Entrainment critical velocities

For velocities in excess of the critical velocity, that is, when entrainment occurs,... 

Diffusion Flame. When a slow stream of fuel g s flows from a tube into the atmosphere, air diffuses across the boundary of the stream and Brms an envelope of expl mixture around a core of gas. The core decreases in height until it disappears at some distance above the tube. It thus assumes the shape of a cone. On ignition, a flame front spreads thru the mixture and stabilizes itself around the cooe of fuel gas. The hydrocarbons in common fuel gases crack to form free C H. The shell of carbon-bearing gas so formed gives such flames their luminosity Turbulent Jet Flame. When a gas stream issues from an orifice above a certain critical velocity, it breaks up into a turbulent jet that entrains the surrounding air. The flame of such a jet consists of random patches of combustion and no cohesive combustion surface exists... 

These capture mechanisms are dependent on the critical re-entrainment velocity, which is the velocity at which droplets first break up from the rock surface and constrictions and are re-entrained into the flow stream. This critical velocity is a function of surface properties of the system and the droplet-size to pore-size ratio. Small double-layer repulsive forces and small droplet-size to pore-size ratios lead to large critical velocities. Soo and Radke (29) found the effect of velocity on emulsion flow in porous media to be dependent on the capillary number ([xv/0a, where x is fluid viscosity, v is velocity, is porosity, and a is surface tension). At low capillary numbers... 

Fluidized This is an expanded condition in which the solids particles are supported by drag forces caused by the gas phase passing through the interstices among the particles at some critical velocity. The superficial gas velocity upward is less than the terminal setting velocity of the solids particles the gas velocity is not sufficient to entrain and convey continuously all the solids. Specifically, the sohds phase and the gas phase are intermixed and together behave as a boU-ingjluid (Fig. 12-28). The gas forms the continuous phase, but the bulk density is not much lower than a continuous packed bed of solids. 

Drainage Failure — Similar to entrainment, this type of failure is related to the speed of the water current, except that it affects the oil directly at the boom. After critical velocity is reached, large amounts of the oil contained directly at the boom can be swept under the boom by the current. Both entrainment and drainage failure are more likely to occur with lighter oils. One or both of these two types of failure can occur, depending on the currents and the design of the boom. 

Boom failure — The failure of a containment boom to contain oil due to excessive winds, waves, or currents or improper deployment. Boom failure may be manifested in oil underflow, oil splashover, submergence or planing of the boom, or structural breakage. (See also Critical Velocity, Entrainment Failure.)... 

Entrainment failure — A type of boom failure resulting from excessive current speed or velocity. The head wave formed upstream of the oil mass contained within a boom becomes unstable and oil droplets are torn off and become entrained or drawn into the flow of water beneath the boom. (See also Boom failure, Critical velocity, Head wave.)... 

Continuing increases in operating velocity beyond that required at turbulent fluidization, a critical velocity, commonly called the transport velocity /tr. wiH be reached where a significant particle entrainment occurs. Beyond this point, continuing operation of the bed will not be possible without recycle of the entrained solids. The bed is now said to be in the fast fluidization regime. The transition velocity has been correlated by Bi et al. (1995) as... 

Another type of instability can occur when an upflow riser is directly coupled with a downcomer that returns entrained particles to the bottom of the riser. A pressure balance between the riser and the downcomer is required to maintain steady operation. If the gas velocity is decreased at a given solids circulation rate, a critical state may be reached at which steady operation at a given solids flux is impossible instability occurs because solids cannot be fed to the riser at the prescribed rate. Such an instability, referred to as standpipe-induced (Bi et al., 1993), occurs at a lower critical velocity for a higher solids holdup in the riser. The point of instability can be predicted based on an analysis of the pressure balance in the riser-downcomer loop (Bi and Zhu, 1993). To circumvent stand-pipe-induced instability, the solids inventory in the standpipe needs to be sufficiently high or, alternatively, the riser needs to be uncoupled from the downcomer, e.g., by employing screw feeders. 

Petrov J, Sedev R, Petrov P. (1992) Effect of geometry on steady wetting kinetics and critical velocity of film entrainment. Adv Colloid Interface Sci 38 229 269. 

Vapor space velocities normally should not exceed 100% of critical experience demonstrates that this keeps liquid entrainment into the flare line within acceptable limits. However, a velocity of 175% of critical is permitted when one is applyingthe 1.5 times Design Pressure Rule to remote contingencies,... 

