Wall friction factors

Xb Particle-wall friction factor in bend As Particle-wall friction factor in straight pipe pu Loose-poured bulk density, kg nr3 Py Air density, kg mr3 ps Particle density, kg nr3... 

Fig. 5.16 Wall friction factor as a function of Rev for the flow between parallel plates with velocity V entering through the lower plate and leaving through the upper plate.

Two-phase pressure drop can typically be correlated with two models, i.e. homogeneous or separated. Homogeneous fluid models are well suited to emulsions and flow with negligible surface forces, where the two-phase mixture can be treated as a single fluid with appropriately averaged physical properties of the individual phases. Separated flow models consider that the two phases flow continuously and separated by an interface across which momentum can be transferred (Angeli and Hewitt 1999). The simplest patterns that can be easily modelled are separated and annular flow (Brauner 1991 Rovinsky et al. 1997 Bannwart 2001). In this case, momentum balances are written for both phases with appropriate interfacial and wall friction factors. 

The legitimacy of employing Blasius type models for the shear stresses in stratified flows was checked in several studies. Kowalski made direct measurements of the Reynolds shear stress in the gas for horizontal stratified flow in pipes and found that the gas-wall friction factors are well approximated by the Blasius equation provided that the hydraulic diameter is utilized [64]. For the liquid phase, Andritsos and Hanratty [28] found that the use of the Blasius equation to calculate introduces some error. However, improvements achieved by using a more complicated model for which is based on velocity profile and eddy viscosity concepts, were found to be of mild effect on the integral flow characteristics. 

Design a positive pressure dilute-phase pneumatic transport system to carry 500 kg/h of a powder of particle density 1800 kg/m and mean particle size 150 pm across a horizontal distance of 100 m and a vertical distance of 20 m using ambient air. Assume that the pipe is smooth, that four 90° bends are required and that the allowable pressure loss is 0.7 bar. See below for Blasius correlation for the gas-wall friction factor for smooth pipes. 

Blasius correlation for the gas-wall friction factor for smooth pipes fg = 0.079 Re ° ... 

Mindziul and Kmiec [23 25] investigated the aerodynamics of the gas solid flow in a pneumatic flash dryer. Their mathematical model was based on the continuity equation for both the gas and the solid phase and momentum equations for the solid phase and the solid gas mixture. Heat and mass transfer were neglected. Although the drying apparatus was composed of three elements with varying cross-sectional area, one-dimensional model was solved. The effect of various empirical correlations for solid-wall friction factor has been investigated. The results... 

L. K6sa, A. Verba, G. Bogn, Measurement of Wall Friction Factor in Fluidised... 

Tf - apparent viscosity, Pas p - wall friction factor, -p - density of driving air, kg/m r - shear stress. Pa... 

The specific form of the distributed wall friction factor, Eq. [16.34], for natural-circulation flows, has been the subject of extensive investigations. Todreas and Kazimi (1990) present a summary to that time, including rod bundle data by Gruszynski and Viskanta (1983). Swapnalee and Vijayan (2011) and Ambrosini et al. (2004) are additional examples. The special consideration required for supercritical thermodynamic states has been noted earUer in this chapter (eg, Pioro and Duffey, 2003 Yadav et al., 2012b). Natural-circulation flows, having bulk motions, are somewhat different from natural convection and low-flow forced convection. The necessity for a continuous representation of the friction factor for wall-distributed resistance is an additional critical aspect of stability of NCLs as discussed in Section 16.10. 

The loop flow resistance is specialized to the cases that are considered in this chapter as follows. The local irreversible losses are neglected, mainly to save on equation processing. The distributed wall friction factor correlation formulation is considered in the following. 

For constant wall-friction factor in the turbulent flow regime,... 

Meissner and Loffler then perform a moment-of-momentum balance on the gas considering the friction at the cylindrical wall using a wall friction factor,... 

In order to compute certain key cyclone characteristics, such as the internal spin velocity, vocs, or the particle cut size in the inner vortex core, X50, it is necessary to first compute the gas-phase and total gas-plus-solids wall friction factors, fair and /, respectively. Gas-phase wall friction factors for both cylindrical and conical cyclones as a function of body Reynolds number and relative wall roughness are presented in Fig. 6.1.3. Muschelknautz and Trefz define the cyclone body Reynolds number (compare with Eq. 4.2.8) as ... 

We may note that, above a body Rep of about 2000, the gas-phase wall friction factor is essentially independent of Rep. In this region it depends primarily on the relative wall roughness kg/R, as in ordinary flow through pipes. We can also observe that fair becomes independent of kg/R for Rep < 1000, that is, in the laminar flow regime. This too is analogous to ordinary flow in pipes. 

Given An industrial demisting cyclone system consists of three pairs of identical cyclones which share a common hopper, as shown in Fig. 13.B.1. It is estimated that the wall friction factor in the ducting leading up to the cyclone is 0.019 or about 30% greater than that for gas-only. 

In this section we give expressions for the wall and interfacial friction factors and corresponding shear stresses, starting with the wall friction factor and shear stress. 

An alternative method for estimating the wall friction factor is to use a standard pipe friction factor equation, such as the explicit formula of Swamee and Jain, using the equivalent diameter of the film in Rei. Thus,... 

Wall friction factor according to Liang-Biao and Kaziz ... 

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