Two-dimensional Cylindrical Coordinates Research Articles

Thermal-magnetic coupling inhomogeneous temperature field analysis of cylindrical eddy current brakes

With the increasing requirements for safety and reliability, it is now necessary to analyze the thermal characteristics to the same extent as the electromagnetic design for eddy current brakes(ECB), because the working characteristic will be greatly influenced by temperature. In this paper, the transient thermal-magnetic coupling analysis of permanent magnet cylindrical eddy current brake, which is used as the recoil mechanism in artillery, is presented. First, the structure and working principle of this ECB are described in detail. Second, the analytical electromagnetic model is established by multilayer theory to derive the heat source of this ECB. Thirdly, the thermal-magnetic coupling model is established to calculate the dynamic inhomogeneous temperature field of the ECB. The heat conduction equation is solved in different regions with inhomogeneous internal heat source by Finite Difference method(FDM) in two-dimensional cylindrical coordinate. Finally, the validity of the proposed model is verified by commercial Finite Element software. The thermal characteristic and its effects on braking force is analyzed during working. The maximum value of temperature approximately rises by 16℃ in each firing. The braking force will decline by 8% considering temperature.

Second order symmetry-preserving conservative intersection-based remapping method in two-dimensional cylindrical coordinates

The importance of preserving physical symmetry in arbitrary Lagrangian-Eulerian (ALE) simulations is well recognized. In the past decades, first order spherical-symmetry-preserving Lagrangian and ALE methods in two-dimensional cylindrical coordinates were developed. And there are also several works about second order spherical-symmetry-preserving cell-centered Lagrangian schemes. The goal of this paper is to develop Second order spherical-symmetry-preserving intersection-based remapping method in two-dimensional cylindrical coordinates. The method is capable to preserve one-dimensional spherical symmetry when the old grid is equiangular polar mesh and the rezoning algorithm only moves points in the radial directions by the same amount for all points with the same spherical radius. The remapping method has second order accuracy almost uniformly (the accuracy drops to first order close to the revolution axis), has good properties such as conservation for mass, momentum and total energy. The symmetry-preserving property and second order accuracy of our new remapping method are proved mathematically and demonstrated by several numerical examples.

Debye Representation of Frequency Dependent Ground for LEMP Analysis With RC-FDTD

Finite-difference time-domain (FDTD) method combined with the recursive convolution technique is applied to compute lightning electromagnetic pulses (LEMP) for dispersive ground adopting Longmire and Smith (LS) model in two-dimensional cylindrical coordinates. The novelty of our study is that, to the best of our knowledge, the LEMP simulation has been realized in the time-domain for the first time by directly using the parameters of the LS dispersive soil model by treating the ground as a multipole Debye medium without using approximate techniques such as vector fitting. As a numerical example, the LEMP is simulated above and under the dispersive ground with buried rock formation, which is also modeled as the dispersive Debye medium. The performed simulations are compared at distances of 500 m, 5 km, and 50 km away from the lightning channel for both first stroke and subsequent stroke. The results show that the case of dispersive ground and the rock leads to a difference of up to 61.77% with respect to using constant electrical parameters.

Mathematical Model Represents the Effect of Flexible Endoscopy on Suspension Fluid Flow

In this manuscript, peristaltic transport induced by a sinusoidal traveling wave in the case for a viscous incompressible Newtonian fluid mixed with rigid spherical particles in the presence of a flexible inner tube, where the inner tube is also moving with a sinusoidal traveling wave of moderate amplitude is studied. The governing equations of the mixture (fluid-particle suspension) are written in two-dimensional cylindrical coordinates. The long-wavelength approximation is used to simplify the system of equations (d<<1). The velocities distribution for both fluid and particles are obtained and evaluated numerically with discussion for special cases. The flow rate, pressure drop, friction forces and shear stress at the outer and inner walls of tubes are derived and represented graphically. In the urinary system, peristalsis is due to involuntary muscular contractions of the ureter wall which drives urine from the kidneys to the bladder through the ureters. A mathematical analysis of peristaltic flow with application to the ureter in presence of flexible endoscopy (Peristaltic Endoscope) is taken as a real application in this study. Finally, conclusions of the research and recommendations for future work are discussed. The results obtained may be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.

