scholarly journals Two-dimensional jet aimed vertically upwards

1993 ◽  
Vol 34 (4) ◽  
pp. 393-400 ◽  
Author(s):  
Jean-Marc Vanden-Broeck
Keyword(s):  
Free Surface ◽  
Incompressible Fluid ◽  
Finite Differences ◽  
Two Dimensional ◽  
Free Surfaces ◽  
Inviscid Incompressible Fluid ◽  
Surface Profiles

AbstractA steady two-dimensional jet of an inviscid incompressible fluid rising and falling under gravity is considered. The jet is aimed vertically upwards and the flow is assumed to be bounded entirely by two free surfaces. The problem is solved numerically by finite differences. Accurate results for the free surface profiles are presented.

On some problems of similarity flow of fluid with a free surface

1969 ◽  
Vol 36 (4) ◽  
pp. 805-829 ◽  
Author(s):  
Z. N. Dobrovol'skaya
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Singular Integral Equation ◽  
Incompressible Fluid ◽  
Singular Integral ◽  
Classical Problem ◽  
Flow Region ◽  
Hydrodynamic Characteristics ◽  
Two Dimensional ◽  
Free Surfaces

The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratios x/v0t, y/v0t, where x, y are Cartesian co-ordinates, t is time and v0 is a constant of the velocity dimension.The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.

scholarly journals Some Nonlinear Vortex Solutions

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Michael C. Haslam ◽  
Christopher J. Smith ◽  
Ghada Alobaidi ◽  
Roland Mallier
Keyword(s):  
Steady State ◽  
Incompressible Fluid ◽  
Poisson Equation ◽  
Specific Form ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Vortex Solutions

We consider the steady-state two-dimensional motion of an inviscid incompressible fluid which obeys a nonlinear Poisson equation. By seeking solutions of a specific form, we arrive at some interesting new nonlinear vortex solutions.

scholarly journals Some cases of the steady two-dimensional percolation of water through ground

1940 ◽  
Vol 175 (962) ◽  
pp. 346-365 ◽  
Keyword(s):  
Free Surface ◽  
Water Table ◽  
Two Dimensional ◽  
Free Surfaces ◽  
Water Basin ◽  
Special Cases ◽  
Method Of Solution ◽  
Earth Embankment ◽  
Upper Level ◽  
Tail Water

In this paper we examine three cases of steady two-dimensional motion of water through uniform permeable ground and obtain exact mathematical solutions of the problems which are investigated. In the cases considered the ground soaked with water is bounded by impervious surfaces, boundaries of water-basins and free surfaces. (The term “free surface” is used to denote that surface in ground-water motions which engineers call the “water table”.) Further, with the exception of the free surfaces, the boundaries are restricted to be plane. These problems do not involve seepage surfaces, but the method can, in certain cases, be applied to problems in which plane seepage surfaces occur. As we are considering only two-dimensional problems the plane surfaces are represented by straight lines in the representative plane—as for example in figure 1. In this figure LBCM is an earth embankment. AB is the boundary of the head water-basin, BC is the impervious base of the embankment and CD is the boundary of the tail water-basin. AE is the free surface or water table, that is, the upper level of the water which is percolating through the embankment. Above AE the pores between the particles of soil are filled with air. ED is the seepage surface, that is, the surface of the embankment through which water is steadily leaking and falling into the tail water. We assume that in the region of flow the “inertia forces” are neglected and that Darcy’s law is satisfied, that is, that the frictional forces per unit volume between the water and the permeable ground are proportional to the first power of the “percolation velocity”. The percolation velocity is defined as the limiting value of the ratio of discharge to area as the area tends to zero, it being understood that the discharge is measured in a direction normal to the area and that “area” includes not only the clearance between particles of soil but also the soil itself. A general method of solution has been given by one of the authors in a previous paper (Davison 1936 a ). The present paper is a development of this work and contains, in § 2, a lemma which is useful in special cases. As examples of this, three problems are discussed below.

Numerical solution for two-dimensional flow under sluice gates using the natural element method

2010 ◽  
Vol 37 (12) ◽  
pp. 1550-1559 ◽  
Author(s):  
Farhang Daneshmand ◽  
S.A. Samad Javanmard ◽  
Tahereh Liaghat ◽  
Mohammad Mohsen Moshksar ◽  
Jan F. Adamowski
Keyword(s):  
Free Surface ◽  
Numerical Technique ◽  
Surface Profile ◽  
Nonlinear Boundary Conditions ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Natural Element Method ◽  
Natural Element ◽  
Surface Profiles ◽  
Element Method

Fluid loads on a variety of hydraulic structures and the free surface profile of the flow are important for design purposes. This is a difficult task because the governing equations have nonlinear boundary conditions. The main objective of this paper is to develop a procedure based on the natural element method (NEM) for computation of free surface profiles, velocity and pressure distributions, and flow rates for a two-dimensional gravity fluid flow under sluice gates. Natural element method is a numerical technique in the field of computational mechanics and can be considered as a meshless method. In this analysis, the fluid was assumed to be inviscid and incompressible. The results obtained in the paper were confirmed via a hydraulic model test. Calculation results indicate a good agreement with previous flow solutions for the water surface profiles and pressure distributions throughout the flow domain and on the gate.

