Cylindrical Coordinate System Research Articles

Advancing electromagnetic field modeling in axially anisotropic media with conformal method in 3D cylindrical coordinate systems

A conformal methodology for solving electromagnetic fields in axially anisotropic media in 3D cylindrical coordinate systems is proposed for the investigation of high-power microwave devices filled with such media. This method leverages the material properties of axially anisotropic media and employs the finite integral technique for solution. A simplified conformal algorithm is utilized for the boundaries of the computational region, extending the traditional conformal method for axially anisotropic media in 3D cylindrical coordinates. The proposed methodology is validated through simulations of TM01 and TE01 mode propagation in a circular waveguide filled with the medium. Subsequently, the method is integrated into particle-in-cell simulations, and an X-band relativistic backward wave oscillator filled with an axially anisotropic medium exhibiting azimuthal conductivity is numerically modeled. The results demonstrate that the medium with azimuthal conductivity effectively mitigates asymmetric modes in the relativistic backward wave oscillator, aligning with published literature. This study offers technical insights for research on high-power microwave devices incorporating axially anisotropic media, potentially facilitating the development of innovative microwave devices with enhanced performance characteristics.

Oscillations of a spherical particle in the presence of a flat interface separating two fluid phases

An analytical–numerical approach based on collocation techniques is introduced to examine the challenge of characterizing Stokes flow induced by a spherical particle in perpendicular motion to a plane interface that divides two semi-infinite, immiscible viscous fluid phases. The movement is examined under the conditions of low Reynolds and capillary numbers, where the interface undergoes negligible deformation. We contemplate both the rectilinear oscillations along and the rotational oscillation around an axis that is perpendicular to the interface. A comprehensive solution is formed by combining basic solutions in both cylindrical and spherical coordinate systems through superposition. Firstly, the boundary conditions at the fluid–fluid interface are fulfilled through Fourier–Bessel transforms, followed by addressing the conditions at the particle’s surface using a boundary collocation scheme. The drag force and torque coefficients, both in-phase and out-of-phase, acting on the particle are determined with satisfactory convergence across different geometric and physical parameter values. These results are illustrated through graphs and tables. We compare our results of drag force and torque coefficients with existing data in the literature, specifically for the limiting cases. The outcomes of this study highlight the substantial impact of the interface on both drag force and torque coefficients. This inquiry is driven by the necessity to enhance our comprehension of the fluid tapping mode in atomic force microscope devices, particularly when this mode involves an interface substrate with another fluid.

Numerical modelling of flow field at shaft spillways with the marguerite-shaped inlets

By decreasing the entrained air flow discharge and improving the hydraulic characteristics of vertical shaft spillways, Marguerite-shaped inlets (MSIs) can mitigate the effects of swirling flow surrounding their inlet. The hydraulic and hydrodynamic characteristics of flow around MSIs under orifice flow regime were numerically investigated, applying different geometrical parameters. This inlet configuration can decrease the strength of swirling flow and increase the flow discharge through the shaft. The finite-volume method and the re-normalisation group k–ε turbulence model were employed to solve the governing equations of motion in a cylindrical coordinate system and a two-phase air–water flow on the water free-surface. Increasing the height and length of the blades of the MSIs was found to increase the area of the barriers against swirling flow, weaken the swirling flow strength, engender a more uniform flow and lower the water free-surface level. Extremely long or high blades, however, resulted in an intense collision of the flow with the spillway and increased the water free-surface level and the swirling flow strength at the MSI.

On viscoelastic blood in a locally narrow artery with magnetic field: application of distributed-order time fractional Maxwell model

Purpose. The study of hemorheology of heterogeneous vessels is of importance for the therapy of cardiovascular diseases. The present paper aims to investigate the effects of the height parameter of the stenosis, the Reynolds number, the relaxation time and the Hartmann number on the blood flow by applying distributed order time fractional Maxwell model. Methodology. Distributed order time fractional Maxwell constitutive fluid model is used to simulate viscoelastic blood flowing in a narrowing blood vessel with uniform magnetic field. The continuity and momentum equations are established in two-dimensional cylindrical coordinate system for calculation. With vorticity-stream function method, the finite difference technique, combined with the fractional derivative L1 interpolation approximation, is utilized to obtain numerical solutions of velocity and wall shear stress. The effectiveness of the numerical method is verified. Outcomes. It reveals the choice of relaxation time in the governing equation has an influence on the results. The numerical results show that an appropriate increase of Reynolds number can reduce the possibility of vessel damage. Furthermore, when the height parameter of the stenosis increases, the damage to the vessel wall is getting serious. Besides, the wall shear stress along the blood vessel increases with the increase of the magnetic field, but the wall shear stress in the narrowest part of the blood vessel changes little.