Conservative and Spherical Symmetry Preserving Control Volume Staggered Lagrangian Scheme in Two-Dimensional Cylindrical Coordinates

Conservative and Spherical Symmetry Preserving Control Volume Staggered Lagrangian Scheme in Two-Dimensional Cylindrical Coordinates

Thermocapillary motion of a solid cylinder near a liquid–gas interface

The motion of a solid, infinitely long cylinder perpendicular to a convective liquid–gas interface due to thermocapillarity is investigated via an analytical model. If the cylinder temperature differs from the bulk temperature, a temperature gradient exists along the liquid–gas interface. This results in surface tension gradients at the liquid–gas interface, causing fluid flow around the particle, which induces propulsion. For small particles and, thus, small Péclet and Reynolds numbers, the steady-state equations for temperature and flow fields are solved exactly using two-dimensional bipolar cylindrical coordinates. The velocity of the cylinder as a function of separation distance from the liquid–gas interface is determined for the case of a constant temperature or a constant heat flux on the surface of the cylinder. A larger temperature gradient at the liquid–gas interface in the latter system leads to a larger cylinder velocity and a higher propulsion efficiency. The thermocapillary effect results in larger force on a cylinder than forces arising from other self-propulsion mechanisms.

Bidirectional Return-Stroke Model for the Calculation of Lightning Electromagnetic Fields

This article focuses on the bidirectional return-stroke propagation phenomenon in the initiation process of lightning return stroke. Different from the conventional return-stroke model, the return-stroke current waves in the bidirectional return-stroke model are considered to propagate simultaneously in both the upward and downward directions at two different speeds from the junction point, where the downward and upward leaders connect with each other. The finite-difference time-domain (FDTD) method in the two-dimensional cylindrical coordinate is employed for the calculation. From the simulation results of the bidirectional return-stroke model, it can be found that compared with the conventional return-stroke model, initial peaks will appear at the rising edges both for the vertical electric field and azimuthal magnetic field at the certain conditions. The influences of characteristic parameters, including the height of junction point, the propagation velocities of downward return strokes, and the ground conductivity, on the computed results are analyzed. To accurately reproduce the radiated electromagnetic fields, the bidirectional propagation model should be taken into consideration.

Numerical Analysis of Non-Fourier Heat Transfer in a Solid Cylinder with Dual-Phase-Lag Phenomenon

In this study, transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition. Governing equations for the model are expressed in two-dimensional cylindrical coordinates; the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method. Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model. On the contrary, thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model. Also the effect of relaxation time in dual-phase-lag model has been taken on consideration.

Hybrid numerical model of the plasma flow dynamics in open magnetic systems

The report provides a brief overview of the numerical models used to solve plasma physics problems. The necessity of using hybrid models is shown, and a hybrid model that can be used in computer modeling of plasma flows in open magnetic systems is considered in more detail. The features of using hybrid models in two-dimensional cylindrical coordinates are given. To solve the equations of particle motion, the Boris algorithm is considered and its improvement is proposed based on the analytical solution of equations at a time step. We present a number of results of numerical simulation of the interaction of plasma flows obtained on the basis of a hybrid model. The calculations were performed in relation to the conditions of laboratory experiments with laser plasma at the KI-1 facility of the ILF SB RAS and the conditions of the diamagnetic regime at the CAT facility of the INP SB RAS.

Two-Dimensional Model for Perovskite Nanorod Solar Cells: A Dark Case Study

Nanorod geometry has witnessed a massive focus in the past few years for enhancing the solar cells performance. It improves the cell efficiency because of the carrier transport perpendicular to light absorption directions. Perovskite materials, such as the methylammonium lead iodide also have attracted great attention because of the low cost, simple manufacture process, and good optical properties. These advantages of both nanorod structures and perovskite materials imply that PNSC is a very promising candidate in energy harvesting applications. This increases the demand for accurate and fast models for the analysis and for the optimization of these cells. In this article, we present an analytical model for nanorod solar cells. The model solves the semiconductor equations (Poisson's equation and continuity equations) in two-dimensional cylindrical coordinates. It is based on using the conformal mapping theory as an approximation for potential and electric field estimation. It also uses separation of variables process in solving the two-dimensional continuity equation for both radial and axial directions. The analytical model was applied on a TiO2/ perovskite / spiro-MeOTAD cell to produce the dark current. The results of this model were compared with that of a numerical finite element model and achieved good matching.

Lightning Strike to a Tall-Grounded Object: Part 2—LEMP Calculation With a Channel Approximation

Lightning electromagnetic pulse (LEMP) waveforms associated with lightning strikes to the 634-m high Tokyo Skytree are calculated by the finite-difference time-domain (FDTD) method in the two-dimensional (2-D) cylindrical coordinate. The three-dimensional (3-D) tortuous lightning channel and the tall strike object are represented by an “equivalent vertical” phased-current-source array. The current propagation speed along the equivalent vertical lighting channel is determined in two steps: first, the channel is projected on a plane including the strike object and a field observation point, and then it is converted into the straight vertical channel right above the strike object. Thus, the height-dependent lightning-current propagation speed along the equivalent channel depends on the direction of the observation point. The proposed method greatly reduces computational resources required for calculating LEMPs without deteriorating accuracy since it allows the use of the 2-D FDTD method. LEMP waveforms measured at a horizontal distance of 27, 57, and 101 km (in different directions) from the strike object are accurately reproduced by the proposed method. The results clarified that the lower region of the tortuous lightning has a large influence on the wavefront of the LEMPs at a horizontal distance ranging from 20 to 100 km from the strike point.