The aerodynamic forces on an oscillating aerofoil in a free jet

1955 ◽  
Vol 229 (1177) ◽  
pp. 235-250 ◽  
Keyword(s):  
Wind Tunnel ◽  
Incompressible Fluid ◽  
Classical Theory ◽  
Direct Application ◽  
Two Dimensional ◽  
Aerodynamic Forces ◽  
Small Oscillations ◽  
Free Jet ◽  
Inviscid Incompressible Fluid ◽  
Wind Tunnel Measurements

The forces acting on an aerofoil placed centrally in a two-dimensional jet of inviscid incompressible fluid are calculated exactly for the case when the aerofoil is performing small oscillations about its mean position. The theory is a generalization of the classical theory due to Theodorsen and others for an oscillating aerofoil in an infinite stream. The results, which are expressed in terms of a ‘generalized Theodorsen function’, have a direct application to the correction of open-jet wind-tunnel measurements on oscillating aerofoils.

scholarly journals On periodic Stokesian Hele-Shaw flows with surface tension

2008 ◽  
Vol 19 (6) ◽  
pp. 717-734 ◽  
Author(s):  
J. ESCHER ◽  
B.-V. MATIOC
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Incompressible Fluid ◽  
Classical Solution ◽  
Small Perturbation ◽  
Darcy’S Law ◽  
Viscous Incompressible Fluid ◽  
Darcy's Law ◽  
Two Dimensional ◽  
Unique Classical Solution

In this paper we consider a 2π-periodic and two-dimensional Hele-Shaw flow describing the motion of a viscous, incompressible fluid. The free surface is moving under the influence of surface tension and gravity. The motion of the fluid is modelled using a modified version of Darcy's law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution for a domain which is a small perturbation of a cylinder. Moreover, we identify the equilibria of the flow and study their stability.

The distortion of a bubble in a corner flow

2000 ◽  
Vol 11 (2) ◽  
pp. 171-179 ◽  
Author(s):  
E. OZUGURLU ◽  
J.-M. VANDEN-BROECK
Keyword(s):  
Incompressible Fluid ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Corner Flow

The distortion of a two-dimensional bubble (or drop) in a corner flow of an inviscid incompressible fluid is considered. Numerical solutions are obtained by series truncation. The results confirm and extend previous calculations.

The formation of vortex streets

1962 ◽  
Vol 13 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Frederick H. Abernathy ◽  
Richard E. Kronauer
Keyword(s):  
Incompressible Fluid ◽  
Vortex Street ◽  
Bluff Bodies ◽  
Two Dimensional ◽  
Vortex Sheets ◽  
Linear Interaction ◽  
Inviscid Incompressible Fluid ◽  
Fixed Distance ◽  
Vortex Streets ◽  
Non Linear

The formation of vortex streets in the wake of two-dimensional bluff bodies can be explained by considering the non-linear interaction of two infinite vortex sheets, initially a fixed distance, h, apart, in an inviscid incompressible fluid. The interaction of such sheets (represented in the calculation by rows of point-vortices) is examined in detail for various ratios of h to the wavelength, a, of the initial disturbance. The number and strength of the concentrated regions of vorticity formed in the interaction depend very strongly on h/a. The non-linear interaction of the two vortex sheets explains both the cancellation of vorticity and vortex-street broadening observed in the wakes of bluff bodies.

Simulation of Microstructural Evolution in Polycrystalline Films

1990 ◽  
Vol 202 ◽  
Author(s):  
H. J. Frost
Keyword(s):  
Free Surface ◽  
Surface Energy ◽  
Film Thickness ◽  
Grain Boundaries ◽  
Grain Growth ◽  
Driving Force ◽  
Three Dimensional ◽  
Grain Structure ◽  
Two Dimensional ◽  
Free Surfaces

ABSTRACTThis paper will review the topic of computer simulation of the evolution of grain structure in polycrystalline thin films, with particular attention to the modelling of the grain growth process. If the grain size is small compared to the film thickness, then the grain structure is three-dimensional. As the grains grow to become larger than the film thickness, so that most grains traverse the entire thickness of the film, the microstructure may approach the conditions for a two-dimensional grain structure. Both two- and three-dimensional grain growth have been simulated by various authors.When the grains become large enough for the microstructure to be two-dimensional, the surface energy associated with the two free surfaces of the film becomes comparable to the surface energy of the grain boundaries. In this condition, the free surface may profoundly effect the grain growth. One effect is that grooves may develop along the lines where the grain boundaries meet the free surfaces. This grooving may pin the boundaries against further migration and lead to grain-growth stagnation. Another possible effect is that differences in the free surface energy for grains with different crystallographic orientation may provide a driving force for the migration of the boundaries which is additional to that provided by grain boundary capillarity. Grains with favorable orientations will grow at the expense of grains with unfavorable orientations. The coupling of grain-growth stagnation with an additional driving force can produce abnormal or secondary grain growth in which a few grains grow very large by consuming the normal grains.

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