Inclined flows

In vertical downward flow as well as in upward and downward inclined flows, the flow patterns that can be observed are essentially similar to those described above, and the definitions used can be applied. Experimental data on flow patterns and the transition boundaries are usually mapped on a two dimensional plot. Two basic types of coordinates are generally used for this mapping - one that uses dimensional coordinates such as superficial velocities, mass superficial velocities, or momentum flux and another that uses dimensionless coordinates in which some kind of dimensionless groups are used as coordinates. The dimensional coordinates maps are inherently limited to the range of data and flow conditions under which the experiments were conducted. In spite of this limitation, it is widely used because of its simplicity and ease of use. Figure 24 provides an example of such a map. 

Aziz, Z. B., and Klinzing, G. E., Plug Flow Transport of Cohesive Coal Horizontal and Inclined Flows, Powder Tech., 55 97-105 (1988)... 

CORRECTION FACTOR FOR RELIEF LINE FRICTION FOR UPWARDS INCLINED FLOW WITH Fi = 0.1... 

Fig. 11 defines flow patterns for horizontal (and inclined) flow ... 

Measurements of t. carried out by Andritsos and Hanratty [28] in 2.54cm and 9.53cm horizontal pipes (for air-liquid, liquid viscosities of 1-70 centipoise) and by Andreussi and Person [73] in slightly inclined flows showed that the values of fjf increase dramatically when K-H waves are present. However, for smooth interface they found that fJf = 1, thus substantiating the assumption that for smooth... 

As a corollary, it can be stated that the condition of unstable dynamic waves or ill-posedness is sufficient to indicate instability, whereas the condition of c < 0, or well-posedness, is necessary but insufficient to ensure stability. The above ideas and interpretations as detailed above with regards to the horizontal system of Figure 8 also prevail basically in inclined flows, although limiting stability and well-posedness boundaries may demonstrate entirely different structures (Brauner and Moalem Maron [45]). 

The common flow patterns for horizontal and slightly upward inclined flows in a pipe are illustrated in Figure 22.13. Though the two-phase flow patterns in horizontal pipes are... 

The effect of different pipe wall materials has been probed by Rizk (1973) and others. This effect, however, appears to be minor and even of little consequence when a fine powder coats the conveying line wall. For inclined flow Klinzing et al. (1989) has given a frictional representation that covers all kinds of inclined flows from horizontal to vertical ... 

New models for inclined flows are appearing, such as the work of Matsouk (1996) on inclined two-layer models The correct design of inclined flow must be based on empirical data on the critical slope. The principles reviewed in this chapter apply to dredging and transporting sand, gravei, coai, steei shot, and rocks from SAG, rod, or ball mills, cyclone underflows, and tailings, etc., which often have particle sizes larger than 70 p,m (mesh 200). 

Z.B. Aziz and G.E. Klinzing, Plug flow transport of cohesive coal horizontal and inclined flows. Powder Technology 5S, pp.97-105 (1988). 

Friction on the boundaries of the sliding bed. Inclined flow of the 1.4-2.0-mm-sand mixture at... 

Measurement of the component fractions (oc), and velocities (Vc), is particularly important in horizontal and inclined flows where these distributions may be highly skewed. 

The flow conditions investigated in this paper involve both near-homogeneous and skew profiles produced by inclined flow. 

Tables 1 and 2 below show results for vertical and inclined flow (test section at 15° fix)m vertical). In the first case, both ERT and the Miniature Conductivity Probe (MCP) show a relatively uniform distribution of the void flaction and velocity. The results for both parameters are compared with the reference values obtained fl om the weighing hoppers and gradiomanometer (see Section 3.1). Both sets of measmements compare well with the reference measurements, although the void flaction reading for the MCP is rather low.

The ERT results for the inclined flow case are particularly pleasing. Visual observation shows a marked variation of void fl action and velocity, indeed some solids on the lower side of the pipe were observed moving against the flow, i.e. down the pipe. The representation of void fraction and velocity across the plane of interrogation, reconstructed from ERT measurements, confirm the visual observations. 

Very dense shearing flows involve multiple and/or repeated collisions that violate the assumption of instantaneous, uncorrelated, binary collisions on which simple kinetic theory is based. Because of the practical importance of very dense shearing flows in a gravitational field, we describe an extension of the simple kinetic theory that maintains much of the structure of the simpler theory. We phrase and solve a boundary value problem for a dense, inclined flow of dissipative spheres using this extension of the kinetic theory. The numerical solution of this problem reproduces the features of such flows observed in numerical simulations. Finally, we compare the profiles that result from a numerical solution with those of a simple, analytic, approximation theory. 

Jenkins, J. T. 2007. Dense inclined flows of inelastic spheres. Granular Matter 10, 47-52. 

Jenkins, J. T. and D. Berzi. 2012. Kinetic theory applied to inclined flows. Granular Matter 14, 79-84. 

Mukherjee, H. and Brill, J.P., Empirical equations to predict flow patterns in two-phase inclined flow. International Journal of Multiphase Flow, 11(3), 299-315,1985. 

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