Simulation of the multiphase flow in bubble columns with stability-constrained multi-fluid CFD models

- SCMF CFD models feature the use of stability condition to close two-fluid models.
- The lumped ratio of drag coefficient to bubble diameter is supplied by the new model.
- SCMF models offer better prediction without using empirical correlations or adjusting parameters.
- Phase separation into three fluids at the level of conservation equations is not necessary.
- Stability condition reflecting the compromise of two dominant mechanisms is the essence.

The simulation of multiphase flow using multi-fluid CFD models is pertinent to the closure models for drag coefficient and bubble diameter, and empirical correlations or adjustable model parameters were inevitably needed. We proposed the stability-constrained multi-fluid models (SCMF) in our previous works based on the Dual-Bubble-Size (DBS) model and Energy-Minimization Multi-Scale (EMMS) concept. It utilized a stability condition to close the two-fluid models through the ratio of drag coefficient to bubble diameter. The stability condition reflects the compromise of two dominant mechanisms relevant to small bubbles or large bubbles. In this study, we further compared the three SCMF models with experiments and other multi-fluid models, i.e., the two-fluid models with Schiller-Naumann drag or Simonnet drag, the three-fluid model with Krishna drag, and the two-fluid model integrated with the population balance model (PBM). The SCMF models can offer better prediction without the need of empirical correlations or adjusting parameters for both the homogeneous and heterogeneous regimes. We further compared SCMF-A (gas and liquid phases), SCMF-B (dense and dilute phases) and SCMF-C (small bubble, large bubble and liquid) models. The three models are different in terms of the phase separation at the level of conservation equations. We found that SCMF-C cannot give further remarkable improvement, suggesting that the phase separation into three fluids at the level of conservation equations is not necessary, and the essential lies in the stability condition in the DBS model which reflects the compromise of two different dominant mechanisms represented by the two bubble classes. This may enhance our understanding on the mechanisms of scale separation in model developments.