Panayiotis Vafeas

Investigation on streamers propagating into a helium jet in air at atmospheric pressure: Electrical and optical emission analysis

The plasma produced due to streamers guided by a dielectric tube and a helium jet in atmospheric air is herein studied electrically and optically. Helium streamers are produced inside the dielectric tube of a coaxial dielectric-barrier discharge and, upon exiting the tube, they propagate into the helium jet in air. The axisymmetric velocity field of the neutral helium gas while it penetrates the air is approximated with the PISO algorithm. At the present working conditions, turbulence helium flow is avoided. The system is driven by sinusoidal high voltage of variable amplitude (0–11 kV peak-to-peak) and frequency (5–20 kHz). It is clearly shown that a prerequisite for streamer development is a continuous flow of helium, independently of the sustainment or not of the dielectric-barrier discharge. A parametric study is carried out by scanning the range of the operating parameters of the system and the optimal operational window for the longest propagation path of the streamers in air is determined. For this...

Low-frequency solution for a perfectly conducting sphere in a conductive medium with dipolar excitation

This contribution concerns the interaction of an arbitrarily orientated, time-harmonic, magnetic dipole with a perfectly conducting sphere embedded in a homogeneous conductive medium. A rigorous low-frequency expansion of the electromagnetic field in positive integral powers (jk) to n, k complex wavenumber of the exterior medium, is constructed. The first n = 0 vector coefficient (static or Rayleigh) of the magnetic field is already available, so emphasis is on the calcu- lation of the next two nontrivial vector coefficients (at n = 2 and at n = 3) of the magnetic field. Those are found in closed form from exact solutions of coupled (at n = 2, to the one at n = 0) or uncoupled (at n = 3) vector Laplace equations. They are given in compact fashion, as infinite series expansions of vector spherical harmonics with scalar coefficients (for n = 2). The good accuracy of both in-phase (the real part) and quadrature (the imaginary part) vector components of the diffusive magnetic field are illustrated by numerical computations in a realistic case of mineral exploration of the Earth by inductive means. This canonical representation, not available yet in the literature to this time (beyond the static term), may apply to other practical cases than this one in geoelectromagnetics, whilst it adds useful reference re- sults to the already ample library of scattering by simple shapes using analytical methods.

LOW-FREQUENCY DIPOLAR EXCITATION OF A PERFECT ELLIPSOIDAL CONDUCTOR

This paper deals with the scattering by a perfectly conductive ellipsoid under magnetic dipolar excitation at low frequency. The source and the ellipsoid are embedded in an infinite homogeneous conducting ground. The main idea is to obtain an analytical solution of this scattering problem in order to have a fast numerical estimation of the scattered field that can be useful for real data inversion. Maxwell equations and boundary conditions, describing the problem, are firstly expanded using low-frequency expansion of the fields up to order three. It will be shown that fields have to be found incrementally. The static one (term of order zero) satisfies the Laplace equation. The next non-zero term (term of order two) is more complicated and satisfies the Poisson equation. The order-three term is independent of the previous ones and is described by the Laplace equation. They constitute three different scattering problems that are solved using the separated variables method in the ellipsoidal coordinate system. Solutions are written as expansions on the few analytically known scalar ellipsoidal harmonics. Details are given to explain how those solutions are achieved with an example of numerical results.

Electromagnetic Low-Frequency Dipolar Excitation of Two Metal Spheres in a Conductive Medium

This work concerns the low-frequency interaction of a time-harmonic magnetic dipole, arbitrarily orientated in the three-dimensional space, with two perfectly conducting spheres embedded within a homogeneous conductive medium. In such physical applications, where two bodies are placed near one another, the 3D bispherical geometry fits perfectly. Considering two solid impenetrable (metallic) obstacles, excited by a magnetic dipole, the scattering boundary value problem is attacked via rigorous low-frequency expansions in terms of integral powers (????)??, where ??=0, ?? being the complex wave number of the exterior medium, for the incident, scattered, and total non-axisymmetric electric and magnetic fields. We deal with the static (??=0) and the dynamic (??=1,2,3) terms of the fields, while for ??=4 the contribution has minor significance. The calculation of the exact solutions, satisfying Laplace’s and Poisson’s differential equations, leads to infinite linear systems, solved approximately within any order of accuracy through a cut-off procedure and via numerical implementation. Thus, we obtain the electromagnetic fields in an analytically compact fashion as infinite series expansions of bispherical eigenfunctions. A simulation is developed in order to investigate the effect of the radii ratio, the relative position of the spheres, and the position of the dipole on the real and imaginary parts of the calculated scattered magnetic field.

