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.

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 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.

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.

Fluid motions induced by an electric current discharge

1972 ◽  
Vol 329 (1576) ◽  
pp. 71-81 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Flow Field ◽  
Electric Current ◽  
Kinematic Viscosity ◽  
Conducting Fluid ◽  
Total Current ◽  
Fluid Density ◽  
Current Discharge ◽  
Monotonically Increasing Function ◽  
Increasing Function

In this paper we consider the flow field induced by an electric current discharge emerging from a small hole (mathematically a point) of a plane wall, bounding an incompressible viscous conducting fluid. The current is directed radially from the discharge. In earlier work, where the effect of the velocity on the electromagnetic field was neglected, it was shown that the velocity field contains singularities, and therefore the solution breaks down, when K = 2 J 2 0 / πρv 2 > K crit ≈ 300.1. Here J 0 is the total current of the discharge, ρ the fluid density and v the coefficient of kinematic viscosity. It is found that for a finitely conducting fluid when account is taken of the effect of the velocity on the electromagnetic field, K crit is a monotonically increasing function of α = 4 πvσ where σ is the electrical conductivity of the fluid. The interaction of this flow field with that due to a jet or sink of momentum, emerging from the same hole as the electric current discharge, is also considered in some detail.

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.

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.

Magnetohydrodynamic flow in a container due to the discharge of an electric current from a finite size electrode

1978 ◽  
Vol 362 (1711) ◽  
pp. 509-523 ◽  
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Electric Current ◽  
Stokes Flow ◽  
Equatorial Plane ◽  
Finite Size ◽  
Magnetohydrodynamic Flow ◽  
Point Electrode ◽  
Equatorial Radius ◽  
Constant Potential

In this paper we consider the Stokes flow field generated in a hemispheroidal container by the axisymmetric discharge of an electric current. The current is discharged from a circular electrode which is at the centre of the equatorial plane of the spheroid. The electrode is assumed to be at a constant potential. The equatorial radius of the spheroid is a and that of the electrode is k , the annulus k ≼ r ≼ a being a free surface. For a given container depth it is shown that as k increases the intensity of the flow field decreases and when the depth of the container is comparable to k the intensity of the flow field is only a small fraction of that associated with the point electrode case. As one might expect, the vorticity has a singularity at the rim of the electrode. When the width of the annulus forming the free surface is small, relative to the radius of the electrode, an eddy is formed about the rim of the electrode. As the annulus increases the eddy decreases in size until it eventually disappears.

Electrohydrodynamics of a liquid drop: the development of the flow field

1973 ◽  
Vol 334 (1598) ◽  
pp. 343-356 ◽  
Keyword(s):  
Steady State ◽  
Flow Field ◽  
Electric Field ◽  
Liquid Drop ◽  
Drop Surface ◽  
Steady State Flow ◽  
Field Stress ◽  
State Flow ◽  
Developing Flow ◽  
Set Up

In this paper we consider the development of the flow field in and about a liquid drop immersed in a conducting fluid, induced by an electric field stress. We place special emphasis to the case when the applied electric field is a d.c. field. We assume that the electric field stress is set up instantaneously and investigate the development of the flow field as the drop is being deformed. Thus, the present work is an extension of Sir Geoffrey Taylor’s work concerning the steady state flow field set up by a d.c. field and the author’s work concerning the quasi-steady state flow generated by an a.c. field. In the case of a d.c. field, the fluid circulation in the proximity of the drop surface initially forms closed loops which eventually propagate to infinity. Also, in the proximity of the drop surface, the developing flow field may be more intense and even directed in opposite sense in comparison with that of the steady state. In the limit, when the time t tends to infinity, the solution presented here converges to the solutions established in the papers referred to above.

On the Influence of the Slot Orifice in Diesel Common Rail Nozzle

2018 ◽  
Vol 11 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Giancarlo Chiatti ◽  
Ornella Chiavola ◽  
Fulvio Palmieri ◽  
Roberto Pompei
Keyword(s):  
Cross Section ◽  
Flow Rate ◽  
Experimental Analysis ◽  
Common Rail ◽  
Spray Angle ◽  
The Novel ◽  
Hydraulic Behavior ◽  
Reference Information ◽  
Light Duty ◽  
Set Up

Background:The paper deals with a diesel common rail nozzle in which a novel orifice layout is implemented.Objective:Its influence on the nozzle mechanical-hydraulic behavior and on the spray shape transient development is experimentally investigated.Methods:In the research, a solenoid injector for light duty diesel engines is equipped with the novel nozzle prototype and tested. The prototype layout is described, pointing out the features of the nozzle orifices, in which a Slot cross-section is adopted; the investigation is accomplished extending the hydraulic tests and the spray visualizations to a reference nozzle with standard holes. The influence of the hole layout on the mechanical-hydraulic behavior of the nozzle is assessed by experimental analysis based on the rate of injection measurement, in comparison with the reference nozzle. Once the hydraulic behavior of the novel nozzle has been characterized in terms of mass flow rate, the slot influence on the spray shape is assessed analyzing the macroscopic features such as the penetration distance and the spray angle, in non evaporative conditions. The study is carried out under transient injection conditions, for different injection pressures, up to 1400 bar.Results:The results on spray characteristics also provide reference information to set up spray models suited to take the Slot orifice into account.

Nanoparticle Precipitation in a T-Mixer: Coupling Experimental and Numerical Investigations of the Fluid Dynamics With the Solid Formation Processes

2006 ◽  
Author(s):  
Johannes Gradl ◽  
Florian Schwertfirm ◽  
Hans-Christoph Schwarzer ◽  
Hans-Joachim Schmid ◽  
Michael Manhart ◽  
...  
Keyword(s):  
Flow Field ◽  
Fluid Dynamic ◽  
Concentration Field ◽  
Population Balance ◽  
Mixing Process ◽  
Image Velocimetry ◽  
Modeling Material ◽  
Field Information ◽  
Set Up ◽  
3D Information

Mixing and consequently fluid dynamic is a key parameter to tailor the particle size distribution (PSD) in nanoparticle precipitation. Due to fast and intensive mixing a static T-mixer configuration is capable for synthesizing continuously nanoparticles. The flow and concentration field of the applied mixer is investigated experimentally at different flow rates by Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF). Due to the PIV measurements the flow field in the mixer was characterized qualitatively and the mixing process itself is quantified by the subsequent LIF-measurements. A special feature of the LIF set up is to detect structures in the flow field, which are smaller than the Batchelor length. Thereby a detailed insight into the mixing process in a static T-Mixer is given. In this study a CFD-based approach using Direct Numerical Simulation (DNS) in combination with the solid formation kinetics solving population balance equations (PBE) is applied, using barium sulfate as modeling material. A Lagrangian Particle Tracking strategy is used to couple the flow field information with a micro mixing model and with the classical theory of nucleation. We found that the DNS-PBE approach including macro and micro mixing, combined with the population balance is capable of predicting the full PSD in nanoparticle precipitation for different operating parameters. Additionally to the resulting PSD, this approach delivers a 3D-information about all running subprocesses in the mixer, i.e. supersaturation built-up or nucleation, which is visualized for different process variables.

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