Axisymmetric Field Research Articles

Axisymmetric General Steady-State Solution for Poroelastic Media

In this paper, the axisymmetric general steady-state solution for porous media is presented. And the completeness of the P-Ns representation for the axisymmetric displacement field equation is proved directly from the equations governing the displacement field, which can be applied to homogeneous and isotropic poroelastic materials. At last, the Boussinesq general solution and Timpe general solution are obtained from P-N General Solution.

Linearized multipole solutions and their representation

The monopole solution of the Einstein vacuum field equations (Schwarzschild’s solution) in Weyl coordinates involves a metric function that can be interpreted as the gravitational potential of a bar of length 2 m with constant linear density. The question addressed in this work is whether similar representations can be constructed for Weyl solutions other than the spherically symmetric one. A new family of static solutions of the axisymmetric vacuum field equations generalizing the M–Q(1) solution (Hernández-Pastora and Martín 1993 Class. Quantum Grav.10 2581) is developed. These represent slight deviations from spherical symmetry in terms of the relativistic multipole moments (RMM) we wish the solution to contain. A Newtonian object referred to as a dumbbell can be used to describe these solutions in a simple form by means of the density of this object, since the physical properties of the relativistic solution are characterized by its behaviour. The density profile of the dumbbell, which is given in terms of the RMM of the solution, allows us to distinguish general multipole Weyl solutions from the constant-density Schwarzschild solution. The range of values of the multipole moments that generate positive-definite density profiles is also calculated. The bounds on the multipole moments that arise from this density condition are identical to those required for a well-behaved infinite-redshift surface g00 = 0.

Analysis of general multipolar images on dielectric layers for the calculation of DEP force

An axisymmetric field problem of a sphere and a multi-layered planer dielectric body is investigated based on the multipolar expansion method. First, the multipolar potential, produced by the sphere and expressed in the spherical coordinate system, is re-written in the cylindrical coordinate system as an integral of Bessel function. Then the field problem is solved with the boundary conditions at the planer interface of the dielectrics, and the obtained potential is written back to spherical harmonics, which can be regarded as “image multipoles” inside the dielectric body. The “images” influences back the “multipoles” on the sphere, and the field can be determined by solving these relations in self-consistent manner. DEP force exerted on the particle is calculated as the multipolar interaction, as well as the capacitance for the case involving a conducting sphere and a conducting plane.

Axisymmetric thermo-elasticity field in a functionally graded circular plate of transversely isotropic material

This paper presents a set of axisymmetric analytical solutions of the thermo-elasticity field induced by the external thermal load, in a heterogeneous circular plate. The plate can be either simply supported or clamped, and the properties of the transversely isotropic material are assumed to be functions of the thickness coordinate. Three typical types of thermal boundary conditions are considered and the corresponding temperature fields are determined. A direct displacement method is used to solve the governing equations for the elastic field in plate. The displacement functions pertinent to the current problem are solved by a step-by-step procedure of integration. The corresponding integral constants are determined by using the cylindrical boundary conditions in the Saint-Venant’s sense. In the present solutions, all of the material coefficients can vary independently and continuously along the thickness direction. Numerical calculations are performed to validate the present solutions and to show their applications to a heterogeneous model. The influence of the material heterogeneity is finally addressed. Since no ad hoc hypotheses on the elastic deformations of the plate are introduced, the present solution can be a nature benchmark to various plate theories and numerical codes.

On the asymptotic balance between electric and magnetic energies for hydromagnetic relativistic flows

In the equations of classical magnetohydrodynamics, the displacement current is considered vanishingly small due to low plasma velocities. For velocities comparable to the speed of light, the full relativistic electromagnetic equations must be used. In the absence of gravitational forcings and with an isotropic Ohm's law, it is proved that for poloidal magnetic field and velocity and toroidal electric field, the electric and magnetic energies tend to be equivalent in average for large times. This represents a partial extension of Cowling's theorem for axisymmetric fields.

Vapor nucleation on a wettable nanoparticle carrying a non-central discrete electric charge

We have studied thermodynamics of vapor nucleation on a spherical wettable dielectric nanoparticle carrying a discrete electric charge located at a certain distance from the particle center. New general equations for the chemical potential of a condensate molecule in the droplet around the particle, the work of the droplet formation and the droplet shape as functions of the effective radius of condensate film, and the value of an electric charge and its location with respect to the particle center have been derived analytically. These equations take into account both the effects of the non-central electric field and the disjoining pressure in the thin liquid film forming the droplet. Under the assumption of small distortion of the droplet shape in the axisymmetric electric field of non-central discrete charge from the spherical one, these equations have been simultaneously solved analytically. The obtained explicit formulas for the condensate chemical potential, the work of droplet formation, and the droplet shape have been numerically investigated for the case of the charge adsorbed below and above the surface of the particle. It has been shown that the effect of the electric field of non-central charge reveals itself in decreasing the maximum value of the condensate chemical potential in the droplet and shifting it away from the particle surface. As a result, the threshold value of the vapor supersaturation for barrierless nucleation and the activation barrier for barrier nucleation on the charged nanosized nuclei diminish in comparison with nucleation on nuclei with central charge. The effect is larger for smaller nuclei. It decreases with increase in the dielectric constant of the nuclei in the case of charge location below the particle surface.

