Axisymmetric State Research Articles

On the transitional wake past a streamwise rotating prolate spheroid

Direct numerical simulations are performed to study the behavior of the wake behind a 5:2 streamwise rotating prolate spheroid. The Reynolds number Re = 1000 under different rotational speeds over a large range of 0≤Ω≤3 is considered, where Ω is the non-dimensional rotational speed based on the freestream velocity and the volume-equivalent diameter of the prolate spheroid. By successively increasing the rotational speed, seven distinct flow regimes were identified and explored: steady state, low-speed steady rotation state, axisymmetric state, high-speed steady rotation state, twofold rotational symmetrical state (TFRS), quasi-periodic vortex shedding state (QVS), and weakly chaotic state. Among these wake regimes, the TFRS regime is reported for the first time, and it can be interpreted as an outcome of the stabilizing influence of the spheroid's rotation acting to restore the wake structure to an axisymmetric state. It is found that the rotation of the prolate spheroid has a stabilizing effect under low rotational speeds. Furthermore, the coupling mechanism between the rotational double helical structure and vortex shedding in the QVS regime has been revealed. The results of this study contribute to closing the knowledge gap regarding the wake dynamics of a streamwise rotating prolate spheroid.

ЦИЛИДРИЧЕСКАЯ ОБОЛОЧКА С ЗАПОЛНИТЕЛЕМ

In the article we will consider cylindrical shells, their definition and properties of cylindrical shells, as well as examples of their application. We will also consider methods for calculating cylindrical shells. A cylindrical shell is a geometric body formed by turning a rectangle around one of its sides. The result is a cylinder whose bases are two parallel and equal rectangles, and the side surface is a surface formed by rotating the rectangle around one of its sides. Cylindrical shells have two main elements – the base and the side surface. The bases of the cylindrical shell are parallel and equal rectangles, and the side surface is a surface formed by rotating the rectangle around one of its sides. A cylindrical shell with filling is considered. They are in an axisymmetric stress state. The case is considered when the filler has the shape of a hollow cylinder or an elastic cone. The results of calculations for each case are presented.

Capture dynamics and driving method of origami capture mechanism in orbit

This article focuses on the dynamic problem of origami capture mechanism capturing space debris in orbit. It delves into the envelope characteristics of the origami capture mechanism, analyzing the motion laws of its axisymmetric folding state. Furthermore, it establishes a kinematic model for the axisymmetric envelope of the origami capture mechanism. A rigid body dynamic model of the origami capture mechanism and a generalized torque equation for the hinge at the crease were established based on the D–H parameter method and the Lagrange method. The enveloping process of the origami capture mechanism in the microgravity environment was simulated using ADAMS software, and the accuracy of the rigid body dynamics model of the origami capture mechanism and the generalized moment equation of the hinge at the crease was verified. Using Ls-Dyna software to simulate the capture process of space debris by force-driven and displacement-driven flexible origami capture mechanisms in microgravity environments, the results show that displacement-driven origami capture mechanisms can quickly capture space debris and are suitable for capturing large-sized space debris; The force-driven origami capture mechanism can quickly complete envelope capture of space debris, suitable for capturing small-sized space debris.

Vortex breakdown in the small Mach number regimes

The effect of compressibility for flow inside the cylinder with the top rotating lid (Vogel-Escudier flow) is examined. Three-dimensional Navier–Stokes equations for compressible flow in Cartesian coordinates are used to simulate the flow using open-source OpenFOAM software. The Mach number (Ma) of the flow is varied from 0.1 to 0.3, and the Reynolds number (Re) is varied from 1000 to 5000 for a fixed aspect ratio (Γ = 2.5) of the cylinder. The flow is found to have a transition from a steady axisymmetric state to a non-axisymmetric state exhibiting multiple azimuthal waves as the Mach number and the Reynolds number are varied. The flow field changes significantly with an increase in Ma for unsteady flow at higher Re. An increase in Ma increases the side wall azimuthal instability, as found in the perturbation contour plots and time series analysis. Further, we reconstruct phase portraits to show the dynamics of the flow finally becoming chaotic as the Reynolds number is increased to 5000. Finally, we support the argument with Lyapunov exponents for the higher Re samples. The Lyapunov Exponent is found to increase with Ma.

