Equilibrium Field Research Articles

A fast Eulerian method for disperse two-phase flow

We propose a variant of the Eulerian method for two-phase flow that is valid for small particle response time τ. For small τ, the particle velocity field v ( x ,t) approaches a unique, equilibrium field, independent of initial conditions. A precise inequality is derived specifying how small τ must be for this to occur. When it does, v ( x ,t) depends only on local fluid quantities (velocity and its spatial and temporal derivatives), and may be expressed as an expansion in τ. We derive an expansion which generalizes those of previous researchers. The first-order truncation of this expansion may be computed efficiently, so by using it to approximate v, the method avoids the need to solve additional partial differential equations, and therefore is much faster than the standard Eulerian method. Results from a direct numerical simulation of turbulent channel flow indicate that this first-order approximation of v is sufficiently accurate. Static tests performed at one time-instance show the actual velocities of particles evolved in a Lagrangian fashion are estimated well by evaluating the first-order approximation of v at the particles' positions. In particular, turbophoresis is represented accurately. Dynamic tests examine the effect of using the first-order approximation of v to evolve particles. The distribution of particles evolved in this way differs little from that of particles evolved using the standard Lagrangian method, indicating that static errors do not accumulate over time. In particular, the approximate method accurately captures preferential concentration in regions of high strain and low vorticity. Analogous results hold for bubbles. Therefore, for sufficiently small particles of any density, the first-order approximation to v is accurate, so the proposed variant of the Eulerian method is both accurate and fast.

Adsorption and gas transport in coal microstructure: investigation and evaluation by quantitative X-ray CT imaging

Natural gas (methane) production from coal seams is recognized as one of the valuable energy sources due to high storage capacity of coal to store gas at low pressures. It is known that coal composition, pore structure, and mineral matter properties affect both the amount of adsorbed quantity and kinetics of adsorption when the coals are considered for natural gas production or mediums for storing gas, mainly methane or carbon dioxide Experiments in the field of adsorption equilibrium and dynamics usually investigate the adsorption properties on crushed coal samples within a certain range of particle sizes. This data can be used to obtain an average behavior representing the very heterogeneous coal–gas system. But, although individual pores are not likely influenced by crushing, this process destroys the natural integrity and continuity of the porous medium and mixes all the lithotypes and minerals in the same batch. This makes it impossible to investigate and differentiate the behavior of different microstructures and lithotypes. In this study, gas transport and adsorption were investigated on a 3.8-cm diameter core of a medium volatile bituminous coal from Gelik seam in the Zonguldak Basin (Northwestern Turkey) by using quantitative X-ray computerized tomography (CT) imaging technique to visualize the interior of the coal during the experiment. Coal was subjected to time-varying xenon (although not a perfect analog for methane, it provides good contrast under X-rays) gas pressure for the experiment. Adsorbed amounts at different locations were determined by scanning the coal at different times. Qualitative CT images and quantitative image data were used to investigate and compare the regions where gas is transported and stored as well as the rate of adsorption at different regions having different pore structure, and composition. The SEM and CT imaging techniques used in this study enabled us to investigate the coal microstructure falling into macropore range (>1 μm with SEM and 0.3135 mm with CT). This study clearly demonstrates that, for the specific coal sample and xenon gas conditions, different structures (in the length scale given above) and lithotypes have different adsorption capacity and rate behavior. SEM images were also used to define the regions showing different adsorption behavior.

Design of equilibrium field control coil system of TPE-RX

A design and related studies of equilibrium field control coil system of TPE-RX reversed field pinch (RFP) machine are described. Here the equilibrium field control coil system stands for the coils to produce poloidal magnetic field necessary for the plasma equilibrium condition. The configuration and the number of turns of the equilibrium field control coil system were designed so as to minimize the field error for reducing the plasma–wall interaction, especially at the shell gap of the thick metal shell. The design method of the equilibrium field control coil system taking account of an iron core with two yokes and the thick metal shell with the poloidal shell gap is described. As a result of the design of the equilibrium field control coil system, field error at the plasma surface is less than 1.0%. The field error can be canceled for wide range of the plasma equilibrium condition by adding the compensatory vertical field. Construction of TPE-RX was successfully completed at the end of 1997 and the coil system showed the expected performances.

