Axisymmetric Field Research Articles

The Use of an Equivalent Temperature Field to Emulate an Induced Residual Stress Field in a Rotating Disk Due to Full Or Partial Rotational Autofrettage

Abstract The evaluation of equivalent temperature fields for cylindrical and spherical pressure vessels to imitate autofrettage induced residual stresses has been successfully implemented in studying crack growth in autofrettaged vessels by the finite element method. Rotational autofrettage is a recent method that can be employed for strengthening hollow disks used in many turbomachinery. The evaluation of the equivalent temperature field becomes pivotal in the performance assessment of autofrettaged cracked disks subjected to high rotational speed. In this work, an equivalent thermal loading method for emulating the residual stress field in a hollow rotating disk, induced by full or partial rotational autofrettage in a finite element analysis is suggested. An analytical, or a numerical discrete solution, evaluating the equivalent temperature field for an arbitrary axisymmetric residual stress field, induced in a rotating disk due to rotational autofrettage, is developed. This solution is implemented in a finite element analysis to emulate the original rotational autofrettage induced residual stresses in a typical rotating disk. Applying the equivalent temperature field, the residual stresses obtained in the finite element analysis, are further corroborated with the original residual stress field introduced by rotational autofrettage. It is found that the developed equivalent temperature fields excellently reproduce the residual stress fields, within less than 1%, induced by both full or partial rotational autofrettage.

Optical Magnus radiation force and torque on a dielectric layered cylinder with a spinning absorptive dielectric core.

A dielectric cylindrical shell material with an inner stationary absorptive core (or, equivalently, a concentric layered cylinder) illuminated by an axisymmetric wave field (in 2D) with arbitrary polarization will experience a time-averaged radiation force along the direction of wave propagation, whereas the transverse component vanishes as required by symmetry. Counterintuitively, the present analysis shows that when the inner absorptive core material rotates with an initial angular velocity Ω0 around its main geometrical axis, a transverse radiation force component arises (in addition to a longitudinal force) as well as an axial radiation torque component in plane waves. This phenomenon is the analog of the classical hydrodynamic Magnus effect. In this analysis, the instantaneous rest-frame theory and the modal series expansion method in cylindrical coordinates are utilized to formulate the EM/optical scattering from a cylindrical shell with arbitrary thickness, and to compute the optical radiation force and torque vector components. Particular emphases are given on the size parameter of the cylindrical shell, the layer thickness, the angular rotation of the inner absorptive core, and the polarization (TM or TE) of the incident plane waves. Numerical computations illustrate the analysis and explicate the behaviors of the longitudinal, transverse, and axial radiation force and torque components. Related applications for the optical Magnus effect in radiation force and torque investigations can benefit from the results of the present analysis in spin-optics, rotational Doppler shift for optical waves, optical tweezers, optical manipulation of elongated spinning objects, and particle rotation.

Optical Magnus effect in the photophoresis of a spinning absorptive dielectric circular cylinder.

When a stationary absorptive dielectric cylinder suspended in a gas (such as air) is illuminated by an axisymmetric wave field (such as plane waves), the transverse (T) photophoretic asymmetry factor (PAF) vanishes as required by geometrical symmetry [Appl. Opt.60, 7937 (2021) APOPAI0003-693510.1364/AO.435306]. Counter-intuitively, when the cylinder possesses an initial angular velocity Ω0 with a sufficiently small acceleration and spins around its main axis in the illuminating field of axisymmetric plane waves, it is shown here that the T-PAF (which is directly proportional to the T-photophoretic force vector component) is quantifiable, in analogy with the Magnus effect in hydrodynamics where a force perpendicular to the axis of the cylinder and to the propagation direction arises. Based upon the instantaneous rest-frame theory and the partial-wave series expansion method in cylindrical coordinates, the internal electric field of the spinning absorptive dielectric cylinder is determined and utilized to compute both the longitudinal (L) and T-PAFs. Particular emphases are given on the size parameter of the cylinder, its angular rotation, the light absorption inside its core material and the polarization (TM or TE) of the incident plane waves. The dimensionless intensity function (DIF) is also computed, which reveals quantitative information on the heated portions within the internal absorptive core material of the cylinder. Numerical computations illustrate the analysis and explicate the behaviors of the DIF and the L- and T-PAFs, which predict the emergence of the forward, neutral, and reverse optical/electromagnetic Magnus effect in the photophoresis of an absorptive dielectric cylinder and related applications in spin optics, optical tweezers, optical manipulation of elongated objects, and radiative transfer research.

