scholarly journals Diffusion-drift model of ion migration over interstitial sites of a two-dimensional lattice

2019 ◽  
Vol 55 (3) ◽  
pp. 355-365
Author(s):  
N. A. Poklonski ◽  
A. O. Bury ◽  
N. G. Abrashina-Zhadaeva ◽  
S. A. Vyrko
Keyword(s):  
Electric Field ◽  
Ion Current ◽  
Finite Difference Approximation ◽  
Square Lattice ◽  
Difference Approximation ◽  
Water Molecules ◽  
Ion Migration ◽  
Drift Model ◽  
Stationary Electric Field ◽  
Electric Potentials

An analytical and numerical modeling of the process of obtaining hydroxyl radicals OH0 and atomic hydrogen H0 from water molecules on a square lattice based on electrical neutralization of ions OH− on an anode and ions H+ on a cathode is conducted. The numerical solution of a system of equations describing a stationary migration of ions H+ and OH− over the interstitial sites of a square lattice located in an external electric field is considered. The ions H+ and OH− in the interstitial sites of a square lattice are generated as a result of dissociation of a water molecule under the action of external electromagnetic radiation and external constant (stationary) electric field. It is assumed that anode and cathode are unlimited ion sinks. The problem is solved using the finite difference approximation for the initial system of differential equations with the construction of an iterative process due to the nonlinearity of the constituent equations. It is shown by using calculation that the dependence of the ion current on a difference of electric potentials between anode and cathode is sublinear.

Enhanced Passive Thermal Management of Grid-Scale Power Routers Utilizing Ionic Wind

2014 ◽  
Author(s):  
Noris Gallandat ◽  
J. Rhett Mayor
Keyword(s):  
Heat Transfer ◽  
Electric Field ◽  
Mixed Boundary ◽  
Control Volume ◽  
Vertical Channel ◽  
Mixed Boundary Conditions ◽  
Thermal Design ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Ionic Wind

This paper presents a numerical model assessing the potential of ionic wind as a heat transfer enhancement method for the cooling of grid distribution assets. Distribution scale power routers (13–37 kV, 1–10 MW) have stringent requirements regarding lifetime and reliability, so that any cooling technique involving moving parts such as fans or pumps are not viable. Increasing the air flow — and thereby enhancing heat transfer — through Corona discharge could be an attractive solution to the thermal design of such devices. In this work, the geometry of a rectangular, vertical channel with a corona electrode at the entrance is considered. The multiphysics problem is characterized by a set of four differential equations: the Poisson equation for the electric field and conservation equations for electric charges, momentum and energy. The electrodynamics part of the problem is solved using a finite difference approximation (FDA). Solutions for the potential, electric field and free charge density are presented for a rectangular control volume with mixed boundary conditions.

scholarly journals The Impact of the Electric Field on Surface Condensation of Water Vapor: Insight from Molecular Dynamics Simulation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 64 ◽  
Author(s):  
Qin Wang ◽  
Hui Xie ◽  
Zhiming Hu ◽  
Chao Liu
Keyword(s):  
Molecular Dynamics ◽  
Water Vapor ◽  
Electric Field ◽  
Intermolecular Forces ◽  
Dynamics Simulation ◽  
Water Molecules ◽  
Attraction Force ◽  
Condensation Rate ◽  
Shape Transformation ◽  
The Impact

In this study, molecular dynamics simulations were carried out to study the coupling effect of electric field strength and surface wettability on the condensation process of water vapor. Our results show that an electric field can rotate water molecules upward and restrict condensation. Formed clusters are stretched to become columns above the threshold strength of the field, causing the condensation rate to drop quickly. The enhancement of surface attraction force boosts the rearrangement of water molecules adjacent to the surface and exaggerates the threshold value for shape transformation. In addition, the contact area between clusters and the surface increases with increasing amounts of surface attraction force, which raises the condensation efficiency. Thus, the condensation rate of water vapor on a surface under an electric field is determined by competition between intermolecular forces from the electric field and the surface.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

Sign in / Sign up

Export Citation Format

Share Document