Bubble shape under the action of electric forces

In the present paper, a study of bubble dynamics in adiabatic conditions (i.e. with no heat and mass transfer) is carried out in order to understand the fundamental physics ruling the evolution of their interface, and open the way to the comprehension of more complex heat and mass transfer issues involving them. An external electric field is applied to the system to investigate the potentiality of this technique to enhance phase separation and heat transfer. A new numerical method for EHD action on a growing bubble has been developed combining VOF and level-set methods. To experimentally validate it, well-defined and simple boundary conditions have been selected: all the forms of heat and mass transfer have been excluded from the system, and an axisymmetric electric field configuration has been chosen in order to adopt a 2-D simulation. In the experimental apparatus a steady bubble stemming from an orifice in a still fluid (FC-72) has been produced, and a dc potential up to 20kV was applied to a ring-shaped electrode coaxial with the orifice. In this way, in a first instance, all the dynamical effects have been eliminated, and a clear location of the three phase contact line, which is pinned to the orifice, has been defined. The bubble profile obtained from the experiment has been digitized and compared successfully with the outcomes of the numerical method. Furthermore, the study of the local curvature of the interface allowed the development of a new theory of the local electrical stress to be included in the capillary equation, which compares well with experimental data. Finally, the validated numerical method has been used to predict the bubble shape in the absence of gravity, in preparation of microgravity experiments.

Performance Analysis of a Coil Launcher Based on Improved CFM and Nonoverlapping Mortar FEM

Performance analysis of a coil launcher is very important for experimental research and electromagnetic optimization design. To check the effect of the improvement and analyze electromagnetic transient in a coil launcher, a field coupling circuit simulation method is introduced in this paper. Initially, the current of drive coils is calculated by the circuit model based on improved current filament method, and then the exciting current is loaded in 2-D axisymmetric field model. The field model is built based on nonoverlapping mortar finite-element method (NO-MFEM). NO-MFEM divides the whole domain into two subdomains: one contains the movable part (armature), and the other contains the source current (coils). The two subdomains are discretized independently and the two sets of meshes are nonconforming on the interface. When the movable part changes its location, it is necessary only to change the node coordinates in movable subdomains and information of mortar nodes and elements. In this paper, performance analysis of a three-stage coaxial induction coil launcher is carried out based on the proposed field-circuit method. The correspondence of the simulation results proves the validity of the field-circuit method.

Acoustic radiation force on a sphere without restriction to axisymmetric fields

The analysis presented at the previous ASA meeting related to investigation of the acoustic radiation force on a sphere embedded in a soft elastic medium with shear modulus that is several orders of magnitude smaller than its bulk modulus. The acoustic field was assumed to be axisymmetric and the spherical scatterer to be located on the axis of the acoustic beam. When one of these conditions is violated, the problem loses its symmetry. In this talk, the acoustic radiation force is considered in the more general case of nonaxisymmetric fields. The calculation is performed in Lagrangian coordinates. All acoustic fields, incident as well as scattered, depend on all three spherical coordinates. The incident and scattered waves, which include both potential and solenoidal parts, are expanded with respect to spherical harmonics. An analytical expression for the acoustic radiation force derived in this investigation may contain as many spherical harmonics as needed. In limiting cases when the scatterer is in liquid and only two modes, monopole and dipole, remain in the scattered fields, the solution for the acoustic radiation force recovers the results reported by Gor’kov [Sov. Phys. Doklady 6, 773 (1962)]. [Work supported by NIH DK070618 and EB011603.]

Finite-difference method on electrostatics field calculation in oil storage tank

This paper starts with the basic principle of Finite-Difference Method, combined with the practical application of the method, focusing on the difference scheme of Poisson equation and Laplace equation in 2D Electric Field and Axisymmetrical Field under the square grid partition. This study solves the Finite-Difference Method on electrostatics field calculation and introduces discretization on the Dirichlet Problem in oil storage tanker. The Finite-Difference Method gives the analytic solutions of the potential equations by changing the continuous field problems into discrete system. The numerical solutions of discrete points could infinitely approximate the real solution of the continuous field through discrete model.