数値シミュレーションで得られた上陸前の台風Faxai (1915)の強度・構造変化

A numerical simulation of Typhoon Faxai (1915), which made landfall with a central pressure of 960 hPa in the Kanto region of Japan, was conducted using a nonhydrostatic numerical model with a 1-km grid spacing. Faxai sustained a symmetric structure until the landfall and caused severe damage due to strong winds. The simulation successfully simulated the realistic track and intensity of Faxai for 48 h around landfall. The simulated intensity was strong until the time of landfall, and the spatial size of the vortex was small. The structure of the simulated Faxai, identified as having an axisymmetric flow field and eyewall, was similar to that of a welldeveloped tropical cyclone (TC) in the tropics. Around the TC center, the surface latent heat flux was over 300 W m−2 until landfall, and the vertical wind shear was less than 9 m s−1 between the 1.5- and 12.0-km altitudes, which is relatively weak at midlatitudes. The maximum potential intensity (MPI) was calculated using environmental parameters around the simulated TC. The simulated and best track TC intensities exceeded the MPI for approximately 12 h before landfall, that is, the TC was in a superintense state. The superintensity was mainly caused by the presence of supergradient wind, which, in turn, resulted from the strong intensity and axisymmetric structure of the typhoon. The simulated TC satisfies the assumptions for the formulation of the MPI during the quasi-steady state, except for the gradient wind balance, implying that the structure of a TC is similar to that of a developed TC in the tropics. The present analyses suggest that the strong intensity of Faxai results from favorable environmental conditions and vortex structure.

An Analytical Study of Creeping Flow of a Second‐Order Fluid through a Small Diameter Leaky Tube with Linearly Diminishing Absorption

This study is focused on investigating the effects of linear absorption parameter on creeping flow of a second‐order fluid through a narrow leaky tube. These flows are experienced in several biological and industrial procedures, for instance, in proximal convoluted tubule of a human kidney, in hemodialysis devices, in filtration processes of food industry, journal bearing, and slide bearing. Inertial effects are neglected due to creeping motion assumption and low Reynolds number. Langlois recursive approach method is used to linearize the governing compatibility equation and to obtain an approximate analytical solution by reverse solution method. Analytical expressions for various physically important quantities like velocity profile, bulk flow, mean pressure drop in longitudinal direction, wall shear stress, leakage flux, fractional absorption, and stream function are obtained in dimensionless form. The obtained solution shows great similarity with the already available work in the literature. Variation in flow variables with linear absorption parameter is analysed in detail. The special case of uniform absorption in creeping motion of second‐order fluid is presented in a separate section. It is noticed that velocity field, in case of uniform absorption, is independent of non‐Newtonian parameters. Therefore, it is asserted that any two dimensional axisymmetric Newtonian velocity fields is also a solution for second‐order fluids with identical boundary conditions.

New transform to project axisymmetric deflection fields along arbitrary rays

Axisymmetric tomography is used to extract quantitative information from line-of-sight measurements of gas flow and combustion fields. For instance, background-oriented schlieren (BOS) measurements are typically inverted by tomographic reconstruction to estimate the density field of a high-speed or high-temperature flow. Conventional reconstruction algorithms are based on the inverse Abel transform, which assumes that rays are parallel throughout the target object. However, camera rays are not parallel, and this discrepancy can result in significant errors in many practical imaging scenarios. We present a generalization of the Abel transform for use in tomographic reconstruction of light-ray deflections through an axisymmetric target. The new transform models the exact path of camera rays instead of assuming parallel paths, thereby improving the accuracy of estimates. We demonstrate our approach with a simulated BOS scenario in which we reconstruct noisy synthetic deflection data across a range of camera positions. Results are compared to state-of-the-art Abel-based algorithms. Reconstructions computed using the new transform are consistently more stable and accurate than conventional reconstructions.

Nonlinear dynamics of a solid particle in an acoustically excited viscoelastic fluid. I. Acoustic streaming.

An analytical theory is developed for acoustic streaming induced by an axisymmetric acoustic wave field around an isotropic solid spherical particle in a compressible viscoelastic fluid. The particle is assumed to undergo pulsation, translation, and shape deformations of all orders. The fluid motion is described by the compressible Oldroyd-B model. No restrictions are imposed on the particle size with respect to the acoustic wavelength and the viscous penetration depth. The obtained analytical solutions are used in numerical simulations. It is shown that in the general case, the streaming velocity magnitude decreases with increasing polymer viscosity. Increasing relaxation time (elasticity) of the polymer solution leads to increasing streaming velocity magnitude as long as the relaxation time remains relatively small. It is also observed that the variation of the polymer viscosity and the relaxation time can change the pattern of streamlines.