Effects of magnetic helicity on 3D equilibria and self-organized states in KTX reversed field pinch

The reversed field pinch (RFP) is a toroidal magnetic configuration in which plasmas can spontaneously transform into different self-organized states. Among various states, the ‘quasi-single-helical’ (QSH) state has a dominant component for the magnetic field and significantly improves confinement. Many theoretical and experimental efforts have investigated the transitions among different states. This paper employs the multi-region relaxed magnetohydrodynamic model to study the properties of QSH and other states. The stepped-pressure equilibrium code (SPEC) is used to compute MHD equilibria for the Keda Torus eXperiment (KTX). The toroidal volume of KTX is partitioned into two subvolumes by an internal transport barrier. The geometry of this barrier is adjusted to achieve force balance across the interface, ensuring that the plasma in each subvolume is force-free and that magnetic helicity is conserved. By varying the parameters, we generate distinct self-organized states in KTX. Our findings highlight the crucial role of magnetic helicity in shaping these states. In states with low magnetic helicity in both subvolumes, the plasma exhibits axisymmetric behavior. With increasing core helicity, the plasma gradually transforms from an axisymmetric state to a double-axis helical state and finally to a single-helical-axis state. Elevated core magnetic helicity leads to a more pronounced dominant mode of the boundary magnetic field and a reduced core magnetic shear. This is consistent with previous experimental and numerical results in other RFP devices. We find a linear relationship between the plasma current and helicity in different self-organized states. Our findings suggest that KTX may enter the QSH state when the toroidal current reaches 0.72 MA. This study demonstrates that the stellarator equilibrium code SPEC unveils crucial RFP equilibrium properties, rendering it applicable to a broad range of RFP devices and other toroidal configurations.

Kinks on elliptical convergent shock waves in hypersonic flow

Kinks commonly appear on the convergent shock surface when an internal conical flow deviates from the axisymmetric state. In this paper, the formation mechanisms of kinks on internal conical shocks (ICSs) generated by elliptical ring wedges with typical entry aspect ratios ( $AR{\rm s}$ ) in a Mach 6 flow are revealed using a theoretical method, in which the spatial evolution of the three-dimensional elliptical ICS is converted into a temporal evolution of a two-dimensional elliptical moving shock (EMS) using the hypersonic equivalence principle. To simultaneously track the shock front of the EMS and the disturbances propagating along it, a front-disturbance tracking method (FDTM) based on geometrical shock dynamics is proposed. It is found that the shock–compression disturbances from the same family initially near the major axis catch up with the disturbance initially emitted from the major axis to form kinks on the EMS. The equivalent kink formation positions predicted by the FDTM always lag behind the real kink formation positions on the elliptical ICS because the applicability of the hypersonic equivalence principle decays as the shock strengthens along the incoming flow direction. The accuracy of the equivalent kink formation positions predicted by the FDTM gradually declines with the reduction in $AR$ , but it can be significantly improved for all $AR{\rm s}$ after a modification of the equivalent relationship using the shock angle in the major plane of the elliptical ICS, which provides a new way to solve the kinks on the elliptical ICS.

Influence of preliminary compressive deformation on the spall strength of aluminum single crystal

Spall strength is an important property of material subjected to the shock wave loading. It substantially depends on the initial microstructure and its evolution during the preliminary shock compression. By an example of aluminum single crystal, a number of random axisymmetric compressed states are examined by means of molecular dynamics (MD) simulations, different deformation modes are revealed and the spall strength is calculated during subsequent volumetric tensile tests. A domain of elastic states with the spall strength of about 9 GPa, plastically deformed (dislocation plasticity) states with the spall strength of 6–7 GPa and the states with BCC phase transformations and the spall strength in the range 6–9 GPa are revealed as the main scenarios depending on the combination of strains at preliminary compression. MD results are generalized by means of artificial neural networks (ANNs), which allow interpolation between MD-studied points and plotting of continuous dependencies.

