### Abstract

When the coupling of phases in multi-phase flows is very tight, a special treatment of interphase coupling terms is required in order to avoid divergence of iterative sequential solvers. In this article the efficiency of these special treatments is studied in typical fluidized bed conditions, where the coupling of momentum equations is moderate. The interphase coupling algorithms studied are the partially implicit treatment, the Partial Elimination Algorithm (PEA) and the Simultaneous solution of Non-linearly Coupled Equations (SINCE). In addition to these special treatments of linearized coupling terms in momentum equations, the fundamental ideas of the SINCE are applied also to the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE (C)) type pressure correction equation in the framework of the interphase slip algorithm (IPSA).

The resulting solution algorithm referred to as the Interphase Slip Algorithm-Coupled (IPSA-C) then incorporates interface couplings also into the mass balancing shared pressure correction step of the solution. It is shown that these advanced methods to treat interphase coupling terms result in a faster convergence of momentum equations despite the increased number of computational operations required by the algorithms.

For solving of the entire equation set, this better solution efficiency is then almost lost partly because of the sequential structure of the IPSA and, more importantly, because of the assumption of constant volume fractions during the pressure correction step. All the computations are done in the context of a collocated multi-block control volume solver CFDS–FLOW3D.

The resulting solution algorithm referred to as the Interphase Slip Algorithm-Coupled (IPSA-C) then incorporates interface couplings also into the mass balancing shared pressure correction step of the solution. It is shown that these advanced methods to treat interphase coupling terms result in a faster convergence of momentum equations despite the increased number of computational operations required by the algorithms.

For solving of the entire equation set, this better solution efficiency is then almost lost partly because of the sequential structure of the IPSA and, more importantly, because of the assumption of constant volume fractions during the pressure correction step. All the computations are done in the context of a collocated multi-block control volume solver CFDS–FLOW3D.

Original language | English |
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Pages (from-to) | 323-360 |

Journal | Computers and Fluids |

Volume | 28 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1998 |

MoE publication type | A1 Journal article-refereed |

### Keywords

- fluidized beds

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## Cite this

Karema, H., & Lo, S. (1998). Efficiency of interphace coupling algorithms in fluidized bed conditions.

*Computers and Fluids*,*28*(3), 323-360. https://doi.org/10.1016/S0045-7930(98)00028-0