Experimental study of the flow of a yield stress fluid in a 4:1 planar contraction
Creators: name: Hadj Arab, Belaid
Publisher: name: Zenodo
Year: 2025
Subjects: subject: Rheology
subject: viscoplastic
subject: elasto-viscoplastic
subject: planar abrupt contraction

description: The flow of viscoplastic fluids is often encountered in several industrial sectors, such as food pumping,  polymer  formatting  processes,  and  others.  Understanding  their  behavior  and  flow  in different  geometries  is  of  major  importance.  The  rheological  characterization  of  these  fluids is complex due to their intrinsic characteristics, notably the slip effect, as well as the inert unyieldedzones that form at the corners of the contraction when flowing through a rectangular pipe with an abrupt contraction. The main objective of this study is to analyze, firstly, the rheological behavior of Carbopol solutions using laser Doppler velocimetry (LDV) as a non-intrusive, in-situ method. By  measuring  velocity  profiles  and  associated  pressure  drops,  the  analysis  of  flow  curves  will enable us to characterize the rheology of the fluids studied. Two approaches are used. The first involves  fitting  the  analytical  profile  to  the  experimental  profile  obtained  by  laser  Doppler velocimetry (LDV), while the second involves converting local velocity profiles into local shear rate profiles, and pressure drops into local shear stress profiles.The flow of this fluid in the rectangular channel was analyzed using LDV, taking into account the associated head losses. Velocity profiles revealed the presence of a moving zone at constant velocity, called 'plug', in the center of the channel, as well as the formation of inert dead zones at the  corners  of  the  contraction.  The  impact  of  contraction  and  inertia  on  flow  structure  was examined first, highlighting the influence of both factors. The interface between the static dead zone and the fluid zone was identified and characterized for various flow rates. Velocity profiles revealed the  existence of a line known as the 'slip line', where all profiles intersect  at a single point. The position of this line is found to be independent of flow  rate, while its velocity varies with  flow  rate,  for  which  a  correlation  has  been  proposed.  This  slip  line  coincides  with  the contraction height. Local shear rate profiles are provided for each flow rate. These profiles show a non-monotonic evolution: they increase from zero at the solid-liquid interface to reach a peak, then decrease again to zero in the 'plug' region at the center of the pipe. This variation suggests the presence of different layers between the solid -liquid interface and the slip line. The position of  the  maximum  shear  rate  line  remains  constant  irrespective  of  flow  rate,  suggesting  that  the width  of  the  zone  between  the  slip  line  and  this  line  remains  constant  for  all  flow  rates.  In addition,  the  study  includes  an  analysis  of  head  losses  upstream,  downstream  and  at  the contraction, for which correlations have been proposed concerning the friction factor  f  and the Euler number Eu as a function of the generalized Reynolds number Regen.