Experimental study on post-fire mechanical properties and fracture behavior of Q690 steel

Fire is one of the most dangerous disasters for high-strength steel structures. After a fire event, the deterioration of mechanical properties of high-strength steel together with the complex stress state generated by external loading may lead to an unexpected failure or collapse of high-strength steel structures. Therefore, it is very critical to evaluate the post-fire behavior of high-strength steel considering stress state effects. This study conducted a series of tests on the Q690 steel specimens after being exposed to high temperatures ranging from 200 to 1000°C with different cooling methods including air-cooling and water-cooling methods. The tested specimens including smooth round specimens, notched round specimens, and grooved plate specimens were designed to consider the failure mode in axisymmetric stress state and plane strain state. To validate the accuracy of the test results, the mechanical properties such as yield strength, ultimate strength, elastic modulus, and ultimate strain were first compared with other test results reported in the literature. The post-fire ultimate strength under different stress states was obtained directly from the test results. Then, the post-fire equivalent plastic strain at fracture of different specimens was obtained from test data together with the finite element analysis results and analyzed under different stress triaxialities and Lode angle parameters. According to this study, an increase in stress triaxiality can result in an increase in ultimate strength but a decrease in the equivalent plastic strain at fracture for Q690 steel after fire. When the exposed temperature was not higher than 800°C, the post-fire strength of the plane strain specimen (Grooved Plane Specimen) was higher than that of the axisymmetric tension specimen (Notched Round Specimen) under a similar stress triaxiality; however, for their post-fire equivalent plastic strain at fracture, the results were opposite.

Anisotropy of turbulence at the core of the tip and hub vortices shed by a marine propeller

Large-eddy simulation on a grid consisting of 5 billion points was utilized to study the properties of turbulence at the core of the tip and hub vortices shed by a marine propeller across working conditions. Turbulence at the core of the tip vortices was found to be initially isotropic, moving towards a ‘cigar-shaped’ axisymmetric state as instability grows, dominated by turbulent fluctuations of the velocity component directed in the radial direction of the cylindrical reference frame centred at the wake axis. The break-up of the coherence of the tip vortices is instead characterized by turbulence recovering an isotropic state. This process is accelerated by growing load conditions of the propeller. In contrast, during instability of the hub vortex, turbulence at its core develops a ‘pancake-shaped’ axisymmetric state, dominated by the fluctuations of the radial and azimuthal velocities. However, at higher propeller loads turbulence at the core of the hub vortex keeps close to isotropy, thanks to a faster instability. Within both tip and hub vortices the deviations from Boussinesq's hypothesis were found very significant, providing evidence of the unsuitability of conventional turbulence modelling. At the core of the tip vortices they become especially large at their break-up and for increasing load conditions of the propeller, equivalent to more intense structures. In contrast, at the core of the hub vortex they were verified to be decreasing functions of the propeller load.

Entropy: An Inspiring Tool for Characterizing Turbulence-Combustion Interaction in Swirling Flames via Direct Numerical Simulations of Non-Premixed and Premixed Flames.

This article focuses on entropy generation in the combustion field, which serves as a useful indicator to quantify the interaction between turbulence and combustion. The study is performed on the direct numerical simulations (DNS) of high pressure non-premixed and premixed swirling flames. By analyzing the entropy generation in thermal transport, mass transport, and chemical reactions, it is found that the thermal transport, driven by the temperature gradient, plays a dominant role. The enstrophy transport analysis reveals that the responses of individual terms to combustion can be measured by the entropy: the vortex stretching and the dissipation terms increase monotonically with the increasing entropy. In high entropy regions, the turbulence behaves as the "cigar shaped" state in the non-premixed flame, while as the axisymmetric state in the premixed flame. A substantial increase in the normal Reynolds stress with the entropy is observed. This is due to the competition between two terms promoted by the entropy, i.e., the velocity-pressure gradient correlation term and the shear production term. As a result, the velocity-pressure gradient correlation tends to isotropize turbulence by transferring energy increasingly from the largest streamwise component to the other smaller normal components of Reynolds stress and is dominated by the fluctuating pressure gradient that increases along the entropy. The shear production term increases with the entropy due to the upgrading alignment of the eigenvectors of strain rate and Reynolds stress tensors.