Axisymmetric Solutions in the Geomagnetic Direction Problem

The magnetic field outside the earth is in good approximation a harmonic vector field determined by its values at the earth’s surface. The direction problem seeks to determine harmonic vector fields vanishing at infinity and with the prescribed direction of the field vector at the surface. In general this type of data neither guarantees the existence nor the uniqueness of solutions of the corresponding nonlinear boundary value problem. To determine conditions for existence, to specify the non-uniqueness and to identify cases of uniqueness is of particular interest when modeling the earth’s (or any other celestial body’s) magnetic field from these data. Here we consider the case of axisymmetric harmonic fields mathbf{B} outside the sphere S^2 subset {{mathbb {R}}}^3. We introduce a rotation number {r!o}in {{mathbb {Z}}} along a meridian of S^2 for any axisymmetric Hölder continuous direction field mathbf{D}ne 0 on S^2 and, moreover, the (exact) decay order 3 le delta in {{mathbb {Z}}} of any axisymmetric harmonic field mathbf{B} at infinity. Fixing a meridional plane and in this plane {r!o}- delta +1 geqq 0 points z_n (symmetric with respect to the symmetry axis and with |z_n| > 1, n = 1,ldots ,{r!o}-delta +1), we prove the existence of an (up to a positive constant factor) unique harmonic field mathbf{B} vanishing at z_n and nowhere else, with decay order delta at infinity, and with direction mathbf{D} at S^2. The proof is based on the global solution of a nonlinear elliptic boundary value problem, which arises from a complex analytic ansatz for the axisymmetric harmonic field in the meridional plane. The coefficients of the elliptic equation are discontinuous and singular at the symmetry axis, and this requires solution techniques that are adapted to this special situation.

The Internal Structure of Mercury's Core Inferred From Magnetic Observations

AbstractPrevious models of Mercury's core magnetic field based on high altitude data from first MESSENGER flybys revealed an axisymmetric structure of the field. Here, we use low altitude MESSENGER data covering the entire mission period to construct spherical harmonic models based on various spatial norms. Although we find a dominantly axisymmetric field, our models nevertheless include detectable deviations from axisymmetry. These non‐axisymmetric features appear at high latitudes, resembling intense geomagnetic flux patches at Earth's core‐mantle boundary. Based on this core field morphology, we then attempt to infer Mercury's internal structure. More specifically, assuming that Mercury's high‐latitude non‐axisymmetric features are concentrated by downwellings at the edge of the planet's inner core tangent cylinder, and accounting for the presence of a stably stratified layer at the top of Mercury's core, we establish a relation between the inner core size and the thickness of the stratified layer. Considering plausible ranges, we propose that Mercury's inner core size is about 500–660 km, which corresponds to a stratified layer thickness of 880–500 km, respectively.

Interfacial Behavior of Particle-Laden Bubbles under Asymmetric Shear Flow.

The behavior of moving bubbles has mostly been studied in an axisymmetric flow field. To extend the knowledge to practical conditions, we investigate the interfacial and hydrodynamic properties of bubbles under asymmetric shear forces. Experiments are performed with a buoyant bubble at the tip of a capillary placed in a defined shear flow in the presence of surfactants, nanoparticles, and glass beads. The response of the interface to the surrounding asymmetric flow is measured under successive reduction of the surface area. Profile analysis tensiometry is utilized to investigate the dynamic surface tension and the surface rheology of the surfactant- and nanoparticle-laden interfaces. Microscopic particle image and tracking velocimetry are used to study the bulk flow and the interfacial mobility of the buoyant bubble. According to our results, the rotational component of the shear flow provokes an interfacial flow, which redistributes the adsorbed surfactants and particles at the interface. In the presence of NPSCs, a contiguous network of particles forms at the interface through densification of surface structures. We show that this interconnected nanoparticle network eventually stops the interfacial flow and decreases the mobility of the glass beads at the interface. The immobilization of the interface is characterized by a dimensionless number, defined as the ratio of the interfacial elasticity to bulk shear forces. This number provides an estimate of the interfacial forces required to impose interfacial immobility at a defined flow field. Our findings can serve as a basis to formulate boundary conditions for refined modeling and to predict the hydrodynamics of bubbles and droplets.

