The axisymmetric flow field induced by a point force in the presence of a plane wall

1982 ◽  
Vol 380 (1779) ◽  
pp. 349-357 ◽  
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Axisymmetric Flow ◽  
Plane Wall ◽  
Point Force ◽  
Nonlinear Flow ◽  
Volume Flux ◽  
Closed Loops ◽  
Meridian Section ◽  
Section Form

In this paper we consider a numerically constructed solution concerning the steady nonlinear flow field generated by a point force of magnitude F 0 in an incompressible fluid bounded by a plane wall. The force is applied at a fixed distance from the wall and is perpendicular to it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F 0 increases this stagnation point is displaced towards or away from the wall depending on whether the force is pointing towards or away from it. It is also found that as F 0 increases the total volume flux per unit force decreases when the force is pointing towards the wall and increases when the force is pointing in the opposite direction. For instance when F 0 is 150 v 2 ρ , where v denotes the coefficient of kinematic viscosity and ρ the fluid density, the total volume flux for the case where the force points away from the wall is several times that for the case where the force points towards the wall.

The nonlinear flow field induced by a point force in the presence of a plane wall

1981 ◽  
Vol 376 (1766) ◽  
pp. 435-450 ◽  
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Plane Wall ◽  
Point Force ◽  
Nonlinear Flow ◽  
Unit Force ◽  
Closed Loops ◽  
Meridian Section ◽  
Continuous Application ◽  
Section Form

A nonlinear solution is constructed representing the steady flow field generated by the continuous application of a constant point force of magnitude F 0 in an incompressible fluid that is bounded by a fixed plane wall. The force is applied at a fixed distance from the wall, is perpendicular to the wall and directed towards it. The streamlines in a meridian section form closed loops which nest at a stagnation point and it is found that as F 0 increases this stagnation point is displaced towards the wall. It is also found that as F 0 increases the total volume flow per unit force decreases.

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

1976 ◽  
Vol 73 (4) ◽  
pp. 641-650 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Flow Field ◽  
Electric Current ◽  
Cross Section ◽  
Analytic Solution ◽  
Closed Loops ◽  
Slow Viscous Flow ◽  
Axial Cross Section ◽  
Section Form

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

Development of the flow field of a point force in an infinite fluid

1979 ◽  
Vol 91 (3) ◽  
pp. 541-546 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Flow Field ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Point Force ◽  
Linear Flow ◽  
Closed Loops ◽  
Stagnation Points ◽  
Dipole Structure ◽  
Field Lines ◽  
Set Up

By means of similarity principles an analytical solution is constructed for the development of the linear flow field due to the instantaneous application of a constant point force in an infinite liquid. If the force is applied at the origin O and if ν denotes distance from O, ν denotes the coefficient of kinematic viscosity of the fluid and t the time from the application of the force, the solution constructed exhibits the following features. Initially the flow field set up has a dipole structure with centre at O and axis along the direction of the impressed force. At a station r this dipole structure persists so long as 4νt [Lt ] r2. In an axial cross-section the field lines form two sets of closed loops about two stagnation points in the equatorial plane. The stagnation points occur at r = 1.76(νt)½ and thus propagate to infinity with speed 0.88(ν/t)½. The steady state is reached algebraically.

The development of magnetohydrodynamic flow due to an electric current discharge

1975 ◽  
Vol 70 (3) ◽  
pp. 509-517 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Flow Field ◽  
Electric Current ◽  
Stagnation Point ◽  
Cross Section ◽  
Kinematic Viscosity ◽  
Magnetohydrodynamic Flow ◽  
Dimensionless Variable ◽  
Closed Loops ◽  
Developing Flow ◽  
Set Up

The development of the magnetohydrodynamic flow field due to the discharge of an electric current J0 from a point on a plate bounding a semi-infinite viscous incompressible conducting fluid is considered. The flow field is the response of the fluid to the Lorentz force set up by the electric current and the associated magnetic field. The problem is formulated in terms of the dimensionless variable (vt)½/r and solved numerically. Here ν is the coefficient of kinematic viscosity, t the time from the application of the electric current and r the distance from the discharge. It is shown that the streamlines of the developing flow field in a cross-section through the axis of the discharge are closed loops about a stagnation point. As the flow field develops, the stagnation point moves to infinity along a ray emanating from the discharge with a speed proportional to t−½. The steady state, within a distance r from the discharge, is practically established when t = r2/ν.

