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.

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.

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.

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.

Flow Visualization by Means of Contactless Inductive Flow Tomography in the Presence of a Magnetic Brake

2015 ◽  
Vol 15 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Matthias Ratajczak ◽  
Thomas Wondrak ◽  
Klaus Timmel ◽  
Frank Stefani ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Flow Field ◽  
Continuous Casting ◽  
Flow Structure ◽  
Cross Section ◽  
Two Dimensional ◽  
Slab Casting ◽  
Two Dimensional Flow

AbstractIn continuous casting DC magnetic fields perpendicular to the wide faces of the mold are used to control the flow in the mold. Especially in this case, even a rough knowledge of the flow structure in the mold would be highly desirable. The contactless inductive flow tomography (CIFT) allows to reconstruct the dominating two-dimensional flow structure in a slab casting mold by applying one external magnetic field and by measuring the flow-induced magnetic fields outside the mold. For a physical model of a mold with a cross section of 140 mm×35 mm we present preliminary measurements of the flow field in the mold in the presence of a magnetic brake. In addition, we show first reconstructions of the flow field in a mold with the cross section of 400 mm×100 mm demonstrating the upward scalability of CIFT.

The Influence of Wrap Angle of Blade on the Internal Flow Field and Hydraulic Performance of Double Suction Pump

2018 ◽  
Author(s):  
Hao Chang ◽  
Weidong Shi ◽  
Wei Li ◽  
Jianrui Liu ◽  
Ling Zhou ◽  
...  
Keyword(s):  
Flow Field ◽  
Cross Section ◽  
Turbulence Model ◽  
Static Pressure ◽  
Internal Flow ◽  
Hydraulic Performance ◽  
Optimal Model ◽  
Suction Pump ◽  
External Characteristic ◽  
Wrap Angle

In order to study the influence rule of wrap angle of blade on the internal flow field and hydraulic performance of double suction pump, 5 kinds of wrap angles of blade with 100°, 110°, 120°, 130° and 140° are designed in this paper. The turbulence model and the grid type are analyzed, the performance of ES350-575 double suction pump is obtained by employ the software CFX. The static pressure and velocity distributions in the cross-section are analyzed. Therefore, the optimal model is obtained, and the relevant external characteristic test is conducted. The result shows that the reasonable increase of the wrap angle of blade can enhance the performance of the pump effectively, which can improve the static pressure and velocity distributions of the internal flow field.

Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

Recent Progress in the 3D Experimentation and Simulation of Nanoindents

2007 ◽  
Vol 550 ◽  
pp. 199-204
Author(s):  
N. Zaafarani ◽  
Franz Roters ◽  
Dierk Raabe
Keyword(s):  
Cross Section ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Physically Based Model ◽  
Rotation Direction ◽  
Crystal Rotation ◽  
Crystal Plasticity Model ◽  
Physically Based ◽  
Set Up ◽  
Rotation Map

This work studies the rotations of a (111) Cu single crystal due to the application of a conical nanoindent. With the aid of a joint high-resolution field emission SEM-EBSD set-up coupled with serial sectioning in a focused ion beam (FIB) system in the form of a cross-beam 3D crystal orientation microscope (3D EBSD) a 3D rotation map underneath the indent could be extracted. When analyzing the rotation directions in the cross section planes (11-2) perpendicular to the (111) surface plane below the indenter tip we observe multiple transition regimes with steep orientation gradients and changes in rotation direction. A phenomenological and a physically-based 3D elastic-viscoplastic crystal plasticity model are implemented in two finite element simulations adopting the geometry and boundary conditions of the experiment. While the phenomenological model predicts the general rotation trend it fails to describe the fine details of the rotation patterning with the frequent changes in sign observed in the experiment. The physically-based model, which is a dislocation density based constitutive model, succeeded to precisely predict the crystal rotation map compared with the experiment. Both simulations over-emphasize the magnitude of the rotation field near the indenter relative to that measured directly below the indenter tip. However, out of the two models the physically-based model reveals better crystal rotation angles

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