No Evidence for Time Variation in Saturn’s Internal Magnetic Field

Abstract The time variation of a planetary magnetic field can reveal important aspects of a planet's interior structure. Searching for time variation in planetary magnetic fields other than Earth has proved challenging owing to the small number of spacecraft missions flown to date, but such a detection may be possible given a sufficiently long baseline for comparison. Here we leverage 38 years of spacecraft magnetometer measurements to search for time variation in Saturn’s internal magnetic field. To isolate the possible signal of time variation, we remove a contemporary high-resolution internal field model, derived from Cassini data, as well as a best-fitting external magnetodisk field model from each of four past mission data sets: Pioneer 11 (1979), Voyager 1 (1980), Voyager 2 (1981), and Cassini Saturn Orbit Insertion (2004). We then attempt to fit the resulting signal with an axisymmetric internal field model. Overall, we find no evidence of time variation on a multidecadal timescale. Our results lend support to the existence of a stably stratified layer in Saturn and have comparative planetology implications for Jupiter’s interior structure and dynamics.

Design of simple stellarator using tilted toroidal field coils

This paper deals with the design of the stellarator field with the simple coil set. In order to realize the stellarator field by the simple coil set, tilted toroidal field coils are used for creating the rotational transform. Sixteen tilted TF coils create the small radial field and large vertical field. If the axisymmetric poloidal field coil can compensate for the larger vertical field of tilted TF coils, the stellarator field can be realized. The formation of clear and nested flux surfaces is confirmed, and the rotational transform is proportional to the tilting angle of the toroidal field coil. The main features of the magnetic field for the simple stellarator in this paper are the large mirror ripple and small helical ripple. This is a similar property to the quasi-isodynamic configuration like the Wendelstein 7-X stellarator. The collisionless orbit for the proton is studied. For a moderate tilting angle of the toroidal field coil, the confinement of the passing and trapped particles improves.

Deconvolving signals of the stretched exponential form.

A solution is presented for parametrically deconvolving an axisymmetric intrinsic field signal when it is expected to conform to the stretched exponential family of functions (SEF). Except for the Gaussian SEF, computable analytical models for the forward Abel transform of SEFs did not exist until recently. I will highlight a novel mathematical identity that has facilitated this calculation and show how to use the 2D models for the Abel transform to reconstruct the 3D signal to an accuracy of ∼10-6 (or better) under noise-free conditions (possibly even with zero error). Several deconvolution techniques have tested their reconstructions using a noise-free projection of the Gaussian. Under similar conditions, our reconstruction produces errors ∼1950 times lower than 10 other techniques; we get significantly lower errors for other SEFs as well using fewer computing resources. Additionally, unlike other methods, our approach works on unequally spaced data and does not encounter the problem of increasing errors with radii in the outer parts as seen in all other methods. I will describe applications in the imaging of diverse astrophysical and biological systems where SEFs have been used and also highlight the possibility of using the projection of SEFs as basis functions in image deconvolution algorithms.

High-temperature effect on the material constants and elastic moduli for solid rocks

Abstract Thermally coupled constitutive relations are generally used to determine material constants and elastic moduli (Young's modulus and shear modulus) of solid media. Conventional studies on this issue are mainly based on the linear temperature dependence of elastic moduli, whereas analytical difficulties are often encountered in theoretical studies on nonlinear temperature dependence, particularly at high temperatures. This study investigates the thermally coupled constitutive relations for elastic moduli and material constants using the assumption of axisymmetric fields, with applications to geologic materials (marble, limestone and granite). The Taylor power series of the Helmholtz free energy function within dimensionless temperatures could be used to develop the thermally coupled constitutive relations. The thermoelastic equivalent constitutive equations were formulated under the generalized Hooke's law. The material constants of solid rocks were determined by fitting experimental data using axisymmetric stress and strain fields at different temperatures, based on their thermomechanical properties. For these geologic materials, the resultant equivalent elastic moduli and deformations were in good agreement with those from the experimental measurements. Thermal stresses, internal moisture evaporation and internal rock compositions significantly affected the experimental results. This study provides a profound understanding of the thermally coupled constitutive relations that are associated with the thermomechanical properties of solid rocks exposed to high temperatures.