MAST magnetic diagnostics

The mega-ampere spherical tokamak (MAST) experiment is a new, large, low aspect ratio device (R=0.7–0.8 m, a=0.5–0.65 m, maximum BT∼0.63 T at R=0.7 m) operating its first experimental physics campaign. Designed to study a wide variety of plasma shapes with up to 2 MA of plasma current with an aspect ratio down to 1.3, the poloidal field (PF) coils used for plasma formation, equilibrium and shaping are inside the main vacuum vessel. For plasma control and to investigate a wide range of plasma phenomena, an extensive set of magnetic diagnostics have been installed inside the vacuum vessel. More than 600 vacuum compatible, bakeable diagnostic coils are configured in a number of discrete arrays close to the plasma edge with about half the coils installed behind the graphite armour tiles covering the center column. The coil arrays measure the toroidal and poloidal variation in the equilibrium field and its high frequency fluctuating components. Internal coils also measure currents in the PF coils, plasma current, stored energy and induced currents in the mechanical support structures of the coils and graphite armour tiles. The latter measurements are particularly important when halo currents are induced following a plasma termination, for example, when the plasma becomes vertically unstable. The article describes the MAST magnetic diagnostic coil set and their calibration. The way in which coil signals are used to control the plasma equilibrium is described and data from the first MAST experimental campaign presented. These coil data are used as input to the code EFIT [L. Lao et al., Nucl. Fusion 25, 1611 (1985)], for measurement of halo currents in the vacuum vessel structure and for measurements of the structure of magnetic field fluctuations near the plasma edge.

The structure of chaotic magnetic field lines in a tokamak with external nonsymmetric magnetic perturbations

We consider the effects of external nonsymmetric magnetostatic perturbations caused by resonant helical windings and a chaotic magnetic limiter on the plasma confined in a tokamak. The main purpose of both types of perturbation is to create a region in which field lines are chaotic in the Lagrangian sense: two initially nearby field lines diverge exponentially through many turns around the tokamak. The equilibrium field is obtained from the equations of magneto-hydrodynamic equilibrium written down in a polar toroidal coordinate system. The magnetic fields generated by the resonant helical windings and the chaotic magnetic limiter are obtained through an analytical solution of Laplace equation. The magnetic field line equations are integrated to give a Hamiltonian mapping of field lines that we use to characterize the structure of chaotic field lines. In the case of resonant windings, we obtained the map by both numerical integration and a Hamiltonian formulation. For a chaotic limiter, we analytically derived a symplectic map by using a Hamiltonian formulation.

Intersonic Crack Propagation—Part I: The Fundamental Solution

Recent experiments of Rosakis et al. have clearly shown that the crack-tip velocity can exceed the shear wave speed for a crack tip propagating between two weakly bonded, identical and isotropic solids under shear-dominated loading. This has motivated recent theoretical and numerical studies on intersonic crack propagation. We have obtained analytically the fundamental solution for mode-II intersonic crack propagation in this paper. This fundamental solution can provide the general solutions for intersonic crack propagation under arbitrarily initial equilibrium fields. We have also developed a cohesive zone model to determine the crack-tip energy release for an intersonic shear crack.

Pre-accretion metamorphism of the Teloloapan Terrane (southern Mexico): example of burial metamorphism in an island-arc setting

Volcanic and interbedded volcaniclastic rocks of the lower Cretaceous island-arc series of the Teloloapan Terrane in southern Mexico contain metamorphic assemblages characteristic of the zeolite, prehnite–pumpellyite and lower greenschist facies produced by burial metamorphism prior to its accretion to nuclear Mexico. Distribution of secondary assemblages throughout the stratigraphic succession, together with the chemical evolution of metamorphic minerals, reveals a depth-controlled metamorphic zonation characterized by the presence of the diagnostic assemblages laumontite+pumpellyite+epidote and laumontite+celadonite+pumpellyite±epidote (zeolite facies) followed downward by assemblages containing prehnite+pumpellyite±white mica (prehnite–pumpellyite facies) and finally by the presence of the assemblages pumpellyite+actinolite+epidote and epidote+actinolite (greenschist facies). Analysis of assemblages in the Al–Fe 3+–FM–K system, reveals that facies boundaries are discontinuous, involving the disappearance of at least one phase and the appearance and/or extension of the field of equilibrium of other diagnostic minerals and assemblages. Application of empirically based thermobarometers, phase equilibria, mineral chemistry, and petrogenetic grids indicates that the P– T conditions of metamorphism ranged from 175 to 342°C and P<3 kbar. The data further indicate high geothermal gradients of about ∼55°C km −1. Seawater-derived fluids were characterized by high a K, high f O 2 and low X CO 2 .