Neutron tomography of axisymmetric flow fields in porous media

A significant problem in the study of fluid transport in porous media is the ability to visualize the structure of the flow field when moisture contents vary rapidly in space and time. Here we present a method for determining the radial and vertical saturation profiles within axisymmetric preferential flow fields using neutron radiography. Flow fields such as these are surprisingly common in nature and determining the three-dimensional structure of their wetting front region has proven difficult. In this work, the moisture profiles are determined using a simple algorithm for algebraic computed tomography, which gives the three-dimensional structure of the moisture profile with a temporal resolution that is limited only by the desired noise level. The algorithm presented can be translated to radiography done using X-rays or light and is applicable to any rotationally symmetric object.

Analysis of pavement response to subsurface deformations

The paper deals with modeling the response of pavement systems to subsurface deformations. An analytic formulation is developed in the context of layered elastic theory wherein the bottom boundary is distorted in a prescribed manner – forcing the medium to deform. In the basic case considered, an axisymmetric displacement field is imposed, consisting of vertical and radial components. A version of the model, dealing with a single elastic layer deformed only in the vertical direction (with frictionless bottom), is parametrically interrogated to study the influence of layer thickness and modulus on the resulting surface profile and vertical contact stresses. Furthermore, it is shown that by spatially superposing several axisymmetric solutions, general displacement shapes can be reproduced and analyzed. Such a scheme is demonstrated in an inverse type of analysis to a case study dealing with a sagging runway; using measured surface elevations, an attempt is made to backcalculate subsurface deformations and stress changes at the bottom interface of the structure.

Numerical Analysis of Levitation Forces Dynamic Behavior in the HTS-Magnet Levitation System

t is important to simulate the levitation force and its relaxation with time for the designers in the process of designing a HTS (high temperature superconductor)-magnet levitation bearing. In this paper, FEM (finite element method) based on HTSs critical-state model using H formulation was introduced. In the zero field condition, the process of magnetization of a cylindrical HTS bulk was simulated. The result showed that, current would be induced when HTS bulk was put in the external magnetic field, and the induced current tried to prevent the change of the magnetic field in the HTS bulk. When the external field disappeared, HTS bulk trapped some of the field and the bulk was magnetized. HTS-magnet levitation models were built in both the axisymmetric field and the plane field. Forces and their relaxations with time were calculated. In the HTS-magnet levitation system, force faded with time and faded slower as time went on. The force was bigger when the HTS bulk was put closer to the magnet and relaxed a little more.

3D Stereoscopic PIV visualization of the axisymmetric conical internal wave field generated by an oscillating sphere

To date, experimental studies of internal wave velocity fields have been limited to two-dimensional investigations of planar or axisymmetric systems. Here, we present results of the first three-dimensional stereoscopic Particle Image Velocimetry (PIV) visualizations of an internal wave field. The experiments utilize the canonical arrangement of a vertically oscillating sphere, which enables rigorous comparison with recently published theoretical results. The excellent level of agreement between experiment and theory demonstrates the utility of using stereoscopic PIV to study three-dimensional internal waves. Furthermore, the ability to measure all three components of the velocity field gives an alternative perspective on the significance of harmonics generated via nonlinear processes in the vicinity of the oscillating sphere.

Buoyant Magnetic Loops Generated by Global Convective Dynamo Action

Our global 3D simulations of convection and dynamo action in a Sun-like star reveal that persistent wreaths of strong magnetism can be built within the bulk of the convention zone. Here we examine the characteristics of buoyant magnetic structures that are self-consistently created by dynamo action and turbulent convective motions in a simulation with solar stratification but rotating at three times the current solar rate. These buoyant loops originate within sections of the magnetic wreaths in which turbulent flows amplify the fields to much higher values than is possible through laminar processes. These amplified portions can rise through the convective layer by a combination of magnetic buoyancy and advection by convective giant cells, forming buoyant loops. We measure statistical trends in the polarity, twist, and tilt of these loops. Loops are shown to preferentially arise in longitudinal patches somewhat reminiscent of active longitudes in the Sun, although broader in extent. We show that the strength of the axisymmetric toroidal field is not a good predictor of the production rate for buoyant loops or the amount of magnetic flux in the loops that are produced.

