Effect of Buoyancy

The first experimental confirmation that gravity plays a role on spin modes in a liquid/sohd system came from the study of descending fronts in which the viscosity was significantly increased with sihca gel. Masere et al. [101] found that silica gel significantly altered the spin behavior, as predicted by Garbey et al. [77]. Pojman et al. made a similar observation in square reactors [103]. Pojman et al. studied the dependence of spin modes on viscosity with the FP of HDDA with persulfate initiator [106]. They found that the number of spins was independent of the viscosity until a critical viscosity was reached, at which point the spins vanished. 

The question arises why the analysis of llyashenko and Pojman worked so well for the methacryhc acid system even though they did not consider the effect of convection. They induced spin modes by reducing the initial temperature to 0 °C - below the melting point of methacryhc acid. Thus, the system was a sohd/sohd system and so hydrodynamics played only a small role. 

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Taylor instabilities involve effects of buoyancy or acceleration in fluids with variable density a light fluid beneath a heavy fluid is unstable by the Taylor mechanism. The upward propagation of premixed flames in tubes is subject to Taylor instability (11). 

The values of u and A0/AZ are based on assumed conditions of stability class F and stack height wind speed of 2.5 m/s for the stable layer above the inversion. The value of hj incorporates the effect of buoyancy induced dispersion on a/, however, elevated terrain effects are igndred. The equation above is solved by iteration, starting from an initial guess of x , = 5,000 m. The maximum ground-level concentration due to inversion break-up fumigation, Xf, is calculated from ... 

Plume height is based on the assumed F stability and 2.5 m/s wind speed, and the dispersion parameter (o, ) incorporates the effects of buoyancy induced dispersion. If x , is less than 200 m, then no shoreline fumigation calculation is made, since the plume may still be influenced by transitional rise and its interaction with the TIBL is more difficult to model. 

The effect of buoyancy in gases released into the air can be related either to the difference in the molecular weights or to the difference in temperature. Jb characterize the buoyancy for gases with a molecular density significantly different from the density of air, Elterman proposed a parameter P, with units... 

Nonbuoyant jets when the effect of buoyancy is negligible... 

For this safety criterion, we consider the fact that as the velocity decreases with increasing distance from the surface of the tank, it will reach some critical velocity, at which the induced movement of air will be insufficient to overcome the effects of crossdrafts or the buoyancy velocity At this point, we must ensure that the concentration is at, or below, some critical allowable concentration, Qfj,. The values of the critical concentration and velocity will depend (tn particular circumstances, but it is worth noting that must be at least equal to I g in order to overcome the effects of buoyancy, and the appropriate value will depend on the crossdrafts, which typically vary between 0.05 m to 0.5 in s F For the sake of providing examples, we have chosen to be the maximum of the buoyancy velocity and the typical cross-draft velocity. For the critical concentration we have chosen two values, C = 0.05 and C = 0.10. The actual value used by a designer would depend on the toxicity of the contaminant in question. 

Seung Jae Moon, Charn-Jung Kim, Sung Tack Ro. Effects of buoyancy and periodic rotation on the melt flow in a vertical Bridgman configuration. Int J Heat and Mass Transf 40 1X05, 1997. 

The gas motion near a disk spinning in an unconfined space in the absence of buoyancy, can be described in terms of a similar solution. Of course, the disk in a real reactor is confined, and since the disk is heated buoyancy can play a large role. However, it is possible to operate the reactor in ways that minimize the effects of buoyancy and confinement. In these regimes the species and temperature gradients normal to the surface are the same everywhere on the disk. From a physical point of view, this property leads to uniform deposition - an important objective in CVD reactors. From a mathematical point of view, this property leads to the similarity transformation that reduces a complex three-dimensional swirling flow to a relatively simple two-point boundary value problem. Once in boundary-value problem form, the computational models can readily incorporate complex chemical kinetics and molecular transport models. 

We use computational solution of the steady Navier-Stokes equations in cylindrical coordinates to determine the optimal operating conditions.Fortunately in most CVD processes the active gases that lead to deposition are present in only trace amounts in a carrier gas. Since the active gases are present in such small amounts, their presence has a negligible effect on the flow of the carrier. Thus, for the purposes of determining the effects of buoyancy and confinement, the simulations can model the carrier gas alone (or with simplified chemical reaction models) - an enormous reduction in the problem size. This approach to CVD modeling has been used extensively by Jensen and his coworkers (cf. Houtman, et al.) ... 

