Population balance modelling of gas-liquid bubbly flow: capturing coalescence and breakup processes

Computational Fluid Dynamics (CFD) analysis is increasingly being used for the study of complex hydraulic and thermal behaviour in nuclear and chemical engineering research. The bubble column reactors provide an effective mean for heat and mass transfer or even chemical reactions with relatively low maintenance and operation cost. The scale-up and scale-down design of bubble column have acquired great importance from various industries due to its versatile application. To obtain a rational design and better operation, the hydrodynamics of the embedded gas-liquid flow must be understood. Bubbles within the bulk liquid flow undergo deformation, coalescence, breakage and condensation subject to local flow conditions and heat and mass transfer processes. To account for the coalescence and breakup phenomenon of gas-liquid bubbly flows, the population balance modelling (PBM) has been used along with continuity and momentum equations within the two fluid modelling frameworks. A comprehensive population balance model validation study has been done for assessing DQMOM (Direct Quadrature Method of Moments) in simulating gas-liquid flow with wide range of bubble sizes and strong bubble interactions, furthermore the relative merits and capabilities of applying DQMOM has also been studied in comparison to the ABND (Average Bubble Number Density) and MUSIG (MUltiple SIze Group) models under the same gas-liquid flow. Specific attention is directed towards evaluating the performance of DQMOM, ABND model and MUSIG (homogeneous and inhomogeneous) model in capturing the transition from wall peak to core peak radial void fraction distribution especially in large pipe flow, corresponding to the prevalence of lift forces acting on the small- and large-sized bubbles. Numerical results are validated against gas-liquid flow experiments published in literature. The evolution of bubble size and its associated bubble migration due to the lift forces is well described by the inhomogeneous MUSIG approach. The assessment for performance of different population balance approaches reveals that behaviour of breakup and coalescence kernels has dominant effect on solution method of PBM. Hence, the research work is focused to gain more insight on the applicability of existing models in capturing the bubble coalescence and breakage phenomenon in a large bubble column comparable to practical industrial systems. In order to account this subject some widely adopted bubble coalescence and breakage kernels assessment were done in simulating the local hydrodynamic variables (e.g. void fraction and bubble size distribution) in large bubble column. A total of six coalescence and breakage kernels were considered. Numerical results were validated using the experimental data for the large-scale bubble column with inner diameter of 195.3 mm. The physical mechanism of each kernel and its coupling effects with the two-fluid model via interfacial forces has been investigated

Numerical investigation on the performance of coalescence and break-up kernels in subcooled boiling flows in vertical channels

In order to accurately predict the thermal hydraulic of two-phase gas-liquid flows with heat and mass transfer, special numerical considerations are required to capture the underlying physics: characteristics of the heat transfer and bubble dynamics taking place near the heated wall and the evolution of the bubble size distribution caused by the coalescence, break-up, and condensation processes in the bulk subcooled liquid. The evolution of the bubble size distribution is largely driven by the bubble coalescence and break-up mechanisms. In this paper, a numerical assessment on the performance of six different bubble coalescence and break-up kernels is carried out to investigate the bubble size distribution and its impact on local hydrodynamics. The resultant bubble size distributions are compared to achieve a better insight of the prediction mechanisms. Also, the void fraction, bubble Sauter mean diameter, and interfacial area concentration profiles are compared against the experimental data to ensure the validity of the models applied

An assessment of mechanistic breakage and coalescence kernels in poly-dispersed multiphase flow

Gas-liquid bubbly flows (i.e. swarm of discrete gas bubbles suspended in continuous liquid) have a wide range of applications; including mining, pharmaceutical and petroleum industries. Many researches have been carried out to develop an effective design tool for these industries and enhance the efficiency of their systems. Population balance (PB) approach in conjunction with Computational Fluid Dynamics (CFD) technique has been widely recognized as a robust methodology in solving such complex bubbly flows and providing a better understanding of the local flow behaviour. Nonetheless, to model the microscopic bubble interactions, an accurate coalescence and breakup kernel is crucial. Several models have been proposed within literatures for modelling breakup frequency and the daughter size distribution in the breakup mechanism; as well as coalescence frequency and efficiency in coalescence (Liao and Lucas 2009; Liao and Lucas 2010). A thorough assessment of the performance of a number of gas-liquid coalescence and breakage kernels has been carried out to find its effect in modelling the evolution of bubble size distribution in large scale vertical bubble column. A total of four different models were considered (one for breakage and three for coalescence) (Coulaloglou and Tavlarides 1977; Prince and Blanch 1990; Luo and Svendsen 1996; Lehr et al. 2002). To assess the performances under complex flow conditions, validation has been carried out against experimental data of Prasser et al. (2007) measured in the Helmholtz-Zentrum Dresden-Rossendorf (HZRD) facility