Gyroresonant Acceleration of Electrons by an Axisymmetric Transverse Electric Field

Gyroresonant Acceleration of Electrons by an Axisymmetric Transverse Electric Field

Stabilization of plasma vertical position of elongated tokamak using upper and lower triangular coils

Improvement of the vertical stability of tokamak plasma with only local coils above and below the plasma was observed for the first time. The local coils in triangular shape, named upper and lower triangular (ULT) coils, were installed in TOKASTAR-2, a tokamak-stellarator hybrid device at Nagoya University. The ULT coils generate the effective radial magnetic field BReff, which is expected to stabilize the plasma vertical position. The region of the plasma position where vertical displacement events (VDEs) did not occur was extended by applying the ULT magnetic field. Stabilization of the plasma vertical position was related to the ratio of the vertical-direction derivative of the effective radial field generated by the ULT coils, ∂BReff/∂Z, to that of the axisymmetric radial field, ∂BR/∂Z. Moreover, even when VDEs occurred in discharges with the ULT magnetic field, the VDE speed was mitigated by the effect of the ULT magnetic field; the VDE speed increased with ∂BR/∂Z, while decreased with ∂BReff/∂Z.

Weighted Energy Estimates for the Incompressible Navier–Stokes Equations and Applications to Axisymmetric Solutions Without Swirl

We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence of regular global solutions when the initial velocity is an axisymmetric vector field without swirl such that both the initial velocity and its vorticity belong to L 2 ((1 + r 2) -- $\gamma$ 2 dx), with r = x 2 1 + x 2 2 and $\gamma$ $\in$ (0, 2).

Temperature field estimation of an axisymmetric laminar flame via time-of-arrival measurements of acoustic waves, and machine learning

In this study, temperature field estimation was performed via time-of-arrival measurements of acoustic waves and using machine learning. An axisymmetric combustion field created by a McKenna burner was chosen as the measurement region. Electrical discharges served as the acoustic point source, and the acoustic travel times were measured using microphones installed along the periphery of the measurement region. In particular, acoustic waves refract under a temperature gradient, which makes it difficult to obtain an explicit analytic expression for the solution. Hence, a model that predicts the profile from the acoustic travel times was acquired through machine learning. As the number of acoustic paths with different travel times was four, the radial temperature profile was first parameterized by four variables. Then, big data of acoustic travel times corresponding to a set of variable values were produced using a simulator that calculates acoustic trajectories and the corresponding travel times. Finally, the model, in the form of the simplest artificial neural network with a single hidden layer, was trained with the generated big data. The temperature fields were obtained from the measured acoustic travel times using the model and found to match well with those measured using a thermocouple.

Research on Extended Finite Element Method for Axisymmetric Electrostatic Field Based on Liquid Nitrogen with Bubbles

In this paper, the extended finite element method (XFEM) is first applied to account for the weak discontinuity of the axisymmetric electrostatic field. Firstly, the interface between two materials in an element is described by the level set method. The enrichment function is used to modify the shape function of enrichment elements. Secondly, to illustrate the feature of the enrichment function, the distribution diagrams of enrichment functions in sub-elements are drawn. The 3D field can be simplified to an axisymmetric field, which can reduce the difficulty of calculation. Finally, models with bubbles in liquid nitrogen in the axisymmetric field are used to prove the reliability of XFEM. Compared with the conventional finite element method (CFEM), XFEM costs lower computing resources with almost the same computational accuracy.

Interfacial flow of a surfactant-laden interface under asymmetric shear flow

HypothesisThe shear stress of the axisymmetric flow field triggers a nonuniform distribution of the surfactants at the surface of a rising bubble, known as stagnant cap. The formation of the stagnant cap gives rise to Marangoni stresses that reduce the mobility of the interface, which in return reduces the rising velocity. However, the conditions in technological processes usually deviate from the linear rise of a single bubble in a quiescent unbounded liquid. Asymmetric shear can act on the bubble surface e.g. due to the vorticity in the surrounding flow, bubble–bubble interactions, or influence of the reactor wall. A different surfactant distribution at the interface is expected under asymmetric shear, which can change the hydrodynamic behavior of the interface drastically. ExperimentsHere we conduct model experiments with a bubble or a drop at the tip of a capillary placed in a defined flow field. Thereby we investigate the influence of asymmetric shear forces on the interface in the presence of surfactants. Microscopic particle tracking velocimetry is employed to measure the velocity of the surfactant-laden interface for different degrees of asymmetry in the surrounding liquid flow. FindingsWe show a direct experimental observation of the circulating flow at the interface under asymmetric shear, which prevents the formation of the typical stagnant cap. Additionally, we reveal that the interface remains mobile regardless of the surfactant concentration. Our results confirm that increasing the degree of asymmetry increases the shear forces and thus the interfacial velocity.