Surface Heating Calculation of Composite Material Under the Influence of an Electron Beam on the Surface

Introduction. Modern plasma magnetic confinement systems use tungsten as a material in contact with plasma. Under the influence of high-density plasma irradiation, tungsten undergoes cracking, intense erosion, and macro-particle emission. High-temperature ceramics are considered a promising material for protective coating of plasma components, as they are resistant to thermal loads. One possible solution could be a boron carbide coating, which has a high melting temperature.Materials and Methods. The impact of an electron beam on samples of rolled tungsten and boron carbide and tungsten composite was studied in experiments on the BETA setup. The heat from the beam propagates into the samples, with the maximum temperature reached at the center and decreasing towards the edges. The modeling area represents a cross-section of the samples, optimal for a task with a cylindrical coordinate system. The numerical implementation is based on the correction scheme and the marching method.Results. A new model of heating the boron carbide and tungsten composite sample under the influence of surface heating by an electron beam is presented. The model is based on solving the heat conduction equation in an axially symmetric setup with constant values of specific heat capacity, density, and thermal conductivity of metals.Discussion and Conclusions. An analysis of the model of heating the composite material under the influence of surface heating by an electron beam at constant values of density, thermal conductivity, and specific heat capacity has been conducted. The modeling results are in demand for analyzing experimental results and planning experiments at the Beam of Electrons for Materials Test Applications (BETA) facility, created at the Budker Institute of Nuclear Physics SB RAS.

Numerical study on magnetic control of boundary layers in non-Newtonian flows over stretching cylinders using Keller box analysis

This article presents an analysis of the magnetic field’s effects on two-dimensional, two-directional, incompressible, and steady third-grade fluid flow over a stretched circular cylinder. A mathematical model describing the behavior of third-grade fluid in the cylindrical coordinate system is developed, accounting for nonlinear differential conditions. To simplify the analysis, appropriate transformations are applied to convert the fractional differential conditions into ordinary differential conditions. The resulting nonlinear differential framework is solved using the Keller Box method. The influences of several novel parameters on the velocity are depicted and examined. Furthermore, the expression for the skin-friction coefficient is computed and provided. The comparison of the obtained results with existing literature is made and found in good accordance. Through comprehensive numerical simulations and analytical derivations, this study contributes to the understanding of magnetic field control in boundary layers of third-grade fluid over stretching cylinders, with implications for a wide range of practical applications in engineering and fluid dynamics. The stronger influence of the magnetic field, indicating an increase in the Hartmann number, corresponds to suppression of thermal and solutal transport, thereby leading to a decrease in the temperature and concentration gradients. Conversely, the velocity profile exhibits an increase, indicating enhanced fluid motion under the influence of the magnetic field. This behavior is consistent with the magnetohydrodynamic effects, where the Lorentz force induced by the magnetic field alters the fluid flow, resulting in changes in the velocity distribution while impacting temperature and concentration gradients.

A spectroscopic investigation of thermal instability for cylindrical equilibria with background flow

Flows are omnipresent and govern the dynamics of plasma. Solar tornadoes are a class of apparently rotating prominences that might be formed by thermal instability. In spectroscopic studies on thermal instability, background flow is commonly neglected. We here determine the effect of background flow on thermal instability in cylindrical magnetic field configurations. How various parameters affect the distribution of eigenmodes in the MHD spectrum is also explored. We investigate whether discrete thermal modes exist. In an analytical study, we extended upon the literature by including a generic background flow in a cylindrical coordinate system. The non-adiabatic magnetohydrodynamic (MHD) equations are linearised, Fourier-analysed, and examined to understand how a background flow changes the continua. An approximate expression for discrete thermal modes is derived using a Wentzel-Kramers-Brillouin (WKB) analysis. The analytical results are then verified for a benchmark equilibrium using the eigenvalue code Legolas . The eigenfunctions of discrete thermal modes are visualised in 2D and 3D. The thermal continuum is Doppler-shifted due to the background flow, just like the slow and Alfv\'en continua. Discrete modes are altered because the governing equations contain flow-related terms. An approximate expression to predict the appearance of discrete thermal modes based on the equilibrium parameters is derived. All analytical expressions match the numerical results. The distribution of the density perturbations of the discrete thermal modes is not a uniform or singular condensation, due to the shape of the eigenfunctions and the dependence of the assumed waveform on the coordinates and wavenumbers. A 3D visualisation of the total velocity field shows that the helical field is heavily influenced by the radial velocity perturbation. We derived analytic expressions for non-adiabatic MHD modes of a cylindrical equilibrium with background flow and verified them using a coronal equilibrium. However, the equations are valid for and can be applied in other astrophysical environments.

