Entrainment of fluid

The decreased overall density of the mixing layer with combustion increases the dimensions of the large vortices and reduces the rate of entrainment of fluids into the mixing layer [13]. Thus it is appropriate to modify the simple phenomenological approach that led to Eq. (6.31) to account for turbulent diffusion by replacing the molecular diffusivity with a turbulent eddy dif-fusivity. Consequently, the turbulent form of Eq. (6.38) becomes... 

Witze Am. In.st. Aeronaut. Astronaut. J., 12, 417-418 [1974]) gives equations for the centerline velocity decay of different types of subsonic and supersonic circular free jets. Entrainment of surrounding fluid in the region of flow establishment is lower than in the region of estabhshed flow (see Hill, J. Fluid Mech., 51, 773-779 [1972]). Data of Donald and Singer (T/V7/1.S. In.st. Chem. Eng. [London], 37, 255-267... 

The total flow rate of fluid entrained by the surface is... 

Type of bed Moving Entrained Moving Fluid Fluid Entrained... 

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. 

Sawyer, R. A. 1963. Two-dimensional reattaching jet flows including the effects of curvature on entrainment. Journal of Fluid Mechanics, vol. 17, pp. 481-498. 

For a given particle of size d, from the point M where the equilibrium line meets the line of zero vertical velocity (see Fig. 13.4), the critical path of the particle may be defined. All particles of this size between points D and G are entrained in the downward stream and are collected. The remaining particles of this size join in the upward-moving stream of fluid and penetrate the cyclone. The point D may be obtained by tracking back the particle trajectory from the point M using the equation of the particle trajectory, which is given by... 

SFE has been used extensively in the analysis of solid polymers. Supercritical fluid extraction of liquid samples is undertaken less widely because dissolution or entrainment of the matrix can occur. As illustrated elsewhere SFE has also been applied for the analysis of liquid poly(alkylene glycol) (PAG) lubricants and sorbitan ester formulations [370]. The analysis of PAG additives (antioxidants, biocides and anticorrosion, antiwear and antifoaming agents) is hindered by the presence of the low molecular weight PAG matrix (liquid) and therefore a method for the selective separation of additives from PAG is required. The PAG... 

Ionization, sorption, volatilization, and entrainment with fluid and particle motions are important to the fate of synthetic chemicals. Transport and transfer processes encompass a wide variety of time scales. Ionizations are rapid and, thus, usually are treated as equilibria in fate models. In many cases, sorption also can be treated as an equilibrium, although somtimes a kinetic approach is warranted (.2). Transport processes must be treated as time-dependent phenomena, except in simple screening models (.3..4) ... 

When an open tank with a free surface is stirred with an impeller, a vortex will form around the shaft. It is important to prevent this vortex from reaching the impeller, because entrainment of air in the liquid tends to cause foaming. The shape of the free surface depends upon (among other things) the fluid properties, the speed and size of the impeller, the size of the tank, and the depth of the impeller below the free surface. 

A schematic representation of this reactor model is shown in Figure 22.2. Particles of solid reactant B are in BMF, and fluid reactant A is uniform in composition, regardless of its flow pattern. The solid product, consisting of reacted and/or partially reacted particles of B, leaves in only one exit stream as indicated. That is, we assume that no solid particles leave in the exit fluid stream (no elutriation or entrainment of solid). This assumption, together with the assumption, as in the SCM, that particle size does not change with reaction, has an important implication for any particle-size distribution, represented by P(R). The implication is that P(R) must be the same for both the solid feed and the solid exit stream, since there is no accumulation in the vessel in continuous operation. Furthermore, in BMF, the exit-stream properties are the same as those in the vessel Thus, P(R) is the same throughout the system ... 

At sufficiently high velocity of fluid upward through a bed of particles, the particles become entrained and do not settle that is, the particles are carried up with the fluid. Elutriation is the selective removal of particles by entrainment, on the basis of size. 

The increase in velocity seen as part of the Venturi effect simply demonstrates that a given number of fluid particles have to move faster through a narrower section of tube in order to keep the total flow the same. This means an increase in velocity and, as predicted, a reduction in pressure. The resultant drop in pressure can be used to entrain gases or liquids, which allows for applications such as nebulizers and Venturi masks. 

The effect is thought to occur because a moving column of fluid entrains molecules lying close to the curved surface, creating a relatively low pressure,... 

Liepmann, D., and M. Gharib. 1992. The role of streamwise vorticity in the near-held entrainment of round jets. J. Fluid Mechanics 245 643-68. 

Basically the ultimate pressure of fluid entrainment pumps is restricted by the value for the partial pressure of the fluid used at the operating temperature of the pump. In practice one tries to improve this by introducing baffles or cold traps. These are condensers" between fluid entrainment pump and vacuum chamber, so that the ultimate pressure which can be attained in the vacuum chamber is now only limited by the partial pressure of the fluid at the temperature of the baffle. 

The various types of fluid entrainment pumps are essentially distinguished by the density of the pump fluid at the exit of the top nozzle facing the high vacuum side of the pump ... 

Included in the class of fluid-entrainment pumps are not only pumps that use a fast-streaming vapor as the pump fluid, but also liquid jet pumps. The simplest and cheapest vacuum pumps are water jet pumps. As in a vapor pump (see Fig. 2.46 or 2.51), the liquid stream is first released from a nozzle and then, because of turbulence, mixes with the pumped gas in the mixing chamber. Finally, the movement of the water - gas mixture is slowed down in a Venturi tube. The ultimate total pressure in a container that is pumped by a water jet pump is determined by the vapor pressure of the water and, for example, at a water temperature of 15 °C amounts te about 17 mbar. 

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