Slug flow models

Let us first consider the simple flat plate with a liquid metal flowing across it. The Prandtl number for liquid metals is very low, of the order of 0.01. so that the thermal-boundary-layer thickness should be substantially larger than the hydrodynamic-boundary-layer-thickness. The situation results from the high values of thermal conductivity for liquid metals and is depicted in Fig. 6-15. Since the ratio of 8/8, is small, the velocity profile has a very blunt shape over most of the thermal boundary layer. As a first approximation, then, we might assume a slug-flow model for calculation of the heat transfer i.e., we take... 

Why does a slug-flow model yield reasonable results when applied to liquid-metal heat transfer ... 

Using the slug-flow model, show that the boundary-layer energy equation reduces to the same form as the transient-conduction equation for the semi-infinite solid of Sec. 4-3. Solve this equation and compare the solution with the integral analysis of Sec. 6-5. 

Suppose the fluid is highly conducting, such as a liquid metal. In this case, the thermal-boundary-layer thickness will be much greater than the hydrodynamic thickness. This is evidenced by the fact that the Prandtl numbers for liquid metals are very low, of the order of 0.01. For such a fluid, then, we might approximate the actual fluid behavior with a slug-flow model for energy transport in the thermal boundary layer, as outlined in Sec. 6-5. We assume a constant velocity profile... 

It is necessary to caution that the foregoing analysis is a highly idealized one, which has been used primarily to illustrate the effects of magnetic fields on heat transfer. A more realistic analysis would consider the variation of electrical conductivity of the fluid and take into account the exact velocity profile rather than the slug-flow model. A survey of more exact relations for heat transfer in MFD systems is given in Refs. 1 and 2. 

Narayanan et al.88 correlated gas holdup to the superficial gas velocity empirically and found hG oc U0G for U0G < 6.7 cm s 1 and hG oc UoG 8 for 6.7 cm s-1 < Uoc < 21.34 cm s"1. Hovmand and Davidson43 proposed a slug-flow model to correlate the gas holdup in gas-liquid-solid fluidized beds at superficial gas velocities in excess of that required for the incipient fluidization of solids. They correlated the gas holdup and superficial gas velocity by the equation... 

Saxena, S. C. Chen, T. P. Jonke, A. A. A Slug Flow Model for Coal Combustion with Sulfur Emission Control by Limestone or Dolomite Presented at the 70th Annual AIChE Meeting,... 

Figure 8 Conversion as a function of reactor diameter. Bubbling bed models Solid lines two-phase bubbling bed model (19) with a =0 short dashes same model with =0.005 long-short broken lines Orcutt model with mixed dense phase. Slug flow model Hovmand-Davidson (A5,46). For conditions see Table 3.

In advance, comparative fixed-bed measurements were undertaken. It was ensured that the performance of a plug-flow operation with both flows having the same direction is superior to trickle-bed operation, using counter-flow instead. The plug flow was assumed to model the slug-flow behavior in the micro reactor. 

This map has been checked by many researchers, indicating that it is applicable to a wide range of conditions. Also shown in Figure 3.4 are correlations derived by Mishima and Ishii (1984), which used similar basic principles except for the slug-to-churn transition. These authors pointed out that, in view of the practical applications of the separate-fluid model to transient analysis, flow regime criteria based on the superficial velocities of the liquid and gas may not be consistent with the separate-flow model formulation. A direct geometric parameter such as the... 

The first model is more suited to dealing with mixed flow such as bubble flow and slug flow, while the second is more suited to cases where flow is separated, as in stratified and annular flow. 

Figure 3.39 Physical model for slug flow. (From Dukler and Hubbard, 1975. Copyright 1975 by American Chemical Society, Washington, DC. Reprinted with permission.)...

Dukler, A. E., and M. G. Hubbard, 1975, A Model for Gas-Liquid Slug Flow in Horizontal and Near Horizontal Tubes, Ind. Eng Chem. Fundam. 14(4) 337. (3)... 

It is interesting to compare the assumptions made by Bankoff to the restrictions operating in the investigation by Nicklin, Wilkes, and Davidson for slug flow. In their work the velocity component of the slugs due to liquid flow approached the maximum liquid velocity at the tube center-line. If this is also true of the bubbles of Bankoff s model and the bubble rise velocity due to buoyancy is ignored, then the velocity of the bubbles as given by Nicklin et al. would be,... 

Keywords Pneumatic conveying Slug flow Solids deposition CFD model DEM simulation... 

To understand the mechanisms of solids slug flows, a two-dimensional coupled DEM/CFD numerical model was built to simulate the motion of a pre-formed slug (ca. 0.3 m long) in a 1 m long horizontal 50 mm bore pipe as shown in Fig. 1. The pipe was initially filled with a layer of particles, approximately 15 mm thick at the bottom. (The thickness of this stationary layer was determined based on experience from previous experiments and computer test runs). 

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