Velocity saltation

As shown in Fig. 14.2, the material conveying region is bounded by the air-only curve and the stationary-plug curve, where the air merely percolates through or flows above a packed bed of stationary particles. Dense-phase conveying occurs when v, the velocity of air, is below the so-called saltation velocity. 

One major difference between pneumatic transport and hydraulic transport is that the gas-solid interaction for pneumatic transport is generally much smaller than the particle-particle and particle-wall interaction. There are two primary modes of pneumatic transport dense phase and dilute phase. In the former, the transport occurs below the saltation velocity (which is roughly equivalent to the minimum deposit velocity) in plug flow, dune flow, or sliding bed flow. Dilute phase transport occurs above the saltation velocity in suspended flow. The saltation velocity is not the same as the entrainment or pickup velocity, however, which is approximately 50% greater than the saltation velocity. The pressure gradient-velocity relationship is similar to the one for hydraulic transport, as shown in... 

There are a variety of correlations for the saltation velocity, one of the most popular being that of Rizk (1973) ... 

The diameter effect on the saltation velocity is proportional to the 0.4 power of the inlet width. 

The saltation velocity, v., is dependent on cyclone dimensions, particle and fluid properties, v is expressed as ... 

Collection efficiency increases as the gas throughput increases. Kalen and Zenz [14] reported that collection efficiency increases with increasing gas inlet velocity to a minimum tangential velocity. This reaches the point where the dust is re-entrained or not deposited because of saltation. Koch and Licht [12] showed that saltation velocity is consistent with cyclone inlet velocities in the range of 50 to 90ft/sec. 

Inlet velocities—Inlet velocities are normally in the range of 10-30 m/s. Cyclone efficiency increases with inlet velocity up to a certain value at which saltation occurs and particles bounce along the cyclone wall and cannot be separated effectively. The saltation velocity is given, empirically, by [22]... 

The saltation velocity can be calculated based on the procedure presented by Zenz (1964), as follows ... 

Transpose u, the saltation velocity from the following equations ... 

In Equations 3.28 and 3.29, Gj is the flux of solids. For particle size distributions, the largest particle size should be used in these equations in order to avoid underestimation of the saltation velocity. 

Take the initial air velocity as 10% above the saltation velocity, to minimize risk of settling of coarse particles. 

The example is solved in two steps first, the saltation velocity is calculated, and second, the energy losses due to every aspect of the particles moving in the airstream inside the pipe are evaluated to estimate the total pressure drop needed for the particles to complete the conveying distance. 

Adding 10% to the saltation velocity, the initial air velocity in the pneumatic conveying is calculated as... 

The pneumatic conveying system of the previous example consists on 50 m horizontal pipe, two 0.5 m radius bends, and 15 m vertical pipe. Calculate the overall pressure drop on the system if the initial air velocity is 10% over the saltation velocity. 

In this chapter the choking and saltation velocities will be used to mark the boundaries between dilute phase transport and dense phase transport in vertical and horizontal pipelines, respectively. These terms are defined below in considering the relationships between gas velocity, solids mass flow rate and pressure drop per unit length of transport line in both horizontal and vertical transport. 

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