**2. Computer models of slurry pipe flow**

The model of two parts, settling and suspended, is not the only classification, which has been applied to component parts of a settling slurry flow. Shook and Roco [4] postulated a notional third layer without lift forces underneath the settling layer, and a three-layer model was proposed by Doron and Barnea [5] to overcome perceived "limitations" of the two-layer representation. The new model provides a way to identify the relative delay of the solids fraction in a duct or holdup, which none of the other classifications achieve, at least not in a direct way. A more recent *four component model* pioneered by Wilson and Sellgren [6] and revised by Visintainer et al. [7] produces useful pump derating calculations but is based on uniform particle distribution.

Since its invention by K.C. Wilson [2, 3, 8, 9], there have been several references to the two-layer model. At the time of writing a new reference volume, Visintainer et al. [10] contain detailed discussion of it. The author's current version (*2LM*) described in the following pages has completely new coding to overcome instability and interface positioning difficulties of the original in obtaining estimates of the downstream velocity of the settling layer and holdup.

The *limit of stationary deposition velocity* over ranges of particle size, pipe diameters and relative density of grains was published by Wilson [3] in the form of an elegant nomogram constructed using techniques originated by Wood [11] (see Annexe C). The original nomogram did not account for volumetric concentrations, but in later work, Wilson et al. [8] modified the nomogram for a range of concentrations. The results are comparable with those obtained later in this chapter (**Figure 2**).

*Solid-Liquid Pipeflows – Holdup and the Two-Layer Model DOI: http://dx.doi.org/10.5772/intechopen.112023*

#### **Figure 2.**

*Stationary bed loci for horizontal flow of sand in water. The concentration is 0.2 v/v, particle size is 2 mm, pipe diameter is 250 mm. U is the axial pipe velocity, Us is the velocity of the solids and dP/dz is the downstream pressure gradient. Note the classification of each locus by the relative velocity of solids, n.b* <sup>H</sup>*SBL* <sup>¼</sup> *<sup>1</sup>* � *Us U :*

Among other advantages, the simple geometry of the model provides an accessible alternative to an experimental image of a particle distribution, initially at least. For example, the first moment yields the *centre of concentration* of the particle burden about the centre of the duct. This is an indicator of its position and possibly its wear propensity. The second moment can indicate the energy required to achieve optimal particle suspension by swirling action. If available, experimental images of particle distribution can be obtained using, for example, *electrical resistance tomography (ERT)* or *particle image velocimetry (PIV)*.