New computational method for calculating of water droplet–clay contact angles: Based on molecular dynamics

The measurement of the water contact angle (θ) on the surface of clay minerals poses a significant challenge due to their microscopic particle sizes ranging from micrometers to nanometers and their extensive specific surface areas. We introduce an advanced computational framework based on molecular dynamics simulations. This framework leverages the coordination number (CN) differences of the water molecules and effectively eliminates the gaseous water molecules in the droplet equilibrium system. Additionally, our framework uses an alpha-shaped probe ball to accurately determine the three-dimensional (3D) coordinates of the droplet interface and utilizes a feed-forward neural network (FFNN) to optimize the objective function of the 3D-interface; this ensures highly accurate characterization of the interface contour and an accurate computation of θ. Our approach exhibits outstanding performance in typical clay mineral surface-water wetting systems; it significantly overcomes the limitations of the transformed cylindrical coordinate system algorithm and accurately captures the wettability variations under complex environmental conditions. This new θ computational framework provides crucial assistance for the in-depth exploration of the wettability characteristics of clay minerals in complex environments.

General 2-D Analytical Framework for No-Load Analysis of Interior Permanent Magnet Machines

Solving two-dimensional (2-D) Maxwell’s equations in interior permanent magnet (IPM) motors is fairly complex due to the asymmetrical geometry of rotor magnets in the cylindrical coordinate system. This paper presents a general imaging solution to enable the 2-D open-circuit modeling of the family of IPM machines. Interior magnets are replaced/modeled with (i) virtual magnets on the surface of the rotor body (mapping interior magnets to the surface of the rotor body), and (ii) virtual volume current on the surface of the rotor body. The specifications of the virtual magnet (i.e., the remnant flux density) and the virtual volume current (i.e., current density level) are determined via magnetic circuit model. Next, the 2-D flux distribution of the transformed machines are calculated by solving 2-D Maxwell’s equations and considering relevant boundary conditions. Meanwhile, the effect of stator slots on flux profile is accounted by injecting proper amount of surface magnetizing current on the stator bore. Analytical results are supported via finite element method (FEM) and a series of experimental measurements.

Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems

Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems

Propagation characteristics of circumferential feature guided waves propagation in a revolved topological waveguide

In our previous research, propagation characteristics and combined harmonic generation of feature guided waves (FGWs) in welded joints of plate structure, were analyzed theoretically and observed numerically. Circumferential ultrasonic guided waves find extensive applications in assessing rotating structures, highlighting the importance of investigating the propagation characteristics of circumferential feature guided waves (CFGWs) in such revolved topological waveguides. In this study, propagation characteristics of CFGW in revolved topological waveguides are investigated. Semi-analytical finite element (SAFE) method in conjunction with a perfectly matched layer (PML) within a cylindrical coordinate system is used to explore the modal and dispersion characteristics of CFGWs. Second-harmonic generation (SHG) of CFGWs is further analyzed and discussed both in theoretical and numerical manner. Cumulative SHG of selected CFGW mode pairs, propagation in the welded joint of the revolved topological waveguide, is observed successfully. The obtained results demonstrate that the energy trapping effect of CFGWs in the welded joint of revolved topological waveguide amplifies the generation of cumulative second harmonics, thereby enhancing the measurability of SHG of CFGW. This investigation reveals the potential of damage assessment in revolved topological waveguides by CFGWs.

