Slugs velocity

Figure 36. Relation between particle size and reduced slugging velocities for coal particles.

The slug velocity, Usl, is defined as the rising velocity of the slug relative to the particle velocity at its nose and can be expressed as... 

The size, the velocity, and the solid volume fraction of the bubbles and the solids slugs are reflected in the shape and frequency of the force probe response as shown in Fig. 24. The amplitude of the oscillations is a measure of the solid slug velocity and solid volume fraction. Inside the bubbles, the probe response is nearly flat because of the negligible solids fraction inside the bubble. The spread of the peaks and the length of the flat portions of the probe responses are measures of the size and velocity of the solid slugs and gas bubbles respectively. 

For turbulent upward liquid flow, it was found experimentally that the slug velocity is given for superficial liquid Reynolds numbers over 8000 by... 

That is, the component of the slug velocity due to liquid upflow is very nearly the same as the maximum liquid velocity at the tube center for turbulent flow. 

When none of the sets of conditions given in (a), (b), or (c) apply. Fig. 9.10 should be used to predict the slug velocity. 

At this point, it is important to know if the operating gas superficial velocities, which are from 2.5-15 cm/s, are higher than the minimum bubbling velocity and lower than the minimum slugging velocity, respectively. 

R. Pan, P.W. Wypych, Pressure drop and slug velocity in low-velocity pneumatic conveying of bulk solids, Powder Technol. 94 (1997) 123-132. 

Applying the simple two-phase theory to the slugging bed, the average slug velocity in continuous slugging flows can be expressed by [Ormiston et al 1965]... 

If the tube diameter is less than 10 mm, the liquid surface tension will affect the slug velocity and simulation predicts that for diameters less than about 5 mm with water the surface tension can stop the upward motion of the slug causing an air lock, implying careful assessment is required before applying bubbling to the lumen of hollow fiber membranes. 

Calculate the minimum fluidization velocity u f, minimum bubbling velocity Wmbi and minimum slugging velocity s. Because the calculation of ms requires a... 

In the same way, Xu et al. (2013) proposed a correlation (Eq. 2.2.3) that includes the effects of slug velocity Uuc, capillary diameter d, and aqueous to organic phase flow rate ratio q. The capillary diameters for the correlation were 0.6 and 0.8 mm. 

The stroke ratio Ljd = U/((od) is equal to the inverse of the Strouhal number. However, the limitation of stroke ratio definition is the assumption of slug-velocity profile. Holman et al. [3] discussed the formation criteria of synthetic jet based on both numerical simulation and experiment. They observed that the vortex ring needs to withstand the suction velocity during ingestion stroke which is a function of the vortex strength. From dimensional reasoning, they proposed the following criterion for jet formation ... 

A liquid-liquid system flows in a circular cross section capillary with < ( = 0.8mm diameter forming a continuous water phase and a dispersed toluene phase. The flow rate of the continuous phase is Smlmin while the flow rate of the dispersed phase is 4mlmin"k Estimate the pressure drop in the microchannel assuming dispersed slug velocity equals the two-phase velocity. 

Figure 12.18 Concentration profiles of acetic acid in two consecutive slugs with various operation times t (slug length = 1.9 mm, slug velocity 3.33 m s ). Reproduced by permission of Elsevier [51].

In the definition of the capillary number, the slug velocity is slightly higher than the superficial flow velocity. In analogy with the theoretical predictions of Charles [63] for the pipeline flow of slugs (capsules), the slug flow and average flow velocity can be related by... 

We can also describe the head rise at an elbow due to a decrease in slug velocity upon impact with the elbow. For a sudden flow stoppage ... 

In a partial flow stoppage, the head rise would be a fraction of / max However, the rhagnitude of the pressure forces involved depends primarily on the slug-flow velocity. For a liquid-oxygen slug velocity of about 10 fps, the head rise would be an estimated 350 ft (172 psi). 

Calculate the minimum fluidization velocity minimum bubbling velocity and minimum slugging velocity (u ). As the calculation of requires a value of the reactor diameter, which is not known, assume a value and go through the calculations. This velocity represents the maximum permissible velocity and therefore the minimum diameter. From the given volumetric flow rate, calculate the maximum diameter by assuming a velocity of, say, Choose a suitable diameter between these limits. Iteration may be needed. 

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