Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder

The analytical solution of boundary value problem describing the process of penetration of low-frequency magnetic field through thin-walled cylindrical screen with cylindrical inclusion is constructed by use of approximate boundary conditions. The source of the field is a thin thread of infinitely small length with an infinitely small cross-section where current circulates. Thread is located in a plane which is perpendicular to axis of cylindrical screen, in outer region with respect to a screen. Initially the potential of initial magnetic field is represented as spherical harmonic functions, then using addition theorems connecting spherical and cylindrical harmonic functions, it became as cylindrical harmonic functions superposition. Secondary potentials of magnetic field are also presented as superposition of cylindrical harmonic functions in three-dimensional space. It is shown that the solution of formulated boundary value problem is reduced to the solution of linear algebraic equations system for coefficients included in the representation of secondary fields. The influence of some aspects of the problem on the value of the screening coefficient of an external magnetic field when passing through a cylindrical copper screen in the presence of a cylindrical inclusion is studied numerically. Calculation results are presented in graphs form. Obtained results can be used to shield technical devices and biological objects against the effects of magnetic fields to provide ecological surrounding of operating electrical installations and devices.

Computational Modeling of Flow Characteristics in Three Products Hydrocyclone Screen

Three products hydrocyclone screen (TPHS) can be considered as the combination of a conventional hydrocyclone and a cylindrical screen. In this device, particles are separated based on size under the centrifugal classification coupling screening effect. The objective of this work is to explore the characteristics of fluid flow in TPHS using the computational fluid dynamics (CFD) simulation. The 2 million grid scheme, volume fraction model, and linear pressure–strain Reynolds stress model were utilized to generate the economical grid-independence solution. The pressure profile reveals that the distribution of static pressure was axisymmetric, and its value was reduced with the increasing axial depth. The maximum and minimum were located near the tangential inflection point of the feed inlet and the outlets, respectively. However, local asymmetry was created by the left tangential inlet and the right screen underflow outlet. Furthermore, at the same axial height, the static pressure gradually decreased along the wall to the center. Near the cylindrical screen, the pressure difference between the inside and the outside cylindrical screen dropped from positive to negative as the axial depth increased from −35 to −185 mm. Besides, TPHS shows similar distributions of turbulence intensity I, turbulence kinetic energy k, and turbulence dissipation rate ε; i.e., the values fell with the decrease in axial height. Meanwhile, from high to low, the pressure values are distributed in the feed chamber, the cylindrical screen, and conical vessel; the value inside the screen was higher than the outer value.

Mechanism of the Absent Air Column in Three Products Hydrocyclone Screen (TPHS): Experiment and Simulation

Three products hyrdrocyclone screen (TPHS) has been proposed for particle separation based on size. In TPHS, a cylindrical screen was embedded in a conventional hydrocyclone (CH) to combine the centrifugal classification and screening to particle separation based on size. The industrial application of TPHS indicates its better device performance than CH. Although, the earlier studies reveal some common understanding for TPHS, the information of the absent air column remains unknown. Hence, the combination of physical experiment and numerical simulation was considered involving a 75 mm TPHS for this knowledge gap. First, both the computational fluid dynamics (CFD) simulation with Reynolds stress mode and the physical experiment with a high-definition camera illustrate the development process details of a flow field in TPHS. That is, the water was imported along the tangential inlet into TPHS; then under the effects of the feed chamber wall and gravity, the liquid phase spiraled downward until the cylindrical screen passed through the sieve; as the liquid moved to the spigot, it could be discharged in time due to the small underflow port, thus the volume fraction of air rapidly reduced from 1 to 0; subsequently the water filled the TPHS and the absent air column could be observed. Furthermore, the distribution comparisons of air volume fraction and static pressure show that TPHS displayed the absent air core with the negative static pressure in the center region along the z-axis, while CH displayed the opposite features. In addition, despite the different inlet velocity, TPHS consistently presented the vanished air column which could be ascribed to the fact that the present cylindrical screen resulted in positive static pressure distribution inside TPHS.

Shielding from external magnetic fields by rotating magnetic conducting cylindrical shells

Purpose – In many different engineering fields often there is a need to protect regions from electromagnetic interference. According to static and low-frequency magnetic fields the common strategy bases on using a shield made of conductive or ferromagnetic material. Another screening technique uses solenoids that generate an opposite magnetic field to the external one. The purpose of this paper is to discuss the shielding effect for a magnetic and conducting cylindrical screen rotating in an external static magnetic field. Design/methodology/approach – The magnetic flux density is expressed in terms of the magnetic vector potential. Applying the separation of variables method analytical solutions are obtained for an infinitely long magnetic conducting cylindrical screen rotating in a uniform static transverse magnetic field. Findings – Analytical formulas of the shielding factor for a cylindrical screen of arbitrary conductivity and magnetic permeability are given. A magnetic Reynolds number is found to be an appropriate indication of the change in magnetic field inside the screen. Useful simplified expressions are presented. Originality/value – This paper treats in a qualitative way the possibility of static magnetic field shielding by using rotating conducting magnetic cylindrical screens. Analytical solutions are given. If the angular velocity is equal to zero or the relative permeability of the shield is equal to one the shielding factor has forms well known from literature.