Momentum and buoyancy

Figure 26-53 shows the affect of initial momentum and buoyancy of the release. If the material is released as a jet, then the effective height of the release is increased. Furthermore, if the material released is heavier than air (which is the usual case for the release of most hydrocarbons), the plume initially slumps toward the ground until subsequent dilution by air results in a neutrally buoyant cloud. 

The preceding analyses hold only for circular fuel jets. Roper [10] has shown, and the experimental evidence verifies [11], that the flame height for a slot burner is not the same for momentum- and buoyancy-controlled jets. Consider a slot burner of the Wolfhard-Parker type in which the slot width is x and the length is L. As discussed earlier for a buoyancy-controlled situation, the diffusive distance would not be x, but some smaller width, say xb. Following the terminology of Eq. (6.25), for a momentum-controlled slot burner,... 

Plume rise Distance a smoke plume rises above its emission point due to the inherent momentum and buoyancy of the plume. 

In the general case, a buoyant jet has an initial momentum. In the region close to discharge, momentum forces dominate the flow, so it behaves like a nonbuoyant jet. There is an intermediate region where the influence of the initial momentum forces becomes smaller and smaller. In the final region, the buoyancy forces completely dominate the flow and it behaves like a plume. When the jet is supplied at an angle to the vertical direction, it is turned upward by the buoyancy forces and behaves virtually like a vertical buoyant jet in a far field. A negative buoyant jet continuously loses momentum due the opposite direction of buoyancy forces to the supply air momentum and eventually turns downward. 

Figure 8.18 shows spread rates measured for thin films ( 0.2 mm) of polyethylene teraphthalate (PET) and paper laid on fiberglass at various orientations spreading up and down [19]. The results can partly be explained by relating the momentum to buoyancy as... 

Strong buoyancy dominates the flow of the fire. Turbulence and pressure cause the ambient to mix (entrainment) into the fire plume. Momentum and thermal buoyancy... 

One credible leak scenario is a two-phase discharge of ammonia from the tank (possibly due to a hole in the tank due to corrosion). The presence of the dike and the deflection plates will reduce the release momentum and force the liquid to collect in the dike. Assuming that 3.8 kg/s is airborne upon release (the unmitigated scenario), a downwind distance to 1000 ppm was modeled to be 2 km, assuming neutral buoyancy, as shown in Table 4.3. 

The above equations can be solved using numerical methods, i.e., using the same basic procedures as used with forced convection. There is, however, one major difference between the procedures used in forced convection and in mixed convection. In forced convection, the velocity field is independent of the temperature field because fluid properties are here being assumed constant. Thus, in forced convection it is possible to first solve for the momentum and continuity equations and then, once this solution is obtained, to solve for the temperature distribution in tike flow. However, in combined convection, because of the presence of the temperature-dependent buoyancy force term in the momentum equation, all of the equations must be solved simultaneously. Studies of flows for which the boundary layer equations are not applicable are described in [24] to [43]. 

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. 

As a second example, we consider the kinetic equation (KE) for monodisperse, isothermal solid particles suspended in a constant-density gas phase. For clarity, we assume that the particle material density is significantly larger than that of the gas so that only the fluid drag and buoyancy terms are needed to account for momentum exchange between the two phases (Maxey Riley, 1983). In this example, the particles are large enough to have finite inertia and thus they evolve with a velocity that can be quite different than that of the gas phase. 

Of all the approaches, the k-6 model offers the highest relative independence of empirical relations. It appears to be the only one to allow a proper simulation of hydrogen dispersion, because it meets the requirements of describing effects such as turbulence energy in the gas cloud, interaction of the cloud with the atmospheric wind field, the characteristic positive buoyancy, transient sources with initial momentum, and last but not least, gas flow in a complex geometry (buildings, terrain). K-e modeling has been realized in a variety of... 

There could well be circumstances, however, in which a large accidental release at or near ground level is accompanied by sufficient momentum and thermal buoyancy of the gases and steam released, that something approaching the effect of a stack release is achieved. This is a very wide field of study, in which work has been stimulated mainly by the problems... 

Mixing layers, which occur in many engineering applications, are shear layers between fluid streams of different velocities and are characterised by transfer of mass, momentum and energy due to vortex formation. For mixing layers with density stratification, buoyancy forces are important besides shear stress and influence considerably the intensity of mixing. Stratification has been recognised to be of importance in heat exchange between sodium streams of different temperature in the upper plenum of FBRs under decay-heat-removal conditions. 

From a theoretical standpoint, in the presence of mass transfer, the momentum and continuity equations must be supplemented by the species continuity relation for the diffusing (or dissolving component). The coupling between the fluid mechanical and the mass transfer processes arises in three ways first, via the velocity through the bulk transport term in the species continuity equation second, the changes in bubble volume due to the transfer of a component from/to it. This results in a time-dependent normal velocity adjacent to the bubble surface. Finally, as the bubble size changes, the buoyancy force (and hence its velocity) will continually change with time. 

Momentum of the Material Released and Buoyancy. A typical dense gas plume is shown in Figure 2.26. Dense gases may also be released from a vent stack such releases exhibit a combination of dense and Gaussian behavior (Ooms et al., 1974), with initial plume rise due to momentum, followed by plume bendover and sinking due to dense gas effects. Far downwind from the release, due to mixing with fresh air, the plume will behave as a neutrally buoyant cloud. 

Since most releases are in the form of a jet rather than a plume, it is important to assess the effects of initial momentum and air entrainment on the behavior of a jet. Near its release point where the jet velocity differs gready from the wind velocity, a jet entrains ambient air due to shear (velocity difference), grows in size, and becomes diluted. For a simple jet (neutral buoyancy), its upward momentum remains constant while its mass increases. Therrfore, if vertically released, the drag forces increase as the surface area increases and eventually horizontal momentum dominates. The result is that the jet becomes bent over at a certain distance and is dominated by the wind momentum. If the jet has positive buoyancy (buoyant jet), the upward momentum will increase and the initial momentum will become negligible compared to the momentum gained due to the buoyancy. Then, the jet will behave like a plume. The rises of simple or buoyant jets, collectively called plume rises, have been smdied by many researchers and their formulas can be found in Briggs (1975, 1984) or most reviews on atmospheric diffusion (including Hanna et al., 1982). 

As shown in Fig. 6.24, increases with an increase in air fiow rate Qg (cm /s). Also, Foo is 4n increasing function of the vessel diameter D (cm) and the kinematic viscosity of molten slag, Vg, (see Fig. 6.25). The effects of the thickness of molten metal layer, H n (cm), and of molten slag layer, Hs (cm), on the total volume of molten metal droplets, Foo, are shown in Figs. 6.26 and 6.27, respectively. In Fig. 6.26, Foo increases monotonically with the thickness of the molten oil layer. On the other hand, in Fig. 6.27 Foo becomes independent of // when //m exceeds a certain critical value. This value was found to be closely related to the boundary between the momentum-dominant and buoyancy-dominant regions [17]. 

The effective stack height (equivalent to the effective height of the emission) is the sum of the actual stack height, the plume rise due to the exhaust velocity (momentum) of the issuing gases, and the buoyancy rise, which is a function of the temperature of the gases being emitted and the atmospheric conditions. 

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