A transport model for swelling of polyelectrolyte gels in simple and complex geometries

Abstract A model for the swelling of polyelectrolyte gels in salt solutions is developed and solved numerically. The model accounts for the effect of network stress, osmotic pressure, and electrical potential on the species diffusive flux. The osmotic pressure and the network stress are derived from the Helmholtz free energy of the system that is the sum of mixing, elastic, and electrostatic components. One- and two-dimensional swelling in unconstrained and constrained geometries are simulated for a salt–solvent–polymer system. The transient and equilibrium fields of electrical potential, concentrations, deformation, and stress are obtained. Transient overshoots and non-uniformities in the residual profiles are predicted.

Phase relations, singularities and thermobarometry of metamorphic assemblages containing phengite, chlorite, biotite, K-feldspar, quartz and H2O

The phase relations of divariant and trivariant assemblages involving combinations of phengite, chlorite, biotite, K-feldspar, quartz and H2O in the KFASH, KMASH and KFMASH systems were calculated using a single thermodynamic data set (Holland and Powell 1998). The stability fields of the various equilibria are represented in P-T projections by contouring sets of compositional isopleths for the Tschermak (Al2(Fe,Mg)−1Si−1) and FeMg−1 exchanges controlled by the coexisting phases. Five multivariant continuous equilibria, which occur in different regions of P-T-X space, are calibrated as thermobarometers in metamorphic rocks of pelitic to quartzofeldspathic composition. More subtle P-T information, relating to the trajectories (dT/dz) along which reacting rocks have been buried or exhumed, can be extracted from the continuous reactions by investigating the recorded compositional trends in the Al2(Fe,Mg)−1Si−1 and FeMg−1 solutions. Singularities in P-T space are associated with some of these reactions and may result in unusual mineral textures and compositional trends. A fluid-absent singularity has particular petrological significance because it marks the transition between hydration and dehydration along a single reaction with increasing pressure and temperature. This behaviour causes the sequence of reactions among these minerals observed during metamorphism to be critically dependent on the P-T trajectory. Thermobarometric calculations show good agreement with respect to experimental and field-based data for phengite compositions less than about 50 mol% celadonite (<∼3.5 Si p.f.u. phengite).

Properties of Θ-manifolds and one of the forms of the azeotropic relationship

A proof is presented for the theorem on the repetition factors in the alternating sum of the numbers of singular points in the vector field of liquid-vapor equilibrium tie lines.

Influence of Coherent and Random Flows on the Solarf‐Mode

The solar f-mode is referred to as a surface gravity wave that exists right below the solar corona. For a high horizontal wavenumber k, the frequency ω of this mode is given by the dispersion relation ω2 = gk, where g is the surface gravity of the Sun. However, the observations of this mode revealed deviations from this simple dispersion relation. According to these observations, for high values of k, the f-mode frequency is significantly lower than the frequency given by the simple dispersion relation and the line width grows with k. The purpose of this paper is to display some of the features that go into a theoretical description of the flow that occurs in the convection zone and its effect on the spectrum of the f-mode oscillations. In particular, we aim to consider coherent and random flows that may be associated with supergranules and granules. In the case of the coherent horizontal flow V0, we derive a general dispersion equation that is valid for arbitrary equilibrium profiles. The space-dependent flow V0(z) exhibits a singularity at the vertical position z = zc, for which ω/k = V0(zc). As a special example, the case of an isothermal atmosphere and a uniform flow is discussed in detail to show the Doppler effect. In the case of the random flow, we generalize the dispersion relation derived by Murawski & Roberts for a space- and time-dependent velocity field. While the effect of a space-dependent random field is to reduce frequencies and attenuate the f-mode, a time-dependent random flow can increase frequencies and amplify the f-mode. Solving the random dispersion equation numerically for various parameters of the equilibrium and random field, we find that the frequencies and line widths of the random f-mode are close to those observed recently by the Solar and Heliospheric Observatory (SOHO) MDI instrument.

