An analysis of the transition regime of fibre suspension flow in pipes

Abstract

acroscopic fibres in suspension can greatly M modify the flow behavior of the suspending medium. If a suspension of long, flexible fibres is agitated, and if there is insufficient free volume for the fibres to move without interaction, they agglomerate by mechanical entanglement. When agitation ceases, the agglomerates interlock to form large, coherent fibre networks, which possess properties similar to those normally encountered in solid materials.At low bulk velocities in pipe flow, fibres are entangled in a coherent network or plug which occupies almost the entire flow area. Fluid shear is confined to a narrow region between the plug and the pipe wall, and flow resistance is greater than that of the suspending medium flowing alone a t the same rate. At high bulk velocities, turbulent stresses are sufficient to disrupt the plug and individual fibres and agglomerates move relative to each other. Turbulence of the suspending medium is damped by the fibres and fibre agglomerates, and flow resistance a t high bulk velocities is generally lower than that of the suspending medium flowing alone a t the same rate. This phenomenon is termed drag reduction. Over a wide range of bulk velocities between plug flow and fully developed turbulent flow there is a transition regime. In the transition regime fluid shear stresses are insufficient to disrupt the fibre plug completely and flow is characterized by a turbulent fibre/water annulus and a central fibre plug. The diameter of the plug decreases with decreasing fibre concentration and/or increasing bulk velocity. Analysis of flow with a central plugThe following analysis of the effect of a central plug on flow resistance of fibre suspensions is similar to that used by Charles"' to predict pressure gradients accompanying the turbulent flow of water and a neutrally-buoyant, infinitely-long, cylindrical capsule. The essential difference is that a semi-logarithmic velocity' distribution defined by Equation (1) has been used instead of the Prandtl 1/7th power law adopted by Charles. 1(1) K and 8 are constants for a particular suspension. This expression was first developed by Mih and ParkerI2' to represent velocity profiles a t low bulk velocities in the fully developed turbulent flow regime of fiber suspensions. In this analysis it is assumed that Equation (1) also represents velocity profiles in the turbulent fibre/water annulus during transition flow. In the subsequent section this assumption is shown to be valid when the plug is small. u+ = Ilnrl + 6 Cormpondence concerning this paper should be addressed to P. F. W. Lee. P. F. W. Lee is now with The Institute of Paper Chemistry, Appleton. Wisconsin, U.S.A.In Figure 1, curve ADEC represents a typical velocity profile for pipeflow with a central plug. Two velocity profiles for hypothetical, fully developed turbulent flows are also included. ABC has the same average velocity as ADEC, and AFC has the same velocity gradient near the pipe wall and is associated with the same flow resistance as ADEC.By integrating local velocities ...

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