scholarly journals Two Dimensional Incompressible Ideal Flow Around a Small Curve

2012 ◽  
Vol 37 (4) ◽  
pp. 690-731 ◽  
Author(s):  
C. Lacave
Keyword(s):  
Two Dimensional ◽  
Ideal Flow

scholarly journals On the Motion of a Rigid Body in a Two-Dimensional Irregular Ideal Flow

2012 ◽  
Vol 44 (5) ◽  
pp. 3101-3126 ◽  
Author(s):  
Olivier Glass ◽  
Franck Sueur
Keyword(s):  
Rigid Body ◽  
Two Dimensional ◽  
Ideal Flow

scholarly journals Two Dimensional Incompressible Ideal Flow Around a Small Obstacle

2003 ◽  
Vol 28 (1-2) ◽  
pp. 349-379 ◽  
Author(s):  
D. Iftimie ◽  
M. C. Lopes Filho ◽  
H. J. Nussenzveig Lopes
Keyword(s):  
Two Dimensional ◽  
Ideal Flow ◽  
Small Obstacle

An Investigation of the Flow Regime for Hele-Shaw Flow

1969 ◽  
Vol 9 (04) ◽  
pp. 434-442
Author(s):  
R.C. Smith ◽  
R.A. Greenkorn
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Creeping Flow ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Ideal Flow ◽  
Plate Spacing ◽  
Perturbation Pressure

Abstract Hele-Shaw cells are used to model creeping flow through porous media (where Darcy's law is valid). The effects of inertia on flow about obstructions in a Hele-Shaw cell can be calculated by a perturbation method if one can determine a solution to Laplace's equation. Results of a computer solution for flow about circular, square and elliptical obstructions are presented These results show that for a modified presented These results show that for a modified Reynolds number of less than 1, the inertia terms are small; and for values of less than 3, the average streamline predicts the ideal flow. Therefore, the analogy might be used for studying flow in porous media up to a modified Reynolds number of at least 3. Introduction The nature of fluid flow in porous media is of interest in the fields of soil mechanics, ground water flow, petroleum production, filtration and flow, in packed beds. Because it is very difficult to study the phenomenological behavior of flow in porous media, homologs and analogs are used to study flow characteristics. A Hele-Shaw model, made of two closely spaced plates - usually glass - is often used as an analogy to two-dimensional flow in porous media. Hele-Shaw showed experimentally that the streamline configuration for creeping flow around an obstacle located between two closely spaced parallel plates is the same as for two-dimensional parallel plates is the same as for two-dimensional ideal flow about the same obstacle. Stokes verified these observations mathematically. The usual equation of motion for flow in porous media is Darcy's law. The form of the mathematical statement of Darcy's law is identical, within a multiplicative constant, to the expression for the average velocity over the place gap in the plane of a Hele-Shaw model. These models may be used to describe flow in both homogeneous and heterogeneous porous media. In the mathematical proof of the Hele-Shaw analogy it is assumed that the convective terms in the Navier-Stokes equations are negligible and that the equations of motion degenerate to Laplace's equation, with pressure the dependent variable. Whenever a Hele-Shaw model is used as an analogy to flow in porous media, the validity of this assumption is in question. Riegels showed that if convection is not neglected, the velocity distribution around a cylindrical obstruction in the flow field depends on a Reynolds number, the plate spacing, and a dimension characteristic of the obstacle. Riegels solution, a perturbation solution, uses the boundary condition that the flow rate into the obstacle averaged over the plate gap at any point on the obstacle is zero. The method requires that a solution to Poisson's equation for the perturbation pressure be found. Riegels evaluated this solution pressure be found. Riegels evaluated this solution for the case of the cylindrical obstruction. His method may be simplified by eliminating the need for solving Poisson's equation for the perturbation pressure. Instead, an analytic expression for the pressure. Instead, an analytic expression for the perturbation pressure gradient is obtained (valid perturbation pressure gradient is obtained (valid for arbitrary shapes) and used to eliminate pressure from the equations for the perturbation velocities. The results show, for symmetrical shapes, that if N'Re less than 1, the convective acceleration terms are small, and that the average velocities represent ideal flow up m at least N'Re 3, where: ..........................................(1) L is a characteristic dimension of the obstacle perpendicular to flow, b is the plate spacing, mu is perpendicular to flow, b is the plate spacing, mu is viscosity, va is velocity of approach and p is density. SPEJ P. 434

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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