Abstract
Computational Fluid Dynamics is a quite well established tool for carrying out realistic simulations of process apparatuses. However, as a difference from single phase systems, for multiphase systems the development of CFD models is still in progress. Among the two-phase systems, gas–liquid systems are characterised by an additional complexity level, related to the fact that bubble sizes are not known in advance, being rather the result of formation and breakage-coalescence dynamics and therefore of complex phenomena related to flow dynamics and interfacial effects. In the present work, Euler–Euler Reynolds-averaged flow simulations of an air-lift reactor are reported. All bubbles are assumed to share the same size, and a simplified approach is adopted for modelling inter-phase momentum exchange, that involves bubble terminal velocity as the sole parameter needed. Good agreement between simulation results and literature experimental data is found for all the gas flow rates simulated. This result implies that, despite the many simplifications that have to be adopted in order to make them viable, fully predictive CFD simulations of gas–liquid systems can give rise to reasonably accurate predictions of reactor fluid dynamics.
Nomenclature
| Ap | Particle surface, m2 |
| B | Vector body force N m–3 |
| CD | Drag coefficient, dimensionless |
| C1ε | Constant in k –ε model, dimensionless |
| C2ε | Constant in k – ε model, dimensionless |
| C3ε | Constant in k – ε model, dimensionless |
| Cµ | Constant in k – ε model (eq. [8]), dimensionless |
| Fβα | Interphase force term, N m–3 |
| FD | Drag force term, N m−3 |
| Fvm | Virtual mass force term, N m−3 |
| Flift | Lift force term, N m−3 |
| Gα | Term in turbulent kinetic energy transport equation due to body forces |
| N | Agitation speed, rpm |
| NP | Power number, dimensionless |
| Pα | Term in turbulent kinetic energy transport equation due to shear |
| Qg | Gas flow rate, m3 s–1 |
| Re | Reynolds number, dimensionless |
| Sk | Source or sink term in turbulent kinetic energy transport equation |
| Sε | Source or sink term in turbulent energy dissipation transport equation |
| U | Vector of velocity field, m s–1 |
| db | Equivalent bubble diameter, mm |
| g | Gravity acceleration, m s–2 |
| k | turbulent kinetic energy, m2 s–2 |
| r | volume fraction, dimensionless |
| uT | Bubble terminal rise velocity, m s–1 |
| Vp | Particle volume, m3 |
| Greek symbols | |
| α | Subscript for continuous phase |
| β | Subscript for dispersed phase |
| ρα | Density of the liquid phase, kg m–3 |
| ρβ | Density of the gas phase, kg m–3 |
| µ | Viscosity, Pa s |
| µτ | Turbulent viscosity, Pa s |
| ε | Dissipation of turbulent kinetic energy, m2 s–3 |
| σ | Surface tension, N m–1 |
| σK, σε | k – ε model parameters, dimensionless |
References
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