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... 

The critical section of the circuit (Figure 5.3) is where there is no liquid refrigerant left to help move the oil, i.e. the evaporator outlet and the suction pipe back to the compressor. Entrainment velocities of 5-7 m/ s are required to ensure that oil droplets will be carried back by the dry refrigerant gas to the compressor. The principle of continuous fluid velocity means that the evaporator will be in a continuous circuit. This does not imply that it has to be one pipe, since many pipes may be arranged in parallel to get the required heat transfer surface, providing the minimum velocity criteria are met. 

Vapor-Liquid Gravity Separator Design Fundamentals The critical factors in the performance of a horizontal separator are the vapor residence time and the settling rate of the liquid droplets. However, two other factors enter into the design—the vapor velocity must be limited to avoid liquid entrainment, and there must be sufficient freeboard within the vessel to allow for a feed distributor. For vertical separators, the design is based on a vapor velocity that must be less than the settling velocity of the smallest droplet that is to be collected, with due allowance for turbulence and maldistribution of the feed. The vapor residence time is a function of the vapor flow rate (mass), vapor density, and volume of vapor space in the separator, based on the following ... 

The extent of entrainment of the liquid by the vapour rising over a plate has been studied by many workers. The entrainment has been found to vary with the vapour velocity in the slot or perforation, and the spacing used. Strang 60-1, using an air-water system, found that entrainment was small until a critical vapour velocity was reached, above which it increased rapidly. Similar results from Peavy and Baker 6 11 and Colburn 62 have shown the effect on tray efficiency, which is not seriously affected until the entrainment exceeds 0.1 kmol of liquid per kmol of vapour. The entrainment on sieve trays is discussed in Section 11.10.4. 

Here Va and are the true velocities at the entrance, of gas and liquid, respectively, and do is the critical droplet diameter. The value of the Wee depends on the degree of shock at the entrance section e.g., for smooth liquid injection, 22 was used, and for tee entrances, 13 to 16. Collier and Hewitt (C6) also measured entrainment in air-water mixtures, and have extended the same correlation to much wider ranges, using We — 13 in the case of jet injection with the results shown in Fig. 9. Anderson et al. (A5), during mass-transfer studies in a water-air-ammonia system, found en-... 

A recent publication by Zhivaikin (Zl) has reviewed Soviet work on film thickness and entrainment from films, and has presented correlations both for the thickness and for critical entrainment velocities. The relationships, given in terms of dimensionless quantities for downward cocurrent flow, upward cocurrent flow, and gas-liquid counterflow, follow. For laminar flow of liquid alone vertically downward along a pipe wall, the Nusselt equation was found to apply. 

The critical gas velocity, Vocb, at the start of entrainment is expressed by three separate equations, for low, medium and high Reynolds numbers. 

The decrease in film burn-out heat flux with increasing mass velocity of flow at constant quality has been explained by Lacey et al. in the following way. At constant quality, increasing total mass flow rate means increasing mass flow of vapor as well as liquid. It has been shown that above certain vapor rates increased liquid rates do not mean thicker liquid layers, because the increased flow is carried as entrained spray in the vapor. In fact, the higher vapor velocity, combined with a heat flux, might be expected to lead to easy disruption of the film with consequent burn-out, which seems to be what actually occurs at a constant steam mass velocity over very wide ranges of conditions—that is, the critical burn-out steam quality is inversely proportional to the total mass flow rate. 

In film breakdown at burn-out, nucleation may be a factor together with loss by entrainment and evaporation (in excess of spray deposition), and instabilities associated with surface tension. There is evidence for the existence of a critical vapor mass velocity, independent of pressure, above which the film is easily disrupted by heat fiux it is also clear that upstream conditions, including the inlet arrangements, must strongly influence the film breakdown at the exit. 

The question these correlations ask is why does the entrainment rate decrease for smaller particles for some systems whereas in other systems, the entrainment rate correlates with the particle terminal velocity or particle drag. Baeyens infers that particles may be clnstering due to an interparticle adhesion force that becomes dominant at some critical particle diameter. However, no evidence of particle clnsters was reported. Baeyens assnmption was based on fitting their data. Therefore, the role of particle clnstering on entrainment rates was difficult to establish from first principles. 

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