Search results for "Free surface"

3D modeling of doping from the atmosphere in floating zone silicon crystal growth

2017

Abstract Three-dimensional numerical simulations of the inert gas flow, melt flow and dopant transport in both phases are carried out for silicon single crystal growth using the floating zone method. The mathematical model allows to predict the cooling heat flux density at silicon surfaces and realistically describes the dopant transport in case of doping from the atmosphere. A very good agreement with experiment is obtained for the radial resistivity variation profiles by taking into account the temperature dependence of chemical reaction processes at the free surface.

Mixing dynamics in uncovered unbaffled stirred tanks

2014

Abstract The present work is aimed at providing experimental information on mixing rates in an unbaffled vessel under free surface vortexing conditions. The planar laser induced fluorescence (PLIF) technique was used for measuring the dispersion dynamics of a passive tracer over a vertical section of the vessel. In agreement with the quite scant literature information available for these systems, results confirm the existence of two well defined, partially segregated, zones that give rise to a double mixing dynamics behavior. A suitable mixing time definition is proposed and applied to a number of experimental runs with different stirrer geometries and agitation speeds. Results confirm that…

Turbulent Fluid Flow in Closed- and Free-Surface Unbaffled Tanks Stirred by Radial Impellers

1996

Critical wetting in the square Ising model with a boundary field

1990

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH1 acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surfac…

Incomplete self-similarity and flow velocity in gravel bed channels

2000

Velocity measurements, previously carried out using both a miniature current flowmeter and an acoustic Doppler velocimeter, are used to verify the applicability of the incomplete self-similarity theory to deduce the velocity profile in a gravel bed channel. Then, for the velocity profiles having the maximum value below the free surface and for the S-shaped profiles, the power velocity distribution is corrected using a new divergence function. For each value of the depth sediment ratio the nondimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross section. Finally, a semilogarithmic flow resistance equa…

Experimental and numerical study of anomalous thermocapillary convection in liquid gallium

1999

Thermocapillary Marangoni convection of liquid gallium was studied experimentally and numerically. A specially designed experimental setup ensured an oxide-free surface of the liquid gallium for a very long time. The convective flow at the free surface was found to be directed opposite to both buoyancy-driven and ordinary thermocapillary convection. The anomalous direction of the thermocapillary flow was explained by the presence of a small amount of a surface-active contaminant—lead adsorbed at the free surface. Two different approaches were used to describe the observed phenomenon. First, the flow was treated as a pure thermocapillary convection with a modified dependence of the surface t…

Liquid metal free surface dynamics in rotating permanent magnet stirrer

2020

Abstract We study liquid metal stirring by rotating permanent magnets in a laboratory-scale rectangular glass container. The main goal is numerical model validation using experimental free surface shape data. We find reasonable agreement between the experiments and coupled liquid metal magnetohydrodynamics simulations. Since the surface tension forces are not dominant here, free surface is deformed mainly by the dynamic pressure of the bulk flow. Therefore, we can conclude that not only the free surface profile is similar to experiments, but the bulk flow must be also very similar.

Mass transfer and hydrodynamic characteristics of unbaffled stirred bio-reactors: Influence of impeller design

2014

Abstract Unbaffled stirred tanks are increasingly recognized as a viable alternative to common baffled tanks for a range of processes where the presence of baffles is undesirable for some reason. For instance, in the case of shear sensitive cell cultivation (e.g. human cells), unbaffled tanks have been recently found to be able to provide sufficient mass transfer through the free surface vortex. As a consequence the need for bubble formation and subsequent bursting, along with relevant cells damage, is conveniently avoided. In this work the influence of impeller geometry on mass transfer performance and power demand of an unbaffled stirred vessel operating both in sub-critical conditions (t…

Sound conversion phenomena at the free surface of liquid helium. I. Calculation of the coefficients of reflection, transmission, and transformation o…

1980

On the basis of a set of boundary conditions describing quite generally mass and energy transport processes across the free surface of helium II, the acoustic coefficients of reflection, transmission, and transformation of first sound, second sound, and the sound wave propagating in the vapor are calculated in the case of perpendicular incidence of sound waves against the liquid-vapor phase boundary. Considering rigorously the influences of the Onsager surface coefficients, the isobaric thermal expansion coefficients, and the thermal conductivities of the liquid and the vapor, we derive sets of equations from which the acoustic coefficients are determined numerically. For estimations, simpl…

Dip Phenomenon in High-Curved Turbulent Flows and Application of Entropy Theory

2018

The estimation of velocity profile in turbulent open channels is a difficult task due to the significant effects of the secondary flow. The present paper investigates the mechanism of the velocity-dip phenomenon, whereby the location of the maximum velocity appears to be below the free surface. Previous studies conducted in straight channels relate the mechanism of the velocity-dip phenomenon to secondary flow induced by anisotropy of turbulence. This work focuses on high-curved channels where the secondary motion, which is also induced by the channel’s curvature, evolves along the bend. The width-to-depth ratio, B/h, is one of the most important parameters that are affecting the secondary …