Modeling of the Solid Stress Tensor in the MP-PIC Method: A Review of Methods and Applications

Luis Henríquez-Vargas (), Pablo Donoso-García, Lawrence Lackey, Mauricio Bravo-Gutiérrez, Benjamín Cajas, Alejandro Reyes, Nicolás Pailahueque, Isaac Díaz-Aburto and Valeri Bubnovich
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Luis Henríquez-Vargas: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Pablo Donoso-García: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Lawrence Lackey: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Mauricio Bravo-Gutiérrez: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Benjamín Cajas: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Alejandro Reyes: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Nicolás Pailahueque: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Isaac Díaz-Aburto: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile
Valeri Bubnovich: Departamento de Ingeniería Química y Bioprocesos, Universidad de Santiago de Chile, Santiago 9170022, Chile

Mathematics, 2024, vol. 12, issue 23, 1-33

Abstract: In recent years, the fast growth of computational power has allowed the application of computational fluid dynamics (CFD) in a wide range of areas of interest, such as gas–solid unit operations. In this context, the multiphase particle-in-cell (MP-PIC) method appears as an option to represent fluid–particle and particle–particle interactions, avoiding the complexity of tracking each particle and the high computational cost derived from this. The MP-PIC method can represent the particles as a group with the same characteristics, allowing the simulation of gas–solid systems at different scales. To achieve this, the particle–particle interactions are simplified using the solid stress tensor to represent them; this does not require explicit expressions. This approach has a low computational cost, allowing the simulation of industrial cases using just workstations. This paper provides a review of the literature on the solid stress tensor and its commercial and non-commercial applications, including its historical and mathematical development in the description of particle–particle interactions. In addition, to consolidate the knowledge and advancing understanding in this crucial aspect of multiphase flow simulations, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor. In addition, this review identifies the current challenges and opportunities for future research in multiphase systems based on the solid stress tensor.

Keywords: multiphase modeling; particle in cell; fluidization; solid stress model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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