Shielding effect of ring dislocation dipole on penny-shaped crack

Mechanical behavior of strongly crystalline materials can be significantly influenced by the internal dislocation structure and their iteration with micro crack-like defects. Thus, study on the crack-dislocation interaction problems can help to understand the failure mechanism of crystalline materials. Previous theoretical analysis have been mostly limited to plane problems, where the cracks are idealized as straight slit with infinite or zero out plane dimension and the dislocations slip along an inclined straight path starting from the crack tip. In this paper, we explore a new interaction mechanism under axisymmetric deformation state. An unconventional case of a penny-shaped crack interacts with a ring dislocation dipole is considered. Both the ring dislocation dipole and crack are modelled as axisymmetric edge dislocation loops. Solutions for the dislocation loops are obtained using the GKS based method. The mixed boundary value problem is converted into Abel integral equations, which can be solved analytically. Exact closed form solutions for the stress intensity factors (SIFs) in terms of elementary functions are obtained. Numerical studies are conducted to investigate the shielding effect of the ring dislocation dipole on the crack tip SIFs. Conditions for the dislocation to shield the crack are discussed. The present solutions can also be used as weight functions to study the axisymmetric interaction between penny shaped crack and other types of eigenstrain sources.

An analysis of failure in shear versus tension

The micromechanics of ductile failure is revisited using the voided cell model. Emphasis is laid on comparing shearing stress states with axisymmetric states. The unit cell is subjected to proportional loading and fully periodic boundary conditions. The progression of elastic unloading in the unit cell is analyzed, leading to a definition of unhomogeneous yielding. Overall strain localization is determined by evaluating “on the fly” the tangent operator using a perturbation method. The connection between unhomogeneous yielding and strain localization is thus thoroughly investigated. Other potentially critical strain measures are introduced and their relevance to failure by void coalescence or strain localization is discussed. The effects of initial porosity and strain hardening in modulating the relative ductility under tension versus shear are further examined.

Axisymmetric Stress State of an Adhesive Joint of Two Coaxial Pipes. An Improved Theory

Axisymmetric Stress State of an Adhesive Joint of Two Coaxial Pipes. An Improved Theory

ЭЛЕКТРОУПРУГИЕ СВОЙСТВА НАЧАЛЬНО-НАПРЯЖЕННОЙ ПЬЕЗОКЕРАМИКИ PZT-4 С ОДНОНАПРАВЛЕННЫМИ ТУННЕЛЬНЫМИ ПОРАМИ

Prediction results and numerical analysis of effect on effective transversal-isotropic electroelastic properties of porous piezoceramics of PZT-4 with unidirectional cylindrical (tunnel) pores of values of its initial axisymmetric stress state are presented. Effective constants have been identified: Young's and shear modules, Poisson's ratio in the transversal plane of isotropy and the "longitudinally/transverse" piezomodule of porous ceramics, which are most significantly influenced by the nature and values of its initial deformation in comparison with other practically "invariant" constants. It has been found that the "transversal" hydrostatic initial deformation of the porous ceramic has a greater effect on the effective constants of the porous ceramic than the same values of the "longitudinal" axial initial deformation.

Barotropic Instability during Eyewall Replacement

Just before making landfall in Puerto Rico, Hurricane Maria (2017) underwent a concentric eyewall cycle in which the outer convective ring appeared robust while the inner ring first distorted into an ellipse and then disintegrated. The present work offers further support for the simple interpretation of this event in terms of the non-divergent barotropic model, which serves as the basis for a linear stability analysis and for non-linear numerical simulations. For the linear stability analysis the model’s axisymmetric basic state vorticity distribution is piece-wise uniform in five regions: the eye, the inner eyewall, the moat, the outer eyewall, and the far field. The stability of such structures is investigated by solving a simple eigenvalue/eigenvector problem and, in the case of instability, the non-linear evolution into a more stable structure is simulated using the non-linear barotropic model. Three types of instability and vorticity rearrangement are identified: (1) instability across the outer ring of enhanced vorticity; (2) instability across the low vorticity moat; and (3) instability across the inner ring of enhanced vorticity. The first and third types of instability occur when the rings of enhanced vorticity are sufficiently narrow, with non-linear mixing resulting in broader and weaker vorticity rings. The second type of instability, most relevant to Hurricane Maria, occurs when the radial extent of the moat is sufficiently narrow that unstable interactions occur between the outer edge of the primary eyewall and the inner edge of the secondary eyewall. The non-linear dynamics of this type of instability distort the inner eyewall into an ellipse that splits and later recombines, resulting in a vorticity tripole. This type of instability may occur near the end of a concentric eyewall cycle.