Direct quadrature method of moments (DQMOM) approach for vertical gas-liquid bubbly flows of large pipe

Gas-liquid bubbly flows with wide range of bubble sizes are commonly encountered in many industrial gas-liquid flow systems. The performance of direct quadrature method of moments (DQMOM) has been assessed against the homogeneous MUlti-SIze-Group (MUSIG) model and Average Bubble Number Density (ABND) approach in tracking the changes of bubble size distribution and gas volume fraction under complex flow conditions. Numerical studies have been performed to validate predictions from the different population balance approaches against experimental measurements of vertical bubbly flows in a large diameter pipe. In general, predictions of DQMOM were in good agreement with experimental data. The encouraging results demonstrated the capability of DQMOM in capturing the dynamical changes of bubbles size due to bubble interactions and the transition from wall peak to core peak gas volume fraction profiles caused by the presence of small and large bubbles. Predictions of the DQMOM appeared to offer substantial reduction of computational times in reaching a converged solution when compared to MUSIG for the computation of vertical bubbly flows in large diameter pipe

Modeling of bubble size distribution in isothermal gas-liquid flows: Numerical assessment of population balance approaches

Gas-liquid flows are commonly encountered in many industrial flow systems. In many cases, the evolution of bubble size distribution is a crucial factor governing the momentum, heat and mass transfer between phases within the system. Aiming to evaluate the capability of existing models, numerical assessment of three different population balance approaches - direct quadrature method of moments (DQMOM), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) models - is presented in this paper. Model predictions were validated against experimental measurements from medium and large scale bubble columns where bubble sizes within the system were found to be dominant by coalescence and break-up mechanism, respectively. In result of the bubble size change, transitions of phase distribution from wall peak to core peak profile were also found in both experiments. In general, predictions of the three models were in satisfactory agreement with experiment measurements clearly demonstrating its applicability for large scale practical systems. Encouraging results have also been obtained in capturing the evolution of bubble size distribution. Nevertheless, noticeable errors were also found in predictions of the MUSIG and DQMOM model indicating some potential deficiencies of the model. To evaluate the numerical efficiency of the three models, computational requirements of each model were also compared

Capturing coalescence and break-up processes in vertical gas-liquid flows: Assessment of population balance methods

Gas-liquid flows are commonly encountered in industrial flow systems. Numerical studies have been performed to assess the performances of different population balance approaches - direct quadrature method of moments (DQMOMs), average bubble number density (ABND) model and homogeneous MUlti-SIze-Group (MUSIG) model - in tracking the changes of gas void fraction and bubble size distribution under complex flow conditions and to validate the model predictions against experimental measurements from medium- and large-sized vertical pipes. Subject to different gas injection method and flow conditions, bubble size evolution exhibited a coalescence dominant trend in the medium-sized pipe; while bubble break-up was found to be dominant in large-sized pipe. The two experiments were therefore strategically selected for carrying out a thorough examination of existing population balance models in capturing the complicated behaviour of bubble coalescence and break-up. In general, predictions of all the different population balance approaches were in reasonable agreement with experimental data. More importantly, encouraging results have been obtained in adequately capturing the dynamical changes of bubbles size due to bubble interactions and transition from wall peak to core peak gas void fraction profiles. As a compromise between numerical accuracy and computational time, DQMOM has performed rather well in capturing the essential two-phase flow structures within the medium- and large-sized vertical pipes when compared to those of ABND and homogeneous MUSIG models. From a practical perspective, the ABND model may still be considered as a more viable approach for industrial applications of gas-liquid flow systems

Comparative Analysis of Coalescence and Breakage Kernels in Vertical Gas-Liquid Flow

The evolution of bubble size distribution is an important consideration in vertical gas-liquid flow, especially in determining the appropriate mass, momentum, and heat transfer between two phases. In order to adequately capture the distribution and to account for its effect on the local hydrodynamics, which generally represents the dominant flow characteristic in such a practical system, a numerical assessment has been performed to understand the six widely adopted different bubble coalescence and bubble breakage kernels. Three different breakage kernels have been selected where each kernel considers a different shape of the daughter size distribution of the bubbles, such as the U-shape, bell-shape, and M-shape. These are combined with different coalescence kernels. The bubble size distribution, void fraction, interfacial area concentration, and gas velocity profiles are compared against the experimental data. Numerical results reveal that the effect on the two-phase flow structure is mainly due to the application of the different breakage kernels. Moreover, the predicted results also show that the bell-shape daughter size distribution favours equal breakage of bubbles, which could lead to the over-prediction of large bubbles. A more sophisticated model for handling bubble induced turbulence should nonetheless be applied in future investigations of vertical gas-liquid flow