A variational approach for the deformation of a saturated porous solid. A second-gradient theory extending Terzaghi's effective stress principle

The principle of virtual power is used to derive the equilibrium field equations of a porous solid saturated with a fluid, including second density-gradient effects; the intention is the elucidation and extension of the effective stress principle of Terzaghi and Fillunger. In the context of a first density-gradient theory for a saturated solid we interpret the porewater pressure as a Lagrange multiplier in the expression for the deformation energy, assuring that the saturation constraint is verified. We prove that this saturation pressure is distributed among the constituents according to their respective volume fraction (Delesse law) only if they are both true density-preserving. We generalize the Delesse law to the case of compressible constituents. If a material-dependent effective stress contribution is to arise, it is, in general, nonvanishing simultaneously in both the solid and fluid constituents. Moreover, saturation pressure, effective stresses and compressibility constitutive equations determine the exchange volume forces. In a theoretical formulation without non-isotropic strain measures, second density-gradient effects must be incorporated, not only to accommodate for the equilibrium-solid-shear stress and the interaction among neighboring solid-matrix pores, but also to describe internal capillarity effects. The earlier are accounted for by a dependence of the thermodynamic energy upon the density-gradient of the solid, while the latter derives from a mixed density-gradient dependence. Examples illustrate the necessity of these higher gradient effects for properly posed boundary value problems describing the mechanical behaviour of the disturbed rock zone surrounding salt caverns. In particular, we show that solid second-gradient strains allow for the definition of the concept of static permeability, which is distinct from the dynamic Darcy permeability.

A Double Gas‐Hydrate Related Bottom Simulating Reflector at the Norwegian Continental Margin

Abstract: An unusual pattern of two bottom simulating reflections (BSRs) has been observed on seismic profiles from the continental margin offshore Western Norway. One of these reflections (BSR1) extends over large areas and has the characteristics of the classical BSR, that is a phase‐reversed reflection from the base of the gas‐hydrate stability zone. The second BSR (BSR0) occurs at approximately 70 ms two‐way travel time beneath BSR1 and is here called a double BSR. The distribution of BSR0 is more local than that of BSR1 and it does not show the phase‐reversal relative to the sea floor reflection that is characteristic for a BSR at the gas hydrate‐free gas boundary. Results from an industrial borehole, from full waveform inversion of multichannel seismic data, from high‐frequency ocean bottom hydrophones, and interpretation of seismic profiles, clearly indicate that BSR1 is reflected from the base of the methane hydrate equilibrium field. Results from full waveform inversion indicate that BSR0 corresponds to a 16–20 m zone where the velocity drops from about 1.8 km/s to a minimum of 1.4 km/s and then increases again. The low velocity of 1.4 km/s suggests the presence of free gas. The results support the hypothesis that BSR0 is a reflection from the base of gas hydrates containing hydrocarbons with a heavier molecular weight in addition to methane gas. Interference of reflections from the top and base of the low‐velocity zone associated with BSR0 explain why BSR0 is not phase‐reversed.

Start-up without preionization in NOVILLO tokamak

Many tokamak devices require a preionization system in order to start up both the discharge cleaning and the main plasma discharge. A stray vertical magnetic field profile of 100 G at the center of the plasma column has been measured on the NOVILLO tokamak by magnetic probes especially made to study the breakdown process. A new vertical field profile, superimposed to the stray field component parallel to the equilibrium field, is created by two additional compensation poloidal coils. Such arrangement of the vertical field profiles, with a 1/R-dependence, has been found optimum to achieve the plasma breakdown without any preionization system.

Baroclinic Wave Breaking and the Internal Variability of the Tropospheric Circulation

Abstract A simple model of the tropospheric circulation, based on a 10-level primitive equation model, is forced by linearly relaxing the potential temperature toward an idealized, zonally symmetric equilibrium field. The model equations are integrated in time until a statistically steady state is obtained. The local relationship between the state of the background flow, the direction of wave propagation, and subsequent wave breaking at the tropopause level is then investigated. Maps of potential vorticity (PV) on isentropic surfaces are analyzed and all four different types of wave breaking described recently by Peters and Waugh are shown to occur. It is found that cyclonic wave breaking events are usually initiated by poleward fluxes of wave activity, and anticyclonic events by equatorward fluxes. Composites are then used to show that equatorward fluxes are associated with a jet that is locally broad and weak, with relatively strong isentropic PV gradients to its equatorward flank. By contrast, poleward...

