The interactive dynamics of flow and directional solidification in a Hele-Shaw cell Part 1. Experimental investigation of parallel shear flow

2002 ◽  
Vol 470 ◽  
pp. 247-268 ◽  
Author(s):  
M. ZHANG ◽  
T. MAXWORTHY
Keyword(s):  
Shear Flow ◽  
Directional Solidification ◽  
Flow Direction ◽  
Velocity Ratio ◽  
Parallel Flow ◽  
Tilting Angle ◽  
Specimen Material ◽  
Parallel Shear Flow ◽  
Crystal Cells ◽  
Hele Shaw Cell

It is recognized that flow in the melt can have a profound influence on the dynamics of a solidifying interface and hence on the quality of the solidified material. To better understand the effect of fluid flow on the interface morphological stability and on the cellular and dendritic growth, directional solidification experiments were carried out in a horizontally placed Hele-Shaw cell with and without externally imposed parallel shear flow. The specimen material used was SCN–1.0 Wt% acetone. The experiment shows that the transient parallel flow has a stabilizing effect on the planar interface by damping the existing initial perturbations. The left–right symmetry of crystal cells was broken by the parallel flow, with cells tilting toward the incoming flow direction. The tilting angle increased with the velocity ratio. The secondary dendrites were found to either not appear or appear much later on the downstream side of the crystal cells. The wavelengths of the initial perturbations and of the cellular interface were insensitive to the imposed flow.

scholarly journals Flux of Parallel Flow Momentum by Parallel Shear Flow Driven Instability

2016 ◽  
Vol 11 (0) ◽  
pp. 1203018-1203018 ◽  
Author(s):  
Yusuke KOSUGA ◽  
Sanae-I. ITOH ◽  
Kimitaka ITOH
Keyword(s):  
Shear Flow ◽  
Parallel Flow ◽  
Parallel Shear Flow

Non-parallel flow corrections for the stability of shear flows

1973 ◽  
Vol 59 (3) ◽  
pp. 571-591 ◽  
Author(s):  
Chi-Hai Ling ◽  
W. C. Reynolds
Keyword(s):  
Boundary Layer ◽  
Shear Flow ◽  
Parallel Flow ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Blasius Boundary Layer ◽  
Stability Of Shear Flows ◽  
Parallel Shear Flow ◽  
The Stability ◽  
Small Disturbances

The proper corrections for non-parallel flow to the eigenvalues for small disturbances on a nearly parallel shear flow have been determined through a perturbation about the parallel flow solutions. The resulting shifts in the neutral stability curves have been calculated for the Blasius boundary layer, for the two-dimensional jet, and for the two-dimensional flat-plate wake.

scholarly journals Simulation of Flexible Fibre Particle Interaction with a Single Cylinder

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 191
Author(s):  
Naser Hamedi ◽  
Lars-Göran Westerberg
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Fibre Orientation ◽  
Flow Direction ◽  
Particle Interaction ◽  
Orientation Angle ◽  
Factors Affecting ◽  
Single Cylinder ◽  
Flow Past ◽  
Fibre Suspension

In the present study, the flow of a fibre suspension in a channel containing a cylinder was numerically studied for a very low Reynolds number. Further, the model was validated against previous studies by observing the flexible fibres in the shear flow. The model was employed to simulate the rigid, semi-flexible, and fully flexible fibre particle in the flow past a single cylinder. Two different fibre lengths with various flexibilities were applied in the simulations, while the initial orientation angle to the flow direction was changed between 45° ≤ θ ≤ 75°. It was shown that the influence of the fibre orientation was more significant for the larger orientation angle. The results highlighted the influence of several factors affecting the fibre particle in the flow past the cylinder.

The heat/mass transfer to a finite strip at small Péclet numbers

1978 ◽  
Vol 86 (1) ◽  
pp. 49-65 ◽  
Author(s):  
R. C. Ackerberg ◽  
R. D. Patel ◽  
S. K. Gupta
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Shear Flow ◽  
Sodium Hydroxide Solution ◽  
Flow Direction ◽  
Mathematical Problem ◽  
Limiting Current ◽  
Transfer Rates ◽  
Uniform Shear ◽  
Uniform Shear Flow

The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Péclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Péclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.

The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow

1960 ◽  
Vol 7 (1) ◽  
pp. 145-155 ◽  
Author(s):  
Alar Toomre
Keyword(s):  
Shear Flow ◽  
Lateral Displacement ◽  
Reynolds Numbers ◽  
Infinite Cylinder ◽  
List Type ◽  
Displacement Effect ◽  
Simple Method ◽  
Viscous Shear ◽  
Parallel Shear Flow ◽  
Viscous Shear Flow

A simple method is presented in this paper for calculating the secondary velocities, andthe lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’) in the plane of symmetry ahead of an infinitely long cylinder situated normal to a steady, incompressible, slightly viscous shear flow; the cylinder is also perpendicular to the vorticity, which is assumed uniform but small. The method is based on lateral gradients of pressure, these being calculated from the primary flow alone. Profiles of the secondary velocities are obtained at several Reynolds numbers ahead of two specific cylindrical shapes: a circular cylinder, and a flat plate normal to the flow. The displacement effect is derived and, rathe surprisingly, is found to be virtually independent of the Reynolds number.

On the effect of parallel shear flow on the plasmoid instability

2018 ◽  
Vol 25 (10) ◽  
pp. 102117
Author(s):  
M. Hosseinpour ◽  
Y. Chen ◽  
S. Zenitani
Keyword(s):  
Shear Flow ◽  
Parallel Shear Flow

scholarly journals The lift on a small sphere in a slow shear flow

1965 ◽  
Vol 22 (2) ◽  
pp. 385-400 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Kinematic Viscosity ◽  
Lift Force ◽  
Flow Direction ◽  
Functional Dependence ◽  
Small Sphere ◽  
Translation Velocity ◽  
Parabolic Velocity Profile ◽  
Direction Opposite

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

The extension of the Miles-Howard theorem to compressible fluids

1970 ◽  
Vol 43 (4) ◽  
pp. 833-836 ◽  
Author(s):  
G. Chimonas
Keyword(s):  
Growth Rate ◽  
Shear Flow ◽  
Upper Bound ◽  
Unstable Mode ◽  
Vertical Gradient ◽  
Flow Speed ◽  
Incompressible Fluids ◽  
Compressible Fluids ◽  
Sufficient Condition ◽  
Parallel Shear Flow

A statically stable, gravitationally stratified compressible fluid containing a parallel shear flow is examined for stability against infinitesimal adiabatic perturbations. It is found that the Miles–Howard theorem of incompressible fluids may be generalized to this system, so that n2 ≥ ¼U′2 throughout the flow is a sufficient condition for stability. Here n2 is the Brunt–Väissälä frequency and U’ is the vertical gradient of the flow speed. Howard's upper bound on the growth rate of an unstable mode also generalizes to this compressible system.

Second-order recombination in a parallel shear flow

1989 ◽  
Vol 200 ◽  
pp. 389-407 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shear Flow ◽  
Concentration Distribution ◽  
Second Order ◽  
Explicit Solutions ◽  
Far Field ◽  
First Order ◽  
Parallel Shear Flow

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

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