Excitation Equations for Longitudinally-Azimutally Irregular Waveguides Taking into Account the Finite of the Walls Conductivity

Excitation equations for longitudinal-azimuthally irregular waveguides are formulated taking into account losses in the walls. The inner surface of the waveguide walls is given by an arbitrary smooth function b(ϕ, z). The coordinate transformation method replaces the original cylindrical coordinate system r, ϕ, z with a new one ρ, ϕ, z, where ρ = r/(b(ϕ, z)). The new system defines the waveguide boundary as ρ = 1 = const, i. e. the waveguide geometry transforms as a regular cylinder. Taking these functions into account, the standard procedure of the incomplete Galerkin method is used to determine the amplitudes of partial waves. The resulting general equations can be used in the calculation and optimization of both microwave and EHF electronic devices of various types, as well as passive microwave devices of various applications.

Numerical thermal investigation of radiative magnetohydrodynamics axisymmetric Cu-Al2O3/H2O hybrid nanofluid flow over an unsteady radially stretched surface

The current work focuses on conducting a numerical thermal investigation of nanofluid and hybrid nanofluid flow over unsteady radial stretching surfaces. To perform a comprehensive analysis, lamina and hexahedron-shaped Aluminum Oxide (Al2O3) and Copper (Cu) nanomaterial are immersed in water-based fluid. Furthermore, we take into account the impact of magnetohydrodynamics (MHD) and thermal radiation. The cylindrical coordinate system is utilised for mathematical modeling. The governing system of nonlinear PDEs is converted to a system of ODEs by utilising appropriate similarity transformation and then solved numerically in MATLAB. By using graphs and bar charts, we visually depict the impact of significant physical attributes on velocity, temperature, skin friction, and Nusselt numbers. As per the findings, The nanofluid and hybrid nanofluid flow experienced a notable deceleration due to the influence of the suction parameter (S), unsteadiness parameter (A), and magnetic parameter (M). Furthermore, hybrid nanofluid exhibits the lowest temperature and the slowest velocity. In the case of nanofluid composed of Aluminum Oxide (Al2O3) and water (H2O), the highest Nusselt number is observed along with the lowest skin friction. These recent findings hold the potential to offer advantages to academic research, lubrication processes, and the polymer industry. Abbreviations: PDE’s Partial Differential Equation; ODE’s Ordinary Differential Equation; MHD Magnetohydrodynamic

Method of compensating for instrumental uncertainty in measurements using a coordinate measuring ARM

Due to the influence of dynamic factors in various measurement configurations, the degree of uncertainty in measurements using a Coordinate Measuring Arm (CMA) is directly related to the measurement configuration. However, existing models for compensating CMA errors do not account dynamic factors, which impose certain limits for improving the accuracy of CMAs. To solve this issue, a method for residual error correction based on a polynomial model for single-point measurements was proposed. The influence of the CMA configuration on the residual probe error was analyzed. To enhance accuracy, a polynomial model has been developed by studying the relationship between the rotation angles of the CMA's moving elements and the probe coordinates in a cylindrical coordinate system. Experimental results demonstrate that the residual error correction method significantly compensates for instrumental uncertainty, greatly improving the accuracy of measurements using CMAs. Keywords: coordinate measuring arm, measurement error, coordinate measurements, calculation method, single-point residual correction, compensation.

Numerical and statistical analysis of unsteady hydromagnetic hybrid nanofluid flow in a porous medium over an inclined disk with dissipative heat transfer

AbstractThe present analysis deals with the three‐dimensional radiative, convective hybrid nanofluid flow over a rotating and stretching inclined disk under the action of the applied magnetic field, Joule's heating, and viscous dissipation effects. The mathematical model considers nanoparticles graphene oxide (GO) and molybdenum disulfide (MoS) suspended in water as the base fluid within a Darcy medium. The cylindrical coordinate system is used to express continuity, momentum, and energy partial differential equations, out of which momentum and energy partial differential equations are transformed into ordinary differential equations using a suitable transformation method under the boundary‐layer approximation. The transformed equations are further solved using the spectral quasi‐linearization method. Graphical and numerical data are presented to investigate the behavior of velocity and temperature under various parameters and shape factors. The nature of fluid flow at the boundary wall is determined by tables of skin friction and the Nusselt number. Statistical analysis of the parameters for axial and tangential skin friction and the Nusselt number is performed using the quadratic regression model.

