Buoyancy-driven

Heat is often removed by simply allowing it to escape by convection, radiation, and conduction. However, such uncontrolled escape can lead to very large temperature fluctuations. It is better to surround the entire container, heaters and all, with a controUed-temperature cooled chamber. Even then, buoyancy-driven free convection from the ampul can lead to small temperature fluctuations. Jets of air or cooling water appHed directly onto the ampul adjacent to the heater have been employed. Both temperature and flow rate of the coolant should be controlled. 

The buoyancy-driven natural convection along the freezing interface in horizontal operation tends to be fairly vigorous. However, it also leads to sprea ding of the zone at the top owing to convection transport of heat upward. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

L. Davoust, R. Moreau, M. D. Cowley, P. A. Tanguy, F. Bertrand. Numerical and analytical modelling of the MHD buoyancy-driven flow in a Bridgman crystal growth configuration. J Cryst Growth 750 422, 1997. 

In quiescent liquids and in bubble columns, buoyancy-driven coalescence is more important. Large fluid particles with a freely moving surface will also have a low-pressure region at the edge of the particle where the velocity is maximum. This low-pressure region will not only allow the bubble to stretch out and form a spherical cap but also allow other bubbles to move into that area and coalesce. Figure 15.14 shows an example of this phenomenon. 

Figure 2. Radial-axial velocity field and temperature contours for a rotating-disk reactor at an operating condition where a buoyancy-driven recirculation vortex has developed. The disk temperature is HOOK, the Reynolds number is 1000, Gr/Re / = 6.2, fo/f = 1.28, and L/f = 2.16. The disk radius is 4.9 cm, the spin rate is 495 rpm. The maximum axial velocity is 55.3 cm/sec. The gas is helium.

Boundary layer similarity solution treatments have been used extensively to develop analytical models for CVD processes (2fl.). These have been useful In correlating experimental observations (e.g. fi.). However, because of the oversimplified fiow description they cannot be used to extrapolate to new process conditions or for reactor design. Moreover, they cannot predict transverse variations In film thickness which may occur even In the absence of secondary fiows because of the presence of side walls. Two-dimensional fully parabolized transport equations have been used to predict velocity, concentration and temperature profiles along the length of horizontal reactors for SI CVD (17,30- 32). Although these models are detailed, they can neither capture the effect of buoyancy driven secondary fiows or transverse thickness variations caused by the side walls. Thus, large scale simulation of 3D models are needed to obtain a realistic picture of horizontal reactor performance. 

The hypothesis that the transition to complex flow is buoyancy driven is supported by a scaling analysis to estimate the bulk density difference A q required to reverse a viscous flow. For the viscous and gravitational contributions to the flow to be comparable, one needs,... 

Epstein, M., Buoyancy-driven exchange flow through small openings in horizontal partitions, J. Heat Transfer, 1988, 110, 885-93. 

The modeling ideas used in the LEM have recently been extended to include a onedimensional description of the turbulence (Kerstein 1999a). This one-dimensional turbulence (ODT) model has been applied to shear-driven (Kerstein 1999a Kerstein and Dreeben 2000) and buoyancy-driven flows (Kerstein 1999b), as well as to simple reacting shear flows (Echekki et al. 2001 Hewson and Kerstein 2001 Kerstein 2002). Since the... 

In this section primary attention is directed at the turbulent processes that occur in the mixed layer as a result of the interaction between shear-and buoyancy-driven flows. The flux Richardson number Rf gives a measure of the relative importance of the buoyancy terms in the equations of motion, (g/T)w d , as compared to the shear production terms, u w dutbz. 

Dijk P, Berkowitz B (2000) Buoyancy-driven dissolution enhancement in rock fractures. Geology 28 1051-1054... 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

Figure 3.6. Schlieren photographs showing the changes in thickness of the diffusion boundary layer and the behavior of buoyancy-driven convection shown in relation to bulk supersaturation [1], [2]. The figure shows the (111) faceofaBa(N03)2 crystal from an aqueous solution. In region I, only the thickness of the diffusion boundary layer increases in region II, we see unstable lateral convection (HA) and intermittently rising plumes (IIB) and in region III we see steady buoyancy-driven convection.

K. Onuma, K. Tsukamoto, and I. Sunagawa, Effect of buoyancy driven convection upon the surface microtopographs of BalNOjjj and Cdl crystalsJ. Crystal Growth, 98,1989, 384-90... 

Buoyancy-driven flows of a radiatively participating fluid in a vertical cylinder heated from below (with A.G. Salinger, S. Brandon, and J.J. Derby). Proc. Roy. Soc. A442,313-341 (1992). 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

Convection in the crystal growth systems discussed earlier cannot be characterized by analysis with either perfectly aligned vertical temperature gradients or slender cavities, because these systems have spatially varying temperature fields and nearly unit aspect ratios. Even when only one driving force is present, such as buoyancy-driven convection, the flow structure can be quite complex, and little insight into the nonlinear structure of the flow has been gained by asymptotic analysis. 

Figure 7. Regions of buoyancy-driven flow for CZ growth in a high axial magnetic field. The figure is based on the results of Hjellming and Walker...

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