ECsim-CYL: Energy Conserving Semi-Implicit particle in cell simulation in axially symmetric cylindrical coordinates

Based on the previously developed Energy Conserving Semi Implicit Method (ECsim) code, we present its cylindrical implementation, called ECsim-CYL, to be used for axially symmetric problems. The main motivation for the development of the cylindrical version is to greatly improve the computational speed by utilizing cylindrical symmetry. The ECsim-CYL discretizes the field equations in two-dimensional cylindrical coordinates using the finite volume method. For the particle mover, it uses a modification of ECsim’s mover for cylindrical coordinates by keeping track of all three components of velocity vectors, while only keeping radial and axial coordinates of particle positions. In this paper, we describe the details of the algorithm used in the ECsim-CYL and present a series of tests to validate the accuracy of the code including a wave spectrum in a homogeneous plasma inside a cylindrical waveguide and free expansion of a spherical plasma ball in vacuum. The ECsim-CYL retains the stability properties of ECsim and conserves the energy within machine precision, while accurately describing the plasma behavior in the test cases.

Positivity-preserving scheme for two-dimensional advection–diffusion equations including mixed derivatives

In this work, we propose a positivity-preserving scheme for solving two-dimensional advection–diffusion equations including mixed derivative terms, in order to improve the accuracy of lower-order methods. The solution of these equations, in the absence of mixed derivatives, has been studied in detail, while positivity-preserving schemes for mixed derivative terms have received much less attention. A two-dimensional diffusion equation, for which the analytical solution is known, is solved numerically to show the applicability of the scheme. It is further applied to the Fokker–Planck collision operator in two-dimensional cylindrical coordinates under the assumption of local thermal equilibrium. For a thermal equilibration problem, it is shown that the scheme conserves particle number and energy, while the preservation of positivity is ensured and the steady-state solution is the Maxwellian distribution.

Noninvasive temperature monitoring for high intensity focused ultrasound therapy based on electrical impedance tomography

As a new treatment modality with little thermal damage and few cell metastases to surrounding normal tissues, high intensity focused ultrasound (HIFU) therapy is considered to be one of the most promising technologies for tumor therapy in the 21st century. However, noninvasive temperature monitoring for the focal region exhibits great significance of precise thermal dosage control in HIFU treatment. By combining electrical impedance measurement and HIFU, an electrical impedance tomography (EIT) based temperature monitoring method using surface voltages is proposed to reconstruct the distribution of electrical conductivity inside the focal plane on the basis of the temperature dependent electrical impedance of tissues. In theoretical study, a comprehensive system of EIT measurement during HIFU therapy is established. With the consideration of acoustic absorption in viscous tissues, three-dimensional Helmholtz equation for HIFU is simplified into two-dimensional axisymmetric cylindrical coordinates, and the characteristics of temperature rising in the focal region are derived using Pennes bio-heat transfer equation. Then, by introducing the temperature-conductivity relation into tissues, the processing methods for electrical field and surface voltage in the focal region are constructed with constant current injection from two symmetrical electrodes. In simulation study, by applying the experimental parameters of the focused transducer, the distributions of acoustic pressure and temperature are simulated at a fixed acoustic power, and then the corresponding distributions of conductivity in the focal plane are achieved at different treatment times for centric and eccentric focusing. Furthermore, with the simulations of current density and electrical potential generated by the rotating current injection from 16 pairs of symmetrical electrodes, 32×32 voltages are detected by the 32 surface electrodes placed around the focal plane of the model. In conductivity image reconstruction, the modified Newton-Raphson (MNR) algorithm is employed to conduct iterative calculation. It shows that with the increase of HIFU treatment time, the electrical conductivity in the focal region increases accordingly and reaches a maximum value in the center due to the highest acoustic pressure and the most energy accumulation. It is proved that not only the position of the focal center, but also the conductivity distribution inside the focal region can be restored accurately by the proposed EIT based reconstruction algorithm. The favorable results demonstrate the feasibility of temperature monitoring during HIFU therapy, and also provide a new method of evaluating the noninvasive efficacy and controlling the dose based on electrical impedance measurements.

