Effect of Large Particles on the Augmentation of Wall Friction in Vertical Pneumatic and Hydraulic Transport in a Turbulent Fluid
| Autor: | Howard Littman, John D. Paccione |
|---|---|
| Rok vydání: | 2007 |
| Předmět: |
Physics
Turbulence General Chemical Engineering Flow (psychology) Zero (complex analysis) General Chemistry Mechanics Function (mathematics) Gravitational acceleration Industrial and Manufacturing Engineering Physics::Fluid Dynamics symbols.namesake Classical mechanics Froude number symbols Particle Phase velocity |
| Zdroj: | Industrial & Engineering Chemistry Research. 46:3429-3442 |
| ISSN: | 1520-5045 0888-5885 |
| DOI: | 10.1021/ie061058a |
| Popis: | This paper is concerned with prediction of the augmentation of wall friction by large particles (Fp) over that assuming turbulent flow in a pipe without particles (F f ) for vertical pneumatic and hydraulic transport in a turbulent fluid. Our measure of this is the value of the ratio F p /F f . Equations 29 and 32 are derived initially for predicting F p /F f for large particle "parallel" flow pneumatic transport based on the supposition that the particle phase friction factor (f p ) is solely a function of the Froude number, (gD) 1/2 /v where g is the gravitational acceleration, D is the tube diameter, and v is the particle phase velocity. The Froude number, gD/v 2 , is used to derive eq 40, its counterpart for hydraulic transport. These equations are shown to be qualitatively reliable and inconsistent only with the existence of a particle-free zone near the wall observed in experiments for large particle transport. To satisfy this requirement, f p is additionally assumed to be a function of the turbulence response parameter, t R /t e where t R is the particle relaxation time, and t e , the lifetime of the most energetic turbulent eddy. Equations 34 and 41 are our final correlating equations for F p /F f for pneumatic and hydraulic transport, respectively. When t R /t e is large, the particle-wall friction coefficient (f p ) goes to zero to conform with theory and experimental observations. |
| Databáze: | OpenAIRE |
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