On the Stability of Axisymmetric States in the Ginzburg–Landau Theory

On the Stability of Axisymmetric States in the Ginzburg–Landau Theory

Axisymmetric Stress State of Adhesive Joint of a Circular Patch with a Plate Weakened by a Circular Cut-out

Adhesive lap joints are widely used in modern structures. Known analytical mathematical models of the stress state of lap joints describe the joints of straight beams or cylindrical coaxial pipes. It is assumed that the stress state of these structures depends on only one coordinate. The study of the stress state of plates with defects, which are reinforced by patches, in most cases requires the use of at least two-dimensional mathematical models. In this work, it is shown that the axial symmetry of the plate, the cut-out, the patch, and the applied load makes it possible to reduce the problem to a one-dimensional problem in the polar coordinate system. An adhesive lap joint with circular symmetry is considered for the first time. The stress-strain state of the structure is described in an analytical form. Comparison of the results of calculating the stress state of the joint with the results of finite element modelling showed good adequacy of the proposed mathematical model.

Global continuation of a Vlasov model of rotating galaxies

A typical galaxy consists of a huge number of stars attracted to each other by gravity. For instance, the Milky Way has about $ 10^{11} $ stars. In the astrophysics literature such a galaxy is typically modeled by the Vlasov-Poisson system. We prove an existence theorem for axisymmetric steady states of galaxies that may rotate rapidly. Such states are given in terms of a fairly general function $ \phi $ of the particle energy and angular momentum. The set $ {\mathcal K} $ of such states form a connected set in an appropriate function space. Along the set $ {\mathcal K} $, we prove under suitable conditions that either (a) the supports of the galaxies become unbounded or (b) both the rotation speeds and the densities somewhere within the galaxy become unbounded.

Solid mechanics models in application to ophthalmology

The review presents the models on a change in the stress-strain state of the eye shell after vision correction operations and a change in intraocular pressure with the introduction of drugs into the vitreous body. All mathematical models were developed in collaboration with ophthalmologists. Mathematical models that describe the process of determining the true intraocular pressure (IOP) by applanation methods are discussed. New results in solid mechanics were obtained while studying ocular biomechanics problems. For example, the problem of the stability of a spherical shell subjected to a concentrated force and internal pressure was solved and the stability of the axisymmetric equilibrium state of annular inhomogeneous orthotropic plates under normal pressure was studied. The stress-strain states of transversely isotropic spherical and cylindrical layers subjected to internal and external pressures are discussed and the solutions obtained in the framework of the three-dimensional theory are compared with the solutions obtained by non-classical shell theories. This comparison made it possible to assess the accuracy of approximate theories.

Sources of anisotropy in the Reynolds stress tensor in the stable boundary layer

AbstractData collected by 12 sonic anemometers over the Plaine Morte Glacier (Swiss Alps) during the Snow Horizontal Arrays Turbulence Study are used to investigate sources of anisotropy in the Reynolds stress tensor for stable boundary layers. A coarse‐graining approach is applied to evaluate transfers of kinetic energy across scales, and internal gravity waves (IGWs) are detected with a suitable criterion. Both approaches are combined with a classification of anisotropy based on the barycentric map of 1 min Reynolds stress tensors. A wind‐speed threshold is found that discriminates between regimes with a different dominant topology of the Reynolds stress tensor. One‐component and isotropic states are frequent for low wind speed and strong stratification, whereas two‐component axisymmetric states dominate the high wind speed regime with strong vertical shear. Results suggest that the presence of IGWs is mostly responsible for one‐component states, and additionally influences the relative amount of kinetic and potential energy in the perturbation field. To provide supporting evidence, a complementary analysis of a clean IGW detected during a field campaign in Dumosa (Australia) is presented. This case study highlights how waves contribute to drive the Reynolds stress tensor towards the one‐component limit. Cases are shown where a linear detrending procedure may be effective in filtering out waves and avoid their spurious contributions in turbulence statistics.