Propagation Effects on the Electric Field Time Derivatives Generated by the Stepped Leaders and Return Strokes in CG Flashes

In this paper, the effects of propagation over finitely conducting ground on the characteristics of the electric-field time-derivative (dE/dt) pulses, which are generated by the stepped leaders and return strokes in cloud-to-ground (CG) flashes, are investigated. First, a finite-difference time-domain (FDTD) method in two-dimensional (2-D) cylindrical coordinates is proposed. And then, the electric fields produced by different lightning processes are calculated. The current waveform parameters of the stepped leaders are derived based on the MTLE model by trial and error, given the analytical waveform and the measured data at the International Center for Lightning Research and Testing (ICLRT) in Florida, USA. In conclusion, the results demonstrate that the characteristics of the dE/dt pulses, including the peak amplitude, the half-width time, and the 10%-90% rise time, change significantly in propagating over finitely conducting ground. Furthermore, the effects of the parameters (i.e., 10%-90% rise time and half-width time) of the lightning current waveforms on the characteristics of dE/dt pulses are also discussed. The results indicate that the 10%-90% rise time, as compared with the half-width time, has a more significant influence on the characteristics of the dE/dt pulses. Lastly, average energy spectra densities of the simulated dE/dt pulses are calculated, and for comparison purposes, spectral analysis of the data obtained by the very high frequency broadband interferometer are also presented. The theoretical results are consistent with those available experimental data.

The study of the process of evolution of the jet under outflow of water from the supercritical state through a thin nozzle

The dynamics of the water outflow from the initial supercritical state through a thin nozzle is studied. To describe the initial stage of non-stationary process outflow the system of differential equations of conservation of mass, momentum and energy in a two-dimensional cylindrical coordinates with axial symmetry is used. The spatial distribution of pressure and velocity of jet formation was received. It was established that a supersonic regime of outflow at supercritical temperature of 650 K is formed, which have a qualitative agreement for the velocity compared with the Bernoulli analytical solution and the experimental data.

Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.

Physical investigation of dynamic process of the gas-puff Z-pinch through particle-in-cell simulation

In this paper the physical model and numerical algorithm of particle-in-cell (PIC) simulation for gas-puff Z-pinch in two-dimensional cylindrical coordinates are briefly introduced. The code is also developed according to the model and algorithm. The rarefied gas-puff Z-pinch driven by a low current is simulated through the code, and some reasonable results are obtained. The results include the spatiotemporal distributions of current, electromagnetic field, particle positions and density, as well as the trailing mass and current. It is found that the simulated current reflects the plasma Z-pinch characteristics, i.e., the plasma current arrives at a minimum when the plasma enters into stagnation, and it begins to increase after the plasma has moved outwards. The simulated magnetic field agrees well with the theoretic value. The electric field force and magnetic field force experienced by electron are almost the same in magnitude, while the force acting on ion is mainly the electric field force. Firstly the electron is accelerated in the z direction and reaches a velocity, then it moves inward the axis in the same time by the Lorentz force. That causes the separation between electron and ion, and a strong electric field is produced. The produced electric field attracts the ion inward the electron. When the electrons arrive at the axis, they move inversely due to the static repellency among them, while the ions continue to move initially inwards, and later enter into stagnation, and finally collapse. The trailing mass is about 20% of the total Z-pinch plasma, and the maximum trailing current is about 7% of the driven current. In the future the code needs to develop further and realize parallel computation in order to simulate the practical Z-pinch processes by PIC simulation.

Premixed Combustion of a Fine AP/HTPB Composite Propellant Based on Detailed Chemical Kinetics

A model for Premixed Ammonium Perchlorate (AP)/Hydroxyl-terminated Polybutadiene (HTPB) combustion based on detailed chemical kinetics was established on two-dimensional cylindrical coordinates using the Vorticity-Velocity formulation, finite difference methods and several essential mathematical algorithms. This model includes both solid and condensed phase combustion mechanisms and the detailed chemical kinetics of the gas phase with 37 species and 127 reactions. Results obtained from the model, such as temperature and burning rate, match data from experiments. It is found that the model established in the current study is reliable and accurate, and the Vorticity-Velocity approach combined with finite difference methods is capable of and efficient in dealing with premixed AP/HTPB combustion.

Computational Research of Internal Temperature Distribution for Liver Tissues under Laser Irradiation

To study the effect of blood perfusion rate and air convection boundary condition upon heat transfer of liver tissues by establishing heat conduction model of liver tissues under laser irradiation.The analytical solution of the model was solved by homogenizing boundary condition and the numerical solution of the bio-heat transfer model under the two-dimensional cylindrical coordinate was calculated by the Finite Element Method (FEM).The results show that the highest temperature irradiated by laser is on the center point of the surface tissue, and decreases in the radial and axial direction, the temperature in the axial degrades more seriously than that in the radial.This study provides a theoretic bases for laser applications in medicine.