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 analysis was later modified to include some of the factors neglected by Nusselt1213. One of these is the effect of buoyancy forces acting on the liquid film. This results in the pl term in Equation 15.80 being replaced by Pl(pl — Pv ) Such buoyancy forces are usually only important close to the critical point. In most cases, the two most important factors that cause a significant deviation from Equation 15.80 are the presence of vapor shear forces and noncondensable gases in the vapor. Vapor shear forces act to increase the heat transfer coefficient, whereas noncondensable gases act to decrease it. 

This also applies to a body submerged in a fluid that is subject to any acceleration. For example, a solid particle of volume Vs submerged in a fluid within a centrifuge at a point r where the angular velocity is on is subjected to a net radial force equal to Ap on2rVs. Thus, the effect of buoyancy is to effectively reduce the density of the body by an amount equal to the density of the surrounding fluid. 

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... 

Strang el al. (S13), 1937 Flow of water films (IVro - 6-150) inside tubes with stationary second phase of tetralin, kerosine, and 4 oils of various densities and viscosities. Effect of buoyancy forces on film thickness determined. 

In the present chapter and in the following two chapters, which are concerned with turbulent boundary layer flows and with turbulent duct flows, respectively, consideration will be restricted to forced flows, i.e., the effect of buoyancy forces on the mean flow and on the turbulence structure will be assumed to be negligible. Some discussion of the effect of buoyancy forces on turbulent flows will be given in Chapter 9. 

Effect of buoyancy forces on flow over a square and a circular cylinder. 

This chapter has been concerned with flows in wb ch the buoyancy forces that arise due to the temperature difference have an influence on the flow and heat transfer values despite the presence of a forced velocity. In extemai flows it was shown that the deviation of the heat transfer rate from that which would exist in purely forced convection was dependent on the ratio of the Grashof number to the square of the Reynolds number. It was also shown that in such flows the Nusselt number can often be expressed in terms of the Nusselt numbers that would exist under the same conditions in purely forced and purely free convective flows. It was also shown that in turbulent flows, the buoyancy forces can affect the turbulence structure as well as the momentum balance and that in turbulent flows the heat transfer rate can be decreased by the buoyancy forces in assisting flows whereas in laminar flows the buoyancy forces essentially always increase the heat transfer rate in assisting flow. Some consideration was also given to the effect of buoyancy forces on internal flows. 

Merkin, J.H.. "The Effect of Buoyancy Forces on the Boundary-Layer Flow over a Semi-Infinite Vertical Flat Plate in a Uniform Free Stream , J. Fluid Mech., Vol. 35, pp.439-450, 1969. 

The Effect of Buoyancy on the Thermal Ignition of Carbon Monoxide... 

In this paper, we report on a calculation which shows the effect of buoyancy on thermal ignition of a homogeneous mixture. 

The general problem has been to extend the usefulness of the induction parameter model proposed by Oran et al. (1). This induction parameter model (IPM) is proposed as a means to enable one to estimate, relatively easily, the energy necessary to achieve ignition when using a thermal heating source Much of the calibration of this model, for example the effect of deposition volume (quench volume), can be done with one-dimensional models, and shock tube experiments. There are phenomena, however, which must be studied in two or three dimensions. Examples are turbulence and buoyancy. This paper discusses the effect of buoyancy and possible extensions to the IPM. 

As can be seen from equation (3 - 7) there is no mechanism to allow for the effects of buoyancy. In section (V) we will discuss a possible extension. 

The calculations presented here are intended to show the effect of buoyancy on the ignition properties of a homogeneous fuel-oxydizer mixture, in this case carbon monoxide-oxygen. The experimental cell chosen was 1.2 cm in height, and 1.6 cm in diameter. The grid system was 40 x 40 for the ma n gricj and 39 x 39 for the grid used to carry the time histories i / and . The initial species composition was CO + 20. ... 

When Boussinesq approximation is adopted in full conservation equations, it is noted that the effect of buoyancy force appears in terms of GrjRe where Gr is the Grashof number and Re is the Reynolds number defined in terms of appropriate length, velocity and temperature scales. However, Leal et al. (1973) and Sparrow Minkowycz (1962) have shown that the equivalent buoyancy parameter with the boundary layer assump-... 

In general, dynamic hysteresis is smaller with smaller cross-sectional area because the effect of buoyancy is less. Thus, the dynamic hysteresis is not a measure of surface characteristics. Intrinsic hysteresis is a measure of the surface dynamic stability of the surface. 

This is the equation that governs the fluid motion in the boundaiy layer due to the effect of buoyancy. Note that the momcnmni equation involves the temperature, and thus the momentum and energy equations must be solved simultaneously. 

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