Model of an E-cored probe over layered conductor containing corrosion for eddy current testing

PurposeIn eddy current nondestructive testing, ferrite-cored probes are usually used to detect and locate defects such as cracks and corrosion in conductive materials. However, the generic analytical model for evaluating corrosion in layered conductor using ferrite-cored probe has not yet been developed. The purpose of this paper is to propose and verify the analytical model of an E-cored probe for evaluating corrosion in layered conductive materials.Design/methodology/approachA cylindrical coordinate system is adopted and the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived first, and then the expansion coefficients of the solution are obtained by matching the boundary and interface conditions between the regions and the subregions. Finally the closed-form expression of the impedance of the multi-turn coil is derived by using the truncated region eigenfunction expansion (TREE) method, and the impedance calculation is carried out in Mathematica. In the frequency range of 100 Hz to 10 kHz, the impedance changes of the E-cored coil and air-cored coil due to the layered conductor containing corrosion are calculated, respectively, and the influences of corrosion on the coil impedance change are investigated.FindingsAn analytical model for the detection and evaluating of corrosion in layered conductive materials using E-cored probe is proposed. The model can quickly and accurately calculate the impedance change of E-cored coil due to corrosion in layered conductor. The correctness of the analytical model is verified by finite element method and experiments.Originality/valueAn accurate theoretical model of E-cored probe for evaluating corrosion of multilayer conductor is presented. The analytical model can be used to detect the inhomogeneity of layered conductor, design ferrite-cored probe or directly evaluate the corrosion defects of layered conductors.

Solutions with a Flat Horizon in D Dimensions within the Cubic Form of f(Q) Gravity

Given the AdS/CFT relationship, the study of higher-dimensional AdS black holes is extremely important. Furthermore, since the restriction derived from f(Q)’s field equations prevents it from deriving spherically symmetric black hole solutions, the result is either Q′=0 or fQQ=0. Utilizing the cylindrical coordinate system within the context the cubic form of f(Q) theory while imposing the condition of a coincident gauge, we establish the existence of static solutions in D-dimensions. The power-law ansatz, which is the most practical based on observations, will be used in this study, where f(Q)=Q+12γQ2+13γQ3−2Λ and the condition D≥4 are met. These solutions belong to a new solution class, the properties of which are derived only from the non-metricity Q modification, since they do not have a general relativity limit. We examine the singularities present in the solutions by calculating the non-metricity and curvature invariant values. In conclusion, we compute thermodynamic parameters such as Gibbs free energy, Hawking temperature, and entropy. These thermodynamic calculations confirm that our model is stable.

Construction of Solutions of the Helmholtz Equation in a Cylindrical Coordinate System in the Form of Homogeneous Polynomials in Two Biorthogonal Systems of Functions

Construction of Solutions of the Helmholtz Equation in a Cylindrical Coordinate System in the Form of Homogeneous Polynomials in Two Biorthogonal Systems of Functions

Выделение гироскопических инерционных сил из центробежных и кориолисовых инерционных сил

The purpose of the study is to identify in the equations of dynamics of mechanical systems generalized gyroscopic inertial forces, consisting of a part of centrifugal and Coriolis inertial forces, indica¬ting the bodies whose movements form these forces. The methods of research refer to mechanics of body systems, systems analysis and robotics. The results of the study allow us to write out general formulas for calculating generalized centrifugal, Coriolis and gyroscopic inertial forces through partial derivatives on generalized coordinates from elements of the matrix of inertial coefficients in the expression of kinetic energy of arbitrary mechanical system. In the process of analyzing these formulas for systems of bodies with an open tree structure, such as orbital stations with manipulators on board or walking vehicles in the single-supported walking phase, the bodies whose movements affect the occurrence of the listed inertial forces are highlighted. For robot manipulation systems we present examples of the equations of dynamics, in which all possible inertial forces are highlighted and the bodies that form them are indicated. Conclusion. Singling out the gyroscopic forces allows you to simplify the formula for calculating the power consumption of drives, because the power of these forces is zero. This fact, in particular, allows to simplify the expression of the minimizing functional in the problem of energy optimal control. The isolated centrifugal forces can be used to realize program motions of some bodies of manipulators with polar, cylindrical, spherical and angular coordinate systems without expenditure of power consumed by their drives.

On analytical study of heat transfer phenomenon in special-shape soldering iron

The work presents the results of the analytical solution of the phenomenon of heat transfer in soldering iron of a special shape. For analysis, differential equations in partial derivatives from many variables were used, where initial and boundary conditions were given, according to experimental data. Partial equations were obtained in the process of solving by the method of separating variables. The resulting finite function of coordinate variables in the cylindrical coordinate system and time is derived from the original equation.