The round laminar jet: the development of the flow field

1977 ◽  
Vol 80 (4) ◽  
pp. 673-683 ◽  
Author(s):  
C. Sozou ◽  
W. M. Pickering
Keyword(s):  
Flow Field ◽  
Stagnation Point ◽  
Dipole Axis ◽  
Dimensionless Variable ◽  
Closed Loops ◽  
Laminar Jet ◽  
Variable Λ ◽  
Developing Flow ◽  
Straight Line ◽  
Axis Of Symmetry

The development of the flow field of a jet emanating from a point source of momentum in an infinite incompressible fluid of density σ is considered. The flow field is assumed to be due to the application of a constant force F0 at the origin. The problem is formulated in terms of the dimensionless variable λ = (vt)½/r, where v is the kinematic viscosity of the fluid, t the time from the application of the force and r the distance from the origin. At a station r the flow field is dipolar, with the dipole axis in the direction of F0, for all t satisfying the inequalities vt Lt; r2 and F0t2 [Lt ] 4πρr4. Also, at a given time t the streamlines of the developing flow field in a section through the axis of symmetry of the problem form closed loops about a stagnation point. If this occurs at λ = λm, the stagnation point propagates to infinity, along a straight line emanating from the origin, with speed v½/2λmt½, where λm = λm(F0) decreases as F0 increases. The larger F0 is the faster the steady state is established.

scholarly journals Semi-Inverse Design of Compressor Cascades, Including Supersonic Inflow

1990 ◽  
Author(s):  
A. Kirschner ◽  
H. Stoff
Keyword(s):  
Flow Field ◽  
Design Method ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Design Procedure ◽  
Meridional Plane ◽  
Simple Method ◽  
Blade Loading ◽  
Through Flow ◽  
Blade Element

A cascade design-method is presented which complements the meridional through-flow design procedure of turbomachines. Starting from an axisymmetric flow field and the streamline geometry in the meridional plane this simple method produces a solution for the quasi three-dimensional flow field and the blade-element geometry on corresponding stream surfaces. In addition, it provides intra-blade data on loss and turning required for a consistent design and a convenient means of optimizing blade loading. The purpose of this paper is to describe the theoretical basis of the method and to illustrate its application in the design of transonic compressors.

scholarly journals Numerical simulation of the dimensional transformation of atomization in a supersonic aerodynamic atomization dust-removing nozzle based on transonic speed compressible flow

2020 ◽  
Vol 7 (3) ◽  
pp. 597-610 ◽  
Author(s):  
Tian Zhang ◽  
Deji Jing ◽  
Shaocheng Ge ◽  
Jiren Wang ◽  
Xiangxi Meng ◽  
...  
Keyword(s):  
Flow Field ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Three Dimensional Model ◽  
Speed Flow ◽  
Complex Process ◽  
Study Results ◽  
Laval Nozzles

Abstract To simulate the transonic atomization jet process in Laval nozzles, to test the law of droplet atomization and distribution, to find a method of supersonic atomization for dust-removing nozzles, and to improve nozzle efficiency, the finite element method has been used in this study based on the COMSOL computational fluid dynamics module. The study results showed that the process cannot be realized alone under the two-dimensional axisymmetric, three-dimensional and three-dimensional symmetric models, but it can be calculated with the transformation dimension method, which uses the parameter equations generated from the two-dimensional axisymmetric flow field data of the three-dimensional model. The visualization of this complex process, which is difficult to measure and analyze experimentally, was realized in this study. The physical process, macro phenomena and particle distribution of supersonic atomization are analyzed in combination with this simulation. The rationality of the simulation was verified by experiments. A new method for the study of the atomization process and the exploration of its mechanism in a compressible transonic speed flow field based on the Laval nozzle has been provided, and a numerical platform for the study of supersonic atomization dust removal has been established.

The motion of a droplet subjected to linear shear flow including the presence of a plane wall

1995 ◽  
Vol 302 ◽  
pp. 45-63 ◽  
Author(s):  
W. S. J. Uijttewaal ◽  
E. J. Nijhof
Keyword(s):  
Shear Flow ◽  
Flow Field ◽  
Theoretical Models ◽  
Boundary Integral ◽  
Plane Wall ◽  
Time Dependent ◽  
Fluid Inertia ◽  
Linear Shear ◽  
Material Element ◽  
Migration Velocities

A fluid droplet subjected to shear flow deforms and rotates in the flow. In the presence of a wall the droplet migrates with respect to a material element in the undisturbed flow field. Neglecting fluid inertia, the Stakes problem for the droplet is solved using a boundary integral technique. It is shown how the time-dependent deformation, orientation, circulation and droplet viscosity. The migration velocities are calculated in the directions parallel and perpendicular to the wall, and compared with theoretical models and expeeriments. The results reveal some of the shortcomings of existiong models although not all diserepancies between our calculations and known experiments could be clarified.

Non-axisymmetric flow field in an axial impulse turbine

2008 ◽  
Vol 22 (1) ◽  
pp. 166-170 ◽  
Author(s):  
Byeung Jun Lim ◽  
Seung Jin Song
Keyword(s):  
Flow Field ◽  
Axisymmetric Flow ◽  
Impulse Turbine
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