James F. Hoburg

Wire-duct precipitator field and charge computation using finite element and characteristics methods

Abstract A model is described for computation of charge density and electric field structures in wire-duct electrostatic precipitators. The model employs an iterative technique, wherein the finite element method is used to compute electric potential structure for an assumed charge density distribution, and the method of characteristics is used to compute charge density structure for an assumed electric field distribution. The computed potential values are in excellent agreement with experimental data, including a region which has produced disagreement in prior models.

Donor cell-finite element descriptions of wire-duct precipitator fields, charges and efficiencies

Computations of electric field and charge density structures and resultant efficiencies in wire-duct electrostatic precipitators are described. The computation is based on the finite-element method as a means for computing potential and electric field for a known charge distribution, and a donor cell method, which imposes conservation of charge in integral form as a means for computing charge densities for a known field structure, with iterative convergence to self-consistent solutions. The solution region is discretized by the Delaunay algorithm. This division simultaneously provides the triangles needed for the finite-element method and the Voronoi polygons over which charge conservation is imposed. Thus, a natural geometric interface is established between the finite-element method and the donor cell description. Results are shown in models which include the time-averaged effect of turbulence through a diffusivity coefficient, bipolar ionic species modeling back ionization, and the effect of particulate space charge.<<ETX>>

Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients

The interface between two miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium tangential electric field is studied experimentally and theoretically. A bulk-coupled electrohydrodynamic instability associated with the diffusive distribution of fluid conductivity at the interface is experimentally observed. The configuration is modelled using a layer of exponentially varying conductivity spliced on each surface to a constant-conductivity fluid half-space. Over-stable (propagating) modes are discovered and characterized in terms of the complex growth rate and fastest growing wavenumber, with the conductivity ratio and an inertia-viscosity time-constant ratio as parameters. In the low inertia limit, growth rates are governed by the electric-viscous time τ = η/e E 2 . Instability is found also with the layer of varying conductivity bounded by rigid equipotential walls. A physical mechanism leading to theoretically determined fluid streamlines in the form of propagating cells is described. At relatively high electric fields, large-scale mixing of the fluid components is observed. Photocell measurements of distributions of average fluid properties demonstrate evolution in time on a scale determined by τ.

Electrohydrodynamic mixing and instability induced by co‐linear fields and conductivity gradients

Scaling laws for field induced mixing of a semi‐insulating liquid of uniform viscosity η and permittivity e, but of inhomogeneous conductivity, are deduced for motions with characteristic times long compared with viscous‐diffusion and charge relaxation times. In an electric field, E, time is shown to scale with electric‐viscous time τev=η/eE2. An experiment involving mixing of a highly conducting thin layer into a lesser conducting bulk region uses temporal current evolution to confirm scaling. A simple mixing model is shown to correlate with experimental results. Linear instability mechanisms underlying the mixing process are described by a bulk‐coupled model, with viscous diffusion effects included. Eigenfrequencies are determined as they depend on conductivity variation and ratio of viscous diffusion to electric‐viscous time. Static instabilities and overstabilities are predicted. Corresponding eigenfunctions and streamlines lend insights into the onset of instability leading to a turbulent mixing state.

Stable Levitation of a Passive Magnetic Bearing

A design for a passive magnetic bearing system that can stably levitate a rotor in all directions is described. The bearing system consists of levitation magnets coupled with a Halbach array stabilizer, which induces currents in stabilization coils, in order to overcome the inherent instability of a system composed only of permanent magnets. The levitation magnet system consists of two pairs of annular ring magnets which provide an upward magnetic levitation force to counteract the downward gravitational force of the rotor. The Halbach array stabilizer consists of two stabilization coils shifted in angular position with respect to one another and centered in the vertical direction between two rotating Halbach arrays. Magnetic fields from permanent magnets are calculated using superposition of fields due to patches of magnetization charge at surfaces where the magnetization is discontinuous. Induced currents in the stabilization coils are calculated by computing the time derivative of the magnetic flux through those coils. Magnetic forces on the rotor are computed using a superposition of forces on each patch of magnetization charge. The entire magnetic bearing system, consisting of both the levitation magnets and the Halbach array stabilizer, is stable to both vertical and lateral displacements. Results are compared with a simpler straightened approximation of the Halbach array stabilizer.

Modeling maglev passenger compartment static magnetic fields from linear Halbach permanent-magnet arrays

Passenger compartment magnetic field levels in a low-speed magnetic levitation (maglev) vehicle that uses linear Halbach permanent-magnet arrays for both levitation and propulsion are computed through superposition of fields due to patches of magnetization charge at surfaces where the magnetization is discontinuous. End effects due to the finite lengths of the arrays lead to fields that decay much less rapidly with distance from the arrays than the near-field exponential decay based on array wavelength, and do not have the strong side/weak side character of the near fields. End effects dominate the maglev passenger compartment fields. Contour plots of computed fields due to the magnet arrays for a specific maglev design show field magnitudes of about 1.5 G at floor level, 0.5 G at seat level, and 0.2 G at head level.

A Student-Oriented Finite Element Program for Electrostatic Potential Problems

The use of FINEL, a finite element program for electrostatic potential problems, in an electrical and computer engineering undergraduate course in field analysis at Carnegie-Mellon University is described. Motivation for this coverage derives from the widespread introduction and rapid growth of the method in the context of practical applications. FINEL is accompanied by PLOTR, a program for drawing the finite element grid and equipotential lines on a Tektronix plotting terminal or CALCOMP plotter. Finite element grids and equipotential structures for several specific problems are shown.

Interfacial electrohydrodynamic instability in normal electric field

Surface‐coupled electrohydrodynamic instability at the interface between miscible fluid components with identical permittivity, mass density, and viscosity but disparate conductivities, as stressed by an equilibrium normal electric field, is described in the instantaneous relaxation limit. Long wave, inertia‐dominated and short wave, viscous‐dominated regimes of the dispersion relation are identified. Experimental studies, using freon 113 as a base liquid, compare observed interfacial displacements as functions of time with growth rates predicted by the model. Correlation varies from almost perfect to experimental growth only 0.1 as fast as predicted by theory, with all observed motions in the inertia‐dominated regime. Instability dynamics at the scale of interfacial conductivity distribution are documented by allowing diffusion before electric field application.

Magnetic Fields and Forces in Permanent Magnet Levitated Bearings

Magnetic fields and magnetic forces from magnetic bearings made of circular Halbach permanent-magnet arrays are computed and analyzed. The magnetic fields are calculated using superposition of fields due to patches of magnetization charge at surfaces where the magnetization is discontinuous. The magnetic force from the magnetic bearing is computed using superposition of forces on each patch of magnetization charge. The magnetic force from a Halbach array magnetic bearing is compared to an annular ring bearing of the same dimensions. A comparison is also made between the results obtained using the magnetic surface charge method and the simpler approximate method using a 2-D analytic representation of the Halbach array fields.

Can computers really help students understand electromagnetics

Some motivations and experiences of a professor who became active twelve years ago in the development of educational software for use in teaching and learning engineering electromagnetics are described. Categories of educational tools are defined, exemplified, discussed, and ranked in order of effectiveness. The author provides opinions as to what has and has not been accomplished. >