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\begin{document}

\title{Radial Distribution of Solids Concentration in Downer}



\author[1]{Fan Yiping}%
\author[2]{Yafei Zhao}%
\author[1]{Chunxi Lu}%
\affil[1]{China University of Petroleum}%
\affil[2]{China University of Petroleum Beijing}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\begin{abstract}
Two different radial solids concentration distributions in downer have
been reported, i.e. the ^ \selectlanguage{english}shape combining with reverse-core-annulus and
the core-annulus structures. The occurrence of these two patterns has
not been quantitatively interpreted. In this paper, the aerodynamic
theory is used in two-phase flow analysis. A transverse force on the
particles, i.e. the Kutta-Joukowski transverse force, is introduced to
explain and quantify the formations of these two radial solids
concentration distributions in downer. This force is the function of the
particle velocity gradient, the slip velocity and the gas density. Based
on the available experimental data proposed in the published
literatures, the distribution of the Kutta-Joukowski transverse force in
downer is discussed. The results show that this force is the main factor
for these two profiles occurrence.%
\end{abstract}%



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