Search results for "Free surface"
showing 10 items of 42 documents
The impacts of the ALE and hydrostatic-pressure approaches on the energy budget of unsteady free-surface flows
2008
Abstract This paper focuses on the energy budget in the calculation of unsteady free-surface flows on moving grids with and without using the ‘arbitrary Lagrangian–Eulerian’ (ALE) formulation or hydrostatic-pressure assumption. The numerical tool is an in-house general-purpose solver for the unsteady, incompressible and homogeneous Navier–Stokes equations in a Cartesian domain. An explicit fractional-step method and co-located finite-volume method are used for the second-order accurate integrations in time and space. The test cases are nonlinear and linear irrotational standing waves, which allow to characterise the impacts of an ALE or Eulerian formulation with moving grids by comparison w…
Lithospheric stresses in Rayleigh–Bénard convection: effects of a free surface and a viscoelastic Maxwell rheology
2015
A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the ‘sticky air’ method
2012
SUMMARY Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so-called ‘sticky air’ approach has gained interest as a free-surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosityfluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostati…
Analytical Study of the Thermal Induced Oscillations Known as Heartbeats
1998
Abstract A laser beam traveling horizontally at a short distance below the free surface of an absorbing solution exhibits various oscillatory states (periodic, quasiperiodic, and chaotic) which depend on both the buoyancy (Archimedes force) and the thermal coefficient of the surface tension (Marangoni effect). The beam oscillations have been called “heartbeats.” In this work, the heartbeats were produced by pumping 1-(2-pyridylazo)-2-naphthol (PAN) solutions in silicone oil with an Ar+continuous-wave laser beam. The relationships between PAN concentration and the other parameters that control the oscillatory behavior were studied. The frequency of the oscillations sensitively varied with sm…
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…
Unbaffled, Stirred Bioreactors for Animal Cell Cultivation
2017
One of the main features of animal cell bioreactors is that the cultured cells lack a strong membrane and are therefore more prone to shear damage. It is widely accepted that animal cell damage in aerated bioreactors is mainly related to burst bubbles at the air–liquid interface. A viable alternative to sparged bioreactors, aimed at minimizing cell damage, may be represented by uncovered, unbaffled, stirred tanks, which are able to provide sufficient mass transfer through the deep free surface vortex that takes place under agitation. As a consequence the need for bubble formation and subsequent bursting accompanied by cell damage is conveniently avoided. In this chapter, mass transfer perfo…
Application of AC and DC magnetic field for surface wave excitation to enhance mass transfer
2020
Abstract Refining the metallic melts and removal of contaminants from the free surface may be sped up by increasing the surface area of mass exchange interface. It is relevant to both the case of volatile impurity evaporation in a vacuum as well as the case of chemical reactions when the continuous crust of reaction products should be interrupted. Previously proposed low-frequency AC magnetic field excitation of intense surface waves is limited by skin-effect. The induced sign-alternating forcing at high dimensionless frequency values becomes dominantly pulsing at considerably higher than unity values, delivering time-averaged stirring without intense surface waves. Superimposing DC magneti…
Orientation and order in thin films of a combined liquid crystalline polymer
1994
The order in thin films of a combined liquid crystalline polymer is studied by X-ray reflection. Films of thicknesses of less than 200 nm on float glass are investigated as a function of temperature. The polymer with mesogenic groups in the main and side-chains exhibits smectic and cholesteric mesophases. Measurements in the smectic phases show a Bragg peak and smectic layers are oriented parallel to the substrate. The sample is thus macroscopically ordered by the influence of substrate and free surface. The film surface is very smooth after spincoating; surface roughness is typically 0.8 nm. First annealing of samples leads to a significant roughening of the free surface; roughness increas…
Surface reconstruction of the lamellar morphology in a symmetric poly(styrene-block-butadiene-block-methyl methacrylate) triblock copolymer: A tappin…
1996
The surface morphology of a symmetric poly(styrene-block-butadiene-block-methyl methacrylate) triblock copolymer (PS-b-PB-b-PMMA) with 6 wt % PB has been investigated by tapping mode scanning force microscopy (SFM). The results are compared to the bulk morphology as determined by transmission electron microscopy (TEM). In solvent-cast films PS/PMMA lamellae are formed, which are oriented nearly perpendicular to the free surface. Like in the bulk, also at the free film surface polybutadiene spheres are located at the lamellar PS/PMMA interface. However, contrary to the bulk, the surface morphology includes a large number of defects such as curved lamellar and disclinations, and the lamellar …
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.