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\begin{document}

\title{A scaled MP-PIC method for bubbling fluidization}



\author[1]{Xing Zhao}%
\author[1]{Yong Jiang}%
\author[1]{Fei Li}%
\author[1]{Wei Wang}%
\affil[1]{Institute of Process Engineering Chinese Academy of Sciences}%


\vspace{-1em}



  
  \date{May 22, 2024}


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\begin{abstract}
Coarse-grained methods have been widely used in simulations of gas-solid
fluidization. However, as a key parameter, the coarse-graining ratio,
and its relevant scaling law is still far from reaching a consensus. In
this work, a scaling law is developed based on a similarity analysis,
and then it is used to scale the multi-phase particle-in-cell (MP-PIC)
method, and validated in the simulation of two bubbling fluidized beds.
The simulation result shows this scaled MP-PIC can reduce the errors of
solids volume fraction and velocity distributions over a wide range of
coarse-graining ratios. In future, we expect that a scaling law with
consideration of the heterogeneity inside a parcel or numerical particle
will further improve the performance of coarse-grained modeling in
simulation of fluidized beds.%
\end{abstract}%



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\textbf{Hosted file}

\verb`fig 1.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 2.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 3.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 4.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 5.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 6.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 7.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 8.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 9.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig 10.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`fig C1.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

\textbf{Hosted file}

\verb`fig C2.pptx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

\textbf{Hosted file}

\verb`Table. 1 Scaling laws for coarse-grained models in literature.docx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

\textbf{Hosted file}

\verb`Table. 2 The characteristic quantities adopted in dimensionless equation.docx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

\textbf{Hosted file}

\verb`Table. 3 Sample particle parameters in original and scaled MP-PIC.docx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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\verb`Table. 4 Numerical settings for bubbling bed 165 and bed 266.docx`  available at \url{https://authorea.com/users/436207/articles/538701-a-scaled-mp-pic-method-for-bubbling-fluidization}

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