Acceleration buoyancy

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). 

Several additional studies [Winitzer, Sep. ScL, 8(1), 45 (1973) ibid., 8(6), 647 (1973) Maru, Wasan, and Kintner, Chem. Eng. Set., 26, 1615 (1971) and Rapacchietta and Neumann, J. Colloid Inteiface ScL, 59(3), 555 (1977)] which include body forces such as gravitational acceleration and buoyancy have been made. A typical example of a force balance describing suen a system (Fig. 22-39) is summarized in Eq. (22-41). 

The analytical method of jet trajectory study developed by Shepelev allows the derivation of several other useful features and is worth describing. On the schematic of a nonisothermal jet supplied at some angle to the horizon (Fig. 7.25), 5 is the jet s axis, X is the horizontal axis, and Z is the vertical axis. The ordinate of the trajectory of this jet can be described as z = xtga a- Az, where Az is the jet s rise due to buoyancy forces. To evaluate Az, the elementary volume dW with a mass equal to dm dV on the jet s trajectory was considered. The buoyancy force influencing this volume can be described as dP — g(p -Pj). Vertical acceleration of the volume under the consideration is j — dP / dm — -p,)/ g T,-T / T. Vertical... 

The flow field created within the protection zone depends mainly on the density difference between supply air and room air (Fig. 10.90). With vertical flow the supply air should be isothermal or cooler than ambient air. If it were warmer, the extension of the controlled flow would be reduced due to buoyancy effects, resulting in the supply air not reaching the operator s breathing zone. As the. supply air cannot be used for heating, the operator s thermal comfort should be maintained, preferably with radiant heaters in cold environments. If the supply air temperature is lower than the room air, the denser supply air accelerates down to the operator, and for continuity reasons the supply flow contracts. Excessive temperature differences result in a reduced controlled flow area with thermal discomfort, and should only be used in special cases. 

Buoyancy in some form is employed in nearly all categories of underwater and surface systems to support them above the ocean bottom or to minimize their submerged weight. The buoyant material can assume many different structural forms utilizing a wide variety of densities. The choice of materials is severely restricted by operational requirements, since different environmental conditions exist. For example, lighter, buoyant liquids can be more volatile than heavier liquids. This factor can have a deleterious effect on a steel structure by accelerating stress corrosion or increasing permeability in reinforced plastics. 

Another question that arises is the limiting size of the gas bubbles. As the bubble volume Vj, increases, the buoyancy force V gAp of the bubble increases (g is the acceleration of gravity and Ap is the density difference between the liquid and the gas). The bubble will tear away from the electrode surface as soon as this buoyancy force becomes larger than the forceretaining the bubbles. 

When a particle falls under the influence of gravity, it will accelerate until the combination of the frictional drag in the fluid and buoyancy force balances the opposing gravitational force. If the particle is assumed to be a rigid sphere, at this terminal velocity, a force balance gives3,4,7,8... 

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. 

Figure 5-6 The initial acceleration and buoyancy of the released material affects the plume character. The dispersion models discussed in this chapter represent only ambient turbulence. Adapted from Steven R. Hanna and Peter J. Drivas, Guidelines for Use of Vapor Cloud Dispersion Models (New York American Institute of Chemical Engineers, 1987), p. 6.

Given the condition that buoyancy can play a significant role, the fuel gases start with an axial velocity and continue with a mean upward acceleration g due to buoyancy. The velocity of the fuel gases v is then given by... 

At steady-state terminal velocity, the acceleration term in the force balance (B9) on a moving submerged body is zero, and the balance may be written so that gravity forces are balanced by the sum of buoyancy and resistance forces. 

When a raindrop ceases to accelerate, its weight is balanced by the drag force (buoyancy is negligible) ... 

A stationary particle suspended in a fluid experiences a buoyancy force Fb, evaluated from Archimedes principle as the weight of fluid displaced, pfgv, where pf is the fluid density, g is the acceleration due to gravity and v is the volume of the particle. If the particle begins to move the fluid will exert an additional force, the drag force, made up of two components the skin friction drag, which is a direct result of the shear stress at the surface due to fluid viscosity, and the form drag due to differences of pressure over the surface of the particle. 

Using the techniques discussed in section III and IV we have been able to study the effect of acceleration on ignition of a homogeneous fuel oxydizer mixture. The ability to study multidimensional effects (buoyancy, turbulence etc.) hinges on the use of numerical methods (slow-flow, asymptotic chemistry etc.) which circumvent the time constraints encountered in brute force techniques. These methods go hand in hand with modem fast computers, especially vector machines where judicious programming allows us to attain the actual memory or CPU cycle time. 

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