The role of material parameters and mechanical stresses on magnetic and magnetostrictive hysteresis

The proposed micromagnetic model (Voltairas et al., Int. J. Engng. Sci., accepted for publication) is extended to account for shearing strains. We assume that the ferromagnetic material is a single cubic crystal, the magnetization reverses coherently and the strains are uniform. The equilibrium field equations are derived from the free energy functional. The role of the material parameters and the applied stresses ( inverse magnetostriction effect) on the magnetization and magnetostriction curves is examined in detail.

NO2 sensor based on InP epitaxial thin layers

n-InP epitaxial thin layers are exposed to concentrations of a diluted oxidizing gas: NO2. In the presence of this gas, the resistance measured parallel to the surface of the InP layer, between ohmic contacts, increases. The magnitude of its variations depends on several parameters: the operating temperature, the thickness and the doping concentration level of the InP layer, and the gas concentration. A theoretical model of the action of the gas is proposed, mixing chemisorption equilibrium and surface field effect. The experimental results are in agreement with the theoretical predictions.

An alternative expression of piezoelectric representation and its application in inclusion problem

This paper intends to conform the mathematical correspondence between electric and mechanical variables to the physical correspondence in electroelastic problem when a piezoelectric material is subjected to stress field σij and electric field Ei or displacement u and electric displacement Di. Ei is expressed with an antisymmetric electric field tensor Vij , and Di is expressed with an antisymmetric electric displacement tensor Pij which can be expressed with ‘induction potential’ ψi. Then stress equilibrium and electric field equations can be described by a second order canonical differential equation system of ui and ψi. As an example, the coupled electroelastic fields in an inclusion or inhomogeneity embedded in an infinite matrix are obtained in a manner directly analogous to Eshelby’s classical elastic solution. The electroelastic fields inside the ellipsoidal inclusion or inhomogeneity and just outside the ellipsoidal inclusion or inhomogeneity are also given. In addition, we analyze the energies of the inclusion. The results in this paper are the backbone in the development of the electric damage theory and ferroelectric constitutive theory.

Minimum Weight Design of Fillet Welds Using Convex Formulation

This paper presents a discrete formulation of the nonlinear minimum weight design of welded connections, in which global throat stresses along every fillet are approximated by piecewise linear shape functions. With this formulation it is possible to find the set of throat thicknesses of a welded connection that gives the minimum amount of weld metal necessary to support an arbitrary set of external actions and a stress field in equilibrium with these actions and satisfying a strength criterion. The formulation adopted involves a linear form of objective function and equilibrium equations, which, together with the convex character of the nonlinear constraints, gives a full convex set of constraints and consequently a global optimum of the objective function. Moreover, the structure of the set of constraints makes it possible to demonstrate that stress and throat thickness values are unique at the optimum, which allows the optimum stress distributions to be simplified, to establish practical design recommendations. Realistic conditions can be imposed on the stress field. The problem is solved with a very accessible and well-known scientific library, which allows this method to be implemented by anyone involved in welding practice. The method proposed is developed for the case of a planar connection. Two practical applications using the strength criterion of Eurocode 3 are included, discussing the results obtained for two types of common arrangements and showing that numerical results are consistent and central processing unit times reasonably low.

Empirically Based Gamma-Distributed Random Wall Pressure Field in Silo

Measurements show that silo wall pressures exhibit large fluctuations in time and space during discharge of the silo. This observation is important for the design of the silo wall because spatial pressure variations may impose substantial bending moments in the silo wall that otherwise may be small or vanishing due to the carrying ability of the membrane forces in the silo wall. Information about the stochastic properties of this pressure variation cannot be obtained from any existing continuum model for the silo medium flowing within the confinement of the silo. Therefore the modeling must presently be tied to statistical analyses of the empirical evidence combined with simple mechanical principles. This paper analyzes the same data set as that analyzed by Munch-Andersen et al., but on the basis of a completely different and physically less disputable stochastic pressure field model than the one considered by them. It is shown that an explicitly constructed gamma distribution type of field in equilibrium...