scholarly journals Convection in directionally solidifying alloys under inclined rotation

2000 ◽  
Vol 412 ◽  
pp. 93-123 ◽  
Author(s):  
C. A. CHUNG ◽  
FALIN CHEN
Keyword(s):  
Boundary Layer ◽  
Inclination Angle ◽  
Boundary Layer Flow ◽  
Fluid Layer ◽  
Longitudinal Mode ◽  
Point Of View ◽  
Induced Flow ◽  
Layer Flow ◽  
Parallel Shear Flow ◽  
Induced Velocity

In an experiment on binary alloys directionally solidifying from below, Sample & Hellawell (1984) showed that the plume convection can be successfully prohibited by rotating the cooling tank around an inclined axis. In the present paper we interpret their experimental observation by an analytical approach. Results show that there is a flow induced by the inclination. The induced flow in the fluid layer is a parallel shear flow consisting of three parts: the thermal boundary-layer flow, the solute boundary- layer flow, and the Ekman-layer flow. In the mush, the induced flow is also a parallel flow but of much smaller velocity, consisting of two flows of opposite directions. The induced velocity in the fluid layer increases with inclination angle and decreases with the effective Taylor number Te. The induced velocity in the mush also increases with inclination angle but remains virtually the same on varying the speed of rotation. The linear stability analysis of the mushy layer shows that, due mostly to the reduction of buoyancy, the mush becomes more stable as the inclination angle increases. In the precession-only case, the most-unstable mode of instability is the longitudinal mode, which propagates in a direction perpendicular to the induced flow. In the spin (with or without precession) case, the instability modes propagating in different directions are of equal stability. Because the induced flow changes direction with a frequency equal to the spin angular velocity, the flow scans over all the directions of the system and stabilizes equally the modes in different directions. We conclude on the basis of the present results and from the practical point of view that spin-only rotation is more effective than the precession-only rotation in stabilizing the convection during solidification.

Vortex Instability in Buoyancy-Induced Flow over Inclined Heated Surfaces in Porous Media

1979 ◽  
Vol 101 (4) ◽  
pp. 660-665 ◽  
Author(s):  
C. T. Hsu ◽  
Ping Cheng
Keyword(s):  
Boundary Layer ◽  
Inclination Angle ◽  
Boundary Layer Flow ◽  
Heated Surface ◽  
Wave Number ◽  
Heated Plate ◽  
Local Similarity ◽  
Linear Temperature ◽  
Vortex Instability ◽  
Layer Flow

A linear stability analysis is performed for the study of the onset of vortex instability in free convective flow over an inclined heated surface in a porous medium. The undisturbed state is assumed to be the steady two-dimensional buoyancy-induced boundary layer flow which is characterized by a non-linear temperature profile. By a scaling argument, it is shown that the length scales of disturbances are smaller than those for the undisturbed boundary layer flow, thus, confirming the so-called “bottling effects” whereby the disturbances are confined within the boundary layer. By neglecting the lowest order terms in the three-dimensional disturbances equations, the simplified equations are solved based on the local similarity approximations, wherein the disturbances are assumed to have a weak dependence in the streamwise direction. The resulting eigenvalue problem is solved numerically. The critical parameter and the critical wave number of disturbances at the onset of vortex instability are computed for different prescribed wall temperature distribution of the inclined surface. It is found that the larger the inclination angle with respect to the vertical, the more susceptible is the flow for the vortex mode of disturbances; and in the limit of zero inclination angle (i.e., a vertical heated plate) the flow is stable for this form of disturbances.

A Note on the Induced Flow and Heat Transfer Due to a Deforming Cone Rotating in a Quiescent Fluid

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Boundary Layer ◽  
Layer Structure ◽  
Rotating Disk ◽  
Relevant Information ◽  
Point Of View ◽  
Physical Parameters ◽  
Rotating Disk Flow ◽  
Flow And Heat Transfer ◽  
Induced Flow ◽  
Layer Flow

This short brief is to address the boundary layer flow of motion due to a rotating as well as stretchable/shrinkable flexible cone in an otherwise still fluid. It is shown that the relevant information on the progress of the triggered boundary layer structure can be obtainable from the limiting traditional deformable rotating disk flow of von Karman, recently published in the literature. Thus, the physical parameters of great interest from the engineering point of view concerning a cone of a particular apex angle can be easily deduced as a multiplying factor corresponding to the deformable rotating disk flow.

The spreading of insoluble surfactant at the free surface of a deep fluid layer

1995 ◽  
Vol 293 ◽  
pp. 349-378 ◽  
Author(s):  
O. E. Jensen
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Boundary Layer Flow ◽  
Fluid Layer ◽  
Active Material ◽  
Lower Boundary ◽  
Leading Edge ◽  
Surface Contamination ◽  
Surface Boundary ◽  
Layer Flow

The unsteady spreading of an insoluble monolayer containing a fixed mass of surface-active material over the initially horizontal free surface of a viscous fluid layer is investigated. A flow driving the spreading is induced by gradients in surface tension, which arise from the nonuniform surfactant distribution. Distinct phases in the flow's dynamics are distinguished by a time T = H02/v, where H0 is the fluid depth and v its viscosity. For times t [Lt ] T, i.e. before the lower boundary has any significant influence on the flow, a laminar sub-surface boundary-layer flow is generated. The effects of gravity, capillarity, surface diffusion or surface contamination may be weak enough for the flow to drive a substantial unsteady displacement of the free surface, upward behind the monolayer's leading edge and downward towards its centre. Similarity solutions are identified describing the spreading of a localized planar monolayer strip (which spreads like t1/2) or an axisymmetric drop (which spreads like t3/8); using the Prandtl transformation, the associated boundary-layer problems are solved numerically. Quasi-steady sub-layers are shown to exist at the centre and at the leading edge of the monolayer; that due to surface contamination, for example, may eventually grow to dominate the flow, in which case spreading proceeds like t3/4. Once t = O(T), vorticity created at the free surface has diffused down to the lower boundary and the flow changes character, slowing appreciably. The dynamics of this stage are modelled by reducing the problem to a single nonlinear diffusion equation. For a spreading monolayer strip or drop, the transition from an inertia-dominated (boundary-layer) flow to a viscosity-dominated (thin-film) flow is predicted to be largely complete once t ≈ 85 T.

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