## 1 Introduction
Over the past decade, Computational Fluid Dynamics (CFD) methods in combination with the Discrete Elements Method (DEM), which was first proposed by [PERSON] and [PERSON] [36], have become the basis for the study of gas-solid systems [37; 38; 39; 40; 41; 42; 43; 44; 45; 46]. Numerical simulation allows us to study how the features of the interactions of the medium and particles on a small scale affect the properties of the fluidized bed as a whole [5; 16; 47]. Currently, there is a comprehensive list of computational fluid dynamics software packages. A performance comparison of modern software packages are given in Table 1.  
From the listed computational fluid dynamics software packages, ANSYS Fluent was selected to solve the problems of hydrodynamics and heat transfer in the fluidized bed due to the following advantages:  
1. The modules of geometry and computational mesh construction and visualization of results built into ANSYS Workbench are well synchronized with each other, allowing one to quickly make changes to the model, if necessary, and to process the simulation results without the use of other programs. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Performance Comparison**} & \multicolumn{3}{c}{**Computational Fluid Dynamics Software Packages**} \\ \cline{2-4}  & **OpenFOAM (v11)** & **ANSYS Fluent (2021R1)** & **FlowVision (3.13.03)** \\ \hline
1 & 2 & 3 & 4 \\ \hline Manufacturer & The OpenFOAM Foundation, Ltd., London, UK & ANSYS, Inc., USA, Ansys Drive Canonsburg, PA USA & LLC \"TESIS\", Moscow, Russia \\ \hline \multirow{4}{*}{The need for additional software tools for the creation of geometry of the computational domain and for the visualization of calculations} & The program is provided together with a set of independent utilities for the creation of geometry, calculation area and the visualization of results & ANSYS Fluent is part of the ANSYS Student with a set of independent utilities for the creation of geometry, creation of geometry, calculation area and the visualization of results & The program has separate modules for the creation of geometry of the computational domain and the visualization of the resulting solution \\ \hline Numerical method & Final volumes & Final volumes & Final volumes \\ \hline \multirow{4}{*}{Built-in turbulence models} & Raynolds Averaged Simulation (RAS), Detached Eddy Simulation (DES), Large Eddy Simulation (LES) & Spalart-Allmaras model, \(k\)-\(\omega\), Reynolds stress, Detached Eddy Simulation (DES), Large Eddy Simulation (LES) & \(k\)-\(\epsilon\), \(k\)-\(\omega\), Spalart-Allmaras, Large Eddy Simulation (DES), Large Eddy Simulation (LES) \\ \hline Possibility of compressible flow simulation & Possible (including supersonic) & Possible (including supersonic) & Possible supersonic) \\ \hline Possibility of multiphase flow simulation & Possible & Possible & Possible only through [PERSON]’s approach \\ \hline Computational mesh & Structured and non-structured mesh & Structured and non-structured mesh & Adaptive mesh structured locally \\ \hline Possibility of chemical reaction & Possible & Possible & Possible \\ \hline Possibility of combustion simulation & Combustion with chemical reaction & Combustion with chemical reaction & Combustion with chemical reaction \\ \hline Intended use & General purpose & General purpose & Aero- and hydrodynamics \\ \hline \multirow{4}{*}{Source code expandability} & Open source code (C++ language) allows one to modify any module or any utility of the program & It is possible to add custom-made models directly to the source code & The source code is not expanded \\ \hline License type & Free & Commercial & Commercial \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Performance comparison of some modern computational fluid dynamics software packages [48; 49; 50]. 2. ANSYS Fluent provides both a wide choice of models and a wide possibility of their parameterization, which is a key factor in this work.