Adaptation of the Fourier–Hankel method for deflection tomographic reconstruction of axisymmetric field

In this work, we describe an adaptation of Fourier-Hankel method to Abel inversion for the deflection tomographic reconstruction of axisymmetric temperature field. This technique is compared with existing methods to test the accuracy and error propagation using simulated Moiré stripes of natural convection flow above a heated horizontal disk in air. Simpson's 1/3rd rule and one-point and two-point formulas are used in this comparison. The results showed that the proposed technique for Abel inversion is accurate and has the powerful capacity to control the smoothing degree of noise in the inversion process.

Discussion of Direct Numerical Simulation Method for Supercritical Carbon Dioxide Jet Flow

A kind of direct numerical simulation method suitable for supercritical carbon dioxide jet flow has been discussed in this paper. The form of dimensionless nonconservative compressible Navier-Stokes equations in a two-dimensional cartesian coordinate system is derived in detail. High accurate finite difference compact schemes based on non-uniform grid system are introduced to solve the equations. The simulation results of the three vortex pairing phenomenon of plane mixing layer and a compressible axisymmetric jet flow field show that the discussed numerical simulation method is feasible to calculate the supercritical carbon dioxide jet fluid. And it is found that the difficulties of splitting the convective terms in conservation Navier-Stokes equations, which are brought by the supercritical carbon dioxide fluid pressure state equation, can be avoided by solving the nonconservative compressible Navier-Stokes equations.

The orientation dependence of quasar single-epoch black hole mass scaling relationships

Black hole masses are estimated for radio-loud quasars using several self-consistent scaling relationships based on emission-line widths and continuum luminosities. The emission lines used, H-beta, Mg II, and C IV, have different dependencies on orientation as estimated by radio core dominance. We compare differences in the log of black hole masses estimated from different emission lines and show that they depend on radio core dominance in the sense that core-dominated, jet-on objects have systematically smaller H-beta and Mg II determined masses compared to those from C IV, while lobe-dominated edge-on objects have systematically larger H-beta and Mg II determined masses compared to those from C IV. The effect is consistent with the H-beta line width, and to a lesser extent that of Mg II, being dependent upon orientation in the sense of a axisymmetric velocity field plus a projection effect. The size of the effect is nearly an order of magnitude in black hole mass going from one extreme orientation to the other. We find that radio spectral index is a good proxy for radio core dominance and repeating this analysis with radio spectral index yields similar results. Accounting for orientation could in principle significantly reduce the scatter in black hole mass scaling relationships, and we quantify and offer a correction for this effect cast in terms of radio core dominance and radio spectral index.

Evolution of axisymmetric weakly turbulent mixtures interacting with shock or rarefaction waves

This paper deals with the interaction of a shock or a rarefaction wave with a weakly turbulent mixture of perfect gases. Assuming weak density-velocity fluctuations, Kovasznay decomposition applies and linear theories can be used to predict the evolution of the joint spectrum of density and velocity during the interaction. In this work, the upstream spectrum is restricted to axisymmetric fields free of acoustic perturbations, in order to comply with shock tube experimental conditions. Besides, spectral anisotropy is limited to a first order spherical harmonic decomposition. With these assumptions, transfer matrices can be obtained which relate the Reynolds stresses, turbulent mass flux and density variance after interaction to their counterparts before interaction. Results are given for both shock waves and rarefaction or compression waves; they are intended to help improve one-point statistical turbulence models applied to shock tube experiments.

Self-consistent simulations of a von Kármán type dynamo in a spherical domain with metallic walls

We have performed numerical simulations of boundary-driven dynamos using a three-dimensional nonlinear magnetohydrodynamical model in a spherical shell geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into motion by the counter-rotation of the two hemispheric walls. The resulting flow is of von Kármán type, consisting of a layer of zonal velocity close to the outer wall and a secondary meridional circulation. Above a certain forcing threshold, the mean flow is unstable to non-axisymmetric motions within an equatorial belt. For fixed forcing above this threshold, we have studied the dynamo properties of this flow. The presence of a conducting outer wall is essential to the existence of a dynamo at these parameters. We have therefore studied the effect of changing the material parameters of the wall (magnetic permeability, electrical conductivity, and thickness) on the dynamo. In common with previous studies, we find that dynamos are obtained only when either the conductivity or the permeability is sufficiently large. However, we find that the effect of these two parameters on the dynamo process are different and can even compete to the detriment of the dynamo. Our self-consistent approach allow us to analyze in detail the dynamo feedback loop. The dynamos we obtain are typically dominated by an axisymmetric toroidal magnetic field and an axial dipole component. We show that the ability of the outer shear layer to produce a strong toroidal field depends critically on the presence of a conducting outer wall, which shields the fluid from the vacuum outside. The generation of the axisymmetric poloidal field, on the other hand, occurs in the equatorial belt and does not depend on the wall properties.