form, that the maximum vertical velocity wave vector components are produced in the region nearest the wall and that extended transient coherent structures are produced in the boundary layer at a vertical location slightly below the mid-point of the boundary layer.