Stokes flow in ellipsoidal geometry

Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid con...

Influence of Atmospheric Pressure Guided Streamers (Plasma Bullets) on the Working Gas Pattern in Air

This paper is devoted to the study of gas flow fields related to helium atmospheric pressure guided streamer (plasma bullet) propagation in the air. For very weak up to moderate helium flows, the modification induced to the gas flow field by the plasma ignition is demonstrated; it is shown that the turbulent flow region is expanded and two conditions must be fulfilled regarding the working gas profile in the air for streamer propagation, i.e., laminar flow and high concentration in this laminar flow region.

THE 3D HAPPEL MODEL FOR COMPLETE ISOTROPIC STOKES FLOW

The creeping flow through a swarm of spherical particles that move with constant velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity in a quiescent Newtonian fluid is analyzed with a 3D sphere-in-cell model. The mathematical treatment is based on the two-concentric-spheres model. The inner sphere comprises one of the particles in the swarm and the outer sphere consists of a fluid envelope. The appropriate boundary conditions of this non-axisymmetric formulation are similar to those of the 2D sphere-incell Happel model, namely, nonslip flow condition on the surface of the solid sphere and nil normal velocity component and shear stress on the external spherical surface. The boundary value problem is solved with the aim of the complete Papkovich-Neuber differential representation of the solutions for Stokes flow, which is valid in non-axisymmetric geometries and provides us with the velocity and total pressure fields in terms of harmonic spherical eigenfunctions. The solution of this 3D model, which is self-sufficient in mechanical energy, is obtained in closed form and analytical expressions for the velocity, the total pressure, the angular velocity, and the stress tensor fields are provided.

Comparison of differential representations for radially symmetric Stokes flow

Papkovich and Neuber (PN), and Palaniappan, Nigam, Amaranath, and Usha (PNAU) proposed two different representations of the velocity and the pressure fields in Stokes flow, in terms of harmonic and biharmonic functions, which form a practical tool for many important physical applications. One is the particle-in-cell model for Stokes flow through a swarm of particles. Most of the analytical models in this realm consider spherical particles since for many interior and exterior flow problems involving small particles, spherical geometry provides a very good approximation. In the interest of producing ready-to-use basic functions for Stokes flow, we calculate the PNAU and the PN eigensolutions generated by the appropriate eigenfunctions, and the full series expansion is provided. We obtain connection formulae by which we can transform any solution of the Stokes system from the PN to the PNAU eigenform. This procedure shows that any PNAU eigenform corresponds to a combination of PN eigenfunctions, a fact that reflects the flexibility of the second representation. Hence, the advantage of the PN representation as it compares to the PNAU solution is obvious. An application is included, which solves the problem of the flow in a fluid cell filling the space between two concentric spherical surfaces with Kuwabara-type boundary conditions.

LOW-FREQUENCY ELECTROMAGNETIC MODELING AND RETRIEVAL OF SIMPLE OREBODIES IN A CONDUCTIVE EARTH

As relevant in mineral exploration of the Earth using inductive electromagnetic means, (diffusive) scattering by a perfectly conducting ellipsoidal anomaly placed in a homogeneous conductive medium and illuminated by a time-harmonic magnetic dipole, is considered by means of a low frequency expansion in positive integral powers of (jk), k complex wavenumber of the exterior medium. The aim is to construct a simple yet robust model of the fields to identify the anomaly when magnetic fields are collected nearby. The approach is illustrated by field calculations and inversions of both synthetic and experimental data.

The Avascular Tumour Growth in the Presence of Inhomogeneous Physical Parameters Imposed from a Finite Spherical Nutritive Environment

A well-known mathematical model of radially symmetric tumour growth is revisited in the present work. Under this aim, a cancerous spherical mass lying in a finite concentric nutritive surrounding is considered. The host spherical shell provides the tumor with vital nutrients, receives the debris of the necrotic cancer cells, and also transmits to the tumour the pressure imposed on its exterior boundary. We focus on studying the type of inhomogeneity that the nutrient supply and the pressure field imposed on the host exterior boundary, can exhibit in order for the spherical structure to be supported. It turns out that, if the imposed fields depart from being homogeneous, only a special type of interrelated inhomogeneity between nutrient and pressure can secure the spherical growth. The work includes an analytic derivation of the related boundary value problems based on physical conservation laws and their analytical treatment. Implementations in cases of special physical interest are examined, and also existing homogeneous results from the literature are fully recovered.