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Schrödinger–Kirchhoff–Hardy $p$–fractional equations without the Ambrosetti–Rabinowitz condition

## Numerical simulation of fluidization for application in oxyfuel combustion

 Department of Mathematics, FNSPE CTU in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic

* Corresponding author: Pavel Strachota

Received  January 2019 Revised  October 2019 Published  December 2019

This paper is concerned with the simulation of multiphase flow hydrodynamics in an experimental oxyfuel fluidized bed combustor designed for biomass fuels. The aim is to perform cross-validation between several models and solvers that differ in the description of some phenomena in question. We focus on the influence of turbulence modeling, inter-phase drag force models, the presence of biomass in the mixture. Also the possibility to simplify the full 3D description to a quasi-1D model is tested. However, the results indicate that such simplification is not suitable for chaotic phenomena in considered scenarios. The models were developed using ANSYS Fluent and OpenFOAM CFD software packages as well as our in-house CFD code CFBSim. The quantities relevant for comparison (the densities of the dispersed solid phases and the phase velocities) are presented in the form of cross-section averaged vertical profiles.

Citation: Michal Beneš, Pavel Eichler, Jakub Klinkovský, Miroslav Kolář, Jakub Solovský, Pavel Strachota, Alexandr Žák. Numerical simulation of fluidization for application in oxyfuel combustion. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020232
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##### References:
Dimensions of the combustion chamber and meshes considered. (A) Dimensions of the cross-section of combustion chamber. (B) Coarse mesh generated by ANSYS Meshing. (C) Cross-section of the mesh in ANSYS. (D) Cross-section of the mesh in OpenFOAM generated by BlockMesh
Profiles of the gas velocity averaged across the cross-section of the chamber obtained from the simulations for the circulating (upper curves) and bubbling (lower curves) fluidization regimes
ANSYS Fluent simulation of the sand particles dynamics in the lower part of the combustion chamber in the bubbling regime shown by means of the sand volume fraction. Time sequence of snapshots of the longitudinal slice through the center of the 3D domain is displayed. The sequence shows a two-dimensional image of penetration dynamics of the gas phase (the lighter regions) through sand particles (their distribution is indicated by darker regions)
Linear density of sand particles along the vertical axis of the combustion chamber. Circulating regime
Velocity of sand particles averaged across the cross-section of the chamber. Circulating regime
Comparison of biomass linear densities between 1D CFBSim code and ANSYS Fluent
Comparison between the profiles of the biomass velocity averaged over the cross-section of the chamber obtained by 1D CFBSim code and ANSYS Fluent
Velocity of sand particles averaged across the cross-section of the chamber in circulating regime for Gidaspow [7] and Syamlal [13] drag models
Linear density of sand particles in circulating regime in dependence on drag models according to Gidaspow [7] and Syamlal [13]
Comparison of linear densities of sand particles with RAS turbulence model and laminar flow available in the OpenFOAM package (solver twoPhaseEulerFoam)
Comparison of the profiles of the velocity of sand particles averaged over the cross-section of the chamber obtained using the RAS turbulence model and laminar flow model available in the OpenFOAM package (solver twoPhaseEulerFoam). The profiles are also compared with the velocity profile obtained by the 1D CFBSim model
Comparison of linear densities in the two-phase laminar model (OpenFOAM solver twoPhaseEulerFoam) and three-phase laminar model (OpenFOAM solver reactingMultiphaseEulerFoam)
Comparison of particle velocities averaged over the cross-section of the chamber in the two-phase laminar model (OpenFOAM solver twoPhaseEulerFoam) and three-phase laminar model (OpenFOAM solver reactingMultiphaseEulerFoam)
Comparison of the gas velocity averaged over the cross-section of the chamber under the oxyfuel setting and the air setting. Computed in ANSYS Fluent
Comparison of the velocity of sand particles averaged over the cross-section of the chamber under the oxyfuel setting and the air setting. Computed in ANSYS Fluent
Comparison of the linear density of sand particles under the oxyfuel setting and the air setting. Computed in ANSYS Fluent
Phase properties corresponding to given temperature and gas composition (air, oxyfuel). Diameter $d_b$ is calculated so that the volume of a particle corresponds to the average volume of biomass pellets used in [11]. Note that the kinematic viscosity values of all the phases have the same order of magnitude ($\propto 10^{-4}\:\mathrm{m}^2\;\mathrm{s}^{-1}$)
 Temperature $T = 1000 \: \mathrm{K}$ Air - density $\rho_g = 0.3564 \: \mathrm{kg}\;\mathrm{m}^{-3}$ Air - dynamic viscosity $\mu_g = 4.1923 \cdot 10^{-5} \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Oxyfuel gas - density $\rho_g = 0.495 \: \mathrm{kg} \; \mathrm{m}^{-3}$ Oxyfuel gas - dynamic viscosity $\mu_g = 5.8227 \cdot 10^{-5} \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Sand - particle diameter $d_s = 0.78 \: \mathrm{mm}$ Sand - density $\rho_s = 2655 \: \mathrm{kg} \; \mathrm{m}^{-3}$ Sand - dynamic viscosity [7] $\mu_s = 0.5 \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Sand - packing limit $0.59$ Biomass (Miscanthus) - particle diameter $d_b = 10.36 \: \mathrm{mm}$ Biomass (Miscanthus) - density $\rho_b = 603 \: \mathrm{kg} \; \mathrm{m}^{-3}$ Biomass (Miscanthus) - dynamic viscosity [7] $\mu_b = 0.5 \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Biomass (Miscanthus) - packing limit $0.5$
 Temperature $T = 1000 \: \mathrm{K}$ Air - density $\rho_g = 0.3564 \: \mathrm{kg}\;\mathrm{m}^{-3}$ Air - dynamic viscosity $\mu_g = 4.1923 \cdot 10^{-5} \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Oxyfuel gas - density $\rho_g = 0.495 \: \mathrm{kg} \; \mathrm{m}^{-3}$ Oxyfuel gas - dynamic viscosity $\mu_g = 5.8227 \cdot 10^{-5} \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Sand - particle diameter $d_s = 0.78 \: \mathrm{mm}$ Sand - density $\rho_s = 2655 \: \mathrm{kg} \; \mathrm{m}^{-3}$ Sand - dynamic viscosity [7] $\mu_s = 0.5 \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Sand - packing limit $0.59$ Biomass (Miscanthus) - particle diameter $d_b = 10.36 \: \mathrm{mm}$ Biomass (Miscanthus) - density $\rho_b = 603 \: \mathrm{kg} \; \mathrm{m}^{-3}$ Biomass (Miscanthus) - dynamic viscosity [7] $\mu_b = 0.5 \: \mathrm{kg} \; \mathrm{m}^{-1} \; \mathrm{s}^{-1}$ Biomass (Miscanthus) - packing limit $0.5$
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